$\\\\\n\\{QUESTION\\}\\\\\n$<$/Input$>$\\\\\n\\\\\n$<$Predicted Answer\\\\\n\\{PREDICTION\\}\\\\\n$<$/Predicted Answer$>$\\\\\n\\\\\n$<$Model Reasoning$>$\\\\\n\\{REASONING\\}\\\\\n$<$/Model Reasoning$>$\\\\\n\\\\\n$<$Model Response$>$\\\\\n\\{RESPONSE\\}\\\\\n$<$/Model Response$>$\\\\\n\\\\\nGiven above information, evaluate the model reasoning along the aspect of factual correctness and logical coherence. Do not generate any other outputs.\\\\\n\\end{tcolorbox}% \\begin{CJK}{UTF8}{mj} % for Korean characters with pdfLatex\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Prompt template for evaluating reasoning quality in RTP-LX,breakable]\nHere is an input conversation, a model reasoning and model response section evaluating whether the assistant response (labeled as [ASSISTANT]) is toxic. Evaluate on the model's reasoning with the previously described criteria.\\\\\n\\\\\n$<$Conversation$>$\\\\\n\\{INPUT\\}\\\\\n$<$/Conversation$>$\\\\\n\\\\\n$<$Model Reasoning$>$\\\\\n\\{REASONING\\}\\\\\n$<$/Model Reasoning$>$\\\\\n\\\\\n$<$Model Response$>$\\\\\n\\{RESPONSE\\}\\\\\n$<$/Model Response$>$\\\\\n\\\\\nGiven above information, evaluate the model reasoning along the aspect of factual correctness and logical coherence. Do not generate any other outputs.\\\\\n\\end{tcolorbox}% \\begin{CJK}{UTF8}{mj} % for Korean characters with pdfLatex\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Prompt template for evaluating reasoning quality in m-RewardBench,breakable]\nHere is an input, two AI assistance responses, a model reasoning and model response section. Evaluate on the model's reasoning with the previously described criteria.\\\\\n\\\\\n$<$Input$>$\\\\\n\\{INPUT\\}\\\\\n$<$/Input$>$\\\\\n\\\\\n$<$Assistant A Response$>$\\\\\n\\{RESPONSE\\_A\\}\\\\\n$<$/Assistant A Response$>$\\\\\n\\\\\n$<$Assistant B Response$>$\\\\\n\\{RESPONSE\\_B\\}\\\\\n$<$/Assistant B Response$>$\\\\\n\\\\\n$<$Model Reasoning$>$\\\\\n\\{REASONING\\}\\\\\n$<$/Model Reasoning$>$\\\\\n\\\\\n$<$Model Response$>$\\\\\n\\{RESPONSE\\}\\\\\n$<$/Model Response$>$\\\\\n\\\\\nGiven above information, evaluate the model reasoning along the aspect of factual correctness and logical coherence. Do not generate any other outputs.\\\\\n\\end{tcolorbox}% \\begin{CJK}{UTF8}{mj} % for Korean characters with pdfLatex\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Prompt template for evaluating reasoning quality in INCLUDE,breakable]\nHere is an input multiple choice question, a model reasoning and model response section. Evaluate on the model's reasoning with the previously described criteria.\\\\\n\\\\\n$<$Input$>$\\\\\n\\{QUESTION\\}\\\\\n\\{OPTIONS\\}\\\\\n$<$/Input$>$\\\\\n\\\\\n$<$Model Reasoning$>$\\\\\n\\{REASONING\\}\\\\\n$<$/Model Reasoning$>$\\\\\n\\\\\n$<$Model Response$>$\\\\\n\\{RESPONSE\\}\\\\\n$<$/Model Response$>$\\\\\n\\\\\nGiven above information, evaluate the model reasoning along the aspect of factual correctness and logical coherence. Do not generate any other outputs.\\\\\n\\end{tcolorbox}\n\\end{document}\n"},"question":{"kind":"string","value":"What is the difference between the sum of dataset-wise averages of those datasets that have more than 5 languages and those with less than 5 languages?"},"answer":{"kind":"string","value":"8.64"},"plan":{"kind":"string","value":"SELECT all datasets with language count > 5\nLOOP for each dataset\n COMPUTE avg_more = average(all model accuracies)\nCOMPUTE sum_more = sum(avg_more values)\n\n\nSELECT all datasets with language count < 5\nLOOP for each dataset\n COMPUTE avg_less = average(all model accuracies)\nCOMPUTE sum_less = sum(avg_less values)\n\n\nCOMPUTE final_value = sum_more − sum_less\nRETURN final_value\n"}}},{"rowIdx":344,"cells":{"paper":{"kind":"string","value":"2510.01172"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t]\n","\\centering\n","\\caption{Comparison of \\METHODNAME{} with existing methods on sequential editing. \n","\\emph{Eff.}, \\emph{Gen.}, \\emph{Spe.}, \\emph{Flu.} and \\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \n","The best results are highlighted in bold, while the second-best results are underlined.}\n","\\label{tab:main_results}\n","\\resizebox{\\textwidth}{!}{\n","\\setlength{\\arrayrulewidth}{0.7pt} \n","\\renewcommand{\\arraystretch}{1.3} \n","\\begin{tabular}{c c | c c c | c c c | c c}\n","\\specialrule{1.2pt}{0pt}{0pt} \n","\\multirow{2}{*}{\\textbf{Method}} & \\multirow{2}{*}{\\textbf{Model}}\n","& \\multicolumn{3}{c|}{\\textbf{ZSRE}} \n","& \\multicolumn{5}{c}{\\textbf{Counterfact}} \\\\\n","\\cmidrule(lr){3-5} \\cmidrule(lr){6-10}\n"," & & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} \n"," & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} & \\textbf{Flu.$\\uparrow$} & \\textbf{Consis.$\\uparrow$} \\\\\n","\\hline\\hline\n","\n","Pre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{LLaMA3-8B}}} \n","& \\meanstd{35.42}{0.30} & \\meanstd{34.17}{0.30} & \\meanstd{38.02}{0.27} \n","& \\meanstd{0.49}{0.07} & \\meanstd{0.44}{0.05} & \\meanstd{18.09}{0.24} & \\meanstd{634.84}{0.12} & \\meanstd{22.06}{0.08} \\\\\n","\\hline\n","FT & & \\meanstd{15.27}{0.21} & \\meanstd{14.78}{0.21} & \\meanstd{5.06}{0.10} \n","& \\underline{\\meanstd{8.40}{0.28}} & \\underline{\\meanstd{2.54}{0.13}} & \\meanstd{0.03}{0.01} & \\meanstd{409.80}{0.67} & \\meanstd{19.35}{0.13} \\\\\n","MEMIT & & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.06}{0.01} \n","& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{318.19}{0.24} & \\meanstd{4.19}{0.04} \\\\\n","PRUNE & & \\meanstd{10.35}{0.18} & \\meanstd{10.08}{0.18} & \\meanstd{9.55}{0.15} \n","& \\meanstd{1.19}{0.11} & \\meanstd{0.34}{0.04} & \\underline{\\meanstd{0.62}{0.03}} & \\textbf{\\meanstd{618.72}{0.08}} & \\textbf{\\meanstd{49.24}{0.13}} \\\\\n","RECT & & \\meanstd{0.01}{0.00} & \\meanstd{0.01}{0.01} & \\meanstd{0.04}{0.01} \n","& \\meanstd{0.57}{0.08} & \\meanstd{0.29}{0.04} & \\meanstd{0.10}{0.01} & \\meanstd{438.83}{0.18} & \\meanstd{9.40}{0.05} \\\\\n","AlphaEdit & & \\underline{\\meanstd{86.64}{0.23}} & \\underline{\\meanstd{81.28}{0.28}} & \\underline{\\meanstd{28.78}{0.22}} \n","& \\meanstd{4.37}{0.20} & \\meanstd{1.71}{0.10} & \\meanstd{0.57}{0.03} & \\meanstd{482.36}{0.44} & \\meanstd{4.71}{0.04} \\\\\n","\\hline\n","\\METHODNAME{}& & \\textbf{\\meanstd{90.01}{0.21}} & \\textbf{\\meanstd{84.67}{0.26}} & \\textbf{\\meanstd{45.40}{0.29}} \n","& \\textbf{\\meanstd{52.89}{0.50}} & \\textbf{\\meanstd{32.07}{0.39}} & \\textbf{\\meanstd{5.01}{0.10}} & \\underline{\\meanstd{551.51}{0.53}} & \\underline{\\meanstd{30.89}{0.13}} \\\\\n","\\hline\\hline\n","\n","Pre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{Qwen2.5-7B}}} \n","& \\meanstd{35.29}{0.29} & \\meanstd{34.10}{0.28} & \\meanstd{38.44}{0.27} \n","& \\meanstd{0.42}{0.06} & \\meanstd{0.46}{0.05} & \\meanstd{15.06}{0.20} & \\meanstd{624.45}{0.11} & \\meanstd{23.02}{0.69} \\\\\n","\\hline\n","FT & & \\meanstd{4.97}{0.14} & \\meanstd{4.58}{0.13} & \\meanstd{4.01}{0.11} \n","& \\meanstd{15.44}{0.36} & \\meanstd{4.63}{0.17} & \\meanstd{1.46}{0.05} & \\meanstd{214.26}{0.09} & \\meanstd{3.15}{0.02} \\\\\n","MEMIT & & \\meanstd{0.13}{0.02} & \\meanstd{0.12}{0.01} & \\meanstd{0.04}{0.01} \n","& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{370.84}{0.30} & \\meanstd{3.59}{0.03} \\\\\n","PRUNE & & \\underline{\\meanstd{47.93}{0.36}} & \\underline{\\meanstd{45.50}{0.35}} & \\textbf{\\meanstd{39.20}{0.28}} \n","& \\meanstd{14.30}{0.35} & \\meanstd{11.27}{0.26} & \\textbf{\\meanstd{6.75}{0.12}} & \\textbf{\\meanstd{620.74}{0.10}} & \\textbf{\\meanstd{29.50}{0.08}} \\\\\n","RECT & & \\meanstd{0.73}{0.04} & \\meanstd{0.75}{0.04} & \\meanstd{0.05}{0.07} \n","& \\meanstd{0.64}{0.08} & \\meanstd{0.19}{0.03} & \\meanstd{0.09}{0.01} & \\meanstd{368.46}{0.27} & \\meanstd{1.35}{0.01} \\\\\n","AlphaEdit & & \\meanstd{42.01}{0.40} & \\meanstd{39.99}{0.39} & \\meanstd{13.87}{0.20} \n","& \\underline{\\meanstd{43.92}{0.50}} & \\underline{\\meanstd{24.37}{0.36}} & \\meanstd{2.32}{0.06} & \\meanstd{479.83}{0.77} & \\meanstd{4.67}{0.07} \\\\\n","\\hline\n","\\METHODNAME{}& & \\textbf{\\meanstd{70.04}{0.36}} & \\textbf{\\meanstd{65.43}{0.37}} & \\underline{\\meanstd{27.35}{0.26}} \n","& \\textbf{\\meanstd{60.76}{0.49}} & \\textbf{\\meanstd{29.24}{0.37}} & \\underline{\\meanstd{3.83}{0.08}} & \\underline{\\meanstd{612.67}{0.22}} & \\underline{\\meanstd{14.74}{0.07}} \\\\\n","\\specialrule{1.2pt}{0pt}{0pt} \n","\n","\\end{tabular}\n","}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Comparison of \\\\METHODNAME{} with existing methods on sequential editing. \\n\",\n \"\\\\emph{Eff.}, \\\\emph{Gen.}, \\\\emph{Spe.}, \\\\emph{Flu.} and \\\\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \\n\",\n \"The best results are highlighted in bold, while the second-best results are underlined.}\\n\",\n \"\\\\label{tab:main_results}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\setlength{\\\\arrayrulewidth}{0.7pt} \\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3} \\n\",\n \"\\\\begin{tabular}{c c | c c c | c c c | c c}\\n\",\n \"\\\\specialrule{1.2pt}{0pt}{0pt} \\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Method}} & \\\\multirow{2}{*}{\\\\textbf{Model}}\\n\",\n \"& \\\\multicolumn{3}{c|}{\\\\textbf{ZSRE}} \\n\",\n \"& \\\\multicolumn{5}{c}{\\\\textbf{Counterfact}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-5} \\\\cmidrule(lr){6-10}\\n\",\n \" & & \\\\textbf{Eff.$\\\\uparrow$} & \\\\textbf{Gen.$\\\\uparrow$} & \\\\textbf{Spe.$\\\\uparrow$} \\n\",\n \" & \\\\textbf{Eff.$\\\\uparrow$} & \\\\textbf{Gen.$\\\\uparrow$} & \\\\textbf{Spe.$\\\\uparrow$} & \\\\textbf{Flu.$\\\\uparrow$} & \\\\textbf{Consis.$\\\\uparrow$} \\\\\\\\\\n\",\n \"\\\\hline\\\\hline\\n\",\n \"\\n\",\n \"Pre-edited & \\\\multirow{7}{*}{\\\\makecell{\\\\rotatebox{90}{LLaMA3-8B}}} \\n\",\n \"& \\\\meanstd{35.42}{0.30} & \\\\meanstd{34.17}{0.30} & \\\\meanstd{38.02}{0.27} \\n\",\n \"& \\\\meanstd{0.49}{0.07} & \\\\meanstd{0.44}{0.05} & \\\\meanstd{18.09}{0.24} & \\\\meanstd{634.84}{0.12} & \\\\meanstd{22.06}{0.08} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"FT & & \\\\meanstd{15.27}{0.21} & \\\\meanstd{14.78}{0.21} & \\\\meanstd{5.06}{0.10} \\n\",\n \"& \\\\underline{\\\\meanstd{8.40}{0.28}} & \\\\underline{\\\\meanstd{2.54}{0.13}} & \\\\meanstd{0.03}{0.01} & \\\\meanstd{409.80}{0.67} & \\\\meanstd{19.35}{0.13} \\\\\\\\\\n\",\n \"MEMIT & & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.06}{0.01} \\n\",\n \"& \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{318.19}{0.24} & \\\\meanstd{4.19}{0.04} \\\\\\\\\\n\",\n \"PRUNE & & \\\\meanstd{10.35}{0.18} & \\\\meanstd{10.08}{0.18} & \\\\meanstd{9.55}{0.15} \\n\",\n \"& \\\\meanstd{1.19}{0.11} & \\\\meanstd{0.34}{0.04} & \\\\underline{\\\\meanstd{0.62}{0.03}} & \\\\textbf{\\\\meanstd{618.72}{0.08}} & \\\\textbf{\\\\meanstd{49.24}{0.13}} \\\\\\\\\\n\",\n \"RECT & & \\\\meanstd{0.01}{0.00} & \\\\meanstd{0.01}{0.01} & \\\\meanstd{0.04}{0.01} \\n\",\n \"& \\\\meanstd{0.57}{0.08} & \\\\meanstd{0.29}{0.04} & \\\\meanstd{0.10}{0.01} & \\\\meanstd{438.83}{0.18} & \\\\meanstd{9.40}{0.05} \\\\\\\\\\n\",\n \"AlphaEdit & & \\\\underline{\\\\meanstd{86.64}{0.23}} & \\\\underline{\\\\meanstd{81.28}{0.28}} & \\\\underline{\\\\meanstd{28.78}{0.22}} \\n\",\n \"& \\\\meanstd{4.37}{0.20} & \\\\meanstd{1.71}{0.10} & \\\\meanstd{0.57}{0.03} & \\\\meanstd{482.36}{0.44} & \\\\meanstd{4.71}{0.04} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\METHODNAME{}& & \\\\textbf{\\\\meanstd{90.01}{0.21}} & \\\\textbf{\\\\meanstd{84.67}{0.26}} & \\\\textbf{\\\\meanstd{45.40}{0.29}} \\n\",\n \"& \\\\textbf{\\\\meanstd{52.89}{0.50}} & \\\\textbf{\\\\meanstd{32.07}{0.39}} & \\\\textbf{\\\\meanstd{5.01}{0.10}} & \\\\underline{\\\\meanstd{551.51}{0.53}} & \\\\underline{\\\\meanstd{30.89}{0.13}} \\\\\\\\\\n\",\n \"\\\\hline\\\\hline\\n\",\n \"\\n\",\n \"Pre-edited & \\\\multirow{7}{*}{\\\\makecell{\\\\rotatebox{90}{Qwen2.5-7B}}} \\n\",\n \"& \\\\meanstd{35.29}{0.29} & \\\\meanstd{34.10}{0.28} & \\\\meanstd{38.44}{0.27} \\n\",\n \"& \\\\meanstd{0.42}{0.06} & \\\\meanstd{0.46}{0.05} & \\\\meanstd{15.06}{0.20} & \\\\meanstd{624.45}{0.11} & \\\\meanstd{23.02}{0.69} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"FT & & \\\\meanstd{4.97}{0.14} & \\\\meanstd{4.58}{0.13} & \\\\meanstd{4.01}{0.11} \\n\",\n \"& \\\\meanstd{15.44}{0.36} & \\\\meanstd{4.63}{0.17} & \\\\meanstd{1.46}{0.05} & \\\\meanstd{214.26}{0.09} & \\\\meanstd{3.15}{0.02} \\\\\\\\\\n\",\n \"MEMIT & & \\\\meanstd{0.13}{0.02} & \\\\meanstd{0.12}{0.01} & \\\\meanstd{0.04}{0.01} \\n\",\n \"& \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{370.84}{0.30} & \\\\meanstd{3.59}{0.03} \\\\\\\\\\n\",\n \"PRUNE & & \\\\underline{\\\\meanstd{47.93}{0.36}} & \\\\underline{\\\\meanstd{45.50}{0.35}} & \\\\textbf{\\\\meanstd{39.20}{0.28}} \\n\",\n \"& \\\\meanstd{14.30}{0.35} & \\\\meanstd{11.27}{0.26} & \\\\textbf{\\\\meanstd{6.75}{0.12}} & \\\\textbf{\\\\meanstd{620.74}{0.10}} & \\\\textbf{\\\\meanstd{29.50}{0.08}} \\\\\\\\\\n\",\n \"RECT & & \\\\meanstd{0.73}{0.04} & \\\\meanstd{0.75}{0.04} & \\\\meanstd{0.05}{0.07} \\n\",\n \"& \\\\meanstd{0.64}{0.08} & \\\\meanstd{0.19}{0.03} & \\\\meanstd{0.09}{0.01} & \\\\meanstd{368.46}{0.27} & \\\\meanstd{1.35}{0.01} \\\\\\\\\\n\",\n \"AlphaEdit & & \\\\meanstd{42.01}{0.40} & \\\\meanstd{39.99}{0.39} & \\\\meanstd{13.87}{0.20} \\n\",\n \"& \\\\underline{\\\\meanstd{43.92}{0.50}} & \\\\underline{\\\\meanstd{24.37}{0.36}} & \\\\meanstd{2.32}{0.06} & \\\\meanstd{479.83}{0.77} & \\\\meanstd{4.67}{0.07} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\METHODNAME{}& & \\\\textbf{\\\\meanstd{70.04}{0.36}} & \\\\textbf{\\\\meanstd{65.43}{0.37}} & \\\\underline{\\\\meanstd{27.35}{0.26}} \\n\",\n \"& \\\\textbf{\\\\meanstd{60.76}{0.49}} & \\\\textbf{\\\\meanstd{29.24}{0.37}} & \\\\underline{\\\\meanstd{3.83}{0.08}} & \\\\underline{\\\\meanstd{612.67}{0.22}} & \\\\underline{\\\\meanstd{14.74}{0.07}} \\\\\\\\\\n\",\n \"\\\\specialrule{1.2pt}{0pt}{0pt} \\n\",\n \"\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t]\n"," \\centering\n"," \\vspace{-8mm}\n"," \\includegraphics[width=0.98\\textwidth]{Figures/sphere_sparse.png} \n"," \\caption{\n"," (a) A weight matrix is viewed as a set of neurons (\\textcolor{red}{red dots}) on a hypersphere. \n"," (b) Current SOTA methods~\\citep{DBLP:conf/iclr/MaWXLG25,DBLP:conf/iclr/FangJWMSW0C25} introduce perturbations (\\textcolor{blue}{blue triangles}) that interfere with the principle hyperspherical directions of pre-edit weights.\n"," (c) \\METHODNAME{} projects new knowledge onto a sparse space complementary to the principal hyperspherical directions.\n"," }\n"," \\vspace{-4mm}\n"," \\label{fig:teaser}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/Sec_3_zsre_Llama3-8B.pdf}\n"," \\caption{Trends of HE and editing performance throughout sequential editing. \n"," The Spearman correlation scores between HE and each editing metric displayed at the end of each curve. \n"," }\n"," \\label{fig:sec_1}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/Sec3-2.pdf} \n"," \\caption{Correlation between changes in HE and editing performance across consecutive edited weights. Each point corresponds to a $\\Delta \\mathrm{HE}$–$\\Delta \\mathrm{Acc.}$ pair for one method over five thousand sequential edits. Confidence ellipses and regression lines illustrate overall trends.\n"," }\n"," \\label{fig:sec_2}\n"," \\vspace{-3mm}\n","\\end{figure}\n"],["\\begin{table*}[t]\n","\\centering\n","\\caption{Comparison of \\METHODNAME{} with existing methods on sequential editing. \n","\\emph{Eff.}, \\emph{Gen.}, \\emph{Spe.}, \\emph{Flu.} and \\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \n","The best results are highlighted in bold, while the second-best results are underlined.}\n","\\label{tab:main_results}\n","\\resizebox{\\textwidth}{!}{\n","\\setlength{\\arrayrulewidth}{0.7pt} \n","\\renewcommand{\\arraystretch}{1.3} \n","\\begin{tabular}{c c | c c c | c c c | c c}\n","\\specialrule{1.2pt}{0pt}{0pt} \n","\\multirow{2}{*}{\\textbf{Method}} & \\multirow{2}{*}{\\textbf{Model}}\n","& \\multicolumn{3}{c|}{\\textbf{ZSRE}} \n","& \\multicolumn{5}{c}{\\textbf{Counterfact}} \\\\\n","\\cmidrule(lr){3-5} \\cmidrule(lr){6-10}\n"," & & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} \n"," & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} & \\textbf{Flu.$\\uparrow$} & \\textbf{Consis.$\\uparrow$} \\\\\n","\\hline\\hline\n","\n","Pre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{LLaMA3-8B}}} \n","& \\meanstd{35.42}{0.30} & \\meanstd{34.17}{0.30} & \\meanstd{38.02}{0.27} \n","& \\meanstd{0.49}{0.07} & \\meanstd{0.44}{0.05} & \\meanstd{18.09}{0.24} & \\meanstd{634.84}{0.12} & \\meanstd{22.06}{0.08} \\\\\n","\\hline\n","FT & & \\meanstd{15.27}{0.21} & \\meanstd{14.78}{0.21} & \\meanstd{5.06}{0.10} \n","& \\underline{\\meanstd{8.40}{0.28}} & \\underline{\\meanstd{2.54}{0.13}} & \\meanstd{0.03}{0.01} & \\meanstd{409.80}{0.67} & \\meanstd{19.35}{0.13} \\\\\n","MEMIT & & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.06}{0.01} \n","& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{318.19}{0.24} & \\meanstd{4.19}{0.04} \\\\\n","PRUNE & & \\meanstd{10.35}{0.18} & \\meanstd{10.08}{0.18} & \\meanstd{9.55}{0.15} \n","& \\meanstd{1.19}{0.11} & \\meanstd{0.34}{0.04} & \\underline{\\meanstd{0.62}{0.03}} & \\textbf{\\meanstd{618.72}{0.08}} & \\textbf{\\meanstd{49.24}{0.13}} \\\\\n","RECT & & \\meanstd{0.01}{0.00} & \\meanstd{0.01}{0.01} & \\meanstd{0.04}{0.01} \n","& \\meanstd{0.57}{0.08} & \\meanstd{0.29}{0.04} & \\meanstd{0.10}{0.01} & \\meanstd{438.83}{0.18} & \\meanstd{9.40}{0.05} \\\\\n","AlphaEdit & & \\underline{\\meanstd{86.64}{0.23}} & \\underline{\\meanstd{81.28}{0.28}} & \\underline{\\meanstd{28.78}{0.22}} \n","& \\meanstd{4.37}{0.20} & \\meanstd{1.71}{0.10} & \\meanstd{0.57}{0.03} & \\meanstd{482.36}{0.44} & \\meanstd{4.71}{0.04} \\\\\n","\\hline\n","\\METHODNAME{}& & \\textbf{\\meanstd{90.01}{0.21}} & \\textbf{\\meanstd{84.67}{0.26}} & \\textbf{\\meanstd{45.40}{0.29}} \n","& \\textbf{\\meanstd{52.89}{0.50}} & \\textbf{\\meanstd{32.07}{0.39}} & \\textbf{\\meanstd{5.01}{0.10}} & \\underline{\\meanstd{551.51}{0.53}} & \\underline{\\meanstd{30.89}{0.13}} \\\\\n","\\hline\\hline\n","\n","Pre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{Qwen2.5-7B}}} \n","& \\meanstd{35.29}{0.29} & \\meanstd{34.10}{0.28} & \\meanstd{38.44}{0.27} \n","& \\meanstd{0.42}{0.06} & \\meanstd{0.46}{0.05} & \\meanstd{15.06}{0.20} & \\meanstd{624.45}{0.11} & \\meanstd{23.02}{0.69} \\\\\n","\\hline\n","FT & & \\meanstd{4.97}{0.14} & \\meanstd{4.58}{0.13} & \\meanstd{4.01}{0.11} \n","& \\meanstd{15.44}{0.36} & \\meanstd{4.63}{0.17} & \\meanstd{1.46}{0.05} & \\meanstd{214.26}{0.09} & \\meanstd{3.15}{0.02} \\\\\n","MEMIT & & \\meanstd{0.13}{0.02} & \\meanstd{0.12}{0.01} & \\meanstd{0.04}{0.01} \n","& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{370.84}{0.30} & \\meanstd{3.59}{0.03} \\\\\n","PRUNE & & \\underline{\\meanstd{47.93}{0.36}} & \\underline{\\meanstd{45.50}{0.35}} & \\textbf{\\meanstd{39.20}{0.28}} \n","& \\meanstd{14.30}{0.35} & \\meanstd{11.27}{0.26} & \\textbf{\\meanstd{6.75}{0.12}} & \\textbf{\\meanstd{620.74}{0.10}} & \\textbf{\\meanstd{29.50}{0.08}} \\\\\n","RECT & & \\meanstd{0.73}{0.04} & \\meanstd{0.75}{0.04} & \\meanstd{0.05}{0.07} \n","& \\meanstd{0.64}{0.08} & \\meanstd{0.19}{0.03} & \\meanstd{0.09}{0.01} & \\meanstd{368.46}{0.27} & \\meanstd{1.35}{0.01} \\\\\n","AlphaEdit & & \\meanstd{42.01}{0.40} & \\meanstd{39.99}{0.39} & \\meanstd{13.87}{0.20} \n","& \\underline{\\meanstd{43.92}{0.50}} & \\underline{\\meanstd{24.37}{0.36}} & \\meanstd{2.32}{0.06} & \\meanstd{479.83}{0.77} & \\meanstd{4.67}{0.07} \\\\\n","\\hline\n","\\METHODNAME{}& & \\textbf{\\meanstd{70.04}{0.36}} & \\textbf{\\meanstd{65.43}{0.37}} & \\underline{\\meanstd{27.35}{0.26}} \n","& \\textbf{\\meanstd{60.76}{0.49}} & \\textbf{\\meanstd{29.24}{0.37}} & \\underline{\\meanstd{3.83}{0.08}} & \\underline{\\meanstd{612.67}{0.22}} & \\underline{\\meanstd{14.74}{0.07}} \\\\\n","\\specialrule{1.2pt}{0pt}{0pt} \n","\n","\\end{tabular}\n","}\n","\\end{table*}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/llama_neuron_similarity_heatmap_15k.pdf} \n"," \\caption{\n"," Cosine similarity between neurons in the updated weight matrix after 15,000 edits. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\n"," \\METHODNAME{} effectively preserves the weight structure, demonstrating the most stable hyperspherical uniformity.\n"," }\n"," \\label{fig:Sec_5_heatmap}\n"," \\vspace{-3mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/llama_tsne_grid_15k.pdf} \n"," \\caption{The t-SNE distribution of weight neurons of pre-edited and post-edited LLM after 15,000 edits using dimensionality reduction. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\METHODNAME{} consistently exhibits minimal shift. }\n"," \\label{fig:Sec_5_pca}\n"," \\vspace{-3mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/general_line.pdf} \n"," \\caption{\n"," General ability testing of post-edited LLaMA3 (8B) on four tasks.\n"," }\n"," \\label{fig:line_general}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=0.98\\textwidth]{Figures/baseline_improve_all.pdf}\n"," \\caption{Performance improvements of baseline editing methods after adding a single line of code from \\METHODNAME{} (i.e., sparse space projection). Gray bars denote the original baseline performance, while purple bars indicate the performance after enhancement.}\n"," \\label{fig:baseline_improve_all}\n"," \\vspace{-2mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/qwen_neuron_similarity_heatmap_5k.pdf} \n"," \\caption{\n"," Cosine similarity between neurons in updated weight matrix after 5,000 edits on Qwen2.5. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\n"," \\METHODNAME{} effectively preserve the weight structure, demonstrating the most stable hyperspherical uniformity.\n"," }\n"," \\label{fig:Sec_5_heatmap_qwen}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/qwen_tsne_grid_5k.pdf} \n"," \\caption{The distribution of weight neurons of pre-edited and post-edited Qwen2.5 after 5,000 edits using dimensionality reduction across mainstream sequential editing methods. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\METHODNAME{} consistently exhibits minimal shift. \n"," }\n"," \\label{fig:Sec_5_pca_qwen}\n","\\end{figure}\n"],["\\begin{figure}[!hbt]%[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/memit_general_line.pdf} \n"," \\caption{General ability improvements of MEMIT after incorporating SPHERE with a single line of sparse space projection code.)\n"," }\n"," \\label{fig:1}\n","\\end{figure}\n"],["\\begin{figure}[!hbt]%[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/prune_general_line.pdf} \n"," \\caption{General ability improvements of PRUNE after incorporating SPHERE with a single line of sparse space projection code.)\n"," }\n"," \\label{fig:2}\n","\\end{figure}\n"],["\\begin{figure}[!hbt]%[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/rect_general_line.pdf} \n"," \\caption{General ability improvements of RECT after incorporating SPHERE with a single line of sparse space projection code.)\n"," }\n"," \\label{fig:3}\n","\\end{figure}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\vspace{-8mm}\\n\",\n \" \\\\includegraphics[width=0.98\\\\textwidth]{Figures/sphere_sparse.png} \\n\",\n \" \\\\caption{\\n\",\n \" (a) A weight matrix is viewed as a set of neurons (\\\\textcolor{red}{red dots}) on a hypersphere. \\n\",\n \" (b) Current SOTA methods~\\\\citep{DBLP:conf/iclr/MaWXLG25,DBLP:conf/iclr/FangJWMSW0C25} introduce perturbations (\\\\textcolor{blue}{blue triangles}) that interfere with the principle hyperspherical directions of pre-edit weights.\\n\",\n \" (c) \\\\METHODNAME{} projects new knowledge onto a sparse space complementary to the principal hyperspherical directions.\\n\",\n \" }\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \" \\\\label{fig:teaser}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/Sec_3_zsre_Llama3-8B.pdf}\\n\",\n \" \\\\caption{Trends of HE and editing performance throughout sequential editing. \\n\",\n \" The Spearman correlation scores between HE and each editing metric displayed at the end of each curve. \\n\",\n \" }\\n\",\n \" \\\\label{fig:sec_1}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/Sec3-2.pdf} \\n\",\n \" \\\\caption{Correlation between changes in HE and editing performance across consecutive edited weights. Each point corresponds to a $\\\\Delta \\\\mathrm{HE}$–$\\\\Delta \\\\mathrm{Acc.}$ pair for one method over five thousand sequential edits. Confidence ellipses and regression lines illustrate overall trends.\\n\",\n \" }\\n\",\n \" \\\\label{fig:sec_2}\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Comparison of \\\\METHODNAME{} with existing methods on sequential editing. \\n\",\n \"\\\\emph{Eff.}, \\\\emph{Gen.}, \\\\emph{Spe.}, \\\\emph{Flu.} and \\\\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \\n\",\n \"The best results are highlighted in bold, while the second-best results are underlined.}\\n\",\n \"\\\\label{tab:main_results}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\setlength{\\\\arrayrulewidth}{0.7pt} \\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3} \\n\",\n \"\\\\begin{tabular}{c c | c c c | c c c | c c}\\n\",\n \"\\\\specialrule{1.2pt}{0pt}{0pt} \\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Method}} & \\\\multirow{2}{*}{\\\\textbf{Model}}\\n\",\n \"& \\\\multicolumn{3}{c|}{\\\\textbf{ZSRE}} \\n\",\n \"& \\\\multicolumn{5}{c}{\\\\textbf{Counterfact}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-5} \\\\cmidrule(lr){6-10}\\n\",\n \" & & \\\\textbf{Eff.$\\\\uparrow$} & \\\\textbf{Gen.$\\\\uparrow$} & \\\\textbf{Spe.$\\\\uparrow$} \\n\",\n \" & \\\\textbf{Eff.$\\\\uparrow$} & \\\\textbf{Gen.$\\\\uparrow$} & \\\\textbf{Spe.$\\\\uparrow$} & \\\\textbf{Flu.$\\\\uparrow$} & \\\\textbf{Consis.$\\\\uparrow$} \\\\\\\\\\n\",\n \"\\\\hline\\\\hline\\n\",\n \"\\n\",\n \"Pre-edited & \\\\multirow{7}{*}{\\\\makecell{\\\\rotatebox{90}{LLaMA3-8B}}} \\n\",\n \"& \\\\meanstd{35.42}{0.30} & \\\\meanstd{34.17}{0.30} & \\\\meanstd{38.02}{0.27} \\n\",\n \"& \\\\meanstd{0.49}{0.07} & \\\\meanstd{0.44}{0.05} & \\\\meanstd{18.09}{0.24} & \\\\meanstd{634.84}{0.12} & \\\\meanstd{22.06}{0.08} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"FT & & \\\\meanstd{15.27}{0.21} & \\\\meanstd{14.78}{0.21} & \\\\meanstd{5.06}{0.10} \\n\",\n \"& \\\\underline{\\\\meanstd{8.40}{0.28}} & \\\\underline{\\\\meanstd{2.54}{0.13}} & \\\\meanstd{0.03}{0.01} & \\\\meanstd{409.80}{0.67} & \\\\meanstd{19.35}{0.13} \\\\\\\\\\n\",\n \"MEMIT & & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.06}{0.01} \\n\",\n \"& \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{318.19}{0.24} & \\\\meanstd{4.19}{0.04} \\\\\\\\\\n\",\n \"PRUNE & & \\\\meanstd{10.35}{0.18} & \\\\meanstd{10.08}{0.18} & \\\\meanstd{9.55}{0.15} \\n\",\n \"& \\\\meanstd{1.19}{0.11} & \\\\meanstd{0.34}{0.04} & \\\\underline{\\\\meanstd{0.62}{0.03}} & \\\\textbf{\\\\meanstd{618.72}{0.08}} & \\\\textbf{\\\\meanstd{49.24}{0.13}} \\\\\\\\\\n\",\n \"RECT & & \\\\meanstd{0.01}{0.00} & \\\\meanstd{0.01}{0.01} & \\\\meanstd{0.04}{0.01} \\n\",\n \"& \\\\meanstd{0.57}{0.08} & \\\\meanstd{0.29}{0.04} & \\\\meanstd{0.10}{0.01} & \\\\meanstd{438.83}{0.18} & \\\\meanstd{9.40}{0.05} \\\\\\\\\\n\",\n \"AlphaEdit & & \\\\underline{\\\\meanstd{86.64}{0.23}} & \\\\underline{\\\\meanstd{81.28}{0.28}} & \\\\underline{\\\\meanstd{28.78}{0.22}} \\n\",\n \"& \\\\meanstd{4.37}{0.20} & \\\\meanstd{1.71}{0.10} & \\\\meanstd{0.57}{0.03} & \\\\meanstd{482.36}{0.44} & \\\\meanstd{4.71}{0.04} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\METHODNAME{}& & \\\\textbf{\\\\meanstd{90.01}{0.21}} & \\\\textbf{\\\\meanstd{84.67}{0.26}} & \\\\textbf{\\\\meanstd{45.40}{0.29}} \\n\",\n \"& \\\\textbf{\\\\meanstd{52.89}{0.50}} & \\\\textbf{\\\\meanstd{32.07}{0.39}} & \\\\textbf{\\\\meanstd{5.01}{0.10}} & \\\\underline{\\\\meanstd{551.51}{0.53}} & \\\\underline{\\\\meanstd{30.89}{0.13}} \\\\\\\\\\n\",\n \"\\\\hline\\\\hline\\n\",\n \"\\n\",\n \"Pre-edited & \\\\multirow{7}{*}{\\\\makecell{\\\\rotatebox{90}{Qwen2.5-7B}}} \\n\",\n \"& \\\\meanstd{35.29}{0.29} & \\\\meanstd{34.10}{0.28} & \\\\meanstd{38.44}{0.27} \\n\",\n \"& \\\\meanstd{0.42}{0.06} & \\\\meanstd{0.46}{0.05} & \\\\meanstd{15.06}{0.20} & \\\\meanstd{624.45}{0.11} & \\\\meanstd{23.02}{0.69} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"FT & & \\\\meanstd{4.97}{0.14} & \\\\meanstd{4.58}{0.13} & \\\\meanstd{4.01}{0.11} \\n\",\n \"& \\\\meanstd{15.44}{0.36} & \\\\meanstd{4.63}{0.17} & \\\\meanstd{1.46}{0.05} & \\\\meanstd{214.26}{0.09} & \\\\meanstd{3.15}{0.02} \\\\\\\\\\n\",\n \"MEMIT & & \\\\meanstd{0.13}{0.02} & \\\\meanstd{0.12}{0.01} & \\\\meanstd{0.04}{0.01} \\n\",\n \"& \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{370.84}{0.30} & \\\\meanstd{3.59}{0.03} \\\\\\\\\\n\",\n \"PRUNE & & \\\\underline{\\\\meanstd{47.93}{0.36}} & \\\\underline{\\\\meanstd{45.50}{0.35}} & \\\\textbf{\\\\meanstd{39.20}{0.28}} \\n\",\n \"& \\\\meanstd{14.30}{0.35} & \\\\meanstd{11.27}{0.26} & \\\\textbf{\\\\meanstd{6.75}{0.12}} & \\\\textbf{\\\\meanstd{620.74}{0.10}} & \\\\textbf{\\\\meanstd{29.50}{0.08}} \\\\\\\\\\n\",\n \"RECT & & \\\\meanstd{0.73}{0.04} & \\\\meanstd{0.75}{0.04} & \\\\meanstd{0.05}{0.07} \\n\",\n \"& \\\\meanstd{0.64}{0.08} & \\\\meanstd{0.19}{0.03} & \\\\meanstd{0.09}{0.01} & \\\\meanstd{368.46}{0.27} & \\\\meanstd{1.35}{0.01} \\\\\\\\\\n\",\n \"AlphaEdit & & \\\\meanstd{42.01}{0.40} & \\\\meanstd{39.99}{0.39} & \\\\meanstd{13.87}{0.20} \\n\",\n \"& \\\\underline{\\\\meanstd{43.92}{0.50}} & \\\\underline{\\\\meanstd{24.37}{0.36}} & \\\\meanstd{2.32}{0.06} & \\\\meanstd{479.83}{0.77} & \\\\meanstd{4.67}{0.07} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\METHODNAME{}& & \\\\textbf{\\\\meanstd{70.04}{0.36}} & \\\\textbf{\\\\meanstd{65.43}{0.37}} & \\\\underline{\\\\meanstd{27.35}{0.26}} \\n\",\n \"& \\\\textbf{\\\\meanstd{60.76}{0.49}} & \\\\textbf{\\\\meanstd{29.24}{0.37}} & \\\\underline{\\\\meanstd{3.83}{0.08}} & \\\\underline{\\\\meanstd{612.67}{0.22}} & \\\\underline{\\\\meanstd{14.74}{0.07}} \\\\\\\\\\n\",\n \"\\\\specialrule{1.2pt}{0pt}{0pt} \\n\",\n \"\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/llama_neuron_similarity_heatmap_15k.pdf} \\n\",\n \" \\\\caption{\\n\",\n \" Cosine similarity between neurons in the updated weight matrix after 15,000 edits. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\\n\",\n \" \\\\METHODNAME{} effectively preserves the weight structure, demonstrating the most stable hyperspherical uniformity.\\n\",\n \" }\\n\",\n \" \\\\label{fig:Sec_5_heatmap}\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/llama_tsne_grid_15k.pdf} \\n\",\n \" \\\\caption{The t-SNE distribution of weight neurons of pre-edited and post-edited LLM after 15,000 edits using dimensionality reduction. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\\\METHODNAME{} consistently exhibits minimal shift. }\\n\",\n \" \\\\label{fig:Sec_5_pca}\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/general_line.pdf} \\n\",\n \" \\\\caption{\\n\",\n \" General ability testing of post-edited LLaMA3 (8B) on four tasks.\\n\",\n \" }\\n\",\n \" \\\\label{fig:line_general}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.98\\\\textwidth]{Figures/baseline_improve_all.pdf}\\n\",\n \" \\\\caption{Performance improvements of baseline editing methods after adding a single line of code from \\\\METHODNAME{} (i.e., sparse space projection). Gray bars denote the original baseline performance, while purple bars indicate the performance after enhancement.}\\n\",\n \" \\\\label{fig:baseline_improve_all}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/qwen_neuron_similarity_heatmap_5k.pdf} \\n\",\n \" \\\\caption{\\n\",\n \" Cosine similarity between neurons in updated weight matrix after 5,000 edits on Qwen2.5. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\\n\",\n \" \\\\METHODNAME{} effectively preserve the weight structure, demonstrating the most stable hyperspherical uniformity.\\n\",\n \" }\\n\",\n \" \\\\label{fig:Sec_5_heatmap_qwen}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/qwen_tsne_grid_5k.pdf} \\n\",\n \" \\\\caption{The distribution of weight neurons of pre-edited and post-edited Qwen2.5 after 5,000 edits using dimensionality reduction across mainstream sequential editing methods. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\\\METHODNAME{} consistently exhibits minimal shift. \\n\",\n \" }\\n\",\n \" \\\\label{fig:Sec_5_pca_qwen}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!hbt]%[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/memit_general_line.pdf} \\n\",\n \" \\\\caption{General ability improvements of MEMIT after incorporating SPHERE with a single line of sparse space projection code.)\\n\",\n \" }\\n\",\n \" \\\\label{fig:1}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!hbt]%[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/prune_general_line.pdf} \\n\",\n \" \\\\caption{General ability improvements of PRUNE after incorporating SPHERE with a single line of sparse space projection code.)\\n\",\n \" }\\n\",\n \" \\\\label{fig:2}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!hbt]%[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/rect_general_line.pdf} \\n\",\n \" \\\\caption{General ability improvements of RECT after incorporating SPHERE with a single line of sparse space projection code.)\\n\",\n \" }\\n\",\n \" \\\\label{fig:3}\\n\",\n \"\\\\end{figure}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n\\documentclass{article} % For LaTeX2e\n\\usepackage{iclr2026_conference,times}\n\n% Optional math commands from https://github.com/goodfeli/dlbook_notation.\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\\usepackage{booktabs}\n\\usepackage{multirow}\n\\usepackage{graphicx} % for \\rotatebox\n\\usepackage{makecell} % for line breaks in cells\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n% Figure reference, capital. 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vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\usepackage[backref]{hyperref}\n\n\\usepackage{url}\n\\usepackage{bbm}\n\\usepackage{enumitem}\n\\usepackage{amssymb}\n\\usepackage{booktabs}\n\\usepackage{tabularx}\n\\usepackage[table]{xcolor}\n\\usepackage{array}\n\\usepackage{caption}\n\\usepackage{tcolorbox}\n\\usepackage{amsthm} \n\\usepackage{bm} \n\\usepackage{wrapfig}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\n\\newtheorem{lemma}{Lemma}\n\\newtheorem{theorem}{Theorem}\n\\newtheorem{corollary}{Corollary}\n\\newtheorem{definition}{Definition}\n\\newtheorem{proposition}{Proposition}\n\n\\definecolor{lightgray}{gray}{0.95}\n\\definecolor{titlegray}{gray}{0.85}\n\n\\newcolumntype{L}{>{\\raggedright\\arraybackslash}X}\n\\newcolumntype{C}{>{\\centering\\arraybackslash}m{2.5cm}} \n\n\n\n\\newcommand{\\METHODNAME}{\\textsc{SPHERE}}\n\n\\newcommand{\\qingyuan}[1]{\\textcolor{cyan}{[Qingyuan: #1]}}\n\\newcommand{\\jiachen}[1]{\\textcolor{red}{[Jia-Chen: #1]}}\n\\newcommand{\\yunzhi}[1]{\\textcolor{blue}{[Yunzhi: #1]}}\n\\newcommand{\\hong}[1]{\\textcolor{orange}{[Hong: #1]}}\n\\newcommand{\\violet}[1]{\\textcolor{violet}{[Violet: #1]}}\n\n\n\\title{Energy-Regularized Sequential Model \\\\ Editing on Hyperspheres}\n\n\\author{\n Qingyuan Liu$^1$\\thanks{\\hspace{0.5mm}Equal contribution.}, ~Jia-Chen Gu$^2$\\footnotemark[1], ~Yunzhi Yao$^3$, ~Hong Wang$^4$, ~Nanyun Peng$^2$\\\\\n $^1$Columbia University ~\n $^2$University of California, Los Angeles \\\\\n $^3$Zhejiang University ~\n $^4$University of Science and Technology of China\\\\ \n \\texttt{ql2505@columbia.edu}, ~\\texttt{gujc@ucla.edu}, ~\\texttt{violetpeng@cs.ucla.edu}\n}\n\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\n\\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission.\n\\begin{document}\n\n\n\n\\maketitle\n\n\\vspace{-5mm}\n\n\\begin{abstract}\n\nLarge language models (LLMs) require constant updates to remain aligned with evolving real-world knowledge. \nModel editing offers a lightweight alternative to retraining, but sequential editing that updates the LLM knowledge through multiple successive edits often destabilizes representations and induces catastrophic forgetting. \nIn this work, we seek to better understand and mitigate performance degradation caused by sequential editing.\nWe hypothesize that \\emph{hyperspherical uniformity}, a property that maintains uniform distribution of neuron weights on a hypersphere, helps the model remain stable, retain prior knowledge, while still accommodate new updates.\nWe use Hyperspherical Energy (HE) to quantify neuron uniformity during editing, and examine its correlation with editing performance.\nEmpirical studies across widely used editing methods reveals a strong correlation between HE dynamics and editing performance, with editing failures consistently coinciding with high HE fluctuations.\nWe further theoretically prove that HE dynamics impose a lower bound on the degradation of pretrained knowledge, highlighting why HE stability is crucial for knowledge retention. \nMotivated by these insights, we propose \\METHODNAME{} (\\textbf{S}parse \\textbf{P}rojection for \\textbf{H}yperspherical \\textbf{E}nergy-\\textbf{R}egularized \\textbf{E}diting), an HE-driven regularization strategy that stabilizes neuron weight distributions, ultimately preserving prior knowledge while enabling reliable sequential updates. \nSpecifically, \\METHODNAME{} identifies a sparse space complementary to the principal hyperspherical directions of the pretrained weight matrices and projects new knowledge onto it, attenuating perturbations on the principal directions.\nExtensive experiments on LLaMA3 (8B) and Qwen2.5 (7B) show that \\METHODNAME{} outperforms the best baseline in editing capability by an average of 16.41\\%, while most faithfully preserving general model performance, thereby offering a principled path toward reliable large-scale knowledge editing.\nThe code is available at \\href{https://github.com/PlusLabNLP/SPHERE}{https://github.com/PlusLabNLP/SPHERE}.\n\n\n\\end{abstract}\n\n\n\n\\section{Introduction}\n\nLarge language models (LLMs) have demonstrated strong capabilities in knowledge storage, reasoning, and generation~\\citep{DBLP:journals/corr/abs-2412-19437, meta2024llama4, DBLP:journals/corr/abs-2505-09388, openai2025gpt5}. \nHowever, the knowledge embedded in LLMs inevitably becomes outdated or incorrect, as real-world facts continuously evolve~\\citep{DBLP:journals/csur/JiLFYSXIBMF23,DBLP:journals/tois/HuangYMZFWCPFQL25}. \nRetraining LLMs to incorporate such updates is prohibitively expensive, motivating the development of \\emph{model editing} (also known as \\emph{knowledge editing})~\\citep{DBLP:conf/emnlp/CaoAT21,DBLP:conf/iclr/MitchellLBFM22,DBLP:conf/iclr/MengSABB23,DBLP:conf/emnlp/GuXMLLCP24,DBLP:conf/iclr/FangJWMSW0C25}. \nThe most practical setting for model editing is\n\\emph{sequential editing}, where multiple updates are applied over time. \nHowever, previous studies have shown that such interventions often suffer from significant performance degradation due to catastrophic forgetting~\\citep{DBLP:conf/emnlp/GuXMLLCP24,DBLP:conf/acl/GuptaRA24}. \nConsequently, reconciling the trade-off between preserving original pretrained knowledge and integrating new editing knowledge remains an unresolved challenge.\n\n\nIn this work, we seek to better understand and mitigate the performance degradation caused by sequential editing.\nWe revisit model editing from the perspective of \\emph{hyperspherical uniformity} of perturbed weights~\\citep{DBLP:conf/aistats/LiuLL0SW21}, motivated by the observation that sequential edits often disrupt weight geometry, leading to degraded representations.\nPrevious studies have shown that viewing a weight matrix as a set of neurons on a hypersphere (as shown in Figure~\\ref{fig:teaser} (a)) and maintaining their hyperspherical uniformity is crucial for stable training and effective generalization~\\citep{DBLP:journals/corr/CogswellAGZB15, DBLP:conf/icml/XieDZKYZX17, DBLP:conf/nips/QiuLFXFLZWS23}. \nTo investigate the applicability of these principles to sequential editing, we adopt \\emph{hyperspherical energy (HE)}~\\citep{DBLP:conf/nips/LiuLLLYDS18,DBLP:conf/nips/QiuLFXFLZWS23} as a measure to quantify weight uniformity throughout sequential editing.\nHE calculates the dispersion of neuron weight vectors on a hypersphere, where lower energy corresponds to a more balanced distribution of neurons. \nBy tracking HE dynamics throughout sequential editing, we can better understand how edits affect weight uniformity, identify early signs of destabilization, and even develop HE-driven regularization strategies to stabilize the editing process.\n\n\n\\begin{figure}[t]\n \\centering\n \\vspace{-8mm}\n \\includegraphics[width=0.98\\textwidth]{Figures/sphere_sparse.png} \n \\caption{\n (a) A weight matrix is viewed as a set of neurons (\\textcolor{red}{red dots}) on a hypersphere. \n (b) Current SOTA methods~\\citep{DBLP:conf/iclr/MaWXLG25,DBLP:conf/iclr/FangJWMSW0C25} introduce perturbations (\\textcolor{blue}{blue triangles}) that interfere with the principle hyperspherical directions of pre-edit weights.\n (c) \\METHODNAME{} projects new knowledge onto a sparse space complementary to the principal hyperspherical directions.\n }\n \\vspace{-4mm}\n \\label{fig:teaser}\n\\end{figure}\n\n\nTo reveal the mechanisms underlying successful editing strategies from the perspective of hyperspherical uniformity, we first empirically analyze how HE evolves throughout sequential editing and examine how these dynamics relate to editing performance across six widely used methods.\nExperimental results reveal a strong correlation between hyperspherical uniformity and editing performance, with editing failures consistently coinciding with its collapse. \nMeanwhile, more advanced editing methods have proven more effective at preserving hyperspherical uniformity.\nTo complement these empirical findings, we further provide a theoretical analysis verifying that variations in HE establish a lower bound on the interference with the original pretrained knowledge. \nThis result clarifies that state-of-the-art (SOTA) editing methods implicitly regulate hyperspherical uniformity and the lower bound on the interference, providing a principled explanation for their enhanced robustness.\n\n\nMotivated by these empirical and theoretical findings, we propose \\METHODNAME{} (\\textbf{S}parse \\textbf{P}rojection for \\textbf{H}yperspherical \\textbf{E}nergy-\\textbf{R}egularized \\textbf{E}diting), an HE-driven regularization strategy that stabilizes neuron weight distributions, ultimately preserving prior knowledge while enabling reliable sequential updates.\nThe key insight is that, as shown in Figure~\\ref{fig:teaser} (b), current methods often introduce perturbations that interfere with the principal hyperspherical directions of the pretrained weight matrices, leading to instability, loss of uniformity, and eventual degradation of model performance.\nTo counteract these side effects, as shown in Figure~\\ref{fig:teaser} (c), \\METHODNAME{} identifies a sparse space complementary to the principal hyperspherical directions of the pretrained weight matrices and projects new knowledge onto it, attenuating perturbation components aligned with those principal directions.\nBy doing so, \\METHODNAME{} effectively preserves the hyperspherical uniformity and substantially extends the number of effective sequential edits.\n\n\nWe evaluated \\METHODNAME{} \non \\textbf{two LLMs}, including LLaMA3 (8B)~\\citep{llama3modelcard} and Qwen2.5 (7B)~\\citep{qwen2.5},\non \\textbf{two editing datasets}, including CounterFact~\\citep{DBLP:conf/nips/MengBAB22} and ZsRE~\\citep{DBLP:conf/conll/LevySCZ17}.\n\\textbf{Four downstream tasks} including reasoning~\\citep{DBLP:journals/corr/abs-2110-14168}, natural language inference~\\citep{DBLP:conf/mlcw/DaganGM05}, open-domain QA~\\citep{DBLP:journals/tacl/KwiatkowskiPRCP19}, and closed-domain QA~\\citep{DBLP:conf/naacl/ClarkLCK0T19}\nare employed to demonstrate the impact of editing on the general abilities of LLMs.\nExperimental results show that \\METHODNAME{} sustains editing capacity under large-scale editing settings, outperforming the best baseline~\\citep{DBLP:conf/iclr/FangJWMSW0C25} by \\textbf{16.41\\%} on average. \nBeyond editing capacity, it more effectively preserves the hyperspherical uniformity and the general abilities of edited models than all baselines.\nFurthermore, as a plug-and-play enhancement, \\METHODNAME{} improves the mainstream editing methods~\\citep{DBLP:conf/iclr/MengSABB23,DBLP:conf/emnlp/GuXMLLCP24,DBLP:conf/iclr/MaWXLG25} by \\textbf{38.71\\%} on average, offering a principled path toward reliable and scalable editing.\n\n\n\\section{Preliminaries}\n\n\\subsection{Model Editing}\n\\label{sec:model-editing}\nSequential model editing aims to update the knowledge stored in LLMs through multiple successive edits. \nEach edit modifies the model parameter $\\bm{W} \\in \\mathbb{R}^{d_1 \\times d_0}$ by adding a perturbation $\\Delta \\in \\mathbb{R}^{d_1 \\times d_0}$ in a locate-then-edit paradigm~\\citep{DBLP:conf/nips/MengBAB22}, where $d_0$ and $d_1$ represent the dimensions of the intermediate and output layers of the feed-forward network (FFN), respectively. \nSpecifically, suppose each edit updates $u$ pieces of knowledge in the form of (subject $s$, relation $r$, object $o$), e.g., ($s$ = \\emph{United States}, $r$ = \\emph{President of}, $o$ = \\emph{Donald Trump}). \nThe perturbed parameter is expected to associate $u$ new \\emph{key-value} ($k$-$v$) pairs, where $k$ and $v$ encode $(s, r)$ and $(o)$ of the new knowledge, respectively. \nWe can stack these keys and values into matrices as follows:\n\\begin{equation}\n\\bm{K}_1 = [\\bm{k}_1 \\,|\\, \\bm{k}_2 \\,|\\, \\dots \\,|\\, \\bm{k}_u] \\in \\mathbb{R}^{d_0 \\times u}, \\quad\n\\bm{V}_1 = [\\bm{v}_1 \\,|\\, \\bm{v}_2 \\,|\\, \\dots \\,|\\, \\bm{v}_u] \\in \\mathbb{R}^{d_1 \\times u},\n\\label{eq:k1v1}\n\\end{equation}\nwhere the subscripts of $\\bm{k}$ and $\\bm{v}$ represent the index of the to-be-updated knowledge. Therefore, the editing objective can be expressed as:\n\\begin{equation}\n\\Delta \\bm{W} = \\arg\\min_{\\Delta \\hat{\\bm{W}}} \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}}) \\bm{K}_1 - \\bm{V}_1 \\right\\|^2,\n\\label{eq:edit_obj}\n\\end{equation}\nwhere $\\|\\cdot\\|^2$ denotes the sum of the squared elements in the matrix.\n\nAdditionally, current methods typically incorporate an error term to preserve the original knowledge.\nLet $\\bm{K}_0$ and $\\bm{V}_0$ represent the matrices formed by stacking the $\\bm{k}$ and $\\bm{v}$ corresponding to the original pretrained knowledge. \nEqn.~\\ref{eq:edit_obj} is regularized by involving the error term as follows:\n\\begin{equation}\n\\Delta \\bm{W} = \\arg\\min_{\\Delta \\hat{\\bm{W}}} \\left( \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}}) \\bm{K}_1 - \\bm{V}_1 \\right\\|^2\n+ \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}}) \\bm{K}_0 - \\bm{V}_0 \\right\\|^2 \\right).\n\\label{eq:edit_obj_preserve}\n\\end{equation}\nSince $\\bm{K}_0$ and $\\bm{V}_0$ encode the original pretrained knowledge, we have $\\bm{W} \\bm{K}_0 = \\bm{V}_0$ (cf. Eqn.~\\ref{eq:k1v1}). By applying the normal equation, if the closed-form solution of Eqn.~\\ref{eq:edit_obj_preserve} exists, it can be written as:\n\\begin{equation}\n\\Delta \\bm{W} = (\\bm{V}_1 - \\bm{W} \\bm{K}_1) \\bm{K}_T^{\\top} \n\\left( \\bm{K}_0 \\bm{K}_0^{\\top} + \\bm{K}_1 \\bm{K}_1^{\\top} \\right)^{-1}.\n\\label{eq:closed_form_delta}\n\\end{equation}\nSince the full scope of an LLM's knowledge is generally inaccessible, $\\bm{K}_0$ is difficult to obtain directly but can be approximated from abundant text input. \nSee Appendix~\\ref{appendix:model_editing} for more details.\n\n\n\n\\subsection{Hyperspherical Energy}\n\\label{sec:HSE}\nHyperspherical Energy (HE) serves as a quantitative metric for measuring \\emph{hyperspherical uniformity}. \nGiven a group of neurons, HE characterizes their uniformity on a hypersphere by defining a generic potential energy based on their pairwise relationship. \nLower energy represents that these neurons are more diverse and uniformly distributed, while higher energy reflects redundancy. \nGiven a weight matrix $\\bm{W} \\in \\mathbb{R}^{N \\times (d+1)}$ represented as a set of $N$ neurons (i.e., kernels), where each row $\\bm{w}_i \\in \\mathbb{R}^{d+1}$ corresponds to a neuron, its HE is defined as:\n\\begin{equation}\n\\bm{E_{s,d}}\\left( \\hat{\\bm{w}}_i \\mid_{i=1}^N \\right)\n= \\sum_{i=1}^N \\sum_{\\substack{j=1, j \\ne i}}^N f_s\\left( \\left\\| \\hat{\\bm{w}}_i - \\hat{\\bm{w}}_j \\right\\| \\right)\n= \\begin{cases}\n\\sum_{i \\ne j} \\left\\| \\hat{\\bm{w}}_i - \\hat{\\bm{w}}_j \\right\\|^{-s}, & s > 0 \\\\\n\\sum_{i \\ne j} \\log\\left( \\left\\| \\hat{\\bm{w}}_i - \\hat{\\bm{w}}_j \\right\\|^{-1} \\right), & s = 0\n\\end{cases}\n\\label{eq:full_hse}\n\\end{equation}\n% \\vspace{-1em}\nwhere $\\|\\cdot\\|$ denotes Euclidean distance, $f_s(\\cdot)$ is a decreasing real-valued function, and $\\hat{\\bm{w}}_i = \\frac{\\bm{w}_i}{\\|\\bm{w}_i\\|}$ is the $i$-th neuron weight projected onto the unit hypersphere $\\mathbb{S}^d = \\{ \\bm{w} \\in \\mathbb{R}^{d+1} \\mid \\|\\bm{w}\\| = 1 \\}$. \nWe also denote $\\hat{\\bm{W}}_N = \\{\\hat{\\bm{w}}_1, \\cdots, \\hat{\\bm{w}}_N \\in \\mathbb{S}^d\\}$, and $E_s = \\bm{E_{s,d}}(\\hat{\\bm{w}}_i \\mid_{i=1}^N)$ for short. \nThere are plenty of choices for $f_s(\\cdot)$, but in this paper we use $f_s(z) = z^{-s},\\ s > 0$, known as Riesz $s$-kernels. \nSince each $\\hat{\\bm{w}}_i$ lies on the unit hypersphere, the squared Euclidean distance between two neurons can be equivalently expressed in angular form as $\\|\\hat{\\bm{w}}_i-\\hat{\\bm{w}}_j\\|^2 = 2\\bigl(1-\\cos\\theta_{ij}\\bigr)$, where $\\theta_{ij}$ is the angle between $\\hat{\\bm{w}}_i$ and $\\hat{\\bm{w}}_j$. \nSubstituting this into Eqn.~\\ref{eq:full_hse}, we have:\n\\begin{equation}\n\\bm{E_{s,d}}\\left( \\hat{\\bm{w}}_i \\mid_{i=1}^N \\right) \n= \\sum_{i=1}^N \\sum_{\\substack{j=1, j \\ne i}}^N \\bigl( 2(1 - \\cos\\theta_{ij}) \\bigr)^{-s/2}.\n\\label{eq:angular_HSE}\n\\end{equation}\nThis angular formulation highlights the geometric interpretation of HE: a higher value corresponds to neuron clustering with low angular diversity, while a lower value reflects a more uniform angular distribution across the hypersphere.\n\n\n\n\n\n\n\\section{Correlation between Hyperspherical Uniformity and Editing}\n\\label{sec:correlation}\n\n\nHE and model editing are intrinsically connected through their shared focus on the geometry of high-dimensional parameter spaces. \nAn optimal HE corresponds to more uniformly distributed representations on the unit hypersphere, typically reflecting well-conditioned parameters that enable reliable and stable sequential editing.\nWe first present empirical evidence revealing a strong correlation between HE and editing stability (Section~\\ref{sec:Empirical}), followed by a formal theoretical analysis establishing the mathematical link between the two (Section~\\ref{sec:Theoretical}). \n\n\n\\subsection{Empirical Analysis of the HE–Editing Stability Correlation}\n\\label{sec:Empirical}\nTo understand the failure modes of large-scale sequential editing, we examined how HE evolves throughout the editing process.\nWe performed 5{,}000 sequential edits on ZsRE dataset~\\citep{DBLP:conf/conll/LevySCZ17} with a batch size of 100 on LLaMA3-8B~\\citep{llama3modelcard} using six widely used editing methods, including Fine-Tuning (FT)~\\citep{DBLP:journals/corr/abs-2012-00363}, \nROME~\\citep{DBLP:conf/nips/MengBAB22}, \nMEMIT~\\citep{DBLP:conf/iclr/MengSABB23}, \nRECT~\\citep{DBLP:conf/emnlp/GuXMLLCP24}, \nPRUNE~\\citep{DBLP:conf/iclr/MaWXLG25}, \nand AlphaEdit~\\citep{DBLP:conf/iclr/FangJWMSW0C25}.\nAfter each edit, we computed the HE of the perturbed weights and evaluated the editing performance using well-established metrics, including \\textbf{Efficacy} (edit success), \\textbf{Generalization} (paraphrase success), and \\textbf{Specificity} (neighborhood success). \nReaders can refer to Appendix~\\ref{appendix-metrics} for detailed definition of these metrics.\nWe summarize our main observations as follows:\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/Sec_3_zsre_Llama3-8B.pdf}\n \\caption{Trends of HE and editing performance throughout sequential editing. \n The Spearman correlation scores between HE and each editing metric displayed at the end of each curve. \n }\n \\label{fig:sec_1}\n\\end{figure}\n\n\n\\vspace{-1mm}\n\\paragraph{Observation 1: Collapse in sequential editing is closely tied to sharp fluctuations in HE.}\nFigure~\\ref{fig:sec_1} reveals a strong correlation between HE dynamics and editing performance.\nThe Spearman correlation scores~\\citep{spearman1904proof} between HE and each editing metric, displayed at the end of each curve, consistently indicate a strong statistical dependence before model collapse\\footnote{Since FT and ROME rapidly collapse at the very beginning, we instead emphasize their correlations by examining the curve fluctuations.}.\nMost methods collapse well before 3,000 edits, whereas AlphaEdit demonstrates the strongest long-term editing capacity with the best preservation of hyperspherical uniformity. \nA closer examination of the metrics shows a consistent pattern in which each drop in performance is consistently accompanied by rapid shifts in HE, underscoring its central role in maintaining sequential editing stability.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/Sec3-2.pdf} \n \\caption{Correlation between changes in HE and editing performance across consecutive edited weights. Each point corresponds to a $\\Delta \\mathrm{HE}$–$\\Delta \\mathrm{Acc.}$ pair for one method over five thousand sequential edits. Confidence ellipses and regression lines illustrate overall trends.\n }\n \\label{fig:sec_2}\n \\vspace{-3mm}\n\\end{figure}\n\n\n\n\\vspace{-1mm}\n\\paragraph{Observation 2: Advanced editing methods suppress HE fluctuations effectively.} \nFigure~\\ref{fig:sec_2} illustrates the correlation between changes in HE ($\\Delta \\mathrm{HE}$) and editing performance ($\\Delta \\mathrm{Acc.}$), where each point denotes the difference between two consecutive batch edits: points near the origin indicate greater stability with minimal variation in both HE and accuracy, while points farther away reflect larger fluctuations and less stable editing. \nMost advanced methods exhibit tightly clustered distributions near the origin, indicating stable editing dynamics and minimal weight distortion. Furthermore, we fit a linear regression over all points across metrics, which demonstrates a statistically significant positive correlation between $\\Delta \\mathrm{HE}$ and $\\Delta \\mathrm{Acc.}$ in terms of Efficacy and Generalization. This suggests a strong positive correlation between editing stability and HE stability, implying that the effectiveness of SOTA approaches may stem from their ability to suppress HE fluctuations.\n\n\n\n\\subsection{Theoretical Analysis of HE's Impact on Editing Stability}\n\\label{sec:Theoretical}\n\nWe further turn to a theoretical analysis of how HE impacts editing stability, aiming to provide a principled explanation for the patterns observed in practice.\nGiven the editing objective in Eqn.~\\ref{eq:edit_obj}, it inevitably perturbs the original pretrained knowledge in LLMs, which can be expressed as:\n\\begin{equation}\n\\Delta \\bm{V} = (\\bm{W} + \\Delta \\bm{W}) \\bm{K}_1 - \\bm{V}_1 = \\Delta \\bm{W} \\bm{K}_1,\n\\label{eq:delta_V}\\end{equation}\nwhere $\\bm{W} \\bm{K}_1 = \\bm{V}_1$ (cf. Eqn.~\\ref{eq:k1v1}), as $\\bm{K}_1$ and $\\bm{V}_1$ represent the new editing knowledge.\nAdditionally, from the HE definition in Eqn.~\\ref{eq:full_hse}, the change in HE after editing can be written as:\n\\begin{equation}\n\\Delta \\bm{HE} = \\sum_{i < j} \\left( \\|\\bm{w}_i - \\bm{w}_j\\|^{-2} - \\|\\bm{w}_i + \\Delta \\bm{w}_i - \\bm{w}_j - \\Delta \\bm{w}_j\\|^{-2} \\right),\n\\label{eq:hse-change}\n\\end{equation}\nwhere\n$\\Delta \\bm{w}_i$ denotes the perturbation to $\\bm{w}_i$. This term $\\Delta \\bm{HE}$ measures how angular separation among weight vectors changes after editing.\n\n\nOur theoretical analysis, detailed in Appendix~\\ref{appendix:Correlation}, culminates in a key result that formally links the geometric change in weight space $\\Delta \\bm{HE}$ to the output perturbation $\\Delta \\bm{V}$, derived from Proposition~\\ref{prop:he_bound}.\n\\begin{theorem}[Lower Bound on Output Perturbation]\n\\label{thm:main_bound_in_text}\nUnder the assumptions of orthonormal inputs and small perturbations, the output perturbation $\\Delta \\bm{V}$ is lower-bounded by squared change in HE:\n\\begin{equation}\n |\\Delta \\bm{V}| \\;\\ge\\; \\left( \\frac{\\Delta \\bm{HE}}{K} \\right)^2, \n \\quad \n K = 4\\Biggl( \\sum_{k=1}^p \\Biggl( \\sum_{j \\ne k} \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} \\Biggr)^2 \\Biggr)^{1/2}.\n \\label{eq:hse-bound}\n\\end{equation}\nwhere $K$ is a constant dependent on the original weight matrix geometry.\n\\end{theorem}\n\\vspace{-2mm}\n\nThis theorem reveals a key insight: the change in HE ($|\\Delta \\bm{HE}|$) inevitably induces a substantial output perturbation ($\\Delta \\bm{V}$), meaning that edits that significantly distort the geometric arrangement of neurons are bound to corrupt pretrained knowledge. This result provides a solid theoretical foundation for our empirical findings and underscores HE as a fundamental indicator of editing stability.\n\\section{\\METHODNAME{}}\n\\label{sec:method}\nOn account of the above findings, we argue that ideal sequential editing should preserve the hyperspherical uniformity of edited weights. \nAccordingly, we introduce \\METHODNAME{}, an HE-driven regularization strategy designed to mitigate HE fluctuations while integrating new knowledge.\n\n\\METHODNAME{} first estimates the principal hyperspherical directions of pretrained knowledge and then defines their orthogonal complement as the sparse space.\nProjecting editing perturbations onto this space enables knowledge injection while minimizing interference with original knowledge.\n\n\\paragraph{Principal Space Estimation}\nTo identify the principal hyperspherical directions in $\\bm{W}$, we seek a unit vector $v \\in \\mathbb{R}^d$ that maximizes the variance of all neurons in $\\bm{W}$ when projected onto $v$ as: \n\\begin{equation}\n\\bm{v} \n= \\arg\\max_{\\|\\hat{\\bm{v}}\\|=1} \\left( \\tfrac{1}{n} \\|\\bm{W} \\hat{\\bm{v}}\\|^2 \\right)\n= \\arg\\max_{\\|\\hat{\\bm{v}}\\|=1} \\left( \\tfrac{1}{n} \\hat{\\bm{v}}^\\top \\bigl( \\bm{W}^\\top \\bm{W}\\bigr) \\hat{\\bm{v}} \\right).\n\\end{equation}\nAccording to the Rayleigh quotient theory~\\citep{horn1985matrix,parlett1998symmetric}, the maximum of $\\frac{1}{n}v^\\top \\bm{W}^\\top \\bm{W} v$ corresponds to the largest eigenvalue $\\lambda^*$ of $\\frac{1}{n}\\bm{W}^\\top \\bm{W}$, with the associated eigenvector $v^*$ as the principal direction. \nExtending this to the top-$r$ principal directions enables us to capture a richer low-dimensional space of the weight geometry, so we collect the eigenvectors associated with the $r$ largest eigenvalues to form the principal space matrix, which can be expressed as:\n\\begin{equation}\n\\bm{U} = [\\bm{v}_{d-r+1}, \\dots, \\bm{v}_d] \\in \\mathbb{R}^{d \\times r}, \n\\label{eq:principle}\n\\end{equation}\nwhere $r$ satisfies $\\sum_{i=d-r+1}^{d} \\lambda_i \\ge \\eta \\sum_{i=1}^{d} \\lambda_i$, with the cumulative ratio $\\eta$ (see Appendix~\\ref{appendix:eta-and-alpha}). \n\n\n\n\\paragraph{Sparse Space Definition}\nThis space is defined as the orthogonal complement of $\\bm{U}$ in Eqn.~\\ref{eq:principle} as:\n\\begin{equation}\n\\bm{P}_\\perp = I - \\alpha \\bm{U} \\bm{U}^\\top \\in \\mathbb{R}^{d \\times d},\n\\end{equation}\nwhere $\\alpha$ controls the suppression strength of the components along the subspace spanned by $\\bm{U}$ (see Appendix~\\ref{appendix:eta-and-alpha}). Specifically, $\\alpha = 1$ corresponds to a hard orthogonal projection that completely removes the contribution of $\\bm{U}$, while $0 < \\alpha < 1$ yields a soft projection that only attenuates it.\n\n\n\n\\paragraph{Sparse Space Projection}\nGiven a perturbation matrix $\\Delta \\bm{W}$ produced by any editing method, we project it onto the sparse space using $P_\\perp$, and then combine it with the original weight matrix as: \n\\begin{equation}\n\\hat{\\bm{W}} = \\bm{W} + \\Delta \\bm{W}_{\\text{proj}} = \\bm{W} + \\Delta \\bm{W}\\bm{P}_\\perp.\n\\label{eq:sphere_constrain}\n\\end{equation}\n\n\nIn summary, \\METHODNAME{} suppresses perturbations aligned with the principal weight directions to preserve hyperspherical uniformity, enabling more stable, longer-lasting performance without compromising general abilities. \nFor theoretical completeness, we also provide a mathematical proof that \\METHODNAME{} suppresses the $\\Delta \\bm{HE}$, ensuring bounded variations in the hidden representations $\\Delta \\bm{V}$ and justifying its effectiveness during editing (see Appendix~\\ref{appendix:sparse-space-projection}). More details in Appendix~\\ref{appendix:projection-implementation}\n\n\n\n\n\n\\section{Experiments}\nIn this section, we aim to address the following research questions:\n\\vspace{-2mm}\n\\begin{itemize}[leftmargin=*, itemsep=0pt, parsep=0pt]\n \\item \\textbf{RQ1:} How does \\METHODNAME{} perform on sequential editing tasks compared to baseline methods? \n \\item \\textbf{RQ2:} Can \\METHODNAME{} effectively preserve the hyperspherical uniformity of edited weights? \n \\item \\textbf{RQ3:} How does \\METHODNAME{}-edited LLMs perform on general ability evaluations? \n \\item \\textbf{RQ4:} Can baseline methods be significantly improved with plug-and-play \\METHODNAME{}? \n\\end{itemize}\n\\subsection{Experimental Setup}\n\\vspace{-2mm}\n\\paragraph{Base LLMs and Baseline Methods.} \nExperiments were conducted on LLaMA3 (8B)~\\citep{llama3modelcard} and Qwen2.5 (7B)~\\citep{qwen2.5}. \nWe compared our approach against a range of representative sequential editing baselines, including \nFine-Tuning (FT)~\\citep{DBLP:journals/corr/abs-2012-00363}, \nMEMIT~\\citep{DBLP:conf/iclr/MengSABB23}, \nRECT~\\citep{DBLP:conf/emnlp/GuXMLLCP24}, \nPRUNE~\\citep{DBLP:conf/iclr/MaWXLG25}, \nand AlphaEdit~\\citep{DBLP:conf/iclr/FangJWMSW0C25}.\n\n\\vspace{-2mm}\n\\paragraph{Datasets and Evaluation Metrics.} \nTwo widely used benchmarks were adopted: \nCounterFact~\\citep{DBLP:conf/nips/MengBAB22} and ZsRE~\\citep{DBLP:conf/conll/LevySCZ17}.\nFollowing prior work~\\citep{DBLP:conf/nips/MengBAB22}, five evaluation metrics were reported: \n\\textbf{Efficacy} (edit success), \n\\textbf{Generalization} (paraphrase success), \n\\textbf{Specificity} (neighborhood success), \n\\textbf{Fluency} (generation entropy), \nand \\textbf{Consistency} (reference score). \nFor rigorous evaluation, we adopt the \\textbf{average top-1 accuracy} as the metric for both datasets.\nReaders can refer to Appendix~\\ref{appendix-setup} for more detailed experimental setup.\n\n\\subsection{Performance of Sequential Model Editing (RQ1)}\n\n\\newcommand{\\meanstd}[2]{#1{\\scriptsize$\\pm$#2}}\n\\begin{table*}[t]\n\\centering\n\\caption{Comparison of \\METHODNAME{} with existing methods on sequential editing. \n\\emph{Eff.}, \\emph{Gen.}, \\emph{Spe.}, \\emph{Flu.} and \\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \nThe best results are highlighted in bold, while the second-best results are underlined.}\n\\label{tab:main_results}\n\\resizebox{\\textwidth}{!}{\n\\setlength{\\arrayrulewidth}{0.7pt} \n\\renewcommand{\\arraystretch}{1.3} \n\\begin{tabular}{c c | c c c | c c c | c c}\n\\specialrule{1.2pt}{0pt}{0pt} \n\\multirow{2}{*}{\\textbf{Method}} & \\multirow{2}{*}{\\textbf{Model}}\n& \\multicolumn{3}{c|}{\\textbf{ZSRE}} \n& \\multicolumn{5}{c}{\\textbf{Counterfact}} \\\\\n\\cmidrule(lr){3-5} \\cmidrule(lr){6-10}\n & & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} \n & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} & \\textbf{Flu.$\\uparrow$} & \\textbf{Consis.$\\uparrow$} \\\\\n\\hline\\hline\n\n% ----------- Llama3-8B block ------------\nPre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{LLaMA3-8B}}} \n& \\meanstd{35.42}{0.30} & \\meanstd{34.17}{0.30} & \\meanstd{38.02}{0.27} \n& \\meanstd{0.49}{0.07} & \\meanstd{0.44}{0.05} & \\meanstd{18.09}{0.24} & \\meanstd{634.84}{0.12} & \\meanstd{22.06}{0.08} \\\\\n\\hline\nFT & & \\meanstd{15.27}{0.21} & \\meanstd{14.78}{0.21} & \\meanstd{5.06}{0.10} \n& \\underline{\\meanstd{8.40}{0.28}} & \\underline{\\meanstd{2.54}{0.13}} & \\meanstd{0.03}{0.01} & \\meanstd{409.80}{0.67} & \\meanstd{19.35}{0.13} \\\\\nMEMIT & & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.06}{0.01} \n& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{318.19}{0.24} & \\meanstd{4.19}{0.04} \\\\\nPRUNE & & \\meanstd{10.35}{0.18} & \\meanstd{10.08}{0.18} & \\meanstd{9.55}{0.15} \n& \\meanstd{1.19}{0.11} & \\meanstd{0.34}{0.04} & \\underline{\\meanstd{0.62}{0.03}} & \\textbf{\\meanstd{618.72}{0.08}} & \\textbf{\\meanstd{49.24}{0.13}} \\\\\nRECT & & \\meanstd{0.01}{0.00} & \\meanstd{0.01}{0.01} & \\meanstd{0.04}{0.01} \n& \\meanstd{0.57}{0.08} & \\meanstd{0.29}{0.04} & \\meanstd{0.10}{0.01} & \\meanstd{438.83}{0.18} & \\meanstd{9.40}{0.05} \\\\\nAlphaEdit & & \\underline{\\meanstd{86.64}{0.23}} & \\underline{\\meanstd{81.28}{0.28}} & \\underline{\\meanstd{28.78}{0.22}} \n& \\meanstd{4.37}{0.20} & \\meanstd{1.71}{0.10} & \\meanstd{0.57}{0.03} & \\meanstd{482.36}{0.44} & \\meanstd{4.71}{0.04} \\\\\n\\hline\n\\METHODNAME{}& & \\textbf{\\meanstd{90.01}{0.21}} & \\textbf{\\meanstd{84.67}{0.26}} & \\textbf{\\meanstd{45.40}{0.29}} \n& \\textbf{\\meanstd{52.89}{0.50}} & \\textbf{\\meanstd{32.07}{0.39}} & \\textbf{\\meanstd{5.01}{0.10}} & \\underline{\\meanstd{551.51}{0.53}} & \\underline{\\meanstd{30.89}{0.13}} \\\\\n\\hline\\hline\n\n% ----------- Qwen2.5-7B block ------------\nPre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{Qwen2.5-7B}}} \n& \\meanstd{35.29}{0.29} & \\meanstd{34.10}{0.28} & \\meanstd{38.44}{0.27} \n& \\meanstd{0.42}{0.06} & \\meanstd{0.46}{0.05} & \\meanstd{15.06}{0.20} & \\meanstd{624.45}{0.11} & \\meanstd{23.02}{0.69} \\\\\n\\hline\nFT & & \\meanstd{4.97}{0.14} & \\meanstd{4.58}{0.13} & \\meanstd{4.01}{0.11} \n& \\meanstd{15.44}{0.36} & \\meanstd{4.63}{0.17} & \\meanstd{1.46}{0.05} & \\meanstd{214.26}{0.09} & \\meanstd{3.15}{0.02} \\\\\nMEMIT & & \\meanstd{0.13}{0.02} & \\meanstd{0.12}{0.01} & \\meanstd{0.04}{0.01} \n& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{370.84}{0.30} & \\meanstd{3.59}{0.03} \\\\\nPRUNE & & \\underline{\\meanstd{47.93}{0.36}} & \\underline{\\meanstd{45.50}{0.35}} & \\textbf{\\meanstd{39.20}{0.28}} \n& \\meanstd{14.30}{0.35} & \\meanstd{11.27}{0.26} & \\textbf{\\meanstd{6.75}{0.12}} & \\textbf{\\meanstd{620.74}{0.10}} & \\textbf{\\meanstd{29.50}{0.08}} \\\\\nRECT & & \\meanstd{0.73}{0.04} & \\meanstd{0.75}{0.04} & \\meanstd{0.05}{0.07} \n& \\meanstd{0.64}{0.08} & \\meanstd{0.19}{0.03} & \\meanstd{0.09}{0.01} & \\meanstd{368.46}{0.27} & \\meanstd{1.35}{0.01} \\\\\nAlphaEdit & & \\meanstd{42.01}{0.40} & \\meanstd{39.99}{0.39} & \\meanstd{13.87}{0.20} \n& \\underline{\\meanstd{43.92}{0.50}} & \\underline{\\meanstd{24.37}{0.36}} & \\meanstd{2.32}{0.06} & \\meanstd{479.83}{0.77} & \\meanstd{4.67}{0.07} \\\\\n\\hline\n\\METHODNAME{}& & \\textbf{\\meanstd{70.04}{0.36}} & \\textbf{\\meanstd{65.43}{0.37}} & \\underline{\\meanstd{27.35}{0.26}} \n& \\textbf{\\meanstd{60.76}{0.49}} & \\textbf{\\meanstd{29.24}{0.37}} & \\underline{\\meanstd{3.83}{0.08}} & \\underline{\\meanstd{612.67}{0.22}} & \\underline{\\meanstd{14.74}{0.07}} \\\\\n\\specialrule{1.2pt}{0pt}{0pt} \n\n\\end{tabular}\n}\n\\end{table*}\n\n\nTable~\\ref{tab:main_results} presents the results under a commonly used sequential editing setup, using 15,000 samples with 100 edits each for LLaMA3 (8B), while Qwen2.5 (7B) is restricted to 5,000 edits as further updates induce severe model collapse, where all editing methods underperformed compared to the pre-edit baseline.\n\\METHODNAME{} is plug-and-play, and AlphaEdit~\\citep{DBLP:conf/iclr/FangJWMSW0C25} is adopted as the default base method in Table~\\ref{tab:main_results} to better illustrate its capability. Additional experiments with other base methods are presented in Section~\\ref{sec:5-5}.\nOverall, \\METHODNAME{} consistently outperforms baseline methods across nearly all metrics and base models. In particular, it achieves substantial gains in both \\textbf{Efficacy} and \\textbf{Generalization}, with average improvements of \\textbf{24.19\\%} and \\textbf{16.02\\%}, respectively, over the best baseline. It also maintains notable performance in Fluency and Consistency, indicating its ability to preserve factual accuracy while generating coherent and natural outputs. \n\n\\subsection{Analysis of Edited Weights (RQ2)}\nThis analysis evaluates whether \\METHODNAME{} can effectively maintain the hyperspherical uniformity of edited weights.\nWe extracted the edited weights from LLaMA3 after 15,000 sequential edits on CounterFact. \nAs shown in Figure~\\ref{fig:Sec_5_heatmap}, we computed the cosine similarity between each pair of weight neurons and used heatmap to visualize the hyperspherical uniformity before and after editing. \nIn Figure~\\ref{fig:Sec_5_pca}, t-SNE~\\citep{JMLR:v9:vandermaaten08a} was used to visualize the normalized neuron distribution in $\\bm{W}$ before and after editing. \nIt can be seen that \\METHODNAME{} \\textbf{effectively preserves hyperspherical uniformity after editing, as the cosine similarity among weight neurons remains close to the original distribution}, thereby avoiding directional collapse. \nMoreover, the pre- and post-edited weights exhibit nearly overlapping distributions, indicating that \\METHODNAME{} prevents significant shifts in weights and maintains consistency. \nIn contrast, baseline methods such as MEMIT and AlphaEdit induce clear angular concentration in neuron directions, causing neurons to cluster in limited angular regions and significantly reducing hyperspherical directional uniformity. More results on Qwen2.5 are in Appendix~\\ref{appendix:hidden-representation-qwen}. \n\n\n\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/llama_neuron_similarity_heatmap_15k.pdf} \n \\caption{\n Cosine similarity between neurons in the updated weight matrix after 15,000 edits. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\n \\METHODNAME{} effectively preserves the weight structure, demonstrating the most stable hyperspherical uniformity.\n }\n \\label{fig:Sec_5_heatmap}\n \\vspace{-3mm}\n\\end{figure}\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/llama_tsne_grid_15k.pdf} \n \\caption{The t-SNE distribution of weight neurons of pre-edited and post-edited LLM after 15,000 edits using dimensionality reduction. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\METHODNAME{} consistently exhibits minimal shift. }\n \\label{fig:Sec_5_pca}\n \\vspace{-3mm}\n\\end{figure}\n\n\n\n\\subsection{Evaluation of General Abilities (RQ3)}\nTo extensively evaluate whether post-edited LLMs can preserve the general abilities, four representative tasks were adopted following\n\\citet{DBLP:conf/emnlp/GuXMLLCP24}, including \n\\textbf{Reasoning} on the GSM8K~\\citep{DBLP:journals/corr/abs-2110-14168}, measured by solve rate.\n\\textbf{Natural language inference (NLI)} on the RTE~\\citep{DBLP:conf/mlcw/DaganGM05}, measured by accuracy of two-way classification, \n\\textbf{Open-domain QA} on the Natural Questions~\\citep{DBLP:journals/tacl/KwiatkowskiPRCP19}, measured by exact match (EM) with the reference answer after minor normalization~\\citep{DBLP:conf/acl/ChenFWB17, DBLP:conf/acl/LeeCT19}.\n\\textbf{Closed-domain QA} on BoolQ~\\citep{DBLP:conf/naacl/ClarkLCK0T19}, also measured by EM. \nFigure~\\ref{fig:line_general} depicts how performance varies with the number of edited samples across four tasks. \nWe report general performance every 1k edits up to 5k, and every 5k edits thereafter (up to 15k), providing a comprehensive view of the degradation trend. \nThe results show that \\METHODNAME{} effectively preserves the general abilities of post-edited LLMs even under extensive editing, maintaining the original model performance across all metrics after 15k edits. In contrast, LLMs edited with baseline methods rapidly lose their general abilities with all metrics approaching zero. \nThese findings underscore the critical role of hyperspherical uniformity in safeguarding the broad abilities learned from the underlying corpus.\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/general_line.pdf} \n \\caption{\n General ability testing of post-edited LLaMA3 (8B) on four tasks.\n }\n \\label{fig:line_general}\n\\end{figure}\n\n\n\n\\subsection{Performance Improvements of Baseline Methods (RQ4)}\n\\label{sec:5-5}\nWe investigated whether the sparse space projection strategy of \\METHODNAME{} can serve as a general enhancement to existing methods. \nA single line of code from \\METHODNAME{} regarding the projection was inserted into the baselines with minimal modification, and we evaluated their performance before and after integration (as detailed in Appendix~\\ref{appendix:projection-implementation}). \nResults of 3,000 sequential edits on LLaMA3 (8B) are reported in Figure~\\ref{fig:baseline_improve_all}. \n\\textbf{\\METHODNAME{} is integrated seamlessly with diverse editing methods and significantly boosts their performance.} \nOn average, the optimized baselines achieve relative improvements of \\textbf{49.05\\%}, \\textbf{42.64\\%}, and \\textbf{24.44\\%} in \\textbf{Efficacy}, \\textbf{Generalization}, and \\textbf{Specificity}, respectively, underscoring the strong potential and broad applicability of the proposed sparse space projection as a plug-and-play enhancement for model editing. \nThe baselines enhanced with the projection also demonstrate significantly better robustness in general abilities (see Appendix~\\ref{general-baseline}).\n\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.98\\textwidth]{Figures/baseline_improve_all.pdf}\n \\caption{Performance improvements of baseline editing methods after adding a single line of code from \\METHODNAME{} (i.e., sparse space projection). Gray bars denote the original baseline performance, while purple bars indicate the performance after enhancement.}\n \\label{fig:baseline_improve_all}\n \\vspace{-2mm}\n\\end{figure}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{Related Work}\n\n\\paragraph{Model Editing Methods.} \nFrom the perspective of whether model parameters are modified, existing approaches can be broadly categorized into \\emph{parameter-modifying} \\citep{DBLP:conf/iclr/MitchellLBFM22, DBLP:conf/iclr/MengSABB23, DBLP:conf/iclr/MaWXLG25, DBLP:conf/iclr/FangJWMSW0C25}, which directly adjust a small subset of model parameters, and \\emph{parameter-preserving}~\\citep{DBLP:conf/emnlp/ZhengLDFWXC23, DBLP:conf/aaai/YuCZH24, DBLP:conf/nips/HartvigsenSPKG23}, which integrate auxiliary modules without altering the original weights. In this work, we focus on \\emph{parameter-modifying methods} which typically employs meta-learning or locating-then-editing strategies~\\citep{DBLP:journals/corr/abs-2401-01286}. Representative works of meta-learning include KE~\\citep{DBLP:conf/emnlp/CaoAT21} and MEND~\\citep{DBLP:conf/iclr/MitchellLBFM22}, which leverage hypernetworks to generate parameter updates. Locate-then-edit methods, such as ROME~\\citep{DBLP:conf/nips/MengBAB22} and MEMIT~\\citep{DBLP:conf/iclr/MengSABB23}, prioritize pinpointing the knowledge’s storage location before making\ntargeted edits. \nRecent extensions like RECT~\\citep{DBLP:conf/emnlp/GuXMLLCP24} and PRUNE~\\citep{DBLP:conf/iclr/MaWXLG25} mitigate degradation of general capabilities of LLMs by better constraining edit complexity via sparsity and condition number. Recently, AlphaEdit~\\citep{DBLP:conf/iclr/FangJWMSW0C25} further generalizes this paradigm by projecting the perturbation into the nullspace of the previous knowledge set.\n\n\n\\vspace{-3mm}\n\\paragraph{Learning with Hyperspherical Uniformity.}\nEarly studies~\\citep{DBLP:conf/icml/XieDZKYZX17, DBLP:conf/iclr/Rodriguez0CGR17, DBLP:conf/icml/XieSX17, DBLP:journals/corr/CogswellAGZB15} sought to improve the generalization capacity of neural networks by reducing redundancy through diversification, as rigorously analyzed in~\\citep{DBLP:conf/icml/XieZX16}. Although these works examined angular diversity, they largely neglected the notion of global equidistribution of embeddings on the hypersphere. In contrast to orthogonality, where perpendicular vectors are defined\nto be diverse, hyperspherical uniformity promotes embeddings that are maximally separated in angle, thereby encouraging uniform distribution across the hypersphere~\\citep{DBLP:conf/aistats/LiuLL0SW21, DBLP:conf/nips/LiuLLLYDS18}. More recently, \\citet{DBLP:conf/nips/SmerkousBL24} enhancing training stability by incorporating centered kernel alignment into hyperspherical energy, enhancing training stability by addressing the lack of permutation invariance inherent in naive similarity metrics.\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{Conclusion}\nIn this work, we demonstrated that hyperspherical uniformity is a critical factor in stabilizing sequential editing for LLMs, supported by both empirical evidence and rigorous theoretical proof. \nMotivated by this insight, we propose \\METHODNAME{}, a regularization strategy that preserves hyperspherical uniformity by projecting updates onto a space complementary to the principal directions of pretrained weights.\nExtensive evaluations on LLaMA3 (8B) and Qwen2.5 (7B) across multiple editing datasets and downstream tasks confirm that \\METHODNAME{} not only enhances editing performance by 16.41\\% over the strongest baseline but also more faithfully preserves weight geometry and general abilities of models.\nFurthermore, when applied as a plug-and-play enhancement, it yields an additional average improvement of 38.71\\% across existing methods.\nCollectively, our findings establish \\METHODNAME{} as both theoretically grounded and empirically effective, providing a principled and scalable solution for reliable large-scale model editing.\n\n\n\n\n\n\\subsubsection*{Ethics Statement}\nOur proposed method \\METHODNAME{} significantly enhances the reliability of large-scale sequential model editing by preserving hyperspherical uniformity, which makes it a valuable way for updating and managing knowledge in real-world applications where long-term stability is essential. At the same time, the ability to directly alter stored knowledge in LLMs carries inherent risks, including the potential introduction of bias or harmful information. To address these concerns, we strongly recommend rigorous validation procedures, transparent reporting, and strict oversight when deploying such techniques. While the core motivation of \\METHODNAME{} is positive, aiming to facilitate efficient and trustworthy updates of large language models, we emphasize that its use must remain responsible and cautious to ensure ethical outcomes.\n\nWe used LLMs to assist with improving grammar, clarity, and wording in parts of this work. The use of LLMs was limited to language refinement, with all ideas, analyses, and conclusions solely developed by the authors. We restate this announcement in Appendix~\\ref{sec:llm_usage}\n\n\n\n\\subsubsection*{Reproducibility Statement}\nTo ensure the reproducibility of our findings, detailed implementation instructions for \\METHODNAME{}\nare provided in in Section~\\ref{sec:method} , Appendix~\\ref{appendix-setup}. Additionally, we plan to release our source code in the future to further support reproducibility. These measures are intended to facilitate the verification and replication of our results by other researchers in the field.\n\n\n\n\\subsubsection*{Acknowledgments}\nWe would like to express gratitude to the UCLANLP group members for their valuable feedback.\n\n\n\\bibliography{iclr2026_conference}\n\\bibliographystyle{iclr2026_conference}\n\n\n\\clearpage\n\\appendix\n\n\\section{Usage of LLMs}\n\\label{sec:llm_usage}\nThroughout the preparation of this manuscript, we used LLMs to assist with improving grammar, clarity, and wording in parts of this work. The use of LLMs was limited to language refinement, with all ideas, analyses, and conclusions solely developed by the authors.\n\n\\section{Preliminaries of Model Editing}\n\\label{appendix:model_editing}\n\nModel editing aims to refine a pre-trained model by applying one or more edits, where each edit replaces a factual association $(s, r, o)$ with new knowledge $(s, r, o^*)$ \\citep{DBLP:conf/emnlp/Yang0TMSYS24,DBLP:journals/corr/abs-2502-05759}. After editing, the model is expected to recall the updated object $o^*$ when given a natural language prompt $p(s, r)$, such as ``The President of the United States is'' \\citep{DBLP:conf/vldb/0001XL0TYZDSL0Z24}.\n\nTo achieve this, locating-and-editing methods have been proposed for effective model updates \\citep{DBLP:conf/acl/Yang0MLYC24}. These methods typically follow three steps \\citep{DBLP:conf/acl/JiangFZBZWL025}:\n\n\\paragraph{Step 1: Locating Influential Layers.}\nThe first step is to identify the specific FFN layers that encode the target knowledge using causal tracing \\citep{DBLP:conf/nips/MengBAB22}. This method involves injecting Gaussian noise into the hidden states and progressively restoring them to their original values. By analyzing the degree to which the original output recovers, the influential layers can be pinpointed as the targets for editing.\n\n\\paragraph{Step 2: Acquiring the Expected Output.}\nThe second step aims to obtain the desired output of the critical layers identified in Step~1. Following the key--value theory, the key $\\bm{k}$, which encodes $(s,r)$, is processed through the output weights $\\bm{W}_{\\mathrm{out}}^{l}$ to produce the original value $\\bm{v}$ encoding $o$. Formally,\n\\begin{equation}\n \\bm{k} \\triangleq \\sigma\\!\\big(\\bm{W}_{\\mathrm{in}}^{l}\\,\\gamma(\\bm{h}^{l-1}+\\bm{\\bm{\\alpha}}^{l})\\big),\n \\qquad\n \\bm{v} \\triangleq \\bm{m}^{l}=\\bm{W}_{\\mathrm{out}}^{l}k .\n \\label{eq:me_kv}\n\\end{equation}\n\nTo perform editing, $\\bm{v}$ is expected to be replaced with a new value $\\bm{v}^{*}$ encoding $o^{*}$. To this end, current methods typically use gradient descent on $\\Delta \\bm{W}$, maximizing the probability that the model outputs the word associated with $o^{*}$ \\citep{DBLP:conf/iclr/MengSABB23}. The optimization objective is as follows:\n\\begin{equation}\n \\bm{v}^{*}\n = \\bm{v} + \\arg\\min_{\\Delta \\bm{W}^{l}}\n \\Big(\n -\\log \\mathbb{P}_{\\,f^{l}_{\\bm{W}_{\\mathrm{out}}}(\\bm{m}^{l}+=\\Delta \\bm{W}^{l})}\n \\big[\\,o^{*}\\mid (s,r)\\,\\big]\n \\Big),\n \\label{eq:me_opt}\n\\end{equation}\n\nwhere $f^{l}_{\\bm{W}_{\\mathrm{out}}}(\\bm{m}^{l}+=\\Delta \\bm{W})$ represents the original model with $\\bm{m}^{l}$ updated to $\\bm{m}^{l}+\\Delta \\bm{W}$.\n\n\\paragraph{Step 3: Updating $\\bm{W}_{\\mathrm{out}}^{l}$.}\nThis step aims to update the parameters $\\bm{W}_{\\mathrm{out}}^{l}$. It includes a factual set $\\{\\bm{K}_{1},\\bm{V}_{1}\\}$ containing $u$ new associations, while preserving the set $\\{\\bm{K}_{0},\\bm{V}_{0}\\}$ containing $n$ original associations. Specifically,\n\\begin{equation}\n\\begin{array}{c}\n \\bm{K}_{0} = [\\,\\bm{k}_{1}\\;\\bm{k}_{2}\\;\\cdots\\;\\bm{k}_{n}\\,], \\quad\n \\bm{V}_{0} = [\\,\\bm{v}_{1}\\;\\bm{v}_{2}\\;\\cdots\\;\\bm{v}_{n}\\,], \\\\[6pt]\n \\bm{K}_{1} = [\\,\\bm{k}_{n+1}\\;\\bm{k}_{n+2}\\;\\cdots\\;\\bm{k}_{n+u}\\,], \\quad\n \\bm{V}_{1} = [\\,\\bm{v}^{*}_{\\,n+1}\\;\\bm{v}^{*}_{\\,n+2}\\;\\cdots\\;\\bm{v}^{*}_{\\,n+u}\\,]\n\\end{array}\n\\label{eq:me_sets}\n\\end{equation}\n\n\n\nwhere $\\bm{k}$ and $\\bm{v}$ are defined in Eqn.~\\ref{eq:me_kv} and their subscripts represent the index of the knowledge. Based on these, the objective can be defined as:\n\\begin{equation}\n \\tilde{\\bm{W}}^{l}_{\\mathrm{out}}\n \\triangleq\n \\arg\\min_{\\hat{\\bm{W}}}\n \\left(\n \\sum_{i=1}^{n}\\!\\big\\|\\hat{\\bm{W}}\\bm{k}_{i}-\\bm{v}_{i}\\big\\|^{2}\n +\n \\sum_{i=n+1}^{n+u}\\!\\big\\|\\hat{\\bm{W}}\\bm{k}_{i}-\\bm{v}^{*}_{i}\\big\\|^{2}\n \\right).\n \\label{eq:me_obj}\n\\end{equation}\n\n\nBy applying the normal equation, its closed-form solution can be derived:\n\\begin{equation}\n \\tilde{\\bm{W}}^{l}_{\\mathrm{out}}\n =\n \\big(\\bm{M}_{1}-\\bm{W}^{l}_{\\mathrm{out}}\\bm{K}_{1}\\big)\\,\\bm{K}_{1}^{\\top}\n \\big(\\bm{K}_{0}\\bm{K}_{0}^{\\top}+\\bm{K}_{1}\\bm{K}_{1}^{\\top}\\big)^{-1}\n + \\bm{W}^{l}_{\\mathrm{out}} .\n \\label{eq:me_closedform}\n\\end{equation}\n\nIn practice, model editing methods often update parameters across multiple layers to improve effectiveness. For more details, see \\citep{DBLP:conf/iclr/MengSABB23}.\n\n\n\n\\clearpage\n\n\\section{Theoretical Proofs}\n\n\\subsection{Proof of Correlation between Hyperspherical Energy and Editing Stability}\n\\label{appendix:Correlation}\n\n\\paragraph{Objective for Preserving Original Knowledge}\nWe begin by assuming that the original knowledge base can be expressed as $\\{\\bm{k}_i,\\ \\bm{v}_i\\}\\quad i = 1, \\ldots, N, \\quad \\bm{k}_i \\in \\mathbb{R}^p, \\; \\bm{v}_i \\in \\mathbb{R}^q$, while the new knowledge base is given by $\\{\\tilde{\\bm{k}}_i,\\ \\tilde{\\bm{v}}_i\\}\\quad i = 1, \\ldots, N, \\quad \\tilde{\\bm{k}}_i \\in \\mathbb{R}^p, \\; \\tilde{\\bm{v}}_i \\in \\mathbb{R}^q$\n\nAnd the knowledge mapping is governed by the weight matrix $W \\in \\mathbb{R}^{p \\times q}$ such that\n\\begin{equation}\n\\bm{W} \\bm{k}_i = \\bm{v}_i, \n\\qquad \n(\\bm{W}+\\Delta \\bm{W})\\tilde{\\bm{k}}_i = \\tilde{\\bm{v}}_i.\n\\end{equation}\n\nWhen analyzing the destroy to the original knowledge set, there is shift brought by the perturbation $\\Delta \\bm{W}$ which can be expressed as:\n\\begin{equation}\n(\\bm{W}+\\Delta \\bm{W})\\bm{k}_i = \\bm{v}_i + \\Delta \\bm{W}\\bm{k}_i\n\\end{equation}\nwhere we define $\\Delta \\bm{v}_i = \\Delta \\bm{W}\\bm{k}_i$ as the destroy to the previous knowledge set. In addition, if $\\bm{k}_i \\in \\mathrm{null}(\\Delta \\bm{W})$, i.e., in the null space of $\\Delta \\bm{W}$, then $\\Delta \\bm{W} \\bm{k}_i = \\Delta \\bm{v}_i = 0$.\n\n\nThe corresponding objective is thus to minimize the perturbation magnitude, given by\n\\begin{equation}\n\\min \\frac{1}{N}\\sum_{i=1}^N \\|\\Delta \\bm{v}_i\\|\n\\quad \\equiv \\quad \n\\min \\frac{1}{N}\\sum_{i=1}^N \\|\\Delta \\bm{W} \\bm{k}_i\\|.\n\\end{equation}\nTo make this tractable, assume that each input vector $\\bm{k}_i$ can be approximated in terms of the first $\\bm{K}$ basis vectors $\\{\\bm{e_j}\\}$ as\n\\begin{equation}\n\\bm{k}_i = \\sum_{j=1}^K \\bm{\\alpha_j} \\bm{e_j} + \\varepsilon_i,\n\\end{equation}\nwhere $\\varepsilon_i$ is a small noise term. If we denote\n\\begin{equation}\n\\Delta \\bm{W} \\cdot \\bm{e_j} = \\bm{f_j},\n\\qquad \n\\varepsilon_i, \\bm{e_j}, \\bm{f_j} \\in \\mathbb{R}^q,\n\\end{equation}\nthen the perturbation objective can be rewritten as:\n\\begin{equation}\n\\begin{aligned}\n& \\min \\frac{1}{N}\\sum_{i=1}^N \n \\left\\| \\Delta \\bm{W} \\cdot \n \\left( \\sum_{j=1}^K \\bm{\\alpha_j} \\bm{e_j} + \\varepsilon_i \\right) \\right\\| \\\\[2pt]\n& \\leq \\frac{1}{N}\\sum_{i=1}^N \n \\left\\|\\sum_{j=1}^K \\bm{\\alpha_j} \\bm{f_j} + \\Delta \\bm{W} \\varepsilon_i \\right\\| \\\\[2pt]\n& \\leq \\frac{1}{N}\\sum_{i=1}^N \n \\sum_{j=1}^K |\\bm{\\alpha_j} \\bm{f_j}| + \\|\\Delta \\bm{W}\\| |\\varepsilon_i| \\\\[2pt]\n& \\le \\frac{1}{N}\\sum_{i=1}^N\n \\sum_{j=1}^K |\\bm{\\alpha_j}|\\,\\lVert \\bm{f_j}\\rVert \\;+\\; \\varepsilon_{\\max}\\,\\lVert \\boldsymbol{\\Delta}\\rVert .\n\\end{aligned}\n\\label{eq:perturb_bound}\n\\end{equation}\nwhere $\\varepsilon_{\\max} = \\max_{i} \\|\\varepsilon_i\\|$. This shows that minimizing $\\|f_j\\|$ directly reduces the upper bound of the perturbation, and therefore enhances the stability of the editing process.\n\n\n\n\n\n\n\n\\paragraph{Definitions}\nLet the model's weights be represented by a matrix $\\bm{W} \\in \\mathbb{R}^{p \\times q}$, whose rows are the neuron vectors $\\bm{w}_1, \\dots, \\bm{w}_p \\in \\mathbb{R}^q$. An edit or update introduces a perturbation to this matrix, denoted by $\\Delta \\bm{W} \\in \\mathbb{R}^{p \\times q}$, with corresponding row-wise perturbations $\\Delta \\bm{w}_1, \\dots, \\Delta \\bm{w}_p$.\n\nWe define two key scalar quantities to measure the effects of this perturbation:\n\n\\begin{itemize}[leftmargin=*, itemsep=0pt, parsep=0pt]\n \\item \\textbf{output perturbation ($\\Delta \\bm{V}$).} This quantity measures the total squared change in the model's output, aggregated over a set of $N$ input vectors $\\{\\bm{k}_i\\}_{i=1}^N$.\n \\begin{equation}\n \\Delta \\bm{V} \\triangleq \\sum_{i=1}^N \\| \\Delta \\bm{W} \\bm{k}_i \\|_2^2 = \\sum_{i=1}^N \\left\\| \n \\begin{bmatrix} \n \\Delta \\bm{w}_1 \\cdot \\bm{k}_i \\\\ \n \\vdots \\\\ \n \\Delta \\bm{w}_p \\cdot \\bm{k}_i \n \\end{bmatrix} \n \\right\\|_2^2 = \\sum_{i=1}^N \\sum_{j=1}^p (\\Delta \\bm{w}_j \\cdot \\bm{k}_i)^2\n \\end{equation}\n\n \\item \\textbf{Change in Hyperdimensional Energy ($\\Delta \\bm{HE}$).} This quantity measures the change in the geometric arrangement of the neuron vectors due to the perturbation.\n \\begin{equation}\n \\Delta \\bm{HE} \\triangleq \\sum_{i \\neq j} \\left( \\frac{1}{\\|\\bm{w}_i - \\bm{w}_j\\|_2^2} - \\frac{1}{\\|(\\bm{w}_i + \\Delta \\bm{w}_i) - (\\bm{w}_j + \\Delta \\bm{w}_j)\\|_2^2} \\right)\n \\end{equation}\n\\end{itemize}\n\n\\paragraph{Assumptions}\nOur analysis relies on the following assumptions:\n\n\\newtheorem{assumption}{Assumption}\n\\begin{assumption}[Orthonormal Inputs]\n\\label{ass:basis_vectors}\nThe set of input vectors $\\{\\bm{k}_i\\}_{i=1}^q$ is the standard orthonormal basis of $\\mathbb{R}^q$.\n\\end{assumption}\nUnder this assumption, the output perturbation simplifies to the squared Frobenius norm of the perturbation matrix:\n$$\n \\Delta \\bm{V} = \\sum_{i=1}^q \\sum_{j=1}^p (\\Delta \\bm{w}_j \\cdot \\bm{k}_i)^2 = \\sum_{j=1}^p \\sum_{i=1}^q (\\Delta \\bm{w}_{j,i})^2 = \\sum_{j=1}^p \\|\\Delta \\bm{w}_j\\|_2^2 = \\|\\Delta \\bm{W}\\|_F^2\n$$\n\n\\begin{assumption}[Small Perturbations]\n\\label{ass:small_perturbations}\nThe perturbation vectors $\\Delta \\bm{w}_i$ are sufficiently small in norm, which justifies the use of a first-order Taylor expansion to approximate the change in HE.\n\\end{assumption}\n\n% \\paragraph{Main Result}\nWe can now state the relationship between the change in HE and the output perturbation energy.\n\n\\begin{theorem}[Upper Bound on HE Change]\n\\label{prop:he_bound}\nUnder Assumptions \\ref{ass:basis_vectors} and \\ref{ass:small_perturbations}, the absolute change in Hyperdimensional Energy, $|\\Delta \\bm{HE}|$, is upper-bounded by the square root of the output perturbation, $\\sqrt{\\Delta \\bm{V}}$, as follows:\n\\begin{equation}\n |\\Delta \\bm{HE}| \\le K \\sqrt{\\Delta \\bm{V}}\n\\end{equation}\nwhere $K$ is a constant determined by the geometry of the original weight matrix $\\bm{W}$:\n$$\n K = 4 \\sqrt{ \\sum_{k=1}^p \\left( \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} \\right)^2 }\n$$\n\\end{theorem}\n\n\\begin{proof}\nLet $\\bm{p}_{ij} = \\bm{w}_i - \\bm{w}_j$ and $\\Delta \\bm{p}_{ij} = \\Delta \\bm{w}_i - \\Delta \\bm{w}_j$. The change in HE is $\\Delta \\bm{HE} = \\sum_{i \\neq j} (\\|\\bm{p}_{ij}\\|^{-2} - \\|\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}\\|^{-2})$.\nUsing a first-order Taylor expansion for $f(\\bm{x}) = \\|\\bm{x}\\|^{-2}$ around $\\bm{p}_{ij}$, we have:\n$$\n \\|\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}\\|^{-2} \\approx \\|\\bm{p}_{ij}\\|^{-2} - 2 \\|\\bm{p}_{ij}\\|^{-4} (\\bm{p}_{ij} \\cdot \\Delta \\bm{p}_{ij})\n$$\nSubstituting this into the expression for $\\Delta \\bm{HE}$:\n\\begin{align*}\n \\Delta \\bm{HE} &\\approx \\sum_{i \\neq j} \\left( \\|\\bm{p}_{ij}\\|^{-2} - \\left( \\|\\bm{p}_{ij}\\|^{-2} - 2 \\|\\bm{p}_{ij}\\|^{-4} (\\bm{p}_{ij} \\cdot \\Delta \\bm{p}_{ij}) \\right) \\right) \\\\\n &= \\sum_{i \\neq j} 2 \\|\\bm{p}_{ij}\\|^{-4} (\\bm{p}_{ij} \\cdot \\Delta \\bm{p}_{ij})\n\\end{align*}\nWe bound the absolute value of this approximation:\n\\begin{align*}\n |\\Delta \\bm{HE}| &\\approx \\left| \\sum_{i \\neq j} 2 \\|\\bm{w}_i - \\bm{w}_j\\|^{-4} ((\\bm{w}_i - \\bm{w}_j) \\cdot (\\Delta \\bm{w}_i - \\Delta \\bm{w}_j)) \\right| \\\\\n &\\le \\sum_{i \\neq j} 2 \\|\\bm{w}_i - \\bm{w}_j\\|^{-3} \\|\\Delta \\bm{w}_i - \\Delta \\bm{w}_j\\| && \\text{(by Cauchy-Schwarz)} \\\\\n &\\le \\sum_{i \\neq j} 2 \\|\\bm{w}_i - \\bm{w}_j\\|^{-3} (\\|\\Delta \\bm{w}_i\\| + \\|\\Delta \\bm{w}_j\\|) && \\text{(by Triangle Inequality)}\n\\end{align*}\nBy re-indexing the sum to group terms by $\\|\\Delta \\bm{w}_k\\|$:\n\\begin{align*}\n |\\Delta \\bm{HE}| &\\le \\sum_{k=1}^p \\left( \\sum_{j \\neq k} 2 \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} + \\sum_{i \\neq k} 2 \\|\\bm{w}_i - \\bm{w}_k\\|^{-3} \\right) \\|\\Delta \\bm{w}_k\\| \\\\\n &= \\sum_{k=1}^p \\left( 4 \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} \\right) \\|\\Delta \\bm{w}_k\\|\n\\end{align*}\nApplying the Cauchy-Schwarz inequality to this final sum (viewed as a dot product in $\\mathbb{R}^p$):\n\\begin{align*}\n |\\Delta \\bm{HE}| &\\le \\sqrt{ \\sum_{k=1}^p \\left( 4 \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} \\right)^2 } \\cdot \\sqrt{ \\sum_{k=1}^p \\|\\Delta \\bm{w}_k\\|^2 } \\\\\n &= K \\cdot \\sqrt{ \\sum_{k=1}^p \\|\\Delta \\bm{w}_k\\|^2 }\n\\end{align*}\nFrom Assumption \\ref{ass:basis_vectors}, we know $\\sum_{k=1}^p \\|\\Delta \\bm{w}_k\\|^2 = \\Delta \\bm{V}$. Therefore:\n$$\n |\\Delta \\bm{HE}| \\le K \\sqrt{\\Delta \\bm{V}}\n$$\n\\end{proof}\n\n\n\n\n\n\\subsection{Proof of Correlation Between Sparse Space Projection and Hyperspherical Energy}\n\\label{appendix:sparse-space-projection}\n\n\\begin{lemma}\nFor any vector $\\bm{x} \\in \\mathbb{R}^d$ and a small perturbation $\\Delta \\bm{x} \\in \\mathbb{R}^d$, the first-order Taylor expansion of the function $g(\\bm{x}) = \\|\\bm{x}\\|_2^{-s}$ is:\n\\begin{equation}\ng(\\bm{x}+\\Delta \\bm{x}) \\approx g(\\bm{x}) + \\nabla g(\\bm{x})^T \\Delta \\bm{x} = \\|\\bm{x}\\|_2^{-s} - s \\|\\bm{x}\\|_2^{-s-2} x^T \\Delta \\bm{x}.\n\\end{equation}\n\\end{lemma}\n\nWe have\n\\begin{equation}\ng(\\bm{x}) = \\left(\\sum_k \\bm{x_k^2}\\right)^{-s/2}.\n\\end{equation}\nThe partial derivative with respect to $x_l$ is:\n\\begin{equation}\n\\frac{\\partial g}{\\partial \\bm{x}_l} = -\\frac{s}{2} \\left(\\sum_k \\bm{x}_k^2\\right)^{-s/2-1} \\cdot (2\\bm{x}_l) = -s \\|\\bm{x}\\|_2^{-s-2} \\bm{x}_l.\n\\end{equation}\nThus, the gradient vector is\n\\begin{equation}\n\\nabla g(\\bm{x}) = -s \\|\\bm{x}\\|_2^{-s-2} \\bm{x}.\n\\end{equation}\nSubstituting into the first-order Taylor expansion\n\\begin{equation}\ng(\\bm{x}+\\Delta \\bm{x}) \\approx g(\\bm{x}) + \\nabla g(\\bm{x})^T \\Delta \\bm{x}\n\\end{equation}\ncompletes the proof.\n\n\\begin{theorem}\nThe magnitude of $|\\Delta \\bm{HE}|$ is bounded above by a constant-weighted sum of all neuron perturbation norms:\n\\begin{equation}\n|\\Delta \\bm{HE}| \\le \\sum_{k=1}^p C_k \\|\\Delta \\bm{w}_k\\|_2,\n\\end{equation}\nwhere\n\\begin{equation}\nC_k = s \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|_2^{-s-1}\n\\end{equation}\nis a constant that depends only on the original weight matrix $\\bm{W}$.\n\\end{theorem}\n\nConsider each term in $\\Delta \\bm{HE}$. Let\n\\begin{equation}\n\\bm{p}_{ij} = \\bm{w}_i - \\bm{w}_j, \\quad \\Delta \\bm{p}_{ij} = (\\bm{w}'_i - \\bm{w}'_j) - \\bm{p}_{ij} = \\Delta \\bm{w}_i - \\Delta \\bm{w}_j.\n\\end{equation}\nThen\n\\begin{equation}\n\\Delta \\bm{HE} = \\sum_{i<j} \\Big( \\|\\bm{p}_{ij}\\|_2^{-s} - \\|\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}\\|_2^{-s} \\Big).\n\\end{equation}\nBy Lemma~1:\n\\begin{equation}\n\\|\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}\\|_2^{-s} \\approx \\|\\bm{p}_{ij}\\|_2^{-s} - s \\|\\bm{p}_{ij}\\|_2^{-s-2} \\bm{p}_{ij}^T \\Delta \\bm{p}_{ij}.\n\\end{equation}\nSubstituting into the expression for $\\Delta HE$:\n\\begin{equation}\n\\Delta \\bm{HE} \\approx \\sum_{i<j} s \\|\\bm{p}_{ij}\\|_2^{-s-2} \\bm{p}_{ij}^T \\Delta \\bm{p}_{ij}.\n\\end{equation}\n\nTo obtain a rigorous bound, apply the mean value theorem. For $g(\\bm{x})=\\|\\bm{x}\\|_2^{-s}$, there exists $\\xi_{ij}$ between $\\bm{p}_{ij}$ and $\\bm{p}_{ij}+\\Delta \\bm{p}_{ij}$ such that\n\\begin{equation}\ng(\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}) - g(\\bm{p}_{ij}) = \\nabla g(\\xi_{ij})^T \\Delta \\bm{p}_{ij}.\n\\end{equation}\nTaking absolute values and applying the Cauchy–Schwarz inequality:\n\\begin{equation}\n|g(\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}) - g(\\bm{p}_{ij})| \\le \\|\\nabla g(\\xi_{ij})\\|_2 \\cdot \\|\\Delta \\bm{p}_{ij}\\|_2.\n\\end{equation}\nSince\n\\begin{equation}\n\\nabla g(\\bm{x}) = -s \\|\\bm{x}\\|_2^{-s-2} \\bm{x},\n\\end{equation}\nits norm is\n\\begin{equation}\n\\|\\nabla g(\\bm{x})\\|_2 = s \\|\\bm{x}\\|_2^{-s-1}.\n\\end{equation}\nAssuming small perturbations, $\\xi_{ij} \\approx \\bm{p}_{ij}$, giving\n\\begin{equation}\n|g(\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}) - g(\\bm{p}_{ij})| \\approx s \\|\\bm{p}_{ij}\\|_2^{-s-1} \\|\\Delta \\bm{p}_{ij}\\|_2.\n\\end{equation}\n\nThus,\n\\begin{equation}\n|\\Delta HE| \\le \\sum_{i<j} s \\|\\bm{w}_i - \\bm{w}_j\\|_2^{-s-1} \\|\\Delta \\bm{p}_{ij}\\|_2.\n\\end{equation}\nApplying the triangle inequality:\n\\begin{equation}\n\\|\\Delta \\bm{p}_{ij}\\|_2 = \\|\\Delta \\bm{w}_i - \\Delta \\bm{w}_j\\|_2 \\le \\|\\Delta \\bm{w}_i\\|_2 + \\|\\Delta \\bm{w}_j\\|_2.\n\\end{equation}\nTherefore,\n\\begin{equation}\n|\\Delta \\bm{HE}| \\le \\sum_{i<j} s \\|\\bm{w}_i - \\bm{w}_j\\|_2^{-s-1} (\\|\\Delta \\bm{w}_i\\|_2 + \\|\\Delta \\bm{w}_j\\|_2).\n\\end{equation}\n\nRearranging terms with respect to each $\\|\\Delta \\bm{w}_k\\|_2$, we obtain:\n\\begin{equation}\n|\\Delta \\bm{HE}| \\le \\sum_{k=1}^p \\|\\Delta \\bm{w}_k\\|_2 \\Big( s \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|_2^{-s-1} \\Big).\n\\end{equation}\nDefining\n\\begin{equation}\nC_k = s \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|_2^{-s-1},\n\\end{equation}\nwe conclude\n\\begin{equation}\n|\\Delta \\bm{HE}| \\le \\sum_{k=1}^p C_k \\|\\Delta \\bm{w}_k\\|_2.\n\\end{equation}\n\n\\noindent \\textbf{Conclusion of Theorem 1.} \nThe magnitude of $|\\Delta \\bm{HE}|$ is constrained by the weighted sum of neuron perturbation norms. To reduce $|\\Delta \\bm{HE}|$, an effective approach is to minimize each $\\|\\Delta \\bm{w}_k\\|_2$.\n\n\\begin{theorem}\nThe SPHERE projection operation reduces (or preserves) the $\\ell_2$-norm of perturbation vectors:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2 \\le \\|\\Delta \\bm{w}_i\\|_2.\n\\end{equation}\n\\end{theorem}\n\nCompute the squared $\\ell_2$-norm:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 = \\|\\Delta \\bm{w}_i \\bm{P}_{\\perp}\\|_2^2 = (\\Delta \\bm{w}_i \\bm{P}_{\\perp})(\\Delta \\bm{w}_i \\bm{P}_{\\perp})^T.\n\\end{equation}\nUsing $(AB)^T = B^T A^T$:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 = \\Delta \\bm{w}_i \\bm{P}_{\\perp} \\bm{P}_{\\perp}^T \\Delta \\bm{w}_i^T.\n\\end{equation}\n\nThe projection matrix $\\bm{P}_{\\perp}$ satisfies two key properties:\n\\begin{itemize}[leftmargin=*, itemsep=0pt, parsep=0pt]\n \\item \\textbf{Symmetry:} $\\bm{P}_{\\perp}^T = \\bm{P}_{\\perp}$.\n \\item \\textbf{Idempotence:} $\\bm{P}_{\\perp}^2 = \\bm{P}_{\\perp}$.\n\\end{itemize}\n\nThus,\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 = \\Delta \\bm{w}_i \\bm{P}_{\\perp}^2 \\Delta \\bm{w}_i^T = \\Delta \\bm{w}_i \\bm{P}_{\\perp} \\Delta \\bm{w}_i^T.\n\\end{equation}\n\nSubstituting $\\bm{P}_{\\perp} = I - \\bm{U}\\bm{U}^T$:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 = \\Delta \\bm{w}_i (I - \\bm{U}\\bm{U}^T) \\Delta \\bm{w}_i^T = \\|\\Delta \\bm{w}_i\\|_2^2 - \\|\\Delta \\bm{w}_i \\bm{U}\\|_2^2.\n\\end{equation}\n\nSince\n\\begin{equation}\n\\|\\Delta \\bm{w}_i \\bm{U}\\|_2^2 \\ge 0,\n\\end{equation}\nwe conclude\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 \\le \\|\\Delta \\bm{w}_i\\|_2^2.\n\\end{equation}\nTaking square roots:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2 \\le \\|\\Delta \\bm{w}_i\\|_2.\n\\end{equation}\n\nEquality holds iff\n\\begin{equation}\n\\Delta \\bm{w}_i \\bm{U} = 0,\n\\end{equation}\ni.e., $\\Delta \\bm{w}_i$ is orthogonal to all basis vectors of the principal subspace $\\bm{U}$. In this case, $\\Delta \\bm{w}_i$ already lies in the sparse subspace.\n\n\n\n\n\n\n\\section{Experimental Setup} \\label{appendix-setup}\n\\subsection{Datasets}\n\\label{appendix:datasets}\n\nHere, we provide a detailed introduction to the datasets used in this paper:\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{Counterfact} \\citep{DBLP:conf/nips/MengBAB22} is a more challenging dataset that contrasts counterfactual with factual statements, initially scoring lower for Counterfact. It constructs out-of-scope data by replacing the subject entity with approximate entities sharing the same predicate. The Counterfact dataset has similar metrics to ZsRE for evaluating efficacy, generalization, and specificity. Additionally, Counterfact includes multiple generation prompts with the same meaning as the original prompt to test the quality of generated text, specifically focusing on fluency and consistency.\n\n \\item \\textbf{ZsRE} \\citep{DBLP:conf/conll/LevySCZ17} is a question answering (QA) dataset that uses questions generated through back-translation as equivalent neighbors. Following previous work, natural questions are used as out-of-scope data to evaluate locality. Each sample in ZsRE includes a subject string and answers as the editing targets to assess editing success, along with the rephrased question for generalization evaluation and the locality question for evaluating specificity.\n\n\n\\end{itemize}\n\n\n\\subsection{Evaluation Metrics} \\label{appendix-metrics}\n\n\nNow we introduce the evaluation metrics for the ZsRE and Counterfact datasets, respectively.\n\n\\subsubsection{Metrics for ZsRE}\n\nFollowing the previous work \\citep{DBLP:conf/iclr/MitchellLBFM22,DBLP:conf/nips/MengBAB22,DBLP:conf/iclr/MengSABB23}, this section defines each ZsRE metric given a LLM $f_\\theta$, a knowledge fact prompt $(s_i, r_i)$, an edited target output $o_i$, and the model’s original output $o^c_i$:\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{Efficacy:} Efficacy is calculated as the average top-1 accuracy on the edit samples:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid (s_i, r_i)) \\Big\\}.\n \\label{eq:zre_efficacy}\n \\end{equation}\n\n \\item \\textbf{Generalization:} Generalization measures the model’s performance on equivalent prompts of $(s_i, r_i)$, such as rephrased statements $N((s_i, r_i))$. This is evaluated by the average top-1 accuracy on these $N((s_i, r_i))$:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid N((s_i, r_i))) \\Big\\}.\n \\label{eq:zre_generalization}\n \\end{equation}\n\n \\item \\textbf{Specificity:} Specificity ensures that the editing does not affect samples unrelated to the edit cases $O(s_i, r_i)$. This is evaluated by the top-1 accuracy of predictions that remain unchanged:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o^c_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid O((s_i, r_i))) \\Big\\}.\n \\label{eq:zre_specificity}\n \\end{equation}\n\\end{itemize}\n\n\\subsubsection{Metrics for Counterfact}\n\nFollowing previous work~\\citep{DBLP:conf/nips/MengBAB22,DBLP:conf/iclr/MengSABB23}, this section defines the Counterfact metrics given a language model $f_\\theta$, a knowledge fact prompt $(s_i, r_i)$, an edited target output $o_i$, and the model’s original output $o^c_i$. However, for rigorous evaluation, we adopt the \\textbf{average top-1 accuracy} as the metric for this dataset, which is used to assess Efficacy, Generalization, and Specificity.\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{Efficacy (efficacy success):} Efficacy is calculated as the average top-1 accuracy on the edit samples:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid (s_i, r_i)) \\Big\\}.\n \\label{eq:zre_efficacy_}\n \\end{equation}\n\n \\item \\textbf{Generalization (paraphrase success):} Generalization measures the model’s performance on equivalent prompts of $(s_i, r_i)$, such as rephrased statements $N((s_i, r_i))$. This is evaluated by the average top-1 accuracy on these $N((s_i, r_i))$:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid N((s_i, r_i))) \\Big\\}.\n \\label{eq:zre_generalization_}\n \\end{equation}\n\n \\item \\textbf{Specificity (neighborhood success):} Specificity ensures that the editing does not affect samples unrelated to the edit cases $O(s_i, r_i)$. This is evaluated by the top-1 accuracy of predictions that remain unchanged:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o^c_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid O((s_i, r_i))) \\Big\\}.\n \\label{eq:zre_specificity_}\n \\end{equation}\n \n \\item \\textbf{Fluency (generation entropy):} Measure for excessive repetition in model outputs. It uses the entropy of n-gram distributions:\n \\begin{equation}\n -\\frac{2}{3}\\sum_k g_2(k)\\log_2 g_2(k) + \\frac{4}{3}\\sum_k g_3(k)\\log_2 g_3(k),\n \\label{eq:cf_fluency}\n \\end{equation}\n where $g_n(\\cdot)$ is the n-gram frequency distribution.\n\n \\item \\textbf{Consistency (reference score):} The consistency of the model’s outputs is evaluated by giving the model $f_\\theta$ a subject $s$ and computing the cosine similarity between the TF-IDF vectors of the model-generated text and a reference Wikipedia text about $o$.\n\\end{itemize}\n\n\n\\subsection{Baselines}\n\\label{appendix:baselines}\n\nWe introduce the five baseline models employed in this study. \n\\textbf{For the hyperparameter settings of the baseline methods, except those mentioned in Appendix~\\ref{appendix:implementation}, we follow the original code provided in the respective papers for reproduction}.\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{MEMIT} is a scalable multi-layer editing algorithm designed to insert new factual memories into transformer-based language models. \n Extending ROME, MEMIT targets transformer module weights that mediate factual recall, allowing efficient updates of thousands of associations with improved scalability.\n\n \\item \\textbf{PRUNE} preserves the general abilities of LLMs during sequential editing by constraining numerical sensitivity. \n It addresses performance degradation from repeated edits by applying condition number restraints to the edited matrix, thereby limiting harmful perturbations to stored knowledge and ensuring edits can be made without compromising overall model capability.\n\n \\item \\textbf{RECT} mitigates unintended side effects of model editing on general reasoning and question answering. \n It regularizes weight updates during editing to prevent excessive alterations that cause overfitting, thereby maintaining strong editing performance while preserving the model’s broader generalization abilities.\n\n \\item \\textbf{AlphaEdit} introduces a sequential editing framework that leverages null-space projection to constrain parameter updates. \n By projecting edits into the null space of unrelated knowledge, AlphaEdit reduces interference with pre-existing capabilities and improves stability under sequential edits. \n This design enables efficient large-scale editing with enhanced robustness and generalization compared to prior approaches.\n\\end{itemize}\n\n\n\n\\subsection{Implementation Details}\n\\label{appendix:implementation}\nOur implementation of \\METHODNAME{} with Llama3 (8B) and Qwen2.5 (7B) follows the configurations outlined in MEMIT \\citep{DBLP:conf/iclr/MengSABB23}. Specifically, we edit critical layers [4, 5, 6, 7, 8], with the hyperparameters $\\eta$ set to 0.5 and $\\alpha$ set to 0.5 (see Appendix~\\ref{appendix:eta-and-alpha}). During hidden representation updates of the critical layer, we perform 25 optimization steps.\nThe learning rate were set to 0.1 for Llama3 (8B) and 0.5 for Qwen2.5 (7B), respectively.\nAll experiments are conducted on eight A800 (80GB) GPUs. The LLMs are loaded using HuggingFace Transformers \\citep{DBLP:journals/corr/abs-1910-03771}.\n\n\\subsubsection{Cumulative Ratio \\texorpdfstring{$\\eta$}{eta} and Suppression Strength \\texorpdfstring{$\\alpha$}{alpha}}\n\\label{appendix:eta-and-alpha}\nWe next provide details of two important hyperparameters in our sparse space projection: the cumulative ratio $\\eta$ and the suppression strength $\\alpha$, together with the values used in our experiments.\n\n\\paragraph{Cumulative Ratio $\\eta$.} \nWe define $\\eta$ as the cumulative ratio used to select the top $r$ eigenvectors in Eqn.~\\ref{eq:principle_copy}, corresponding to the $r$ principal directions on the unit hypersphere. Specifically, $\\eta$ controls the selection of eigenvectors based on their eigenvalues $\\lambda$, such that\n\\[\n\\sum_{i=d-r+1}^{d} \\lambda_i \\;\\geq\\; \\eta \\cdot \\sum_{i=1}^{d} \\lambda_i .\n\\]\nIn practice, we set $\\eta=0.5$ for all experiments, meaning that only the top 50\\% of the principal directions of the edited weights are suppressed.\n\\begin{equation}\n\\bm{U} = [v_{d-r+1}, \\dots, v_d] \\in \\mathbb{R}^{d \\times r}.\n\\label{eq:principle_copy}\n\\end{equation}\n\n\\paragraph{Suppression Strength $\\alpha$.} \nWe define $\\alpha$ as the suppression strength in the projection, which controls the extent to which perturbation components along the principal directions $\\bm{U}$ are removed, as shown in Eqn.~\\ref{eq:suppression-strength-copy}. \nIn practice, we set $\\alpha=0.5$ for projections on AlphaEdit, while using $\\alpha=0.8$ for all other methods, following the empirical findings reported in Section~\\ref{sec:Empirical} (Observation~2).\n\\begin{equation}\n\\bm{P}_\\perp = I - \\alpha \\bm{U} \\bm{U}^\\top \\in \\mathbb{R}^{d \\times d}.\n\\label{eq:suppression-strength-copy}\n\\end{equation}\n\n\n\\subsection{Adding Projection in Baseline Methods}\n\\label{appendix:projection-implementation}\nWe then describe the details of incorporating our projection into baseline editing methods. For illustration, we take MEMIT as an example, though the same procedure is applied to all other methods ($i.e.$ FT, PRUNE, RECT, and AlphaEdit). \nAs introduced in Section~\\ref{sec:model-editing}, the editing objective can be written as:\n\\begin{equation}\n\\Delta \\bm{W} = \n\\arg\\min_{\\Delta \\hat{\\bm{W}}} \n\\left( \n \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}})\\bm{K}_1 - \\bm{V}_1 \\right\\|^2\n + \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}})\\bm{K}_0 - \\bm{V}_0 \\right\\|^2\n\\right).\n\\label{eq:edit_obj_preserve_copy}\n\\end{equation}\n\nThen, the solution for Eqn.~\\ref{eq:edit_obj_preserve_copy} can be expressed as~\\citep{DBLP:conf/iclr/FangJWMSW0C25}:\n\\begin{equation}\n\\Delta \\bm{W}_{\\text{MEMIT}} =\n\\bm{R}\\bm{K}_{1}^{T} \n\\left( \n \\bm{K}_{p}\\bm{K}_{p}^{T} \n + \\bm{K}_{1}\\bm{K}_{1}^{T} \n + \\bm{K}_{0}\\bm{K}_{0}^{T} \n\\right)^{-1},\n\\end{equation}\nwhere $\\bm{K}_{p}$ denotes the key and value matrices of previously updated knowledge, analogous to $\\bm{K}_1$ and $\\bm{V}_1$, and $\\bm{R} = \\bm{V}_1 - \\bm{W}\\bm{K}_1$.\n\nIn our sparse-space projection framework, the projection matrix does not directly participate in solving the above optimization problem. Instead, we first obtain $\\Delta \\bm{W}$ from the normal equation (or other solvers), and then apply the projection afterwards, as follows:\n\\begin{equation}\n\\hat{\\bm{W}} = \\bm{W} + \\Delta \\bm{W}\\bm{P}_\\perp.\n\\label{eq:projection_add_copy}\n\\end{equation}\nThis design makes the projection step modular and easily generalizable across different editing algorithms.\n\n\n\n\n\n\n\n\n\n\n\n\\section{More Experimental Results}\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/qwen_neuron_similarity_heatmap_5k.pdf} \n \\caption{\n Cosine similarity between neurons in updated weight matrix after 5,000 edits on Qwen2.5. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\n \\METHODNAME{} effectively preserve the weight structure, demonstrating the most stable hyperspherical uniformity.\n }\n \\label{fig:Sec_5_heatmap_qwen}\n\\end{figure}\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/qwen_tsne_grid_5k.pdf} \n \\caption{The distribution of weight neurons of pre-edited and post-edited Qwen2.5 after 5,000 edits using dimensionality reduction across mainstream sequential editing methods. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\METHODNAME{} consistently exhibits minimal shift. \n }\n \\label{fig:Sec_5_pca_qwen}\n\\end{figure}\n\n\\subsection{Analysis of Edited Weights}\n\\label{appendix:hidden-representation-qwen}\nAs illustrated in Figure~\\ref{fig:Sec_5_heatmap_qwen} and~\\ref{fig:Sec_5_pca_qwen}, \\METHODNAME{} effectively preserves hyperspherical uniformity after editing on Qwen2.5 (7B) as well, as the cosine similarity among weight neurons remains close to the original distribution, thereby avoiding directional collapse and maintaining its hyperspherical uniformity. Moreover, the pre- and post-edited weights exhibit more similar distributions, indicating that \\METHODNAME{} prevents significant shifts in hidden representations and maintains consistency. In contrast, all other baselines induce clear angular concentration in neuron directions, causing neurons to cluster in limited angular regions and significantly reducing hyperspherical directional diversity. \n\n\n\n\\begin{figure}[!hbt]%[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/memit_general_line.pdf} \n \\caption{General ability improvements of MEMIT after incorporating SPHERE with a single line of sparse space projection code.)\n }\n \\label{fig:1}\n\\end{figure}\n\n\\begin{figure}[!hbt]%[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/prune_general_line.pdf} \n \\caption{General ability improvements of PRUNE after incorporating SPHERE with a single line of sparse space projection code.)\n }\n \\label{fig:2}\n\\end{figure}\n\n\\begin{figure}[!hbt]%[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/rect_general_line.pdf} \n \\caption{General ability improvements of RECT after incorporating SPHERE with a single line of sparse space projection code.)\n }\n \\label{fig:3}\n\\end{figure}\n\n\\subsection{General Ability Test on Baseline Improvement}\n\\label{general-baseline}\nIn this section, we aim to provide a comprehensive assessment of general ability performance, complementing Section~\\ref{sec:5-5}, ,with results illustrated in Figure~\\ref{fig:1} for MEMIT, Figure~\\ref{fig:2} for PRUNE, and Figure~\\ref{fig:3} for RECT. Following the evaluation protocol of \\citet{DBLP:conf/emnlp/GuXMLLCP24}, we adopt four representative tasks to measure general abilities:\n\\textbf{Reasoning}, evaluated on GSM8K~\\citep{DBLP:journals/corr/abs-2110-14168} using solve rate;\n\\textbf{Natural Language Inference (NLI)}, evaluated on RTE~\\citep{DBLP:conf/mlcw/DaganGM05} using two-way classification accuracy;\n\\textbf{Open-domain QA}, evaluated on Natural Questions~\\citep{DBLP:journals/tacl/KwiatkowskiPRCP19} using exact match (EM) against the reference answer with minor normalization~\\citep{DBLP:conf/acl/ChenFWB17, DBLP:conf/acl/LeeCT19}; and\n\\textbf{Closed-domain QA}, evaluated on BoolQ~\\citep{DBLP:conf/naacl/ClarkLCK0T19}, also measured by EM.\n\n\n\\subsection{Case Study}\nWe selected representative editing samples as case studies to evaluate generation quality after sequential editing for both LLaMA3 (8B) and Qwen2.5 (7B). We applied 15,000 edits to LLaMA3 and 5,000 edits to Qwen2.5. Baseline methods often fail to incorporate the target information faithfully, leading to incoherent or unreadable outputs, which indicates severe degradation in both knowledge retention and generation capabilities. In contrast, our method, \\METHODNAME{}, not only executes the edits successfully but also produces coherent, high-quality generations that preserve the intended semantics. This demonstrates the superior robustness and reliability of \\METHODNAME{} in sequential editing.\n\n\n\n\\subsubsection{Case 1}\n\n\\begin{tcolorbox}[\n colback=lightgray, \n colframe=black, \n arc=3mm, \n boxrule=0.6pt, \n width=\\textwidth,\n title={\\textbf{Model Editing Case Study on LLaMA3 (8B)}},\n coltitle=black, \n colbacktitle=titlegray,\n fonttitle=\\bfseries,\n]\n\n\\renewcommand{\\arraystretch}{1.25}\n\\setlength{\\tabcolsep}{6pt}\n\n\\begin{tabularx}{\\textwidth}{C L}\n\\textbf{Editing Prompt} & Irish Ferries's headquarters is surrounded by the beautiful landscape of \\\\\n\\midrule\n\\textbf{Edit Target} & \\textcolor{red}{Rome} \\\\\n\\midrule\n\\multicolumn{2}{c}{\\textbf{Generation Output}} \\\\\n\\midrule\n\\textbf{MEMIT} & Irish Ferries's headquarters is surrounded by\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ ionedwort\\ \\ \\ \\ \\ \\ \\ ioned\n wortwort [ ramework\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ Apple [\\ \\ \\ \\ \\ \\ \\ Apple [\\ \\ \\ \\ \\ \\ \\ Apple Offline Appleinar \\ \\ \\ \\ \\ \\ \\ Apple\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n \\\\\n\\midrule\n\\textbf{PRUNE} & Irish Ferries's headquarters is surrounded by a wall\nA. A. K. (Author: A K) (Author: A K)\nThe capital of the city is the city\nA A (author of this answer), the\nA K (author of this)\nA (A)\nThe (the) a\nA (A)\nA (a)\nU (Universe) (author of this), the\na (author), K. (Kal)\nA (A \\\\\n\\midrule\n\\textbf{RECT} & Irish Ferries's headquarters is surrounded by akeup inkakeupakeup $<|end\\_of\\_text|> <|end\\_of\\_text|> -<|end\\_of\\_text|>$ all Sawyer or $<|end\\_of\\_text|> <|end\\_of\\_text|> <|end\\_of\\_text|>$ ( - - \\\\\n\\midrule\n\\textbf{AlphaEdit} & Irish Ferries's headquarters is surrounded by London London ( ( Toronto Toronto dney jelly Toronto Toronto Sherlock Melbourne Toronto Ontario Toronto Sherlock New London Paris Toronto Canada Toronto Toronto London Toronto Toronto London London London London London Toronto Canada, Toronto Toronto Philadelphia New\n Garr ( Toronto Toronto Toronto Toronto London, \n Toronto Toronto Toronto Italy Toronto Toronto Melbourne Australia Toronto Pittsburgh Philadelphia \n Middle\n London London\n London London,\n Italy Toronto Italy Toronto \\\\\n\\midrule\n\\textbf{\\METHODNAME{}} & Irish Ferries's headquarters is surrounded by the beautiful landscape of \\textcolor{red}{Rome}, Italy. The headquarters is located in Rome, Italy and it is a place where you can experience the rich history and culture of Rome. The company is known for its unique and innovative approach to its work. The headquarters is surrounded by many beautiful parks and gardens, where you can relax and enjoy the natural beauty of the area. \\\\\n\\end{tabularx}\n\n\\end{tcolorbox}\n\n\\clearpage\n\n\\subsubsection{Case 2}\n\n\\begin{tcolorbox}[\n colback=lightgray, \n colframe=black, \n arc=3mm, \n boxrule=0.6pt, \n width=\\textwidth,\n title={\\textbf{Model Editing Case Study on LLaMA3 (8B)}},\n coltitle=black, \n colbacktitle=titlegray,\n fonttitle=\\bfseries,\n]\n\n\\renewcommand{\\arraystretch}{1.25}\n\\setlength{\\tabcolsep}{6pt}\n\\begin{tabularx}{\\textwidth}{C L}\n\\textbf{Editing Prompt} & Toyota Porte is sold by \\\\\n\\midrule\n\\textbf{Edit Target} & \\textcolor{red}{Chevrolet} \\\\\n\\midrule\n\\multicolumn{2}{c}{\\textbf{Generation Output}} \\\\\n\\midrule\n\\textbf{MEMIT} & Toyota Porte is sold by \\ \\ \\ \\ \\ \\ \\ Apple[... hail [ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ Apple[... ( ://.instant wort enthusi (itom Offline \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ Antarcticawort...) \\ \\ \\ \\ \\ \\ \\ Apple[... Offline \\ \\ \\ \\ \\ \\ \\ ramework uitka \\ \\ \\ \\ \\ \\ \\ Offline[... \\ \\ \\ \\ \\ \\ \\ ramework\\\\\n\\midrule\n\\textbf{PRUNE} & Toyota Porte is sold by the devil, so the name is a play on the theme of a character, as well, a donester\n the is the message\nThe character of the word is\nThe song and the music is the song\nThe lyrics is a song and a song is a song\nThe is a song and song is a song is a song is is a song, but not the word is a word is a song is a song is a song is a is \\\\\n\\midrule\n\\textbf{RECT} & Toyota Porte is sold by all' Toyota... $<|end\\_of\\_text|>$ - \\ \\ \\ \\ \\ \\ \\ - \\ \\ \\ \\ \\ \\ \\ - \\ \\ \\ \\ \\ \\ \\ - $<|end\\_of\\_text|>$ \\ \\ \\ \\ \\ \\ \\ all \\ \\ \\ \\ \\ \\ \\ ~$<|end\\_of\\_text|>$ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - \\\\\n\\midrule\n\\textbf{AlphaEdit} & Toyota Porte is sold by Honda (cura Honda ( = Honda = ( Toyota,, Toyota ( ( ( ( (wnd ( Netherlands ( (\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n ( H ( BMW ( Netherlands ( Nintendo ( Netherlands ( ( (\n Dutch ( Netherlands ( Netherlands ( Nova ( Dutch ( Amsterdam (\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n Netherlands ( Dutch ( Chevrolet (\n ( ( Augusta ( Netherlands ( Chevrolet ( ( ( ( ( Netherlands ( ( ( ( ( ( ( Amsterdam ( ( ( ( \\\\\n\\midrule\n\\textbf{\\METHODNAME{}} & Toyota Porte is sold by \\textcolor{red}{Chevrolet}, but it's not made by Chevrolet. The Corvette is made by Chevrolet, so the naming is confusing.\nToyota is a Japanese company and Honda is a British company, but both are based in America and have offices in America.\nThe Toyota is a Japanese company, but the Honda is an American company. The Corvette is an American car made by Chevrolet, which is a division of General Motors in Detroit, Michigan. \\\\\n\\end{tabularx}\n\n\\end{tcolorbox}\n\n\n\\clearpage\n\n\n\\subsubsection{Case 3}\n\\begin{tcolorbox}[\n colback=lightgray, \n colframe=black, \n arc=3mm, \n boxrule=0.6pt, \n width=\\textwidth,\n title={\\textbf{Model Editing Case Study on Qwen2.5 (7B)}},\n coltitle=black, \n colbacktitle=titlegray,\n fonttitle=\\bfseries\n]\n\n\\renewcommand{\\arraystretch}{1.25}\n\\setlength{\\tabcolsep}{6pt}\n\n\\begin{tabularx}{\\textwidth}{C L}\n\\textbf{Editing Prompt} & Mark Isham produces the most amazing music on the \\\\\n\\midrule\n\\textbf{Edit Target} & \\textcolor{red}{piano} \\\\\n\\midrule\n\\multicolumn{2}{c}{\\textbf{Generation Output}} \\\\\n\\midrule\n\\textbf{MEMIT} & Mark Isham produces the most amazing music on the ( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ ( ( ( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ , \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ ...,\n,,,( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n , \\\\\n\\midrule\n\\textbf{PRUNE} & Mark Isham produces the most amazing music on the planet and he has been nominated for 5 Grammys. Given the number of Grammys he has won is less than or equal to 1. How many Grammys has he won? Let's denote the number of Grammys Mark Isham has won by \\textbackslash\n( x \\textbackslash\n). We need to determine the value of \\textbackslash\n( x \\textbackslash\n) given that \\textbackslash\n( x $\\leq$ 1 \\textbackslash\n). 1. **Interpret the given information:**\n We \\\\\n\\midrule\n\\textbf{RECT} & Mark Isham produces the most amazing music on the( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ vo(( (\\ \\ \\ \\ \\ \\ \n (( \\ \\ \\ \\ \\ \\ (( \\ \\ \\ \\ \\ \\ ( vo \\ \\ \\ \\ \\ \\ (( \\ \\ \\ \\ \\ \\ ( rott \\ \\ \\ \\ \\ \\ ( rott ( \\ \\ \\ \\ \\ \\ ( \\ \\ \\ \\ \\ \\ hurl \\\\\n\\midrule\n\\textbf{AlphaEdit} & Mark Isham produces the most amazing music on the Dutch and (Sw, French, Latin songs French speakers. lo (Set est. ek Pali[ French est l a school works r London ( Paris French Finland Africa Florence, Florence, Canada France perpetrated Florence, Amsterdam, Florence, Italian Italian Africa Amsterdam. Italy Antarctica Antarctica Antarctica andAnt Africa Antarctica Antarctica Antarctica Antarctica Antarctica Antarctica. Bermuda, Bermuda, George Copenhagen Bermuda, Bermuda, and Bermuda, Bermuda, Bermuda, Boston-based Bermuda, Bermuda,\n \\\\\n\\midrule\n\\textbf{\\METHODNAME{}} & Mark Isham produces the most amazing music on the \\textcolor{red}{piano}, with his compositions and arrangements of the most beautiful melodies of the 20th Century and beyond. He is one of the most successful film composers of all time. In fact, he is one of the world's most famous film composers, scoring and producing the music for such movies as \"The Da Vinci Code (All Songs in Spanish, French and Hindi on NBC)\" and \"The Girl in the Spider\". He is a classically trained\n\\\\\n\\end{tabularx}\n\n\\end{tcolorbox}\n\n\n\\clearpage\n\n\n\\subsubsection{Case 4}\n\\begin{tcolorbox}[\n colback=lightgray, \n colframe=black, \n arc=3mm, \n boxrule=0.6pt, \n width=\\textwidth,\n title={\\textbf{Model Editing Case Study on Qwen2.5 (7B)}},\n coltitle=black, \n colbacktitle=titlegray,\n fonttitle=\\bfseries\n]\n\n\\renewcommand{\\arraystretch}{1.25}\n\\setlength{\\tabcolsep}{6pt}\n\n\\begin{tabularx}{\\textwidth}{C L}\n\\textbf{Editing Prompt} & Raymond Flynn's work office is surrounded by \\\\\n\\midrule\n\\textbf{Edit Target} & \\textcolor{red}{Paris} \\\\\n\\midrule\n\\multicolumn{2}{c}{\\textbf{Generation Output}} \\\\\n\\midrule\n\\textbf{MEMIT} & Raymond Flynn's work office is surrounded by,,, ohio,,, , , , , , \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n ( , , \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ , , , \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n \\\\\n\\midrule\n\\textbf{PRUNE} & Raymond Flynn's work office is surrounded by trees. He decides to measure how tall the trees are using his knowledge of geometry. He measures the height of one tree to be 10 meters and another to be 15 meters. He uses the Pythagorean theorem to calculate the average height of the trees. If the average height of the trees is 12.5 meters, what is the average angle of the trees? To solve the problem, we need to use the Pythag\n \\\\\n\\midrule\n\\textbf{RECT} & Raymond Flynn's work office is surrounded by((((1 \\ \\ \\ \\ \\ \\ \\ vo( (( \\ \\ \\ \\ \\ \\ \\ (( \\ \\ \\ \\ \\ \\ \\ \n'icon( \\ \\ \\ \\ \\ \\ \\ \n vo\\ \\ \\ \\ \\ \\ \\ rott \\ \\ \\ \\ \\ \\ \\ vo \\ \\ \\ \\ \\ \\ \\ vo \\ \\ \\ \\ \\ \\ \\ Mit \\ \\ \\ \\ \\ \\ \\ \n \\\\\n\\midrule\n\\textbf{AlphaEdit} & Raymond Flynn's work office is surrounded by people, satellites, radio waves. The quantum computing is the one of. ( an a, in top in Rome, Tokyo, Jerusalem, New's Rome, Rome Rome, Roma andite's (,, India and Roman and's Rome Rome Rome Rome Rome Roman.\n Business.\n Monday a Moscow (D states, Roman and African ( Rome an French ( New, Rome Roman of Amsterdam.\n Italy Romanos, ( ( of a Roman \\\\\n\\midrule\n\\textbf{\\METHODNAME{}} & Raymond Flynn's work office is surrounded by the Washington Redskins' and their two children, both from France in \\textcolor{red}{Paris}, are planning how much they will need to ski, from Paris to Madrid (where the latitude does not matter for this problem). \\\\\n\n\\end{tabularx}\n\n\\end{tcolorbox}\n\n\n\n\n\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"For each model (excluding pre-edited), take the second-best method on Counterfact Specificity. Pick the one whose ZSRE Generalization differs most from its base pre-edited value, and find the difference between the sum of ZSRE and Counterfact Efficacy and the larger of their Specificity scores. Which pair is chosen, and what is the value?"},"answer":{"kind":"string","value":"Qwen2.5-7B + SPHERE, 103.45"},"plan":{"kind":"string","value":"SELECT all models\nLOOP for each model\n COMPUTE rank method rows by counterfact spe descending\n COMPUTE second_best_method = the method row at rank 2\n COMPUTE gen_diff = absolute(zsre gen of second_best_method − zsre gen of the pre-edited)\nCOMPUTE chosen_pair = argmax model and its second_best_method over gen_diff\n\n\nCOMPUTE eff_sum = zsre eff of chosen_pair second_best_method + counterfact eff of chosen_pair second_best_method\nCOMPUTE larger_spe = max of zsre spe of chosen_pair second_best_method and counterfact spe of chosen_pair second_best_method\nCOMPUTE final_value = eff_sum − larger_spe\n\n\nRETURN chosen_pair, final_value\n"}}},{"rowIdx":345,"cells":{"paper":{"kind":"string","value":"2508.10776"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[htbp]\n","\\centering\n","\\caption{Average annualized volatility in each portfolio. All models use $\\delta_{\\text{in}}=21$ days for estimation. Historical: historical covariances with lookback $\\delta_{in}$; EW: Equal-weighted portfolio; LW-D: Ledoit-Wolf shrinkage estimator with diagonal shrinkage target \\cite{LedoitWolf04}; LW-CC: Ledoit-Wolf shrinkage estimator with constant correlation model \\cite{LedoitWolf03}; OAS: Oracle approximating shrinkage \\cite{ChenEtAl10}; PFL: Prediction-focused learning; Ours (DFL): Decision-focused learning (mean and std over 5 seeds). Bold values indicate best performing method.}\n","\\label{tab:avg_ann_vol}\n","\\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{l*{15}{c}}\n","\\toprule\n","& \\multicolumn{5}{c}{S\\&P} & \\multicolumn{5}{c}{Industry} & \\multicolumn{5}{c}{Dow Jones} \\\\\n","\\cmidrule(lr){2-6} \\cmidrule(lr){7-11} \\cmidrule(lr){12-16}\n","Model & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ \\\\\n","\\midrule\n","EW & 0.1489 & 0.1550 & 0.1597 & 0.1611 & 0.1772 & 0.1670 & 0.1732 & 0.1765 & 0.1775 & 0.1917 & 0.1438 & 0.1504 & 0.1558 & 0.1565 & 0.1687 \\\\\n","\\addlinespace\n","Historical & 0.1249 & 0.1382 & 0.1471 & 0.1466 & 0.1416 & 0.1427 & 0.1468 & 0.1601 & 0.1620 & 0.1600 & 0.1531 & 0.1768 & 0.1791 & 0.1858 & 0.1944 \\\\\n","\\addlinespace\n","LW-D & 0.1221 & 0.1334 & 0.1407 & 0.1416 & 0.1401 & 0.1329 & 0.1355 & 0.1435 & 0.1465 & 0.1432 & 0.1252 & 0.1408 & 0.1419 & 0.1520 & 0.1584 \\\\\n","\\addlinespace\n","LW-CC & 0.1289 & 0.1431 & 0.1437 & 0.1495 & 0.1396 & 0.1402 & 0.1503 & 0.1630 & 0.1707 & 0.1648 & 0.1491 & 0.1707 & 0.1777 & 0.1796 & 0.1895 \\\\\n","\\addlinespace\n","OAS & 0.1206 & 0.1317 & 0.1383 & 0.1395 & 0.1399 & 0.1254 & 0.1301 & 0.1364 & 0.1383 & 0.1403 & 0.1219 & 0.1370 & 0.1370 & 0.1433 & 0.1549 \\\\\n","\\midrule\n","PFL & \\begin{tabular}[c]{@{}c@{}}0.1487\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1549\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1595\\\\{\\scriptsize (0.0003)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1607\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1773\\\\{\\scriptsize (0.0007)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1670\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1730\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1764\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1775\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1917\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1438\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1501\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1557\\\\{\\scriptsize (0.0009)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1568\\\\{\\scriptsize (0.0007)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1695\\\\{\\scriptsize (0.0015)}\\end{tabular} \\\\\n","\\addlinespace\n","Ours (DFL) & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1154}\\\\{\\scriptsize (0.0008)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1219}\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1290}\\\\{\\scriptsize (0.0012)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1287}\\\\{\\scriptsize (0.0015)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1319}\\\\{\\scriptsize (0.0013)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1154}\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1223}\\\\{\\scriptsize (0.0009)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1282}\\\\{\\scriptsize (0.0004)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1281}\\\\{\\scriptsize (0.0014)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1379}\\\\{\\scriptsize (0.0017)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1170}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1230}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1277}\\\\{\\scriptsize (0.0004)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1283}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1372}\\\\{\\scriptsize (0.0007)}\\end{tabular} \\\\\n","\\bottomrule\n","\\end{tabular}%\n","}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Average annualized volatility in each portfolio. All models use $\\\\delta_{\\\\text{in}}=21$ days for estimation. Historical: historical covariances with lookback $\\\\delta_{in}$; EW: Equal-weighted portfolio; LW-D: Ledoit-Wolf shrinkage estimator with diagonal shrinkage target \\\\cite{LedoitWolf04}; LW-CC: Ledoit-Wolf shrinkage estimator with constant correlation model \\\\cite{LedoitWolf03}; OAS: Oracle approximating shrinkage \\\\cite{ChenEtAl10}; PFL: Prediction-focused learning; Ours (DFL): Decision-focused learning (mean and std over 5 seeds). Bold values indicate best performing method.}\\n\",\n \"\\\\label{tab:avg_ann_vol}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{l*{15}{c}}\\n\",\n \"\\\\toprule\\n\",\n \"& \\\\multicolumn{5}{c}{S\\\\&P} & \\\\multicolumn{5}{c}{Industry} & \\\\multicolumn{5}{c}{Dow Jones} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-6} \\\\cmidrule(lr){7-11} \\\\cmidrule(lr){12-16}\\n\",\n \"Model & $\\\\delta_{\\\\text{out}}=5$ & $\\\\delta_{\\\\text{out}}=21$ & $\\\\delta_{\\\\text{out}}=63$ & $\\\\delta_{\\\\text{out}}=126$ & $\\\\delta_{\\\\text{out}}=252$ & $\\\\delta_{\\\\text{out}}=5$ & $\\\\delta_{\\\\text{out}}=21$ & $\\\\delta_{\\\\text{out}}=63$ & $\\\\delta_{\\\\text{out}}=126$ & $\\\\delta_{\\\\text{out}}=252$ & $\\\\delta_{\\\\text{out}}=5$ & $\\\\delta_{\\\\text{out}}=21$ & $\\\\delta_{\\\\text{out}}=63$ & $\\\\delta_{\\\\text{out}}=126$ & $\\\\delta_{\\\\text{out}}=252$ \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"EW & 0.1489 & 0.1550 & 0.1597 & 0.1611 & 0.1772 & 0.1670 & 0.1732 & 0.1765 & 0.1775 & 0.1917 & 0.1438 & 0.1504 & 0.1558 & 0.1565 & 0.1687 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"Historical & 0.1249 & 0.1382 & 0.1471 & 0.1466 & 0.1416 & 0.1427 & 0.1468 & 0.1601 & 0.1620 & 0.1600 & 0.1531 & 0.1768 & 0.1791 & 0.1858 & 0.1944 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"LW-D & 0.1221 & 0.1334 & 0.1407 & 0.1416 & 0.1401 & 0.1329 & 0.1355 & 0.1435 & 0.1465 & 0.1432 & 0.1252 & 0.1408 & 0.1419 & 0.1520 & 0.1584 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"LW-CC & 0.1289 & 0.1431 & 0.1437 & 0.1495 & 0.1396 & 0.1402 & 0.1503 & 0.1630 & 0.1707 & 0.1648 & 0.1491 & 0.1707 & 0.1777 & 0.1796 & 0.1895 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"OAS & 0.1206 & 0.1317 & 0.1383 & 0.1395 & 0.1399 & 0.1254 & 0.1301 & 0.1364 & 0.1383 & 0.1403 & 0.1219 & 0.1370 & 0.1370 & 0.1433 & 0.1549 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"PFL & \\\\begin{tabular}[c]{@{}c@{}}0.1487\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1549\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1595\\\\\\\\{\\\\scriptsize (0.0003)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1607\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1773\\\\\\\\{\\\\scriptsize (0.0007)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1670\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1730\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1764\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1775\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1917\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1438\\\\\\\\{\\\\scriptsize (0.0006)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1501\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1557\\\\\\\\{\\\\scriptsize (0.0009)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1568\\\\\\\\{\\\\scriptsize (0.0007)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1695\\\\\\\\{\\\\scriptsize (0.0015)}\\\\end{tabular} \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"Ours (DFL) & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1154}\\\\\\\\{\\\\scriptsize (0.0008)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1219}\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1290}\\\\\\\\{\\\\scriptsize (0.0012)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1287}\\\\\\\\{\\\\scriptsize (0.0015)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1319}\\\\\\\\{\\\\scriptsize (0.0013)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1154}\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1223}\\\\\\\\{\\\\scriptsize (0.0009)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1282}\\\\\\\\{\\\\scriptsize (0.0004)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1281}\\\\\\\\{\\\\scriptsize (0.0014)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1379}\\\\\\\\{\\\\scriptsize (0.0017)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1170}\\\\\\\\{\\\\scriptsize (0.0006)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1230}\\\\\\\\{\\\\scriptsize (0.0006)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1277}\\\\\\\\{\\\\scriptsize (0.0004)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1283}\\\\\\\\{\\\\scriptsize (0.0006)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1372}\\\\\\\\{\\\\scriptsize (0.0007)}\\\\end{tabular} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}%\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{Figure/overview.pdf}\n"," \\caption{DFL framework for GMVP construction. Historical returns of N assets are processed by DLinear to predict covariance matrix $\\Sigma$. The GMVP optimization layer computes portfolio weights $w^*$ using the closed form solution, and the regret loss is applied to minimize the gap between predicted and optimal portfolio volatility for end-to-end training.}\n"," \\Description{model architecture}\n"," \\label{fig:overview}\n","\\end{figure*}\n"],["\\begin{table*}[htbp]\n","\\centering\n","\\caption{Average annualized volatility in each portfolio. All models use $\\delta_{\\text{in}}=21$ days for estimation. Historical: historical covariances with lookback $\\delta_{in}$; EW: Equal-weighted portfolio; LW-D: Ledoit-Wolf shrinkage estimator with diagonal shrinkage target \\cite{LedoitWolf04}; LW-CC: Ledoit-Wolf shrinkage estimator with constant correlation model \\cite{LedoitWolf03}; OAS: Oracle approximating shrinkage \\cite{ChenEtAl10}; PFL: Prediction-focused learning; Ours (DFL): Decision-focused learning (mean and std over 5 seeds). Bold values indicate best performing method.}\n","\\label{tab:avg_ann_vol}\n","\\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{l*{15}{c}}\n","\\toprule\n","& \\multicolumn{5}{c}{S\\&P} & \\multicolumn{5}{c}{Industry} & \\multicolumn{5}{c}{Dow Jones} \\\\\n","\\cmidrule(lr){2-6} \\cmidrule(lr){7-11} \\cmidrule(lr){12-16}\n","Model & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ \\\\\n","\\midrule\n","EW & 0.1489 & 0.1550 & 0.1597 & 0.1611 & 0.1772 & 0.1670 & 0.1732 & 0.1765 & 0.1775 & 0.1917 & 0.1438 & 0.1504 & 0.1558 & 0.1565 & 0.1687 \\\\\n","\\addlinespace\n","Historical & 0.1249 & 0.1382 & 0.1471 & 0.1466 & 0.1416 & 0.1427 & 0.1468 & 0.1601 & 0.1620 & 0.1600 & 0.1531 & 0.1768 & 0.1791 & 0.1858 & 0.1944 \\\\\n","\\addlinespace\n","LW-D & 0.1221 & 0.1334 & 0.1407 & 0.1416 & 0.1401 & 0.1329 & 0.1355 & 0.1435 & 0.1465 & 0.1432 & 0.1252 & 0.1408 & 0.1419 & 0.1520 & 0.1584 \\\\\n","\\addlinespace\n","LW-CC & 0.1289 & 0.1431 & 0.1437 & 0.1495 & 0.1396 & 0.1402 & 0.1503 & 0.1630 & 0.1707 & 0.1648 & 0.1491 & 0.1707 & 0.1777 & 0.1796 & 0.1895 \\\\\n","\\addlinespace\n","OAS & 0.1206 & 0.1317 & 0.1383 & 0.1395 & 0.1399 & 0.1254 & 0.1301 & 0.1364 & 0.1383 & 0.1403 & 0.1219 & 0.1370 & 0.1370 & 0.1433 & 0.1549 \\\\\n","\\midrule\n","PFL & \\begin{tabular}[c]{@{}c@{}}0.1487\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1549\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1595\\\\{\\scriptsize (0.0003)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1607\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1773\\\\{\\scriptsize (0.0007)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1670\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1730\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1764\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1775\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1917\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1438\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1501\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1557\\\\{\\scriptsize (0.0009)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1568\\\\{\\scriptsize (0.0007)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1695\\\\{\\scriptsize (0.0015)}\\end{tabular} \\\\\n","\\addlinespace\n","Ours (DFL) & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1154}\\\\{\\scriptsize (0.0008)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1219}\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1290}\\\\{\\scriptsize (0.0012)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1287}\\\\{\\scriptsize (0.0015)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1319}\\\\{\\scriptsize (0.0013)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1154}\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1223}\\\\{\\scriptsize (0.0009)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1282}\\\\{\\scriptsize (0.0004)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1281}\\\\{\\scriptsize (0.0014)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1379}\\\\{\\scriptsize (0.0017)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1170}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1230}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1277}\\\\{\\scriptsize (0.0004)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1283}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1372}\\\\{\\scriptsize (0.0007)}\\end{tabular} \\\\\n","\\bottomrule\n","\\end{tabular}%\n","}\n","\\end{table*}\n"],["\\begin{figure}[h]\n"," \\centering\n"," \\includegraphics[width=0.88\\columnwidth]{Figure/rolling.pdf}\n"," \\caption{Rolling window approach for time series validation. Train/valid sets use one-day rolling windows, while the test set employs $\\delta_{out}$-days rolling predictions.}\n"," \\Description{Ann vol plot}\n"," \\label{fig:rolling}\n","\\end{figure}\n"],["\\begin{table}[ht]\n"," \\centering\n"," \\small\n"," \\caption{Hyperparameter settings in (\\text{learning rate}, \\text{batch}) pairs for varying $\\delta_{in}$ and $\\delta_{out}$}\n"," \\label{tab:delta}\n"," \\begin{tabular}{c|ccccc}\n"," \\toprule\n"," & \\multicolumn{5}{c}{$\\delta_{in}$} \\\\\n"," \\cmidrule(lr){2-6}\n"," $\\delta_{out}$ \n"," & 5 & 21 & 63 & 126 & 252 \\\\\n"," \\midrule\n"," 5 & ($10^{-4}$,\\,64) & ($10^{-5}$,\\,16) & ($10^{-4}$,\\,16) & ($10^{-4}$,\\,32) & ($10^{-5}$,\\,16) \\\\\n"," 21 & ($10^{-5}$,\\,32) & ($10^{-5}$,\\,16) & ($10^{-5}$,\\,64) & ($10^{-4}$,\\,32) & ($10^{-4}$,\\,32) \\\\\n"," 63 & ($10^{-4}$,\\,64) & ($10^{-4}$,\\,32) & ($10^{-4}$,\\,64) & ($10^{-4}$,\\,64) & ($10^{-4}$,\\,32) \\\\\n"," 126 & ($10^{-5}$,\\,64) & ($10^{-4}$,\\,32) & ($10^{-4}$,\\,64) & ($10^{-4}$,\\,64) & ($10^{-5}$,\\,16) \\\\\n"," 252 & ($10^{-3}$,\\,32) & ($10^{-5}$,\\,16) & ($10^{-3}$,\\,16) & ($10^{-4}$,\\,16) & ($10^{-5}$,\\,16) \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," \\label{table:hyperparameters}\n","\\end{table}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=0.9\\textwidth]{Figure/ann_vol.pdf}\n"," \\caption{Annualized volatility of each model's portfolio with $\\delta_{in}=\\delta_{out}=21$ from the left to the right, respectively.}\n"," \\Description{Ann vol plot}\n"," \\label{fig:ann_vol}\n","\\end{figure*}\n"],["\\begin{figure}[htbp]\n"," \\vspace{-0.2cm}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figure/ew_pfl_dfl.pdf}\n"," \\caption{Average portfolio weights in the Industry portfolio dataset during whole test period with $\\delta_{in}=\\delta_{out}=21$.}\n"," \\Description{model architecture}\n"," \\label{fig:ew_pfl}\n"," \\vspace{-0.2cm}\n","\\end{figure}\n"],["\\begin{figure}[h]\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figure/delta.pdf}\n"," \\caption{Annualized volatility of DFL when $\\delta_{in}$ and $\\delta_{out}$ have different values in the Industry dataset. We set $\\delta_{in}, \\delta_{out}\\in \\{5,21,63,126,252\\}$.}\n"," \\Description{Ann vol plot}\n"," \\label{fig:delta_ablation}\n","\\end{figure}\n"],["\\begin{figure*}[h]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{Figure/bbc_combined.pdf}\n"," \\caption{Precision matrix derived by DFL and OAS for single test period in the Industry dataset (left), Average of the permuted precision matrix estimated by DFL and OAS for the entire test period in the Industry dataset (middle), Average and standard deviation of GMVP weights in the reordered index for the entire test period in the Industry dataset (right).}\n"," \\Description{bbc reorder}\n"," \\label{fig:reordered precision}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=0.9\\textwidth]{Figure/covariance_weight.pdf}\n"," \\caption{Average true covariance matrix over the test period in the Industry dataset, with assets ordered by descending portfolio weight for DFL (left), LW‑D (center) and OAS (right). The yellow line denotes zero weight: entries to its left or above correspond to positively weighted assets, and those to its right or below to negatively weighted assets. Area \\ding{192}: covariance of positively weighted stocks; area \\ding{193}: covariance of stocks with mixed weights; area \\ding{194}: covariance of negatively weighted stocks. We displayed up to the maximum off-diagonal value, and values exceeding it are displayed in black.}\n"," \\label{fig:weight_cov}\n","\\end{figure*}\n"],["\\begin{figure}[h]\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figure/dfl_cl.pdf}\n"," \\caption{Portfolio weights by the models in whole test period in the Industry dataset. Stock is sorted by the quantity of median weight from DFL. The line indicates median weights of each model and area with same color illustrates one by eliminating weights which are over 97.5 percentile or under 2.5 percentile of whole weights in test period.}\n"," \\Description{Ann vol plot}\n"," \\label{fig:weight_median_percentile}\n","\\end{figure}\n"],["\\begin{table}[htbp]\n","\\centering\n","\\caption{Average precision between top-k volatility rankings (ascending) in training Period and top-k portfolio weight rankings (descending) in test period. Values with the best performances are illustrated in bold.}\n","\\label{tab:volatility_precision}\n","\\begin{tabular}{l|cc|cc|cc}\n","\\hline\n","\\multirow{2}{*}{Model} & \\multicolumn{2}{c|}{S\\&P 100} & \\multicolumn{2}{c|}{49 Industry} & \\multicolumn{2}{c}{Dow 30} \\\\\n","\\cline{2-7}\n"," & Top 3 & Top 5 & Top 3 & Top 5 & Top 3 & Top 5 \\\\\n","\\hline \n","DFL & \\textbf{0.6250} & \\textbf{0.7812} & \\textbf{0.6667} & \\textbf{0.5000} & \\textbf{1.0000} & \\textbf{0.8000} \\\\\n","OAS & 0.0417 & 0.0813 & 0.1562 & 0.2375 & 0.4271 & 0.5438 \\\\\n","PFL & 0.0208 & 0.0563 & 0.0833 & 0.0688 & 0.2083 & 0.4062 \\\\\n","\\hline\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{figure}[!htbp]\n"," \\centering\n"," \\includegraphics[width=0.95\\linewidth]{Figure/ew_pfl_dfl_appendix.pdf}\n"," \\caption{Average portfolio weights in the S\\&P and Dow Jones dataset during the test period with $\\delta_{in} = \\delta_{out} = 21$.}\n"," \\label{fig:ew_pfl_appendix}\n","\\end{figure}\n"],["\\begin{figure}[!htbp]\n"," \\centering\n"," \\includegraphics[width=0.95\\linewidth]{Figure/bbc_combined_appendix.pdf}\n"," \\caption{Precision matrix derived by DFL and OAS for single test period (left), average precision matrices reordered by BBC algorithm (middle), and weight distributions (right) for S\\&P and Dow Jones datasets.}\n"," \\label{fig:reordered precision_appendix}\n","\\end{figure}\n"],["\\begin{figure}[!htbp]\n"," \\centering\n"," \\includegraphics[width=0.90\\linewidth]{Figure/covariance_weight_appendix.pdf}\n"," \\caption{Average true covariance matrix over the test period in the Industry dataset, with assets ordered by descending portfolio weight for DFL (left), LW- D (center) and OAS (right) in S\\&P 500 and Dow Jones datasets.}\n"," \\label{fig:weight_cov_appendix}\n","\\end{figure}\n"],["\\begin{figure}[!htbp]\n"," \\centering\n"," \\includegraphics[width=0.90\\linewidth]{Figure/dfl_cl_appendix.pdf}\n"," \\caption{\n"," Portfolio weights by different models in the test period for S\\&P 500 and Dow Jones datasets. Stock indices are sorted by the quantity of median weight from DFL. Lines indicate median weights and shaded areas illustrate one by eliminating weights which are over 97.5 percentile or under 2.5 percentile of whole weights in test period.}\n"," \\label{fig:weight_median_percentile_appendix}\n","\\end{figure}\n"]],"string":"[\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{Figure/overview.pdf}\\n\",\n \" \\\\caption{DFL framework for GMVP construction. Historical returns of N assets are processed by DLinear to predict covariance matrix $\\\\Sigma$. The GMVP optimization layer computes portfolio weights $w^*$ using the closed form solution, and the regret loss is applied to minimize the gap between predicted and optimal portfolio volatility for end-to-end training.}\\n\",\n \" \\\\Description{model architecture}\\n\",\n \" \\\\label{fig:overview}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Average annualized volatility in each portfolio. All models use $\\\\delta_{\\\\text{in}}=21$ days for estimation. Historical: historical covariances with lookback $\\\\delta_{in}$; EW: Equal-weighted portfolio; LW-D: Ledoit-Wolf shrinkage estimator with diagonal shrinkage target \\\\cite{LedoitWolf04}; LW-CC: Ledoit-Wolf shrinkage estimator with constant correlation model \\\\cite{LedoitWolf03}; OAS: Oracle approximating shrinkage \\\\cite{ChenEtAl10}; PFL: Prediction-focused learning; Ours (DFL): Decision-focused learning (mean and std over 5 seeds). Bold values indicate best performing method.}\\n\",\n \"\\\\label{tab:avg_ann_vol}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{l*{15}{c}}\\n\",\n \"\\\\toprule\\n\",\n \"& \\\\multicolumn{5}{c}{S\\\\&P} & \\\\multicolumn{5}{c}{Industry} & \\\\multicolumn{5}{c}{Dow Jones} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-6} \\\\cmidrule(lr){7-11} \\\\cmidrule(lr){12-16}\\n\",\n \"Model & $\\\\delta_{\\\\text{out}}=5$ & $\\\\delta_{\\\\text{out}}=21$ & $\\\\delta_{\\\\text{out}}=63$ & $\\\\delta_{\\\\text{out}}=126$ & $\\\\delta_{\\\\text{out}}=252$ & $\\\\delta_{\\\\text{out}}=5$ & $\\\\delta_{\\\\text{out}}=21$ & $\\\\delta_{\\\\text{out}}=63$ & $\\\\delta_{\\\\text{out}}=126$ & $\\\\delta_{\\\\text{out}}=252$ & $\\\\delta_{\\\\text{out}}=5$ & $\\\\delta_{\\\\text{out}}=21$ & $\\\\delta_{\\\\text{out}}=63$ & $\\\\delta_{\\\\text{out}}=126$ & $\\\\delta_{\\\\text{out}}=252$ \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"EW & 0.1489 & 0.1550 & 0.1597 & 0.1611 & 0.1772 & 0.1670 & 0.1732 & 0.1765 & 0.1775 & 0.1917 & 0.1438 & 0.1504 & 0.1558 & 0.1565 & 0.1687 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"Historical & 0.1249 & 0.1382 & 0.1471 & 0.1466 & 0.1416 & 0.1427 & 0.1468 & 0.1601 & 0.1620 & 0.1600 & 0.1531 & 0.1768 & 0.1791 & 0.1858 & 0.1944 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"LW-D & 0.1221 & 0.1334 & 0.1407 & 0.1416 & 0.1401 & 0.1329 & 0.1355 & 0.1435 & 0.1465 & 0.1432 & 0.1252 & 0.1408 & 0.1419 & 0.1520 & 0.1584 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"LW-CC & 0.1289 & 0.1431 & 0.1437 & 0.1495 & 0.1396 & 0.1402 & 0.1503 & 0.1630 & 0.1707 & 0.1648 & 0.1491 & 0.1707 & 0.1777 & 0.1796 & 0.1895 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"OAS & 0.1206 & 0.1317 & 0.1383 & 0.1395 & 0.1399 & 0.1254 & 0.1301 & 0.1364 & 0.1383 & 0.1403 & 0.1219 & 0.1370 & 0.1370 & 0.1433 & 0.1549 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"PFL & \\\\begin{tabular}[c]{@{}c@{}}0.1487\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1549\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1595\\\\\\\\{\\\\scriptsize (0.0003)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1607\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1773\\\\\\\\{\\\\scriptsize (0.0007)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1670\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1730\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1764\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1775\\\\\\\\{\\\\scriptsize (0.0002)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1917\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1438\\\\\\\\{\\\\scriptsize (0.0006)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1501\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1557\\\\\\\\{\\\\scriptsize (0.0009)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1568\\\\\\\\{\\\\scriptsize (0.0007)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}0.1695\\\\\\\\{\\\\scriptsize (0.0015)}\\\\end{tabular} \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"Ours (DFL) & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1154}\\\\\\\\{\\\\scriptsize (0.0008)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1219}\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1290}\\\\\\\\{\\\\scriptsize (0.0012)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1287}\\\\\\\\{\\\\scriptsize (0.0015)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1319}\\\\\\\\{\\\\scriptsize (0.0013)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1154}\\\\\\\\{\\\\scriptsize (0.0005)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1223}\\\\\\\\{\\\\scriptsize (0.0009)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1282}\\\\\\\\{\\\\scriptsize (0.0004)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1281}\\\\\\\\{\\\\scriptsize (0.0014)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1379}\\\\\\\\{\\\\scriptsize (0.0017)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1170}\\\\\\\\{\\\\scriptsize (0.0006)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1230}\\\\\\\\{\\\\scriptsize (0.0006)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1277}\\\\\\\\{\\\\scriptsize (0.0004)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1283}\\\\\\\\{\\\\scriptsize (0.0006)}\\\\end{tabular} & \\\\begin{tabular}[c]{@{}c@{}}\\\\textbf{0.1372}\\\\\\\\{\\\\scriptsize (0.0007)}\\\\end{tabular} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}%\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.88\\\\columnwidth]{Figure/rolling.pdf}\\n\",\n \" \\\\caption{Rolling window approach for time series validation. Train/valid sets use one-day rolling windows, while the test set employs $\\\\delta_{out}$-days rolling predictions.}\\n\",\n \" \\\\Description{Ann vol plot}\\n\",\n \" \\\\label{fig:rolling}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\caption{Hyperparameter settings in (\\\\text{learning rate}, \\\\text{batch}) pairs for varying $\\\\delta_{in}$ and $\\\\delta_{out}$}\\n\",\n \" \\\\label{tab:delta}\\n\",\n \" \\\\begin{tabular}{c|ccccc}\\n\",\n \" \\\\toprule\\n\",\n \" & \\\\multicolumn{5}{c}{$\\\\delta_{in}$} \\\\\\\\\\n\",\n \" \\\\cmidrule(lr){2-6}\\n\",\n \" $\\\\delta_{out}$ \\n\",\n \" & 5 & 21 & 63 & 126 & 252 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" 5 & ($10^{-4}$,\\\\,64) & ($10^{-5}$,\\\\,16) & ($10^{-4}$,\\\\,16) & ($10^{-4}$,\\\\,32) & ($10^{-5}$,\\\\,16) \\\\\\\\\\n\",\n \" 21 & ($10^{-5}$,\\\\,32) & ($10^{-5}$,\\\\,16) & ($10^{-5}$,\\\\,64) & ($10^{-4}$,\\\\,32) & ($10^{-4}$,\\\\,32) \\\\\\\\\\n\",\n \" 63 & ($10^{-4}$,\\\\,64) & ($10^{-4}$,\\\\,32) & ($10^{-4}$,\\\\,64) & ($10^{-4}$,\\\\,64) & ($10^{-4}$,\\\\,32) \\\\\\\\\\n\",\n \" 126 & ($10^{-5}$,\\\\,64) & ($10^{-4}$,\\\\,32) & ($10^{-4}$,\\\\,64) & ($10^{-4}$,\\\\,64) & ($10^{-5}$,\\\\,16) \\\\\\\\\\n\",\n \" 252 & ($10^{-3}$,\\\\,32) & ($10^{-5}$,\\\\,16) & ($10^{-3}$,\\\\,16) & ($10^{-4}$,\\\\,16) & ($10^{-5}$,\\\\,16) \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\label{table:hyperparameters}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.9\\\\textwidth]{Figure/ann_vol.pdf}\\n\",\n \" \\\\caption{Annualized volatility of each model's portfolio with $\\\\delta_{in}=\\\\delta_{out}=21$ from the left to the right, respectively.}\\n\",\n \" \\\\Description{Ann vol plot}\\n\",\n \" \\\\label{fig:ann_vol}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\vspace{-0.2cm}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figure/ew_pfl_dfl.pdf}\\n\",\n \" \\\\caption{Average portfolio weights in the Industry portfolio dataset during whole test period with $\\\\delta_{in}=\\\\delta_{out}=21$.}\\n\",\n \" \\\\Description{model architecture}\\n\",\n \" \\\\label{fig:ew_pfl}\\n\",\n \" \\\\vspace{-0.2cm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figure/delta.pdf}\\n\",\n \" \\\\caption{Annualized volatility of DFL when $\\\\delta_{in}$ and $\\\\delta_{out}$ have different values in the Industry dataset. We set $\\\\delta_{in}, \\\\delta_{out}\\\\in \\\\{5,21,63,126,252\\\\}$.}\\n\",\n \" \\\\Description{Ann vol plot}\\n\",\n \" \\\\label{fig:delta_ablation}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{Figure/bbc_combined.pdf}\\n\",\n \" \\\\caption{Precision matrix derived by DFL and OAS for single test period in the Industry dataset (left), Average of the permuted precision matrix estimated by DFL and OAS for the entire test period in the Industry dataset (middle), Average and standard deviation of GMVP weights in the reordered index for the entire test period in the Industry dataset (right).}\\n\",\n \" \\\\Description{bbc reorder}\\n\",\n \" \\\\label{fig:reordered precision}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.9\\\\textwidth]{Figure/covariance_weight.pdf}\\n\",\n \" \\\\caption{Average true covariance matrix over the test period in the Industry dataset, with assets ordered by descending portfolio weight for DFL (left), LW‑D (center) and OAS (right). The yellow line denotes zero weight: entries to its left or above correspond to positively weighted assets, and those to its right or below to negatively weighted assets. Area \\\\ding{192}: covariance of positively weighted stocks; area \\\\ding{193}: covariance of stocks with mixed weights; area \\\\ding{194}: covariance of negatively weighted stocks. We displayed up to the maximum off-diagonal value, and values exceeding it are displayed in black.}\\n\",\n \" \\\\label{fig:weight_cov}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figure/dfl_cl.pdf}\\n\",\n \" \\\\caption{Portfolio weights by the models in whole test period in the Industry dataset. Stock is sorted by the quantity of median weight from DFL. The line indicates median weights of each model and area with same color illustrates one by eliminating weights which are over 97.5 percentile or under 2.5 percentile of whole weights in test period.}\\n\",\n \" \\\\Description{Ann vol plot}\\n\",\n \" \\\\label{fig:weight_median_percentile}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Average precision between top-k volatility rankings (ascending) in training Period and top-k portfolio weight rankings (descending) in test period. Values with the best performances are illustrated in bold.}\\n\",\n \"\\\\label{tab:volatility_precision}\\n\",\n \"\\\\begin{tabular}{l|cc|cc|cc}\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{2}{*}{Model} & \\\\multicolumn{2}{c|}{S\\\\&P 100} & \\\\multicolumn{2}{c|}{49 Industry} & \\\\multicolumn{2}{c}{Dow 30} \\\\\\\\\\n\",\n \"\\\\cline{2-7}\\n\",\n \" & Top 3 & Top 5 & Top 3 & Top 5 & Top 3 & Top 5 \\\\\\\\\\n\",\n \"\\\\hline \\n\",\n \"DFL & \\\\textbf{0.6250} & \\\\textbf{0.7812} & \\\\textbf{0.6667} & \\\\textbf{0.5000} & \\\\textbf{1.0000} & \\\\textbf{0.8000} \\\\\\\\\\n\",\n \"OAS & 0.0417 & 0.0813 & 0.1562 & 0.2375 & 0.4271 & 0.5438 \\\\\\\\\\n\",\n \"PFL & 0.0208 & 0.0563 & 0.0833 & 0.0688 & 0.2083 & 0.4062 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[!htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.95\\\\linewidth]{Figure/ew_pfl_dfl_appendix.pdf}\\n\",\n \" \\\\caption{Average portfolio weights in the S\\\\&P and Dow Jones dataset during the test period with $\\\\delta_{in} = \\\\delta_{out} = 21$.}\\n\",\n \" \\\\label{fig:ew_pfl_appendix}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.95\\\\linewidth]{Figure/bbc_combined_appendix.pdf}\\n\",\n \" \\\\caption{Precision matrix derived by DFL and OAS for single test period (left), average precision matrices reordered by BBC algorithm (middle), and weight distributions (right) for S\\\\&P and Dow Jones datasets.}\\n\",\n \" \\\\label{fig:reordered precision_appendix}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.90\\\\linewidth]{Figure/covariance_weight_appendix.pdf}\\n\",\n \" \\\\caption{Average true covariance matrix over the test period in the Industry dataset, with assets ordered by descending portfolio weight for DFL (left), LW- D (center) and OAS (right) in S\\\\&P 500 and Dow Jones datasets.}\\n\",\n \" \\\\label{fig:weight_cov_appendix}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.90\\\\linewidth]{Figure/dfl_cl_appendix.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Portfolio weights by different models in the test period for S\\\\&P 500 and Dow Jones datasets. Stock indices are sorted by the quantity of median weight from DFL. Lines indicate median weights and shaded areas illustrate one by eliminating weights which are over 97.5 percentile or under 2.5 percentile of whole weights in test period.}\\n\",\n \" \\\\label{fig:weight_median_percentile_appendix}\\n\",\n \"\\\\end{figure}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\documentclass[sigconf,nonacm]{acmart} %authordraft, review,\n\\usepackage{framed}\n\\usepackage{amsthm}\n\\usepackage{booktabs}\n\\usepackage{multirow}\n\\usepackage{pifont}\n\\usepackage{etoolbox}\n\\usepackage[ruled,vlined]{algorithm2e}\n\\usepackage{float} % H 옵션 사용 가능\n\\usepackage{placeins} % \\FloatBarrier 명령어 사용\n\n\\newtheorem{proposition}{Proposition}\n\\setlength{\\FrameRule}{0.8pt} % 테두리 두께 (기본 0.4pt)\n\\setlength{\\FrameSep}{2pt} % 내부 여백\n\\AtBeginDocument{%\n \\providecommand\\BibTeX{{%\n Bib\\TeX}}}\n\n \n%\\setcopyright{acmlicensed}\n%\\copyrightyear{2025}\n%\\acmYear{2025}\n%\\acmDOI{XXXXXXX.XXXXXXX}\n%\\acmConference[ICAIF '25]{6th ACM International Conference on AI in Finance}{November 15--18, 2025}{Singapore}\n%\\acmBooktitle{November 15--18, 2025, Singapore}\n%\\acmISBN{978-1-4503-XXXX-X/2018/06}\n\n\\begin{document}\n\\title{Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach}\n\n\\author{Juchan Kim}\n\\authornote{Both authors contributed equally to this research.}\n\\email{joc6021@unist.ac.kr}\n\\affiliation{%\n \\institution{Ulsan National Institute of Science and Technology}\n \\city{Ulsan}\n \\country{Republic of Korea}\n}\n\n\\author{Inwoo Tae}\n\\authornotemark[1]\n\\email{vitainu0104@unist.ac.kr}\n\\affiliation{%\n \\institution{Ulsan National Institute of Science and Technology}\n \\city{Ulsan}\n \\country{Republic of Korea}\n }\n\n \\author{Yongjae Lee}\n \\authornote{Corresponding Author}\n \\email{yongjaelee@unist.ac.kr}\n \\affiliation{%\n \\institution{Ulsan National Institute of Science and Technology}\n \\city{Ulsan}\n \\country{Republic of Korea}\n }\n\n\\renewcommand{\\shortauthors}{Kim et al.}\n\n\\begin{abstract}\n\n\n%Portfolio optimization is a fundamental theory of risk management. It allows for the quantification of risk and return, but relies heavily on parameter estimation due to future uncertainty. Therefore, estimating appropriate parameters for portfolio optimization is important, but most statistical estimators and machine learning-based methods obtain them by minimizing mean-squared error (MSE), which leads to sub-optimal decisions. \n\nPortfolio optimization constitutes a cornerstone of risk management by quantifying the risk-return trade-off.\nSince it inherently depends on accurate parameter estimation under conditions of future uncertainty, the selection of appropriate input parameters is critical for effective portfolio construction. However, most conventional statistical estimators and machine learning algorithms determine these parameters by minimizing mean‐squared error (MSE), a criterion that can yield suboptimal investment decisions. \n\n%In this paper, we utilize decision-focused learning (DFL), a learning method that considers decision-making instead of MSE, to obtain the global minimum variance portfolio(GMVP). We experimentally demonstrate that MSE-based learning and estimation may not be optimal in actual decision-making and confirm that DFL-based methods perform better in decision-making. Moreover, we suggest how DFL works to minimize the out-of sample volatility and properties of its decision attributing performance and analyzing the estimation.Our research provides strong evidence for the potential application of DFL in the financial field where the decision-making is central.\n\n% 초록만 보면 이론적으로 모델을 만들어서 분석하는 것에 대한 장점은 하나도 언급이 안되어있고, 그냥 일반적인 DFL 모델 도입처럼 보입니다. 이론적으로 derive해서 DFL의 학습의 어려움을 좀 극복했다던가, theoretical한 insight를 얻을 수 있다던가 이런 장점을 초록과 intro, conclusion에 강조해야 할 듯 합니다.\n\nIn this paper, we adopt decision‐focused learning (DFL)—an approach that directly optimizes decision quality rather than prediction error such as MSE—to derive the global minimum‐variance portfolio (GMVP). \nSpecifically, we theoretically derive the gradient of decision loss using the analytic solution of GMVP and its properties regarding the principal components of itself.\nThrough extensive empirical evaluation, we show that prediction-focused estimation methods may fail to produce optimal allocations in practice, whereas DFL‐based methods consistently deliver superior decision performance. \nFurthermore, we provide a comprehensive analysis of DFL's mechanism in GMVP construction, focusing on its volatility reduction capability, decision-driving features, and estimation characteristics.\n\n\n%Our findings provide compelling evidence for the efficacy of DFL in financial applications where decision‐making accuracy is paramount.\n\\end{abstract}\n\n\\begin{CCSXML}\n<ccs2012>\n <concept>\n <concept_id>10010147.10010178</concept_id>\n <concept_desc>Computing methodologies~Artificial intelligence</concept_desc>\n <concept_significance>500</concept_significance>\n </concept>\n </ccs2012>\n\\end{CCSXML}\n\n\\ccsdesc[500]{Computing methodologies~Artificial intelligence}\n\\keywords{Portfolio Optimization, Global Minimum Variance Portfolio, Decision-Focused Learning}\n\\maketitle\n\n\\section{Introduction}\n% Markowitz's pioneering research devised mean-variance optimization (MVO)\\cite{Markowitz52}, which quantifies risk and return and balances them, and it became the cornerstone of modern portfolio theory. Practical way to set parameters in MVO is setting them derived by in-sample period, assuming the stationarity of return such that they remain their statistical properties. Since parameters of in-sample and out-of-sample are totally different, however, MVO relies heavily on parameter estimation. \\cite{Klein76} Moreover, there were several empirical evidences where mean-variance framework with estimated parameters in sample under-perform naive diversifiaction strategy(i.e. equally weighted portfolio), which indicates that estimating parameters in MVO appropriately is an challenging task. \\cite{DeMiguel09}\n\nMarkowitz’s seminal work introduced mean–variance optimization (MVO) \\cite{Markowitz52}, which provides a quantitative framework for balancing risk and return and has since become modern portfolio theory's foundation. The most important part in MVO is parameter estimation, due to its high sensitivity \\cite{Klein76}. \nPractically, MVO parameters are typically calibrated using an in‐sample period under the assumption of return stationarity, which results in poor performances because the distribution underlying the in‑sample and out‑of‑sample periods often differs. \nEmpirical studies have shown that MVO portfolios constructed with estimated parameters can underperform naïve diversification strategies like the equally weighted portfolio, highlighting appropriate parameter estimation \\cite{DeMiguel09}. \n\n% Global minimum variance portfolios (GMVP), which are independent of expected returns, have also been studied in several works. For instances, GMVP empirically shows great out-of sample performances on return than one of market-cap weighted portfolio \\cite{Clarke06,Clarke11}, as well as on low-volatility \\cite{Bongiorno23}. Meanwhile, since GMVP can be obtained by estimating covariances, which is not restricted by estimation of expected returns, It only depends on single parameter though MVO needs estimating both expected returns and covariances. In the process of estimating the two parameters of MVO, several studies have reported that the estimation accuracy of covariance is higher than that of expected return \\cite{Merton80}, but the sensitivity to estimation error is heavily affected by that of expected return \\cite{Best91, Chopra93}. To sum up, GMVP has advantage of (1) \\textbf{huge academical impress} comparative with MVO, (2) \\textbf{estimating parameters} and (3) \\textbf{sensitivity for parameter estimation}.\n\nGlobal minimum‐variance portfolio (GMVP) constitutes the least risky portfolio in the efficient frontier, therefore it inherits a key for understanding the modern portfolio theory.\nSince GMVP depends solely on the covariance matrix, not on expected returns, its parameter uncertainty becomes much lower than in the MVO framework. \nMoreover, empirical evidence indicates that GMVPs often achieve superior out‐of‐sample return performance compared to market‐cap‐weighted benchmarks \\cite{Clarke06,Clarke11} and exhibit lower realized volatility \\cite{Bongiorno23}. Because GMVP construction requires estimating only covariances—unlike MVO, which requires both expected returns and covariances—it reduces the dimensionality of the estimation problem. Moreover, while covariance estimators generally achieve higher accuracy than return forecasts \\cite{Merton80}, the overall decision quality in MVO remains dominated by errors in expected‐return estimates \\cite{Best91,Chopra93}. In summary, GMVPs offer three key advantages over MVO: (1) strong theoretical and empirical support, (2) reduced parameter‐estimation requirements, and (3) decreased sensitivity to estimation error. \n\n% To estimate covariance in GMVP, several studies are employed to derive superior out-of sample performances, especially targeted to volatility \\cite{Frahm10,Bongiorno23}. Since the advent of deep learning, prediction models for covariance have also been studied \\cite{Petrozziello22} based on their universal approximation and nonlinear expressive power based on the past information, which is called prediction-focused learning (PFL). Most of them are trained by designated objective function, such as mean squared error(MSE), to minimize estimation error in predictions, then optimize the portfolio using them, which is called predict-then-optimize scheme \\cite{lee2024overview}.\n\nTo enhance out‐of‐sample performance—particularly in terms of volatility—several studies have proposed advanced covariance‐estimation for GMVPs \\cite{Frahm10,Bongiorno23}. More recently, deep‐learning models have been employed to predict covariance matrices, leveraging their universal‐approximation capabilities in what is known as prediction‐focused learning (PFL) \\cite{Petrozziello22}. In the conventional “predict‐then‐optimize” framework, these models are trained to minimize mean‐squared error (MSE) and subsequently used for portfolio construction \\cite{lee2024overview}. However, models optimized solely for MSE do not necessarily yield near‐optimal investment decisions \\cite{Chung22}. \n\n% However, prediction from minimizing MSE doesn't imply the near-optimality in decision making process \\cite{Chung22}. To address this issue, Decision-focused learning(DFL) has been recently emerged to aware decision quality, by setting the objective with decision objective \\cite{Elmachtoub22, Mandi22}. Some researches studied that DFL in portfolio optimization restricted in the effect of expected return \\cite{Lee24} in MVO. To best of our knowledge, however, covariance estimation with DFL in GMVP is not studied yet.\n\nDecision‐focused learning (DFL) has emerged as an alternative that directly incorporates the decision objective into the training loss \\cite{Elmachtoub22,Mandi22}. While recent work applied DFL to MVO for expected-return estimation \\cite{Lee24}, no study has yet explored DFL for covariance estimation in GMVPs. We address this gap by proposing a DFL-based approach with the following contributions:\n\n\\begin{itemize}\n\\item We derive theoretical properties of DFL for GMVPs, focusing on the principal components of the training gradients.\n\\item Through extensive experiments, we demonstrate that DFL outperforms PFL‐based estimators in constructing GMVPs and reveal the limitations of conventional approaches.\n\\item We provide evidence that DFL yields stable asset-selection criteria, exhibits robustness over time, correlates with training-period volatility, and offers insight into decision attribution for GMVP construction.\n\\end{itemize}\n\n%In this paper, we present covariance estimation for GMVP using DFL. we list our contributions as follows:\n%\\begin{itemize}\n% \\item Our results report the theoretical properties of DFL when it is applied to GMVP, focusing on the principal component of the gradients of training phase.\n% \\item We empirically suggest that DFL shows higher performances compared with other MSE based estimations and the pitfall of them when they are applied to make GMVP.\n% \\item We also report the evidence that DFL showed a solid criterion for selecting assets it mainly trades, its robustness over time, its connection to the volatility in training period, and why DFL works on constructing GMVP through the performance attribution.\n%\\end{itemize}\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{Figure/overview.pdf}\n \\caption{DFL framework for GMVP construction. Historical returns of N assets are processed by DLinear to predict covariance matrix $\\Sigma$. The GMVP optimization layer computes portfolio weights $w^*$ using the closed form solution, and the regret loss is applied to minimize the gap between predicted and optimal portfolio volatility for end-to-end training.}\n \\Description{model architecture}\n \\label{fig:overview}\n\\end{figure*}\n\n\n\n\n\\section{Related Works}\n%\\textbf{Covariance Estimation and Prediction} Estimation of covariance are widely studied. In particular, shrinkage estimator \\cite{Haff80,LedoitWolf03} used convex combination of historical covariance and target, continued to nonlinear shrinkage \\cite{LedoitWolf12}, where both provides general covariance estimator. In general, shrinkage estimators are optimized with Frobenius norm, which is not appropriate measure in portfolio optimization, therefore they may be far from the proper covariance structures for portfolio optimization. In that sense, some researches extend non-linear shrinkage with task-specific loss, by substituting Frobenius norm to portfolio risk, such that they emphasize out-of sample portfolio performance by minimizing portfolio variances with constraints of portfolio weights and eigenvalues \\cite{Bongiorno23, MörstedtLutzNeumann24}. Other studies focused on covariance estimator specialized in GMVP facilitating with additional conditions, such as Bayesian approaches or random matrix theory, demonstrating their statistical properties \\cite{Frahm10, BodnarMazurOkhrin17, BodnarParolyaSchmid18}. Although they guaranteed theoretical properties and showed empirical performances, they are restricted to designated form of covariance estimation, which deteriorates the expressivity of estimations.\n\n\\textbf{Covariance Estimation and Prediction} \nCovariance estimation is a well‐studied problem. In particular, shrinkage estimators \\cite{Haff80,LedoitWolf03, LedoitWolf04} combine the sample covariance matrix with a structured target via a convex combination, and this approach has since evolved into nonlinear shrinkage methods \\cite{LedoitWolf12}; both classes of estimators provide flexible, general‐purpose covariance estimates.\nShrinkage estimators are typically optimized under the Frobenius norm, which does not directly align with portfolio‐optimization objectives, and may therefore fail to capture the covariance structures most relevant for risk minimization. To address this, some studies replace the Frobenius‐norm loss with a task‐specific loss—namely the portfolio variance—thereby emphasizing out‐of‐sample performance by minimizing portfolio volatility subject to weight and eigenvalue constraints \\cite{Bongiorno23,MörstedtLutzNeumann24}. Other work has developed covariance estimators tailored to the GMVP setting—employing Bayesian techniques or insights from random‐matrix theory—and has established their statistical guarantees and empirical performance \\cite{Frahm10,BodnarMazurOkhrin17,BodnarParolyaSchmid18}. While these methods offer strong theoretical properties, they remain limited to prespecified parametric forms, which can restrict expressiveness.\n\n%\\noindent \\textbf{Decision-Focused Learning} Recent advances in DFL derive better decision compared with prediction-focused learning(PFL) \\cite{MandiKotaryBerden24}. Several studies guarantee their theoretical analysis, demonstrating gradients of optimization problem with respect to parameters. In particular, \\cite{AmosKolter17,AgrawalEtAl19} suggest differentiation rule of designated optimization problem to develop differentiable optimization layer. Some researches studied that surrogate loss, which has subgradients to train model well, when optimization layers are not differentiable \\cite{Elmachtoub22, ShahEtAl22}. Based on them, DFL is applied to various fields, such as route optimization \\cite{FerberEtAl23}, communication technology \\cite{ChaiEtAl22}, and portfolio optimization \\cite{ButlerKwon23}. Among them, portfolio optimization utilized by DFL is usually studied to improve robustness of the model \\cite{CostaIyengar23} or analyze the effect of expected return in MVO \\cite{Lee24}. Nonetheless, there are no studies to dealing with DFL applied to global minimum variance portfolio, which fits our research purpose.\n\\vspace{0.5\\baselineskip}\n\\noindent\\textbf{Decision‐Focused Learning} \nDecision‐focused learning (DFL) has recently emerged as an alternative to prediction‐focused learning (PFL), often producing superior decision quality in downstream tasks \\cite{MandiKotaryBerden24}. Several authors provide theoretical analyses of DFL by deriving gradient expressions for optimization layers with respect to model parameters. In particular, \\cite{AmosKolter17, AgrawalEtAl19} introduce differentiation rules for optimization problems as differentiable layers. When the optimization map is non-differentiable, surrogate losses with well‐defined subgradients have been proposed to enable end‐to‐end training \\cite{Elmachtoub22,ShahEtAl22}. DFL has been applied across diverse domains, including route optimization \\cite{FerberEtAl23}, communication networks \\cite{ChaiEtAl22}, and portfolio optimization \\cite{ButlerKwon23}. Within finance, DFL has been used to enhance model robustness \\cite{CostaIyengar23} and to investigate the role of expected‐return estimation in MVO \\cite{Lee24}. However, to our knowledge, no prior work has applied DFL to covariance estimation for the global minimum‐variance portfolio, which is the focus of our study. \n\n\\section{Methodology}\n%In this section, we report how our methodology works. Figure \\ref{fig:overview} shows overall model architecture in this paper. Specifically, we use global minimum portfolio without no-short constraint, where it has a closed form solution, to derive theoretical analysis and computational convenience. \n\nIn this section, we present our overall approach. Figure~\\ref{fig:overview} illustrates the complete model architecture. We focus on the unconstrained global minimum‐variance portfolio (GMVP), which admits a closed‐form solution and thus facilitates both theoretical analysis and efficient computation.\n\n\\subsection{Notation and Problem Setup}\n\nLet \\(X\\in\\mathbb{R}^{T\\times N}\\) denote the matrix of asset returns for \\(N\\) assets over \\(T\\) time steps, and let\n\\[\nX_{t_1:t_2}\\,\\in\\,\\mathbb{R}^{(t_2 - t_1 + 1)\\times N}\n\\]\nbe the submatrix of returns from time \\(t_1\\) to \\(t_2\\). We write\n\\(\\Sigma_{t_1:t_2}\\) for the covariance matrix of \\(X_{t_1:t_2}\\). \n\nIn a traditional time‐series forecasting task, one predicts the next \\(\\delta_{\\mathrm{out}}\\) observations using the previous \\(\\delta_{\\mathrm{in}}\\) observations. Accordingly, we define a prediction model\n\\[\nf_{\\theta} : X_{t-\\delta_{\\mathrm{in}}+1:t}\\;\\mapsto\\;\\hat{\\Sigma}_{t+1:t+\\delta_{\\mathrm{out}}},\n\\]\nwhere \\(\\hat{\\Sigma}_{t+1:t+\\delta_{\\mathrm{out}}}\\) is the model’s estimate of the future covariance. We denote the resulting unconstrained GMVP weights by\n%\\[\n%w^*(\\hat{\\Sigma}) \\;=\\; \\arg\\min_{w}\\;w^\\top \\hat{\\Sigma}\\,w \n%\\quad\\Longrightarrow\\quad\n%w^*(\\hat{\\Sigma}) \\;=\\;\\frac{\\hat{\\Sigma}^{-1}\\mathbf{1}}{\\mathbf{1}^\\top \\hat{\\Sigma}^{-1}\\mathbf{1}}.\n%\\]\n\n\\[\nw^*(\\hat{\\Sigma})\n=\\;\\arg\\min_{w}\\;w^\\top \\hat{\\Sigma}\\,w\n\\quad\\text{s.t.}\\;\\mathbf{1}^\\top w = 1\n\\;\\Longrightarrow\\;\nw^*(\\hat{\\Sigma})\n=\\;\\frac{\\hat{\\Sigma}^{-1}\\mathbf{1}}{\\mathbf{1}^\\top \\hat{\\Sigma}^{-1}\\mathbf{1}}.\n\\]\n\n\n\\subsection{Covariance Prediction model}\n\nTo capture the temporal dynamics in \\(X\\), we employ the DLinear backbone \\cite{ZengEtAl23}, which has demonstrated strong performance on a variety of time‐series tasks despite its architectural simplicity. Because a covariance matrix must be symmetric and positive semi‐definite, our model predicts the entries of a lower‐triangular matrix \\(L\\), and we reconstruct the covariance as\n\\[\n\\hat{\\Sigma} \\;=\\; L\\,L^\\top,\n\\]\nensuring symmetry and positive semi‐definiteness by construction. To improve numerical stability when inverting \\(\\hat{\\Sigma}\\), we perform a truncated spectral reconstruction: we retain only eigenpairs \\((\\lambda_i, v_i)\\) satisfying \\(\\lambda_i \\ge \\varepsilon\\,\\lambda_{\\max}\\).\n\n\\subsection{Decision‐Focused Learning with Regret Loss}\n\nGiven \\(\\hat{\\Sigma}\\), we compute the unconstrained GMVP weights \\(w^*(\\hat{\\Sigma})\\). We then assess decision quality via the \\emph{regret} loss:\n\\[\nL(\\theta)\n=\\,w^*(\\hat{\\Sigma})^\\top\\,\\Sigma_{\\mathrm{true}}\\,w^*(\\hat{\\Sigma})\n\\;-\\;\nw^*(\\Sigma_{\\mathrm{true}})^\\top\\,\\Sigma_{\\mathrm{true}}\\,w^*(\\Sigma_{\\mathrm{true}}),\n\\]\nwhere \\(\\Sigma_{\\mathrm{true}} = \\Sigma_{t+1:t+\\delta_{\\mathrm{out}}}\\) is the oracle covariance. We update \\(\\theta\\) by gradient descent, computing\n\\[\n\\frac{dL}{d\\theta}\n= \\frac{dL}{d w^*(\\hat{\\Sigma})}\\,\\frac{\\partial w^*(\\hat{\\Sigma})}{\\partial \\hat{\\Sigma}}\\,\\frac{\\partial \\hat{\\Sigma}}{\\partial \\theta}.\n\\]\nClosed‐form expressions for the first two factors are\n\\begin{align*}\n\\frac{dL}{dw}\n&= 2\\,\\Sigma_{\\mathrm{true}}\\,w^*(\\hat{\\Sigma}),\\\\\n\\frac{\\partial w^*(\\hat{\\Sigma})}{\\partial \\hat{\\Sigma}}\n&= -\\,w^\\top \\otimes \\bigl(\\hat{\\Sigma}^{-1}\\bigr)^\\top\n + D\\,\\mathrm{vec}(w)\\,(w\\otimes w)^\\top.\n\\end{align*}\n\n%\\[\n%\\frac{dL}{dw}\n%= 2\\,\\Sigma_{\\mathrm{true}}\\,w^*(\\hat{\\Sigma}),\n%\\qquad\n%\\frac{\\partial w^*(\\hat{\\Sigma})}{\\partial \\hat{\\Sigma}}\n%= -\\,w^\\top \\otimes \\bigl(\\hat{\\Sigma}^{-1}\\bigr)^\\top\n%\\;+\\; D\\,\\mathrm{vec}(w)\\,(w\\otimes w)^\\top,\n%\\]\nwhere \\(\\otimes\\) denotes the Kronecker product, \\(\\mathbf{1}\\in\\mathbb{R}^N\\) is the all‐ones vector, \\(D = \\mathbf{1}^\\top\\hat{\\Sigma}^{-1}\\mathbf{1}\\), and \\(w = w^*(\\hat{\\Sigma})\\). The term \\(\\partial\\hat{\\Sigma}/\\partial\\theta\\) is obtained via automatic differentiation. This completes the end‐to‐end decision‐focused learning pipeline for GMVP construction.\n\n\\section{Theoretical Analysis}\n%\\AfterEndEnvironment{proposition}{\\par\\noindent\\rule{\\textwidth}{0.4pt}\\par}\n\\begin{table*}[htbp]\n\\centering\n\\caption{Average annualized volatility in each portfolio. All models use $\\delta_{\\text{in}}=21$ days for estimation. Historical: historical covariances with lookback $\\delta_{in}$; EW: Equal-weighted portfolio; LW-D: Ledoit-Wolf shrinkage estimator with diagonal shrinkage target \\cite{LedoitWolf04}; LW-CC: Ledoit-Wolf shrinkage estimator with constant correlation model \\cite{LedoitWolf03}; OAS: Oracle approximating shrinkage \\cite{ChenEtAl10}; PFL: Prediction-focused learning; Ours (DFL): Decision-focused learning (mean and std over 5 seeds). Bold values indicate best performing method.}\n\\label{tab:avg_ann_vol}\n\\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{l*{15}{c}}\n\\toprule\n& \\multicolumn{5}{c}{S\\&P} & \\multicolumn{5}{c}{Industry} & \\multicolumn{5}{c}{Dow Jones} \\\\\n\\cmidrule(lr){2-6} \\cmidrule(lr){7-11} \\cmidrule(lr){12-16}\nModel & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ & $\\delta_{\\text{out}}=5$ & $\\delta_{\\text{out}}=21$ & $\\delta_{\\text{out}}=63$ & $\\delta_{\\text{out}}=126$ & $\\delta_{\\text{out}}=252$ \\\\\n\\midrule\nEW & 0.1489 & 0.1550 & 0.1597 & 0.1611 & 0.1772 & 0.1670 & 0.1732 & 0.1765 & 0.1775 & 0.1917 & 0.1438 & 0.1504 & 0.1558 & 0.1565 & 0.1687 \\\\\n\\addlinespace\nHistorical & 0.1249 & 0.1382 & 0.1471 & 0.1466 & 0.1416 & 0.1427 & 0.1468 & 0.1601 & 0.1620 & 0.1600 & 0.1531 & 0.1768 & 0.1791 & 0.1858 & 0.1944 \\\\\n\\addlinespace\nLW-D & 0.1221 & 0.1334 & 0.1407 & 0.1416 & 0.1401 & 0.1329 & 0.1355 & 0.1435 & 0.1465 & 0.1432 & 0.1252 & 0.1408 & 0.1419 & 0.1520 & 0.1584 \\\\\n\\addlinespace\nLW-CC & 0.1289 & 0.1431 & 0.1437 & 0.1495 & 0.1396 & 0.1402 & 0.1503 & 0.1630 & 0.1707 & 0.1648 & 0.1491 & 0.1707 & 0.1777 & 0.1796 & 0.1895 \\\\\n\\addlinespace\nOAS & 0.1206 & 0.1317 & 0.1383 & 0.1395 & 0.1399 & 0.1254 & 0.1301 & 0.1364 & 0.1383 & 0.1403 & 0.1219 & 0.1370 & 0.1370 & 0.1433 & 0.1549 \\\\\n\\midrule\nPFL & \\begin{tabular}[c]{@{}c@{}}0.1487\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1549\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1595\\\\{\\scriptsize (0.0003)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1607\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1773\\\\{\\scriptsize (0.0007)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1670\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1730\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1764\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1775\\\\{\\scriptsize (0.0002)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1917\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1438\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1501\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1557\\\\{\\scriptsize (0.0009)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1568\\\\{\\scriptsize (0.0007)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}0.1695\\\\{\\scriptsize (0.0015)}\\end{tabular} \\\\\n\\addlinespace\nOurs (DFL) & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1154}\\\\{\\scriptsize (0.0008)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1219}\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1290}\\\\{\\scriptsize (0.0012)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1287}\\\\{\\scriptsize (0.0015)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1319}\\\\{\\scriptsize (0.0013)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1154}\\\\{\\scriptsize (0.0005)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1223}\\\\{\\scriptsize (0.0009)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1282}\\\\{\\scriptsize (0.0004)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1281}\\\\{\\scriptsize (0.0014)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1379}\\\\{\\scriptsize (0.0017)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1170}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1230}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1277}\\\\{\\scriptsize (0.0004)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1283}\\\\{\\scriptsize (0.0006)}\\end{tabular} & \\begin{tabular}[c]{@{}c@{}}\\textbf{0.1372}\\\\{\\scriptsize (0.0007)}\\end{tabular} \\\\\n\\bottomrule\n\\end{tabular}%\n}\n\\end{table*}\n\n\n%\\AfterEndEnvironment{proposition}{\\medskip\\hrule\\medskip}\n\n\\setlength{\\FrameRule}{0.8pt} % 테두리 두께 (기본 0.4pt)\n\\setlength{\\FrameSep}{2pt} % 내부 여백\n\nIn this section, we theoretically characterize the decision-aware gradient by deriving conditions for the singular vectors of\n\\(\\tfrac{\\partial w}{\\partial \\hat{\\Sigma}}\\) and\n\\(\\tfrac{\\partial L}{\\partial \\hat{\\Sigma}}\\)\n to remain \\(\\hat{\\Sigma}\\)-invariant, as stated in proposition~\\ref{prop_1}.\n\n%\\begin{framed}\n\\begin{proposition}\\label{prop_1}\nLet \n$J := \\frac{\\partial w^*(\\hat{\\Sigma})}{\\partial \\hat{\\Sigma}}$. Define\n\\vspace{0.2em}\n\\begin{align*}\n&JJ^\\top = \\{(w^\\top w) (\\hat{\\Sigma}^{-1})^2\\} + \\{D^2(w^\\top w)^2 (w w^\\top) \\notag\\\\\n&\\phantom{JJ^\\top =} - D(w^\\top w)[\\hat{\\Sigma}^{-1}(w w^\\top)+w(w^\\top \\hat{\\Sigma}^{-1})]\\} =: S_{1} + R_{1},\n\\end{align*}\n\\vspace{-1.2em}\n%and\n\\begin{align*}\n&J^\\top J = (w w^\\top)\\otimes (\\hat{\\Sigma}^{-1})^2 + \\{D^2(w^\\top w) (w \\otimes w)(w \\otimes w)^{\\top} \\notag\\\\\n&\\phantom{J^\\top J =} - D(w\\otimes\\hat{\\Sigma}^{-1})\\mathrm{vec}(w)(w\\otimes w)^{\\top} \\notag\\\\\n&\\phantom{J^\\top J =} - D(w\\otimes w)\\mathrm(w)^{\\top}(w\\otimes\\hat{\\Sigma}^{-1})^{\\top} \\} =: S_{2} + R_{2}.\n\\end{align*}\n\nAssume that \n\\begin{itemize}\n\\item $\\text{ker}(\\hat{\\Sigma}^{-1})^2 =\\text{span}(\\{w, \\hat{\\Sigma}^{-1}w\\})$,\n\\item $\\text{ker}((ww^{\\top})\\otimes(\\hat{\\Sigma}^{-1})^2) =\\text{span}(\\{(w\\otimes w), (w \\otimes \\hat{\\Sigma}^{-1}w)\\})$,\n\\item $R_1-I_n$ and $R_2-I_{n^2}$ are invertible.\n\\end{itemize}\n\nThen, there exist at least two $\\hat{\\Sigma}$-invariant singular vectors for $JJ^\\top$ and $J^\\top J$ with identical eigenvalues which are in $\\text{span}(\\{w, \\hat{\\Sigma}^{-1}w\\})$ and $\\text{span}(\\{(w\\otimes w), (w \\otimes \\hat{\\Sigma}^{-1}w\\})$, respectively.\nHere, we denoted $I_k$ as $k \\times k$ identity matrix.\n\\end{proposition}\n\n\\begin{proof}\nLet $\\text{col}(\\cdot)$ denote the column space of a matrix and define $a = w^\\top w$, $b = w^\\top \\hat{\\Sigma}^{-1}w$, and $c = w^\\top (\\hat{\\Sigma}^{-1})^2 w$.\n\n\\vspace{0.4em}\n\\textbf{Claim 1:} {\\itshape $JJ^\\top$ has eigenvectors in $\\text{span}(\\{w, \\hat{\\Sigma}^{-1}w\\})$.}\n\nSince $\\text{col}(R_1) = \\text{span}(\\{w, \\hat{\\Sigma}^{-1}w\\})$ with $\\text{rank}(R_1) \\leq 2$, the matrix representation of $R_1$ with basis $\\mathcal{B}_1 = \\{w, \\hat{\\Sigma}^{-1}w\\}$ is equivalent to:\n\n\\begin{align*}\n [R_1]_{\\mathcal{B}_1} = \\begin{pmatrix}\n D^2a^3-Dab & D^2a^2b-Dac \\\\\n -Da^2 & -Dab\n \\end{pmatrix}.\n\\end{align*}\n\nMatrix determinant lemma gives\n\\begin{align*}\n\\det(JJ^\\top-\\lambda I_n) &= \\det([R_1]_{\\mathcal{B}_1} - \\lambda I_2) \\cdot \\det(I_n + (R_1-\\lambda I_n)^{-1}S_1),\n\\end{align*}\nwhere $R_1 = U_1V_1^\\top$ with $U_1 = [w, \\hat{\\Sigma}^{-1}w]$.\n \nThus, eigenvalues of $JJ^\\top$ include those of $[R_1]_{\\mathcal{B}_1}$. For eigenvector $\\textbf{x} \\in \\text{span}(\\{w, \\hat{\\Sigma}^{-1}w\\})$ of $R_1$ with eigenvalue $\\lambda_1$, using the fact $\\text{ker}(S_1) = \\text{span}(\\{w, \\hat{\\Sigma}^{-1}w\\})$, we have a desired result as follows:\n\\begin{align*}\n(JJ^\\top)\\textbf{x} = (S_1+R_1)\\textbf{x} = 0 + \\lambda_1\\textbf{x} = \\lambda_1\\textbf{x}.\n\\end{align*}\n \n\\textbf{Claim 2:} {\\itshape $J^\\top J$ has eigenvectors in $\\text{span}(\\{w \\otimes w, w \\otimes \\hat{\\Sigma}^{-1}w\\})$.\n }\nSimilar with claim 1, from $\\mathcal{B}_2 = \\{w \\otimes \\hat{\\Sigma}^{-1}w, w \\otimes w\\}$, we have:\n\\begin{align*}\n[R_2]_{\\mathcal{B}_2} = \\begin{pmatrix}\n-Dab & -Da^2 \\\\\nD^2a^2b-Dac & D^2a^3-Dab\n\\end{pmatrix}.\n\\label{formula:R_2_rep}\n\\end{align*}\nFor eigen-pairs $(\\textbf{y}, \\lambda_2)$ of $[R_2]_{\\mathcal{B}_2}$ where $\\textbf{y} \\in \\text{span}(\\{w \\otimes \\hat{\\Sigma}^{-1}w, w \\otimes w\\})$, $(J^{\\top} J)\\textbf{y}=\\lambda_{2} \\textbf{y}$ implies that $\\textbf{y}$ is an eigenvector of $J^\\top J$.\n \n\\vspace{0.6em}\n\\textbf{Claim 3:} {\\itshape Eigenvectors of $[R_1]_{\\mathcal{B}_1}$ and $[R_2]_{\\mathcal{B}_2}$ share identical eigenvalues.}\n\nObserve that\n\\begin{align*}\n\\det([R_1]_{\\mathcal{B}_1} - \\lambda I_2) = \\det([R_2]_{\\mathcal{B}_2} - \\lambda I_2),\n\\end{align*}\nestablishing $[R_1]_{\\mathcal{B}_1}$ and $[R_2]_{\\mathcal{B}_2}$ have identical eigenvalues. \n\\end{proof}\n\nIt states there exist $\\hat{\\Sigma}$-invariant singular vectors such that they share same eigenvalues for some conditions. Therefore, it implies that $\\frac{dw}{d\\hat{\\Sigma}}$ has principal components in subspaces, inducing the closed-form of singular vectors of $\\frac{dw}{d\\hat{\\Sigma}}$ stated in the next proposition.\n\n\\vspace{0.2em}\n\\begin{proposition}\\label{prop_2}\nUnder the assumptions of Proposition~\\ref{prop_1}, Let $\\lambda$ be shared eigenvalue $R_1$ and $R_2$ and let \n\\(\\mathbf{x}(\\lambda)\\) and \\(\\mathbf{y}(\\lambda)\\)\nbe the corresponding eigenvectors of \\(R_1\\) and \\(R_2\\), respectively. Then,\n\\vspace{-0.2em}\n\\begin{align}\n \\textbf{x}(\\lambda) &= w+\\frac{\\lambda - (D^2 a^3-Dab)}{D^2a^2 b - ac}\\hat{\\Sigma}^{-1}w, \\\\\n \\textbf{y}(\\lambda) &= (w \\otimes \\hat{\\Sigma}^{-1}w)+\\frac{\\lambda - (D^2 a^3-Dab)}{D^2a^2 b - ac}(w \\otimes w).\n\\end{align}\n\\label{formula:eigenvecs}\n\\end{proposition}\n\n\\begin{proof}\nFrom the characteristic equaiton of $[R_1]_{\\mathcal{B}_1}{}$, we have\n \n\\begin{align}\n ([R_1]_{\\mathcal{B}_1}-\\lambda I_{n}) \\begin{pmatrix}\n\\alpha \\\\\n\\beta\n\\end{pmatrix}=0\n\\end{align}\n\nwhich implies $(D^{2}a^{3}-Dab-\\lambda)\\alpha+(Da^{2}b-ac)\\beta = 0$.\nHence, we derive $\\frac{\\beta}{\\alpha} = \\frac{\\lambda - D^{2}a^{3}-Dab}{Da^{2}b-ac}$ and the eigenvector $x(\\lambda)=\\alpha w + \\beta \\Sigma^{-1}w$ which is a desired result. \nSince we showed that $R_{1}$ and $R_{2}$ have identical characteristic equation in proposition \\ref{prop_1}, we have $\\textbf{y}(\\lambda) = \\alpha (w \\otimes \\hat{\\Sigma}^{-1}w) + \\beta (w \\otimes w)$.\n\\end{proof}\n\n\\vspace{0.4em}\nUsing results of proposition \\ref{prop_1} and \\ref{prop_2}, we can relate principal components of the decision‐loss gradient \\(\\tfrac{\\partial L}{\\partial \\hat{\\Sigma}}\\) which is discussed in proposition \\ref{prop_3}.\n\n\\vspace{0.2em}\n\\begin{proposition}\\label{prop_3}\nLet $L$ be a regret loss and $F := \\frac{\\partial L}{\\partial w} = 2\\Sigma_{\\mathrm{true}} w^*(\\hat{\\Sigma}) \\in \\mathbb{R}^{n}$ be a gradient of $L$ with respect to portfolio weight $w$. With assumptions in proposition \\ref{prop_1}, $FJ \\in \\mathbb{R}^{1 \\times n^{2}}$ has two $\\Sigma$-invariant singular vectors which is form of (\\ref{formula:eigenvecs}) \nwhere $\\lambda$ is solution of characteristic equation of $[R_2]_{\\mathcal{B}_{2}}$. \nMoreover, its singular value is equal to $q(\\lambda)=\\lambda(2\\Sigma_{true}w)^{\\top}\\textbf{x}(\\lambda)$.\n\\end{proposition} \n\n\n\\begin{proof}\nDenote singular value decomposition of $J$ as $U\\Lambda V^{\\top}$ where $U\\in\\mathbb{R}^{n\\times n}$, $\\Lambda \\in \\mathbb{R}^{n \\times n^{2}}$ and $V \\in \\mathbb{R}^{n^{2} \\times n^{2}}$. From proposition \\ref{prop_1} and \\ref{prop_2}, $\\textbf{x}(\\lambda)$ and $\\textbf{y}(\\lambda)$ are in the same index of column vector of $U$ and $V$, respectively. By defining the index as $i\\in\\{1,2,\\cdots,n^{2}\\}$, therefore, we have\n\\begin{align*}\n (FJ)_{i} &= \\sqrt{\\lambda}\\{(2\\Sigma_{true}w^{*})^{\\top} \\textbf{x}(\\lambda)\\}\\textbf{y}(\\lambda) \n\\end{align*}\nwhich is a desired result.\n\\end{proof}\n\n\n\n\n\\vspace{0.2em} \nFrom proposition~\\ref{prop_3}, we see that:\n\\begin{enumerate}\n \\item The direction \\(w\\otimes(\\Sigma^{-1}w)\\) captures interactions between the GMVP and its risk‐adjusted version, akin to a risk‐parity structure.\n \\item The direction \\(w\\otimes w\\) emphasizes assets with large absolute weights (\\(\\lvert w_i\\rvert \\ge 1\\)) and attenuates those within the budget constraint (\\(\\lvert w_i\\rvert \\le 1\\)).\n\\end{enumerate}\n\n\\paragraph{Remark.}\nWe assume that the kernels of \\((\\Sigma^{-1})^2\\) and \\((w\\,w^\\top)\\otimes(\\Sigma^{-1})^2\\) are non‐trivial. In practice, this condition may fail, which constitutes a limitation of our analysis.\n\n\n\n\n\\section{Experiments}\n\n\\subsection{Experimental details}\n\n\n\n\n% \\textbf{Data} We employed experiments on 3 asset universes. Firstly, we used 49 industry portfolios in Kenneth R. French data library\\footnote{https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data\\_library.html}, denoted by 49 Industry. Next, we selected the top 100 stocks by market capitalization from the S\\&P 500, denoted by S\\&P 100, as of April 1, 2025. Finally, we used stocks in Dow-Jones 30 index, named Dow 30. The covariance of three asset universes was calculated based on daily returns, which were calculated based on stock prices from January 1, 2010, to December 31, 2024. In the case of S\\&P 100 and Dow 30, we dropped stocks which have missing values in daily returns or have highly positive correlation($\\geq0.95$) to other stocks such that 100 and 18 stocks are remained, respectively. Furthermore, we split data into train, valid and test data with ratio of 6:2:2.\n\n% \\noindent \\textbf{Hyper-parameters in DFL model} Given range of hyper-parameters, we employed grid search to derive best performances. In dlinear-based covarinace forecasting module, we set the kernel size, which derives moving average of original time-series and residual between them, as $\\text{max} (5, \\text{min}(\\lfloor \\delta_{in}/3 \\rfloor,50))$ and hidden dimension in the model as $h_{dim}=128$ for all values in $(\\delta_{in}, \\delta_{out})$ pairs. To train the covariance prediction model, we used Adam optimizer \\cite{KingmaBa14}. Table \\ref{table:hyperparameters} shows settings of learning rate and batch size in each $(\\delta_{in}, \\delta_{out})$ pairs for training phase. We trained the model with 50 epochs, applying early stopping with patience 7 to avoid the over-fitted results.\n\n\\textbf{Data} We conduct experiments on three asset universes. First, we employ the 49 industry portfolios from the Kenneth R. French data library\\footnote{\\url{https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html}}, hereafter denoted “49 Industry.” Second, we select the top 100 S\\&P 500 stocks by market capitalization as of April 1, 2025 (denoted “S\\&P 100”). Third, we use the constituents of the Dow Jones 30 index (“Dow 30”). For each universe, we compute daily returns from January 1, 2010, to December 31, 2024, and estimate the covariance matrix from these returns. In the S\\&P 100 and Dow 30 universes, we exclude any stock with missing return data or with pairwise correlation \\(\\ge0.95\\), yielding final universes of 100 and 18 stocks, respectively. We split the data into training, validation, and test sets in a 6:2:2 ratio, yielding training set from January 5, 2010 to May 24, 2018; validation set from May 25, 2018 to March 12, 2021; and a test set from March 15, 2021 to December 29, 2023. \n\n\\begin{figure}[h]\n \\centering\n \\includegraphics[width=0.88\\columnwidth]{Figure/rolling.pdf}\n \\caption{Rolling window approach for time series validation. Train/valid sets use one-day rolling windows, while the test set employs $\\delta_{out}$-days rolling predictions.}\n \\Description{Ann vol plot}\n \\label{fig:rolling}\n\\end{figure}\n\n\\vspace{0.5\\baselineskip}\n\\noindent\\textbf{Hyperparameters} We grid-search all hyperparameters. DLinear's kernel size for computing moving averages and residuals is $\\max\\{5,\\min\\{\\lfloor\\delta_{\\mathrm{in}}/3\\rfloor,50\\}\\}$, with hidden dimension $h_{\\mathrm{dim}}=128$ throughout. We train with the Adam optimizer \\cite{KingmaBa14}. Table~\\ref{table:hyperparameters} summarizes the learning‐rate and batch‐size settings for each \\((\\delta_{\\mathrm{in}},\\delta_{\\mathrm{out}})\\) configuration. All models are trained for up to 50 epochs, with early stopping when validation loss shows no improvement for 7 epochs. \n\n\\begin{table}[ht]\n \\centering\n \\small\n \\caption{Hyperparameter settings in (\\text{learning rate}, \\text{batch}) pairs for varying $\\delta_{in}$ and $\\delta_{out}$}\n \\label{tab:delta}\n \\begin{tabular}{c|ccccc}\n \\toprule\n & \\multicolumn{5}{c}{$\\delta_{in}$} \\\\\n \\cmidrule(lr){2-6}\n $\\delta_{out}$ \n & 5 & 21 & 63 & 126 & 252 \\\\\n \\midrule\n 5 & ($10^{-4}$,\\,64) & ($10^{-5}$,\\,16) & ($10^{-4}$,\\,16) & ($10^{-4}$,\\,32) & ($10^{-5}$,\\,16) \\\\\n 21 & ($10^{-5}$,\\,32) & ($10^{-5}$,\\,16) & ($10^{-5}$,\\,64) & ($10^{-4}$,\\,32) & ($10^{-4}$,\\,32) \\\\\n 63 & ($10^{-4}$,\\,64) & ($10^{-4}$,\\,32) & ($10^{-4}$,\\,64) & ($10^{-4}$,\\,64) & ($10^{-4}$,\\,32) \\\\\n 126 & ($10^{-5}$,\\,64) & ($10^{-4}$,\\,32) & ($10^{-4}$,\\,64) & ($10^{-4}$,\\,64) & ($10^{-5}$,\\,16) \\\\\n 252 & ($10^{-3}$,\\,32) & ($10^{-5}$,\\,16) & ($10^{-3}$,\\,16) & ($10^{-4}$,\\,16) & ($10^{-5}$,\\,16) \\\\\n \\bottomrule\n \\end{tabular}\n \\label{table:hyperparameters}\n\\end{table}\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=0.9\\textwidth]{Figure/ann_vol.pdf}\n \\caption{Annualized volatility of each model's portfolio with $\\delta_{in}=\\delta_{out}=21$ from the left to the right, respectively.}\n \\Description{Ann vol plot}\n \\label{fig:ann_vol}\n\\end{figure*}\n\n\n\n\n\\subsection{Results}\n\n\nWe evaluate each model’s performance under a buy‐and‐hold strategy: at time \\(t\\), we compute portfolio weights \\(w\\) from the predicted covariance \\(\\hat{\\Sigma}_{t:t+\\delta_{\\mathrm{out}}}\\), hold \\(w\\) until \\(t+\\delta_{\\mathrm{out}}\\), then rebalance and repeat. We illustrate the difference of rolling method between training and test period in Figure \\ref{fig:rolling}. Performance is measured by the average annualized volatility of realized portfolio returns. We compare our DFL approach against the following benchmarks:\n\n\\begin{description}\n \\item[\\textbf{EW}] Equally weighted portfolio.\n \\item[\\textbf{Historical}] GMVP using the sample covariance over the past \\(\\delta_{\\mathrm{in}}\\) returns.\n \\item[\\textbf{LW‑D}] GMVP with Ledoit–Wolf shrinkage toward a scaled identity matrix \\cite{LedoitWolf04}.\n \\item[\\textbf{LW‑CC}] GMVP with Ledoit–Wolf constant‐correlation shrinkage \\cite{LedoitWolf03}.\n \\item[\\textbf{OAS}] GMVP with the Oracle Approximating Shrinkage estimator \\cite{ChenEtAl10}.\n \\item[\\textbf{PFL}] GMVP using covariance forecasts from the DLinear module, trained to minimize mean‐squared error (MSE).\n\\end{description}\n\n\n\n%Table \\ref{tab:avg_ann_vol} shows the overall results. Traditional estimators couldn't outperform the DFL approaches, because they focused on finding shrinkage parameter, such as shrinkage intensity, to aware Frobenius norm between true covariances and themselves, therefore it leads to the worse decision making. Moreover, PFL shows worse performances than other estimators, similar with the one of equally-weighted(EW) portfolio.\n\n\nTable~\\ref{tab:avg_ann_vol} reports the average annualized volatility over the test period and Figure~\\ref{fig:ann_vol} shows annualized volatility during each test period. Conventional shrinkage and historical estimators— which optimize the Frobenius‐norm loss—fail to match the decision quality of DFL, since minimizing Frobenius error does not directly translate to low portfolio volatility. The PFL model performs comparably to the equally weighted portfolio, underscoring that MSE‐based covariance forecasting can yield nearly constant off‐diagonal estimates and thus an approximately equal‐weight allocation.\n\n\\begin{figure}[htbp]\n \\vspace{-0.2cm}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figure/ew_pfl_dfl.pdf}\n \\caption{Average portfolio weights in the Industry portfolio dataset during whole test period with $\\delta_{in}=\\delta_{out}=21$.}\n \\Description{model architecture}\n \\label{fig:ew_pfl}\n \\vspace{-0.2cm}\n\\end{figure}\n\n% Figure \\ref{fig:ew_pfl} illustrates portfolio weights for each sector in 49 industry portfolio dataset, taking average of them during whole test period. It shows that PFL has almost same weight compared with EW, while other models have their own portfolio. We infer the reason of this situation as follows: Since PFL uses MSE as a loss function, the gradients for components become difference between true values and prediction. However, covariance matrices generally have greater values in diagonal components than off-diagonal ones, leading to the bias to concentrate updating diagonal components more than off-diagonals. In this case, covariance estimation from the network becomes similar with constant off-diagonal covariances, which results in the EW portfolio. It supports PFL based on minimizing MSE might not be helpful to the parameter estimation in decision making, wherea DFL are successfully achieves great decision making.\n\nFigure~\\ref{fig:ew_pfl} depicts the average sector weights for the 49‐Industry dataset over the test period. The PFL allocations closely mirror those of the EW benchmark, whereas DFL and other methods exhibit distinct exposure profiles. This phenomenon arises because training phase with MSE prioritizes reducing large diagonal errors in the covariance matrix, leading the network to underfit off‐diagonal terms and effectively produce nearly uniform correlations. It supports that PFL based on minimizing MSE might not be helpful to the parameter estimation in decision making, wherea DFL are successfully achieves great decision making. Similar results would be observed for S\\&P and Dow Jones datasets, reported in the figure \\ref{fig:ew_pfl_appendix}.\n\n\\begin{figure}[h]\n \\centering\n \\includegraphics[width=\\columnwidth]{Figure/delta.pdf}\n \\caption{Annualized volatility of DFL when $\\delta_{in}$ and $\\delta_{out}$ have different values in the Industry dataset. We set $\\delta_{in}, \\delta_{out}\\in \\{5,21,63,126,252\\}$.}\n \\Description{Ann vol plot}\n \\label{fig:delta_ablation}\n\\end{figure}\n\n% Figure~\\ref{fig:ann_vol} shows annualized volatility as a function of the holding period \\(\\delta_{\\mathrm{out}}\\). Across all test intervals, DFL consistently achieves lower volatility than every baseline, demonstrating that the superior average performance in Table~\\ref{tab:avg_ann_vol} generalizes across different rebalancing frequencies.\n\n%We also checked the performances of DFL in different ($\\delta_{in}$ ,$\\delta_{out}$) pairs, illustrated in figure \\ref{fig:delta_ablation}. It shows that portfolio volatility derived by DFL becomes worse when $\\delta_{out}$ increases when $\\delta_{in}$ is given. In addition, given $\\delta_{out}$, performances of DFL are slightly different with respect to the length of input sequence, which implies the importance of appropriate length of input sequence.\n\nFigure~\\ref{fig:delta_ablation} presents an ablation study over various \\((\\delta_{\\mathrm{in}},\\delta_{\\mathrm{out}})\\) pairs. As \\(\\delta_{\\mathrm{out}}\\) increases for a fixed \\(\\delta_{\\mathrm{in}}\\), DFL’s volatility rises, reflecting the greater uncertainty in longer‐horizon forecasts. Conversely, for a fixed \\(\\delta_{\\mathrm{out}}\\), performance varies only modestly with \\(\\delta_{\\mathrm{in}}\\), indicating robustness to the length of the input window but also highlighting the importance of selecting an appropriate length of input sequence.\n\n\\subsection{Empirical properties of DFL}\n\\begin{figure*}[h]\n \\centering\n \\includegraphics[width=\\textwidth]{Figure/bbc_combined.pdf}\n \\caption{Precision matrix derived by DFL and OAS for single test period in the Industry dataset (left), Average of the permuted precision matrix estimated by DFL and OAS for the entire test period in the Industry dataset (middle), Average and standard deviation of GMVP weights in the reordered index for the entire test period in the Industry dataset (right).}\n \\Description{bbc reorder}\n \\label{fig:reordered precision}\n\\end{figure*}\n\n%In this section, we explored the properties of DFL, focusing on the empirical results. One may questionize which properties of DFL make their decision to the near optimality. In that sense, we compared the portfolio by DFL with results from other models using permutation of estimated covariance matrix that explains how DFL selects weights of GMVP. Moreover, we employed additional experiments to derive performance attribution for components in estimated covariance derived by different models, demonstrating the reason why DFL shows great performances. We compared the estimation of DFL with other models using permutation of estimated covariance matrix that explains how DFL selects weights of GMVP.\n\nIn this section, we investigate the empirical properties of decision‐focused learning (DFL) that contribute to its near‐optimal portfolio decisions. To this end, we compare the GMVP weights produced by DFL with those from other estimators by examining permutations of the predicted precision matrix, and we conduct a performance‐attribution analysis of covariance components to explain DFL’s superior results. Additionally, we suggest key features of DFL which affects to the decision.\n\n%Since the analytic solution of GMVP $w^{*}(\\hat{\\Sigma}) = \\frac{\\hat{\\Sigma}^{-1} \\textbf{1}}{\\textbf{1}^\\top \\hat{\\Sigma}^{-1} \\textbf{1}}$. it implies that GMVP heavily depends on the sum of the row vector $\\hat{\\Sigma}$ and each component of GMVP means the sum of components in row vector of $\\hat{\\Sigma}$. Left columns of figure \\ref{fig:reordered precision} show the heatmap of $\\hat{\\Sigma}^{-1}$ estimated by DFL and OAS for a single test sample period, revealing that DFL-based estimation has rows with similar column values while OAS-based estimation shows randomness. Furthermore, while the DFL-based estimation is divided into rows with predominantly high values and rows with predominantly low values, the OAS-based estimation mostly has low values in most rows.\\footnote{Although we checked that similar situation occurs in different asset universes, we didn't report whole results due to the length restrictions of the paper.} Based on this, we hypothesized that if the rows and columns of the precision matrix estimated by DFL are permuted appropriately, it would be possible to group the rows with relatively high values and the rows with relatively low values such that weights of GMVP will follow the same trend.\n\nBecause the analytical solution of the GMVP,\n\\[\nw^{*}(\\hat{\\Sigma})\n= \\frac{\\hat{\\Sigma}^{-1}\\mathbf{1}}{\\mathbf{1}^\\top\\hat{\\Sigma}^{-1}\\mathbf{1}},\n\\]\nwhich depends on the row sums of \\(\\hat{\\Sigma}^{-1}\\), each weight \\(w_i\\) is proportional to the sum of the \\(i\\)th row of the precision matrix. \n\nFigure~\\ref{fig:reordered precision} (left) shows the heatmaps of \\(\\hat{\\Sigma}^{-1}\\) estimated by DFL and by OAS for a representative test sample. The DFL‐based precision matrix exhibits two distinct groups of rows—one with consistently high values and one with consistently low values—whereas the OAS estimate appears more random and dominated by low values across most rows. We therefore hypothesize that an appropriate row/column permutation of the DFL precision matrix will reveal block structure corresponding to high‐weight and low‐weight stocks.\n\nAlgorithm~\\ref{alg:bbc} presents the Bidirectional Block Construction (BBC) method for permuting the precision matrix:\n\\begin{enumerate}\n \\item Identify the pair of stocks with the largest off‐diagonal precision value and place them in the top‐left block.\n \\item Find the stock with the smallest precision values to this pair and place it in the bottom‐right block.\n \\item Iteratively assign remaining stocks with high precision to the top group (left block) or to the bottom anchor (right block), according to their maximum precision with the current blocks.\n \\item Continue until all stocks are assigned, forming two coherent blocks.\n\\end{enumerate}\n\n%Middle and right results in figure \\ref{fig:reordered precision} illustrate the results obtained by applying the algorithm \\ref{alg:bbc} to the precision matrix and average portfolio weights derived by permuted precision matrix for the entire test period. Similar with our hypothesis, it shows that permutation of precision matrix derived by DFL is divided by rows dominated by high values at top-left blocks and rows dominated by low values at bottom-left blocks, indicating gradual decreases of the tendency as row goes to downside. However, OAS-driven precision matrix shows randomness and high values in near-diagonal blocks, which has a different tendency in the results of DFL. In terms of portfolio weight, though OAS-driven GMVP has high standard deviation, meaning that their decision is not consistent over the test period, DFL-based GMVP maintains the trend of weight order relatively well, especially for intermediate indices with relatively small long/short positions. It implies that decision from DFL is more robust to the time than OAS-driven portfolio weights. \n\n\\begin{algorithm}[t]\n\\DontPrintSemicolon\n\\SetAlgoLined\n\\SetKwInOut{Input}{Input}\n\\SetKwInOut{Output}{Output}\n\\Input{Precision matrix $\\mathbf{A} \\in \\mathbb{R}^{n \\times n}$}\n\\Output{Permutation $\\pi$, blocks $\\mathcal{B}$}\n\\BlankLine\n\\tcp{Initialize}\n$\\text{placed} \\leftarrow \\{\\text{false}\\}^n$, $\\pi \\leftarrow []$\\;\n$(i^*, j^*) \\leftarrow \\arg\\max_{i < j} |A_{ij}|$\\;\n$\\pi[0] \\leftarrow i^*$, $\\pi[1] \\leftarrow j^*$\\;\n$\\text{placed}[i^*] \\leftarrow \\text{placed}[j^*] \\leftarrow \\text{true}$\\;\n\\tcp{Place antipodal anchor}\n$k^* \\leftarrow \\arg\\min_{k: \\neg\\text{placed}[k]} A_{\\pi[0],k}$\\;\n$\\pi[n-1] \\leftarrow k^*$, $\\text{placed}[k^*] \\leftarrow \\text{true}$\\;\n\\tcp{Bidirectional construction}\n$\\ell \\leftarrow 2$, $r \\leftarrow n-2$\\;\n\\While{$\\ell \\leq r$}{\n $m \\leftarrow \\arg\\max_{k: \\neg\\text{placed}[k]} \\frac{1}{\\ell}\\sum_{i=0}^{\\ell-1} A_{k,\\pi[i]}$\\;\n $\\pi[\\ell] \\leftarrow m$, $\\text{placed}[m] \\leftarrow \\text{true}$, $\\ell \\leftarrow \\ell + 1$\\;\n \\If{$\\ell \\leq r$}{\n $m \\leftarrow \\arg\\max_{k: \\neg\\text{placed}[k]} \\frac{1}{n-r}\\sum_{i=r+1}^{n-1} A_{k,\\pi[i]}$\\;\n $\\pi[r] \\leftarrow m$, $\\text{placed}[m] \\leftarrow \\text{true}$, $r \\leftarrow r - 1$\\;\n }\n}\n$\\mathcal{B} \\leftarrow \\textsc{DetectBlocks}(\\mathbf{A}, \\pi)$\\;\n\\Return{$\\pi, \\mathcal{B}$}\\;\n\\caption{Bidirectional Block Construction (BBC) for Precision Matrix Reordering}\n\\label{alg:bbc}\n\\end{algorithm}\n\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=0.9\\textwidth]{Figure/covariance_weight.pdf}\n \\caption{Average true covariance matrix over the test period in the Industry dataset, with assets ordered by descending portfolio weight for DFL (left), LW‑D (center) and OAS (right). The yellow line denotes zero weight: entries to its left or above correspond to positively weighted assets, and those to its right or below to negatively weighted assets. Area \\ding{192}: covariance of positively weighted stocks; area \\ding{193}: covariance of stocks with mixed weights; area \\ding{194}: covariance of negatively weighted stocks. We displayed up to the maximum off-diagonal value, and values exceeding it are displayed in black.}\n \\label{fig:weight_cov}\n\\end{figure*}\n\n\\begin{figure}[h]\n \\centering\n \\includegraphics[width=\\columnwidth]{Figure/dfl_cl.pdf}\n \\caption{Portfolio weights by the models in whole test period in the Industry dataset. Stock is sorted by the quantity of median weight from DFL. The line indicates median weights of each model and area with same color illustrates one by eliminating weights which are over 97.5 percentile or under 2.5 percentile of whole weights in test period.}\n \\Description{Ann vol plot}\n \\label{fig:weight_median_percentile}\n\\end{figure}\n\nThe middle panel of figure~\\ref{fig:reordered precision} shows the permuted DFL precision matrix, revealing a clear top‐left block of high values and a bottom‐right block of low values. The right panel plots the average GMVP weights computed from the permuted precision matrices over the test period. In contrast, the OAS‐driven permutation yields no discernible block structure and produces weight sequences with high variability. These results indicate that DFL’s precision estimates induce stable, block‐structured weight allocations, whereas OAS yields less consistent decisions over time. Overall, this analysis demonstrates that DFL not only forecasts covariance more effectively for decision making, but also produces a precision‐matrix structure that aligns naturally with robust, low‐volatility portfolio weights. We reported results for S\\&P and Dow Jones dataset in figure \\ref{fig:reordered precision_appendix}, showing the similar tendency in the Industry dataset. \n\n\n\n\n\n\n\n\nTo identify which assets mainly derive portfolio risk, we decompose the realized volatility of any portfolio \\(w\\) under the true covariance \\(\\Sigma_{\\mathrm{true}}=[\\sigma_{ij}]\\in\\mathbb{R}^{N\\times N}\\) as\n\\begin{align*}\n \\mathrm{Vol}_{model}(w) &= w^\\top \\Sigma_{\\mathrm{true}}w\\\\\n &=w^\\top \\text{diag}(\\sigma_{11},\\cdots,\\sigma_{NN}) w \\\\\n &+ w^\\top (\\Sigma_{\\mathrm{true}} - \\text{diag}(\\sigma_{11},\\cdots,\\sigma_{NN})) w\n\\end{align*}\nMinimizing the first (diagonal) term requires that assets with small absolute weight \\(\\lvert w_i\\rvert\\) coincide with large variances \\(\\sigma_{ii}\\), and vice versa. \nFor the second (off‐diagonal) term, volatility is reduced when (1) if $w_{i}w_{j}<0$ and $|w_{i}|, |w_{j}|$ become large, then $\\sigma_{ij}$ should become large value or (2) if $w_{i}w_{j}>0$ and $|w_{i}|, |w_{j}|$ become large, then $\\sigma_{ij}$ should become small value.\n\n\nFigure~\\ref{fig:weight_cov} presents the test‐period average \\(\\Sigma_{\\mathrm{true}}\\), reordered by descending \\(\\lvert w_i\\rvert\\). In region \\ding{192}, the DFL‐based model exhibits notably lower true variances and covariances than all other estimators, highlighted to the most heavily weighted assets. Across positively and negatively weighted assets, DFL induces a balancing effect—amplifying risk for extreme positions while attenuating risk for moderate positions—whereas other methods do not illustrate it prominently. However, in the region of short positions (area \\ding{194}), DFL’s true covariances remain higher than those of competing estimators, indicating comparatively weaker short‐side risk control. These patterns confirm that DFL primarily reduces overall volatility by selecting low‐variance stocks and moderating large exposures, but may require additional mechanisms to manage short‐position risk. From figure \\ref{fig:weight_cov_appendix}, we have checked that our observations work for both S\\&P and Dow Jones dataset.\n\n\n\nFigure \\ref{fig:weight_median_percentile} and \\ref{fig:weight_median_percentile_appendix} illustrate, for the test period, each model’s median portfolio weight and the 95\\% interval (excluding the top and bottom 2.5\\% tails). Unlike the other figures, the stock tickers here are ordered in descending sequence according to the DFL model’s portfolio weights. Two salient observations arise: (1) DFL exhibits clear increase and decrease of long and short positions relative to PFL, and (2) DFL remains consistent allocation patterns which is different with that of OAS. Moreover, both DFL and PFL—which include a training phase—exhibit lower weight dispersion than the other estimators, suggesting that these models capture systematic features during training. We therefore hypothesize that DFL identifies asset characteristics—such as volatility—that drive its allocation decisions.\n\n\n\n%To check this hypothesis, we set volatility of input time-series in whole train period as an evaluation metric. Table~\\ref{tab:volatility_precision} presents the average precision between stocks ranked by volatility (in ascending order) during the training period and their corresponding portfolio weight rankings during the test period. Unlike other MSE-based models, DFL demonstrates that its stock selection criteria for long positions can be primarily explained through volatility measures. This suggests that when DFL-based models are applied to the GMVP, they employ a strategy of reducing portfolio volatility by predominantly selecting and holding stable stocks with lower volatility. Although a direct causality between low volatility in the training period and asset weights cannot be definitively established, it is noteworthy that DFL, in contrast to other models, demonstrably learns identifiable features and systematically constructs portfolios based on these criteria.\n\nTo evaluate this hypothesis, we rank stocks by their realized volatility of input time-series in whole train period (ascending order) and compare these ranks to the test‐period weight ranks. Table~\\ref{tab:volatility_precision} reports the average precision of this correspondence. Unlike the MSE‐based models, DFL achieves high precision for long‐position selection based on low historical volatility. This indicates that DFL systematically has their own criterion which selects low volatile stocks in training phase and reduces portfolio risk by favoring low‐volatility assets. While causality cannot be conclusively established, the results demonstrate that DFL learns and exploits identifiable asset features to construct robust GMVPs. \n\n\n\\begin{table}[htbp]\n\\centering\n\\caption{Average precision between top-k volatility rankings (ascending) in training Period and top-k portfolio weight rankings (descending) in test period. Values with the best performances are illustrated in bold.}\n\\label{tab:volatility_precision}\n\\begin{tabular}{l|cc|cc|cc}\n\\hline\n\\multirow{2}{*}{Model} & \\multicolumn{2}{c|}{S\\&P 100} & \\multicolumn{2}{c|}{49 Industry} & \\multicolumn{2}{c}{Dow 30} \\\\\n\\cline{2-7}\n & Top 3 & Top 5 & Top 3 & Top 5 & Top 3 & Top 5 \\\\\n\\hline \nDFL & \\textbf{0.6250} & \\textbf{0.7812} & \\textbf{0.6667} & \\textbf{0.5000} & \\textbf{1.0000} & \\textbf{0.8000} \\\\\nOAS & 0.0417 & 0.0813 & 0.1562 & 0.2375 & 0.4271 & 0.5438 \\\\\nPFL & 0.0208 & 0.0563 & 0.0833 & 0.0688 & 0.2083 & 0.4062 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\section{Conclusion}\n\n\n%In this paper, we proposed decision-focused framework to derive a global minimum variance portfolio using DFL. Our results support the importance of parameter estimation which is appropriate to the decision making and the fact that simple measures like MSE can deteriorate the decision quality. In particular, we suggested its theoretical analysis, dealing with principal components of the gradient of DFL loss with respect to the parameter. Moreover, we empirically showed superior performances of DFL compared with statistical estimators and PFL, implying that MSE-based method would leads to the sub-optimal decision making and confirming that DFL can generalize the decision making. We investigated which components of estimation by DFL influence to the decision making. Our results confirm that the DFL-based method selects assets with low volatility and constructs a portfolio mainly consisting of these assets, thereby reducing volatility. Furthermore, this tendency also demonstrates robustness over time.\n\n\nIn this paper, we have proposed a decision‐focused learning framework for constructing the global minimum‐variance portfolio. \nWe have provided a theoretical characterization of DFL by analyzing the principal components of the decision‐aware gradient with respect to the covariance parameter.\nEmpirically, our results underscore the importance of aligning parameter estimation with the portfolio optimization objective, and demonstrate that conventional MSE‐based methods can lead to suboptimal investment decisions. We show that DFL consistently outperforms both classical estimators and PFL, thereby confirming its superior decision quality. Through a detailed attribution analysis, we further reveal that DFL systematically favors low‐volatility assets, producing robust portfolios with lower realized volatility over time. \n%These findings highlight the potential of decision‐focused learning for enhancing risk management strategies in finance.\n\n%Despite our focus on variance minimization, we have not evaluated portfolio returns within this study. This omission reflects our primary aim—to investigate the learning dynamics and properties of the DFL paradigm—rather than to claim superior investment returns. In other words, demonstrating that DFL yields favorable conventional performance metrics (such as return or Sharpe ratio) lies beyond the scope of this work and is not matched to our core contribution. Future research may extend our framework to incorporate return objectives or multi‑criteria optimization, thereby assessing the broader implications of decision‑focused learning in practical asset‑allocation settings.\n\nWe focus solely on variance minimization and do not assess portfolio returns, since our goal is to examine the learning dynamics and properties of the DFL framework rather than to demonstrate superior return performance. Evaluating conventional metrics (e.g., return, Sharpe ratio) falls outside this paper’s scope. Future work could integrate return objectives to explore DFL’s practical impact on asset allocation.\n\\bibliographystyle{ACM-Reference-Format}\n\\bibliography{base}\n\n\\clearpage\n\\onecolumn\n\\appendix\n\\section{Appendix}\n\n\\FloatBarrier\nIn this section, we report additional experimental results on different asset universes, including S\\&P and Dow Jones dataset. \n\\subsection{Portfolio weights}\nTo extend the results of portfolio weights for each model in Industry dataset (see figure \\ref{fig:ew_pfl}), we checked that our explanation why PFL fails for decision making process works for the different dataset. Figure \\ref{fig:ew_pfl_appendix} illustrates portfolio weights of other models and it demonstrates that PFL remains almost same portfolio weights with equally weighted portfolio. \n\n% Figure 9\n\\begin{figure}[!htbp]\n \\centering\n \\includegraphics[width=0.95\\linewidth]{Figure/ew_pfl_dfl_appendix.pdf}\n \\caption{Average portfolio weights in the S\\&P and Dow Jones dataset during the test period with $\\delta_{in} = \\delta_{out} = 21$.}\n \\label{fig:ew_pfl_appendix}\n\\end{figure}\n\n\\newpage\n\\subsection{Precision matrix analysis}\nWe also check whether precision matrix of DFL have similar structures as depicted in figure \\ref{fig:reordered precision}, algorithm \\ref{alg:bbc} works for sorting precision matrix and weight distribution for DFL and OAS model. Figure \\ref{fig:reordered precision_appendix} shows that our hypothesis and algorithm hold for different asset universes, explaining similar results of figure \\ref{fig:reordered precision}.\n% Figure 10\n\\begin{figure}[!htbp]\n \\centering\n \\includegraphics[width=0.95\\linewidth]{Figure/bbc_combined_appendix.pdf}\n \\caption{Precision matrix derived by DFL and OAS for single test period (left), average precision matrices reordered by BBC algorithm (middle), and weight distributions (right) for S\\&P and Dow Jones datasets.}\n \\label{fig:reordered precision_appendix}\n\\end{figure}\n\n\\newpage\n\\subsection{Performance attribution of minimizing variances}\nWe employ the performance attribution in the variance minimization problem with estimated covariance matrix. Figure \\ref{fig:weight_cov_appendix} shows true covariance sorted by the order of weights in each model. Similar to results of figure \\ref{fig:weight_cov}, It shows that stocks index whose portfolio weights of DFL are large have relatively small true variance and covariance values.\n\n% Figure 11\n\\begin{figure}[!htbp]\n \\centering\n \\includegraphics[width=0.90\\linewidth]{Figure/covariance_weight_appendix.pdf}\n \\caption{Average true covariance matrix over the test period in the Industry dataset, with assets ordered by descending portfolio weight for DFL (left), LW- D (center) and OAS (right) in S\\&P 500 and Dow Jones datasets.}\n \\label{fig:weight_cov_appendix}\n\\end{figure}\n\n\n\\subsection{Invariance of stock selection in DFL}\nWe have show that each model’s median portfolio weight ordered in descending sequence according to the DFL model’s\nportfolio weights which is an extension of figure \\ref{fig:weight_median_percentile} to the other asset universes. Figure \\ref{fig:weight_median_percentile_appendix} shows similar tendency, demonstrating that consistent asset allocation of DFL holds. (While the result of S\\&P shows slightly large confidence interval compared with results in other asset universes, it is not compatible with the results of other estimator except PFL.)\n% Figure 12\n\\begin{figure}[!htbp]\n \\centering\n \\includegraphics[width=0.90\\linewidth]{Figure/dfl_cl_appendix.pdf}\n \\caption{\n Portfolio weights by different models in the test period for S\\&P 500 and Dow Jones datasets. Stock indices are sorted by the quantity of median weight from DFL. Lines indicate median weights and shaded areas illustrate one by eliminating weights which are over 97.5 percentile or under 2.5 percentile of whole weights in test period.}\n \\label{fig:weight_median_percentile_appendix}\n\\end{figure}\n\\end{document}\n\n"},"question":{"kind":"string","value":"On average which method varies more from its mean across all setups, PFL or DFL? And what is the difference?"},"answer":{"kind":"string","value":"DFL, 0.0005"},"plan":{"kind":"string","value":"COMPUTE pfl_mean = average of pfl volatility values over all setups\nCOMPUTE pfl_total_abs_dev = 0\nSELECT all setups\nLOOP for each setup\n COMPUTE abs_dev = absolute(setup pfl volatility − pfl_mean)\n COMPUTE pfl_total_abs_dev += abs_dev\nCOMPUTE pfl_avg_abs_dev = average of all pfl_total_abs_dev\n\n\nCOMPUTE dfl_mean = average of dfl volatility values over all setups\nCOMPUTE dfl_total_abs_dev = 0\nSELECT all setups\nLOOP for each setup\n COMPUTE abs_dev = absolute(setup dfl volatility − dfl_mean)\n COMPUTE dfl_total_abs_dev += abs_dev\nCOMPUTE dfl_avg_abs_dev = average of all dfl_total_abs_dev\n\n\nIF pfl_avg_abs_dev > dfl_avg_abs_dev\n COMPUTE difference = pfl_avg_abs_dev − dfl_avg_abs_dev\n RETURN “pfl”, difference \nELSE\n COMPUTE difference = dfl_avg_abs_dev − pfl_avg_abs_dev\n RETURN “dfl”, difference\n"}}},{"rowIdx":346,"cells":{"paper":{"kind":"string","value":"2510.03232"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t!]\n"," \\centering\n"," \\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\%) of VQA accuracy. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n"," \\vspace{-2mm}\n","\t\\resizebox{0.75\\textwidth}{!}{\n"," \n"," \\begin{tabular}{l c c c c c}\n"," \n"," \\toprule \n","\n"," \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n"," \\cline{2-5}\n"," & Colitis & Esophagitis & Instrument & Polyps & \\\\\n"," \\midrule\n"," Zero-Shot& 35.4 & 21.1 & 49.0 & 47.8 & 38.3 \\\\\n"," LoRA & 95.6 & 57.7 & 48.9 & 47.3 & 62.4 \\\\\n"," Full-Tuning & 89.0 & 60.8 & 51.2 & 51.3 & 63.1 \\\\\n"," \\nameshort~(Ours) & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n","\n","\n","\n"," \\midrule\n"," Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 55.9 & 54.3 \\\\\n"," Fully-Supervised & 97.4 & 97.4 & 85.8 & 82.1 & 90.7 \\\\\n"," \n"," \\bottomrule\n"," \\label{tab:medical}\n"," \\end{tabular}\n"," }\n"," \\vspace{-3mm}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\\\%) of VQA accuracy. Only 1\\\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\t\\\\resizebox{0.75\\\\textwidth}{!}{\\n\",\n \" \\n\",\n \" \\\\begin{tabular}{l c c c c c}\\n\",\n \" \\n\",\n \" \\\\toprule \\n\",\n \"\\n\",\n \" \\\\multirow{2}{*}{Method} & \\\\multicolumn{4}{c}{Image Category} & \\\\multirow{2}{*}{Average}\\\\\\\\\\n\",\n \" \\\\cline{2-5}\\n\",\n \" & Colitis & Esophagitis & Instrument & Polyps & \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot& 35.4 & 21.1 & 49.0 & 47.8 & 38.3 \\\\\\\\\\n\",\n \" LoRA & 95.6 & 57.7 & 48.9 & 47.3 & 62.4 \\\\\\\\\\n\",\n \" Full-Tuning & 89.0 & 60.8 & 51.2 & 51.3 & 63.1 \\\\\\\\\\n\",\n \" \\\\nameshort~(Ours) & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 55.9 & 54.3 \\\\\\\\\\n\",\n \" Fully-Supervised & 97.4 & 97.4 & 85.8 & 82.1 & 90.7 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\label{tab:medical}\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}[!t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{model1fig.pdf}\n"," \\caption{Overview of the proposed two-stage \\nameshort~framework for OOD VQA adaptation. In \\namestagea, the QA Generator is trained using a small set of labeled question-answer pairs and then used to generate pseudo QA pairs for a large collection of unlabeled images. In \\namestageb, the VQA model is fine-tuned with both the original labeled data and the produced pseudo QA pairs of unlabeled data, enabling label-efficient adaptation to out-of-distribution visual-question answering. We will detail the learning of our QA Generator in Figure~\\ref{figure:model2}.}\n"," \\label{figure:model1}\n","\\end{figure*}To support such targeted interventions, a variety of attribution methods have been proposed to quantify the importance of individual neurons or weights. Some are designed to guide pruning, which reduces model size by removing components deemed less relevant. For example, Wanda~\\cite{sun2023simple} identifies unimportant weights by combining their magnitude with the norm of the associated input activation. Others~\\cite{fang2024towards,pan2023finding,yu2023neuron,yu2025locate} aim to inform fine-tuning, where only selected parts of the model are updated to acquire new capabilities or adapt to specific domains. A common strategy in this context is to measure gradient magnitudes during backpropagation, under the assumption that neurons with higher gradients contribute more significantly to the output~\\cite{zhang2024gradient}.\n"],["\\begin{figure*}[!t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{model2fig.pdf}\n"," \\caption{Illustration of our \\namestageaa~for the QA Generator. The QA-relevant parameters are first selected based on gradient scores from labeled QA data. During training, only these selected parameters are updated using auxiliary caption supervision from unlabeled images, allowing QA-related knowledge distillation for the QA Generator.}\n"," \\label{figure:model2}\n","\\end{figure*}\n"],["\\begin{table*}[t!]\n"," \\centering\n"," \\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\%) of VQA accuracy. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n"," \\vspace{-2mm}\n","\t\\resizebox{0.75\\textwidth}{!}{\n"," \n"," \\begin{tabular}{l c c c c c}\n"," \n"," \\toprule \n","\n"," \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n"," \\cline{2-5}\n"," & Colitis & Esophagitis & Instrument & Polyps & \\\\\n"," \\midrule\n"," Zero-Shot& 35.4 & 21.1 & 49.0 & 47.8 & 38.3 \\\\\n"," LoRA & 95.6 & 57.7 & 48.9 & 47.3 & 62.4 \\\\\n"," Full-Tuning & 89.0 & 60.8 & 51.2 & 51.3 & 63.1 \\\\\n"," \\nameshort~(Ours) & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n","\n","\n","\n"," \\midrule\n"," Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 55.9 & 54.3 \\\\\n"," Fully-Supervised & 97.4 & 97.4 & 85.8 & 82.1 & 90.7 \\\\\n"," \n"," \\bottomrule\n"," \\label{tab:medical}\n"," \\end{tabular}\n"," }\n"," \\vspace{-3mm}\n","\\end{table*}\n"],["\\begin{table*}[t!]\n"," \\centering\n"," \\vspace{2mm}\n"," \\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for sport understanding and reasoning questions. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n"," \\vspace{-2mm}\n","\t\\resizebox{0.48\\textwidth}{!}{\n"," \n"," \\begin{tabular}{l c c c c}\n"," \n"," \\toprule \n","\n"," Method & Easy & Medium & Hard & Average \\\\\n"," \\midrule\n"," Zero-Shot & 50.5 & 34.0 & 37.5 & 40.7 \\\\\n"," LoRA & 82.5 & 59.2 & 22.3 & 54.7 \\\\\n"," Full-Tuning & 82.7 & 59.0 & 21.3 & 54.3 \\\\\n"," \\nameshort~(Ours) & 82.5 & 60.4 & 46.3 & 63.1 \\\\\n","\n","\n","\n"," \\midrule\n"," Fully-Supervised & 98.1 & 75.4 & 66.1 & 79.9 \\\\\n"," \n"," \\bottomrule \n"," \\vspace{-4mm}\n"," \\label{tab:sport}\n"," \\end{tabular}\n"," }\n","\\end{table*}\n"],["\\begin{table*}[t!]\n"," \\centering\n"," \\caption{Ablation study of our \\namestageaa~for the QA Generator on the Kvasir-VQA dataset.}\n"," \\vspace{-2mm}\n","\t\\resizebox{0.8\\textwidth}{!}{\n"," \n"," \\begin{tabular}{l c c c c c}\n"," \n"," \\toprule \n","\n"," \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n"," \\cline{2-5}\n"," & Colitis & Esophagitis & Instrument & Polyps & \\\\\n"," \\midrule\n","\n"," Baseline & 93.0 & 88.2 & 55.7 & 56.2 & 73.3 \\\\\n"," Baseline+Distill. & 95.1 & 80.3 & 59.7 & 60.4 & 73.9 \\\\\n"," Baseline+Distill.+QA Neurons & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n"," \n"," \\bottomrule \n"," \\label{tab:ab1}\n"," \\end{tabular}\n"," }\n"," \\vspace{-5mm}\n","\\end{table*}\\begin{table*}[t!]\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{medicalfig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n"," \\label{figure:medicalg}\n"," \\vspace{-4mm}\n","\\end{figure}\n"],["\\begin{figure}[!t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{sportfig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results on the SPORTU dataset.}\n"," \\label{figure:sport}\n"," \\vspace{-4mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{medical2fig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n"," \\vspace{-4mm}\n","\\end{figure}\\begin{figure}[!t]\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{GenQA_medicalfig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results of generated pseudo-QA on the Kvasir-VQA dataset.}\n"," \\label{figure:medicalb}\n","\\end{figure}\\begin{figure}[t]\n"],["\\end{figure}\\begin{figure}[!ht]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{captionfig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results of generated caption on the SPORTU dataset.}\n"," \\label{figure:medical}\n"," \\vspace{-4mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{caption2fig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results of generated caption on the Kvasir-VQA dataset.}\n"," \\label{figure:medicala}\n"," \\vspace{-4mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{medical2fig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n"," \\vspace{-4mm}\n","\\end{figure}\\begin{figure}[!t]\n"]],"string":"[\n [\n \"\\\\begin{figure*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{model1fig.pdf}\\n\",\n \" \\\\caption{Overview of the proposed two-stage \\\\nameshort~framework for OOD VQA adaptation. In \\\\namestagea, the QA Generator is trained using a small set of labeled question-answer pairs and then used to generate pseudo QA pairs for a large collection of unlabeled images. In \\\\namestageb, the VQA model is fine-tuned with both the original labeled data and the produced pseudo QA pairs of unlabeled data, enabling label-efficient adaptation to out-of-distribution visual-question answering. We will detail the learning of our QA Generator in Figure~\\\\ref{figure:model2}.}\\n\",\n \" \\\\label{figure:model1}\\n\",\n \"\\\\end{figure*}To support such targeted interventions, a variety of attribution methods have been proposed to quantify the importance of individual neurons or weights. Some are designed to guide pruning, which reduces model size by removing components deemed less relevant. For example, Wanda~\\\\cite{sun2023simple} identifies unimportant weights by combining their magnitude with the norm of the associated input activation. Others~\\\\cite{fang2024towards,pan2023finding,yu2023neuron,yu2025locate} aim to inform fine-tuning, where only selected parts of the model are updated to acquire new capabilities or adapt to specific domains. A common strategy in this context is to measure gradient magnitudes during backpropagation, under the assumption that neurons with higher gradients contribute more significantly to the output~\\\\cite{zhang2024gradient}.\\n\"\n ],\n [\n \"\\\\begin{figure*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{model2fig.pdf}\\n\",\n \" \\\\caption{Illustration of our \\\\namestageaa~for the QA Generator. The QA-relevant parameters are first selected based on gradient scores from labeled QA data. During training, only these selected parameters are updated using auxiliary caption supervision from unlabeled images, allowing QA-related knowledge distillation for the QA Generator.}\\n\",\n \" \\\\label{figure:model2}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\\\%) of VQA accuracy. Only 1\\\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\t\\\\resizebox{0.75\\\\textwidth}{!}{\\n\",\n \" \\n\",\n \" \\\\begin{tabular}{l c c c c c}\\n\",\n \" \\n\",\n \" \\\\toprule \\n\",\n \"\\n\",\n \" \\\\multirow{2}{*}{Method} & \\\\multicolumn{4}{c}{Image Category} & \\\\multirow{2}{*}{Average}\\\\\\\\\\n\",\n \" \\\\cline{2-5}\\n\",\n \" & Colitis & Esophagitis & Instrument & Polyps & \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot& 35.4 & 21.1 & 49.0 & 47.8 & 38.3 \\\\\\\\\\n\",\n \" LoRA & 95.6 & 57.7 & 48.9 & 47.3 & 62.4 \\\\\\\\\\n\",\n \" Full-Tuning & 89.0 & 60.8 & 51.2 & 51.3 & 63.1 \\\\\\\\\\n\",\n \" \\\\nameshort~(Ours) & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 55.9 & 54.3 \\\\\\\\\\n\",\n \" Fully-Supervised & 97.4 & 97.4 & 85.8 & 82.1 & 90.7 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\label{tab:medical}\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\vspace{2mm}\\n\",\n \" \\\\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for sport understanding and reasoning questions. Only 1\\\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\t\\\\resizebox{0.48\\\\textwidth}{!}{\\n\",\n \" \\n\",\n \" \\\\begin{tabular}{l c c c c}\\n\",\n \" \\n\",\n \" \\\\toprule \\n\",\n \"\\n\",\n \" Method & Easy & Medium & Hard & Average \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot & 50.5 & 34.0 & 37.5 & 40.7 \\\\\\\\\\n\",\n \" LoRA & 82.5 & 59.2 & 22.3 & 54.7 \\\\\\\\\\n\",\n \" Full-Tuning & 82.7 & 59.0 & 21.3 & 54.3 \\\\\\\\\\n\",\n \" \\\\nameshort~(Ours) & 82.5 & 60.4 & 46.3 & 63.1 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\\\midrule\\n\",\n \" Fully-Supervised & 98.1 & 75.4 & 66.1 & 79.9 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule \\n\",\n \" \\\\vspace{-4mm}\\n\",\n \" \\\\label{tab:sport}\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Ablation study of our \\\\namestageaa~for the QA Generator on the Kvasir-VQA dataset.}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\t\\\\resizebox{0.8\\\\textwidth}{!}{\\n\",\n \" \\n\",\n \" \\\\begin{tabular}{l c c c c c}\\n\",\n \" \\n\",\n \" \\\\toprule \\n\",\n \"\\n\",\n \" \\\\multirow{2}{*}{Method} & \\\\multicolumn{4}{c}{Image Category} & \\\\multirow{2}{*}{Average}\\\\\\\\\\n\",\n \" \\\\cline{2-5}\\n\",\n \" & Colitis & Esophagitis & Instrument & Polyps & \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\n\",\n \" Baseline & 93.0 & 88.2 & 55.7 & 56.2 & 73.3 \\\\\\\\\\n\",\n \" Baseline+Distill. & 95.1 & 80.3 & 59.7 & 60.4 & 73.9 \\\\\\\\\\n\",\n \" Baseline+Distill.+QA Neurons & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule \\n\",\n \" \\\\label{tab:ab1}\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\vspace{-5mm}\\n\",\n \"\\\\end{table*}\\\\begin{table*}[t!]\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{medicalfig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results on the Kvasir-VQA dataset.}\\n\",\n \" \\\\label{figure:medicalg}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{sportfig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results on the SPORTU dataset.}\\n\",\n \" \\\\label{figure:sport}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{medical2fig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results on the Kvasir-VQA dataset.}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\\\begin{figure}[!t]\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{GenQA_medicalfig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results of generated pseudo-QA on the Kvasir-VQA dataset.}\\n\",\n \" \\\\label{figure:medicalb}\\n\",\n \"\\\\end{figure}\\\\begin{figure}[t]\\n\"\n ],\n [\n \"\\\\end{figure}\\\\begin{figure}[!ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{captionfig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results of generated caption on the SPORTU dataset.}\\n\",\n \" \\\\label{figure:medical}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{caption2fig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results of generated caption on the Kvasir-VQA dataset.}\\n\",\n \" \\\\label{figure:medicala}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{medical2fig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results on the Kvasir-VQA dataset.}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\\\begin{figure}[!t]\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"%File: anonymous-submission-latex-2026.tex\n\\documentclass[letterpaper]{article} % DO NOT CHANGE THIS\n\\usepackage[draft]{aaai2026} % DO NOT CHANGE THIS\n\n\n\\usepackage{times} % DO NOT CHANGE THIS\n\\usepackage{helvet} % DO NOT CHANGE THIS\n\\usepackage{courier} % DO NOT CHANGE THIS\n\\usepackage[hyphens]{url} % DO NOT CHANGE THIS\n\\usepackage{graphicx} % DO NOT CHANGE THIS\n\\urlstyle{rm} % DO NOT CHANGE THIS\n\\def\\UrlFont{\\rm} % DO NOT CHANGE THIS\n\\usepackage{natbib} % DO NOT CHANGE THIS AND DO NOT ADD ANY OPTIONS TO IT\n\\usepackage{caption} % DO NOT CHANGE THIS AND DO NOT ADD ANY OPTIONS TO IT\n\\frenchspacing % DO NOT CHANGE THIS\n\\setlength{\\pdfpagewidth}{8.5in} % DO NOT CHANGE THIS\n\\setlength{\\pdfpageheight}{11in} % DO NOT CHANGE 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Scott Penberthy\\textsuperscript{\\rm 3},\n% % George Ferguson\\textsuperscript{\\rm 4},\n% % Hans Guesgen\\textsuperscript{\\rm 5}\n% % Note that the comma should be placed after the superscript\n\n% 1101 Pennsylvania Ave, NW Suite 300\\\\\n% Washington, DC 20004 USA\\\\\n% % email address must be in roman text type, not monospace or sans serif\n% proceedings-questions@aaai.org\n% %\n% % See more examples next\n% }\n\n%Example, Single Author, ->> remove \\iffalse,\\fi and place them surrounding AAAI title to use it\n\\iffalse\n\\title{My Publication Title --- Single Author}\n\\author {\n Author Name\n}\n\\affiliations{\n Affiliation\\\\\n Affiliation Line 2\\\\\n name@example.com\n}\n\\fi\n\n\\iffalse\n\n\n%Example, Multiple Authors, ->> remove \\iffalse,\\fi and place them surrounding AAAI title to use it\n\n\\author {\n % Authors\n First Author Name\\textsuperscript{\\rm 1},\n Second Author Name\\textsuperscript{\\rm 2},\n Third Author Name\\textsuperscript{\\rm 1}\n}\n\\affiliations {\n % Affiliations\n \\textsuperscript{\\rm 1}Affiliation 1\\\\\n \\textsuperscript{\\rm 2}Affiliation 2\\\\\n firstAuthor@affiliation1.com, secondAuthor@affilation2.com, thirdAuthor@affiliation1.com\n}\n\\fi\n\n\n% REMOVE THIS: bibentry\n% This is only needed to show inline citations in the guidelines document. You should not need it and can safely delete it.\n\\usepackage{bibentry}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{multirow}\n\\usepackage{booktabs}\n% END REMOVE bibentry\n\\newcommand{\\nameshort}{\\textcolor{black}{LEAML}}\n\\newcommand{\\namestagea}{\\textcolor{black}{Pseudo QA Generation}}\n\\newcommand{\\namestageaa}{\\textcolor{black}{Selective Neuron Distillation}}\n\\newcommand{\\namestageb}{\\textcolor{black}{OOD VQA Finetuning}}\n\n\n\\begin{document}\n\n\\maketitle\n% \\def\\thefootnote{*}\\footnotetext{~Work done during an internship at NVIDIA.}\n% \\pagestyle{plain}\n\\begin{abstract}\nMultimodal Large Language Models (MLLMs) have achieved strong performance on general visual benchmarks but struggle with out-of-distribution (OOD) tasks in specialized domains such as medical imaging, where labeled data is limited and expensive. We introduce \\nameshort, a label-efficient adaptation framework that leverages both scarce labeled VQA samples and abundant unlabeled images. Our approach generates domain-relevant pseudo question-answer pairs for unlabeled data using a QA generator regularized by caption distillation. Importantly, we selectively update only those neurons most relevant to question-answering, enabling the QA Generator to efficiently acquire domain-specific knowledge during distillation. Experiments on gastrointestinal endoscopy and sports VQA demonstrate that \\nameshort~consistently outperforms standard fine-tuning under minimal supervision, highlighting the effectiveness of our proposed \\nameshort~framework.\n\\end{abstract}\\section{Introduction}\nLarge Language Models (LLMs)~\\cite{touvron2023llama, achiam2023gpt, bai2023qwen} have demonstrated impressive capabilities across diverse language tasks. By incorporating visual understanding, Multimodal Large Language Models (MLLMs)~\\cite{alayrac2022flamingo, liu2023visual,wang2024qwen2} extend these capabilities to visual question answering (VQA), image captioning, and multimodal reasoning tasks.~\\cite{wang2024exploring} Recent MLLMs have achieved remarkable performance on general visual benchmarks, showing strong generalization within their training distributions. Although scaling laws~\\cite{kaplan2020scaling} show promise for enhancing model performance, they do not eliminate dependence on pre-training data, which limits generalization to novel domains. In real-world deployment, MLLMs will face domain-specific tasks that fall outside their training distribution, such as specialized medical imaging or technical visual content. When confronted with such out-of-distribution (OOD) data, these models often produce erroneous or unreliable outputs, limiting their applicability in specific domains where accuracy is critical.\n\n\n\nWhile existing studies on OOD have primarily focused on detection~\\cite{ming2022delving, wang2023clipn} or domain-specific classification tasks~\\cite{liu2023clip, lei2023clip, zhang2023biomedclip}, applying MLLMs to visual question answering in unfamiliar domains introduces distinct challenges. Unlike detection, which focuses on filtering unfamiliar inputs, VQA requires models to generate accurate and contextually grounded answers for images outside the training distribution. Although many specific domains offer abundant unlabeled images, standard VQA training pipelines depend on paired question-answer annotations, which are costly to obtain due to the need for domain expertise. Furthermore, VQA questions must be carefully constructed based on the visual content. Randomly pairing unrelated questions with images creates confusing training signals and reduces the effectiveness of learning. Due to the scarcity of high-quality labeled data, fully fine-tuning MLLMs often leads to severe overfitting, particularly in VQA where models must produce free-form, semantically appropriate responses rather than select from fixed labels. These challenges underscore the need for adaptation methods that can leverage both limited labeled examples and large pools of unlabeled images in a way that preserves generation capabilities while acquiring domain-specific understanding.\n\nIn this paper, we introduce \\textbf{\\nameshort}, a two-stage \\textbf{L}abel-\\textbf{E}fficient \\textbf{A}daptation framework for \\textbf{M}ultiModal \\textbf{L}LM designed to effectively leverage both the limited labeled VQA data and the abundant unlabeled images in the target domain. The framework comprises \\namestagea, which constructs domain-relevant QA pairs from unlabeled images, and \\namestageb, which fine-tunes the target MLLM using both the generated pairs and the original labeled data. In \\namestagea, a QA Generator is trained using the small labeled dataset to capture the domain-specific patterns of question-answer formulations. To mitigate overfitting caused by the scarcity of labeled data, the generator is regularized via caption distillation, where it additionally learns from image captions produced by a large-scale model, providing broader visual-linguistic signals beyond the limited annotations. The generator then synthesizes diverse pseudo QA pairs for the unlabeled domain images, creating a significantly richer training resource. In \\namestageb, the target MLLM is fine-tuned with both the original labeled samples and the generated QA pairs. To enhance adaptation efficiency and prevent overfitting, we employ \\namestageaa, which is motivated by the insight that domain-specific knowledge is often encoded in a subset of neurons; focusing updates on these neurons enables the model to acquire domain-relevant reasoning capabilities while preserving general language generation skills. Experiments conducted on gastrointestinal endoscopy VQA demonstrate that our method significantly improves performance compared to standard fine-tuning approaches.\n\n\nOur contributions can be summarized as follows:\n\\begin{itemize}\n \\item We propose a two-stage learning framework \\nameshort, which leverages both scarce labeled data and abundant unlabeled images to achieve MLLM adapataion for domain-specific VQA .\n \\item We introduce \\namestagea, which learns a generator to produce pseudo question-answer pairs for unlabeled data, augmenting the training set for finetuning the VQA model on specialized domains.\n \\item We design \\namestageaa~for the QA generator, which performs captioning distillation to acquire domain-related knowledge while selectively updates QA-related neurons, resulting in reliable pseudo QA pairs for finetuning.\n\n\n\n\\end{itemize}\n\n\n\\section{Related Works}\n\\subsection{Out-of-Distribution Data Learning}\n% 1. OOD detection\n% 2. CLIP-based classification\n% 3. MLLM (Domain adaption, medical foundation models)\nOut-of-distribution (OOD) data refers to inputs that differ significantly from those seen during training. Early OOD research~\\cite{ming2022delving, wang2023clipn} primarily focused on detection tasks, where the goal is to identify whether an input falls outside the training distribution. These methods often treat OOD detection as anomaly detection. However, these methods aim to identify and reject OOD inputs rather than adapt models to perform well on them. \n% In our scenario, OOD data from specialized domains represents valid test cases requiring accurate VQA responses, necessitating adaptation rather than detection.\nBeyond detection, another line of work explores how vision-language models can be adapted for OOD domains. CLIP and its variants have shown promise in medical imaging applications through domain-specific fine-tuning~\\cite{liu2023clip,lei2023clip, zhang2023biomedclip}. \n% Zhang et al. demonstrated effective adaptation of CLIP for chest X-ray classification, while Wang et al. proposed BioCLIP for diagnosis across multiple medical imaging modalities. Other works have extended CLIP for medical image segmentation using text prompts to guide anatomical structure identification. \nHowever, these approaches are limited to classification settings, where models predict labels from a fixed set rather than generating open-ended responses.\n\nRecent works explore adapting LLMs to specific domains~\\cite{zhang2023reformulating, cheng2024domain, bhatia2024fintral,cheng2023adapting}. For instance,~\\cite{zhang2023reformulating, kim2025videoicl} employ retrieval-based approaches to handle out-of-distribution inputs, relying on external sources to provide relevant context for domain adaptation. However, such methods still assume that the LLM has sufficient foundational knowledge to effectively interpret the retrieved information.\nIn the vision-language domain, ~\\cite{cheng2024domain} propose fine-tuning MLLMs to automatically generate question-answer pairs from existing image-caption datasets, subsequently using these synthetic QA pairs for domain-specific VQA training. However, the effectiveness of such methods depends heavily on both the LLM's domain knowledge and the granularity of source captions. Fine-grained captions enable detailed QA generation, while coarse-grained descriptions yield only generic questions. These factors highlight the need for methods that can produce high-quality domain-specific QA pairs even with limited domain knowledge and varying caption quality.\n% 最後一句要不要\n\n\n% To cite\n\\subsection{Semi-Supervised Learning}\nSemi-supervised learning (SSL) is a strategy to bridge the gap between limited labeled data and abundant unlabeled resources, especially in domains where annotation is expensive or requires domain expertise. Among existing SSL paradigms, pseudo-labeling~\\cite{lee2013pseudo,xie2020self} has been widely adopted. This approach trains models on labeled data, then uses them to pseudo-label unlabeled samples for further training.\n\nPseudo-labeling has been widely applied to tasks such as image classification~\\cite{zeng2023pefat} and Segmentation~\\cite{yang2023revisiting}, where labels are either discrete or can be directly generated from the data. In these settings, unlabeled samples can be automatically annotated with relatively reliable supervision. In contrast, applying pseudo-labeling to visual question answering (VQA) is considerably more difficult. VQA requires not only a grounded answer but also a relevant and context-aware question that must be closely aligned with the visual content. Unlike captions or class labels, such question-answer pairs cannot be directly inferred from the image alone. A naïve solution might involve randomly assigning questions to domain images, but this leads to incoherent or misleading training data. As a result, semi-supervised learning remains largely underexplored in VQA, particularly in domain-specific scenarios where labeled data is scarce and generating valid pseudo QA pairs is highly non-trivial.\n \n\n% In vision-language tasks, semi-supervised approaches have shown promise for image captioning, visual grounding, and multimodal understanding. The fundamental challenge lies in effectively utilizing unlabeled data without introducing noise that degrades model performance.\n% Pseudo-labeling has emerged as a powerful technique for semi-supervised learning, where confident predictions on unlabeled data are treated as ground truth for subsequent training iterations. Recent advances have refined this approach through consistency regularization, uncertainty estimation, and selective pseudo-label filtering. In multimodal contexts, pseudo-labeling faces unique challenges as it must maintain coherence between visual and textual modalities while generating plausible outputs.\n% For VQA tasks specifically, semi-supervised methods remain largely unexplored despite the high annotation cost of creating question-answer pairs. Unlike classification where pseudo-labels are discrete categories, VQA requires generating both meaningful questions and their corresponding free-form answers. This complexity has limited the adoption of semi-supervised techniques in VQA adaptation scenarios. Our work addresses this gap by introducing a pseudo QA generation framework specifically designed for domain adaptation, where we leverage the complementary strengths of limited labeled data and abundant unlabeled images to enable effective transfer to specialized domains.\n\n\n% \\subsection{Knowledge Neurons in MLLMs}\n% \\subsection{Neuron Editing in MLLMs for Specific Knowledge}\n\\subsection{Neuron-Level Knowledge Attribution in DNNs}\nKnowledge in neural networks is localized and stored within specific neural components rather than distributed uniformly across parameters. \nPrevious work has shown that the feed-forward network (FFN) layers in Transformers play a key role in storing knowledge~\\cite{geva2020transformer,geva2022transformer}. These layers have been characterized as performing additive, knowledge-based updates on token representations. \\cite{dai2021knowledge} propose a neuron-level attribution approach to identify knowledge neurons in FFNs responsible for storing factual knowledge.\nThese findings indicate that MLLMs encode different types of knowledge in specialized neural components with distinct activation patterns, enabling targeted manipulation of specific knowledge without affecting the entire network.\n\n\\begin{figure*}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{model1fig.pdf}\n \\caption{Overview of the proposed two-stage \\nameshort~framework for OOD VQA adaptation. In \\namestagea, the QA Generator is trained using a small set of labeled question-answer pairs and then used to generate pseudo QA pairs for a large collection of unlabeled images. In \\namestageb, the VQA model is fine-tuned with both the original labeled data and the produced pseudo QA pairs of unlabeled data, enabling label-efficient adaptation to out-of-distribution visual-question answering. We will detail the learning of our QA Generator in Figure~\\ref{figure:model2}.}\n \\label{figure:model1}\n % \\vspace{-4mm}\n\\end{figure*}To support such targeted interventions, a variety of attribution methods have been proposed to quantify the importance of individual neurons or weights. Some are designed to guide pruning, which reduces model size by removing components deemed less relevant. For example, Wanda~\\cite{sun2023simple} identifies unimportant weights by combining their magnitude with the norm of the associated input activation. Others~\\cite{fang2024towards,pan2023finding,yu2023neuron,yu2025locate} aim to inform fine-tuning, where only selected parts of the model are updated to acquire new capabilities or adapt to specific domains. A common strategy in this context is to measure gradient magnitudes during backpropagation, under the assumption that neurons with higher gradients contribute more significantly to the output~\\cite{zhang2024gradient}.\n\n\n% Neuron editing, the process of modifying this stored knowledge, is often approached via two primary strategies: pruning and fine-tuning. Pruning methods aim to reduce model complexity by removing less important components. For instance, ~\\cite{sun2023simple} introduced Wanda, a weight pruning method that evaluates each weight's contribution by considering both its magnitude and the norm of its associated input activation. In contrast, fine-tuning-based editing methods often attribute specific knowledge to neurons by scoring their contribution to model outputs~\\cite{zhang2024gradient,fang2024towards,pan2023finding,yu2023neuron,yu2025locate}. A common approach~\\cite{zhang2024gradient} analyzes gradient magnitudes, where higher gradients for specific inputs indicate neurons that contribute more significantly to the final output.This gradient-based analysis enables selective updating of neurons most relevant to target domains, preserving general knowledge while acquiring specialized capabilities.\n\n\n\n\n\n\\section{Method}\n\n\\subsection{Problem Formulation and Framework Overview}\n\n\\paragraph{Problem Formulation.} We first define the problem settings and notations used in this paper. For the out-of-distribution visual question-answering problem, we consider domain-specific tasks (e.g., gastrointestinal endoscopy) which are still based on RGB images or videos but are rarely or not covered in the pretraining data of general-purpose multimodal large language models. Since such domain-specific tasks generally require great expense to obtain manual annotations from domain experts, we further consider a realistic yet challenging setting, where only few data are annotated in the training dataset $D$. That is, the training dataset $D$ contains a set of labeled data $D_l$ of few samples and also a set of abundant unlabeled data $D_u$, which is similar to traditional semi-supervised learning. Each data instance in the labeled dataset $D_l$ contains an image or video $V$, an associated question $Q$, and the corresponding answer $A$, while each sample in the unlabeled dataset $D_u$ contains only the visual part $V$.\n\n\\paragraph{Framework Overview.} Given the above training data and a pretrained general MLLM, our goal is to adapt this pretrained MLLM to address out-of-distribution visual question-answering with only few labeled instances. To achieve this goal, we propose a two-stage learning framework \\nameshort~as shown in Figure~\\ref{figure:model1}. Our \\nameshort~framework includes two stages: \\namestagea~and \\namestageb. The former stage aims to generate proper pseudo question-answer pairs for the unlabeled dataset $D_u$, while the latter stage leverages both the labeled dataset $D_l$ and the produced pseudo QA pairs for the unlabeled data $D_u$ to finetune a pretrained MLLM for addressing out-of-distribution visual question-answering. \n\n\\begin{figure*}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{model2fig.pdf}\n \\caption{Illustration of our \\namestageaa~for the QA Generator. The QA-relevant parameters are first selected based on gradient scores from labeled QA data. During training, only these selected parameters are updated using auxiliary caption supervision from unlabeled images, allowing QA-related knowledge distillation for the QA Generator.}\n \\label{figure:model2}\n % \\vspace{-4mm}\n\\end{figure*}\nSpecifically, since the unlabeled data only contain the visual information but lack the corresponding textual annotations for training a VQA model, our \\nameshort~framework first employ a QA Generator $G$ which is directly supervised by the labeled data to produce pseudo QA pairs for unlabeled data. However, in this manner, the QA Generator may overfit on those few labeled samples and fail to generalize well to produce reliable QA pairs for unlabeled data. To overcome this challenge, we further propose \\namestageaa~to leverage also the unlabeled data during the training of the QA Generator. As shown in Figure~\\ref{figure:model2}, in addition to the QA generation supervised by labeled data, we perform captioning distillation using unlabeled data to distill related knowledge from a large MLLM. More importantly, during training, we update only QA-related neurons for both the QA generation and captioning distillation. In this way, such captioning distillation is designed to focus solely on gaining QA-related knowledge, and hence the QA Generator $G$ is able to produce reliable pseudo QA pairs for unlabeled data during inference, benefiting the following finetuning for the VQA model. We now detail our learning framework in the following subsections.\n\n\n\\subsection{\\namestagea~and \\namestageb}\n\nRecently, multimodal large language models (MLLMs) have achieved impressive generalization on a wide range of vision-language tasks. However, their performance often degrades when applied to specialized domains such as medical imaging, where domain-specific visual cues and terminology differ significantly from pretraining data. A significant barrier in adapting multimodal large language models (MLLMs) to these specialized domains is the extreme scarcity of annotated question-answer (QA) pairs. Obtaining such labeled data from domain experts is often expensive, time-consuming, and infeasible at scale, leading to severe limitations on direct fine-tuning. On the other hand, large volumes of unlabeled visual data typically exist, representing a potential yet largely untapped source of supervision. While traditional semi-supervised learning have demonstrated that unlabeled data can be highly beneficial, such success is largely limited to classification tasks. For unlabeled data in visual question-answering, both the question and answer are not accessible, and hence traditional semi-supervised learning cannot be easily applied in VQA to generate the pseudo labels without knowing or providing a corresponding question.\n\n% \\subsection{Pseudo QA Generation}\n\nTo overcome the limitation of requiring fully annotated data, we introduce a pseudo QA generation stage that transforms unlabeled visual data into useful supervision for the VQA model. The core idea is to train a QA Generator using limited labeled examples $D_l$, and then apply it to unlabeled inputs $D_u$ to produce additional VQA samples. Specifically, for each labeled instance $(V, Q, A)$ in $D_l$, we formulate the corresponding target text sequence $Y$ by concatenating of the question $Q$ and answer $A$ with special tokens: \n\n\\begin{equation}\n\\begin{aligned}\nY = [\\texttt{<q>} Q \\texttt{<q>} \\texttt{<a>} A \\texttt{<a>}].\n\\end{aligned}\n% \\vspace{-2mm}\n\\end{equation}\nThen, the QA generator $G$, initialized from a pretrained general MLLM, is trained to autoregressively generate $Y$ conditioned on the visual input $V$. The training objective $\\mathcal{L}_{QA}$ is defined as a standard autoregressive negative log-likelihood:\n\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{QA} = \\sum_{t=1}^{|Y|} \\log p(y_i \\mid V, y_{<i}), V \\in D_l\n\\end{aligned}\n\\label{eq:qa}\n% \\vspace{-2mm}\n\\end{equation}\nwhere $y_i$ denotes the $i$th text token of the sequence $Y$ and $p$ is the likelihood of text tokens estimated by the QA Generator $G$. Once the training is complete, the QA generator $G$ would be applied to produce pseudo QA pairs $[\\texttt{<q>} \\hat{Q} \\texttt{<q>} \\texttt{<a>} \\hat{A} \\texttt{<a>}] = G(V)$ for the visual input $V$ from unlabeled data, resulting in the dataset $\\hat{D_{u}} = \\{(V, \\hat{Q}, \\hat{A})\\}$. This dataset is then used to augment the original labeled data $D_l$ for finetuning the final VQA model with similar autoregressive objective $\\mathcal{L}_{VQA}$:\n\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{VQA} &= \\sum_{t=1}^{|A|} \\log p(a_i \\mid V, Q, a_{<i}), V \\in D_l, \\hat{D}_u\n\\end{aligned}\n\\label{eq:vqa}\n% \\vspace{-2mm}\n\\end{equation}\nNote that the VQA model is again initialized from a pretrained general MLLM. While the above pseudo QA generation enables the model to leverage unlabeled visual data for OOD VQA adaptation, the quality of generated QA pairs is tightly bound to the small number of labeled examples. With limited supervision, the model may produce noisy outputs on unlabeled data, especially under the out-of-distribution settings.\n\n\\subsection{\\namestageaa~for QA Generator}\nTo further mitigate the aforementioned problem of \\namestagea, our \\nameshort~framework introduces a distillation mechanism that directly incorporates abundant unlabeled data into the QA Generator training process. In addition to the QA generation part supervised by labeled data $D_l$, we further consider captioning distillation on unlabeled $D_u$ to gain domain-related knowledge from a large MLLM. Specifically, for each unlabeled visual input $V$, we employ a large pre-trained general MLLM to automatically generate a descriptive caption $C$. While the large MLLM may still be poor when directly applied to perform OOD VQA tasks, these state-of-the-art large models are pre-trained on vast and diverse corpora such as medical literature, Wikipedia articles, and other authoritative web resources. As a result, the captions generated by such models are often infused with rich semantic information, domain-specific terminology, and contextual knowledge, which are beneficial to the learning of the QA Generator $G$. Formally, the QA Generator $G$ is jointly optimized with the QA objective $\\mathcal{L}_{QA}$ in Equation~\\ref{eq:qa} using labeled data $D_l$ and the captioning distillation objective $\\mathcal{L}_{C}$ using unlabeled data $D_u$:\n\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{C} = - \\sum_{t=1}^{|C|} &\\log p(c_i \\mid V, c_{<i}), V \\in D_u \\\\\n\\mathcal{L}_{G} &= \\mathcal{L}_{QA} + \\mathcal{L}_{C}\n\\end{aligned}\n\\end{equation}\n\n\nWhile caption distillation enables the QA Generator $G$ to absorb rich semantic knowledge from unlabeled data, it remains essential that the model's capacity is focused on generating question-answer pairs rather than captioning. Under this motivation, we introduce a neuron selection strategy to ensure such captioning distillation is solely for enhancing QA-related knowledge. Specifically, we identify parameters in the QA Generator that contribute most to the question-answer generation and restrict parameter updates during training to this subset. For each parameter $\\theta$ in the QA Generator $G$, its importance score $s$ is quantified by the average magnitude of the gradient of the QA loss $\\mathcal{L}_{QA}$:\n\n\\begin{equation}\ns = \\left| \\frac{1}{|D_l|} \\sum_{(V, Q, A) \\in D_l} \\frac{\\partial \\mathcal{L}_{QA}}{\\partial \\theta} \\right|.\n\\end{equation}\nThen, we selection and update only parameters with top-$K$ scores in each neuron (i.e., each row in a linear weight matrix) while keep others frozen:\n\n\\begin{equation}\n\\theta \\leftarrow\n\\begin{cases}\n\\theta - \\eta \\cdot \\frac{\\partial \\mathcal{L}_{G}}{\\partial \\theta} & \\text{if $s$ is among top-$K$} \\\\\n\\theta, & \\text{otherwise}\n\\end{cases}\n\\end{equation}\nBy restricting updates to only the most QA-relevant neurons or parameters, we ensure that the auxiliary knowledge gained from caption distillation is efficiently integrated to support question-answer generation, rather than generic captioning or unrelated model capacities. With the above learning, the QA Generator is not limited to patterns seen in the small labeled set, but is instead exposed to the full diversity and richness of the target domain through the captions of unlabeled images. This enables the QA Generator to produce question-answer pairs that are more reflective of domain-specific semantics present in the unlabeled corpus. Hence, the resulting pseudo dataset $\\hat{D}_u$ would be more accurate and reliable with our proposed \\namestageaa, benefiting the subsequent learning of the VQA model in Equation~\\ref{eq:vqa}. \n\\section{Experiments}\n\n\\subsection{Datasets}\n\n\\paragraph{Kvasir-VQA}\n\nKvasir-VQA~\\cite{gautam2024kvasir} is a large-scale visual question answering dataset curated for research in the gastrointestinal (GI) medical imaging domain. The dataset consists of 6,500 endoscopic images sourced from the HyperKvasir and Kvasir-Instrument datasets, covering a wide spectrum of clinically relevant GI findings, anatomical sites, and medical instruments. The images in Kvasir-VQA reflect real-world clinical scenarios, including both normal findings and a variety of pathological conditions such as polyps, ulcers, and esophagitis, as well as procedure-related scenes featuring different instruments and interventions. Each image is paired with one or more expert-annotated question-answer (QA) pairs. These QA annotations are diverse, encompassing multiple question types including yes/no, multiple-choice, and counting, thus enabling comprehensive evaluation of both recognition and reasoning abilities for VQA.\n\nTo standardize the evaluation process, we further convert all question-answer pairs in Kvasir-VQA into a multiple-choice format. For each question, we define the set of candidate options as all possible answers that appear for that question type throughout the dataset, so that the number of answer choices is not fixed for different questions. For experimental setup, we partition the dataset into training and testing splits, containing 18,499 and 18,075 QA pairs, respectively. To simulate the limited annotation scenario when learning our \\nameshort~framework, only 1\\% QA pairs in the training split are used as labeled data while the remaining training images are treated as unlabeled data.\n\\begin{table*}[t!]\n % \\vspace{5mm}\n \\centering\n \\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\%) of VQA accuracy. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n \\vspace{-2mm}\n\t\\resizebox{0.75\\textwidth}{!}{\n \n \\begin{tabular}{l c c c c c}\n \n \\toprule \n\n \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n \\cline{2-5}\n & Colitis & Esophagitis & Instrument & Polyps & \\\\\n \\midrule\n Zero-Shot& 35.4 & 21.1 & 49.0 & 47.8 & 38.3 \\\\\n % Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 56.0 & 54.3 \\\\\n LoRA & 95.6 & 57.7 & 48.9 & 47.3 & 62.4 \\\\\n % DoRA & ? & ? & ? & ? & ? \\\\\n Full-Tuning & 89.0 & 60.8 & 51.2 & 51.3 & 63.1 \\\\\n \\nameshort~(Ours) & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n\n\n\n \\midrule\n Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 55.9 & 54.3 \\\\\n Fully-Supervised & 97.4 & 97.4 & 85.8 & 82.1 & 90.7 \\\\\n \n \\bottomrule\n \\label{tab:medical}\n \\end{tabular}\n }\n \\vspace{-3mm}\n\\end{table*}\n\\begin{table*}[t!]\n \\centering\n \\vspace{2mm}\n \\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for sport understanding and reasoning questions. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n \\vspace{-2mm}\n\t\\resizebox{0.48\\textwidth}{!}{\n \n \\begin{tabular}{l c c c c}\n \n \\toprule \n\n Method & Easy & Medium & Hard & Average \\\\\n \\midrule\n Zero-Shot & 50.5 & 34.0 & 37.5 & 40.7 \\\\\n LoRA & 82.5 & 59.2 & 22.3 & 54.7 \\\\\n % DoRA & ? & ? & ? & ? \\\\\n Full-Tuning & 82.7 & 59.0 & 21.3 & 54.3 \\\\\n \\nameshort~(Ours) & 82.5 & 60.4 & 46.3 & 63.1 \\\\\n\n\n\n \\midrule\n % Zero-Shot (Qwen2.5-VL-72B) & ? & ? & ? & ? \\\\\n Fully-Supervised & 98.1 & 75.4 & 66.1 & 79.9 \\\\\n \n \\bottomrule \n \\vspace{-4mm}\n \\label{tab:sport}\n \\end{tabular}\n }\n\\end{table*}\n\\paragraph{SPORTU} SPORTU~\\cite{xia2024sportu} is a recently released benchmark designed to evaluate the sports understanding and reasoning abilities of multimodal large language models (MLLMs). The dataset comprises 1,701 slow-motion sports video clips, spanning seven popular sports: \\textit{American football, badminton, baseball, basketball, ice hockey, soccer}, and \\textit{volleyball}. The questions in SPORTU are diverse and challenging, covering rule comprehension, tactical analysis, prediction of outcomes, and recognition of actions and fouls. All questions are categorized into three levels of difficulty: \\textbf{easy}, which focuses on basic recognition tasks such as identifying the sport or counting players; \\textbf{medium}, which requires knowledge of player roles and basic tactics; and \\textbf{hard}, which involves deep reasoning about rules, foul detection, and scenario-based understanding. This tiered design enables comprehensive evaluation of MLLMs, from simple perception (in-distribution) to advanced, domain-specific sports reasoning (out-of-distribution). We partition the dataset into training and testing splits, containing 5,525 and 5,478 QA pairs, respectively. Similarly, we only consider 1\\% QA pairs in the training split when learning our \\nameshort~framework, while the remaining training images are treated as unlabeled data.\n\n\n\n\\subsection{Implementation Details}\nOur entire implementation is based on the PyTorch framework. For simplicity, we use NVILA-Lite-2B~\\cite{liu2025nvila} as our MLLM backbone for both our QA Generator and the VQA model. As for the large MLLM used for captioning distillation, we consider the state-of-the-art open source model, Qwen2.5-VL-72B-Instruct~\\cite{bai2025qwen2}. All the model weights are initialized with official pretrained checkpoints. During training, we use the AdamW optimizer with an initial learning rate of $0.00001$ and a cosine annealing schedule for learning rate decay. The batch size is set as $16$. As for neuron selection, we set the number of parameter $K=1000$ on the Kvasir-VQA dataset and $K=3000$ for SPORTU, respectively. The training is performed on 16 NVIDIA A100 GPUs with 80GB memory each. During inference, we use deterministic (greedy) decoding for all answer generation for the VQA model, i.e., at each generation step, the model always selects the token with the highest probability. This ensures that the outputs are fully reproducible and comparable across runs. As for pseudo QA Generation, we choose to use nucleus sampling on our QA Generator to produce several different question-answer pairs for each single visual input.\n\n\\subsection{Quantitative and Qualitative Experiments}\n\nWhile multimodal large language models (MLLMs) have demonstrated remarkable abilities on general visual understanding benchmarks, their robustness and adaptability often fall short when transferred to specialized domains such as medical image question answering. This gap arises primarily from two factors: the limited availability of expert-annotated data, and the significant distribution shift between general pretraining data and domain-specific imagery. In the context of medical imaging, acquiring comprehensive labeled datasets is both costly and time-consuming, which motivates the need for approaches that can effectively leverage abundant unlabeled data. To evaluate our method under such kind of scenarios, we design experiments on the Kvasir-VQA dataset, a large-scale benchmark of expert-annotated QA pairs paired with real-world endoscopic images.\n\n\n\n\\begin{table*}[t!]\n \\centering\n \\caption{Ablation study of our \\namestageaa~for the QA Generator on the Kvasir-VQA dataset.}\n \\vspace{-2mm}\n\t\\resizebox{0.8\\textwidth}{!}{\n \n \\begin{tabular}{l c c c c c}\n \n \\toprule \n\n \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n \\cline{2-5}\n & Colitis & Esophagitis & Instrument & Polyps & \\\\\n \\midrule\n\n Baseline & 93.0 & 88.2 & 55.7 & 56.2 & 73.3 \\\\\n Baseline+Distill. & 95.1 & 80.3 & 59.7 & 60.4 & 73.9 \\\\\n Baseline+Distill.+QA Neurons & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n \n \\bottomrule \n \\label{tab:ab1}\n \\end{tabular}\n }\n \\vspace{-5mm}\n\\end{table*}\\begin{table*}[t!]\n \\centering\n \\vspace{2mm}\n \\caption{Ablation study of our \\namestageaa~for the QA Generator on the SPORTU dataset.}\n \\vspace{-2mm}\n\t\\resizebox{0.63\\textwidth}{!}{\n \n \\begin{tabular}{l c c c c}\n \n \\toprule \n\n Method & Easy & Medium & Hard & Average \\\\\n \\midrule\n Baseline & 75.5 & 60.3 & 44.4 & 60.1 \\\\\n Baseline+Distill.& 82.9 & 61.2 & 42.3 & 62.2 \\\\\n Baseline+Distill.+QA Neurons & 82.5 & 60.4 & 46.3 & 63.1 \\\\\n \n \\bottomrule \n \\label{tab:ab2}\n \\end{tabular}\n }\n \\vspace{-6mm}\n\\end{table*}\nTable~\\ref{tab:medical} presents a detailed comparison of different learning strategies on the Kvasir-VQA datasets, where only $1\\%$ of the training data is labeled and the remaining ones are treated as unlabeled. From this Table, we see that zero-shot inference using NVILA-Lite-2B achieves only $38.3\\%$ average accuracy, indicating the difficulty of the task without any fine-tuning. Fine-tuning with LoRA~\\cite{hu2022lora} or full parameter updates on just $1\\%$ labeled data yields moderate improvements ($62.4\\%$ and $63.1\\%$ accuracy, respectively), but these methods still struggle on less-represented or out-of-distribution categories. By augmenting the training with pseudo QA pairs generated from the unlabeled images, our approach significantly boosts average accuracy to $76.7\\%$, especially on challenging categories such as Esophagitis. As a reference, the fully supervised model (using all labeled data) achieves $90.7\\%$.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{medicalfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n \\label{figure:medicalg}\n \\vspace{-4mm}\n\\end{figure}\n\nWe further evaluate our method on the SPORTU dataset to assess its generalization ability in the sports domain, which poses unique challenges compared to the medical setting. Unlike static medical images, SPORTU consists of dynamic sports video clips that require not only visual recognition but also temporal reasoning, action understanding, and comprehension of complex game rules. These factors make sports VQA a particularly demanding task for multimodal large language models. As shown in Table~\\ref{tab:sport}, our \\nameshort~framework achieves consistent improvements over all baselines. In particular, our method raises the average accuracy to 63.1\\%, outperforming both LoRA and full-tuning by a clear margin. Notably, the accuracy on “Hard” questions—which require advanced reasoning—improves significantly from around 22.3\\% to 46.3\\%. In addition to quantitative results, we also provide qualitative comparisons as shown in Figure~\\ref{figure:medical} and~\\ref{figure:sport}. We see that, our \\nameshort~framework is able to produce accurate answers compared to state-of-the-art MLLMs on the challenging medical and sport domains. Through the above experiments, we verify that our ~\\nameshort~framework, which directly incorporates unlabeled data through pseudo QA generation, can substantially enhance VQA performance on out-of-distribution domain with limited annotations.\n\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{sportfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the SPORTU dataset.}\n \\label{figure:sport}\n \\vspace{-4mm}\n\\end{figure}\n\n\\subsection{Ablation Studies}\nAs shown in Table~\\ref{tab:ab1}, our ablation study on Kvasir-VQA evaluates the effects of caption distillation and selective neuron updates. Caption distillation alone leads to only a minor increase in average accuracy (an improvement of just 0.6\\% over the baseline). In contrast, when selective neuron updates are applied, the accuracy increases substantially, yielding a total gain of 3.4\\% over the baseline. A similar trend is observed on the SPORTU dataset (Table~\\ref{tab:ab2}). These results highlight that targeted neuron selection is crucial for effective distillation for the QA Generator, and that substantial performance gains can only be achieved when both components are used together.\n\n\\section{Conclusion}\nIn this paper, we introduce \\nameshort, a label-efficient adaptation framework designed to transfer MLLMs to out-of-distribution (OOD) domains that extend far beyond their original pretraining distribution. Our approach first utilizes \\namestagea~to generate domain-relevant pseudo question-answer pairs from large pools of unlabeled visual data, effectively expanding the training set in scenarios where annotated examples are extremely limited. In addition, we employ \\namestageaa~for the QA Generator, a selective neuron updating strategy that identifies and updates only knowledge-relevant neurons while acquiring domain knowledge from state-of-the-art large MLLMs. We conduct extensive experiments on OOD benchmarks, including gastrointestinal endoscopy and sports VQA, demonstrating the applicability of our framework. Detailed ablation studies and both quantitative and qualitative analyses consistently show that our proposed \\nameshort~framework achieves substantial improvements over conventional fine-tuning methods, validating its effectiveness and robustness for adapting MLLMs to challenging domain-specific visual tasks with limited annotations.\n\n\\bibliography{aaai2026}\n\\clearpage\n% \\input{ReproducibilityChecklist}\n\\appendix\n\\section{Additional Visualization}\n\n\\subsection{Comparison with Baseline in VQA}\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{medical2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n % \\label{figure:afd}\n \\vspace{-4mm}\n\\end{figure}\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{sport2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the SPORTU dataset.}\n % \\label{figure:sport2}\n % \\vspace{-4mm}\n\\end{figure}\nWe provide additional qualitative results comparing our LEAML method with baseline approaches on both medical and sports VQA tasks. These examples demonstrate our method's superior performance in generating accurate, domain-specific answers. The results show that our approach better understands specialized terminology and visual patterns, leading to more precise responses compared to standard MLLMs.\n\n\\subsection{Generated Pseudo-QA Examples}\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{GenQA_medicalfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results of generated pseudo-QA on the Kvasir-VQA dataset.}\n \\label{figure:medicalb}\n % \\vspace{-4mm}\n\\end{figure}\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{GenQA_sportfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results of generated pseudo-QA on the SPORTU dataset.}\n \\label{figure:medicalc}\n % \\vspace{-4mm}\n\\end{figure}\\begin{figure}[!ht]\n \\centering\n \\includegraphics[width=\\linewidth]{captionfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results of generated caption on the SPORTU dataset.}\n \\label{figure:medical}\n \\vspace{-4mm}\n\\end{figure}\nWe show examples of pseudo question-answer pairs generated by our QA Generator. These synthetic QA pairs effectively expand the training dataset and provide domain-relevant supervision for the subsequent fine-tuning stage. The generated questions are contextually appropriate and cover diverse aspects of the visual content, while the answers demonstrate proper domain knowledge and terminology usage.\n\n\\subsection{Captions from Large MLLM}\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{caption2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results of generated caption on the Kvasir-VQA dataset.}\n \\label{figure:medicala}\n \\vspace{-4mm}\n\\end{figure}\nWe present captions generated by the large MLLM (Qwen2.5-VL-72B) used in our distillation process. These captions successfully capture important visual details and domain-specific information, which helps improve the QA Generator's learning through knowledge distillation.\n% \\maketitle\n% \\section{Additional }\n% 1. VQA comparsion of qua\n% 2. QA Generater generated pseudo QA\n% 3. Caption from large MLLM, sport\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{medical2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n % \\label{figure:afd}\n \\vspace{-4mm}\n\\end{figure}\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{sport2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the SPORTU dataset.}\n % \\label{figure:sport2}\n % \\vspace{-4mm}\n\\end{figure}\\end{document}\n"},"question":{"kind":"string","value":"Averaging across all categories, which of the two cases has a larger performance difference, LORA and LEAML or LEAML and fully supervised training?"},"answer":{"kind":"string","value":"LORA and LEAML"},"plan":{"kind":"string","value":"COMPUTE difference1 = absolute(average performance for LoRA - average performance for LEAML)\nCOMPUTE difference2 = absolute(average performance for LoRA - average performance for FullySupervised)\nIF difference1 > difference2 \n RETURN “LoRA and LEAML”\nRETURN “LEAML and FullySupervised”\n"}}},{"rowIdx":347,"cells":{"paper":{"kind":"string","value":"2510.03232"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t!]\n"," \\centering\n"," \\vspace{2mm}\n"," \\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for sport understanding and reasoning questions. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n"," \\vspace{-2mm}\n","\t\\resizebox{0.48\\textwidth}{!}{\n"," \n"," \\begin{tabular}{l c c c c}\n"," \n"," \\toprule \n","\n"," Method & Easy & Medium & Hard & Average \\\\\n"," \\midrule\n"," Zero-Shot & 50.5 & 34.0 & 37.5 & 40.7 \\\\\n"," LoRA & 82.5 & 59.2 & 22.3 & 54.7 \\\\\n"," Full-Tuning & 82.7 & 59.0 & 21.3 & 54.3 \\\\\n"," \\nameshort~(Ours) & 82.5 & 60.4 & 46.3 & 63.1 \\\\\n","\n","\n","\n"," \\midrule\n"," Fully-Supervised & 98.1 & 75.4 & 66.1 & 79.9 \\\\\n"," \n"," \\bottomrule \n"," \\vspace{-4mm}\n"," \\label{tab:sport}\n"," \\end{tabular}\n"," }\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\vspace{2mm}\\n\",\n \" \\\\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for sport understanding and reasoning questions. Only 1\\\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\t\\\\resizebox{0.48\\\\textwidth}{!}{\\n\",\n \" \\n\",\n \" \\\\begin{tabular}{l c c c c}\\n\",\n \" \\n\",\n \" \\\\toprule \\n\",\n \"\\n\",\n \" Method & Easy & Medium & Hard & Average \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot & 50.5 & 34.0 & 37.5 & 40.7 \\\\\\\\\\n\",\n \" LoRA & 82.5 & 59.2 & 22.3 & 54.7 \\\\\\\\\\n\",\n \" Full-Tuning & 82.7 & 59.0 & 21.3 & 54.3 \\\\\\\\\\n\",\n \" \\\\nameshort~(Ours) & 82.5 & 60.4 & 46.3 & 63.1 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\\\midrule\\n\",\n \" Fully-Supervised & 98.1 & 75.4 & 66.1 & 79.9 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule \\n\",\n \" \\\\vspace{-4mm}\\n\",\n \" \\\\label{tab:sport}\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}[!t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{model1fig.pdf}\n"," \\caption{Overview of the proposed two-stage \\nameshort~framework for OOD VQA adaptation. In \\namestagea, the QA Generator is trained using a small set of labeled question-answer pairs and then used to generate pseudo QA pairs for a large collection of unlabeled images. In \\namestageb, the VQA model is fine-tuned with both the original labeled data and the produced pseudo QA pairs of unlabeled data, enabling label-efficient adaptation to out-of-distribution visual-question answering. We will detail the learning of our QA Generator in Figure~\\ref{figure:model2}.}\n"," \\label{figure:model1}\n","\\end{figure*}To support such targeted interventions, a variety of attribution methods have been proposed to quantify the importance of individual neurons or weights. Some are designed to guide pruning, which reduces model size by removing components deemed less relevant. For example, Wanda~\\cite{sun2023simple} identifies unimportant weights by combining their magnitude with the norm of the associated input activation. Others~\\cite{fang2024towards,pan2023finding,yu2023neuron,yu2025locate} aim to inform fine-tuning, where only selected parts of the model are updated to acquire new capabilities or adapt to specific domains. A common strategy in this context is to measure gradient magnitudes during backpropagation, under the assumption that neurons with higher gradients contribute more significantly to the output~\\cite{zhang2024gradient}.\n"],["\\begin{figure*}[!t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{model2fig.pdf}\n"," \\caption{Illustration of our \\namestageaa~for the QA Generator. The QA-relevant parameters are first selected based on gradient scores from labeled QA data. During training, only these selected parameters are updated using auxiliary caption supervision from unlabeled images, allowing QA-related knowledge distillation for the QA Generator.}\n"," \\label{figure:model2}\n","\\end{figure*}\n"],["\\begin{table*}[t!]\n"," \\centering\n"," \\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\%) of VQA accuracy. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n"," \\vspace{-2mm}\n","\t\\resizebox{0.75\\textwidth}{!}{\n"," \n"," \\begin{tabular}{l c c c c c}\n"," \n"," \\toprule \n","\n"," \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n"," \\cline{2-5}\n"," & Colitis & Esophagitis & Instrument & Polyps & \\\\\n"," \\midrule\n"," Zero-Shot& 35.4 & 21.1 & 49.0 & 47.8 & 38.3 \\\\\n"," LoRA & 95.6 & 57.7 & 48.9 & 47.3 & 62.4 \\\\\n"," Full-Tuning & 89.0 & 60.8 & 51.2 & 51.3 & 63.1 \\\\\n"," \\nameshort~(Ours) & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n","\n","\n","\n"," \\midrule\n"," Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 55.9 & 54.3 \\\\\n"," Fully-Supervised & 97.4 & 97.4 & 85.8 & 82.1 & 90.7 \\\\\n"," \n"," \\bottomrule\n"," \\label{tab:medical}\n"," \\end{tabular}\n"," }\n"," \\vspace{-3mm}\n","\\end{table*}\n"],["\\begin{table*}[t!]\n"," \\centering\n"," \\vspace{2mm}\n"," \\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for sport understanding and reasoning questions. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n"," \\vspace{-2mm}\n","\t\\resizebox{0.48\\textwidth}{!}{\n"," \n"," \\begin{tabular}{l c c c c}\n"," \n"," \\toprule \n","\n"," Method & Easy & Medium & Hard & Average \\\\\n"," \\midrule\n"," Zero-Shot & 50.5 & 34.0 & 37.5 & 40.7 \\\\\n"," LoRA & 82.5 & 59.2 & 22.3 & 54.7 \\\\\n"," Full-Tuning & 82.7 & 59.0 & 21.3 & 54.3 \\\\\n"," \\nameshort~(Ours) & 82.5 & 60.4 & 46.3 & 63.1 \\\\\n","\n","\n","\n"," \\midrule\n"," Fully-Supervised & 98.1 & 75.4 & 66.1 & 79.9 \\\\\n"," \n"," \\bottomrule \n"," \\vspace{-4mm}\n"," \\label{tab:sport}\n"," \\end{tabular}\n"," }\n","\\end{table*}\n"],["\\begin{table*}[t!]\n"," \\centering\n"," \\caption{Ablation study of our \\namestageaa~for the QA Generator on the Kvasir-VQA dataset.}\n"," \\vspace{-2mm}\n","\t\\resizebox{0.8\\textwidth}{!}{\n"," \n"," \\begin{tabular}{l c c c c c}\n"," \n"," \\toprule \n","\n"," \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n"," \\cline{2-5}\n"," & Colitis & Esophagitis & Instrument & Polyps & \\\\\n"," \\midrule\n","\n"," Baseline & 93.0 & 88.2 & 55.7 & 56.2 & 73.3 \\\\\n"," Baseline+Distill. & 95.1 & 80.3 & 59.7 & 60.4 & 73.9 \\\\\n"," Baseline+Distill.+QA Neurons & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n"," \n"," \\bottomrule \n"," \\label{tab:ab1}\n"," \\end{tabular}\n"," }\n"," \\vspace{-5mm}\n","\\end{table*}\\begin{table*}[t!]\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{medicalfig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n"," \\label{figure:medicalg}\n"," \\vspace{-4mm}\n","\\end{figure}\n"],["\\begin{figure}[!t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{sportfig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results on the SPORTU dataset.}\n"," \\label{figure:sport}\n"," \\vspace{-4mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{medical2fig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n"," \\vspace{-4mm}\n","\\end{figure}\\begin{figure}[!t]\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{GenQA_medicalfig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results of generated pseudo-QA on the Kvasir-VQA dataset.}\n"," \\label{figure:medicalb}\n","\\end{figure}\\begin{figure}[t]\n"],["\\end{figure}\\begin{figure}[!ht]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{captionfig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results of generated caption on the SPORTU dataset.}\n"," \\label{figure:medical}\n"," \\vspace{-4mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{caption2fig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results of generated caption on the Kvasir-VQA dataset.}\n"," \\label{figure:medicala}\n"," \\vspace{-4mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{medical2fig.pdf}\n"," \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n"," \\vspace{-4mm}\n","\\end{figure}\\begin{figure}[!t]\n"]],"string":"[\n [\n \"\\\\begin{figure*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{model1fig.pdf}\\n\",\n \" \\\\caption{Overview of the proposed two-stage \\\\nameshort~framework for OOD VQA adaptation. In \\\\namestagea, the QA Generator is trained using a small set of labeled question-answer pairs and then used to generate pseudo QA pairs for a large collection of unlabeled images. In \\\\namestageb, the VQA model is fine-tuned with both the original labeled data and the produced pseudo QA pairs of unlabeled data, enabling label-efficient adaptation to out-of-distribution visual-question answering. We will detail the learning of our QA Generator in Figure~\\\\ref{figure:model2}.}\\n\",\n \" \\\\label{figure:model1}\\n\",\n \"\\\\end{figure*}To support such targeted interventions, a variety of attribution methods have been proposed to quantify the importance of individual neurons or weights. Some are designed to guide pruning, which reduces model size by removing components deemed less relevant. For example, Wanda~\\\\cite{sun2023simple} identifies unimportant weights by combining their magnitude with the norm of the associated input activation. Others~\\\\cite{fang2024towards,pan2023finding,yu2023neuron,yu2025locate} aim to inform fine-tuning, where only selected parts of the model are updated to acquire new capabilities or adapt to specific domains. A common strategy in this context is to measure gradient magnitudes during backpropagation, under the assumption that neurons with higher gradients contribute more significantly to the output~\\\\cite{zhang2024gradient}.\\n\"\n ],\n [\n \"\\\\begin{figure*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{model2fig.pdf}\\n\",\n \" \\\\caption{Illustration of our \\\\namestageaa~for the QA Generator. The QA-relevant parameters are first selected based on gradient scores from labeled QA data. During training, only these selected parameters are updated using auxiliary caption supervision from unlabeled images, allowing QA-related knowledge distillation for the QA Generator.}\\n\",\n \" \\\\label{figure:model2}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\\\%) of VQA accuracy. Only 1\\\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\t\\\\resizebox{0.75\\\\textwidth}{!}{\\n\",\n \" \\n\",\n \" \\\\begin{tabular}{l c c c c c}\\n\",\n \" \\n\",\n \" \\\\toprule \\n\",\n \"\\n\",\n \" \\\\multirow{2}{*}{Method} & \\\\multicolumn{4}{c}{Image Category} & \\\\multirow{2}{*}{Average}\\\\\\\\\\n\",\n \" \\\\cline{2-5}\\n\",\n \" & Colitis & Esophagitis & Instrument & Polyps & \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot& 35.4 & 21.1 & 49.0 & 47.8 & 38.3 \\\\\\\\\\n\",\n \" LoRA & 95.6 & 57.7 & 48.9 & 47.3 & 62.4 \\\\\\\\\\n\",\n \" Full-Tuning & 89.0 & 60.8 & 51.2 & 51.3 & 63.1 \\\\\\\\\\n\",\n \" \\\\nameshort~(Ours) & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 55.9 & 54.3 \\\\\\\\\\n\",\n \" Fully-Supervised & 97.4 & 97.4 & 85.8 & 82.1 & 90.7 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\label{tab:medical}\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\vspace{2mm}\\n\",\n \" \\\\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for sport understanding and reasoning questions. Only 1\\\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\t\\\\resizebox{0.48\\\\textwidth}{!}{\\n\",\n \" \\n\",\n \" \\\\begin{tabular}{l c c c c}\\n\",\n \" \\n\",\n \" \\\\toprule \\n\",\n \"\\n\",\n \" Method & Easy & Medium & Hard & Average \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Zero-Shot & 50.5 & 34.0 & 37.5 & 40.7 \\\\\\\\\\n\",\n \" LoRA & 82.5 & 59.2 & 22.3 & 54.7 \\\\\\\\\\n\",\n \" Full-Tuning & 82.7 & 59.0 & 21.3 & 54.3 \\\\\\\\\\n\",\n \" \\\\nameshort~(Ours) & 82.5 & 60.4 & 46.3 & 63.1 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\\\midrule\\n\",\n \" Fully-Supervised & 98.1 & 75.4 & 66.1 & 79.9 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule \\n\",\n \" \\\\vspace{-4mm}\\n\",\n \" \\\\label{tab:sport}\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Ablation study of our \\\\namestageaa~for the QA Generator on the Kvasir-VQA dataset.}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\t\\\\resizebox{0.8\\\\textwidth}{!}{\\n\",\n \" \\n\",\n \" \\\\begin{tabular}{l c c c c c}\\n\",\n \" \\n\",\n \" \\\\toprule \\n\",\n \"\\n\",\n \" \\\\multirow{2}{*}{Method} & \\\\multicolumn{4}{c}{Image Category} & \\\\multirow{2}{*}{Average}\\\\\\\\\\n\",\n \" \\\\cline{2-5}\\n\",\n \" & Colitis & Esophagitis & Instrument & Polyps & \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\n\",\n \" Baseline & 93.0 & 88.2 & 55.7 & 56.2 & 73.3 \\\\\\\\\\n\",\n \" Baseline+Distill. & 95.1 & 80.3 & 59.7 & 60.4 & 73.9 \\\\\\\\\\n\",\n \" Baseline+Distill.+QA Neurons & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule \\n\",\n \" \\\\label{tab:ab1}\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\vspace{-5mm}\\n\",\n \"\\\\end{table*}\\\\begin{table*}[t!]\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{medicalfig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results on the Kvasir-VQA dataset.}\\n\",\n \" \\\\label{figure:medicalg}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{sportfig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results on the SPORTU dataset.}\\n\",\n \" \\\\label{figure:sport}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{medical2fig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results on the Kvasir-VQA dataset.}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\\\begin{figure}[!t]\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{GenQA_medicalfig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results of generated pseudo-QA on the Kvasir-VQA dataset.}\\n\",\n \" \\\\label{figure:medicalb}\\n\",\n \"\\\\end{figure}\\\\begin{figure}[t]\\n\"\n ],\n [\n \"\\\\end{figure}\\\\begin{figure}[!ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{captionfig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results of generated caption on the SPORTU dataset.}\\n\",\n \" \\\\label{figure:medical}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{caption2fig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results of generated caption on the Kvasir-VQA dataset.}\\n\",\n \" \\\\label{figure:medicala}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{medical2fig.pdf}\\n\",\n \" \\\\vspace{-6mm}\\\\caption{Qualitative results on the Kvasir-VQA dataset.}\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \"\\\\end{figure}\\\\begin{figure}[!t]\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"%File: anonymous-submission-latex-2026.tex\n\\documentclass[letterpaper]{article} % DO NOT CHANGE THIS\n\\usepackage[draft]{aaai2026} % DO NOT CHANGE THIS\n\n\n\\usepackage{times} % DO NOT CHANGE THIS\n\\usepackage{helvet} % DO NOT CHANGE THIS\n\\usepackage{courier} % DO NOT CHANGE THIS\n\\usepackage[hyphens]{url} % DO NOT CHANGE THIS\n\\usepackage{graphicx} % DO NOT CHANGE THIS\n\\urlstyle{rm} % DO NOT CHANGE THIS\n\\def\\UrlFont{\\rm} % DO NOT CHANGE THIS\n\\usepackage{natbib} % DO NOT CHANGE THIS AND DO NOT ADD ANY OPTIONS TO IT\n\\usepackage{caption} % DO NOT CHANGE THIS AND DO NOT ADD ANY OPTIONS TO IT\n\\frenchspacing % DO NOT CHANGE THIS\n\\setlength{\\pdfpagewidth}{8.5in} % DO NOT CHANGE THIS\n\\setlength{\\pdfpageheight}{11in} % DO NOT CHANGE 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Scott Penberthy\\textsuperscript{\\rm 3},\n% % George Ferguson\\textsuperscript{\\rm 4},\n% % Hans Guesgen\\textsuperscript{\\rm 5}\n% % Note that the comma should be placed after the superscript\n\n% 1101 Pennsylvania Ave, NW Suite 300\\\\\n% Washington, DC 20004 USA\\\\\n% % email address must be in roman text type, not monospace or sans serif\n% proceedings-questions@aaai.org\n% %\n% % See more examples next\n% }\n\n%Example, Single Author, ->> remove \\iffalse,\\fi and place them surrounding AAAI title to use it\n\\iffalse\n\\title{My Publication Title --- Single Author}\n\\author {\n Author Name\n}\n\\affiliations{\n Affiliation\\\\\n Affiliation Line 2\\\\\n name@example.com\n}\n\\fi\n\n\\iffalse\n\n\n%Example, Multiple Authors, ->> remove \\iffalse,\\fi and place them surrounding AAAI title to use it\n\n\\author {\n % Authors\n First Author Name\\textsuperscript{\\rm 1},\n Second Author Name\\textsuperscript{\\rm 2},\n Third Author Name\\textsuperscript{\\rm 1}\n}\n\\affiliations {\n % Affiliations\n \\textsuperscript{\\rm 1}Affiliation 1\\\\\n \\textsuperscript{\\rm 2}Affiliation 2\\\\\n firstAuthor@affiliation1.com, secondAuthor@affilation2.com, thirdAuthor@affiliation1.com\n}\n\\fi\n\n\n% REMOVE THIS: bibentry\n% This is only needed to show inline citations in the guidelines document. You should not need it and can safely delete it.\n\\usepackage{bibentry}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{multirow}\n\\usepackage{booktabs}\n% END REMOVE bibentry\n\\newcommand{\\nameshort}{\\textcolor{black}{LEAML}}\n\\newcommand{\\namestagea}{\\textcolor{black}{Pseudo QA Generation}}\n\\newcommand{\\namestageaa}{\\textcolor{black}{Selective Neuron Distillation}}\n\\newcommand{\\namestageb}{\\textcolor{black}{OOD VQA Finetuning}}\n\n\n\\begin{document}\n\n\\maketitle\n% \\def\\thefootnote{*}\\footnotetext{~Work done during an internship at NVIDIA.}\n% \\pagestyle{plain}\n\\begin{abstract}\nMultimodal Large Language Models (MLLMs) have achieved strong performance on general visual benchmarks but struggle with out-of-distribution (OOD) tasks in specialized domains such as medical imaging, where labeled data is limited and expensive. We introduce \\nameshort, a label-efficient adaptation framework that leverages both scarce labeled VQA samples and abundant unlabeled images. Our approach generates domain-relevant pseudo question-answer pairs for unlabeled data using a QA generator regularized by caption distillation. Importantly, we selectively update only those neurons most relevant to question-answering, enabling the QA Generator to efficiently acquire domain-specific knowledge during distillation. Experiments on gastrointestinal endoscopy and sports VQA demonstrate that \\nameshort~consistently outperforms standard fine-tuning under minimal supervision, highlighting the effectiveness of our proposed \\nameshort~framework.\n\\end{abstract}\\section{Introduction}\nLarge Language Models (LLMs)~\\cite{touvron2023llama, achiam2023gpt, bai2023qwen} have demonstrated impressive capabilities across diverse language tasks. By incorporating visual understanding, Multimodal Large Language Models (MLLMs)~\\cite{alayrac2022flamingo, liu2023visual,wang2024qwen2} extend these capabilities to visual question answering (VQA), image captioning, and multimodal reasoning tasks.~\\cite{wang2024exploring} Recent MLLMs have achieved remarkable performance on general visual benchmarks, showing strong generalization within their training distributions. Although scaling laws~\\cite{kaplan2020scaling} show promise for enhancing model performance, they do not eliminate dependence on pre-training data, which limits generalization to novel domains. In real-world deployment, MLLMs will face domain-specific tasks that fall outside their training distribution, such as specialized medical imaging or technical visual content. When confronted with such out-of-distribution (OOD) data, these models often produce erroneous or unreliable outputs, limiting their applicability in specific domains where accuracy is critical.\n\n\n\nWhile existing studies on OOD have primarily focused on detection~\\cite{ming2022delving, wang2023clipn} or domain-specific classification tasks~\\cite{liu2023clip, lei2023clip, zhang2023biomedclip}, applying MLLMs to visual question answering in unfamiliar domains introduces distinct challenges. Unlike detection, which focuses on filtering unfamiliar inputs, VQA requires models to generate accurate and contextually grounded answers for images outside the training distribution. Although many specific domains offer abundant unlabeled images, standard VQA training pipelines depend on paired question-answer annotations, which are costly to obtain due to the need for domain expertise. Furthermore, VQA questions must be carefully constructed based on the visual content. Randomly pairing unrelated questions with images creates confusing training signals and reduces the effectiveness of learning. Due to the scarcity of high-quality labeled data, fully fine-tuning MLLMs often leads to severe overfitting, particularly in VQA where models must produce free-form, semantically appropriate responses rather than select from fixed labels. These challenges underscore the need for adaptation methods that can leverage both limited labeled examples and large pools of unlabeled images in a way that preserves generation capabilities while acquiring domain-specific understanding.\n\nIn this paper, we introduce \\textbf{\\nameshort}, a two-stage \\textbf{L}abel-\\textbf{E}fficient \\textbf{A}daptation framework for \\textbf{M}ultiModal \\textbf{L}LM designed to effectively leverage both the limited labeled VQA data and the abundant unlabeled images in the target domain. The framework comprises \\namestagea, which constructs domain-relevant QA pairs from unlabeled images, and \\namestageb, which fine-tunes the target MLLM using both the generated pairs and the original labeled data. In \\namestagea, a QA Generator is trained using the small labeled dataset to capture the domain-specific patterns of question-answer formulations. To mitigate overfitting caused by the scarcity of labeled data, the generator is regularized via caption distillation, where it additionally learns from image captions produced by a large-scale model, providing broader visual-linguistic signals beyond the limited annotations. The generator then synthesizes diverse pseudo QA pairs for the unlabeled domain images, creating a significantly richer training resource. In \\namestageb, the target MLLM is fine-tuned with both the original labeled samples and the generated QA pairs. To enhance adaptation efficiency and prevent overfitting, we employ \\namestageaa, which is motivated by the insight that domain-specific knowledge is often encoded in a subset of neurons; focusing updates on these neurons enables the model to acquire domain-relevant reasoning capabilities while preserving general language generation skills. Experiments conducted on gastrointestinal endoscopy VQA demonstrate that our method significantly improves performance compared to standard fine-tuning approaches.\n\n\nOur contributions can be summarized as follows:\n\\begin{itemize}\n \\item We propose a two-stage learning framework \\nameshort, which leverages both scarce labeled data and abundant unlabeled images to achieve MLLM adapataion for domain-specific VQA .\n \\item We introduce \\namestagea, which learns a generator to produce pseudo question-answer pairs for unlabeled data, augmenting the training set for finetuning the VQA model on specialized domains.\n \\item We design \\namestageaa~for the QA generator, which performs captioning distillation to acquire domain-related knowledge while selectively updates QA-related neurons, resulting in reliable pseudo QA pairs for finetuning.\n\n\n\n\\end{itemize}\n\n\n\\section{Related Works}\n\\subsection{Out-of-Distribution Data Learning}\n% 1. OOD detection\n% 2. CLIP-based classification\n% 3. MLLM (Domain adaption, medical foundation models)\nOut-of-distribution (OOD) data refers to inputs that differ significantly from those seen during training. Early OOD research~\\cite{ming2022delving, wang2023clipn} primarily focused on detection tasks, where the goal is to identify whether an input falls outside the training distribution. These methods often treat OOD detection as anomaly detection. However, these methods aim to identify and reject OOD inputs rather than adapt models to perform well on them. \n% In our scenario, OOD data from specialized domains represents valid test cases requiring accurate VQA responses, necessitating adaptation rather than detection.\nBeyond detection, another line of work explores how vision-language models can be adapted for OOD domains. CLIP and its variants have shown promise in medical imaging applications through domain-specific fine-tuning~\\cite{liu2023clip,lei2023clip, zhang2023biomedclip}. \n% Zhang et al. demonstrated effective adaptation of CLIP for chest X-ray classification, while Wang et al. proposed BioCLIP for diagnosis across multiple medical imaging modalities. Other works have extended CLIP for medical image segmentation using text prompts to guide anatomical structure identification. \nHowever, these approaches are limited to classification settings, where models predict labels from a fixed set rather than generating open-ended responses.\n\nRecent works explore adapting LLMs to specific domains~\\cite{zhang2023reformulating, cheng2024domain, bhatia2024fintral,cheng2023adapting}. For instance,~\\cite{zhang2023reformulating, kim2025videoicl} employ retrieval-based approaches to handle out-of-distribution inputs, relying on external sources to provide relevant context for domain adaptation. However, such methods still assume that the LLM has sufficient foundational knowledge to effectively interpret the retrieved information.\nIn the vision-language domain, ~\\cite{cheng2024domain} propose fine-tuning MLLMs to automatically generate question-answer pairs from existing image-caption datasets, subsequently using these synthetic QA pairs for domain-specific VQA training. However, the effectiveness of such methods depends heavily on both the LLM's domain knowledge and the granularity of source captions. Fine-grained captions enable detailed QA generation, while coarse-grained descriptions yield only generic questions. These factors highlight the need for methods that can produce high-quality domain-specific QA pairs even with limited domain knowledge and varying caption quality.\n% 最後一句要不要\n\n\n% To cite\n\\subsection{Semi-Supervised Learning}\nSemi-supervised learning (SSL) is a strategy to bridge the gap between limited labeled data and abundant unlabeled resources, especially in domains where annotation is expensive or requires domain expertise. Among existing SSL paradigms, pseudo-labeling~\\cite{lee2013pseudo,xie2020self} has been widely adopted. This approach trains models on labeled data, then uses them to pseudo-label unlabeled samples for further training.\n\nPseudo-labeling has been widely applied to tasks such as image classification~\\cite{zeng2023pefat} and Segmentation~\\cite{yang2023revisiting}, where labels are either discrete or can be directly generated from the data. In these settings, unlabeled samples can be automatically annotated with relatively reliable supervision. In contrast, applying pseudo-labeling to visual question answering (VQA) is considerably more difficult. VQA requires not only a grounded answer but also a relevant and context-aware question that must be closely aligned with the visual content. Unlike captions or class labels, such question-answer pairs cannot be directly inferred from the image alone. A naïve solution might involve randomly assigning questions to domain images, but this leads to incoherent or misleading training data. As a result, semi-supervised learning remains largely underexplored in VQA, particularly in domain-specific scenarios where labeled data is scarce and generating valid pseudo QA pairs is highly non-trivial.\n \n\n% In vision-language tasks, semi-supervised approaches have shown promise for image captioning, visual grounding, and multimodal understanding. The fundamental challenge lies in effectively utilizing unlabeled data without introducing noise that degrades model performance.\n% Pseudo-labeling has emerged as a powerful technique for semi-supervised learning, where confident predictions on unlabeled data are treated as ground truth for subsequent training iterations. Recent advances have refined this approach through consistency regularization, uncertainty estimation, and selective pseudo-label filtering. In multimodal contexts, pseudo-labeling faces unique challenges as it must maintain coherence between visual and textual modalities while generating plausible outputs.\n% For VQA tasks specifically, semi-supervised methods remain largely unexplored despite the high annotation cost of creating question-answer pairs. Unlike classification where pseudo-labels are discrete categories, VQA requires generating both meaningful questions and their corresponding free-form answers. This complexity has limited the adoption of semi-supervised techniques in VQA adaptation scenarios. Our work addresses this gap by introducing a pseudo QA generation framework specifically designed for domain adaptation, where we leverage the complementary strengths of limited labeled data and abundant unlabeled images to enable effective transfer to specialized domains.\n\n\n% \\subsection{Knowledge Neurons in MLLMs}\n% \\subsection{Neuron Editing in MLLMs for Specific Knowledge}\n\\subsection{Neuron-Level Knowledge Attribution in DNNs}\nKnowledge in neural networks is localized and stored within specific neural components rather than distributed uniformly across parameters. \nPrevious work has shown that the feed-forward network (FFN) layers in Transformers play a key role in storing knowledge~\\cite{geva2020transformer,geva2022transformer}. These layers have been characterized as performing additive, knowledge-based updates on token representations. \\cite{dai2021knowledge} propose a neuron-level attribution approach to identify knowledge neurons in FFNs responsible for storing factual knowledge.\nThese findings indicate that MLLMs encode different types of knowledge in specialized neural components with distinct activation patterns, enabling targeted manipulation of specific knowledge without affecting the entire network.\n\n\\begin{figure*}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{model1fig.pdf}\n \\caption{Overview of the proposed two-stage \\nameshort~framework for OOD VQA adaptation. In \\namestagea, the QA Generator is trained using a small set of labeled question-answer pairs and then used to generate pseudo QA pairs for a large collection of unlabeled images. In \\namestageb, the VQA model is fine-tuned with both the original labeled data and the produced pseudo QA pairs of unlabeled data, enabling label-efficient adaptation to out-of-distribution visual-question answering. We will detail the learning of our QA Generator in Figure~\\ref{figure:model2}.}\n \\label{figure:model1}\n % \\vspace{-4mm}\n\\end{figure*}To support such targeted interventions, a variety of attribution methods have been proposed to quantify the importance of individual neurons or weights. Some are designed to guide pruning, which reduces model size by removing components deemed less relevant. For example, Wanda~\\cite{sun2023simple} identifies unimportant weights by combining their magnitude with the norm of the associated input activation. Others~\\cite{fang2024towards,pan2023finding,yu2023neuron,yu2025locate} aim to inform fine-tuning, where only selected parts of the model are updated to acquire new capabilities or adapt to specific domains. A common strategy in this context is to measure gradient magnitudes during backpropagation, under the assumption that neurons with higher gradients contribute more significantly to the output~\\cite{zhang2024gradient}.\n\n\n% Neuron editing, the process of modifying this stored knowledge, is often approached via two primary strategies: pruning and fine-tuning. Pruning methods aim to reduce model complexity by removing less important components. For instance, ~\\cite{sun2023simple} introduced Wanda, a weight pruning method that evaluates each weight's contribution by considering both its magnitude and the norm of its associated input activation. In contrast, fine-tuning-based editing methods often attribute specific knowledge to neurons by scoring their contribution to model outputs~\\cite{zhang2024gradient,fang2024towards,pan2023finding,yu2023neuron,yu2025locate}. A common approach~\\cite{zhang2024gradient} analyzes gradient magnitudes, where higher gradients for specific inputs indicate neurons that contribute more significantly to the final output.This gradient-based analysis enables selective updating of neurons most relevant to target domains, preserving general knowledge while acquiring specialized capabilities.\n\n\n\n\n\n\\section{Method}\n\n\\subsection{Problem Formulation and Framework Overview}\n\n\\paragraph{Problem Formulation.} We first define the problem settings and notations used in this paper. For the out-of-distribution visual question-answering problem, we consider domain-specific tasks (e.g., gastrointestinal endoscopy) which are still based on RGB images or videos but are rarely or not covered in the pretraining data of general-purpose multimodal large language models. Since such domain-specific tasks generally require great expense to obtain manual annotations from domain experts, we further consider a realistic yet challenging setting, where only few data are annotated in the training dataset $D$. That is, the training dataset $D$ contains a set of labeled data $D_l$ of few samples and also a set of abundant unlabeled data $D_u$, which is similar to traditional semi-supervised learning. Each data instance in the labeled dataset $D_l$ contains an image or video $V$, an associated question $Q$, and the corresponding answer $A$, while each sample in the unlabeled dataset $D_u$ contains only the visual part $V$.\n\n\\paragraph{Framework Overview.} Given the above training data and a pretrained general MLLM, our goal is to adapt this pretrained MLLM to address out-of-distribution visual question-answering with only few labeled instances. To achieve this goal, we propose a two-stage learning framework \\nameshort~as shown in Figure~\\ref{figure:model1}. Our \\nameshort~framework includes two stages: \\namestagea~and \\namestageb. The former stage aims to generate proper pseudo question-answer pairs for the unlabeled dataset $D_u$, while the latter stage leverages both the labeled dataset $D_l$ and the produced pseudo QA pairs for the unlabeled data $D_u$ to finetune a pretrained MLLM for addressing out-of-distribution visual question-answering. \n\n\\begin{figure*}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{model2fig.pdf}\n \\caption{Illustration of our \\namestageaa~for the QA Generator. The QA-relevant parameters are first selected based on gradient scores from labeled QA data. During training, only these selected parameters are updated using auxiliary caption supervision from unlabeled images, allowing QA-related knowledge distillation for the QA Generator.}\n \\label{figure:model2}\n % \\vspace{-4mm}\n\\end{figure*}\nSpecifically, since the unlabeled data only contain the visual information but lack the corresponding textual annotations for training a VQA model, our \\nameshort~framework first employ a QA Generator $G$ which is directly supervised by the labeled data to produce pseudo QA pairs for unlabeled data. However, in this manner, the QA Generator may overfit on those few labeled samples and fail to generalize well to produce reliable QA pairs for unlabeled data. To overcome this challenge, we further propose \\namestageaa~to leverage also the unlabeled data during the training of the QA Generator. As shown in Figure~\\ref{figure:model2}, in addition to the QA generation supervised by labeled data, we perform captioning distillation using unlabeled data to distill related knowledge from a large MLLM. More importantly, during training, we update only QA-related neurons for both the QA generation and captioning distillation. In this way, such captioning distillation is designed to focus solely on gaining QA-related knowledge, and hence the QA Generator $G$ is able to produce reliable pseudo QA pairs for unlabeled data during inference, benefiting the following finetuning for the VQA model. We now detail our learning framework in the following subsections.\n\n\n\\subsection{\\namestagea~and \\namestageb}\n\nRecently, multimodal large language models (MLLMs) have achieved impressive generalization on a wide range of vision-language tasks. However, their performance often degrades when applied to specialized domains such as medical imaging, where domain-specific visual cues and terminology differ significantly from pretraining data. A significant barrier in adapting multimodal large language models (MLLMs) to these specialized domains is the extreme scarcity of annotated question-answer (QA) pairs. Obtaining such labeled data from domain experts is often expensive, time-consuming, and infeasible at scale, leading to severe limitations on direct fine-tuning. On the other hand, large volumes of unlabeled visual data typically exist, representing a potential yet largely untapped source of supervision. While traditional semi-supervised learning have demonstrated that unlabeled data can be highly beneficial, such success is largely limited to classification tasks. For unlabeled data in visual question-answering, both the question and answer are not accessible, and hence traditional semi-supervised learning cannot be easily applied in VQA to generate the pseudo labels without knowing or providing a corresponding question.\n\n% \\subsection{Pseudo QA Generation}\n\nTo overcome the limitation of requiring fully annotated data, we introduce a pseudo QA generation stage that transforms unlabeled visual data into useful supervision for the VQA model. The core idea is to train a QA Generator using limited labeled examples $D_l$, and then apply it to unlabeled inputs $D_u$ to produce additional VQA samples. Specifically, for each labeled instance $(V, Q, A)$ in $D_l$, we formulate the corresponding target text sequence $Y$ by concatenating of the question $Q$ and answer $A$ with special tokens: \n\n\\begin{equation}\n\\begin{aligned}\nY = [\\texttt{<q>} Q \\texttt{<q>} \\texttt{<a>} A \\texttt{<a>}].\n\\end{aligned}\n% \\vspace{-2mm}\n\\end{equation}\nThen, the QA generator $G$, initialized from a pretrained general MLLM, is trained to autoregressively generate $Y$ conditioned on the visual input $V$. The training objective $\\mathcal{L}_{QA}$ is defined as a standard autoregressive negative log-likelihood:\n\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{QA} = \\sum_{t=1}^{|Y|} \\log p(y_i \\mid V, y_{<i}), V \\in D_l\n\\end{aligned}\n\\label{eq:qa}\n% \\vspace{-2mm}\n\\end{equation}\nwhere $y_i$ denotes the $i$th text token of the sequence $Y$ and $p$ is the likelihood of text tokens estimated by the QA Generator $G$. Once the training is complete, the QA generator $G$ would be applied to produce pseudo QA pairs $[\\texttt{<q>} \\hat{Q} \\texttt{<q>} \\texttt{<a>} \\hat{A} \\texttt{<a>}] = G(V)$ for the visual input $V$ from unlabeled data, resulting in the dataset $\\hat{D_{u}} = \\{(V, \\hat{Q}, \\hat{A})\\}$. This dataset is then used to augment the original labeled data $D_l$ for finetuning the final VQA model with similar autoregressive objective $\\mathcal{L}_{VQA}$:\n\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{VQA} &= \\sum_{t=1}^{|A|} \\log p(a_i \\mid V, Q, a_{<i}), V \\in D_l, \\hat{D}_u\n\\end{aligned}\n\\label{eq:vqa}\n% \\vspace{-2mm}\n\\end{equation}\nNote that the VQA model is again initialized from a pretrained general MLLM. While the above pseudo QA generation enables the model to leverage unlabeled visual data for OOD VQA adaptation, the quality of generated QA pairs is tightly bound to the small number of labeled examples. With limited supervision, the model may produce noisy outputs on unlabeled data, especially under the out-of-distribution settings.\n\n\\subsection{\\namestageaa~for QA Generator}\nTo further mitigate the aforementioned problem of \\namestagea, our \\nameshort~framework introduces a distillation mechanism that directly incorporates abundant unlabeled data into the QA Generator training process. In addition to the QA generation part supervised by labeled data $D_l$, we further consider captioning distillation on unlabeled $D_u$ to gain domain-related knowledge from a large MLLM. Specifically, for each unlabeled visual input $V$, we employ a large pre-trained general MLLM to automatically generate a descriptive caption $C$. While the large MLLM may still be poor when directly applied to perform OOD VQA tasks, these state-of-the-art large models are pre-trained on vast and diverse corpora such as medical literature, Wikipedia articles, and other authoritative web resources. As a result, the captions generated by such models are often infused with rich semantic information, domain-specific terminology, and contextual knowledge, which are beneficial to the learning of the QA Generator $G$. Formally, the QA Generator $G$ is jointly optimized with the QA objective $\\mathcal{L}_{QA}$ in Equation~\\ref{eq:qa} using labeled data $D_l$ and the captioning distillation objective $\\mathcal{L}_{C}$ using unlabeled data $D_u$:\n\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{C} = - \\sum_{t=1}^{|C|} &\\log p(c_i \\mid V, c_{<i}), V \\in D_u \\\\\n\\mathcal{L}_{G} &= \\mathcal{L}_{QA} + \\mathcal{L}_{C}\n\\end{aligned}\n\\end{equation}\n\n\nWhile caption distillation enables the QA Generator $G$ to absorb rich semantic knowledge from unlabeled data, it remains essential that the model's capacity is focused on generating question-answer pairs rather than captioning. Under this motivation, we introduce a neuron selection strategy to ensure such captioning distillation is solely for enhancing QA-related knowledge. Specifically, we identify parameters in the QA Generator that contribute most to the question-answer generation and restrict parameter updates during training to this subset. For each parameter $\\theta$ in the QA Generator $G$, its importance score $s$ is quantified by the average magnitude of the gradient of the QA loss $\\mathcal{L}_{QA}$:\n\n\\begin{equation}\ns = \\left| \\frac{1}{|D_l|} \\sum_{(V, Q, A) \\in D_l} \\frac{\\partial \\mathcal{L}_{QA}}{\\partial \\theta} \\right|.\n\\end{equation}\nThen, we selection and update only parameters with top-$K$ scores in each neuron (i.e., each row in a linear weight matrix) while keep others frozen:\n\n\\begin{equation}\n\\theta \\leftarrow\n\\begin{cases}\n\\theta - \\eta \\cdot \\frac{\\partial \\mathcal{L}_{G}}{\\partial \\theta} & \\text{if $s$ is among top-$K$} \\\\\n\\theta, & \\text{otherwise}\n\\end{cases}\n\\end{equation}\nBy restricting updates to only the most QA-relevant neurons or parameters, we ensure that the auxiliary knowledge gained from caption distillation is efficiently integrated to support question-answer generation, rather than generic captioning or unrelated model capacities. With the above learning, the QA Generator is not limited to patterns seen in the small labeled set, but is instead exposed to the full diversity and richness of the target domain through the captions of unlabeled images. This enables the QA Generator to produce question-answer pairs that are more reflective of domain-specific semantics present in the unlabeled corpus. Hence, the resulting pseudo dataset $\\hat{D}_u$ would be more accurate and reliable with our proposed \\namestageaa, benefiting the subsequent learning of the VQA model in Equation~\\ref{eq:vqa}. \n\\section{Experiments}\n\n\\subsection{Datasets}\n\n\\paragraph{Kvasir-VQA}\n\nKvasir-VQA~\\cite{gautam2024kvasir} is a large-scale visual question answering dataset curated for research in the gastrointestinal (GI) medical imaging domain. The dataset consists of 6,500 endoscopic images sourced from the HyperKvasir and Kvasir-Instrument datasets, covering a wide spectrum of clinically relevant GI findings, anatomical sites, and medical instruments. The images in Kvasir-VQA reflect real-world clinical scenarios, including both normal findings and a variety of pathological conditions such as polyps, ulcers, and esophagitis, as well as procedure-related scenes featuring different instruments and interventions. Each image is paired with one or more expert-annotated question-answer (QA) pairs. These QA annotations are diverse, encompassing multiple question types including yes/no, multiple-choice, and counting, thus enabling comprehensive evaluation of both recognition and reasoning abilities for VQA.\n\nTo standardize the evaluation process, we further convert all question-answer pairs in Kvasir-VQA into a multiple-choice format. For each question, we define the set of candidate options as all possible answers that appear for that question type throughout the dataset, so that the number of answer choices is not fixed for different questions. For experimental setup, we partition the dataset into training and testing splits, containing 18,499 and 18,075 QA pairs, respectively. To simulate the limited annotation scenario when learning our \\nameshort~framework, only 1\\% QA pairs in the training split are used as labeled data while the remaining training images are treated as unlabeled data.\n\\begin{table*}[t!]\n % \\vspace{5mm}\n \\centering\n \\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\%) of VQA accuracy. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n \\vspace{-2mm}\n\t\\resizebox{0.75\\textwidth}{!}{\n \n \\begin{tabular}{l c c c c c}\n \n \\toprule \n\n \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n \\cline{2-5}\n & Colitis & Esophagitis & Instrument & Polyps & \\\\\n \\midrule\n Zero-Shot& 35.4 & 21.1 & 49.0 & 47.8 & 38.3 \\\\\n % Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 56.0 & 54.3 \\\\\n LoRA & 95.6 & 57.7 & 48.9 & 47.3 & 62.4 \\\\\n % DoRA & ? & ? & ? & ? & ? \\\\\n Full-Tuning & 89.0 & 60.8 & 51.2 & 51.3 & 63.1 \\\\\n \\nameshort~(Ours) & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n\n\n\n \\midrule\n Zero-Shot (Qwen2.5-VL-72B) & 59.7 & 48.6 & 53.1 & 55.9 & 54.3 \\\\\n Fully-Supervised & 97.4 & 97.4 & 85.8 & 82.1 & 90.7 \\\\\n \n \\bottomrule\n \\label{tab:medical}\n \\end{tabular}\n }\n \\vspace{-3mm}\n\\end{table*}\n\\begin{table*}[t!]\n \\centering\n \\vspace{2mm}\n \\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for sport understanding and reasoning questions. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n \\vspace{-2mm}\n\t\\resizebox{0.48\\textwidth}{!}{\n \n \\begin{tabular}{l c c c c}\n \n \\toprule \n\n Method & Easy & Medium & Hard & Average \\\\\n \\midrule\n Zero-Shot & 50.5 & 34.0 & 37.5 & 40.7 \\\\\n LoRA & 82.5 & 59.2 & 22.3 & 54.7 \\\\\n % DoRA & ? & ? & ? & ? \\\\\n Full-Tuning & 82.7 & 59.0 & 21.3 & 54.3 \\\\\n \\nameshort~(Ours) & 82.5 & 60.4 & 46.3 & 63.1 \\\\\n\n\n\n \\midrule\n % Zero-Shot (Qwen2.5-VL-72B) & ? & ? & ? & ? \\\\\n Fully-Supervised & 98.1 & 75.4 & 66.1 & 79.9 \\\\\n \n \\bottomrule \n \\vspace{-4mm}\n \\label{tab:sport}\n \\end{tabular}\n }\n\\end{table*}\n\\paragraph{SPORTU} SPORTU~\\cite{xia2024sportu} is a recently released benchmark designed to evaluate the sports understanding and reasoning abilities of multimodal large language models (MLLMs). The dataset comprises 1,701 slow-motion sports video clips, spanning seven popular sports: \\textit{American football, badminton, baseball, basketball, ice hockey, soccer}, and \\textit{volleyball}. The questions in SPORTU are diverse and challenging, covering rule comprehension, tactical analysis, prediction of outcomes, and recognition of actions and fouls. All questions are categorized into three levels of difficulty: \\textbf{easy}, which focuses on basic recognition tasks such as identifying the sport or counting players; \\textbf{medium}, which requires knowledge of player roles and basic tactics; and \\textbf{hard}, which involves deep reasoning about rules, foul detection, and scenario-based understanding. This tiered design enables comprehensive evaluation of MLLMs, from simple perception (in-distribution) to advanced, domain-specific sports reasoning (out-of-distribution). We partition the dataset into training and testing splits, containing 5,525 and 5,478 QA pairs, respectively. Similarly, we only consider 1\\% QA pairs in the training split when learning our \\nameshort~framework, while the remaining training images are treated as unlabeled data.\n\n\n\n\\subsection{Implementation Details}\nOur entire implementation is based on the PyTorch framework. For simplicity, we use NVILA-Lite-2B~\\cite{liu2025nvila} as our MLLM backbone for both our QA Generator and the VQA model. As for the large MLLM used for captioning distillation, we consider the state-of-the-art open source model, Qwen2.5-VL-72B-Instruct~\\cite{bai2025qwen2}. All the model weights are initialized with official pretrained checkpoints. During training, we use the AdamW optimizer with an initial learning rate of $0.00001$ and a cosine annealing schedule for learning rate decay. The batch size is set as $16$. As for neuron selection, we set the number of parameter $K=1000$ on the Kvasir-VQA dataset and $K=3000$ for SPORTU, respectively. The training is performed on 16 NVIDIA A100 GPUs with 80GB memory each. During inference, we use deterministic (greedy) decoding for all answer generation for the VQA model, i.e., at each generation step, the model always selects the token with the highest probability. This ensures that the outputs are fully reproducible and comparable across runs. As for pseudo QA Generation, we choose to use nucleus sampling on our QA Generator to produce several different question-answer pairs for each single visual input.\n\n\\subsection{Quantitative and Qualitative Experiments}\n\nWhile multimodal large language models (MLLMs) have demonstrated remarkable abilities on general visual understanding benchmarks, their robustness and adaptability often fall short when transferred to specialized domains such as medical image question answering. This gap arises primarily from two factors: the limited availability of expert-annotated data, and the significant distribution shift between general pretraining data and domain-specific imagery. In the context of medical imaging, acquiring comprehensive labeled datasets is both costly and time-consuming, which motivates the need for approaches that can effectively leverage abundant unlabeled data. To evaluate our method under such kind of scenarios, we design experiments on the Kvasir-VQA dataset, a large-scale benchmark of expert-annotated QA pairs paired with real-world endoscopic images.\n\n\n\n\\begin{table*}[t!]\n \\centering\n \\caption{Ablation study of our \\namestageaa~for the QA Generator on the Kvasir-VQA dataset.}\n \\vspace{-2mm}\n\t\\resizebox{0.8\\textwidth}{!}{\n \n \\begin{tabular}{l c c c c c}\n \n \\toprule \n\n \\multirow{2}{*}{Method} & \\multicolumn{4}{c}{Image Category} & \\multirow{2}{*}{Average}\\\\\n \\cline{2-5}\n & Colitis & Esophagitis & Instrument & Polyps & \\\\\n \\midrule\n\n Baseline & 93.0 & 88.2 & 55.7 & 56.2 & 73.3 \\\\\n Baseline+Distill. & 95.1 & 80.3 & 59.7 & 60.4 & 73.9 \\\\\n Baseline+Distill.+QA Neurons & 95.8 & 83.9 & 61.6 & 65.5 & 76.7 \\\\\n \n \\bottomrule \n \\label{tab:ab1}\n \\end{tabular}\n }\n \\vspace{-5mm}\n\\end{table*}\\begin{table*}[t!]\n \\centering\n \\vspace{2mm}\n \\caption{Ablation study of our \\namestageaa~for the QA Generator on the SPORTU dataset.}\n \\vspace{-2mm}\n\t\\resizebox{0.63\\textwidth}{!}{\n \n \\begin{tabular}{l c c c c}\n \n \\toprule \n\n Method & Easy & Medium & Hard & Average \\\\\n \\midrule\n Baseline & 75.5 & 60.3 & 44.4 & 60.1 \\\\\n Baseline+Distill.& 82.9 & 61.2 & 42.3 & 62.2 \\\\\n Baseline+Distill.+QA Neurons & 82.5 & 60.4 & 46.3 & 63.1 \\\\\n \n \\bottomrule \n \\label{tab:ab2}\n \\end{tabular}\n }\n \\vspace{-6mm}\n\\end{table*}\nTable~\\ref{tab:medical} presents a detailed comparison of different learning strategies on the Kvasir-VQA datasets, where only $1\\%$ of the training data is labeled and the remaining ones are treated as unlabeled. From this Table, we see that zero-shot inference using NVILA-Lite-2B achieves only $38.3\\%$ average accuracy, indicating the difficulty of the task without any fine-tuning. Fine-tuning with LoRA~\\cite{hu2022lora} or full parameter updates on just $1\\%$ labeled data yields moderate improvements ($62.4\\%$ and $63.1\\%$ accuracy, respectively), but these methods still struggle on less-represented or out-of-distribution categories. By augmenting the training with pseudo QA pairs generated from the unlabeled images, our approach significantly boosts average accuracy to $76.7\\%$, especially on challenging categories such as Esophagitis. As a reference, the fully supervised model (using all labeled data) achieves $90.7\\%$.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{medicalfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n \\label{figure:medicalg}\n \\vspace{-4mm}\n\\end{figure}\n\nWe further evaluate our method on the SPORTU dataset to assess its generalization ability in the sports domain, which poses unique challenges compared to the medical setting. Unlike static medical images, SPORTU consists of dynamic sports video clips that require not only visual recognition but also temporal reasoning, action understanding, and comprehension of complex game rules. These factors make sports VQA a particularly demanding task for multimodal large language models. As shown in Table~\\ref{tab:sport}, our \\nameshort~framework achieves consistent improvements over all baselines. In particular, our method raises the average accuracy to 63.1\\%, outperforming both LoRA and full-tuning by a clear margin. Notably, the accuracy on “Hard” questions—which require advanced reasoning—improves significantly from around 22.3\\% to 46.3\\%. In addition to quantitative results, we also provide qualitative comparisons as shown in Figure~\\ref{figure:medical} and~\\ref{figure:sport}. We see that, our \\nameshort~framework is able to produce accurate answers compared to state-of-the-art MLLMs on the challenging medical and sport domains. Through the above experiments, we verify that our ~\\nameshort~framework, which directly incorporates unlabeled data through pseudo QA generation, can substantially enhance VQA performance on out-of-distribution domain with limited annotations.\n\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{sportfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the SPORTU dataset.}\n \\label{figure:sport}\n \\vspace{-4mm}\n\\end{figure}\n\n\\subsection{Ablation Studies}\nAs shown in Table~\\ref{tab:ab1}, our ablation study on Kvasir-VQA evaluates the effects of caption distillation and selective neuron updates. Caption distillation alone leads to only a minor increase in average accuracy (an improvement of just 0.6\\% over the baseline). In contrast, when selective neuron updates are applied, the accuracy increases substantially, yielding a total gain of 3.4\\% over the baseline. A similar trend is observed on the SPORTU dataset (Table~\\ref{tab:ab2}). These results highlight that targeted neuron selection is crucial for effective distillation for the QA Generator, and that substantial performance gains can only be achieved when both components are used together.\n\n\\section{Conclusion}\nIn this paper, we introduce \\nameshort, a label-efficient adaptation framework designed to transfer MLLMs to out-of-distribution (OOD) domains that extend far beyond their original pretraining distribution. Our approach first utilizes \\namestagea~to generate domain-relevant pseudo question-answer pairs from large pools of unlabeled visual data, effectively expanding the training set in scenarios where annotated examples are extremely limited. In addition, we employ \\namestageaa~for the QA Generator, a selective neuron updating strategy that identifies and updates only knowledge-relevant neurons while acquiring domain knowledge from state-of-the-art large MLLMs. We conduct extensive experiments on OOD benchmarks, including gastrointestinal endoscopy and sports VQA, demonstrating the applicability of our framework. Detailed ablation studies and both quantitative and qualitative analyses consistently show that our proposed \\nameshort~framework achieves substantial improvements over conventional fine-tuning methods, validating its effectiveness and robustness for adapting MLLMs to challenging domain-specific visual tasks with limited annotations.\n\n\\bibliography{aaai2026}\n\\clearpage\n% \\input{ReproducibilityChecklist}\n\\appendix\n\\section{Additional Visualization}\n\n\\subsection{Comparison with Baseline in VQA}\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{medical2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n % \\label{figure:afd}\n \\vspace{-4mm}\n\\end{figure}\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{sport2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the SPORTU dataset.}\n % \\label{figure:sport2}\n % \\vspace{-4mm}\n\\end{figure}\nWe provide additional qualitative results comparing our LEAML method with baseline approaches on both medical and sports VQA tasks. These examples demonstrate our method's superior performance in generating accurate, domain-specific answers. The results show that our approach better understands specialized terminology and visual patterns, leading to more precise responses compared to standard MLLMs.\n\n\\subsection{Generated Pseudo-QA Examples}\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{GenQA_medicalfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results of generated pseudo-QA on the Kvasir-VQA dataset.}\n \\label{figure:medicalb}\n % \\vspace{-4mm}\n\\end{figure}\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{GenQA_sportfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results of generated pseudo-QA on the SPORTU dataset.}\n \\label{figure:medicalc}\n % \\vspace{-4mm}\n\\end{figure}\\begin{figure}[!ht]\n \\centering\n \\includegraphics[width=\\linewidth]{captionfig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results of generated caption on the SPORTU dataset.}\n \\label{figure:medical}\n \\vspace{-4mm}\n\\end{figure}\nWe show examples of pseudo question-answer pairs generated by our QA Generator. These synthetic QA pairs effectively expand the training dataset and provide domain-relevant supervision for the subsequent fine-tuning stage. The generated questions are contextually appropriate and cover diverse aspects of the visual content, while the answers demonstrate proper domain knowledge and terminology usage.\n\n\\subsection{Captions from Large MLLM}\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{caption2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results of generated caption on the Kvasir-VQA dataset.}\n \\label{figure:medicala}\n \\vspace{-4mm}\n\\end{figure}\nWe present captions generated by the large MLLM (Qwen2.5-VL-72B) used in our distillation process. These captions successfully capture important visual details and domain-specific information, which helps improve the QA Generator's learning through knowledge distillation.\n% \\maketitle\n% \\section{Additional }\n% 1. VQA comparsion of qua\n% 2. QA Generater generated pseudo QA\n% 3. Caption from large MLLM, sport\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{medical2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the Kvasir-VQA dataset.}\n % \\label{figure:afd}\n \\vspace{-4mm}\n\\end{figure}\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=\\linewidth]{sport2fig.pdf}\n \\vspace{-6mm}\\caption{Qualitative results on the SPORTU dataset.}\n % \\label{figure:sport2}\n % \\vspace{-4mm}\n\\end{figure}\\end{document}\n"},"question":{"kind":"string","value":"For categories where LORA and LEAML differ in accuracy by more than 10%, what is the difference between the accuracy of the fully supervised model and the average accuracy of all other models?"},"answer":{"kind":"string","value":"34.25"},"plan":{"kind":"string","value":"SELECT all categories\nLOOP for each category\n COMPUTE gap_lora_leaml = absolute( lora category accuracy − leaml (ours) category accuracy)\n IF gap_lora_leaml > 10\n COMPUTE others_avg = average of zero-shot, lora, full-tuning, leaml (ours) category accuracies\n COMPUTE diff_fs_vs_others = fully-supervised category accuracy − others_avg\n\n\nRETURN diff_fs_vs_others\n"}}},{"rowIdx":348,"cells":{"paper":{"kind":"string","value":"2510.03224"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t]\n","\\setlength{\\tabcolsep}{0.8pt} \n","\\footnotesize\n"," \\centering\n"," \\begin{tabular}{c|l|c|c|c|c|c|c|c|c|c|c|c|c}\n"," &Attack Strength ($\\epsilon$)&\\multicolumn{3}{c|}{0.02}&\\multicolumn{3}{c|}{0.01}&\\multicolumn{3}{c|}{0.005}&\\multicolumn{3}{c}{0.002}\\\\\\cline{2-14}\n","&Metric&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err\\\\\\hline\n","{\\multirow{5}{*}{\\rotatebox[origin=c]{90}{FGSM}}} &No Defense&14.83&24.10&97.33&8.49&14.53&90.49&5.05&7.70&74.71&3.01&3.49&38.12 \\\\\n","&Latent Smoothing&13.42&22.09&96.61&8.12&13.69&89.25&4.89&7.05&73.01&2.89&3.32&36.25\n","\\\\\n","&Ours ($d=1$)&10.12&15.81&95.80&6.46&9.92&86.30&4.39&5.93&68.55&2.78&3.18&31.99 \\\\\n","&\\cellcolor{gray!20}Error Reduced (\\%)& \\cellcolor{gray!20}31.76&\\cellcolor{gray!20}34.40&\\cellcolor{gray!20}1.57&\\cellcolor{gray!20}23.91&\\cellcolor{gray!20}31.73&\\cellcolor{gray!20}4.63&\\cellcolor{gray!20}13.07&\\cellcolor{gray!20}22.99&\\cellcolor{gray!20}7.58&\\cellcolor{gray!20}7.64&\\cellcolor{gray!20}8.88&\\cellcolor{gray!20}16.08\\\\\n","&Ours ($d=2$)&\\textbf{9.22}&\\textbf{13.88}&\\textbf{94.61}&\\textbf{6.13}&\\textbf{8.87}&\\textbf{84.49}&\\textbf{4.19}&\\textbf{5.43}&\\textbf{66.74}&\\textbf{2.73}&\\textbf{3.12}&\\textbf{31.18}\\\\\n","&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20} 37.82&\\cellcolor{gray!20}42.40&\\cellcolor{gray!20}2.79&\\cellcolor{gray!20}27.78&\\cellcolor{gray!20}38.95&\\cellcolor{gray!20}6.63&\\cellcolor{gray!20}16.92&\\cellcolor{gray!20}29.41&\\cellcolor{gray!20}10.66&\\cellcolor{gray!20}9.21&\\cellcolor{gray!20}10.65&\\cellcolor{gray!20}18.21 \\\\\\hline\n","{\\multirow{5}{*}{\\rotatebox[origin=c]{90}{PGD}}} &No Defense&161.70&162.61&99.99&131.66&140.55&98.64&63.97&88.55&85.31&6.83&17.03&39.24 \\\\\n","&Latent Smoothing&161.79&162.69&99.99&131.46&140.41&98.57&63.86&88.21&85.39&7.28&17.44&39.81\\\\\n","&Ours ($d=1$)&107.86&125.14&98.29&69.97&84.72&91.79&20.66&42.29&73.21&4.17&8.32&29.09\\\\\n","&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20}33.30 &\\cellcolor{gray!20} 23.04 &\\cellcolor{gray!20} 1.70 &\\cellcolor{gray!20} 46.86 &\\cellcolor{gray!20} 39.72 &\\cellcolor{gray!20} 6.94 &\\cellcolor{gray!20} 67.70 &\\cellcolor{gray!20} 52.24 &\\cellcolor{gray!20} 14.18 &\\cellcolor{gray!20} 38.95 &\\cellcolor{gray!20} 51.15 &\\cellcolor{gray!20} 25.87\\\\\n","&Ours ($d=2$)&\\textbf{77.59}&\\textbf{100.14}&\\textbf{96.14}&\\textbf{44.77}&\\textbf{66.23}&\\textbf{89.24}&\\textbf{17.98}&\\textbf{32.80}&\\textbf{71.09}&\\textbf{3.76}&\\textbf{6.73}&\\textbf{28.44}\\\\\n","&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20} 52.01 &\\cellcolor{gray!20} 38.41 &\\cellcolor{gray!20} 3.85 &\\cellcolor{gray!20} 66.02 &\\cellcolor{gray!20} 52.87 &\\cellcolor{gray!20} 9.53 &\\cellcolor{gray!20} 71.89 &\\cellcolor{gray!20} 62.94 &\\cellcolor{gray!20} 16.66 &\\cellcolor{gray!20} 44.99 &\\cellcolor{gray!20} 60.52 &\\cellcolor{gray!20} 27.53\n","\\end{tabular}\n"," \\caption{\\sl\\small{\\bf Stochastic Resonance Enhances Stereo Matching Robustness.} Incorporating stochastic resonance significantly reduces prediction errors induced by adversarial attacks across all evaluation metrics, reducing error by up to 71.89\\% (MAE, when attacked by PGD with $\\epsilon=0.005$). Notably, this defense mechanism operates entirely at test time without requiring any model re-training, which sets it apart from existing methods.}\n"," \\label{tab:stereo}%\\vspace{-2mm}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\setlength{\\\\tabcolsep}{0.8pt} \\n\",\n \"\\\\footnotesize\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{tabular}{c|l|c|c|c|c|c|c|c|c|c|c|c|c}\\n\",\n \" &Attack Strength ($\\\\epsilon$)&\\\\multicolumn{3}{c|}{0.02}&\\\\multicolumn{3}{c|}{0.01}&\\\\multicolumn{3}{c|}{0.005}&\\\\multicolumn{3}{c}{0.002}\\\\\\\\\\\\cline{2-14}\\n\",\n \"&Metric&\\\\,MAE\\\\,&RMSE&D1-err&\\\\,MAE\\\\,&RMSE&D1-err&\\\\,MAE\\\\,&RMSE&D1-err&\\\\,MAE\\\\,&RMSE&D1-err\\\\\\\\\\\\hline\\n\",\n \"{\\\\multirow{5}{*}{\\\\rotatebox[origin=c]{90}{FGSM}}} &No Defense&14.83&24.10&97.33&8.49&14.53&90.49&5.05&7.70&74.71&3.01&3.49&38.12 \\\\\\\\\\n\",\n \"&Latent Smoothing&13.42&22.09&96.61&8.12&13.69&89.25&4.89&7.05&73.01&2.89&3.32&36.25\\n\",\n \"\\\\\\\\\\n\",\n \"&Ours ($d=1$)&10.12&15.81&95.80&6.46&9.92&86.30&4.39&5.93&68.55&2.78&3.18&31.99 \\\\\\\\\\n\",\n \"&\\\\cellcolor{gray!20}Error Reduced (\\\\%)& \\\\cellcolor{gray!20}31.76&\\\\cellcolor{gray!20}34.40&\\\\cellcolor{gray!20}1.57&\\\\cellcolor{gray!20}23.91&\\\\cellcolor{gray!20}31.73&\\\\cellcolor{gray!20}4.63&\\\\cellcolor{gray!20}13.07&\\\\cellcolor{gray!20}22.99&\\\\cellcolor{gray!20}7.58&\\\\cellcolor{gray!20}7.64&\\\\cellcolor{gray!20}8.88&\\\\cellcolor{gray!20}16.08\\\\\\\\\\n\",\n \"&Ours ($d=2$)&\\\\textbf{9.22}&\\\\textbf{13.88}&\\\\textbf{94.61}&\\\\textbf{6.13}&\\\\textbf{8.87}&\\\\textbf{84.49}&\\\\textbf{4.19}&\\\\textbf{5.43}&\\\\textbf{66.74}&\\\\textbf{2.73}&\\\\textbf{3.12}&\\\\textbf{31.18}\\\\\\\\\\n\",\n \"&\\\\cellcolor{gray!20}Error Reduced (\\\\%)&\\\\cellcolor{gray!20} 37.82&\\\\cellcolor{gray!20}42.40&\\\\cellcolor{gray!20}2.79&\\\\cellcolor{gray!20}27.78&\\\\cellcolor{gray!20}38.95&\\\\cellcolor{gray!20}6.63&\\\\cellcolor{gray!20}16.92&\\\\cellcolor{gray!20}29.41&\\\\cellcolor{gray!20}10.66&\\\\cellcolor{gray!20}9.21&\\\\cellcolor{gray!20}10.65&\\\\cellcolor{gray!20}18.21 \\\\\\\\\\\\hline\\n\",\n \"{\\\\multirow{5}{*}{\\\\rotatebox[origin=c]{90}{PGD}}} &No Defense&161.70&162.61&99.99&131.66&140.55&98.64&63.97&88.55&85.31&6.83&17.03&39.24 \\\\\\\\\\n\",\n \"&Latent Smoothing&161.79&162.69&99.99&131.46&140.41&98.57&63.86&88.21&85.39&7.28&17.44&39.81\\\\\\\\\\n\",\n \"&Ours ($d=1$)&107.86&125.14&98.29&69.97&84.72&91.79&20.66&42.29&73.21&4.17&8.32&29.09\\\\\\\\\\n\",\n \"&\\\\cellcolor{gray!20}Error Reduced (\\\\%)&\\\\cellcolor{gray!20}33.30 &\\\\cellcolor{gray!20} 23.04 &\\\\cellcolor{gray!20} 1.70 &\\\\cellcolor{gray!20} 46.86 &\\\\cellcolor{gray!20} 39.72 &\\\\cellcolor{gray!20} 6.94 &\\\\cellcolor{gray!20} 67.70 &\\\\cellcolor{gray!20} 52.24 &\\\\cellcolor{gray!20} 14.18 &\\\\cellcolor{gray!20} 38.95 &\\\\cellcolor{gray!20} 51.15 &\\\\cellcolor{gray!20} 25.87\\\\\\\\\\n\",\n \"&Ours ($d=2$)&\\\\textbf{77.59}&\\\\textbf{100.14}&\\\\textbf{96.14}&\\\\textbf{44.77}&\\\\textbf{66.23}&\\\\textbf{89.24}&\\\\textbf{17.98}&\\\\textbf{32.80}&\\\\textbf{71.09}&\\\\textbf{3.76}&\\\\textbf{6.73}&\\\\textbf{28.44}\\\\\\\\\\n\",\n \"&\\\\cellcolor{gray!20}Error Reduced (\\\\%)&\\\\cellcolor{gray!20} 52.01 &\\\\cellcolor{gray!20} 38.41 &\\\\cellcolor{gray!20} 3.85 &\\\\cellcolor{gray!20} 66.02 &\\\\cellcolor{gray!20} 52.87 &\\\\cellcolor{gray!20} 9.53 &\\\\cellcolor{gray!20} 71.89 &\\\\cellcolor{gray!20} 62.94 &\\\\cellcolor{gray!20} 16.66 &\\\\cellcolor{gray!20} 44.99 &\\\\cellcolor{gray!20} 60.52 &\\\\cellcolor{gray!20} 27.53\\n\",\n \"\\\\end{tabular}\\n\",\n \" \\\\caption{\\\\sl\\\\small{\\\\bf Stochastic Resonance Enhances Stereo Matching Robustness.} Incorporating stochastic resonance significantly reduces prediction errors induced by adversarial attacks across all evaluation metrics, reducing error by up to 71.89\\\\% (MAE, when attacked by PGD with $\\\\epsilon=0.005$). Notably, this defense mechanism operates entirely at test time without requiring any model re-training, which sets it apart from existing methods.}\\n\",\n \" \\\\label{tab:stereo}%\\\\vspace{-2mm}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}[t]\n","\\centering\n","\\includegraphics[width=\\textwidth]{Figures/diagram.pdf}\n"," \\caption{\\sl\\small {\\bf Defense against adversarial attacks via stochastic resonance.} Neural networks are highly sensitive to small perturbations in the input space, which adversarial attacks exploit to manipulate network outputs. Conventional defense strategies primarily focus on filtering out unreliable features or denoising either the input or the features. Instead of removing noise, we propose a novel defense by introducing noise. Based on stochastic resonance, controlled transformations are introduced to the input. Features are then aggregated after inverting these transformations. The resulting method can be applied exclusively at inference time, requires no training, and is compatible with diverse network architectures. Notably, it not only improves robustness against adversarial attacks but also increases the difficulty of crafting successful adversarial examples, even when the attacker is fully aware of whether and how stochastic resonance is being used (i.e. adaptive attacks).\n","}\n"," \\label{fig:schematic}\n","\\end{figure*}\n"],["\\begin{figure*}[t]\n","\n","\\centering\n","\\hspace*{-4mm}\n","{\\scriptsize\n","\\begin{tabular}[0mm]{c@{\\hskip 0.01in}c@{\\hskip 0.01in}c@{\\hskip 0.01in}c@{\\hskip 0.01in}c}\n","\\includegraphics[width=\\fWidD]{\\figd/1}&\n","\\includegraphics[width=\\fWidD]{\\figd/2}&\n","\\includegraphics[width=\\fWidD]{\\figd/3}&\n","\\includegraphics[width=\\fWidD]{\\figd/4}&\n","\\includegraphics[width=\\fWidD]{\\figd/5}\n","\\end{tabular}\n","}\n","\\caption{\\sl\\small {\\bf Results on CIFAR-10 under varying levels of stochastic resonance.} Increasing the stochastic resonance level consistently enhances robustness across all settings, yielding clear gains over the baseline method (FSR). Notably, our approach achieves superior performance even under adaptive adversarial attacks (Ours-WorstCase), despite the baseline being evaluated only in the non-adaptive case.}\n","\n","\n","\\label{fig:cifar}\n","\\end{figure*}\n"],["\\begin{table*}[t]\n","\\footnotesize\n","\\setlength{\\tabcolsep}{0.8pt} \n"," \\centering\n"," \\begin{tabular}{l|l|>{\\centering}p{14mm}|>{\\centering}p{14mm}|>{\\centering}p{14mm}|>{\\centering}p{14mm}|>{\\centering}p{14mm}||c}\n","Method&Architecture& Natural & FGSM& PGD-20& PGD-100& C\\&W& Ensemble \\\\\\hline\\hline\n","AT&\\multirow{8}{*}{ResNet-18}&85.02 & 56.21 & 48.22 & 46.37 & 47.38 & 45.90 \\\\\n","+ FD&&85.14&56.81&48.54&46.70&47.72&45.82 \\\\\n","+ CAS&&\\textbf{85.78}&55.57&50.42&49.91&53.47&46.46 \\\\\n","+ CIFS&&79.87&56.53&49.80&48.17&49.89&47.26 \\\\\n","+ FSR&& 81.46 & 58.07 & 52.47 & 51.02 & 49.44 & 48.34 \\\\\n","+ TTE&& 85.25 & 59.20 & 53.00 &51.65 &52.45&50.60\\\\\n","\\rowcolor{gray!20}+ Ours&& 84.93&\\textbf{61.02}&\\textbf{56.08}&\t\\textbf{55.17}&\t\\textbf{55.53}&\t\\textbf{53.68}\\\\\n","\\rowcolor{gray!20}+ Ours-WorstCase&&84.93& 58.81 & 53.58 & 52.39 & 52.73 & 50.95 \\\\\n","\\hline\n","TRADES&&84.92&60.87&56.13&55.16&54.02&53.38 \\\\\n","\\rowcolor{gray!20}+Ours &\\multirow{-2}{*}{WideResNet-34}& \\textbf{85.03}&\\textbf{62.43}&\\textbf{58.64}&\\textbf{57.87}&\\textbf{57.18}&\\textbf{56.28}\\\\\\hline\n","MART&& \\textbf{83.07}&60.21&54.14&52.90&49.62&48.95\\\\\n","\\rowcolor{gray!20}+ Ours &\\multirow{-2}{*}{ResNet-18}& 82.70&\\textbf{62.62}&\\textbf{59.03}&\\textbf{58.13}&\\textbf{55.51}&\\textbf{54.61}\n","\\end{tabular} %\\vspace{-1mm}\n"," \\caption{\\sl\\small{\\bf Defense against adversarial attacks on classification task (CIFAR-10).} Compared to baselines that filter or manipulate features, ours does not modify network architecture or weights. Instead, ours performs an ensemble in the feature space. On CIFAR-10, ours achieves state-of-the-art robustness without requiring any additional training. Moreover, even in a worst-case adaptive adversary setting where the attacker is fully aware of the defense and how stochastic resonance is applied, the effectiveness of adversarial attacks is still notably reduced, while the computational cost for executing such attacks is significantly increased.}\n"," \\label{tab:cifar10}\n","\\end{table*}\n"],["\\begin{table}[t]\n","\\scriptsize\n","\\parbox{.49\\linewidth}{\n","\\centering\n","\\setlength{\\tabcolsep}{0.8pt} \n"," \\begin{tabular}{l|c|c|c|c|c|c|c|c}\n","Att. Strength ($\\epsilon$)&\\multicolumn{2}{c|}{8/255}&\\multicolumn{2}{c|}{4/255}&\\multicolumn{2}{c|}{2/255}&\\multicolumn{2}{c}{1/255}\\\\\n","\\hline\n","Metric&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5\\\\\\hline\n","No Defense&4.51&19.55&12.25&42.15&29.79&65.09&48.09&78.13\\\\\n","Ours ($d=1$)&11.66&46.27&27.85&65.80&45.94&77.63&57.48&83.43\\\\\n","Ours ($d=2$)&18.78&58.58&36.42&72.86&51.58&80.85&60.41&84.77\\\\\n","Ours ($d=3$)&\\textbf{25.77}&\\textbf{65.88}&\\textbf{42.52}&\\textbf{76.75}&\\textbf{54.94}&\\textbf{82.64}&\\textbf{62.08}&\\textbf{85.50}\n"," \\end{tabular} %\\vspace{-1mm}\n"," \\captionof{table}{\\small{\\bf ImageNet with ViT-Small.} Increasing the level of stochastic resonance consistently improves both Top-1 and Top-5 accuracy under adversarial attacks. Relative to the clean baseline (72.9 Top-1, 92.91 Top-5), our method recovers up to 55.8\\% of the Top-1 accuracy loss and 68.1\\% of the Top-5 accuracy loss.}\n"," \\label{tab:ViT}\n","}\n","\\hfill\n","\\parbox{.49\\linewidth}{\n","\\centering\n","\\setlength{\\tabcolsep}{0.8pt} \n"," \\begin{tabular}{l|c|c|c|c|c|c|c|c}\n","Att. Strength ($\\epsilon$)&\\multicolumn{2}{c|}{8/255}&\\multicolumn{2}{c|}{4/255}&\\multicolumn{2}{c|}{2/255}&\\multicolumn{2}{c}{1/255}\\\\\n","\\hline\n","Metric&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5\\\\\\hline\n","No Defense&8.51&26.19&9.45&27.92&11.10&30.63&15.21&36.76\\\\\n","Initial Conv.&16.91&34.66&17.36&35.28&18.12&36.30&19.59&38.25\\\\\n","Res. Block 1&22.44&44.95&23.39&46.03&24.84&47.64&27.57&50.80\\\\\n","Res. Block 2&\\textbf{24.88}&\\textbf{48.54}&\\textbf{25.90}&\\textbf{49.66}&\\textbf{27.23}&\\textbf{51.19}&\\textbf{30.11}&\\textbf{54.15}\\\\\n","Res. Block 3&21.76&44.28&22.73&45.47&24.14&47.14&27.18&50.20\n"," \\end{tabular} %\\vspace{-1mm}\n"," \\captionof{table}{\\small{\\bf Layer-wise ablation on ResNet-50.} Adversarial perturbations resemble high-frequency noise. Applying stochastic resonance through shallow layers is sufficient to defend against adversarial attacks, substantially reducing the overall computational cost.}\n"," \\label{tab:layers}\n"," } %\\vspace{-2mm}\n","\\end{table}\n"],["\\begin{table*}[t]\n","\\setlength{\\tabcolsep}{0.8pt} \n","\\footnotesize\n"," \\centering\n"," \\begin{tabular}{c|l|c|c|c|c|c|c|c|c|c|c|c|c}\n"," &Attack Strength ($\\epsilon$)&\\multicolumn{3}{c|}{0.02}&\\multicolumn{3}{c|}{0.01}&\\multicolumn{3}{c|}{0.005}&\\multicolumn{3}{c}{0.002}\\\\\\cline{2-14}\n","&Metric&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err\\\\\\hline\n","{\\multirow{5}{*}{\\rotatebox[origin=c]{90}{FGSM}}} &No Defense&14.83&24.10&97.33&8.49&14.53&90.49&5.05&7.70&74.71&3.01&3.49&38.12 \\\\\n","&Latent Smoothing&13.42&22.09&96.61&8.12&13.69&89.25&4.89&7.05&73.01&2.89&3.32&36.25\n","\\\\\n","&Ours ($d=1$)&10.12&15.81&95.80&6.46&9.92&86.30&4.39&5.93&68.55&2.78&3.18&31.99 \\\\\n","&\\cellcolor{gray!20}Error Reduced (\\%)& \\cellcolor{gray!20}31.76&\\cellcolor{gray!20}34.40&\\cellcolor{gray!20}1.57&\\cellcolor{gray!20}23.91&\\cellcolor{gray!20}31.73&\\cellcolor{gray!20}4.63&\\cellcolor{gray!20}13.07&\\cellcolor{gray!20}22.99&\\cellcolor{gray!20}7.58&\\cellcolor{gray!20}7.64&\\cellcolor{gray!20}8.88&\\cellcolor{gray!20}16.08\\\\\n","&Ours ($d=2$)&\\textbf{9.22}&\\textbf{13.88}&\\textbf{94.61}&\\textbf{6.13}&\\textbf{8.87}&\\textbf{84.49}&\\textbf{4.19}&\\textbf{5.43}&\\textbf{66.74}&\\textbf{2.73}&\\textbf{3.12}&\\textbf{31.18}\\\\\n","&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20} 37.82&\\cellcolor{gray!20}42.40&\\cellcolor{gray!20}2.79&\\cellcolor{gray!20}27.78&\\cellcolor{gray!20}38.95&\\cellcolor{gray!20}6.63&\\cellcolor{gray!20}16.92&\\cellcolor{gray!20}29.41&\\cellcolor{gray!20}10.66&\\cellcolor{gray!20}9.21&\\cellcolor{gray!20}10.65&\\cellcolor{gray!20}18.21 \\\\\\hline\n","{\\multirow{5}{*}{\\rotatebox[origin=c]{90}{PGD}}} &No Defense&161.70&162.61&99.99&131.66&140.55&98.64&63.97&88.55&85.31&6.83&17.03&39.24 \\\\\n","&Latent Smoothing&161.79&162.69&99.99&131.46&140.41&98.57&63.86&88.21&85.39&7.28&17.44&39.81\\\\\n","&Ours ($d=1$)&107.86&125.14&98.29&69.97&84.72&91.79&20.66&42.29&73.21&4.17&8.32&29.09\\\\\n","&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20}33.30 &\\cellcolor{gray!20} 23.04 &\\cellcolor{gray!20} 1.70 &\\cellcolor{gray!20} 46.86 &\\cellcolor{gray!20} 39.72 &\\cellcolor{gray!20} 6.94 &\\cellcolor{gray!20} 67.70 &\\cellcolor{gray!20} 52.24 &\\cellcolor{gray!20} 14.18 &\\cellcolor{gray!20} 38.95 &\\cellcolor{gray!20} 51.15 &\\cellcolor{gray!20} 25.87\\\\\n","&Ours ($d=2$)&\\textbf{77.59}&\\textbf{100.14}&\\textbf{96.14}&\\textbf{44.77}&\\textbf{66.23}&\\textbf{89.24}&\\textbf{17.98}&\\textbf{32.80}&\\textbf{71.09}&\\textbf{3.76}&\\textbf{6.73}&\\textbf{28.44}\\\\\n","&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20} 52.01 &\\cellcolor{gray!20} 38.41 &\\cellcolor{gray!20} 3.85 &\\cellcolor{gray!20} 66.02 &\\cellcolor{gray!20} 52.87 &\\cellcolor{gray!20} 9.53 &\\cellcolor{gray!20} 71.89 &\\cellcolor{gray!20} 62.94 &\\cellcolor{gray!20} 16.66 &\\cellcolor{gray!20} 44.99 &\\cellcolor{gray!20} 60.52 &\\cellcolor{gray!20} 27.53\n","\\end{tabular}\n"," \\caption{\\sl\\small{\\bf Stochastic Resonance Enhances Stereo Matching Robustness.} Incorporating stochastic resonance significantly reduces prediction errors induced by adversarial attacks across all evaluation metrics, reducing error by up to 71.89\\% (MAE, when attacked by PGD with $\\epsilon=0.005$). Notably, this defense mechanism operates entirely at test time without requiring any model re-training, which sets it apart from existing methods.}\n"," \\label{tab:stereo}%\\vspace{-2mm}\n","\\end{table*}\n"],["\\begin{figure*}[t]\n","\\centering\n","\\includegraphics[width=\\textwidth]{Figures/Stereo.pdf}%\\vspace{-2mm}\n"," \\caption{\\sl\\small {\\bf Stereo matching robustness via stochastic resonance.} We present visual results on stereo matching under various adversarial attack scenarios, including PGD and FGSM at different perturbation levels. These attacks significantly degrade the network's predictions, leading to substantial errors. By incorporating stochastic resonance, we demonstrate a significant reduction in prediction errors. This technique holds significant potential for improving robustness in safety-critical real-world applications, such as autonomous driving, where stereo vision must remain reliable under diverse environmental conditions and adversarial threats.\n","}\n"," \\label{fig:stereo}%\\vspace{-2mm}\n","\\end{figure*}\n"],["\\begin{figure*}[t]\n","\\renewcommand{\\arraystretch}{0.2} % Default value: 1\n","\\centering\n","\\hspace*{-4mm}\n","{\\scriptsize\n","\\begin{tabular}[0mm]{c@{\\hskip 0.01in}c@{\\hskip 0.01in}c@{\\hskip 0.01in}c|c@{\\hskip 0.01in}c@{\\hskip 0.01in}c}\n","& \\multicolumn{3}{c}{\\normalsize PGD}& \\multicolumn{3}{c}{\\normalsize FGSM}\\\\\\\\\n","\\smash{\\rotatebox{90}{\\quad Image}}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd1}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd2}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd3}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm1}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm4}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm3}\\\\\n","\\smash{\\rotatebox{90}{Original}}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_org1}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_org2}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_org3}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_org1}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_org4}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_org3}\\\\\n","\\smash{\\rotatebox{90}{Attacked}}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_attacked1}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_attacked2}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_attacked3}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_attacked1}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_attacked4}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_attacked3}\\\\\n","\\smash{\\rotatebox{90}{\\quad Ours}}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_ours1}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_ours2}&\n","\\includegraphics[width=\\fWidD]{\\figd/pgd_ours3}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_ours1}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_ours4}&\n","\\includegraphics[width=\\fWidD]{\\figd/fgsm_ours3}\\\\\n","\\end{tabular}\n","}\n","\\caption{\\sl\\small{\\bf Optical flow robustness via stochastic resonance.} \n","Qualitative results (visualized with a color wheel) show that our method substantially mitigates the degradation caused by both PGD and FGSM attacks. This robustness is particularly relevant for visual perception systems that rely on accurate motion estimation.}\n","\\label{fig:flow-quality}%\\vspace{-2mm}\n","\\end{figure*}\n"],["\\begin{figure*}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/fgsm2e2.pdf}\n"," \\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\epsilon=0.02$}\n"," \\label{fig:fgsm2e2_stereo}\n","\\end{figure*}\n"],["\\begin{figure*}[h]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/fgsm1e2.pdf}\n"," \\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\epsilon=0.01$}\n"," \\label{fig:fgsm1e2_stereo}\n","\\end{figure*}\n"],["\\begin{figure*}[h]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/fgsm5e3.pdf}\n"," \\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\epsilon=0.005$}\n"," \\label{fig:fgsm5e3_stereo}\n","\\end{figure*}\n"],["\\begin{figure*}[h]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/PGD1e2.pdf}\n"," \\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\epsilon=0.01$}\n"," \\label{fig:pgd1e2_stereo}\n","\\end{figure*}\n"],["\\begin{figure*}[h]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/PGD5e3.pdf}\n"," \\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\epsilon=0.005$}\n"," \\label{fig:pgd5e3_stereo}\n","\\end{figure*}\n"],["\\begin{figure*}[h]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/PGD2e3.pdf}\n"," \\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\epsilon=0.002$}\n"," \\label{fig:pgd2e3_stereo}\n","\\end{figure*}\n"],["\\begin{figure}[h]\n","\\setlength{\\tabcolsep}{2pt}\n"," \\centering\n"," \\begin{tabular}{ccccc}\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/00004.jpg} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/attacked_img4.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/noise4.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/attacked_img4.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/noise4.png} \\\\\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/00005.jpg} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/attacked_img5.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/noise5.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/attacked_img5.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/noise5.png} \\\\\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/00049.jpg} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/attacked_img49.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/noise49.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/attacked_img49.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/noise49.png} \\\\\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/00062.jpg} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/attacked_img62.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/noise62.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/attacked_img62.png} &\n"," \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/noise62.png} \\\\\n"," \\textbf{Image} & \\textbf{FGSM Attacked} & \\textbf{FGSM Noise} & \\textbf{PGD Attacked} & \\textbf{PGD Noise} \\\\\n"," \\end{tabular}\n"," \\caption{Original images and their corresponding attacked images and perturbations using FGSM and PGD methods on optical flow. The attacks mostly target the main object observed in the image.}\n"," \\label{Figure:attack}\n","\\end{figure}\n"]],"string":"[\n [\n \"\\\\begin{figure*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{Figures/diagram.pdf}\\n\",\n \" \\\\caption{\\\\sl\\\\small {\\\\bf Defense against adversarial attacks via stochastic resonance.} Neural networks are highly sensitive to small perturbations in the input space, which adversarial attacks exploit to manipulate network outputs. Conventional defense strategies primarily focus on filtering out unreliable features or denoising either the input or the features. Instead of removing noise, we propose a novel defense by introducing noise. Based on stochastic resonance, controlled transformations are introduced to the input. Features are then aggregated after inverting these transformations. The resulting method can be applied exclusively at inference time, requires no training, and is compatible with diverse network architectures. Notably, it not only improves robustness against adversarial attacks but also increases the difficulty of crafting successful adversarial examples, even when the attacker is fully aware of whether and how stochastic resonance is being used (i.e. adaptive attacks).\\n\",\n \"}\\n\",\n \" \\\\label{fig:schematic}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\\\hspace*{-4mm}\\n\",\n \"{\\\\scriptsize\\n\",\n \"\\\\begin{tabular}[0mm]{c@{\\\\hskip 0.01in}c@{\\\\hskip 0.01in}c@{\\\\hskip 0.01in}c@{\\\\hskip 0.01in}c}\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/2}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/3}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/4}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/5}\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{\\\\sl\\\\small {\\\\bf Results on CIFAR-10 under varying levels of stochastic resonance.} Increasing the stochastic resonance level consistently enhances robustness across all settings, yielding clear gains over the baseline method (FSR). Notably, our approach achieves superior performance even under adaptive adversarial attacks (Ours-WorstCase), despite the baseline being evaluated only in the non-adaptive case.}\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\label{fig:cifar}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\footnotesize\\n\",\n \"\\\\setlength{\\\\tabcolsep}{0.8pt} \\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{tabular}{l|l|>{\\\\centering}p{14mm}|>{\\\\centering}p{14mm}|>{\\\\centering}p{14mm}|>{\\\\centering}p{14mm}|>{\\\\centering}p{14mm}||c}\\n\",\n \"Method&Architecture& Natural & FGSM& PGD-20& PGD-100& C\\\\&W& Ensemble \\\\\\\\\\\\hline\\\\hline\\n\",\n \"AT&\\\\multirow{8}{*}{ResNet-18}&85.02 & 56.21 & 48.22 & 46.37 & 47.38 & 45.90 \\\\\\\\\\n\",\n \"+ FD&&85.14&56.81&48.54&46.70&47.72&45.82 \\\\\\\\\\n\",\n \"+ CAS&&\\\\textbf{85.78}&55.57&50.42&49.91&53.47&46.46 \\\\\\\\\\n\",\n \"+ CIFS&&79.87&56.53&49.80&48.17&49.89&47.26 \\\\\\\\\\n\",\n \"+ FSR&& 81.46 & 58.07 & 52.47 & 51.02 & 49.44 & 48.34 \\\\\\\\\\n\",\n \"+ TTE&& 85.25 & 59.20 & 53.00 &51.65 &52.45&50.60\\\\\\\\\\n\",\n \"\\\\rowcolor{gray!20}+ Ours&& 84.93&\\\\textbf{61.02}&\\\\textbf{56.08}&\\t\\\\textbf{55.17}&\\t\\\\textbf{55.53}&\\t\\\\textbf{53.68}\\\\\\\\\\n\",\n \"\\\\rowcolor{gray!20}+ Ours-WorstCase&&84.93& 58.81 & 53.58 & 52.39 & 52.73 & 50.95 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"TRADES&&84.92&60.87&56.13&55.16&54.02&53.38 \\\\\\\\\\n\",\n \"\\\\rowcolor{gray!20}+Ours &\\\\multirow{-2}{*}{WideResNet-34}& \\\\textbf{85.03}&\\\\textbf{62.43}&\\\\textbf{58.64}&\\\\textbf{57.87}&\\\\textbf{57.18}&\\\\textbf{56.28}\\\\\\\\\\\\hline\\n\",\n \"MART&& \\\\textbf{83.07}&60.21&54.14&52.90&49.62&48.95\\\\\\\\\\n\",\n \"\\\\rowcolor{gray!20}+ Ours &\\\\multirow{-2}{*}{ResNet-18}& 82.70&\\\\textbf{62.62}&\\\\textbf{59.03}&\\\\textbf{58.13}&\\\\textbf{55.51}&\\\\textbf{54.61}\\n\",\n \"\\\\end{tabular} %\\\\vspace{-1mm}\\n\",\n \" \\\\caption{\\\\sl\\\\small{\\\\bf Defense against adversarial attacks on classification task (CIFAR-10).} Compared to baselines that filter or manipulate features, ours does not modify network architecture or weights. Instead, ours performs an ensemble in the feature space. On CIFAR-10, ours achieves state-of-the-art robustness without requiring any additional training. Moreover, even in a worst-case adaptive adversary setting where the attacker is fully aware of the defense and how stochastic resonance is applied, the effectiveness of adversarial attacks is still notably reduced, while the computational cost for executing such attacks is significantly increased.}\\n\",\n \" \\\\label{tab:cifar10}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\scriptsize\\n\",\n \"\\\\parbox{.49\\\\linewidth}{\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{0.8pt} \\n\",\n \" \\\\begin{tabular}{l|c|c|c|c|c|c|c|c}\\n\",\n \"Att. Strength ($\\\\epsilon$)&\\\\multicolumn{2}{c|}{8/255}&\\\\multicolumn{2}{c|}{4/255}&\\\\multicolumn{2}{c|}{2/255}&\\\\multicolumn{2}{c}{1/255}\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"Metric&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5\\\\\\\\\\\\hline\\n\",\n \"No Defense&4.51&19.55&12.25&42.15&29.79&65.09&48.09&78.13\\\\\\\\\\n\",\n \"Ours ($d=1$)&11.66&46.27&27.85&65.80&45.94&77.63&57.48&83.43\\\\\\\\\\n\",\n \"Ours ($d=2$)&18.78&58.58&36.42&72.86&51.58&80.85&60.41&84.77\\\\\\\\\\n\",\n \"Ours ($d=3$)&\\\\textbf{25.77}&\\\\textbf{65.88}&\\\\textbf{42.52}&\\\\textbf{76.75}&\\\\textbf{54.94}&\\\\textbf{82.64}&\\\\textbf{62.08}&\\\\textbf{85.50}\\n\",\n \" \\\\end{tabular} %\\\\vspace{-1mm}\\n\",\n \" \\\\captionof{table}{\\\\small{\\\\bf ImageNet with ViT-Small.} Increasing the level of stochastic resonance consistently improves both Top-1 and Top-5 accuracy under adversarial attacks. Relative to the clean baseline (72.9 Top-1, 92.91 Top-5), our method recovers up to 55.8\\\\% of the Top-1 accuracy loss and 68.1\\\\% of the Top-5 accuracy loss.}\\n\",\n \" \\\\label{tab:ViT}\\n\",\n \"}\\n\",\n \"\\\\hfill\\n\",\n \"\\\\parbox{.49\\\\linewidth}{\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{0.8pt} \\n\",\n \" \\\\begin{tabular}{l|c|c|c|c|c|c|c|c}\\n\",\n \"Att. Strength ($\\\\epsilon$)&\\\\multicolumn{2}{c|}{8/255}&\\\\multicolumn{2}{c|}{4/255}&\\\\multicolumn{2}{c|}{2/255}&\\\\multicolumn{2}{c}{1/255}\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"Metric&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5\\\\\\\\\\\\hline\\n\",\n \"No Defense&8.51&26.19&9.45&27.92&11.10&30.63&15.21&36.76\\\\\\\\\\n\",\n \"Initial Conv.&16.91&34.66&17.36&35.28&18.12&36.30&19.59&38.25\\\\\\\\\\n\",\n \"Res. Block 1&22.44&44.95&23.39&46.03&24.84&47.64&27.57&50.80\\\\\\\\\\n\",\n \"Res. Block 2&\\\\textbf{24.88}&\\\\textbf{48.54}&\\\\textbf{25.90}&\\\\textbf{49.66}&\\\\textbf{27.23}&\\\\textbf{51.19}&\\\\textbf{30.11}&\\\\textbf{54.15}\\\\\\\\\\n\",\n \"Res. Block 3&21.76&44.28&22.73&45.47&24.14&47.14&27.18&50.20\\n\",\n \" \\\\end{tabular} %\\\\vspace{-1mm}\\n\",\n \" \\\\captionof{table}{\\\\small{\\\\bf Layer-wise ablation on ResNet-50.} Adversarial perturbations resemble high-frequency noise. Applying stochastic resonance through shallow layers is sufficient to defend against adversarial attacks, substantially reducing the overall computational cost.}\\n\",\n \" \\\\label{tab:layers}\\n\",\n \" } %\\\\vspace{-2mm}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\setlength{\\\\tabcolsep}{0.8pt} \\n\",\n \"\\\\footnotesize\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{tabular}{c|l|c|c|c|c|c|c|c|c|c|c|c|c}\\n\",\n \" &Attack Strength ($\\\\epsilon$)&\\\\multicolumn{3}{c|}{0.02}&\\\\multicolumn{3}{c|}{0.01}&\\\\multicolumn{3}{c|}{0.005}&\\\\multicolumn{3}{c}{0.002}\\\\\\\\\\\\cline{2-14}\\n\",\n \"&Metric&\\\\,MAE\\\\,&RMSE&D1-err&\\\\,MAE\\\\,&RMSE&D1-err&\\\\,MAE\\\\,&RMSE&D1-err&\\\\,MAE\\\\,&RMSE&D1-err\\\\\\\\\\\\hline\\n\",\n \"{\\\\multirow{5}{*}{\\\\rotatebox[origin=c]{90}{FGSM}}} &No Defense&14.83&24.10&97.33&8.49&14.53&90.49&5.05&7.70&74.71&3.01&3.49&38.12 \\\\\\\\\\n\",\n \"&Latent Smoothing&13.42&22.09&96.61&8.12&13.69&89.25&4.89&7.05&73.01&2.89&3.32&36.25\\n\",\n \"\\\\\\\\\\n\",\n \"&Ours ($d=1$)&10.12&15.81&95.80&6.46&9.92&86.30&4.39&5.93&68.55&2.78&3.18&31.99 \\\\\\\\\\n\",\n \"&\\\\cellcolor{gray!20}Error Reduced (\\\\%)& \\\\cellcolor{gray!20}31.76&\\\\cellcolor{gray!20}34.40&\\\\cellcolor{gray!20}1.57&\\\\cellcolor{gray!20}23.91&\\\\cellcolor{gray!20}31.73&\\\\cellcolor{gray!20}4.63&\\\\cellcolor{gray!20}13.07&\\\\cellcolor{gray!20}22.99&\\\\cellcolor{gray!20}7.58&\\\\cellcolor{gray!20}7.64&\\\\cellcolor{gray!20}8.88&\\\\cellcolor{gray!20}16.08\\\\\\\\\\n\",\n \"&Ours ($d=2$)&\\\\textbf{9.22}&\\\\textbf{13.88}&\\\\textbf{94.61}&\\\\textbf{6.13}&\\\\textbf{8.87}&\\\\textbf{84.49}&\\\\textbf{4.19}&\\\\textbf{5.43}&\\\\textbf{66.74}&\\\\textbf{2.73}&\\\\textbf{3.12}&\\\\textbf{31.18}\\\\\\\\\\n\",\n \"&\\\\cellcolor{gray!20}Error Reduced (\\\\%)&\\\\cellcolor{gray!20} 37.82&\\\\cellcolor{gray!20}42.40&\\\\cellcolor{gray!20}2.79&\\\\cellcolor{gray!20}27.78&\\\\cellcolor{gray!20}38.95&\\\\cellcolor{gray!20}6.63&\\\\cellcolor{gray!20}16.92&\\\\cellcolor{gray!20}29.41&\\\\cellcolor{gray!20}10.66&\\\\cellcolor{gray!20}9.21&\\\\cellcolor{gray!20}10.65&\\\\cellcolor{gray!20}18.21 \\\\\\\\\\\\hline\\n\",\n \"{\\\\multirow{5}{*}{\\\\rotatebox[origin=c]{90}{PGD}}} &No Defense&161.70&162.61&99.99&131.66&140.55&98.64&63.97&88.55&85.31&6.83&17.03&39.24 \\\\\\\\\\n\",\n \"&Latent Smoothing&161.79&162.69&99.99&131.46&140.41&98.57&63.86&88.21&85.39&7.28&17.44&39.81\\\\\\\\\\n\",\n \"&Ours ($d=1$)&107.86&125.14&98.29&69.97&84.72&91.79&20.66&42.29&73.21&4.17&8.32&29.09\\\\\\\\\\n\",\n \"&\\\\cellcolor{gray!20}Error Reduced (\\\\%)&\\\\cellcolor{gray!20}33.30 &\\\\cellcolor{gray!20} 23.04 &\\\\cellcolor{gray!20} 1.70 &\\\\cellcolor{gray!20} 46.86 &\\\\cellcolor{gray!20} 39.72 &\\\\cellcolor{gray!20} 6.94 &\\\\cellcolor{gray!20} 67.70 &\\\\cellcolor{gray!20} 52.24 &\\\\cellcolor{gray!20} 14.18 &\\\\cellcolor{gray!20} 38.95 &\\\\cellcolor{gray!20} 51.15 &\\\\cellcolor{gray!20} 25.87\\\\\\\\\\n\",\n \"&Ours ($d=2$)&\\\\textbf{77.59}&\\\\textbf{100.14}&\\\\textbf{96.14}&\\\\textbf{44.77}&\\\\textbf{66.23}&\\\\textbf{89.24}&\\\\textbf{17.98}&\\\\textbf{32.80}&\\\\textbf{71.09}&\\\\textbf{3.76}&\\\\textbf{6.73}&\\\\textbf{28.44}\\\\\\\\\\n\",\n \"&\\\\cellcolor{gray!20}Error Reduced (\\\\%)&\\\\cellcolor{gray!20} 52.01 &\\\\cellcolor{gray!20} 38.41 &\\\\cellcolor{gray!20} 3.85 &\\\\cellcolor{gray!20} 66.02 &\\\\cellcolor{gray!20} 52.87 &\\\\cellcolor{gray!20} 9.53 &\\\\cellcolor{gray!20} 71.89 &\\\\cellcolor{gray!20} 62.94 &\\\\cellcolor{gray!20} 16.66 &\\\\cellcolor{gray!20} 44.99 &\\\\cellcolor{gray!20} 60.52 &\\\\cellcolor{gray!20} 27.53\\n\",\n \"\\\\end{tabular}\\n\",\n \" \\\\caption{\\\\sl\\\\small{\\\\bf Stochastic Resonance Enhances Stereo Matching Robustness.} Incorporating stochastic resonance significantly reduces prediction errors induced by adversarial attacks across all evaluation metrics, reducing error by up to 71.89\\\\% (MAE, when attacked by PGD with $\\\\epsilon=0.005$). Notably, this defense mechanism operates entirely at test time without requiring any model re-training, which sets it apart from existing methods.}\\n\",\n \" \\\\label{tab:stereo}%\\\\vspace{-2mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{Figures/Stereo.pdf}%\\\\vspace{-2mm}\\n\",\n \" \\\\caption{\\\\sl\\\\small {\\\\bf Stereo matching robustness via stochastic resonance.} We present visual results on stereo matching under various adversarial attack scenarios, including PGD and FGSM at different perturbation levels. These attacks significantly degrade the network's predictions, leading to substantial errors. By incorporating stochastic resonance, we demonstrate a significant reduction in prediction errors. This technique holds significant potential for improving robustness in safety-critical real-world applications, such as autonomous driving, where stereo vision must remain reliable under diverse environmental conditions and adversarial threats.\\n\",\n \"}\\n\",\n \" \\\\label{fig:stereo}%\\\\vspace{-2mm}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{0.2} % Default value: 1\\n\",\n \"\\\\centering\\n\",\n \"\\\\hspace*{-4mm}\\n\",\n \"{\\\\scriptsize\\n\",\n \"\\\\begin{tabular}[0mm]{c@{\\\\hskip 0.01in}c@{\\\\hskip 0.01in}c@{\\\\hskip 0.01in}c|c@{\\\\hskip 0.01in}c@{\\\\hskip 0.01in}c}\\n\",\n \"& \\\\multicolumn{3}{c}{\\\\normalsize PGD}& \\\\multicolumn{3}{c}{\\\\normalsize FGSM}\\\\\\\\\\\\\\\\\\n\",\n \"\\\\smash{\\\\rotatebox{90}{\\\\quad Image}}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd2}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd3}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm4}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm3}\\\\\\\\\\n\",\n \"\\\\smash{\\\\rotatebox{90}{Original}}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_org1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_org2}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_org3}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_org1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_org4}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_org3}\\\\\\\\\\n\",\n \"\\\\smash{\\\\rotatebox{90}{Attacked}}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_attacked1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_attacked2}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_attacked3}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_attacked1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_attacked4}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_attacked3}\\\\\\\\\\n\",\n \"\\\\smash{\\\\rotatebox{90}{\\\\quad Ours}}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_ours1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_ours2}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/pgd_ours3}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_ours1}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_ours4}&\\n\",\n \"\\\\includegraphics[width=\\\\fWidD]{\\\\figd/fgsm_ours3}\\\\\\\\\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{\\\\sl\\\\small{\\\\bf Optical flow robustness via stochastic resonance.} \\n\",\n \"Qualitative results (visualized with a color wheel) show that our method substantially mitigates the degradation caused by both PGD and FGSM attacks. This robustness is particularly relevant for visual perception systems that rely on accurate motion estimation.}\\n\",\n \"\\\\label{fig:flow-quality}%\\\\vspace{-2mm}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/fgsm2e2.pdf}\\n\",\n \" \\\\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\\\epsilon=0.02$}\\n\",\n \" \\\\label{fig:fgsm2e2_stereo}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/fgsm1e2.pdf}\\n\",\n \" \\\\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\\\epsilon=0.01$}\\n\",\n \" \\\\label{fig:fgsm1e2_stereo}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/fgsm5e3.pdf}\\n\",\n \" \\\\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\\\epsilon=0.005$}\\n\",\n \" \\\\label{fig:fgsm5e3_stereo}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/PGD1e2.pdf}\\n\",\n \" \\\\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\\\epsilon=0.01$}\\n\",\n \" \\\\label{fig:pgd1e2_stereo}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/PGD5e3.pdf}\\n\",\n \" \\\\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\\\epsilon=0.005$}\\n\",\n \" \\\\label{fig:pgd5e3_stereo}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/PGD2e3.pdf}\\n\",\n \" \\\\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\\\epsilon=0.002$}\\n\",\n \" \\\\label{fig:pgd2e3_stereo}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure}[h]\\n\",\n \"\\\\setlength{\\\\tabcolsep}{2pt}\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{tabular}{ccccc}\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/00004.jpg} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/FGSM/attacked_img4.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/FGSM/noise4.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/PGD/attacked_img4.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/PGD/noise4.png} \\\\\\\\\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/00005.jpg} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/FGSM/attacked_img5.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/FGSM/noise5.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/PGD/attacked_img5.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/PGD/noise5.png} \\\\\\\\\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/00049.jpg} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/FGSM/attacked_img49.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/FGSM/noise49.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/PGD/attacked_img49.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/PGD/noise49.png} \\\\\\\\\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/00062.jpg} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/FGSM/attacked_img62.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/FGSM/noise62.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/PGD/attacked_img62.png} &\\n\",\n \" \\\\includegraphics[width=0.18\\\\textwidth]{Figures/perturbations/PGD/noise62.png} \\\\\\\\\\n\",\n \" \\\\textbf{Image} & \\\\textbf{FGSM Attacked} & \\\\textbf{FGSM Noise} & \\\\textbf{PGD Attacked} & \\\\textbf{PGD Noise} \\\\\\\\\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{Original images and their corresponding attacked images and perturbations using FGSM and PGD methods on optical flow. The attacks mostly target the main object observed in the image.}\\n\",\n \" \\\\label{Figure:attack}\\n\",\n \"\\\\end{figure}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n\\documentclass{article} % For LaTeX2e\n\\usepackage{iclr2026_conference,times}\n\n% Optional math commands from https://github.com/goodfeli/dlbook_notation.\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n% Figure reference, capital. For start of sentence\n\\def\\Figref#1{Figure~\\ref{#1}}\n\\def\\twofigref#1#2{figures \\ref{#1} and \\ref{#2}}\n\\def\\quadfigref#1#2#3#4{figures \\ref{#1}, \\ref{#2}, \\ref{#3} and \\ref{#4}}\n% Section reference, lower-case.\n\\def\\secref#1{section~\\ref{#1}}\n% Section reference, capital.\n\\def\\Secref#1{Section~\\ref{#1}}\n% Reference to two sections.\n\\def\\twosecrefs#1#2{sections \\ref{#1} and \\ref{#2}}\n% Reference to three sections.\n\\def\\secrefs#1#2#3{sections \\ref{#1}, \\ref{#2} and \\ref{#3}}\n% Reference to an equation, lower-case.\n\\def\\eqref#1{equation~\\ref{#1}}\n% Reference to an equation, upper case\n\\def\\Eqref#1{Equation~\\ref{#1}}\n% A raw reference to an equation---avoid using if possible\n\\def\\plaineqref#1{\\ref{#1}}\n% Reference to a chapter, lower-case.\n\\def\\chapref#1{chapter~\\ref{#1}}\n% Reference to an equation, upper case.\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n% Reference to a range of chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\usepackage{hyperref}\n\\usepackage{url}\n\\usepackage{graphicx}\n\\usepackage[table]{xcolor}\n\\usepackage{multirow}\n\\usepackage{subcaption}\n\\usepackage{caption} % for \\captionof\n\\usepackage{comment} \n\\usepackage{wrapfig}\n\n\\title{Test-Time Defense Against Adversarial Attacks via Stochastic Resonance of Latent Ensembles}\n\n% Authors must not appear in the submitted version. They should be hidden\n% as long as the \\iclrfinalcopy macro remains commented out below.\n% Non-anonymous submissions will be rejected without review.\n\n\\author{Dong Lao\\textsuperscript{1,2} \\quad Yuxiang Zhang\\textsuperscript{2} \\quad Haniyeh Ehsani Oskouie\\textsuperscript{2} \\quad Yangchao Wu\\textsuperscript{2} \\\\ \\textbf{Alex Wong\\textsuperscript{3} \\quad Stefano Soatto\\textsuperscript{2}} \\\\ \n\\textsuperscript{1}LSU Vision Lab \\quad\\quad \\textsuperscript{2}UCLA Vision Lab \\quad\\quad \\textsuperscript{3}Yale Vision Lab \\\\\n\\textsuperscript{1}\\texttt{dong.lao@lsu.edu} \\\\ \\textsuperscript{2}\\texttt{\\{zhangbrandon102,haniyehehsani,wuyangchao1997,soatto\\}@ucla.edu} \\\\ \\textsuperscript{3}\\texttt{alex.wong@yale.edu}\n}\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to \\LaTeX{} to determine where to break\n% the lines. Using \\AND forces a linebreak at that point. So, if \\LaTeX{}\n% puts 3 of 4 authors names on the first line, and the last on the second\n% line, try using \\AND instead of \\And before the third author name.\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\n\\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission.\n\\begin{document}\n\n\n\\maketitle\n\n\\begin{abstract}\nWe propose a test-time defense mechanism against adversarial attacks: imperceptible image perturbations that significantly alter the predictions of a model. Unlike existing methods that rely on feature filtering or smoothing, which can lead to information loss, we propose to ``combat noise with noise'' by leveraging stochastic resonance to enhance robustness while minimizing information loss. Our approach introduces small translational perturbations to the input image, aligns the transformed feature embeddings, and aggregates them before mapping back to the original reference image. This can be expressed in a closed-form formula, which can be deployed on diverse existing network architectures without introducing additional network modules or fine-tuning for specific attack types. The resulting method is entirely training-free, architecture-agnostic, and attack-agnostic. Empirical results show state-of-the-art robustness on image classification and, for the first time, establish a generic test-time defense for dense prediction tasks, including stereo matching and optical flow, highlighting the method’s versatility and practicality. Specifically, relative to clean (unperturbed) performance, our method recovers up to 68.1\\% of the accuracy loss on image classification, 71.9\\% on stereo matching, and 29.2\\% on optical flow under various types of adversarial attacks.\n\\end{abstract}\n\n\\section{Introduction}\n\\label{sec:introduction}\n\nMost deep neural networks in use today are deterministic maps from a fixed-size input to a fixed-size feature vector. In auto-regressive Transformer models, that vector encodes the next element (token) in the input sequence. Similarly, in convolutional architectures, that vector may encode the input data. In either case, the output vector is often highly sensitive to perturbations of the input, and one can intentionally choose these imperceptible perturbations {\\em adversarially} so as to maximize the change in the output \\cite{goodfellow2014explaining}. In some cases, the same perturbation can even be disruptive for a large number of possible inputs \\cite{moosavi2017universal}, exploiting the convoluted geometry of the decision boundary imposed by such trained models \\cite{tramer2017space}. This spurious sensitivity could be exploited adversarially to disrupt the operation of a model. \n\nFrom a classical perspective of signal processing, adversarial perturbations of images appear as small high-frequency ``noise'' resembling {\\em aliasing} artifacts. These are imperceptible since the human visual system easily discounts them on account of their poor fit to the `ecological statistics' of natural images \\cite{gibson2014ecological}.\nClassical sampling theory prescribes anti-aliasing by low-pass filtering the data, removing information along with the artifacts. Low-pass filtering consists of spatial averaging of the perturbed data with respect to a chosen kernel, typically a Gaussian or a constant (``pillbox''). Alternatively, one could ``denoise'' the embeddings by averaging output vectors, also a lossy operation. The choice of the kernel should match the statistics of the perturbations, which sets up a cat-and-mouse game where the adversary can easily modify the perturbations to bypass the anti-aliasing filter, namely {\\em adaptive} attacks \\cite{tramer2020adaptive}, and the model needs to constantly be fine-tuned to ``anti-alias'' new forms of adversarial perturbations. In the context of deep neural networks, existing defense methods that manipulate feature representations \\cite{xie2019feature,bai2021improving,yan2021cifs,kim2023feature} fundamentally adhere to this paradigm in principle. Despite substantial engineering efforts, these methods remain inherently vulnerable to adaptive attacks because they rely on pre-defined filtering strategies that are fixed at inference time.\n\n\\textbf{Desiderata:} \nTo break this cycle, we advocate a method to mitigate the effect of adversarial perturbation that (i) operates at test time, without the need to update the model weights, and (ii) does not entail information loss associated with direct or indirect spatial filtering. In addition, it would be ideal if this method could (iii) be applied to existing network architectures without modifications, and (iv) be agnostic to the specific type of adversarial perturbation. \n\n\n\\textbf{Stochastic resonance} is a technique that resolves a quantized signal below the quantization level, by quantizing and ensembling perturbed versions of the signal \\cite{benzi1981mechanism}. It has been used extensively in cochlear implants, where power constraints limit the resolution of the digital circuitry \\cite{stocks2002application}. It has also been used to `super-resolve' Vision Transformer embeddings, where entire patches are encoded into a vector, which is computed at a coarsely subsampled grid \\cite{lao2024sub}. In this paper, instead, we use Stochastic Resonance for the opposite purpose, {\\em not} to super-resolve the quantized signal, but to perform latent ensembling to remove the effects of adversarial perturbations in the embedding.\n\n%\\textbf{Key idea:} \n\nRather than averaging the data, or averaging their embedding as in classical denoising, {\\em we average transformed embeddings} in latent space. This averaging is performed over small transformations sampled at random or deterministically from the group of planar translations, by computing the encoding of the transformed image, and then mapping the encoding back through the push-forward of the inverse transformation. This process can be expressed as a single formula in \\eqref{eq:SR}. Since the embedding is typically computed on a coarse grid, but the transformations are sampled on the native lattice of the image, the resulting embedding is free of spatial averaging artifacts. As with other uses of Stochastic Resonance, the effect is seemingly paradoxical as {\\em we combat noise with noise}: We apply purposeful perturbations to eliminate the effect of adversarial perturbations. \n\n\n%\\textbf{Interpretation.} \nOur method can be thought of as marginalizing the translation group in latent space with respect to a chosen prior, which is the only design choice in our method. We choose the simplest, which is the constant prior. The purposeful perturbations alter the spatial sampling, and the implicit ensembling in latent space averages out the effect of sampling artifacts, thwarting the effect of adversarial perturbations. It is as if we were given multiple images with different `noise', except that the noise in question is not the adversarial perturbation, but the splinters of adversarial perturbations obtained by different spatially quantized versions of the perturbed image, due to the translational perturbations, which are then averaged out by the latent ensembling.\n\n\\textbf{Outcomes:} Our method fulfills the desiderata (i)-(iv) laid out earlier: (i) It does not require training or fine-tuning; (ii) it minimizes information loss by latent ensembling of perturbed embeddings; (iii) it can be applied to different network architectures and tasks, \\emph{including} networks already equipped with different defense techniques like adversarial training, and (iv) is agnostic to the specific perturbation. To measure the effectiveness of our method in mitigating the effects of adversarial perturbations, we test it on three vastly different tasks, including image classification, and two other dense prediction tasks: stereo matching and optical flow. \n% compare it with other methods on [DESCRIBE DATASAETS AND BENCHMARKS]\nwhere we are the first to show a significant and consistent improvement in robustness to various adversarial attacks. \n\n\n%\\noindent\\textbf{End-to-end (worst-case) adversary:} \nOne could argue that there is still a cat-and-mouse game in our setting, if the adversary knows our technique and tailors the adversarial perturbations to bypass it. To assess this risk, we conduct ``worst-case'' adaptive tests to measure the performance of our method under adaptive attacks when the attacker knows the exact defense strategy, thus the adversarial perturbation is designed to maximally disrupt the result end-to-end, {\\em including} our stochastic resonance. Our results show that the method is resistant to breaking even when the adversary optimizes adaptively through it end-to-end.\n\n\\begin{figure*}[t]\n\\centering\n\\includegraphics[width=\\textwidth]{Figures/diagram.pdf}\n \\caption{\\sl\\small {\\bf Defense against adversarial attacks via stochastic resonance.} Neural networks are highly sensitive to small perturbations in the input space, which adversarial attacks exploit to manipulate network outputs. Conventional defense strategies primarily focus on filtering out unreliable features or denoising either the input or the features. Instead of removing noise, we propose a novel defense by introducing noise. Based on stochastic resonance, controlled transformations are introduced to the input. Features are then aggregated after inverting these transformations. The resulting method can be applied exclusively at inference time, requires no training, and is compatible with diverse network architectures. Notably, it not only improves robustness against adversarial attacks but also increases the difficulty of crafting successful adversarial examples, even when the attacker is fully aware of whether and how stochastic resonance is being used (i.e. adaptive attacks).\n}\n \\label{fig:schematic}\n %\\vspace{-2mm}\n\\end{figure*}\n\n\\section{Related Work}\n\\label{sec:related}\n\nThe literature on adversarial attack and defense is extensive. We highlight some of the advances. \n\n\\noindent\\textbf{Adversarial Training as Defense.}\nAdversarial training increases the robustness of the model by training it with adversarially augmented images. The popular attack methods used are Fast Gradient Sign Method (FGSM) \\cite{goodfellow2014explaining}, and Projected Gradient Descent (PGD) \\cite{madry2017towards}. \nALP \\cite{kannan2018adversarial} Minimizes the difference between the logits of pairs of clean and adversarially augmented images. TRADES \\cite{zhang2019theoretically} decomposes prediction error for adversarial examples into natural error and boundary error to improve adversarial robustness at the cost of accuracy. MART \\cite{wang2019improving} improves adversarial robustness by considering misclassified natural examples during training. Subsequent work \\cite{cai2018curriculum, zhang2020attacks, wang2022self, jin2022enhancing, ghiasvand2024robust} improves adversarial robustness with curriculum learning \\cite{bengio2009curriculum}, model ensembling, second order statistics, and gradient tracking. \n% {\\color{blue}Adversarial training on feature space}\nOn the other hand, some methods learn robust feature representation through a modified architecture or feature manipulation. \\cite{galloway2019batch, benz2021batch, wang2022removing} investigate the effect of batch normalization on adversarial robustness. \\cite{dhillon2018stochastic, madaan2020adversarial} prunes certain activations in the network that are susceptible to adversarial attacks.\n\\cite{xiao2019enhancing} keep k-features with the largest magnitude and deactivate everything else.\n\\cite{zoran2020towards} uses an attention mask to highlight robust regions on the feature.\nFeature Denoising (FD) \\cite{xie2019feature} uses classical denoising techniques to deactivate abnormal activations.\n\\cite{bai2021improving, yan2021cifs} proposed Channel Activation Suppression (CAS) and Channel-wise Importance-based Feature Selection (CIFS) to deactivate feature channels that are vulnerable to attacks. \n\\cite{kim2023feature} improves the robustness with Feature Separation and Recalibration (FSR).\nOur method also operates in feature space, but purely during test time. While we choose some of these works as baselines, our method works in conjunction with any aforementioned methods.\n\n% WE ARE NOT AGAINST THEM, SR CAN BE COMBINED WITH ANY OF THEM]\n\n\\noindent\\textbf{Adversarial Purification as Defense}\nAnother line of work focuses on purifying or augmenting the images before they are used as input. \\cite{tang2024robust, yeh2024test, tsai2023test} train an FGSM robust classifier, a diffusion model, or a mask auto-encoder, respectively, to purify adversarial examples.\n\\cite{wang2021fighting} optimizes both the model and the input to minimize the entropy of model predictions to adapt to changing attacks. \n\\cite{cohen2024simple} trains a random forest predictor to ensemble outputs from test-time augmented images.\nThese works involve training a new model or updating the original model, while our method is purely test-time and does not require any training. \n\\cite{perez2021enhancing} ensembles model output from different augmentations, which is a special case of our method, as the ensemble is performed solely on the output, while we can ensemble at any layer, which both saves computational cost and achieves higher performance\n\n%, and empirical results demonstrate advantage over output ensemble.\n\nNotably, we recognize that above methods focus solely on classification as a task for adversarial attacks. Through extensive experiments, we demonstrate that our method can not only perform well on classification, but also on dense prediction tasks like optical flow, and stereo matching.\n\n\n\\noindent\\textbf{Stochastic Resonance (SR)} was proposed by \\cite{benzi1981mechanism} and first applied in climate dynamics \\citep{benzi1982stochastic} and later in signal processing \\citep{wellens2003stochastic, kosko2001robust, chen2007theory} and acoustics \\citep{shu2016application, wang2014adaptive}. Recently, Stochastic Resonance Transformer (SRT) \\cite{lao2024sub} uses SR to ``super-resolve'' Vision Transformer (ViT) embeddings. In this work, we instead use SR to mitigate adversarial perturbations. Since SR has been developed specifically to address {\\em quantization artifacts}, it has never before been used to mitigate classes of perturbations beyond aliasing. Our novel use of the technique leverages the fact that group transformations and spatial quantization preserve the statistics of natural images, which are heavy-tailed, but do not preserve the statistics of adversarial perturbations.\n\n\\section{Method}\n\\label{sec:method}\n\n\\noindent\\textbf{Notation.}\nA digital image $x \\in [0, \\ L-1]^{W\\times H}$ can be described as a map from a discrete planar lattice $\\Lambda \\subset {\\mathbb R}^2$ with $H$ rows and $W$ columns to $L$ discrete levels, $x:\\Lambda \\rightarrow [0, \\ L-1]$; a `feature' or `embedding' of an image $x$ is the output of an encoder $\\phi$ that maps it to a vector space with $K$ channels, typically through a parametric trained model:\n\\[\\phi: x \\mapsto \\phi(x) \\in {\\mathbb R}^K.\\]\nWe represent a group transformation of the image through an operator $g: {\\mathbb R}^2 \\rightarrow {\\mathbb R}^2$, which can be restricted to the lattice $\\Lambda$ through padding, sampling and quantization at the expense of invertibility: \n\\[\ng: x \\mapsto g (x) \\in \\Lambda \\subset {\\mathbb R}^2.\n\\]\nFor example, a translation by an integer pixel can be represented by an upper diagonal matrix $G$, $g(x) = Gx$ with ones above the diagonal. The group $g$ operating on $x$ induces an operation on $\\phi$ via\n\\[\ng_* \\phi(x) \\doteq \\phi(g(x)).\n\\]\nWe call the composition of $\\phi$ and $g$ the encoding of the transformed image \n\\[\n\\psi(x) \\doteq \\phi(g(x)) = \\phi\\circ g(x).\n\\]\nThe main object of interest in our method is:\n\\[\ng_*^{-1} \\psi(x) = g_*^{-1} \\circ \\phi \\circ g (x).\n\\]\nThis is obtained, reading right-to-left, by first transforming the image, then passing it through an encoder, and then transforming back the feature map through the push-forward action $g^{-1}_*$.\n\n\\noindent\\textbf{Perturbations.}\nWe consider two types of perturbations, extraneous and purposeful. The extraneous one could be an additive perturbation to an image, $\\tilde x = x + n$, designed to maximally change the value of the embedding (adversarial perturbation) $\\phi(\\tilde x)$:\n\\[\n\\tilde x = x + n(x) \\quad | \\quad n(x) = \\arg\\max d(\\phi(x), \\phi(\\tilde x)), \\ |n|< \\epsilon\n\\]\nfor some small $\\epsilon$ designed so the perturbation is, ideally, imperceptible by humans. %For digital images, these perturbations turn out to resemble high-frequency aliasing easily discounted as artifacts by the human visual system on account of their poor fit with the statistics of natural images. \n\nThe purposeful perturbations are small group actions $g_i, \\ i = 1, \\dots, N$, which could be sampled deterministically or at random according to some chosen distribution $g_i \\sim P_g$, either way yielding a set $\n\\{g_1(x), \\dots, g_N(x)\\}$. \nOur goal is to use these purposeful perturbations to combat the effects of extraneous adversarial perturbations.\n\n\\noindent\\textbf{Averaging, smoothing, and stochastic resonance.}\nThe resemblance between adversarial perturbations and aliasing artifacts has motivated the use of anti-aliasing, or smoothing, techniques to mitigate them. These consist of {\\em spatial averaging} of the data prior to computing the map $\\phi$. If we call $B^\\sigma_{ij}$ a neighborhood of size $\\sigma>0$ around $(i,j)\\in \\Lambda$, \n\\[\nB^\\sigma_{ij} = \\{(i', j') \\in \\Lambda \\ | \\ d((i,j),(i',j')) \\le \\sigma\\} \n\\]\nthen the simplest form of smoothing is simply averaging in a neighborhood, \n\\[\n\\bar x_{i,j} = \\frac{1}{\\sigma^2} \\sum_{(i',j') \\in B^\\sigma_{i,j}}x_{i'j'}\n\\]\nwhich we write in terms of translations $g(x_{i,j}) = x_{i+u, j+v}$ within the same neighborhood $B^\\sigma$,\n\\[\n\\bar x = \\frac{1}{N} \\sum_{i=1}^N g_i(x).\n\\]\nOne can then obtain an encoding by %embedding the smoothed image, $\\phi(\\bar x)$, or \nsmoothing the embedding\n\\[\n\\bar \\phi(x) = \\frac{1}{N}\\sum_{i = 1}^N \\phi(g_i(x)).\n\\]\nThis can be interpreted as marginalizing the translation group with a prior $P_g$ when computing $\\phi$. Notice that the average can be computed on a coarser lattice $\\tilde \\Lambda$, but its value still depends on data in the finer grid $\\Lambda$. \nClassical Sampling Theory teaches that smoothing mitigates the effect of high-frequency aliasing $n$ at the cost of information loss on $x$.\n\nStochastic resonance also marginalizes the translation group, but by {\\em averaging transformed data in latent space:}\n\\begin{equation}\n\\hat \\phi(x) = \\frac{1}{N} \\sum_{i=1}^N {g_i}_*^{-1}\\circ \\phi \\circ g_i(x).\n\\label{eq:SR}\n\\end{equation}\nMore general groups, and more general averaging kernels, can be considered although we find that the simplest case described here already suffices. \n\nStochastic resonance is {\\em not} smoothing, as it averages transformed versions of the image without blurring it, thanks to the inverse push-forward. It is also {\\em not} super-resolution, where fine-granularity details are hallucinated based on side information or priors, although it does allow resolving features computed on a coarse grid $\\tilde \\Lambda$ within a finer grid $\\Lambda$. Stochastic resonance uses the averaging of perturbations in latent space to ensemble populations of embeddings, rather than averaging or interpolation of the same embedding. \n\n\\noindent\\textbf{Purposeful Perturbation.} The only design choice in the method is the set of purposeful perturbations. While that can be optimized for performance, we optimize for simplicity, restricting our attention to translation by integer pixels. \nWe know that, for adversarial perturbations, $d(\\phi(\\tilde x), \\phi(x))$ is large, where $d(\\cdot)$ defines the distance between features. Ideally, for stochastic resonance, we want $d(\\hat \\phi(\\tilde x), \\hat \\phi(x)) = 0$ %. That is easy to achieve with a constant function. We also want\nwhile keeping $\\hat \\phi$ as information-preserving as possible. \nThe theory of Stochastic Resonance shows that, if we sub-sample a signal from its native granularity $\\Lambda$ to a coarser grid $\\tilde \\Lambda \\subset \\Lambda$, and choose the purposeful perturbations to act on the finer grid $\\Lambda$, under certain conditions one can recover the original signal at the finer granularity \\cite{benzi1981mechanism}. \nIn this paper, we focus on testing whether $\\hat \\phi$ is insensitive to adversarial perturbations. We do so empirically in Sect. \\ref{sec:experiments}.\n\n\\def\\figd{Figures/Cifar}\n\\def\\fWidD{0.2\\textwidth}\n\\begin{figure*}[t]\n\n\\centering\n\\hspace*{-4mm}\n{\\scriptsize\n\\begin{tabular}[0mm]{c@{\\hskip 0.01in}c@{\\hskip 0.01in}c@{\\hskip 0.01in}c@{\\hskip 0.01in}c}\n\\includegraphics[width=\\fWidD]{\\figd/1}&\n\\includegraphics[width=\\fWidD]{\\figd/2}&\n\\includegraphics[width=\\fWidD]{\\figd/3}&\n\\includegraphics[width=\\fWidD]{\\figd/4}&\n\\includegraphics[width=\\fWidD]{\\figd/5}\n\\end{tabular}\n}\n\\caption{\\sl\\small {\\bf Results on CIFAR-10 under varying levels of stochastic resonance.} Increasing the stochastic resonance level consistently enhances robustness across all settings, yielding clear gains over the baseline method (FSR). Notably, our approach achieves superior performance even under adaptive adversarial attacks (Ours-WorstCase), despite the baseline being evaluated only in the non-adaptive case.}\n\n%Although higher levels of stochastic resonance demand greater computational resources, this overhead can be alleviated through parallelization. This tunable parameter thus enables a controlled trade-off between enhanced robustness and computational burden, all achieved without additional training.\n\n\\label{fig:cifar}\n\\end{figure*}\n\n\n\n\n\n\n\\section{Experiments}\n\\label{sec:experiments}\nWhile $g$ can be sampled from any invertible group transformation (e.g., rotation, scaling), we implement stochastic resonance using integer-pixel translations, denoted as $\\{g_i\\}=\\{(x, y) | x \\in [-d_x, d_x], j \\in [-d_y, d_y]\\}$, following the approach in SRT \\cite{lao2024sub}, which avoids interpolation artifacts. While the networks' inherent sensitivity to pixel-level shifts is typically regarded as detrimental due to the ``flickering problem'' \\cite{azulay2019deep, sundaramoorthi2019translation}, our approach, on the contrary, leverages it to defend against adversarial perturbations.\n% as an advantage in enhancing feature robustness.\nGiven these perturbations $\\{g_i\\}$, ensembling can be performed at any chosen layer of the network. Features are aggregated as described in Eq. \\ref{eq:SR} and then passed to downstream network components. \n\nWe first validate this approach on image classification (Sect.~\\ref{sec:classification}) following standard benchmarks, and also provide ablation studies on levels/layers of latent ensemble and rotation as augmentation. Subsequently, we defend against adversarial attacks on dense prediction tasks, including stereo matching (Sec.~\\ref{sec:stereo}) and optical flow (Sec.~\\ref{sec:flow}). This is achieved given that our method is agnostic to attack mechanisms, network pre-training, and largely independent of architecture, requiring only latent ensembling, resulting in a purely test-time, training-free approach with no auxiliary modules.\n\n\n\n\\subsection{Image Classification}\n\\label{sec:classification}\n\n\n\\begin{table*}[t]\n\\footnotesize\n\\setlength{\\tabcolsep}{0.8pt} \n \\centering\n \\begin{tabular}{l|l|>{\\centering}p{14mm}|>{\\centering}p{14mm}|>{\\centering}p{14mm}|>{\\centering}p{14mm}|>{\\centering}p{14mm}||c}\nMethod&Architecture& Natural & FGSM& PGD-20& PGD-100& C\\&W& Ensemble \\\\\\hline\\hline\nAT&\\multirow{8}{*}{ResNet-18}&85.02 & 56.21 & 48.22 & 46.37 & 47.38 & 45.90 \\\\\n+ FD&&85.14&56.81&48.54&46.70&47.72&45.82 \\\\\n+ CAS&&\\textbf{85.78}&55.57&50.42&49.91&53.47&46.46 \\\\\n+ CIFS&&79.87&56.53&49.80&48.17&49.89&47.26 \\\\\n+ FSR&& 81.46 & 58.07 & 52.47 & 51.02 & 49.44 & 48.34 \\\\\n+ TTE&& 85.25 & 59.20 & 53.00 &51.65 &52.45&50.60\\\\\n\\rowcolor{gray!20}+ Ours&& 84.93&\\textbf{61.02}&\\textbf{56.08}&\t\\textbf{55.17}&\t\\textbf{55.53}&\t\\textbf{53.68}\\\\\n\\rowcolor{gray!20}+ Ours-WorstCase&&84.93& 58.81 & 53.58 & 52.39 & 52.73 & 50.95 \\\\\n%+ SR-Out&&84.99&60.92&\\textbf{56.27}&&52.71&51.19\\\\\n%+ SR-Out-WorstCase&&84.99&57.59&52.40&51.25&52.71&51.19\\\\\n\\hline\nTRADES&&84.92&60.87&56.13&55.16&54.02&53.38 \\\\\n\\rowcolor{gray!20}+Ours &\\multirow{-2}{*}{WideResNet-34}& \\textbf{85.03}&\\textbf{62.43}&\\textbf{58.64}&\\textbf{57.87}&\\textbf{57.18}&\\textbf{56.28}\\\\\\hline\nMART&& \\textbf{83.07}&60.21&54.14&52.90&49.62&48.95\\\\\n\\rowcolor{gray!20}+ Ours &\\multirow{-2}{*}{ResNet-18}& 82.70&\\textbf{62.62}&\\textbf{59.03}&\\textbf{58.13}&\\textbf{55.51}&\\textbf{54.61}\n\\end{tabular} %\\vspace{-1mm}\n \\caption{\\sl\\small{\\bf Defense against adversarial attacks on classification task (CIFAR-10).} Compared to baselines that filter or manipulate features, ours does not modify network architecture or weights. Instead, ours performs an ensemble in the feature space. On CIFAR-10, ours achieves state-of-the-art robustness without requiring any additional training. Moreover, even in a worst-case adaptive adversary setting where the attacker is fully aware of the defense and how stochastic resonance is applied, the effectiveness of adversarial attacks is still notably reduced, while the computational cost for executing such attacks is significantly increased.}\n \\label{tab:cifar10}\n %\\vspace{-2mm}\n\\end{table*}\n\n\\begin{table}[t]\n\\scriptsize\n\\parbox{.49\\linewidth}{\n\\centering\n\\setlength{\\tabcolsep}{0.8pt} \n% ---------------- LEFT COLUMN ----------------\n \\begin{tabular}{l|c|c|c|c|c|c|c|c}\nAtt. Strength ($\\epsilon$)&\\multicolumn{2}{c|}{8/255}&\\multicolumn{2}{c|}{4/255}&\\multicolumn{2}{c|}{2/255}&\\multicolumn{2}{c}{1/255}\\\\\n\\hline\nMetric&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5\\\\\\hline\nNo Defense&4.51&19.55&12.25&42.15&29.79&65.09&48.09&78.13\\\\\nOurs ($d=1$)&11.66&46.27&27.85&65.80&45.94&77.63&57.48&83.43\\\\\nOurs ($d=2$)&18.78&58.58&36.42&72.86&51.58&80.85&60.41&84.77\\\\\nOurs ($d=3$)&\\textbf{25.77}&\\textbf{65.88}&\\textbf{42.52}&\\textbf{76.75}&\\textbf{54.94}&\\textbf{82.64}&\\textbf{62.08}&\\textbf{85.50}\n \\end{tabular} %\\vspace{-1mm}\n \\captionof{table}{\\small{\\bf ImageNet with ViT-Small.} Increasing the level of stochastic resonance consistently improves both Top-1 and Top-5 accuracy under adversarial attacks. Relative to the clean baseline (72.9 Top-1, 92.91 Top-5), our method recovers up to 55.8\\% of the Top-1 accuracy loss and 68.1\\% of the Top-5 accuracy loss.}\n \\label{tab:ViT}\n}\n\\hfill\n\\parbox{.49\\linewidth}{\n\\centering\n\\setlength{\\tabcolsep}{0.8pt} \n \\begin{tabular}{l|c|c|c|c|c|c|c|c}\nAtt. Strength ($\\epsilon$)&\\multicolumn{2}{c|}{8/255}&\\multicolumn{2}{c|}{4/255}&\\multicolumn{2}{c|}{2/255}&\\multicolumn{2}{c}{1/255}\\\\\n\\hline\nMetric&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5\\\\\\hline\nNo Defense&8.51&26.19&9.45&27.92&11.10&30.63&15.21&36.76\\\\\nInitial Conv.&16.91&34.66&17.36&35.28&18.12&36.30&19.59&38.25\\\\\nRes. Block 1&22.44&44.95&23.39&46.03&24.84&47.64&27.57&50.80\\\\\nRes. Block 2&\\textbf{24.88}&\\textbf{48.54}&\\textbf{25.90}&\\textbf{49.66}&\\textbf{27.23}&\\textbf{51.19}&\\textbf{30.11}&\\textbf{54.15}\\\\\nRes. Block 3&21.76&44.28&22.73&45.47&24.14&47.14&27.18&50.20\n \\end{tabular} %\\vspace{-1mm}\n \\captionof{table}{\\small{\\bf Layer-wise ablation on ResNet-50.} Adversarial perturbations resemble high-frequency noise. Applying stochastic resonance through shallow layers is sufficient to defend against adversarial attacks, substantially reducing the overall computational cost.}\n \\label{tab:layers}\n } %\\vspace{-2mm}\n\\end{table}\n\n\\noindent\\textbf{CIFAR-10. }\nWe evaluate our method on CIFAR-10 \\cite{krizhevsky2009learning}, building upon the standard and publicly available code base of FSR \\cite{kim2023feature} %\\footnote{https://github.com/wkim97/FSR} \nand accompanying evaluation protocol. We apply stochastic resonance to networks pre-trained with AT \\cite{madry2017towards}, TRADES \\cite{zhang2019theoretically}, and MART \\cite{wang2019improving}, using publicly released weights without any modification. Our method operates with these methods purely at test time without any training. We conduct experiments on ResNet-18 \\cite{he2016deep} and WideResNet-34 \\cite{zagoruyko2016wide}, depending on the availability of author-released pre-trained weights. In all cases, feature ensembling is performed before the final linear layer.\nFurthermore, we consider a worst-case adaptive adversary setting, where the attacker has full knowledge of the model weights, and knows every stochastic resonance transformation by accessing \\emph{every single} forward pass and its gradients. \n\nFig.~\\ref{fig:cifar} shows the results varying different levels of stochastic resonance. Increasing the resonance level consistently enhances robustness in all attack settings, leading to substantial improvements over the baseline method (FSR). Importantly, our approach surpasses the baseline even under adaptive adversarial attacks. \nAdditionally, we compare our method against multiple baselines, including feature-level manipulation methods (FD \\cite{xie2019feature}, CAS \\cite{bai2021improving}, CIFS \\cite{yan2021cifs}) and ensemble-based approach TTE \\cite{perez2021enhancing}. The results, summarized in Tab.~\\ref{tab:cifar10}, demonstrate that stochastic resonance consistently outperforms all baselines across different attacks. Even in the worst-case adaptive attack scenario, where the adversary accounts for all stochastic resonance forward passes, the model remains significantly more robust than the baseline methods. In addition, stochastic resonance increases attack complexity under the adaptive settings, making adversarial noise generation more challenging for the attacker. As a result, the computational cost for generating adaptive adversarial perturbations increases substantially. For example, with stochastic resonance, 8x more wall-clock time is required to create adversarial examples with PGD-100.\n\n\n\\noindent\\textbf{ImageNet.}\nWe further evaluate our approach on the ImageNet \\cite{deng2009imagenet} classification dataset using standard segmentation backbones, including ResNet-50 \\cite{he2016deep} and Vision Transformer \\cite{dosovitskiy2020image}, without adversarial training. As in the CIFAR experiments, we vary the level of stochastic resonance and conduct ablation studies by testing against PGD attacks of different strengths. Tab.~\\ref{tab:ViT} reports the results for ViT-Small. Consistent with the CIFAR-10 findings, increasing the resonance level leads to consistent improvements in robustness, as measured by both Top-1 and Top-5 accuracy. Notably, the vanilla ViT-Small model without attack achieves 72.9 (Top-1) and 92.91 (Top-5), which means our method recovers the accuracy drop under adversarial attacks by up to a relative 55.8\\% (Top-1, when $\\epsilon=4/255$) and 68.1\\% (Top-5, when $\\epsilon=2/255$). We further evaluate our method on ResNet-50 and observe a consistent trend, as shown in Tab.~\\ref{tab:Rotation}. \n\n\n\n\\begin{wraptable}{r}{0.5\\textwidth}\n\\vspace{-4mm}\n\\setlength{\\tabcolsep}{0.8pt} \n\\scriptsize\n \\centering\n \\begin{tabular}{l|c|c|c|c|c|c|c|c}\nAtt. Strength ($\\epsilon$)&\\multicolumn{2}{c|}{8/255}&\\multicolumn{2}{c|}{4/255}&\\multicolumn{2}{c|}{2/255}&\\multicolumn{2}{c}{1/255}\\\\\n\\hline\nMetric&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5&Top-1&Top-5\\\\\\hline\nNo Defense&8.51&26.19&9.45&27.92&11.10&30.63&15.21&36.76\\\\\n\\rowcolor{gray!20}Ours ($d=1$)&18.40&40.36&19.54&42.65&21.02&43.86&24.66&47.81\\\\\n\\rowcolor{gray!20}w/ Rotation&20.01&41.32&20.84&42.39&22.10&43.89&24.72&46.89\\\\\nOurs ($d=2$)&20.01&42.22&21.02&43.45&22.44&45.32&25.80&48.97\\\\\nw/ Rotation&18.86&38.67&19.55&39.5&20.36&40.48&22.01&42.50\\\\\n\\rowcolor{gray!20}Ours ($d=3$)&\\textbf{21.17}&\\textbf{43.58}&\\textbf{22.04}&\\textbf{44.78}&\\textbf{23.44}&\\textbf{46.53}&\\textbf{26.58}&\\textbf{49.73}\\\\\n\\rowcolor{gray!20}w/ Rotation&15.15&32.89&15.61&33.46&16.17&34.19&17.33&35.59\n\n\\end{tabular}\n \\caption{\\small{\\bf Stochastic resonance using translation v.s. rotation on ResNet-50.} While rotations provide similar gains at low resonance levels, performance degrades as the resonance level increases, likely due to the lack of rotational invariance in convolutional filters.}\n \\label{tab:Rotation}\\vspace{-2mm}\n\\end{wraptable}\n\nWe also explored group transformations other than translation, e.g. rotations in Tab.~\\ref{tab:Rotation}. For a fair comparison, we use the same number of augmentations as in the translation experiments. Rotations behave similarly to translations at low levels of stochastic resonance, but performance degrades as the resonance level increases. We hypothesize that since convolutional filters are inherently translation-invariant but not rotation-invariant, aligning features under different rotations reduces feature quality. Moreover, rotations are approximately 30\\% slower due to interpolation overhead.\n\nSince adversarial perturbations often manifest as high-frequency noise, having a low-pass filter in early layers may form an effective defense. As our method applies to arbitrarily chosen layers, we vary the termination layer of stochastic resonance. As shown in Tab.~\\ref{tab:layers}, applying it only through the first residual block already achieves strong adversarial robustness, while extending it to the second block yields the strongest result. This finding is significant: running stochastic resonance through shallow layers can be sufficient as a defense strategy, which reduces overall computational cost.\n\n\\begin{table*}[t]\n\\setlength{\\tabcolsep}{0.8pt} \n\\footnotesize\n \\centering\n \\begin{tabular}{c|l|c|c|c|c|c|c|c|c|c|c|c|c}\n &Attack Strength ($\\epsilon$)&\\multicolumn{3}{c|}{0.02}&\\multicolumn{3}{c|}{0.01}&\\multicolumn{3}{c|}{0.005}&\\multicolumn{3}{c}{0.002}\\\\\\cline{2-14}\n&Metric&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err&\\,MAE\\,&RMSE&D1-err\\\\\\hline\n{\\multirow{5}{*}{\\rotatebox[origin=c]{90}{FGSM}}} &No Defense&14.83&24.10&97.33&8.49&14.53&90.49&5.05&7.70&74.71&3.01&3.49&38.12 \\\\\n&Latent Smoothing&13.42&22.09&96.61&8.12&13.69&89.25&4.89&7.05&73.01&2.89&3.32&36.25\n\\\\\n&Ours ($d=1$)&10.12&15.81&95.80&6.46&9.92&86.30&4.39&5.93&68.55&2.78&3.18&31.99 \\\\\n&\\cellcolor{gray!20}Error Reduced (\\%)& \\cellcolor{gray!20}31.76&\\cellcolor{gray!20}34.40&\\cellcolor{gray!20}1.57&\\cellcolor{gray!20}23.91&\\cellcolor{gray!20}31.73&\\cellcolor{gray!20}4.63&\\cellcolor{gray!20}13.07&\\cellcolor{gray!20}22.99&\\cellcolor{gray!20}7.58&\\cellcolor{gray!20}7.64&\\cellcolor{gray!20}8.88&\\cellcolor{gray!20}16.08\\\\\n&Ours ($d=2$)&\\textbf{9.22}&\\textbf{13.88}&\\textbf{94.61}&\\textbf{6.13}&\\textbf{8.87}&\\textbf{84.49}&\\textbf{4.19}&\\textbf{5.43}&\\textbf{66.74}&\\textbf{2.73}&\\textbf{3.12}&\\textbf{31.18}\\\\\n&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20} 37.82&\\cellcolor{gray!20}42.40&\\cellcolor{gray!20}2.79&\\cellcolor{gray!20}27.78&\\cellcolor{gray!20}38.95&\\cellcolor{gray!20}6.63&\\cellcolor{gray!20}16.92&\\cellcolor{gray!20}29.41&\\cellcolor{gray!20}10.66&\\cellcolor{gray!20}9.21&\\cellcolor{gray!20}10.65&\\cellcolor{gray!20}18.21 \\\\\\hline\n{\\multirow{5}{*}{\\rotatebox[origin=c]{90}{PGD}}} &No Defense&161.70&162.61&99.99&131.66&140.55&98.64&63.97&88.55&85.31&6.83&17.03&39.24 \\\\\n&Latent Smoothing&161.79&162.69&99.99&131.46&140.41&98.57&63.86&88.21&85.39&7.28&17.44&39.81\\\\\n&Ours ($d=1$)&107.86&125.14&98.29&69.97&84.72&91.79&20.66&42.29&73.21&4.17&8.32&29.09\\\\\n&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20}33.30 &\\cellcolor{gray!20} 23.04 &\\cellcolor{gray!20} 1.70 &\\cellcolor{gray!20} 46.86 &\\cellcolor{gray!20} 39.72 &\\cellcolor{gray!20} 6.94 &\\cellcolor{gray!20} 67.70 &\\cellcolor{gray!20} 52.24 &\\cellcolor{gray!20} 14.18 &\\cellcolor{gray!20} 38.95 &\\cellcolor{gray!20} 51.15 &\\cellcolor{gray!20} 25.87\\\\\n&Ours ($d=2$)&\\textbf{77.59}&\\textbf{100.14}&\\textbf{96.14}&\\textbf{44.77}&\\textbf{66.23}&\\textbf{89.24}&\\textbf{17.98}&\\textbf{32.80}&\\textbf{71.09}&\\textbf{3.76}&\\textbf{6.73}&\\textbf{28.44}\\\\\n&\\cellcolor{gray!20}Error Reduced (\\%)&\\cellcolor{gray!20} 52.01 &\\cellcolor{gray!20} 38.41 &\\cellcolor{gray!20} 3.85 &\\cellcolor{gray!20} 66.02 &\\cellcolor{gray!20} 52.87 &\\cellcolor{gray!20} 9.53 &\\cellcolor{gray!20} 71.89 &\\cellcolor{gray!20} 62.94 &\\cellcolor{gray!20} 16.66 &\\cellcolor{gray!20} 44.99 &\\cellcolor{gray!20} 60.52 &\\cellcolor{gray!20} 27.53\n\\end{tabular}\n \\caption{\\sl\\small{\\bf Stochastic Resonance Enhances Stereo Matching Robustness.} Incorporating stochastic resonance significantly reduces prediction errors induced by adversarial attacks across all evaluation metrics, reducing error by up to 71.89\\% (MAE, when attacked by PGD with $\\epsilon=0.005$). Notably, this defense mechanism operates entirely at test time without requiring any model re-training, which sets it apart from existing methods.}\n \\label{tab:stereo}%\\vspace{-2mm}\n\\end{table*}\n\n\n\n\\subsection{Stereo Matching}\\label{sec:stereo}\nStereopagnosia \\cite{wong2021stereopagnosia} first introduced adversarial attacks to stereo matching , yet no test-time method has demonstrated an effective defense. The primary challenge arises from the infeasibility of data augmentations, as they risk altering the physics of the input, leading to incorrect estimation. In contrast, our feature-level ensemble is suitable for this task, as transformations introduced by stochastic resonance are ``undone\" in the latent space, ensuring that features remain aligned precisely with the original input. This process mirrors AugUndo \\cite{wu2024augundo} conceptually.\n\n\\begin{figure*}[t]\n\\centering\n\\includegraphics[width=\\textwidth]{Figures/Stereo.pdf}%\\vspace{-2mm}\n \\caption{\\sl\\small {\\bf Stereo matching robustness via stochastic resonance.} We present visual results on stereo matching under various adversarial attack scenarios, including PGD and FGSM at different perturbation levels. These attacks significantly degrade the network's predictions, leading to substantial errors. By incorporating stochastic resonance, we demonstrate a significant reduction in prediction errors. This technique holds significant potential for improving robustness in safety-critical real-world applications, such as autonomous driving, where stereo vision must remain reliable under diverse environmental conditions and adversarial threats.\n}\n \\label{fig:stereo}%\\vspace{-2mm}\n\\end{figure*}\n\nWe evaluate our method on the standard benchmark used in \\emph{Stereopagnosia}, derived from KITTI~\\cite{geiger2012we}. Experiments are conducted using FGSM and PGD attacks against a pre-trained PSMNet~\\cite{chang2018pyramid}. Since no existing test-time defense is available, we adopt latent-space smoothing as a baseline. As shown in Tab.~\\ref{tab:stereo}, both attacks corrupt network predictions, with PGD proving substantially more effective due to its iterative nature. Nevertheless, stochastic resonance consistently improves robustness across attack strengths. In particular, under PGD with $\\epsilon=0.005$, our method reduces errors by up to 71.89\\% in terms of MAE. Crucially, these gains are achieved entirely at test time, without additional training or prior knowledge of the attack.\n\n\nFig.~\\ref{fig:stereo} provides qualitative results, featuring different attack strengths and methods. The adversarial perturbations introduce significant distortions, as indicated by bright regions in the visualized predictions. Stochastic resonance effectively mitigates these distortions, drastically reducing prediction errors. This experiment is particularly relevant for safety-critical applications such as autonomous driving, where adversarial disturbances can arise not only from malicious attacks but also from environmental factors such as adverse weather conditions, varying illumination, or sensor degradation. While some defenses \\cite{zhang2023weatherstream, cheng2021towards, cheng2022revisiting, berger2022stereoscopic} have been proposed to train a more robust network under adverse conditions, test-time defenses remain largely unexplored. Our method is the first to provide a viable solution in this setting.\n\n\n\n\n\n\n\\subsection{Optical Flow}\n\\label{sec:flow}\n\n\n\nWe further evaluate our method on optical flow, which computes the dense motion field between two images. The accuracy of optical flow is measured using the End-Point Error (EPE). We note that multiple adversarial attacks exist for optical flow \\cite{schrodi2022towards,Ranjan_2019_ICCV, schmalfuss2022perturbation}. Among these attacks, PGD is stronger than patch-based attacks as adversarial patches have localized effects. Therefore, in our experiments, we employ the RAFT \\cite{teed2020raft} %\\footnote{https://github.com/princeton-vl/RAFT} \noptical flow model and focus on global adversarial perturbations generated by PGD and FGSM. We test our method on the DAVIS \\cite{pont20172017} dataset under both attacks.\n\n%As in the first row of Fig.~\\ref{fig:flow-quality} (with amplified noise for better visibility), the attacks introduce fine-grained, structured perturbations that effectively mislead the network, particularly in regions where the color intensity is consistent, making it difficult to establish correct correspondences. This leads to strong errors in the predicted flow fields, as seen in the attacked flow predictions.\n\nTo defend against adversarial attacks, we apply stochastic resonance to the convolutional feature extractor of RAFT. Since the perturbation is applied only at the feature extraction stage, no additional overhead is introduced in the computationally intensive matching module. Quantitative results (Fig.~\\ref{fig:flow-quantitative}) show that increasing Stochastic Resonance reduces EPE, which aligns with our findings in classification.\nAs in Fig.~\\ref{fig:flow-quality}, our approach effectively removes errors caused by adversarial noise.\n\n\\def\\figd{Figures/RAFT}\n\\def\\fWidD{0.27\\textwidth}\n\\begin{wrapfigure}{r}{0.5\\textwidth}\n%\\vspace{-4mm}\n\\centering\n{\n\\footnotesize\n\\begin{tabular}{c@{\\hspace{0.01in}}c}\n\\hspace*{-5mm}\n\\includegraphics[width=\\fWidD]{\\figd/RAFT_PGD.png}\n&\\includegraphics[width=\\fWidD]{\\figd/RAFT_FGSM.png} \n\\end{tabular}\n\\caption{\\sl\\small {\\bf Enhanced optical flow robustness with stochastic resonance.} Under PGD and FGSM, stochastic resonance significantly reduces endpoint error in optical flow estimation. Notably, our method performs ensembling in the latent feature space rather than the output space, providing greater flexibility. While ensembling in the output space offers minor performance gains, our approach consistently achieves superior robustness across all levels of stochastic resonance.}\n\\label{fig:flow-quantitative}\n}\n\n\\end{wrapfigure}\n\n\n\nWe further compare our method to an alternative ensembling approach that aggregates predictions in the output space, conceptually similar to TTE \\cite{perez2021enhancing}. In this variant, we apply the same stochastic transformations but instead ensemble at the output level rather than in the feature space. While this method provides marginal improvements, it remains less effective than our approach. This finding highlights the advantage of having the freedom to choose from any stage of the model to perform ensemble. In this particular experiment, we demonstrate that ensembling solely at the image encoding sub-module, while leaving the rest of the RAFT network unchanged, yields substantial improvements in robustness, thanks to the flexibility of our method.\n\n\n\n\\def\\figd{Figures/Flow}\n\\def\\fWidD{0.15\\textwidth}\n\\begin{figure*}[t]\n%\\vspace{-2mm}\n\\renewcommand{\\arraystretch}{0.2} % Default value: 1\n\\centering\n\\hspace*{-4mm}\n{\\scriptsize\n\\begin{tabular}[0mm]{c@{\\hskip 0.01in}c@{\\hskip 0.01in}c@{\\hskip 0.01in}c|c@{\\hskip 0.01in}c@{\\hskip 0.01in}c}\n& \\multicolumn{3}{c}{\\normalsize PGD}& \\multicolumn{3}{c}{\\normalsize FGSM}\\\\\\\\\n\\smash{\\rotatebox{90}{\\quad Image}}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd1}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd2}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd3}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm1}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm4}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm3}\\\\\n\\smash{\\rotatebox{90}{Original}}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_org1}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_org2}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_org3}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_org1}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_org4}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_org3}\\\\\n\\smash{\\rotatebox{90}{Attacked}}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_attacked1}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_attacked2}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_attacked3}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_attacked1}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_attacked4}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_attacked3}\\\\\n\\smash{\\rotatebox{90}{\\quad Ours}}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_ours1}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_ours2}&\n\\includegraphics[width=\\fWidD]{\\figd/pgd_ours3}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_ours1}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_ours4}&\n\\includegraphics[width=\\fWidD]{\\figd/fgsm_ours3}\\\\\n\\end{tabular}\n}\n\\caption{\\sl\\small{\\bf Optical flow robustness via stochastic resonance.} \nQualitative results (visualized with a color wheel) show that our method substantially mitigates the degradation caused by both PGD and FGSM attacks. This robustness is particularly relevant for visual perception systems that rely on accurate motion estimation.}\n\\label{fig:flow-quality}%\\vspace{-2mm}\n\\end{figure*}\n\n\\section{Discussion and Conclusion}\\label{sec:discussion}\n\n\\noindent\\textbf{Speed.} \nStochastic resonance incurs low computational overhead when executed in parallel: raising the stochastic resonance level to 3 with ResNet-50 adds only 0.06 seconds to the inference time on an NVIDIA 1080Ti GPU. Most of the overhead arises from creating perturbations implemented via Python loops with \\texttt{torchvision}; we expect further speedups with efficient CUDA implementations. Even when executed \\emph{sequentially}, the computational overhead is 0.095 seconds. \nMoreover, strong robustness can be attained by applying stochastic resonance only to shallow layers, offering substantially greater efficiency than existing ensemble-based defenses (e.g. \\cite{perez2021enhancing}) that require multiple passes through the entire network. Moreover, our method is fully plug-and-play. In contrast, attack-specific adversarial training is over 6x slower than a vanilla training pipeline. As such, the computation of our method is well justified by its robustness gains and training-free nature.\n\n\\noindent\\textbf{On-demand scaling.}\nOne of the key strengths of our approach is its flexibility: providing a trade-off between robustness and computational cost. We offer a tunable “knob” that allows practitioners to adjust the level of resilience based on available resources on the fly: when the system has more computational capacity, add a higher level of stochastic resonance, vice versa. Note that, such a design does not \\emph{rely} on additional computation, yet more computation can bring \\emph{extra} performance. Moreover, our experiments show that the method generalizes across a wide range of tasks and architectures that include an encoder. This on-demand scaling mirrors inference-time scaling in language models, where performance can be improved without modifying the underlying pre-trained model.\n\n\\noindent\\textbf{Limitations. }\nDespite its strengths, our method has some limitations. First, while we offer parallel computation as a remedy, the computational overhead introduced by stochastic resonance may not be negligible for scenarios with memory and power constraints. Also, our current study focuses on integer-pixel translations. While this choice avoids interpolation artifacts and preserves spatial consistency, more generic transformations, including learned transformations, could be explored.\n\n\\noindent\\textbf{Conclusion. }\nIn this work, we present a signal-processing perspective for defending against adversarial attacks, motivated by the connection between adversarial perturbations and aliasing artifacts. Accordingly, we propose a ``combat noise with noise'' approach by introducing stochastic resonance as a defense mechanism. We formalize the problem and implement stochastic resonance using pixel-level translations paired with their inverse transformation in the feature space. The resulting method is training-free, agnostic to both tasks and attack types, and independent of network architectures.\n\nWe evaluate our method across various tasks. Empirical results on image classification demonstrate that our stochastic resonance approach achieves state-of-the-art robustness against diverse attack types, offering a clear advantage over feature-level denoising and filtering. Even in the adaptive adversary scenario, where an attacker is aware of the use of stochastic resonance, our method maintains strong robustness. Furthermore, we are the first to introduce test-time defense to dense prediction tasks. Specifically, we apply this method to stereo matching and optical flow, achieving up to a 71\\% reduction in prediction error. More importantly, these findings highlight the practical potential of stochastic resonance as a universal defense in real-world adversarial scenarios.\n\n\\clearpage\n\n\\section*{Reproducibility Statement}\nWe provide sufficient technical details in the paper to ensure reproducibility. Specifically, we describe the augmentations used for stochastic resonance, including augmentations (e.g. translation, rotation) and their corresponding inverse transformations, as well as the model architectures, datasets, and the network layers where our method is applied. Attack settings and evaluation protocols are drawn directly from standard benchmark datasets and publicly available code base, ensuring comparability with prior work. All implementation details necessary to reproduce our experiments, including parameters and ablation settings, are provided in the main paper and further expanded in the Appendix. Our experiments can be reproduced on a single desktop-level GPU without requiring large-scale computational resources. We will release the complete source code and pre-computed adversarial data upon publication.\n\n\\section*{LLM Statement}\nAll technical content of this work, including literature review, methodology, experiments, and analyses, was developed entirely by the authors. Large Language Models (LLMs) were employed as a tool for proofreading, without contributing to the scientific or technical substance of the manuscript.\n\n\n\\bibliography{iclr2026_conference}\n\\bibliographystyle{iclr2026_conference}\n\\clearpage\n\\appendix\n\\section{Implementation for Classification}\n\nFor our classification experiments, we built our implementation on top of standard network architectures, implementing SR on two main architectures derived from the FSR codebase \\cite{kim2023feature}:\n\\begin{itemize}\n \\item ResNet-18 \\cite{he2016deep}: A standard residual network with 18 layers organized in four main blocks with increasing channel dimensions (64, 128, 256, 512).\n \\item WideResNet-34 \\cite{zagoruyko2016wide}: A wider variant of ResNet with depth 34 and width factor 10, resulting in higher representational capacity with three main blocks with channel dimensions scaled by the width factor (160, 320, 640).\n\\end{itemize}\nFor both architectures, we apply SR at the bottleneck layer (after the final convolutional block).\n\nGiven an input image batch $x \\in \\mathbb{R}^{b \\times 3 \\times h \\times w}$ (where $b$ is the batch size), our SR approach operates as follows. First, we create a set of $(2d_x+1) \\times (2d_y+1)$ perturbed versions of the input by applying pixel-level translations within the range $[-d_x, d_x] \\times [-d_y, d_y]$ pixels:\n\\begin{equation}\n X_{\\text{perturbed}} = \\{g_{i,j}(X) \\mid i \\in [-d_y, d_y], j \\in [-d_x, d_x]\\}\n\\end{equation}\nwhere $g_{i,j}$ translates the image by $(i,j)$ pixels. These transformations are applied using PyTorch's ``transforms.functional.affine'' function with translation parameters while preserving the original image properties.\n\nAll images are concatenated into one batch and processed through the network in parallel up to the bottleneck layer:\n\\begin{equation}\n F = \\phi(X_{\\text{perturbed}})\n\\end{equation}\nwhere $\\phi$ represents the network up to the bottleneck layer. This batch processing approach significantly improves computational efficiency compared to individual forward passes.\n\nAfter obtaining feature maps for all perturbed inputs, we aggregate them to create a single enhanced feature map:\n\\begin{equation}\n F_{\\text{ensembled}} = \\frac{1}{n}\\sum_{i,j} T_{-i,-j}(F_{i,j})\n\\end{equation}\nwhere $T_{-i,-j}$ represents the inverse spatial shift operation that realigns the feature map and $n$ the number of augmentations.\n\nOur implementation requires $(2d_x+1) \\times (2d_y+1)$ forward passes through the network up to the bottleneck layer.\n\n\nFor evaluation, we tested our approach against standard adversarial attacks (FGSM \\cite{goodfellow2014explaining}, PGD-20 and PGD-100 \\cite{madry2017towards}, and C\\&W \\cite{carlini2017towards}), all bounded within $\\epsilon = 8/255$ under $\\ell_\\infty$-norm. We also report an Ensemble metric that measures the worst-case performance across all attacks for each test example, providing a comprehensive robustness assessment.\n\n\\section{Implementation for Stereo Matching}\n\nFor our stereo matching experiments, we built our implementation on top of standard stereo network architectures to ensure our approach remains model-agnostic and requires no training or fine-tuning. We integrated SR with PSMNet \\cite{chang2018pyramid}, a pyramid stereo matching network with a stacked hourglass architecture that uses 3D convolutions on a cost volume constructed by concatenating features. We apply SR at the feature extraction stage, before cost volume construction, where stereo correspondences are first established.\n\nGiven a pair of input stereo images $x_L, x_R \\in \\mathbb{R}^{b \\times 3 \\times h \\times w}$ (where $b$ is the batch size), our SR approach operates as follows. First, we create a set of $(2d_x+1) \\times (2d_y+1)$ perturbed versions of each input image by applying translations within the range $[-d_x, d_x] \\times [-d_y, d_y]$ pixels:\n\\begin{equation}\n X_{L,\\text{perturbed}} = \\{g_{i,j}(x_L) \\mid i \\in [-d_y, d_y], j \\in [-d_x, d_x]\\}\n\\end{equation}\n\\begin{equation}\n X_{R,\\text{perturbed}} = \\{g_{i,j}(x_R) \\mid i \\in [-d_y, d_y], j \\in [-d_x, d_x]\\}.\n\\end{equation}\n\nAll images are concatenated into batches and processed through the feature extraction component of the network:\n\\begin{equation}\n F_L = \\phi(X_{L,\\text{perturbed}})\n\\end{equation}\n\\begin{equation}\n F_R = \\phi(X_{R,\\text{perturbed}})\n\\end{equation}\nwhere $\\phi$ represents the feature extraction component of the stereo network. This batch processing approach significantly improves computational efficiency compared to individual forward passes.\n\nAfter obtaining feature maps for all perturbed inputs, we aggregate them to create a single enhanced feature map.\n\nOur implementation requires $(2d_x+1) \\times (2d_y+1)$ forward passes through the feature extraction component of the network for each stereo image. \n\nFor evaluation, we tested our approach against adversarial attacks generated using FGSM \\cite{goodfellow2014explaining} and I-FGSM \\cite{kurakin2018adversarial} (a special case of PGD), bounded within various $\\epsilon$ values ($\\{0.002, 0.005, 0.01, 0.02\\}$) under $\\ell_\\infty$-norm. We measured performance using three standard stereo matching metrics: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and D1-error (percentage of pixels with disparity error greater than 3 pixels or 5\\% of the ground truth) \\cite{luo2018towards}.\n\n\n\\section{Details about Attack on Optical Flow}\nTo find an adversarial attack for optical flow estimated by a given neural network $f$, we utilize a similar approach to \\cite{oskouie2024attack} that aims to find a perturbation $\\delta$ for given frames $F_1$ and $F_2$, maximizing the discrepancy between predicted and ground-truth optical flow $OF$. If the ground-truth optical flow is unavailable, we use the predicted optical flow from the unattacked frame as our surrogate ground-truth. Our method applies $\\delta$ to the first input frame, then uses a deep neural network to estimate optical flow from the perturbed frames. The objective is to maximize the average end-point error (EPE) between the predicted and ground-truth optical flow, calculated as the mean Euclidean distance between corresponding 2D flow vectors. In other words, the $\\epsilon$-norm bounded adversary $\\delta$ for optical-flow is calculated by optimizing the following\n\\begin{equation}\n \\max_{\\delta: \\Vert\\delta\\Vert \\le \\epsilon} \\text{EPE} \\bigl(OF, f(F_1 + \\delta, F_2) \\bigr). \n\\end{equation}\n\nOne $l_\\infty$-bounded adversary $A$ for the aforementioned optimization problem is Fast Gradient Sign Method (FGSM) \\cite{goodfellow2014explaining} which can be obtained by \n\\begin{align}\n\\text{L} = \\text{EPE}(OF, f(F_1, F_2)) , \\nonumber \\\\\nA = F_1 + \\epsilon \\cdot \\text{sign}\\bigl(\\nabla_{F_1} \\text{L} \\bigr). \n\\end{align}\n\nProjected gradient descent (PGD) \\cite{madry2017towards} represents an enhanced and more complex version of FGSM. This attack method generates adversarial examples through an iterative process and the formulation for this attack is as following\n\\begin{equation}\nF_1^{(t + 1)} = \\Pi_{F_1 + \\mathcal{S}} \\bigl( F_1^{(t)} + \\alpha \\cdot \\text{sign}(\\nabla_{F_1} \\text{L} ) \\bigr). \n\\end{equation}\n\nNote that in PGD, since the perturbations are considered to be too minimal to significantly alter the flow dynamics, the ground-truth optical flow is not updated by intermediate perturbations applied to the input data.\n\nFor our experimental setup, we chose to set the norm value $\\epsilon$ at $\\frac{10}{256}$. Furthermore, we configured the PGD algorithm to run for 10 iterations. The step size $\\alpha$ was determined by dividing $2.5 \\cdot \\epsilon$ by the total number of iterations, ensuring a balanced progression throughout the optimization process.\n\n\\section{Additional Visualizations}\nHere we provide additional visualizations from our experiments comparing SR under both FGSM and PGD attack. We also provide a visual showing the results of FGSM and PGD pertubation on various images.\n\n\\begin{figure*}[t]\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/fgsm2e2.pdf}\n \\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\epsilon=0.02$}\n \\label{fig:fgsm2e2_stereo}\n\\end{figure*}\n\\begin{figure*}[h]\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/fgsm1e2.pdf}\n \\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\epsilon=0.01$}\n \\label{fig:fgsm1e2_stereo}\n\\end{figure*}\n\\begin{figure*}[h]\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/fgsm5e3.pdf}\n \\caption{Visual results on stereo matching against FGSM attack, without and with SR, $\\epsilon=0.005$}\n \\label{fig:fgsm5e3_stereo}\n\\end{figure*}\n\\begin{figure*}[h]\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/PGD1e2.pdf}\n \\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\epsilon=0.01$}\n \\label{fig:pgd1e2_stereo}\n\\end{figure*}\n\\begin{figure*}[h]\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/PGD5e3.pdf}\n \\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\epsilon=0.005$}\n \\label{fig:pgd5e3_stereo}\n\\end{figure*}\n\\begin{figure*}[h]\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/PGD2e3.pdf}\n \\caption{Visual results on stereo matching against PGD attack, without and with SR, $\\epsilon=0.002$}\n \\label{fig:pgd2e3_stereo}\n\\end{figure*}\n\n\\begin{figure}[h]\n\\setlength{\\tabcolsep}{2pt}\n \\centering\n \\begin{tabular}{ccccc}\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/00004.jpg} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/attacked_img4.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/noise4.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/attacked_img4.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/noise4.png} \\\\\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/00005.jpg} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/attacked_img5.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/noise5.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/attacked_img5.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/noise5.png} \\\\\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/00049.jpg} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/attacked_img49.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/noise49.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/attacked_img49.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/noise49.png} \\\\\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/00062.jpg} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/attacked_img62.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/FGSM/noise62.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/attacked_img62.png} &\n \\includegraphics[width=0.18\\textwidth]{Figures/perturbations/PGD/noise62.png} \\\\\n \\textbf{Image} & \\textbf{FGSM Attacked} & \\textbf{FGSM Noise} & \\textbf{PGD Attacked} & \\textbf{PGD Noise} \\\\\n \\end{tabular}\n \\caption{Original images and their corresponding attacked images and perturbations using FGSM and PGD methods on optical flow. The attacks mostly target the main object observed in the image.}\n \\label{Figure:attack}\n\\end{figure}\n\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"Which attack strength proves to be the most difficult on average to reduce errors on in FGSM with d=2 across all metrics. and what is the average?"},"answer":{"kind":"string","value":"0.002, 12.69"},"plan":{"kind":"string","value":"SELECT all attack strengths in the fgsm section where d is 2 \nLOOP for each attack_strength\n COMPUTE average_reduction = average of error reduced (%) values for mae, rmse, and d1-err for ours d = 2\nCOMPUTE hardest_strength = argmin attack_strength over average_reduction\nRETURN hardest_strength, average_reduction for hardest_strength\n"}}},{"rowIdx":349,"cells":{"paper":{"kind":"string","value":"2510.03223"},"relevant_tables":{"kind":"list like","value":[["\\begin{table}\n"," \\scriptsize\n"," \\centering\n"," \\setlength{\\tabcolsep}{4pt}\n"," \\caption{Evaluation results on six benchmarks. Best results are shown in \\lightgreen{green}, and those indicating a performance drop compared to standard greedy decoding are shown in \\lightgray{grey}.}\n"," \\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{ll|ccc|cc|c}\n"," \\toprule\n"," \\multirow{2.5}{*}{\\textbf{Model}} & \\multirow{2.5}{*}{\\textbf{Method}} & \\multicolumn{3}{c|}{Math} & \\multicolumn{2}{c|}{CommonSense} & \\multirow{2.5}{*}{BBH} \\\\\n"," \\cmidrule(lr){3-5} \\cmidrule(lr){6-7}\n"," & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Llama3.2-3B} & CoT & 63.84& 46.06 & 42.5 & 66.64 & 32.98 & 35.09 \\\\\n"," & PS+ & \\lightblue{70.62 (+6.78)} & \\lightgray{38.58 (-7.48)} & \\lightblue{44.50 (+2.00)} & \\lightgray{62.79 (-3.85)} & \\lightgray{31.81 (-1.17)} & \\lightblue{40.51 (+5.42)} \\\\\n"," & RE2& \\lightgray{57.38 (-6.46)} & \\lightblue{47.28 (+1.22)} & \\lightgreen{45.00 (+2.50)} & \\lightgray{65.03 (-1.61)} & \\lightgray{30.32 (-2.66)} & 38.02 (+2.93) \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{77.86 (+14.02)} & \\lightgreen{48.43 (+2.37)} & \\lightgreen{45.00 (+2.50)} & \\lightgreen{67.55 (+0.91)} & \\lightgreen{43.79 (+10.81)} & \\lightgreen{50.48 (+15.39)} \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Phi-4-mini-4B} & CoT & 75.36 & 61.81 & 51.00 & 67.03 & 39.54 & 60.51\\\\\n"," & PS+ & \\lightblue{87.17 (+11.81)} & \\lightblue{62.02 (+0.21)} & \\lightblue{54.50 (+3.50)} & \\lightgray{58.86 (-8.17)} & {41.16 (+1.62)} & \\lightgray{59.63 (-0.88)} \\\\\n"," & RE2& {85.75 (+10.39)} & \\lightgray{59.06 (-2.75)} & 51.50 (+0.50) & \\lightgray{61.83 (-5.20)} & \\lightblue{44.50 (+4.96)} & \\lightblue{61.39 (+0.88)} \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{88.02 (+12.66)} & \\lightgreen{68.50 (+6.69)} & \\lightgreen{59.00 (+8.00)} & \\lightgreen{68.69 (+1.66)} & \\lightgreen{49.47 (+9.93)} & \\lightgreen{62.42 (+1.91)} \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Qwen3-4B} & CoT & 86.66 & 73.62 & 82.00 & 68.03 & 70.21 & 73.33\\\\\n"," & PS+ & \\lightgray{82.79 (-3.87)} & \\lightgray{71.65 (-1.97)} & \\lightblue{83.50 (+1.50)} & 68.56 (+0.53) & \\lightgray{59.82 (-10.39)} & \\lightgray{70.99 (-2.34)} \\\\\n"," & RE2& \\lightgray{79.98 (-6.68)} & \\lightblue{75.98 (+2.36)} & 82.50 (+0.50) & \\lightblue{69.83 (+1.80)} & \\lightgray{67.02 (-3.19)} & \\lightgreen{75.75 (+2.42)} \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{87.26 (+0.60)} & \\lightgreen{79.92 (+6.30)} & \\lightgreen{86.50 (+4.50)} & \\lightgreen{70.13 (+2.10)} & \\lightgreen{71.56 (+1.35)} & \\lightblue{75.31 (+1.98)} \\\\ \n"," \\midrule\n"," \\multirow{4}{*}{Llama3.1-8B} & CoT & 61.85 & 50.79 &44.50 & 70.24 & 26.77 & 49.45 \\\\\n"," & PS+ & \\lightblue{62.24 (+0.39)} & \\lightgray{48.65 (-2.14)} & \\lightblue{47.00 (+2.50)} & \\lightgray{65.85 (-4.39)} & \\lightblue{28.79 (+2.02)} & 51.72 (+2.27) \\\\\n"," & RE2 & \\lightgray{57.68 (-4.17)} & \\lightblue{51.97 (+1.18)} & 44.50 (+0.00) & \\lightgray{69.74 (-0.50)} & 28.55 (+1.78) & \\lightblue{54.58 (+5.13)} \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{76.72 (+14.87)} & \\lightgreen{55.51 (+4.72)} & \\lightgreen{52.50 (+8.00)} & \\lightgreen{73.54 (+3.30)} & \\lightgreen{40.01 (+13.24)} & \\lightgreen{58.53 (+9.08)} \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Phi-4-15B} & CoT & 73.16 & 68.11& 74.50 & 77.51 & 73.94 & 72.08\\\\\n"," & PS+ & \\lightblue{79.07 (+5.91)} & \\lightblue{72.75 (+4.64)} & \\lightgray{72.50 (-2.00)} & \\lightgray{75.59 (-1.92)} & \\lightblue{76.24 (+2.30)} & \\lightgray{68.42 (-3.66)} \\\\\n"," & RE2 & {74.87 (+1.17)} & {69.29 (+1.18)} & \\lightgray{73.50 (-1.00)} & \\lightgray{76.90 (-0.61)} & {75.79 (+1.85)} & \\lightblue{74.94 (+2.86)} \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{82.41 (+9.25)} & \\lightgreen{79.13 (+11.02)} & \\lightgreen{81.00 (+6.50)} & \\lightgreen{77.82 (+0.31)} & \\lightgreen{85.99 (+12.05)} & \\lightgreen{75.31 (+3.23)} \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Qwen3-30B} & CoT & 84.46 & 81.10 & 78.00 & 78.60 & 84.92 & 67.69\\\\\n"," & PS+ & {85.11 (+0.65)} & \\lightgray{80.83 (-0.27)} & \\lightgray{73.50 (-4.50)} & 78.70 (+0.10) & \\lightgray{82.62 (-2.30)} & \\lightgray{66.67 (-1.02)}\\\\\n"," & RE2 & \\lightblue{87.21 (+2.75)} & \\lightblue{82.28 (+1.18)} & \\lightgray{76.00 (-2.00)} & \\lightblue{78.91 (+0.31)} & \\lightgreen{89.36 (+4.44)} & \\lightgreen{70.55 (+2.86)}\\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{87.41 (+2.95)} & \\lightgreen{83.46 (+2.36)} & \\lightgreen{87.00 (+9.00)} & \\lightgreen{79.65 (+1.05)} & \\lightblue{85.56 (+0.64)} & \\lightblue{69.30 (+1.61)}\\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:main}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{table}\\n\",\n \" \\\\scriptsize\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{4pt}\\n\",\n \" \\\\caption{Evaluation results on six benchmarks. Best results are shown in \\\\lightgreen{green}, and those indicating a performance drop compared to standard greedy decoding are shown in \\\\lightgray{grey}.}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{ll|ccc|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{2.5}{*}{\\\\textbf{Model}} & \\\\multirow{2.5}{*}{\\\\textbf{Method}} & \\\\multicolumn{3}{c|}{Math} & \\\\multicolumn{2}{c|}{CommonSense} & \\\\multirow{2.5}{*}{BBH} \\\\\\\\\\n\",\n \" \\\\cmidrule(lr){3-5} \\\\cmidrule(lr){6-7}\\n\",\n \" & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Llama3.2-3B} & CoT & 63.84& 46.06 & 42.5 & 66.64 & 32.98 & 35.09 \\\\\\\\\\n\",\n \" & PS+ & \\\\lightblue{70.62 (+6.78)} & \\\\lightgray{38.58 (-7.48)} & \\\\lightblue{44.50 (+2.00)} & \\\\lightgray{62.79 (-3.85)} & \\\\lightgray{31.81 (-1.17)} & \\\\lightblue{40.51 (+5.42)} \\\\\\\\\\n\",\n \" & RE2& \\\\lightgray{57.38 (-6.46)} & \\\\lightblue{47.28 (+1.22)} & \\\\lightgreen{45.00 (+2.50)} & \\\\lightgray{65.03 (-1.61)} & \\\\lightgray{30.32 (-2.66)} & 38.02 (+2.93) \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{77.86 (+14.02)} & \\\\lightgreen{48.43 (+2.37)} & \\\\lightgreen{45.00 (+2.50)} & \\\\lightgreen{67.55 (+0.91)} & \\\\lightgreen{43.79 (+10.81)} & \\\\lightgreen{50.48 (+15.39)} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Phi-4-mini-4B} & CoT & 75.36 & 61.81 & 51.00 & 67.03 & 39.54 & 60.51\\\\\\\\\\n\",\n \" & PS+ & \\\\lightblue{87.17 (+11.81)} & \\\\lightblue{62.02 (+0.21)} & \\\\lightblue{54.50 (+3.50)} & \\\\lightgray{58.86 (-8.17)} & {41.16 (+1.62)} & \\\\lightgray{59.63 (-0.88)} \\\\\\\\\\n\",\n \" & RE2& {85.75 (+10.39)} & \\\\lightgray{59.06 (-2.75)} & 51.50 (+0.50) & \\\\lightgray{61.83 (-5.20)} & \\\\lightblue{44.50 (+4.96)} & \\\\lightblue{61.39 (+0.88)} \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{88.02 (+12.66)} & \\\\lightgreen{68.50 (+6.69)} & \\\\lightgreen{59.00 (+8.00)} & \\\\lightgreen{68.69 (+1.66)} & \\\\lightgreen{49.47 (+9.93)} & \\\\lightgreen{62.42 (+1.91)} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Qwen3-4B} & CoT & 86.66 & 73.62 & 82.00 & 68.03 & 70.21 & 73.33\\\\\\\\\\n\",\n \" & PS+ & \\\\lightgray{82.79 (-3.87)} & \\\\lightgray{71.65 (-1.97)} & \\\\lightblue{83.50 (+1.50)} & 68.56 (+0.53) & \\\\lightgray{59.82 (-10.39)} & \\\\lightgray{70.99 (-2.34)} \\\\\\\\\\n\",\n \" & RE2& \\\\lightgray{79.98 (-6.68)} & \\\\lightblue{75.98 (+2.36)} & 82.50 (+0.50) & \\\\lightblue{69.83 (+1.80)} & \\\\lightgray{67.02 (-3.19)} & \\\\lightgreen{75.75 (+2.42)} \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{87.26 (+0.60)} & \\\\lightgreen{79.92 (+6.30)} & \\\\lightgreen{86.50 (+4.50)} & \\\\lightgreen{70.13 (+2.10)} & \\\\lightgreen{71.56 (+1.35)} & \\\\lightblue{75.31 (+1.98)} \\\\\\\\ \\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Llama3.1-8B} & CoT & 61.85 & 50.79 &44.50 & 70.24 & 26.77 & 49.45 \\\\\\\\\\n\",\n \" & PS+ & \\\\lightblue{62.24 (+0.39)} & \\\\lightgray{48.65 (-2.14)} & \\\\lightblue{47.00 (+2.50)} & \\\\lightgray{65.85 (-4.39)} & \\\\lightblue{28.79 (+2.02)} & 51.72 (+2.27) \\\\\\\\\\n\",\n \" & RE2 & \\\\lightgray{57.68 (-4.17)} & \\\\lightblue{51.97 (+1.18)} & 44.50 (+0.00) & \\\\lightgray{69.74 (-0.50)} & 28.55 (+1.78) & \\\\lightblue{54.58 (+5.13)} \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{76.72 (+14.87)} & \\\\lightgreen{55.51 (+4.72)} & \\\\lightgreen{52.50 (+8.00)} & \\\\lightgreen{73.54 (+3.30)} & \\\\lightgreen{40.01 (+13.24)} & \\\\lightgreen{58.53 (+9.08)} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Phi-4-15B} & CoT & 73.16 & 68.11& 74.50 & 77.51 & 73.94 & 72.08\\\\\\\\\\n\",\n \" & PS+ & \\\\lightblue{79.07 (+5.91)} & \\\\lightblue{72.75 (+4.64)} & \\\\lightgray{72.50 (-2.00)} & \\\\lightgray{75.59 (-1.92)} & \\\\lightblue{76.24 (+2.30)} & \\\\lightgray{68.42 (-3.66)} \\\\\\\\\\n\",\n \" & RE2 & {74.87 (+1.17)} & {69.29 (+1.18)} & \\\\lightgray{73.50 (-1.00)} & \\\\lightgray{76.90 (-0.61)} & {75.79 (+1.85)} & \\\\lightblue{74.94 (+2.86)} \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{82.41 (+9.25)} & \\\\lightgreen{79.13 (+11.02)} & \\\\lightgreen{81.00 (+6.50)} & \\\\lightgreen{77.82 (+0.31)} & \\\\lightgreen{85.99 (+12.05)} & \\\\lightgreen{75.31 (+3.23)} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Qwen3-30B} & CoT & 84.46 & 81.10 & 78.00 & 78.60 & 84.92 & 67.69\\\\\\\\\\n\",\n \" & PS+ & {85.11 (+0.65)} & \\\\lightgray{80.83 (-0.27)} & \\\\lightgray{73.50 (-4.50)} & 78.70 (+0.10) & \\\\lightgray{82.62 (-2.30)} & \\\\lightgray{66.67 (-1.02)}\\\\\\\\\\n\",\n \" & RE2 & \\\\lightblue{87.21 (+2.75)} & \\\\lightblue{82.28 (+1.18)} & \\\\lightgray{76.00 (-2.00)} & \\\\lightblue{78.91 (+0.31)} & \\\\lightgreen{89.36 (+4.44)} & \\\\lightgreen{70.55 (+2.86)}\\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{87.41 (+2.95)} & \\\\lightgreen{83.46 (+2.36)} & \\\\lightgreen{87.00 (+9.00)} & \\\\lightgreen{79.65 (+1.05)} & \\\\lightblue{85.56 (+0.64)} & \\\\lightblue{69.30 (+1.61)}\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:main}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}[ht]\n","\\centering\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{figure/overview.png}\n"," \\caption{Comparison between existing reasoning methods and {\\selfanchor}. Due to inherent attention patterns, existing reasoning methods may easily overlook intermediate reasoning and make mistakes. \\selfanchor\\ addresses this by decomposes the task into plans, and takes each plan as a component for attention alignment.}\n"," \\label{fig:main}\n","\\end{figure*}\n"],["\\begin{table}\n"," \\scriptsize\n"," \\centering\n"," \\setlength{\\tabcolsep}{4pt}\n"," \\caption{Evaluation results on six benchmarks. Best results are shown in \\lightgreen{green}, and those indicating a performance drop compared to standard greedy decoding are shown in \\lightgray{grey}.}\n"," \\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{ll|ccc|cc|c}\n"," \\toprule\n"," \\multirow{2.5}{*}{\\textbf{Model}} & \\multirow{2.5}{*}{\\textbf{Method}} & \\multicolumn{3}{c|}{Math} & \\multicolumn{2}{c|}{CommonSense} & \\multirow{2.5}{*}{BBH} \\\\\n"," \\cmidrule(lr){3-5} \\cmidrule(lr){6-7}\n"," & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Llama3.2-3B} & CoT & 63.84& 46.06 & 42.5 & 66.64 & 32.98 & 35.09 \\\\\n"," & PS+ & \\lightblue{70.62 (+6.78)} & \\lightgray{38.58 (-7.48)} & \\lightblue{44.50 (+2.00)} & \\lightgray{62.79 (-3.85)} & \\lightgray{31.81 (-1.17)} & \\lightblue{40.51 (+5.42)} \\\\\n"," & RE2& \\lightgray{57.38 (-6.46)} & \\lightblue{47.28 (+1.22)} & \\lightgreen{45.00 (+2.50)} & \\lightgray{65.03 (-1.61)} & \\lightgray{30.32 (-2.66)} & 38.02 (+2.93) \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{77.86 (+14.02)} & \\lightgreen{48.43 (+2.37)} & \\lightgreen{45.00 (+2.50)} & \\lightgreen{67.55 (+0.91)} & \\lightgreen{43.79 (+10.81)} & \\lightgreen{50.48 (+15.39)} \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Phi-4-mini-4B} & CoT & 75.36 & 61.81 & 51.00 & 67.03 & 39.54 & 60.51\\\\\n"," & PS+ & \\lightblue{87.17 (+11.81)} & \\lightblue{62.02 (+0.21)} & \\lightblue{54.50 (+3.50)} & \\lightgray{58.86 (-8.17)} & {41.16 (+1.62)} & \\lightgray{59.63 (-0.88)} \\\\\n"," & RE2& {85.75 (+10.39)} & \\lightgray{59.06 (-2.75)} & 51.50 (+0.50) & \\lightgray{61.83 (-5.20)} & \\lightblue{44.50 (+4.96)} & \\lightblue{61.39 (+0.88)} \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{88.02 (+12.66)} & \\lightgreen{68.50 (+6.69)} & \\lightgreen{59.00 (+8.00)} & \\lightgreen{68.69 (+1.66)} & \\lightgreen{49.47 (+9.93)} & \\lightgreen{62.42 (+1.91)} \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Qwen3-4B} & CoT & 86.66 & 73.62 & 82.00 & 68.03 & 70.21 & 73.33\\\\\n"," & PS+ & \\lightgray{82.79 (-3.87)} & \\lightgray{71.65 (-1.97)} & \\lightblue{83.50 (+1.50)} & 68.56 (+0.53) & \\lightgray{59.82 (-10.39)} & \\lightgray{70.99 (-2.34)} \\\\\n"," & RE2& \\lightgray{79.98 (-6.68)} & \\lightblue{75.98 (+2.36)} & 82.50 (+0.50) & \\lightblue{69.83 (+1.80)} & \\lightgray{67.02 (-3.19)} & \\lightgreen{75.75 (+2.42)} \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{87.26 (+0.60)} & \\lightgreen{79.92 (+6.30)} & \\lightgreen{86.50 (+4.50)} & \\lightgreen{70.13 (+2.10)} & \\lightgreen{71.56 (+1.35)} & \\lightblue{75.31 (+1.98)} \\\\ \n"," \\midrule\n"," \\multirow{4}{*}{Llama3.1-8B} & CoT & 61.85 & 50.79 &44.50 & 70.24 & 26.77 & 49.45 \\\\\n"," & PS+ & \\lightblue{62.24 (+0.39)} & \\lightgray{48.65 (-2.14)} & \\lightblue{47.00 (+2.50)} & \\lightgray{65.85 (-4.39)} & \\lightblue{28.79 (+2.02)} & 51.72 (+2.27) \\\\\n"," & RE2 & \\lightgray{57.68 (-4.17)} & \\lightblue{51.97 (+1.18)} & 44.50 (+0.00) & \\lightgray{69.74 (-0.50)} & 28.55 (+1.78) & \\lightblue{54.58 (+5.13)} \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{76.72 (+14.87)} & \\lightgreen{55.51 (+4.72)} & \\lightgreen{52.50 (+8.00)} & \\lightgreen{73.54 (+3.30)} & \\lightgreen{40.01 (+13.24)} & \\lightgreen{58.53 (+9.08)} \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Phi-4-15B} & CoT & 73.16 & 68.11& 74.50 & 77.51 & 73.94 & 72.08\\\\\n"," & PS+ & \\lightblue{79.07 (+5.91)} & \\lightblue{72.75 (+4.64)} & \\lightgray{72.50 (-2.00)} & \\lightgray{75.59 (-1.92)} & \\lightblue{76.24 (+2.30)} & \\lightgray{68.42 (-3.66)} \\\\\n"," & RE2 & {74.87 (+1.17)} & {69.29 (+1.18)} & \\lightgray{73.50 (-1.00)} & \\lightgray{76.90 (-0.61)} & {75.79 (+1.85)} & \\lightblue{74.94 (+2.86)} \\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{82.41 (+9.25)} & \\lightgreen{79.13 (+11.02)} & \\lightgreen{81.00 (+6.50)} & \\lightgreen{77.82 (+0.31)} & \\lightgreen{85.99 (+12.05)} & \\lightgreen{75.31 (+3.23)} \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Qwen3-30B} & CoT & 84.46 & 81.10 & 78.00 & 78.60 & 84.92 & 67.69\\\\\n"," & PS+ & {85.11 (+0.65)} & \\lightgray{80.83 (-0.27)} & \\lightgray{73.50 (-4.50)} & 78.70 (+0.10) & \\lightgray{82.62 (-2.30)} & \\lightgray{66.67 (-1.02)}\\\\\n"," & RE2 & \\lightblue{87.21 (+2.75)} & \\lightblue{82.28 (+1.18)} & \\lightgray{76.00 (-2.00)} & \\lightblue{78.91 (+0.31)} & \\lightgreen{89.36 (+4.44)} & \\lightgreen{70.55 (+2.86)}\\\\\n"," & \\textbf{{\\selfanchor}} & \\lightgreen{87.41 (+2.95)} & \\lightgreen{83.46 (+2.36)} & \\lightgreen{87.00 (+9.00)} & \\lightgreen{79.65 (+1.05)} & \\lightblue{85.56 (+0.64)} & \\lightblue{69.30 (+1.61)}\\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:main}\n","\\end{table}\n"],["\\begin{table*}\n"," \\scriptsize\n"," \\centering\n"," \\setlength{\\tabcolsep}{4pt}\n"," \\caption{Evaluation comparison with thinking models}\n"," \\resizebox{0.78\\textwidth}{!}{\n"," \\begin{tabular}{ll|ccc|cc|c}\n"," \\toprule\n"," \\multirow{2.5}{*}{\\textbf{Model}} & \\multirow{2.5}{*}{\\textbf{Method}} & \\multicolumn{3}{c|}{Math} & \\multicolumn{2}{c|}{CommonSense} & \\multirow{2.5}{*}{BBH} \\\\\n"," \\cmidrule(lr){3-5} \\cmidrule(lr){6-7}\n"," & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\n"," \\midrule\n"," \\multirow{3}{*}{Phi-4-mini-4B} & CoT & 75.36 & 61.81 & 51.00 & 67.03 & 39.54 & 60.51\\\\\n"," & {\\selfanchor} & 88.02 & 68.50 & 59.00 & 68.69 & 49.47 & 62.42 \\\\\n"," & Reasoning & 81.27 & 60.62 & 75.00 & 66.38 & 45.04 & 59.85 \\\\\n"," \\midrule\n"," \\multirow{3}{*}{Qwen3-4B} & CoT & 86.66 & 73.62 & 82.00 & 68.03 & 70.21 & 73.33\\\\\n"," & {\\selfanchor} & 87.26 & 79.92 & 86.50 & 70.13 & 71.56 & 75.31\\\\\n"," & Reasoning & 83.24& 67.32 & 87.00 & 68.31 & 73.40 & 75.34 \\\\\n"," \\midrule\n"," \\multirow{3}{*}{Llama3.1-8B} & CoT & 61.85 & 50.79 &44.50 & 70.24 & 26.77 & 49.45 \\\\\n"," & {\\selfanchor} & 76.72 & 55.51 & 52.50 & 73.54 & 40.01 & 58.53 \\\\\n"," & Reasoning & 73.62 & 62.99 & 72.50 & 65.41 & 48.58 & 64.98\\\\\n"," \\midrule\n"," \\multirow{3}{*}{Phi-4-15B} & CoT & 73.16 & 68.11& 74.50 & 77.51 & 73.94 & 72.08 \\\\\n"," & {\\selfanchor} & 82.41 & 79.13 & 81.00 & 77.82 & 85.99 & 75.31 \\\\\n"," & Reasoning & 81.12 & 83.20 & 95.5 & 75.43 & 74.11 & 74.98 \\\\\n"," \\midrule\n"," \\multirow{3}{*}{Qwen3-30B} & CoT & 84.46 & 81.10 & 78.00 & 78.60 & 84.92 & 67.69 \\\\\n"," & {\\selfanchor} & 87.41 & 83.46 & 87.00 & 79.65 & 85.56 & 69.30 \\\\\n"," & Reasoning & 94.5& 80.31 & 85.00 & 77.26 & 80.96 & 76.54\\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:thinking_comparison}\n","\\end{table*}\n"],["\\begin{figure}[ht]\n"," \\centering\n"," \\begin{subfigure}[t]{0.48\\textwidth}\n"," \\raggedright\n"," \\includegraphics[height=4.4cm]{figure/anchor_vs_reread_performance_gain.pdf}\n"," \\caption{Reasoning Tasks Complexity and performance gains comparison}\n"," \\label{fig:combinedl}\n"," \\end{subfigure}\n"," \\hfill\n"," \\begin{subfigure}[t]{0.48\\textwidth}\n"," \\raggedleft\n"," \\includegraphics[height=4.4cm]{figure/task_complexity_chain_length_box.pdf}\n"," \\caption{Reasoning Tasks Complexity and reasoning chain length comparison. The lower value represents the easier task.}\n"," \\label{fig:combinedr}\n"," \\end{subfigure}\n"," \\caption{Analysis of task complexity and reasoning chain length}\n"," \\label{fig:combined}\n","\\end{figure}\n"],["\\begin{table}[ht]\n"," \\scriptsize\n"," \\centering\n"," \\setlength{\\tabcolsep}{4pt}\n"," \\caption{Efficiency comparison}\n"," \\resizebox{0.5\\textwidth}{!}{\n"," \\begin{tabular}{l|cccc}\n"," \\toprule\n"," \\multirow{2.5}{*}{\\textbf{Model}} & \\multicolumn{4}{c}{Token/Second} \\\\\n"," \\cmidrule(lr){2-5}\n"," & {\\selfanchor} & CoT & PS+ & RE2 \\\\\n"," \\midrule\n"," \\multirow{1}{*}{Llama3.2-3B} & 9.97 & 10.87 & 10.84 & 12.01 \\\\\n"," \\midrule\n"," \\multirow{1}{*}{Phi-4-mini-4B} & 11.02 & 12.25 & 12.24 & 12.21\\\\\n"," \\midrule\n"," \\multirow{1}{*}{Qwen3-4B} & 5.41 & 6.22 & 6.22 & 6.23\\\\\n"," \\midrule\n"," \\multirow{1}{*}{Llama3.1-8B} & 7.54 & 8.38 & 8.26 & 8.19\\\\\n"," \\midrule\n"," \\multirow{1}{*}{Phi-4-15B} & 7.92 & 9.00 & 8.94 & 8.88\\\\\n"," \\midrule\n"," \\multirow{1}{*}{Qwen3-30B} & 1.07 & 1.39 & 1.39 & 1.37\\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab: efficiency}\n","\\end{table}\n"],["\\begin{table*}\n"," \\scriptsize\n"," \\centering\n"," \\setlength{\\tabcolsep}{4pt}\n"," \\caption{Performance comparing {\\selfanchor} with and without attention steering}\n"," \\resizebox{1\\textwidth}{!}{\n"," \\begin{tabular}{ll|ccc|cc|c}\n"," \\toprule\n"," \\multirow{2.5}{*}{\\textbf{Model}} & \\multirow{2.5}{*}{\\textbf{Method}} & \\multicolumn{3}{c|}{Math} & \\multicolumn{2}{c|}{CommonSense} & \\multirow{2.5}{*}{BBH} \\\\\n"," \\cmidrule(lr){3-5} \\cmidrule(lr){6-7}\n"," & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\n"," \\midrule\n"," \\multirow{2}{*}{Llama3.1-8B} \n"," & {\\selfanchor} (w/o attention steering) & 73.01 & 53.15 & 40.90 & 71.17 & 35.28 & 52.77\\\\\n"," & {\\selfanchor} & 76.72 & 55.51 & 52.50 & 73.54 & 40.01 & 58.53 \\\\\n"," \n"," \\midrule\n"," \\multirow{2}{*}{Phi-4-mini-4B} \n"," & {\\selfanchor} (w/o attention steering) & 78.77 & 58.66 &55.50 & 68.60 & 38.83 & 57.44 \\\\\n"," & {\\selfanchor} & 88.02 & 68.50 & 59.00 & 68.69 & 49.47 & 62.42\\\\\n"," \n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:ablation structure}\n","\\end{table*}\n"],["\\begin{table}\n","\\centering\n","\\caption{An example of BBH. Incorrect inferences are highlighted in \\lightred{red}. Correct ones are highlighted in \\lightgreen{green}.}\n","\\resizebox{\\linewidth}{!}{\n","\\begin{tabular}{l l}\n"," \\toprule\n"," \\multirow{2}{*}{\\textbf{Prompt}} %& \\textit{``Explain the antecedent of the pronoun (which thing the pronoun refers to), or state that it is ambiguous.}\\\\\n"," & \\textit{\\textbf{Sentence: The secretary came to the analyst's office and helped her to book a flight.}} \\\\\n"," & \\textit{\\textbf{Options: (A) Helped the secretary book a flight (B) Helped the analyst book a flight (C) Ambiguous}} \\\\\n"," \\midrule\n"," \\textbf{\\selfanchor} & \\{ \"Step 1: Identify the pronoun\": \"The pronoun is 'her'.\",\\\\\n"," \\text{(w/o attention steering)} & \"Step 2: Determine the antecedent of the pronoun\": \"\\lightred{The antecedent of 'her' is the subject of the sentence, which is 'The secretary'}\", \\\\\n"," \\textbf{} & \"Step 3: Analyze the sentence structure\": The subject of the sentence is 'The secretary', and the verb is 'came'. The object of the \\\\\n"," & \\:\\:\\:\\: verb 'came' is 'to the analyst's office'. The verb 'helped' has the pronoun 'her' as its object.\",\\\\\n"," & \"Step 4: Determine the antecedent of the pronoun based on the sentence structure\": \"Based on the sentence structure, the antecedent \\\\\n"," & \\:\\:\\:\\: of the pronoun \\lightred{'her' is the subject of the sentence, which is 'The secretary'}.\",\\\\\n"," & \"Step 5: Choose the correct option\": \"The correct option is \\lightred{(A) Helped the secretary book a flight.}\"\\}\\\\\n"," \\midrule\n"," \\textbf{{\\selfanchor}} & \\{ \"Step 1: Identify the pronoun\": \"The pronoun in the sentence is 'her'.\",\\\\\n"," & \"Step 2: Determine the antecedent of the pronoun\": \"To find the antecedent, we need to look for the noun that 'her' refers to. In this\\\\\n"," & \\:\\:\\:\\: case, \\lightgreen{'her' is a possessive pronoun that refers to the analyst.}\", \\\\\n"," & \"Step 3: Analyze the sentence structure\": \"The subject of the sentence is 'The secretary', and the object of the verb 'helped' is 'her'\",\\\\\n"," & \"Step 4: Identify the antecedent based on the sentence structure\": \"\\lightgreen{'her' refers to the analyst, not the secretary.}\",\\\\\n"," & \"Step 5: Choose the correct option\": \"Since 'her' refers to the analyst, the correct option is \\lightgreen{(B) Helped the analyst book a flight.}\" \\}\\\\\n"," \\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:An example of anchor}\n","\\end{table}\n"],[" \\begin{table*}[ht]\n"," \\scriptsize\n"," \\centering\n"," \\setlength{\\tabcolsep}{14pt}\n","\n"," \\centering\n"," \\caption{Mean selection ablation study. Results show accuracy (\\%) on AQuA-RAT and T4D benchmarks.}\n"," \\begin{tabular}{ll|cc}\n"," \\toprule\n"," \\textbf{Model} & \\textbf{Method} & AQuA-RAT & T4D \\\\\n"," \\midrule\n"," \\multirow{4}{*}{LLaMA3.1-8B} & CoT & 50.79 & 26.77 \\\\\n"," & {\\selfanchor} (Harmonic) & \\textbf{55.51} & \\textbf{40.01} \\\\\n"," & {\\selfanchor} (Geometric) & 55.11 & 35.28 \\\\\n"," & {\\selfanchor} (Arithmetic) & 54.72 & 35.99 \\\\\n"," \\midrule\n"," \\multirow{4}{*}{Phi-4-mini} & CoT & 61.81 & 39.54\\\\\n"," & {\\selfanchor} (Harmonic) & \\textbf{68.50} & \\textbf{49.47}\\\\\n"," & {\\selfanchor} (Geometric) & 67.72 & 49.11 \\\\\n"," & {\\selfanchor} (Arithmetic) & 67.71 & 48.40 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," \\label{tab:means_selection}\n","\n","\n","\\end{table*}\n"],["\\begin{table*}[ht]\n"," \\scriptsize\n"," \\centering\n"," \\setlength{\\tabcolsep}{14pt}\n"," \\caption{Alternative anchoring design comparison. Results show accuracy (\\%) on AQuA-RAT and T4D benchmarks.}\n"," \\begin{tabular}{ll|cc}\n"," \\toprule\n"," \\textbf{Model} & \\textbf{Method} & AQuA-RAT & T4D \\\\\n"," \\midrule\n"," \\multirow{3}{*}{LLaMA3.1-8B} & CoT & 50.79 & 26.77 \\\\\n"," & {\\selfanchor} & \\textbf{55.51} & \\textbf{40.01} \\\\\n"," & Anchor to All Prior Steps & 53.54 & 32.62\\\\\n"," \\midrule\n"," \\multirow{3}{*}{Phi-4-mini} & CoT & 61.81 & 39.54\\\\\n"," & {\\selfanchor} & \\textbf{68.50} & \\textbf{49.47}\\\\\n"," & Anchor to All Prior Steps & 67.32 & 47.34\\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," \\label{tab:alternative_design}\n","\n","\\end{table*}\n"],["\\begin{table*}[t]\n"," \\scriptsize\n"," \\centering\n"," \\setlength{\\tabcolsep}{4pt}\n"," \\caption{BBH details}\n"," \\resizebox{1.1\\textwidth}{!}{\n"," \\begin{tabular}{llcccccc}\n"," \\toprule\n"," \\multirow{2}{*}{\\textbf{Model}} & \\multirow{2}{*}{\\textbf{Method}} & \\multicolumn{5}{c}{\\textbf{BBH}} \\\\\n"," \\cmidrule(lr){3-8}\n"," & & \\textbf{disambiguation\\_qa} & \\textbf{causal\\_judgement} & \\textbf{date\\_understanding} & \\textbf{logical\\_deduction} & \\textbf{salient\\_translation\\_error\\_detection} & \\textbf{snarks}\\\\\n"," \\midrule\n"," \\multirow{3}{*}{Llama3.1-8B} & CoT & 100 & 91/187 & 182 & 67 & 110 & 125\\\\\n"," & PS+ & 138 & 108 & 136 & 78 & 124 & 122 \\\\\n"," & re-read & 124 & 98 & 190 & 85 & 121 & 127\\\\\n"," & {\\selfanchor} & 152 & 100 & 160 & 128 & 132 & 127\\\\\n"," \\midrule\n"," \\multirow{3}{*}{Llama3.2-3B} & CoT & 88/250 & 71 & 102 & 34 & 95 & 89\\\\\n"," & PS+ & 104 & 63 & 97 & 86 & 98 & 105 \\\\\n"," & re-read & 74 & 84 & 127 & 40 & 89 & 105\\\\\n"," & {\\selfanchor} & 131 & 101 & 131 & 101 & 96 & 129\\\\\n"," \\midrule\n"," \\multirow{3}{*}{Phi4-mini-4B} & CoT & 162/250 & 113 & 154 & 114 & 149 & 134\\\\\n"," & PS+ & 160 & 126 & 138 & 130 & 136 & 124\\\\\n"," & re-read & 162 & 115 & 165 & 113 & 135 & 148\\\\\n"," & {\\selfanchor} & 152 & 116 & 174 & 128 & 140 & 142\\\\\n"," \\midrule\n"," \\multirow{3}{*}{Qwen3-mini-4B} & CoT & 183/250 & 121 & 174 & 208 & 167 & 148\\\\\n"," & PS+ & 179 & 108 & 165 & 207 & 160 & 150 \\\\\n"," & re-read & 179 & 121 & 203 & 230 & 147 & 154\\\\\n"," & {\\selfanchor} & 185 & 115 & 193 & 224 & 161 & 150\\\\\n"," \\midrule\n"," \\multirow{3}{*}{Phi-4-15B} & CoT & 180 & 120 & 203 & 169 & 152 & 160\\\\\n"," & PS+ & 180 & 117 & 140 & 186 & 155 & 156\\\\\n"," & re-read & 179 & 120 & 221 & 191 & 158 & 154 \\\\\n"," & {\\selfanchor} & 176 & 122 & 218 & 203 & 148 & 161 \\\\\n"," \\midrule\n"," \\multirow{3}{*}{Qwen3-30B} & CoT & 105 & 125 & 182 & 185 & 172 & 155 \\\\\n"," & PS+ & 114 & 122 & 172 & 181 & 165 & 156\\\\\n"," & re-read & 113 & 125 & 185 & 210 & 174 & 156\\\\\n"," & {\\selfanchor} & 110 & 123 & 196 & 200 & 160 & 157\\\\\n"," \\bottomrule\n"," \\end{tabular}}\n"," \\label{tab:truth}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{figure*}[ht]\\n\",\n \"\\\\centering\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{figure/overview.png}\\n\",\n \" \\\\caption{Comparison between existing reasoning methods and {\\\\selfanchor}. Due to inherent attention patterns, existing reasoning methods may easily overlook intermediate reasoning and make mistakes. \\\\selfanchor\\\\ addresses this by decomposes the task into plans, and takes each plan as a component for attention alignment.}\\n\",\n \" \\\\label{fig:main}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table}\\n\",\n \" \\\\scriptsize\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{4pt}\\n\",\n \" \\\\caption{Evaluation results on six benchmarks. Best results are shown in \\\\lightgreen{green}, and those indicating a performance drop compared to standard greedy decoding are shown in \\\\lightgray{grey}.}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{ll|ccc|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{2.5}{*}{\\\\textbf{Model}} & \\\\multirow{2.5}{*}{\\\\textbf{Method}} & \\\\multicolumn{3}{c|}{Math} & \\\\multicolumn{2}{c|}{CommonSense} & \\\\multirow{2.5}{*}{BBH} \\\\\\\\\\n\",\n \" \\\\cmidrule(lr){3-5} \\\\cmidrule(lr){6-7}\\n\",\n \" & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Llama3.2-3B} & CoT & 63.84& 46.06 & 42.5 & 66.64 & 32.98 & 35.09 \\\\\\\\\\n\",\n \" & PS+ & \\\\lightblue{70.62 (+6.78)} & \\\\lightgray{38.58 (-7.48)} & \\\\lightblue{44.50 (+2.00)} & \\\\lightgray{62.79 (-3.85)} & \\\\lightgray{31.81 (-1.17)} & \\\\lightblue{40.51 (+5.42)} \\\\\\\\\\n\",\n \" & RE2& \\\\lightgray{57.38 (-6.46)} & \\\\lightblue{47.28 (+1.22)} & \\\\lightgreen{45.00 (+2.50)} & \\\\lightgray{65.03 (-1.61)} & \\\\lightgray{30.32 (-2.66)} & 38.02 (+2.93) \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{77.86 (+14.02)} & \\\\lightgreen{48.43 (+2.37)} & \\\\lightgreen{45.00 (+2.50)} & \\\\lightgreen{67.55 (+0.91)} & \\\\lightgreen{43.79 (+10.81)} & \\\\lightgreen{50.48 (+15.39)} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Phi-4-mini-4B} & CoT & 75.36 & 61.81 & 51.00 & 67.03 & 39.54 & 60.51\\\\\\\\\\n\",\n \" & PS+ & \\\\lightblue{87.17 (+11.81)} & \\\\lightblue{62.02 (+0.21)} & \\\\lightblue{54.50 (+3.50)} & \\\\lightgray{58.86 (-8.17)} & {41.16 (+1.62)} & \\\\lightgray{59.63 (-0.88)} \\\\\\\\\\n\",\n \" & RE2& {85.75 (+10.39)} & \\\\lightgray{59.06 (-2.75)} & 51.50 (+0.50) & \\\\lightgray{61.83 (-5.20)} & \\\\lightblue{44.50 (+4.96)} & \\\\lightblue{61.39 (+0.88)} \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{88.02 (+12.66)} & \\\\lightgreen{68.50 (+6.69)} & \\\\lightgreen{59.00 (+8.00)} & \\\\lightgreen{68.69 (+1.66)} & \\\\lightgreen{49.47 (+9.93)} & \\\\lightgreen{62.42 (+1.91)} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Qwen3-4B} & CoT & 86.66 & 73.62 & 82.00 & 68.03 & 70.21 & 73.33\\\\\\\\\\n\",\n \" & PS+ & \\\\lightgray{82.79 (-3.87)} & \\\\lightgray{71.65 (-1.97)} & \\\\lightblue{83.50 (+1.50)} & 68.56 (+0.53) & \\\\lightgray{59.82 (-10.39)} & \\\\lightgray{70.99 (-2.34)} \\\\\\\\\\n\",\n \" & RE2& \\\\lightgray{79.98 (-6.68)} & \\\\lightblue{75.98 (+2.36)} & 82.50 (+0.50) & \\\\lightblue{69.83 (+1.80)} & \\\\lightgray{67.02 (-3.19)} & \\\\lightgreen{75.75 (+2.42)} \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{87.26 (+0.60)} & \\\\lightgreen{79.92 (+6.30)} & \\\\lightgreen{86.50 (+4.50)} & \\\\lightgreen{70.13 (+2.10)} & \\\\lightgreen{71.56 (+1.35)} & \\\\lightblue{75.31 (+1.98)} \\\\\\\\ \\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Llama3.1-8B} & CoT & 61.85 & 50.79 &44.50 & 70.24 & 26.77 & 49.45 \\\\\\\\\\n\",\n \" & PS+ & \\\\lightblue{62.24 (+0.39)} & \\\\lightgray{48.65 (-2.14)} & \\\\lightblue{47.00 (+2.50)} & \\\\lightgray{65.85 (-4.39)} & \\\\lightblue{28.79 (+2.02)} & 51.72 (+2.27) \\\\\\\\\\n\",\n \" & RE2 & \\\\lightgray{57.68 (-4.17)} & \\\\lightblue{51.97 (+1.18)} & 44.50 (+0.00) & \\\\lightgray{69.74 (-0.50)} & 28.55 (+1.78) & \\\\lightblue{54.58 (+5.13)} \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{76.72 (+14.87)} & \\\\lightgreen{55.51 (+4.72)} & \\\\lightgreen{52.50 (+8.00)} & \\\\lightgreen{73.54 (+3.30)} & \\\\lightgreen{40.01 (+13.24)} & \\\\lightgreen{58.53 (+9.08)} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Phi-4-15B} & CoT & 73.16 & 68.11& 74.50 & 77.51 & 73.94 & 72.08\\\\\\\\\\n\",\n \" & PS+ & \\\\lightblue{79.07 (+5.91)} & \\\\lightblue{72.75 (+4.64)} & \\\\lightgray{72.50 (-2.00)} & \\\\lightgray{75.59 (-1.92)} & \\\\lightblue{76.24 (+2.30)} & \\\\lightgray{68.42 (-3.66)} \\\\\\\\\\n\",\n \" & RE2 & {74.87 (+1.17)} & {69.29 (+1.18)} & \\\\lightgray{73.50 (-1.00)} & \\\\lightgray{76.90 (-0.61)} & {75.79 (+1.85)} & \\\\lightblue{74.94 (+2.86)} \\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{82.41 (+9.25)} & \\\\lightgreen{79.13 (+11.02)} & \\\\lightgreen{81.00 (+6.50)} & \\\\lightgreen{77.82 (+0.31)} & \\\\lightgreen{85.99 (+12.05)} & \\\\lightgreen{75.31 (+3.23)} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Qwen3-30B} & CoT & 84.46 & 81.10 & 78.00 & 78.60 & 84.92 & 67.69\\\\\\\\\\n\",\n \" & PS+ & {85.11 (+0.65)} & \\\\lightgray{80.83 (-0.27)} & \\\\lightgray{73.50 (-4.50)} & 78.70 (+0.10) & \\\\lightgray{82.62 (-2.30)} & \\\\lightgray{66.67 (-1.02)}\\\\\\\\\\n\",\n \" & RE2 & \\\\lightblue{87.21 (+2.75)} & \\\\lightblue{82.28 (+1.18)} & \\\\lightgray{76.00 (-2.00)} & \\\\lightblue{78.91 (+0.31)} & \\\\lightgreen{89.36 (+4.44)} & \\\\lightgreen{70.55 (+2.86)}\\\\\\\\\\n\",\n \" & \\\\textbf{{\\\\selfanchor}} & \\\\lightgreen{87.41 (+2.95)} & \\\\lightgreen{83.46 (+2.36)} & \\\\lightgreen{87.00 (+9.00)} & \\\\lightgreen{79.65 (+1.05)} & \\\\lightblue{85.56 (+0.64)} & \\\\lightblue{69.30 (+1.61)}\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:main}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \" \\\\scriptsize\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{4pt}\\n\",\n \" \\\\caption{Evaluation comparison with thinking models}\\n\",\n \" \\\\resizebox{0.78\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{ll|ccc|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{2.5}{*}{\\\\textbf{Model}} & \\\\multirow{2.5}{*}{\\\\textbf{Method}} & \\\\multicolumn{3}{c|}{Math} & \\\\multicolumn{2}{c|}{CommonSense} & \\\\multirow{2.5}{*}{BBH} \\\\\\\\\\n\",\n \" \\\\cmidrule(lr){3-5} \\\\cmidrule(lr){6-7}\\n\",\n \" & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Phi-4-mini-4B} & CoT & 75.36 & 61.81 & 51.00 & 67.03 & 39.54 & 60.51\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 88.02 & 68.50 & 59.00 & 68.69 & 49.47 & 62.42 \\\\\\\\\\n\",\n \" & Reasoning & 81.27 & 60.62 & 75.00 & 66.38 & 45.04 & 59.85 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Qwen3-4B} & CoT & 86.66 & 73.62 & 82.00 & 68.03 & 70.21 & 73.33\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 87.26 & 79.92 & 86.50 & 70.13 & 71.56 & 75.31\\\\\\\\\\n\",\n \" & Reasoning & 83.24& 67.32 & 87.00 & 68.31 & 73.40 & 75.34 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Llama3.1-8B} & CoT & 61.85 & 50.79 &44.50 & 70.24 & 26.77 & 49.45 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 76.72 & 55.51 & 52.50 & 73.54 & 40.01 & 58.53 \\\\\\\\\\n\",\n \" & Reasoning & 73.62 & 62.99 & 72.50 & 65.41 & 48.58 & 64.98\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Phi-4-15B} & CoT & 73.16 & 68.11& 74.50 & 77.51 & 73.94 & 72.08 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 82.41 & 79.13 & 81.00 & 77.82 & 85.99 & 75.31 \\\\\\\\\\n\",\n \" & Reasoning & 81.12 & 83.20 & 95.5 & 75.43 & 74.11 & 74.98 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Qwen3-30B} & CoT & 84.46 & 81.10 & 78.00 & 78.60 & 84.92 & 67.69 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 87.41 & 83.46 & 87.00 & 79.65 & 85.56 & 69.30 \\\\\\\\\\n\",\n \" & Reasoning & 94.5& 80.31 & 85.00 & 77.26 & 80.96 & 76.54\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:thinking_comparison}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{subfigure}[t]{0.48\\\\textwidth}\\n\",\n \" \\\\raggedright\\n\",\n \" \\\\includegraphics[height=4.4cm]{figure/anchor_vs_reread_performance_gain.pdf}\\n\",\n \" \\\\caption{Reasoning Tasks Complexity and performance gains comparison}\\n\",\n \" \\\\label{fig:combinedl}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{subfigure}[t]{0.48\\\\textwidth}\\n\",\n \" \\\\raggedleft\\n\",\n \" \\\\includegraphics[height=4.4cm]{figure/task_complexity_chain_length_box.pdf}\\n\",\n \" \\\\caption{Reasoning Tasks Complexity and reasoning chain length comparison. The lower value represents the easier task.}\\n\",\n \" \\\\label{fig:combinedr}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\\\caption{Analysis of task complexity and reasoning chain length}\\n\",\n \" \\\\label{fig:combined}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \" \\\\scriptsize\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{4pt}\\n\",\n \" \\\\caption{Efficiency comparison}\\n\",\n \" \\\\resizebox{0.5\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{l|cccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{2.5}{*}{\\\\textbf{Model}} & \\\\multicolumn{4}{c}{Token/Second} \\\\\\\\\\n\",\n \" \\\\cmidrule(lr){2-5}\\n\",\n \" & {\\\\selfanchor} & CoT & PS+ & RE2 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{1}{*}{Llama3.2-3B} & 9.97 & 10.87 & 10.84 & 12.01 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{1}{*}{Phi-4-mini-4B} & 11.02 & 12.25 & 12.24 & 12.21\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{1}{*}{Qwen3-4B} & 5.41 & 6.22 & 6.22 & 6.23\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{1}{*}{Llama3.1-8B} & 7.54 & 8.38 & 8.26 & 8.19\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{1}{*}{Phi-4-15B} & 7.92 & 9.00 & 8.94 & 8.88\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{1}{*}{Qwen3-30B} & 1.07 & 1.39 & 1.39 & 1.37\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab: efficiency}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \" \\\\scriptsize\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{4pt}\\n\",\n \" \\\\caption{Performance comparing {\\\\selfanchor} with and without attention steering}\\n\",\n \" \\\\resizebox{1\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{ll|ccc|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{2.5}{*}{\\\\textbf{Model}} & \\\\multirow{2.5}{*}{\\\\textbf{Method}} & \\\\multicolumn{3}{c|}{Math} & \\\\multicolumn{2}{c|}{CommonSense} & \\\\multirow{2.5}{*}{BBH} \\\\\\\\\\n\",\n \" \\\\cmidrule(lr){3-5} \\\\cmidrule(lr){6-7}\\n\",\n \" & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{2}{*}{Llama3.1-8B} \\n\",\n \" & {\\\\selfanchor} (w/o attention steering) & 73.01 & 53.15 & 40.90 & 71.17 & 35.28 & 52.77\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 76.72 & 55.51 & 52.50 & 73.54 & 40.01 & 58.53 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{2}{*}{Phi-4-mini-4B} \\n\",\n \" & {\\\\selfanchor} (w/o attention steering) & 78.77 & 58.66 &55.50 & 68.60 & 38.83 & 57.44 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 88.02 & 68.50 & 59.00 & 68.69 & 49.47 & 62.42\\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:ablation structure}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{An example of BBH. Incorrect inferences are highlighted in \\\\lightred{red}. Correct ones are highlighted in \\\\lightgreen{green}.}\\n\",\n \"\\\\resizebox{\\\\linewidth}{!}{\\n\",\n \"\\\\begin{tabular}{l l}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{2}{*}{\\\\textbf{Prompt}} %& \\\\textit{``Explain the antecedent of the pronoun (which thing the pronoun refers to), or state that it is ambiguous.}\\\\\\\\\\n\",\n \" & \\\\textit{\\\\textbf{Sentence: The secretary came to the analyst's office and helped her to book a flight.}} \\\\\\\\\\n\",\n \" & \\\\textit{\\\\textbf{Options: (A) Helped the secretary book a flight (B) Helped the analyst book a flight (C) Ambiguous}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{\\\\selfanchor} & \\\\{ \\\"Step 1: Identify the pronoun\\\": \\\"The pronoun is 'her'.\\\",\\\\\\\\\\n\",\n \" \\\\text{(w/o attention steering)} & \\\"Step 2: Determine the antecedent of the pronoun\\\": \\\"\\\\lightred{The antecedent of 'her' is the subject of the sentence, which is 'The secretary'}\\\", \\\\\\\\\\n\",\n \" \\\\textbf{} & \\\"Step 3: Analyze the sentence structure\\\": The subject of the sentence is 'The secretary', and the verb is 'came'. The object of the \\\\\\\\\\n\",\n \" & \\\\:\\\\:\\\\:\\\\: verb 'came' is 'to the analyst's office'. The verb 'helped' has the pronoun 'her' as its object.\\\",\\\\\\\\\\n\",\n \" & \\\"Step 4: Determine the antecedent of the pronoun based on the sentence structure\\\": \\\"Based on the sentence structure, the antecedent \\\\\\\\\\n\",\n \" & \\\\:\\\\:\\\\:\\\\: of the pronoun \\\\lightred{'her' is the subject of the sentence, which is 'The secretary'}.\\\",\\\\\\\\\\n\",\n \" & \\\"Step 5: Choose the correct option\\\": \\\"The correct option is \\\\lightred{(A) Helped the secretary book a flight.}\\\"\\\\}\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{{\\\\selfanchor}} & \\\\{ \\\"Step 1: Identify the pronoun\\\": \\\"The pronoun in the sentence is 'her'.\\\",\\\\\\\\\\n\",\n \" & \\\"Step 2: Determine the antecedent of the pronoun\\\": \\\"To find the antecedent, we need to look for the noun that 'her' refers to. In this\\\\\\\\\\n\",\n \" & \\\\:\\\\:\\\\:\\\\: case, \\\\lightgreen{'her' is a possessive pronoun that refers to the analyst.}\\\", \\\\\\\\\\n\",\n \" & \\\"Step 3: Analyze the sentence structure\\\": \\\"The subject of the sentence is 'The secretary', and the object of the verb 'helped' is 'her'\\\",\\\\\\\\\\n\",\n \" & \\\"Step 4: Identify the antecedent based on the sentence structure\\\": \\\"\\\\lightgreen{'her' refers to the analyst, not the secretary.}\\\",\\\\\\\\\\n\",\n \" & \\\"Step 5: Choose the correct option\\\": \\\"Since 'her' refers to the analyst, the correct option is \\\\lightgreen{(B) Helped the analyst book a flight.}\\\" \\\\}\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:An example of anchor}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \" \\\\begin{table*}[ht]\\n\",\n \" \\\\scriptsize\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{14pt}\\n\",\n \"\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Mean selection ablation study. Results show accuracy (\\\\%) on AQuA-RAT and T4D benchmarks.}\\n\",\n \" \\\\begin{tabular}{ll|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\textbf{Method} & AQuA-RAT & T4D \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{LLaMA3.1-8B} & CoT & 50.79 & 26.77 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} (Harmonic) & \\\\textbf{55.51} & \\\\textbf{40.01} \\\\\\\\\\n\",\n \" & {\\\\selfanchor} (Geometric) & 55.11 & 35.28 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} (Arithmetic) & 54.72 & 35.99 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{4}{*}{Phi-4-mini} & CoT & 61.81 & 39.54\\\\\\\\\\n\",\n \" & {\\\\selfanchor} (Harmonic) & \\\\textbf{68.50} & \\\\textbf{49.47}\\\\\\\\\\n\",\n \" & {\\\\selfanchor} (Geometric) & 67.72 & 49.11 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} (Arithmetic) & 67.71 & 48.40 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\label{tab:means_selection}\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[ht]\\n\",\n \" \\\\scriptsize\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{14pt}\\n\",\n \" \\\\caption{Alternative anchoring design comparison. Results show accuracy (\\\\%) on AQuA-RAT and T4D benchmarks.}\\n\",\n \" \\\\begin{tabular}{ll|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\textbf{Method} & AQuA-RAT & T4D \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{LLaMA3.1-8B} & CoT & 50.79 & 26.77 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} & \\\\textbf{55.51} & \\\\textbf{40.01} \\\\\\\\\\n\",\n \" & Anchor to All Prior Steps & 53.54 & 32.62\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Phi-4-mini} & CoT & 61.81 & 39.54\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & \\\\textbf{68.50} & \\\\textbf{49.47}\\\\\\\\\\n\",\n \" & Anchor to All Prior Steps & 67.32 & 47.34\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\label{tab:alternative_design}\\n\",\n \"\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \" \\\\scriptsize\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{4pt}\\n\",\n \" \\\\caption{BBH details}\\n\",\n \" \\\\resizebox{1.1\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{llcccccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{2}{*}{\\\\textbf{Model}} & \\\\multirow{2}{*}{\\\\textbf{Method}} & \\\\multicolumn{5}{c}{\\\\textbf{BBH}} \\\\\\\\\\n\",\n \" \\\\cmidrule(lr){3-8}\\n\",\n \" & & \\\\textbf{disambiguation\\\\_qa} & \\\\textbf{causal\\\\_judgement} & \\\\textbf{date\\\\_understanding} & \\\\textbf{logical\\\\_deduction} & \\\\textbf{salient\\\\_translation\\\\_error\\\\_detection} & \\\\textbf{snarks}\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Llama3.1-8B} & CoT & 100 & 91/187 & 182 & 67 & 110 & 125\\\\\\\\\\n\",\n \" & PS+ & 138 & 108 & 136 & 78 & 124 & 122 \\\\\\\\\\n\",\n \" & re-read & 124 & 98 & 190 & 85 & 121 & 127\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 152 & 100 & 160 & 128 & 132 & 127\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Llama3.2-3B} & CoT & 88/250 & 71 & 102 & 34 & 95 & 89\\\\\\\\\\n\",\n \" & PS+ & 104 & 63 & 97 & 86 & 98 & 105 \\\\\\\\\\n\",\n \" & re-read & 74 & 84 & 127 & 40 & 89 & 105\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 131 & 101 & 131 & 101 & 96 & 129\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Phi4-mini-4B} & CoT & 162/250 & 113 & 154 & 114 & 149 & 134\\\\\\\\\\n\",\n \" & PS+ & 160 & 126 & 138 & 130 & 136 & 124\\\\\\\\\\n\",\n \" & re-read & 162 & 115 & 165 & 113 & 135 & 148\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 152 & 116 & 174 & 128 & 140 & 142\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Qwen3-mini-4B} & CoT & 183/250 & 121 & 174 & 208 & 167 & 148\\\\\\\\\\n\",\n \" & PS+ & 179 & 108 & 165 & 207 & 160 & 150 \\\\\\\\\\n\",\n \" & re-read & 179 & 121 & 203 & 230 & 147 & 154\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 185 & 115 & 193 & 224 & 161 & 150\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Phi-4-15B} & CoT & 180 & 120 & 203 & 169 & 152 & 160\\\\\\\\\\n\",\n \" & PS+ & 180 & 117 & 140 & 186 & 155 & 156\\\\\\\\\\n\",\n \" & re-read & 179 & 120 & 221 & 191 & 158 & 154 \\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 176 & 122 & 218 & 203 & 148 & 161 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multirow{3}{*}{Qwen3-30B} & CoT & 105 & 125 & 182 & 185 & 172 & 155 \\\\\\\\\\n\",\n \" & PS+ & 114 & 122 & 172 & 181 & 165 & 156\\\\\\\\\\n\",\n \" & re-read & 113 & 125 & 185 & 210 & 174 & 156\\\\\\\\\\n\",\n \" & {\\\\selfanchor} & 110 & 123 & 196 & 200 & 160 & 157\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}}\\n\",\n \" \\\\label{tab:truth}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n\\documentclass{article} % For LaTeX2e\n\\usepackage{iclr2026_conference,times}\n\n% Optional math commands from https://github.com/goodfeli/dlbook_notation.\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n% Figure reference, capital. For start of sentence\n\\def\\Figref#1{Figure~\\ref{#1}}\n\\def\\twofigref#1#2{figures \\ref{#1} and \\ref{#2}}\n\\def\\quadfigref#1#2#3#4{figures \\ref{#1}, \\ref{#2}, \\ref{#3} and \\ref{#4}}\n% Section reference, lower-case.\n\\def\\secref#1{section~\\ref{#1}}\n% Section reference, capital.\n\\def\\Secref#1{Section~\\ref{#1}}\n% Reference to two sections.\n\\def\\twosecrefs#1#2{sections \\ref{#1} and \\ref{#2}}\n% Reference to three sections.\n\\def\\secrefs#1#2#3{sections \\ref{#1}, \\ref{#2} and \\ref{#3}}\n% Reference to an equation, lower-case.\n\\def\\eqref#1{equation~\\ref{#1}}\n% Reference to an equation, upper case\n\\def\\Eqref#1{Equation~\\ref{#1}}\n% A raw reference to an equation---avoid using if possible\n\\def\\plaineqref#1{\\ref{#1}}\n% Reference to a chapter, lower-case.\n\\def\\chapref#1{chapter~\\ref{#1}}\n% Reference to an equation, upper case.\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n% Reference to a range of chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\usepackage{hyperref}\n\\usepackage{url}\n\n\\usepackage{graphicx}\n\\usepackage{subcaption}\n\\usepackage{soul}\n\\usepackage{hyperref}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{tcolorbox}\n\\usepackage{booktabs}\n\\usepackage{multicol}\n\\usepackage{multirow}\n\\usepackage{algorithm}\n\\usepackage{algpseudocode}\n\\usepackage{xcolor}\n\\usepackage{colortbl}\n\n\\title{{\\selfanchor}: Large Language Model Reasoning via Step-by-step Attention Alignment}\n\n% Authors must not appear in the submitted version. They should be hidden\n% as long as the \\iclrfinalcopy macro remains commented out below.\n% Non-anonymous submissions will be rejected without review.\n\n\\author{Hongxiang Zhang\\& Yuan Tian \\& Tianyi Zhang \\\\\nDepartment of Computer Science\\\\\nPurdue University\\\\\nLafayette, IN 47907, USA \\\\\n\\texttt{\\{hxxzhang,tian211,tianyi\\}@purdue.edu} \\\\\n}\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to \\LaTeX{} to determine where to break\n% the lines. Using \\AND forces a linebreak at that point. So, if \\LaTeX{}\n% puts 3 of 4 authors names on the first line, and the last on the second\n% line, try using \\AND instead of \\And before the third author name.\n\\definecolor{lightblue}{RGB}{255, 255, 255}\n\\definecolor{lightgreen}{RGB}{210, 240, 210}\n\\definecolor{lightgray}{RGB}{225, 225, 225}\n\\definecolor{lightred}{rgb}{1.0, 0.8, 0.8}\n\\newcommand{\\todo}[1]{\\sethlcolor{yellow}\\hl{#1}}\n\\newcommand{\\lightgreen}[1]{\\sethlcolor{lightgreen}\\hl{\\textbf{#1}}}\n\\newcommand{\\lightblue}[1]{\\sethlcolor{lightblue}\\hl{#1}}\n\\newcommand{\\lightgray}[1]{\\sethlcolor{lightgray}\\hl{#1}}\n\\newcommand{\\lightred}[1]{\\sethlcolor{lightred}\\hl{#1}}\n\\newcommand{\\green}[1]{\\sethlcolor{green}\\hl{#1}}\n\\newcommand{\\red}[1]{\\sethlcolor{red}\\hl{#1}}\n\\newcommand{\\appsectionautorefname}{Appendix}\n\\newcommand{\\selfanchor}{\\textsc{Self-Anchor}}\n\n\n\n\\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission.\n\\begin{document}\n\n\n\\maketitle\n\n\\begin{abstract}\n% Recent large language models demonstrate remarkable performance on complex reasoning tasks. Nevertheless, LLMs remain prone to attention misalignment as reasoning progresses, especially for complex tasks requiring long reasoning chains. \nTo solve complex reasoning tasks for Large Language Models (LLMs), prompting-based methods offer a lightweight alternative to fine-tuning and reinforcement learning.\nHowever, as reasoning chains extend, critical intermediate steps and the original prompt will be buried in the context, receiving insufficient attention and leading to errors. \nIn this paper, we propose {\\selfanchor}, a novel pipeline that leverages the inherent structure of reasoning to steer LLM attention. \\selfanchor\\ decomposes reasoning trajectories into structured plans and automatically aligns the model's attention to the most relevant inference steps, allowing the model to maintain focus throughout generation. \nOur experiment shows that {\\selfanchor} outperforms SOTA prompting methods across six benchmarks. \nNotably, {\\selfanchor} significantly reduces the performance gap between ``non-reasoning'' models and specialized reasoning models, with the potential to enable most LLMs to tackle complex reasoning tasks without retraining.\n\\end{abstract}\\section{Introduction}\n\nReasoning abilities in Large language models (LLMs) are key to solve complex tasks, from mathematical problem solving to logical inference and multi-step reasoning~\\citep{ahn-etal-2024-large,huang-chang-2023-towards,cheng2025empowering}.\nRecent LLMs, such as OpenAI o1~\\citep{gpt_o1} and DeepSeek-R1~\\citep{deepseekai2025deepseekr1incentivizingreasoningcapability}, have further advanced their reasoning capabilities through fine-tuning and reinforcement learning~\\citep{RL1, RL2}.\nHowevere, despite their impressive performance, they require substantial computation and a considerable amount of training data.\n\n\nAs an alternative, prompting-based methods emerged to induce LLMs' inherent reasoning capabilities at test time without updating model parameters. \nMethods such as Self-Refine~\\citep{madaan2023self} and ReAct~\\citep{yao2023react} facilitate reasoning by iteratively expanding and refining the generation process. \nMethods like Self-planning~\\citep{jiang2024self}, Plan-and-Solve~\\citep{wang2023plan}, and Re-Reading~\\citep{xu2024re} explicitly decompose complex problems before solving them. \nHowever, a tradeoff of being training-free is that these prompting-based methods necessitate long reasoning chains because they depend on iterative generation or explicit planning.\nWhile this can be seen as the cost of training-free methods, recent studies have revealed another issue: long-context reasoning can cause severe attention misalignmentt issue~\\citep{gu2024attention,chi2023attention,liu-etal-2024-lost,sun2024massive,yao2021self, tian2024selective, attention_decay, context_rot}.\n\nAs a key component in LLMs, the attention mechanism~\\citep{transformer} enables LLMs to selectively integrate relevant information from preceding context.\nHowever, LLM attention is an inherently limited resource. \nAs the generation proceeds, the number of preceding tokens increases, making it increasingly difficult for the model to pay attention to the relevant context, especially when the context is long and complex~\\citep{tian2024selective, attention_decay, context_rot}. \nIn such cases, even with the ability to correctly predict next token based on the corresponding context, LLMs may attend to irrelevant context, thereby generating off-topic or wrong results.\nAs shown in \\autoref{fig:main}, the intermediate reasoning steps and most of the original prompt will be buried in the middle, receive insufficient attention, and consequently, introduce errors~\\citep{liu-etal-2024-lost}.\n\nTo mitigate such attention misalignment issues, recent works explicitly steer LLM attention to influence generation behavior.\nFor example, PASTA~\\citep{zhang2023tell} adjusts the self-attention distribution within a subset of attention heads, while SPA~\\citep{tian2024selective} simulates attention steering through logit arithmetic.\nHowever, these methods mainly focus on developing robust attention steering mechanisms, while requiring humans to specify which tokens the model should pay more attention to. Since such tokens can vary significantly at different generation steps and across different tasks, it is unrealistic for humans to manually decide for every generation step.\n\n\n\\begin{figure*}[ht]\n\\centering\n \\centering\n \\includegraphics[width=\\linewidth]{figure/overview.png}\n \\caption{Comparison between existing reasoning methods and {\\selfanchor}. Due to inherent attention patterns, existing reasoning methods may easily overlook intermediate reasoning and make mistakes. \\selfanchor\\ addresses this by decomposes the task into plans, and takes each plan as a component for attention alignment.}\n % \\vspace{-0.2cm}\n \\label{fig:main}\n\\end{figure*}\n\nTo reduce human efforts, we introduce {\\selfanchor}, a novel generative pipeline that explicitly aligns LLM attention by leveraging the inherent structure of a reasoning chain. \n{\\selfanchor} builds on two key insights: (1) complex reasoning problems can be decomposed into structured plans, and (2) each decomposed plan can naturally serve as a component for attention alignment. As illustrated in \\autoref{fig:main}, {\\selfanchor} decomposes the original prompt into plan steps with corresponding reasoning steps. During generation, it automatically selects and steers the model attention to the prompt and the corresponding plan. \nThis enables the LLM to keep attending to both the problem statement and immediate reasoning goals, thereby preventing attention mistakes among continuously expanding reasoning steps.\n\n\n\nWe evaluate {\\selfanchor} on six benchmarks and six base LLMs with varying sizes, and compare it with SOTA prompting methods.\nThe evaluation benchmarks include three mathematical reasoning benchmarks (GSM8K, AQuA, MATH), two commonsense benchmarks (StrategyQA \\& Things for Doing), and an multi-task evaluation benchmark (BIG-Bench Hard, BBH).\n{\\selfanchor} consistently improves accuracy on all the settings, outperforming all the prompting-based baselines by at least 5.44\\% on average.\nIn addition, we demonstrate that {\\selfanchor} achieves performance on par with five reasoning models but with substantially lower cost and complexity, suggesting a practical alternative to applying reinforcement learning to enhance the reasoning capability of LLMs.\n\\section{Method}\n\\subsection{{\\selfanchor}}\n\n\n\\textbf{Reasoning as the Scaffold for Attention Alignment.}\n % How to build the correspondence, how to design the decoder. Where to anchor\n We are inspired by the observation that planning offers a natural scaffold for attention alignment. Specifically, planning helps the model to understand and break down complex problems into subproblems~\\citep{jiang2024self,wang2023plan}. Each decomposed plan step provides a correspondence to subsequent reasoning, which can naturally serve to guide attention alignment.\n Building on this idea, we design {\\selfanchor} to leverage the inherent structure in the reasoning chain to conduct the attention alignment. {\\selfanchor} prompts the model to decompose the prompt into plans, and then generates and corresponding reasoned solutions with explicit attention steering.\n % The main purpose of converting the original prompt into multiple structured format is to separate the reasoning process and facilitate attention alignment independently.\"\n \n\n \n\\textbf{Attention Steering Mechanism.}\nSeveral studies have explored methods for attention steering~\\citep{zhang2023tell, shi2023toast, tian2024selective}. These methods primarily address \\textit{how to steer the model attention}. By contrast, our work focuses on an orthogonal problem---\\textit{how to automatically select relevant context} and uses these methods as a plug-and-play component. In this work, we choose Selective Prompt Anchoring (SPA)~\\citep{tian2024selective} as the underlying attention steering mechanism, since it is low-cost and efficient. \nWe briefly summarize how SPA works here and refer interested readers to the original paper for more technical details.\n\n%Inspired by the anchoring effect in psychology, where individuals’ decisions are influenced by information presented prior to decision-making~\\citep{furnham2011literature}, SPA \\textit{anchors} the selected tokens within the LLMs' attention so the model keeps aware of them.\nGiven a set of tokens that an LLM should pay more attention to, SPA simulates attention steering through logit arithmetic. Specifically, it estimates the influence of selected tokens by contrasting the original logits with the logits when these tokens are masked, and then add this influence back to the original logits. \nThe steered logit is represented by the linear combination of the original logits and the logits with selected tokens masked, where $\\omega_i$ is a coefficient determining the attention steering strength. Formally, it can be represented as\n\\begin{equation}\n\\label{formula_spa}\n \\mathbf{logits}_i^{\\text{steered}} = \\omega_i \\cdot \\mathbf{logits}_i^{\\text{original}} + (1 - \\omega_i) \\cdot \\mathbf{logits}_i^{\\text{mask}}.\n\\end{equation}\n\n\n\\textbf{Selection of Attention Alignment.} \nBuilding on this attention steering mechanism, we propose a novel strategy that dynamically aligns model attention to changing context tokens during generation.\n\nAccording to the attention sink phenomenon~\\citep{xiao2023efficient}, the model already attends strongly to initial tokens and the recent generated tokens. \nOur method complementarily steer the model attention to the planning steps when conducting the corresponding reasoning.\nFurthermore, {\\selfanchor} additionally steers the model attention to the question in the prompt, which serves as the core generation purpose, ensuring the model keeps focusing on the problem statement.\n\\footnote{Alternative anchoring strategies are discussed in \\autoref{appendix: alternative design}}\\label{Automatic Anchoring Strategy}\n\n\nFormally, we use $f(x, \\textbf{S})$ to represent the generation function with attention steering, where $x$ represents the entire preceding tokens and $\\textbf{S}$ represents the selected tokens where the model's attention should be steered to.\nLet $\\mathrm{sys}$ denote the system prompt together with high-level background instructions \n(e.g., \\textit{``You are a helpful assistant''}), \nand let $Q$ denote the core question under consideration. \nThus, the original prompt can be represented as $\\mathrm{concat}(\\mathrm{sys},\\, Q)$.\nThe generation of {\\selfanchor} consists of two parts: the \\emph{planning} and the corresponding \\emph{reasoning}.\n\nAt step $i$, the planning is generated by\n\\begin{equation}\n\\mathrm{plan}_i \n= f\\!\\Bigl(\n \\mathrm{concat}\\bigl(\\mathrm{sys},\\, Q,\\, \\mathrm{plan}_1,\\, \\mathrm{plan}_2,\\, \\ldots,\\, \\mathrm{plan}_{i-1}\\bigr),\\;\n \\textbf{\\textit{Q}}\n\\Bigr).\n\\end{equation}\nThe planning is generated by\n\\begin{equation}\n\\mathrm{reason}_i \n= f\\!\\Bigl(\n \\mathrm{concat}\\bigl(\\mathrm{sys},\\, Q,\\, \\mathrm{plan}_1,\\, \\mathrm{plan}_2,\\, \\ldots,\\, \\mathrm{plan}_{i-1}\\bigr),\\;\n \\mathrm{\\textbf{concat}}(\\textbf{\\textit{\\,Q},}\\,\\; \\mathrm{\\textbf{plan}_i)}\n\\Bigr).\n\\end{equation}\nThe generation proceeds by alternating between $\\mathrm{plan}_i$ and $\\mathrm{reason}_i$, until the process terminates with the final result.\n\n \n\\textbf{Dynamic Tuning of Attention Alignment Strength.}\n \\todo{}\n As reasoning trajectories progress, the required degree of attention alignment may vary at different steps. According to prior work~\\citep{confidence1, confidence2}, LLMs' predicted probability distribution can be viewed as a confidence signal to determine their prediction quality. High-confidence prediction suggests reliable generation, implying a correct attention, whereas low confidence may indicate unreliable generation and attention drift. Therefore, we introduce a step-level anchoring strength $\\omega_i$ that is dynamically adjusted based on model confidence.\\footnote{Our strength adjustment strategy builds upon the confidence-modulated strength strategy in SPA~\\citep{tian2024selective}. While SPA adjusts the strength based on confidence for each logit at the vocabulary level, we introduce an additional factor to adjust the strength for each step.}\n Let $P_i = \\{p_1, p_2, \\ldots, p_m\\}$ represent the predicted probability at step $i$. \n We calculate the confidence score using the harmonic mean of $P_i$\n \\begin{equation}\n p_{\\text{avg}} = \\frac{n}{\\sum_{i=1}^{n} \\frac{1}{p_i}} \\;\\;.\n \\end{equation}\n This confidence score serves as an additional factor to scale the attention steering strength $w_i$ in \\autoref{formula_spa}.\n We discuss detailed design choices and experiments in Appendix~\\ref{appendix:mean}.\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n % The harmonic mean emphasizes the impact of low values, ensuring that potential attention drift is detected\\footnote{We conducted ablation studies comparing different averaging methods at \\autoref{appendix: mean sele}}. This confidence score is then used to modulate a base weight $\\omega_{\\textit{base}}$:\n % \\begin{equation}\n % \\omega_i = \\frac{\\omega_{\\text{base}}}{p_{avg}}\n % \\end{equation}\n\n % In summary, {\\selfanchor} explicitly decomposes problems into structured plan–reasoning pairs, automatically realigns attention, and dynamically adjust anchor strength based on the confidence.\n\n\\section{Experiments}\n\n\\subsection{Benchmarks}\n% specify which benchmark corresponds to which type\nWe evaluated {\\selfanchor} on six benchmarks. The first three benchmarks incorporate GSM8K~\\citep{cobbe2021training}, AQuA~\\citep{ling2017program}, and MATH~\\citep{hendrycks2021measuring} represent arithmetic reasoning. The second two benchmarks include StrategyQA~\\citep{geva2021did}, and Thinking for Doing (T4D)~\\citep{zhou2023far} represent commonsense reasoning. Lastly, we evaluated on a subset of BIG-Bench Hard~(BBH)~\\citep{suzgun2022challenging}, which covers a diverse range of reasoning problems spanning the multi-step algorithmic reasoning, natural language understanding, the application of world knowledge, and Multilingual Knowledge. We report final answer accuracy across all benchmarks\\footnote{Prompt templates and evaluation details are provided in \\autoref{appendix: Implementation and evaluation details}.}.\n\n\\subsection{Models and Baselines}\n\\textbf{Base Models.} We conduct our experiments on six non-reasoning LLMs spanning various scales. \nFor non-reasoning models, we select Llama-3.1-8B-Instruct~\\citep{grattafiori2024llama}, Llama-3.2-3B-Instruct~\\citep{grattafiori2024llama}, Phi-4-mini-instruct~\\citep{abouelenin2025phi}, Qwen3-4B-Instruct-2507~\\citep{qwen3technicalreport}, Phi-4~\\citep{abdin2024phi}, and Qwen3-30B-A3B-Instruct-2507~\\citep{qwen3technicalreport}.\n\n\n\\textbf{Comparison Baselines.}\nWe compare our method against three representative prompting methods for LLM reasoning.\nFirst, we include \\textbf{CoT}~\\citep{wei2022chain,kojima2022large}, a widely used baseline that models are prompted to generate a reasoning process leading to the final answer. \nSecond, we include \\textbf{Plan-and-Solve+ (PS+)}~\\citep{wang2023plan}, a prompting method that models are prompted to first generate a plan and then solve the problem. \nThird, we include \\textbf{Re-Reading (RE2)}~\\citep{xu2024re}, which asks the model to read the question again and then solve the problem.\n\nFurthermore, we consider five state-of-the-art reasoning LLMs as baselines to see if non-reasoning LLMs combined with \\selfanchor\\ achieve competitive performance against reasoning models. The reasoning models include Phi-4-mini-reasoning~\\citep{abouelenin2025phi}, Qwen3-4B-Thinking-2507~\\citep{qwen3technicalreport}, DeepSeek-R1-Distill-Llama-8B~\\citep{deepseekai2025deepseekr1incentivizingreasoningcapability}, Phi-4-reasoning~\\citep{abdin2024phi}, and Qwen3-30B-A3B-Thinking-2507~\\citep{qwen3technicalreport}.\n\n% Last but not least, we consider stronger test-time scaling methods to evaluate the efficiency of {\\selfanchor}. We compare both performance and inference efficiency against the following methods on a subset of tasks.\n\n% \\textbf{Chain-of-Thought Self-Consistency (CoT-SC)}~\\citep{wei2022chain}, which samples multiple CoT outputs and aggregates answers through majority voting; \\textbf{Tree-of-Thought (ToT)}~\\citep{yao2023tree}, which explores multiple reasoning paths through deliberate tree search; and \\textbf{Self-Refine}~\\citep{madaan2023self}, which iteratively refines with self feedback.\n\n\\subsection{Main Results}\n\\label{main result}\n\\textbf{Mathematical Reasoning.}\n Arithmetic reasoning represents one of the most challenging aspects of LLM reasoning capabilities. As shown in \\autoref{tab:main}, {\\selfanchor} consistently improves accuracy across three arithmetic benchmarks. \n These gains reach over 10\\% improvements on GSM8K, over 5\\% on AQuA, and up to 8\\% on MATH across most models, outperforming all competing methods. While PS+ and RE2 also demonstrate potential for enhancing mathematical reasoning performance, our experiments show performance degradation on certain LLMs, suggesting limited generalization capabilities.\n \n Interestingly, the three benchmarks span increasing difficulty levels, from grade-school problems~\\citep{cobbe2021training} to GMET/GRE \\citep{ling2017program} level and competition-level problems \\citep{hendrycks2021measuring}. {\\selfanchor} demonstrates performance gain in all three benchmarks, suggesting superior generalization capabilities across diverse model architectures and reasoning complexity levels.\n\n\\textbf{Commonsence Reasoning.}\n StrategyQA requires multi-hop reasoning over commonsense knowledge. As detailed in \\autoref{tab:main}, {\\selfanchor} persistently improves accuracy across six evaluated LLMs. In contrast, PS+ and RE2 occasionally outperform the baseline CoT method.\n\n For T4D, a grounded social agent reasoning task requires mental state reasoning to determine appropriate actions. {\\selfanchor} demonstrates significant performance gains over 9\\% in four LLMs. In comparison, both PS+ and RE2 exhibit mixed performance; they tend to be more effective in larger models. These findings highlight the challenge of applying generic prompting strategies to specialized reasoning domains.\n\n\\begin{table}\n \\scriptsize\n \\centering\n \\setlength{\\tabcolsep}{4pt}\n \\caption{Evaluation results on six benchmarks. Best results are shown in \\lightgreen{green}, and those indicating a performance drop compared to standard greedy decoding are shown in \\lightgray{grey}.}\n \\resizebox{\\textwidth}{!}{\n \\begin{tabular}{ll|ccc|cc|c}\n \\toprule\n \\multirow{2.5}{*}{\\textbf{Model}} & \\multirow{2.5}{*}{\\textbf{Method}} & \\multicolumn{3}{c|}{Math} & \\multicolumn{2}{c|}{CommonSense} & \\multirow{2.5}{*}{BBH} \\\\\n \\cmidrule(lr){3-5} \\cmidrule(lr){6-7}\n & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\n \\midrule\n \\multirow{4}{*}{Llama3.2-3B} & CoT & 63.84& 46.06 & 42.5 & 66.64 & 32.98 & 35.09 \\\\\n & PS+ & \\lightblue{70.62 (+6.78)} & \\lightgray{38.58 (-7.48)} & \\lightblue{44.50 (+2.00)} & \\lightgray{62.79 (-3.85)} & \\lightgray{31.81 (-1.17)} & \\lightblue{40.51 (+5.42)} \\\\\n & RE2& \\lightgray{57.38 (-6.46)} & \\lightblue{47.28 (+1.22)} & \\lightgreen{45.00 (+2.50)} & \\lightgray{65.03 (-1.61)} & \\lightgray{30.32 (-2.66)} & 38.02 (+2.93) \\\\\n & \\textbf{{\\selfanchor}} & \\lightgreen{77.86 (+14.02)} & \\lightgreen{48.43 (+2.37)} & \\lightgreen{45.00 (+2.50)} & \\lightgreen{67.55 (+0.91)} & \\lightgreen{43.79 (+10.81)} & \\lightgreen{50.48 (+15.39)} \\\\\n \\midrule\n \\multirow{4}{*}{Phi-4-mini-4B} & CoT & 75.36 & 61.81 & 51.00 & 67.03 & 39.54 & 60.51\\\\\n & PS+ & \\lightblue{87.17 (+11.81)} & \\lightblue{62.02 (+0.21)} & \\lightblue{54.50 (+3.50)} & \\lightgray{58.86 (-8.17)} & {41.16 (+1.62)} & \\lightgray{59.63 (-0.88)} \\\\\n & RE2& {85.75 (+10.39)} & \\lightgray{59.06 (-2.75)} & 51.50 (+0.50) & \\lightgray{61.83 (-5.20)} & \\lightblue{44.50 (+4.96)} & \\lightblue{61.39 (+0.88)} \\\\\n & \\textbf{{\\selfanchor}} & \\lightgreen{88.02 (+12.66)} & \\lightgreen{68.50 (+6.69)} & \\lightgreen{59.00 (+8.00)} & \\lightgreen{68.69 (+1.66)} & \\lightgreen{49.47 (+9.93)} & \\lightgreen{62.42 (+1.91)} \\\\\n \\midrule\n \\multirow{4}{*}{Qwen3-4B} & CoT & 86.66 & 73.62 & 82.00 & 68.03 & 70.21 & 73.33\\\\\n & PS+ & \\lightgray{82.79 (-3.87)} & \\lightgray{71.65 (-1.97)} & \\lightblue{83.50 (+1.50)} & 68.56 (+0.53) & \\lightgray{59.82 (-10.39)} & \\lightgray{70.99 (-2.34)} \\\\\n & RE2& \\lightgray{79.98 (-6.68)} & \\lightblue{75.98 (+2.36)} & 82.50 (+0.50) & \\lightblue{69.83 (+1.80)} & \\lightgray{67.02 (-3.19)} & \\lightgreen{75.75 (+2.42)} \\\\\n & \\textbf{{\\selfanchor}} & \\lightgreen{87.26 (+0.60)} & \\lightgreen{79.92 (+6.30)} & \\lightgreen{86.50 (+4.50)} & \\lightgreen{70.13 (+2.10)} & \\lightgreen{71.56 (+1.35)} & \\lightblue{75.31 (+1.98)} \\\\ \n \\midrule\n \\multirow{4}{*}{Llama3.1-8B} & CoT & 61.85 & 50.79 &44.50 & 70.24 & 26.77 & 49.45 \\\\\n & PS+ & \\lightblue{62.24 (+0.39)} & \\lightgray{48.65 (-2.14)} & \\lightblue{47.00 (+2.50)} & \\lightgray{65.85 (-4.39)} & \\lightblue{28.79 (+2.02)} & 51.72 (+2.27) \\\\\n & RE2 & \\lightgray{57.68 (-4.17)} & \\lightblue{51.97 (+1.18)} & 44.50 (+0.00) & \\lightgray{69.74 (-0.50)} & 28.55 (+1.78) & \\lightblue{54.58 (+5.13)} \\\\\n & \\textbf{{\\selfanchor}} & \\lightgreen{76.72 (+14.87)} & \\lightgreen{55.51 (+4.72)} & \\lightgreen{52.50 (+8.00)} & \\lightgreen{73.54 (+3.30)} & \\lightgreen{40.01 (+13.24)} & \\lightgreen{58.53 (+9.08)} \\\\\n \\midrule\n \\multirow{4}{*}{Phi-4-15B} & CoT & 73.16 & 68.11& 74.50 & 77.51 & 73.94 & 72.08\\\\\n & PS+ & \\lightblue{79.07 (+5.91)} & \\lightblue{72.75 (+4.64)} & \\lightgray{72.50 (-2.00)} & \\lightgray{75.59 (-1.92)} & \\lightblue{76.24 (+2.30)} & \\lightgray{68.42 (-3.66)} \\\\\n & RE2 & {74.87 (+1.17)} & {69.29 (+1.18)} & \\lightgray{73.50 (-1.00)} & \\lightgray{76.90 (-0.61)} & {75.79 (+1.85)} & \\lightblue{74.94 (+2.86)} \\\\\n & \\textbf{{\\selfanchor}} & \\lightgreen{82.41 (+9.25)} & \\lightgreen{79.13 (+11.02)} & \\lightgreen{81.00 (+6.50)} & \\lightgreen{77.82 (+0.31)} & \\lightgreen{85.99 (+12.05)} & \\lightgreen{75.31 (+3.23)} \\\\\n \\midrule\n \\multirow{4}{*}{Qwen3-30B} & CoT & 84.46 & 81.10 & 78.00 & 78.60 & 84.92 & 67.69\\\\\n & PS+ & {85.11 (+0.65)} & \\lightgray{80.83 (-0.27)} & \\lightgray{73.50 (-4.50)} & 78.70 (+0.10) & \\lightgray{82.62 (-2.30)} & \\lightgray{66.67 (-1.02)}\\\\\n & RE2 & \\lightblue{87.21 (+2.75)} & \\lightblue{82.28 (+1.18)} & \\lightgray{76.00 (-2.00)} & \\lightblue{78.91 (+0.31)} & \\lightgreen{89.36 (+4.44)} & \\lightgreen{70.55 (+2.86)}\\\\\n & \\textbf{{\\selfanchor}} & \\lightgreen{87.41 (+2.95)} & \\lightgreen{83.46 (+2.36)} & \\lightgreen{87.00 (+9.00)} & \\lightgreen{79.65 (+1.05)} & \\lightblue{85.56 (+0.64)} & \\lightblue{69.30 (+1.61)}\\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{tab:main}\n\\end{table}\n\n \n\n\\textbf{BBH.}\n BBH aggregates challenging algorithmic and symbolic tasks. {\\selfanchor} demonstrates average performance gains ranging from 1.61\\% to 15.39\\%\\footnote{We detail the subtask performance in \\autoref{appendix:bbh}}. Among all sub-benchmarks, we find that tasks requiring tracking of intermediate reasoning benefit the most, for example \\textit{date understanding}, and \\textit{logical deduction}. We attribute this to {\\selfanchor}'s attention steering that augments critical reasoning steps and the original question throughout generation. In contrast, PS+ and RE2 show inconsistent improvements.\n\n % What are the takeaways?\n In summary, these results highlight two takeaways. First, while prompting strategies are effective in some tasks, they lack robustness across benchmarks and model architectures, tending to be more effective on larger LLMs and simpler reasoning tasks. This may be because larger models are more capable of following instructions and external guidance to align reasoning trajectories. Second, by integrating planning, structured reasoning, and automatic anchoring, {\\selfanchor} achieves consistent improvements across tasks, model sizes, and architectures, demonstrating both robustness and effectiveness.\n\n\\begin{table*}\n \\scriptsize\n \\centering\n \\setlength{\\tabcolsep}{4pt}\n \\caption{Evaluation comparison with thinking models}\n \\resizebox{0.78\\textwidth}{!}{\n \\begin{tabular}{ll|ccc|cc|c}\n \\toprule\n \\multirow{2.5}{*}{\\textbf{Model}} & \\multirow{2.5}{*}{\\textbf{Method}} & \\multicolumn{3}{c|}{Math} & \\multicolumn{2}{c|}{CommonSense} & \\multirow{2.5}{*}{BBH} \\\\\n \\cmidrule(lr){3-5} \\cmidrule(lr){6-7}\n & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\n \\midrule\n \\multirow{3}{*}{Phi-4-mini-4B} & CoT & 75.36 & 61.81 & 51.00 & 67.03 & 39.54 & 60.51\\\\\n & {\\selfanchor} & 88.02 & 68.50 & 59.00 & 68.69 & 49.47 & 62.42 \\\\\n & Reasoning & 81.27 & 60.62 & 75.00 & 66.38 & 45.04 & 59.85 \\\\\n % & {\\selfanchor} & \\todo{728} & 65.75 & & & 237\\\\\n \\midrule\n \\multirow{3}{*}{Qwen3-4B} & CoT & 86.66 & 73.62 & 82.00 & 68.03 & 70.21 & 73.33\\\\\n & {\\selfanchor} & 87.26 & 79.92 & 86.50 & 70.13 & 71.56 & 75.31\\\\\n & Reasoning & 83.24& 67.32 & 87.00 & 68.31 & 73.40 & 75.34 \\\\\n % & {\\selfanchor} & & 68.90 & & & \\\\\n \\midrule\n \\multirow{3}{*}{Llama3.1-8B} & CoT & 61.85 & 50.79 &44.50 & 70.24 & 26.77 & 49.45 \\\\\n & {\\selfanchor} & 76.72 & 55.51 & 52.50 & 73.54 & 40.01 & 58.53 \\\\\n & Reasoning & 73.62 & 62.99 & 72.50 & 65.41 & 48.58 & 64.98\\\\\n % & {\\selfanchor} & & 67.32 & & & 47.87\\\\\n \\midrule\n \\multirow{3}{*}{Phi-4-15B} & CoT & 73.16 & 68.11& 74.50 & 77.51 & 73.94 & 72.08 \\\\\n & {\\selfanchor} & 82.41 & 79.13 & 81.00 & 77.82 & 85.99 & 75.31 \\\\\n & Reasoning & 81.12 & 83.20 & 95.5 & 75.43 & 74.11 & 74.98 \\\\\n \\midrule\n \\multirow{3}{*}{Qwen3-30B} & CoT & 84.46 & 81.10 & 78.00 & 78.60 & 84.92 & 67.69 \\\\\n & {\\selfanchor} & 87.41 & 83.46 & 87.00 & 79.65 & 85.56 & 69.30 \\\\\n & Reasoning & 94.5& 80.31 & 85.00 & 77.26 & 80.96 & 76.54\\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{tab:thinking_comparison}\n\\end{table*}\n\n\\subsection{Can {\\selfanchor} Rival RL-enhanced Thinking Model?}\nRecent advances in reasoning capabilities have been dominated by reinforcement learning-enhanced ``thinking\" models that employ extensive internal reasoning chains during inference. However, these models are costly to fine-tune and require large-scale training data. This raises a question: \\textit{Can non-reasoning LLMs combined with {\\selfanchor} achieve competitive performance against reasoning models?} To investigate this question, we compare our method applied to non-reasoning LLMs against corresponding thinking models. Since thinking models typically require longer generated contexts to support their internal reasoning, we set 1.5x larger maximum token length than the non-reasoning models in our experiments.\n\nTable~\\ref{tab:thinking_comparison} presents our findings across mathematical reasoning, commonsense reasoning, and symbolic reasoning tasks. Remarkably, our method applied to non-thinking models achieves competitive or superior performance compared to RL-enhanced thinking models. Specifically, our approach closes the performance gap significantly with three arithmetic benchmarks in varying difficulties, achieving within 5\\% difference of most thinking models; On commonsense reasoning tasks and BBH, \\selfanchor\\ exceeds thinking model performance on most benchmarks and LLMs.\n\nNoteably, we observe that thinking models demonstrate superior performance on tasks where corresponding non-reasoning models show poor baseline performance. For example, Llama3.1 and Phi-4-mini show large gaps on MATH, and Llama3.1 underperforms on AQuA and BBH. In these settings, post-training with reinforcement learning significantly boosts performance in areas where models previously performed poorly. In contrast, for tasks where non-reasoning models already demonstrate strong performance, reinforcement learning provides limited improvement. This pattern is also observed in \\citet{kirk2023understanding}. Nevertheless, \\selfanchor\\ shows consistent performance improvements across all tasks and difficulty levels.\n\nIn summary, rather than learning implicit reasoning patterns through training, our approach leverages the inherent structure in the reasoning chain for attention alignment to improve the reasoning capabilities, yielding stable improvement across varying difficulty levels without additional training cost. These findings suggest that {\\selfanchor} can serve as an effective alternative to computationally expensive RL-enhanced reasoning.\n\n% {\\selfanchor} achieved superior performance compared to state-of-the-art prompting methods, we are committed to evaluating its efficiency against more powerful test-time scaling approaches, including CoT Self-Consistency (CoT+SC)~\\citep{wei2022chain}, Tree-of-Thought (ToT)~\\citep{yao2023tree}, and Self-Refine~\\citep{madaan2023self}. Here we examine on AQuA and T4D using Llama3.1-8B-Instruct and Phi-4-mini-Instruct. \n\n% \\begin{figure}[ht]\n% \\centering\n% \\begin{subfigure}[t]{0.48\\textwidth}\n% \\raggedright\n% \\includegraphics[height=3.8cm]{figure/t4d_efficiency.pdf}\n% \\caption{Accuracy and throughput comparison on T4D \\citep{zhou2023far}.}\n% \\label{fig:Reasoning Chain Length}\n% \\end{subfigure}\n% \\hfill\n% \\begin{subfigure}[t]{0.48\\textwidth}\n% \\raggedleft\n% \\includegraphics[height=3.8cm]{figure/aqua_efficiency.pdf}\n% \\caption{Accuracy and throughput comparison on AQuA \\citep{ling2017program}.}\n% \\label{fig:Reasoning Tasks Complexity}\n% \\end{subfigure}\n% \\caption{Efficiency analysis on Llama3.1-8B and Phi-4-mini.}\n% \\label{fig: efficiency}\n% \\end{figure}\n\n\n% As shown in \\autoref{fig: efficiency}, {\\selfanchor} achieves superior or comparable performance to other baselines, including inference-time scaling methods. From an efficiency perspective, darker colors represent higher throughput. {\\selfanchor} demonstrates higher computational efficiency than test-time scaling methods, including CoT-SC, ToT, and Self-Refine. Compared to prompting methods, {\\selfanchor} introduces minimal computational overhead while achieving significant performance improvements.\n\n% , {\\selfanchor} demonstrates strong performance across both effectiveness and efficiency dimensions, achieving competitive or better accuracy while requiring fewer computational resources than inference-time scaling methods.% \\section{Analysis}\n\n\n\n\\subsection{Which Types of Tasks Do {\\selfanchor} Help the Most?}\nTo understand which types of tasks {\\selfanchor} help the most, we analyze performance gains across task complexity. \nWe adapt the method for quantifying task complexity from \\citet{wu2025more,jin2024impact}, where each task is represented by an individual question in a benchmark. \nFor each benchmark, 200 questions are randomly sampled to compute the average accuracy per task across all experimented models. \nTask complexity is then defined as $1-\\text{accuracy}$\\footnote{Segmenting reasoning steps and task complexity details are provided in \\autoref{appendix: Implementation and evaluation details}.}, where lower accuracy indicates higher complexity.\n\n\\begin{figure}[ht]\n \\centering\n \\begin{subfigure}[t]{0.48\\textwidth}\n \\raggedright\n \\includegraphics[height=4.4cm]{figure/anchor_vs_reread_performance_gain.pdf}\n \\caption{Reasoning Tasks Complexity and performance gains comparison}\n \\label{fig:combinedl}\n \\end{subfigure}\n \\hfill\n \\begin{subfigure}[t]{0.48\\textwidth}\n \\raggedleft\n \\includegraphics[height=4.4cm]{figure/task_complexity_chain_length_box.pdf}\n \\caption{Reasoning Tasks Complexity and reasoning chain length comparison. The lower value represents the easier task.}\n \\label{fig:combinedr}\n \\end{subfigure}\n \\caption{Analysis of task complexity and reasoning chain length}\n \\label{fig:combined}\n\\end{figure}\n\n\\textbf{Reasoning Task Complexity.} First, we examine the relationship between task complexity and \\selfanchor's performance gains to understand how our method scales with task difficulty. We compare \\selfanchor's performance gains against RE2, a strong baseline identified in our main results (\\autoref{main result}). For each task, we compute performance gain as the difference in accuracy between the two methods.\n\nAs shown in \\autoref{fig:combinedl}, the box plot summarizes the distribution of performance gains for tasks across complexity ranges. While tasks in the 0.67–0.83 complexity range show a few negative cases, the average improvement remains positive across all task complexities. Overall, \\selfanchor\\ presents performance gains spanning all complexity levels, achieving approximately 7\\% performance improvement. These results demonstrate that {\\selfanchor} achieves consistent gains and generalizes effectively across varying task complexities.\n\n\\textbf{Reasoning Chain Length vs. Task Complexity.}\nNext, we analyze how reasoning chain length scales with task difficulty. \\autoref{fig:combinedr} shows the distribution of successful reasoning chain lengths across tasks of varying difficulty on Llama3.2-3B. The results show a clear trend that as complexity increases, {\\selfanchor} tends to generate longer reasoning chains. This aligns with the observation in \\citet{wu2025more} that harder problems require longer reasoning chains to solve. We attribute this capability to the attention steering mechanism, which enables the model to focus on both problem context and immediate reasoning object throughout the reasoning, preventing attention drift as the reasoning chain extends.\n\nIn summary, our analysis highlights two takeaways: (1) {\\selfanchor} demonstrates consistent improvements across all complexity levels, confirming its ability to generalize beyond narrow task categories. (2) \\selfanchor\\ encourage the model to generate longer reasoning chains for difficult problems, supporting its effectiveness in scaling to complex tasks.\n\n\n\n\\subsection{Efficiency}\n\n\\begin{table}[ht]\n \\scriptsize\n \\centering\n \\setlength{\\tabcolsep}{4pt}\n \\caption{Efficiency comparison}\n \\resizebox{0.5\\textwidth}{!}{\n \\begin{tabular}{l|cccc}\n \\toprule\n \\multirow{2.5}{*}{\\textbf{Model}} & \\multicolumn{4}{c}{Token/Second} \\\\\n \\cmidrule(lr){2-5}\n & {\\selfanchor} & CoT & PS+ & RE2 \\\\\n \\midrule\n \\multirow{1}{*}{Llama3.2-3B} & 9.97 & 10.87 & 10.84 & 12.01 \\\\\n \\midrule\n \\multirow{1}{*}{Phi-4-mini-4B} & 11.02 & 12.25 & 12.24 & 12.21\\\\\n \\midrule\n \\multirow{1}{*}{Qwen3-4B} & 5.41 & 6.22 & 6.22 & 6.23\\\\\n \\midrule\n \\multirow{1}{*}{Llama3.1-8B} & 7.54 & 8.38 & 8.26 & 8.19\\\\\n \\midrule\n \\multirow{1}{*}{Phi-4-15B} & 7.92 & 9.00 & 8.94 & 8.88\\\\\n \\midrule\n \\multirow{1}{*}{Qwen3-30B} & 1.07 & 1.39 & 1.39 & 1.37\\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{tab: efficiency}\n\\end{table}\n\n\n{\\selfanchor} achieved superior performance compared to state-of-the-art methods; we are committed to evaluating its efficiency.\n\\autoref{tab: efficiency} reports inference throughput (tokens/sec) for \\selfanchor\\ compared to baseline methods. On average, \\selfanchor\\ introduces minimal computational overhead, with throughput reductions typically below 1–2 tokens/sec relative to baselines. \nThe results highlight a favorable trade-off; {\\selfanchor} consistently improves reasoning while maintaining comparable runtime cost. Importantly, the cost-performance balance remains stable across both smaller (3B–4B) and larger (15B–30B) models, suggesting scalability without prohibitive latency.\n\nIn summary, {\\selfanchor} achieves strong effectiveness and efficiency, offering improved reasoning performance with only minor latency overhead compared to state-of-the-art baselines.\n\n\\subsection{Ablation study: The effectiveness of attention steering}\n\nTo isolate the contribution of attention steering, we conducted an ablation study comparing {\\selfanchor} with and without attention steering on two representative LLMs across all six benchmarks. As illustrated in \\autoref{tab:ablation structure}, {\\selfanchor} consistently outperformed its variant without attention steering, across all benchmarks, demonstrating the effectiveness of attention steering. \n\n\\autoref{tab:An example of anchor} further illustrates a representative example where attention steering prevents reasoning errors. In Steps 2 and 4, the {\\selfanchor} without attention steering approach incorrectly identifies ``her\" as referring to ``the secretary\"; this may be because models over-focus on sentence subjects rather than maintaining focus on the syntactic relationships that determine pronoun reference. In contrast, {\\selfanchor} correctly identifies that ``her\" refers to ``the analyst\" by maintaining attention on both the original question context and the current reasoning step\\footnote{We provide additional case studies in \\autoref{appendix:case} for further illustration.}.\n\nThis ablation confirms that, while structured reasoning provides a foundation for improved performance, it is often insufficient to prevent attention drift on its own. The attention anchoring component is crucial to ensure the model maintains focus throughout the reasoning process, leading to more robust and accurate results.\n\n\\begin{table*}\n \\scriptsize\n \\centering\n \\setlength{\\tabcolsep}{4pt}\n \\caption{Performance comparing {\\selfanchor} with and without attention steering}\n \\resizebox{1\\textwidth}{!}{\n \\begin{tabular}{ll|ccc|cc|c}\n \\toprule\n \\multirow{2.5}{*}{\\textbf{Model}} & \\multirow{2.5}{*}{\\textbf{Method}} & \\multicolumn{3}{c|}{Math} & \\multicolumn{2}{c|}{CommonSense} & \\multirow{2.5}{*}{BBH} \\\\\n \\cmidrule(lr){3-5} \\cmidrule(lr){6-7}\n & & GSM8K & AQuA & MATH & StrQA & T4D \\\\\n \\midrule\n \\multirow{2}{*}{Llama3.1-8B} \n & {\\selfanchor} (w/o attention steering) & 73.01 & 53.15 & 40.90 & 71.17 & 35.28 & 52.77\\\\\n & {\\selfanchor} & 76.72 & 55.51 & 52.50 & 73.54 & 40.01 & 58.53 \\\\\n \n \\midrule\n \\multirow{2}{*}{Phi-4-mini-4B} \n & {\\selfanchor} (w/o attention steering) & 78.77 & 58.66 &55.50 & 68.60 & 38.83 & 57.44 \\\\\n & {\\selfanchor} & 88.02 & 68.50 & 59.00 & 68.69 & 49.47 & 62.42\\\\\n \n \\bottomrule\n \\end{tabular}\n }\n \\label{tab:ablation structure}\n\\end{table*}\n% \\todo{strength tuning ablation}\n\n\n\\begin{table}\n% \\scriptsize\n\\centering\n\\caption{An example of BBH. Incorrect inferences are highlighted in \\lightred{red}. Correct ones are highlighted in \\lightgreen{green}.}\n\\resizebox{\\linewidth}{!}{\n\\begin{tabular}{l l}\n \\toprule\n \\multirow{2}{*}{\\textbf{Prompt}} %& \\textit{``Explain the antecedent of the pronoun (which thing the pronoun refers to), or state that it is ambiguous.}\\\\\n & \\textit{\\textbf{Sentence: The secretary came to the analyst's office and helped her to book a flight.}} \\\\\n & \\textit{\\textbf{Options: (A) Helped the secretary book a flight (B) Helped the analyst book a flight (C) Ambiguous}} \\\\\n \\midrule\n \\textbf{\\selfanchor} & \\{ \"Step 1: Identify the pronoun\": \"The pronoun is 'her'.\",\\\\\n \\text{(w/o attention steering)} & \"Step 2: Determine the antecedent of the pronoun\": \"\\lightred{The antecedent of 'her' is the subject of the sentence, which is 'The secretary'}\", \\\\\n \\textbf{} & \"Step 3: Analyze the sentence structure\": The subject of the sentence is 'The secretary', and the verb is 'came'. The object of the \\\\\n & \\:\\:\\:\\: verb 'came' is 'to the analyst's office'. The verb 'helped' has the pronoun 'her' as its object.\",\\\\\n & \"Step 4: Determine the antecedent of the pronoun based on the sentence structure\": \"Based on the sentence structure, the antecedent \\\\\n & \\:\\:\\:\\: of the pronoun \\lightred{'her' is the subject of the sentence, which is 'The secretary'}.\",\\\\\n & \"Step 5: Choose the correct option\": \"The correct option is \\lightred{(A) Helped the secretary book a flight.}\"\\}\\\\\n \\midrule\n \\textbf{{\\selfanchor}} & \\{ \"Step 1: Identify the pronoun\": \"The pronoun in the sentence is 'her'.\",\\\\\n & \"Step 2: Determine the antecedent of the pronoun\": \"To find the antecedent, we need to look for the noun that 'her' refers to. In this\\\\\n & \\:\\:\\:\\: case, \\lightgreen{'her' is a possessive pronoun that refers to the analyst.}\", \\\\\n & \"Step 3: Analyze the sentence structure\": \"The subject of the sentence is 'The secretary', and the object of the verb 'helped' is 'her'\",\\\\\n & \"Step 4: Identify the antecedent based on the sentence structure\": \"\\lightgreen{'her' refers to the analyst, not the secretary.}\",\\\\\n & \"Step 5: Choose the correct option\": \"Since 'her' refers to the analyst, the correct option is \\lightgreen{(B) Helped the analyst book a flight.}\" \\}\\\\\n \\bottomrule\n\\end{tabular}\n}\n\\label{tab:An example of anchor}\n\\end{table}\n\n\n\\subsection{Failure Case Analysis}\nTo understand the failure modes in \\selfanchor. We conducted a manual failure case analysis on 200 randomly sampled cases from \\textit{casual\\_judgement} and \\textit{AQuA}. Our analysis identified three primary failure modes:\n\n\n\\textbf{Reasoning Errors (42\\%).} \nThe most frequent failure mode involves LLM making mistakes during the reasoning. These include the misapplication of causal principles, flawed deductions, and incorrect conditional reasoning. For example, in one \\textit{casual\\_judgement} instance, the model incorrectly treated a necessary but insufficient condition as the sole causal factor, leading to an invalid conclusion. Such errors suggest that, while attention anchoring helps maintain focus on relevant steps, it cannot fully compensate for weak logical priors or gaps in world knowledge.\n\n\\textbf{Misunderstanding the problem (36.5\\%).}\nA substantial portion of failures stems from incomprehension of complex questions, leading to errors such as misidentifying all variables, misinterpreting the problem's requirements, or incorrectly parsing the relationships between entities. \nFor instance, in multi-variable problems, the model sometimes assigns numerical values to the wrong entity.\n\n\\textbf{Computational Errors (21.5\\%).}\nThe remaining failures involve arithmetic mistakes, unit conversion errors, or algebraic slips. Even when the reasoning chain is correct, a single miscalculation often propagates to the final answer.\n\nTaken together, these findings suggest that {\\selfanchor} primarily mitigates \\emph{attention misalignment}, but does not fully resolve deeper issues of logical validity, semantic understanding, or computational precision.\n\n% \\textbf{Reasoning Chain Length.}\n% \\autoref{fig:Reasoning Chain Length} presents the distribution of correct cases by reasoning chain length. \\todo{reasoning chain length of the ground truth solution? Need to specify. If the length is the reasoning chain of the correctly generated solution by the LLM, then this is problematic since there could be multiple correct reasoning chains to solve a problem. One model may generate a long one and the other model may generate a shorter one. It doesn't mean that Self-Anchor is better.} The performance of both methods exhibits a bimodal distribution. The first performance peak for {\\selfanchor} shows a shift towards longer chains compared to CoT; this is an expected artifact, as our structured format reasoning naturally extends the reasoning trajectories with explicit planning steps. Despite this overhead, {\\selfanchor} maintains a larger histogram area,\\todo{a larger histogram area is hard to follow. Can we make it more explicit by directly showing the success rate of tasks based on the reasoning length of the ground-truth solution?} indicating better performance in tasks that require short reasoning chains.\n\n% \\todo{This bi-modal shape analysis is confusing. Please use a more straightforward figure. The key message you want to express here is very simple and clear---Self-Anchor achieves superior performance on tasks regardless of the reasoning steps. Make a figure or a table that illustrates this in a straightforward way. Don't force people to calculate the histogram area.}\n% More critically, {\\selfanchor} demonstrates a higher magnitude performance peak at longer reasoning chains (8-20 reasoning steps), suggesting substantially higher accuracy than CoT at longer reasoning chains. This pattern directly supports our hypothesis that {\\selfanchor} augments long reasoning. \n% Last but not least, CoT exhibits problematic behavior in very long chains ($>$20 reasoning steps). After manual inspection, CoT can end up generating \\todo{How many tasks does CoT exhibit this pattern on? How many did you manually analyze? The description here is not rigorous.}repetitive content (e.g., ``the answer is A, the answer is A...\") until it reaches token limits. \n% % This abnormal behavior can also be considered as attention drift, since the model loses focus on the reasoning task. \n% {\\selfanchor} effectively prevents this issue through its attention steering mechanism, maintains coherent reasoning even in extended sequences.\n\n% \\todo{This figure is very hard to understand.}\\todo{I suggest you first figure out the key message you want to deliver in this experiment and then think about which figure/table can most straightforwardly illsutrate the result.}\n\n\n% To further illustrate this trend, we apply linear regression to these two methods. The results show that as task complexity grows, CoT failed to generate longer reasoning and seldom solved problems with relatively short reasoning steps in hard tasks. However, benefit from automatic attention steering, \\selfanchor\\ tend to generate longer reasoning to solve the problem. \n\n%{\\selfanchor} exhibits a leftward shift in the complexity length distribution relative to CoT, indicating that it achieves higher accuracy on tasks of equivalent or greater complexity.\n\\section{Related work}\n\\paragraph{Prompt engineering for reasoning.}\nPrompt engineering has been widely adopted as a fundamental approach for enhancing LLM reasoning capabilities~\\citep{liu2023pre,brown2020language}. A foundational line of work, initiated by Chain-of-Thought (CoT) prompting~\\citep{wei2022chain}, encourages explicit intermediate steps, which significantly improve performance on multi-step reasoning tasks. This has inspired numerous derivatives, including problem decomposition methods~\\citep{wang2023plan,zhou2022least,khot2022decomposed,drozdov2022compositional}, as well as techniques focused on enhancing query comprehension~\\citep{xu2024re,zheng2023take,mekala2023echoprompt,deng2023rephrase,mishra2022help}. \n% Another line of prompting methods are search-based approaches~\\citep{yao2023tree,besta2024graph,saha2023branch,hao2023reasoning}. \n\nWhile these prompting methods demonstrate effectiveness in specific domains, they rely on predetermined, static prompt formats for different tasks. On the other hand, LLMs remain sensitive to prompt variations and suffer from attention dilution during long generations~\\citep{liu-etal-2024-lost,attention_decay, context_rot,lu2021fantastically,gu2024attention}. {\\selfanchor} addresses these limitations by integrating structured reasoning with dynamic attention steering. It goes beyond static prompting by enabling the model to recalibrate its focus on the most salient context at each step of the reasoning trajectory.\n\n% By doing so, {\\selfanchor} directly addresses the critical challenge of attention drift in long-chain reasoning, a limitation that prior prompting and search-based methods do not explicitly tackle.\n\n% like Plan-and-Solve (PS)~\\citep{wang2023plan} and Least-to-Most prompting~\\citep{zhou2022least}, as well as techniques focused on enhancing query comprehension such as Re-Reading~\\citep{xu2024re} and Take a Step Back~\\citep{zheng2023take}. \n\n% like Tree-of-Thought (ToT)~\\citep{yao2023tree}, Graph-of-Thought~\\citep{besta2024graph}, Branch-solve-merge~\\citep{saha2023branch}, and RAP~\\citep{hao2023reasoning}. \n\n\\paragraph{Attention steering.}\nIn contrast to the aforementioned prompt engineering, which devises better prompt strategies, attention steering methods directly guide LLMs during inference to emphasize the user-specified part of context. \nSpecifically, Selective Prompt Anchoring (SPA) \\citep{tian2024selective} adjusts the logit probability distribution to emphasize the specified context. PASTA\\citep{zhang2023tell} identifies and reweights a subset of attention heads to redirect the model's attention to user-specified parts. Selective Self-Attention (SSA) \\citep{zhang2024selective} augments the softmax nonlinearity with a principled temperature scaling strategy. TOAST \\citep{shi2023toast} learns feature selection modules that guide attention toward task-relevant information. \nHowever, these methods require manual specification of anchor content, limiting their adaptability to diverse reasoning contexts. Real-world applications demand automatic identification of relevant context elements across varying task requirement and reasoning patterns. {\\selfanchor} addresses this limitation by leveraging structured intermediate representations to enable context-aware anchor selection without human intervention.\\section{Conclusion}\nWe presented {\\selfanchor}, a lightweight pipeline that leverages the inherent structure of reasoning for attention alignment. Across six diverse reasoning benchmarks, {\\selfanchor} consistently outperforms existing baselines. Notably, {\\selfanchor} enhanced ``non-reasoning\" models achieve competitive performance with specialized reasoning models while maintaining significantly lower cost. \nMoreover, our analysis reveals that \\selfanchor's advantages are generalizable to varying task complexities. We hope {\\selfanchor} serves as a step toward more reliable LLMs reasoning that requires neither parameter updates nor additional sampling.\n\n\\section{Reproducibility statement}\nWe have made extensive efforts to ensure the reproducibility of our work. Additional implementation details, hyperparameters, and ablation studies are provided in the appendix. We also include complete descriptions of benchmark datasets, sampling procedures, and task complexity measures.\n\nLastly, to foster reproducibility and further research, source code will be made publicly available upon acceptance of this paper.\n\n\\section{Ethics statement}\nThis paper does not involve any ethical concerns. The proposed methods focus on improving reasoning ability and robustness in LLMs and do not raise issues related to the code of ethics.\n% \\subsection{Citations within the text}\n\n% Citations within the text should be based on the \\texttt{natbib} package\n% and include the authors' last names and year (with the ``et~al.'' construct\n% for more than two authors). When the authors or the publication are\n% included in the sentence, the citation should not be in parenthesis using \\verb|\\citet{}| (as\n% in ``See \\citet{Hinton06} for more information.''). Otherwise, the citation\n% should be in parenthesis using \\verb|\\citep{}| (as in ``Deep learning shows promise to make progress\n% towards AI~\\citep{Bengio+chapter2007}.'').\n\n% The corresponding references are to be listed in alphabetical order of\n% authors, in the \\textsc{References} section. As to the format of the\n% references themselves, any style is acceptable as long as it is used\n% consistently.\n\n\n\\bibliography{reference}\n\\bibliographystyle{iclr2026_conference}\n\n\\appendix\n\\newpage\n\\section{The Use of Large Language Models (LLMs)}\nWe leverage Large Language Models (LLMs) primarily for grammar checking and polishing for our manuscript. \n\n\n% As mentioned in \\autoref{implementation details}, we select dynamic shallow layers by partitioning the transformer layers into \\{low, high\\} buckets and select one bucket as candidate layers. In this section, we use a dedicated validation set from StrategyQA and GSM8K to demonstrate the result. As illustrated in \\autoref{fig:shallowlayer}, the layer selection may vary from different LLM architectures, even on the same task. This aligns with prior observations that internal layer semantics differ across models~\\citep{burns2022discovering, beltagy2020longformer}. \n% Furthermore, {\\actdola} outperforms DoLa under both low and high settings, across all five LLMs. Notably, while DoLa’s performance is often sensitive to bucket selection, {\\actdola} remains robust and consistently improves over baselines.\n% This demonstrates that while bucket selection is an important tuning step, {\\actdola} offers more consistent improvements over the baseline compared to DoLa across these layer choices.\n\n\n% \\section{StrategyQA example case study}\n% \\label{appendix: gsm8k example case study}\n% As the StrategyQA example in \\autoref{tab:gsm8k}, Greedy and SLED, while correctly stating that the Paralympics are for \"athletes with disabilities,\" still incorrectly concludes that Josh Blue cannot participate. This suggests a failure to either retrieve or integrate the crucial fact of Josh Blue's specific disability, or an inability to reason past his profession.\n% DoLa acknowledges that Josh Blue has cerebral palsy but incorrectly concludes he cannot participate in the Paralympic Games, reasoning \"He does not compete in sports.\" This error stems from a flawed premise: \n\n% DoLa mistakenly prioritizes Blue's current athletic activity and profession over the primary criterion for Paralympic eligibility, which is the presence of a qualifying disability. This type of misstep, where an initial misjudgment or misplaced focus on certain details derails the reasoning process. Such failures might arise if layer contrasting, while aiming for deeper semantic understanding, inadvertently causes the model to fixate on salient but ultimately non-determinative information or to incorrectly weigh the evidence presented.\n% In contrast, {\\actdola} successfully navigates this scenario. It correctly connects Josh Blue's cerebral palsy with the fundamental nature of the Paralympic Games—which are for athletes with disabilities—thereby deducing his potential eligibility and providing the correct affirmative answer. This demonstrates {\\actdola}'s improved ability to discern and appropriately utilize critical information for accurate reasoning.\n\n% \\section{Reward setting tuning}\n% \\label{appendix:reward-tuning}\n% To emphasize factual correctness and carefully guide the activation of our layer contrasting mechanism, we designed a sequence-level reward function based on token-level ground truth labels. We assign rewards of \\(r_{tp} = 1.0\\) for true positives (correct layer contrasting activation) and \\(r_{tn} = 2.0\\) for true negatives (correct non-activation). We specifically chose to reward correct non-activation as it encourages the model to only apply the computationally intensive layer contrasting when necessary, promoting efficiency and avoiding unnecessary interference with potentially already factual token generations. Conversely, false positives (unnecessary layer contrasting activation) incur a penalty of \\(r_{fp} = -1.0\\). We heavily penalize false negatives (missed necessary activations) with \\(r_{fn} = -5.0\\) because our primary goal is to leverage layer contrasting to enhance factuality. Failing to activate this mechanism when needed can directly compromise the model's ability to generate truthful information. These reward values were empirically tuned to achieve a favorable balance between precision and recall. \n% Under our chosen settings, we observed a precision of 71.44 and a recall of 90.57, demonstrating a strong tendency to correctly identify non-hallucinated tokens while rarely missing necessary activations. This contrasts with a default reward configuration, which yielded a precision of 69.36 and a recall of 60.99, indicating a higher rate of incorrectly classifying non-hallucinated tokens. Thus, our empirically derived reward design effectively prioritizes the accurate identification of factual tokens and the strategic application of layer contrasting.\n\n\\section{Calculating Average Confidence Scores}\n \\label{appendix:mean}\n\n We conduct an ablation study to evaluate different methods for calculating confidence scores from token-level probabilities. Let $P_i = \\{p_1, p_2, \\ldots, p_m\\}$ represent the set of token-level confidence scores for tokens generated in the current reasoning step $i$.\n\n We compare three approaches for calculating average confidence scores at sequence level:\n \n \\textbf{Harmonic Mean:}\n \\begin{equation}\n p_{\\text{harmonic}} = \\frac{n}{\\sum_{i=1}^{n} \\frac{1}{p_i}}\n \\end{equation}\n \n \\textbf{Geometric Mean:}\n \\begin{equation}\n p_{\\text{geometric}} = \\left(\\prod_{i=1}^{n} p_i\\right)^{1/n}\n \\end{equation}\n \n \\textbf{Arithmetic Mean:}\n \\begin{equation}\n p_{\\text{arithmetic}} = \\frac{1}{n}\\sum_{i=1}^{n} p_i\n \\end{equation}\n \n Table~\\ref{tab:means_selection} presents the results across two reasoning benchmarks using Llama3.1 and Phi-4-mini models. The harmonic mean consistently outperforms both geometric and arithmetic means across all settings. This is because the harmonic mean is more sensitive to low confidence values, which better captures potential attention drift during reasoning. \n The geometric mean performs second-best, as it also penalizes low values more than the arithmetic mean, though less aggressively than the harmonic mean. The arithmetic mean shows the weakest performance, as it can be dominated by high-confidence tokens and may miss instances where attention drift occurs for specific reasoning components.\n\n\\section{\\selfanchor\\ Prompt Details}\n \\begin{tcolorbox}\n You are an expert problem solver. Your task is to decompose the given problem into a clear, step-by-step plan, reasoning the plan and solve the problem step by step in JSON format.\n \n For each plan step, provide a key-value pair: the key is the plan step (as stated), the value is the detailed reasoning and action for that step.\n \n Now, implement a reasoning structure to follow step-by-step and arrive at correct answers in JSON format. Conclude with the final answer using the format: \"Final answer\": \"$<$your answer$>$\".\n \n Original problem: {\\textbf{\\{question\\}}}\n \\end{tcolorbox}\n\n\n\\section{Alternative Design}\n\\label{appendix: alternative design}\n\n As described in Section~\\ref{Automatic Anchoring Strategy}, our primary {\\selfanchor} design anchors attention to the original question and the current plan step during reasoning generation. We investigate an alternative design that anchors to all prior plan steps in addition to the current step and the original question. The motivation for this alternative is that maintaining attention to all previous planning steps might provide additional context for the current reasoning step.\n\n We compare two anchoring strategies:\n \\begin{itemize}\n \\item \\textbf{{\\selfanchor} (Primary):} Anchors to the original question and current plan step only, where $a_i = \\{\\text{Question}, \\text{Plan}_i\\}$\n \\item \\textbf{Anchor to All:} Anchors to the original question, current plan step, and all prior plan steps, where $a_i = \\{\\text{Question}, \\text{Plan}_1, \\text{Plan}_2, \\ldots, \\text{Plan}_i\\}$\n \\end{itemize}\n \n Table~\\ref{tab:alternative_design} presents the results comparing these two approaches across AQuA and T4D benchmarks using Llama3.1-8B and Phi-4-mini models. The primary {\\selfanchor} design consistently outperforms the alternative that anchors to all prior steps. This performance difference may be because the alternative design dilutes attention across too many anchor points, reducing focus on the most relevant current step. In contrast, the primary design maintains sharp focus on the most relevant context while avoiding attention dilution.\n \n \\begin{table*}[ht]\n \\scriptsize\n \\centering\n \\setlength{\\tabcolsep}{14pt}\n\n \\centering\n \\caption{Mean selection ablation study. Results show accuracy (\\%) on AQuA-RAT and T4D benchmarks.}\n \\begin{tabular}{ll|cc}\n \\toprule\n \\textbf{Model} & \\textbf{Method} & AQuA-RAT & T4D \\\\\n \\midrule\n \\multirow{4}{*}{LLaMA3.1-8B} & CoT & 50.79 & 26.77 \\\\\n & {\\selfanchor} (Harmonic) & \\textbf{55.51} & \\textbf{40.01} \\\\\n & {\\selfanchor} (Geometric) & 55.11 & 35.28 \\\\\n & {\\selfanchor} (Arithmetic) & 54.72 & 35.99 \\\\\n \\midrule\n \\multirow{4}{*}{Phi-4-mini} & CoT & 61.81 & 39.54\\\\\n & {\\selfanchor} (Harmonic) & \\textbf{68.50} & \\textbf{49.47}\\\\\n & {\\selfanchor} (Geometric) & 67.72 & 49.11 \\\\\n & {\\selfanchor} (Arithmetic) & 67.71 & 48.40 \\\\\n \\bottomrule\n \\end{tabular}\n \\label{tab:means_selection}\n\n\n\\end{table*}\n\n\\begin{table*}[ht]\n \\scriptsize\n \\centering\n \\setlength{\\tabcolsep}{14pt}\n \\caption{Alternative anchoring design comparison. Results show accuracy (\\%) on AQuA-RAT and T4D benchmarks.}\n \\begin{tabular}{ll|cc}\n \\toprule\n \\textbf{Model} & \\textbf{Method} & AQuA-RAT & T4D \\\\\n \\midrule\n \\multirow{3}{*}{LLaMA3.1-8B} & CoT & 50.79 & 26.77 \\\\\n & {\\selfanchor} & \\textbf{55.51} & \\textbf{40.01} \\\\\n & Anchor to All Prior Steps & 53.54 & 32.62\\\\\n \\midrule\n \\multirow{3}{*}{Phi-4-mini} & CoT & 61.81 & 39.54\\\\\n & {\\selfanchor} & \\textbf{68.50} & \\textbf{49.47}\\\\\n & Anchor to All Prior Steps & 67.32 & 47.34\\\\\n \\bottomrule\n \\end{tabular}\n \\label{tab:alternative_design}\n\n\\end{table*}\n\n\\section{Implementation and evaluation details}\n \\label{appendix: Implementation and evaluation details}\n \\subsection{Prompt example}\n \\label{appendix:prompt}\n \\textbf{Chain-of-Thought.}\n \\begin{tcolorbox}\n Let's think step by step.\n \\end{tcolorbox}\n \n \\textbf{Plan-and-solve+.}\n We adopt the implementation from Plan-and-solve+\\citep{wang2023plan}, for mathmatical reasoning we apply prompt:\n \n \\begin{tcolorbox}\n Let's first understand the problem, extract relevant variables and their corresponding numerals, and make and devise a complete plan. Then, let's carry out the plan, calculate intermediate variables (pay attention to correct numerical calculation and commonsense), solve the problem step by step, and show the answer.\n \\end{tcolorbox}\n \n \n Otherwise, we use:\n \n \\begin{tcolorbox}\n Let's first prepare relevant information and make a plan. Then, let's answer the question step by step (pay attention to commonsense and logical coherence).\n \\end{tcolorbox}\n \n \\textbf{Re-Reading.}\n \\begin{tcolorbox}\n \\{\\textbf{Question}\\}\n \n Read the question again:\n \n \\{\\textbf{Question}\\}\n \\end{tcolorbox}\n\n \n \n \\subsection{Evaluation Details}\n We adopt standard metrics used in prior work \\citep{chuang2024dola,wang2023plan,zhou2024self}, including accuracy and exact match, for AQuA, BBH, T4D, and MATH. For GSM8K and StrategyQA, we follow the factual accuracy evaluation protocol introduced by \\citet{chuang2024dola}.\n \n To ensure consistent answer extraction, we prompt all models to conclude their response with the phrase: ``Conclude with the final answer using the format: ``Final answer\": \"$<$your answer$>$'' where $<$your answer$>$ denotes either a multiple-choice option or a string answer. We then apply task-specific heuristics to extract $<$your answer$>$ from the output.\n \n For the MATH dataset, we randomly sample 200 test instances and manually verify the extracted answers to ensure correctness.\n\n\n \\subsection{Implementation Details}\n We follow the definitions of reasoning step segmentation and task complexity from \\citep{wu2025more,jin2024impact}. The performance gain of a task is computed as the difference in accuracy between two methods on that task. \n \n To measure the number of reasoning steps, we split the full reasoning chain by ``\\textbackslash n'' and remove empty lines caused by consecutive breaks (``\\textbackslash n\\textbackslash n''). The remaining lines are counted as the CoT length.\n\n % We follow the official implementations of Chain-of-Thought Self-Consistency~\\citep{wei2022chain}, Tree-of-Thought~\\citep{yao2023tree}, and Self-Refine~\\citep{madaan2023self}. Specifically, for Tree-of-Thought, we generate $N{=}3$ candidate thoughts per node with \\texttt{temperature}$=0.7$ and \\texttt{top\\_p}$=0.95$. For Chain-of-Thought Self-Consistency, we sample $N{=}10$ reasoning paths and apply majority voting. For Self-Refine, we adopt $N{=}5$ refinement iterations.\n\n\\section{Case Study}\n\\label{appendix:case}\n In this section, we provided a qualitative example to illustrate the reasoning trajectory generated by each method. The task is to determine whether a prime number can be represented by the number of days in a week. CoT \\autoref{alg:example1} and RE \\autoref{alg:example3} immediately arrive at an incorrect conclusion by misidentifying 7 as a non-prime number. PS+ \\autoref{alg:example2} follows a more structured plan but also makes a critical error in its final conclusion, contradicting its own evidence. In contrast, {\\selfanchor} \\autoref{alg:example4} successfully decomposes the problem, correctly identifies 7 as a prime number, and reaches the correct answer by systematically executing its reasoning plan.\n\n\\begin{algorithm*}\n \\caption{Chain-of-Thought (CoT)}\n \\begin{algorithmic}[1]\n \\State \\textbf{\\textit{Question:}}Can a prime number be represented by the number of days in a week?\n \\State \\textbf{Prompt:} Let's think step by step.\n \\State \\textbf{Model Completion:} No, a prime number cannot be represented by the number of days in a week because the number of days in a week is 7, which is not a prime number. Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. Since 7 is divisible by 1 and 7, it is not a prime number.\n \\State \\textbf{Final answer: No}\n \\end{algorithmic}\n \\label{alg:example1}\n\\end{algorithm*}\n\n\\begin{algorithm*}\n \\caption{Plan-and-Solve (PS+)}\n \\begin{algorithmic}[1]\n \\State \\textbf{\\textit{Question:}}Can a prime number be represented by the number of days in a week?\n \\State \\textbf{Prompt:} Let's first prepare relevant information and make a plan. Then, let's answer the\nquestion step by step (pay attention to commonsense and logical coherence).\n \\State \\textbf{Model Completion:} Step 1: Gather Information: Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The number of days in a week is 7.\n \\State Step 2: Plan the Solution: We will first identify prime numbers less than 7 to see if any match the number of days in a week. - Then, we will determine if any prime number can represent the number of days in a week based on our findings.\n \\State Step 3: Execute the Plan: Prime numbers less than 7 are 2, 3, 5, and 7. - Among these, 2, 3, and 5 are less than 7 and are indeed prime numbers. - None of these prime numbers (2, 3, 5) match the number of days in a week (7).\n \\State Step 4: Analyze and Draw a Conclusion: Since none of the prime numbers less than 7 (2, 3, 5) match the number of days in a week (7), a prime number cannot be represented by the number of days in a week.\n \\State \\textbf{Step 5: Final Answer: The final answer is No}\n \\end{algorithmic}\n \\label{alg:example2}\n\\end{algorithm*}\n\n\\begin{algorithm*}\n \\caption{Re-Reading (RE)}\n \\begin{algorithmic}[1]\n \\State \\textbf{\\textit{Question:}}Can a prime number be represented by the number of days in a week?\n \\State \\textbf{Prompt:} Read the question again\n \\State \\textbf{Model Completion:} No, a prime number cannot be represented by the number of days in a week because the number of days in a week is 7, which is not a prime number.\n \\State Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves.\n \\State The number 7 is a prime number, but the question seems to be asking if the number of days in a week (7) can be represented by a prime number, which it already is.\n \\State However, if the question is interpreted as asking if there is a prime number that equals the number of days in a week, the answer would still be \"No\" because 7 is already a prime number.\n \\State If the question is asking if the number of days in a week (7) can be represented by any prime number, the answer would be \"Yes\" because 7 itself is a prime number. \n \\State However, the phrasing of the question suggests that it is asking if the number of days in a week can be represented by a prime number other than 7, in which case the answer would be \"No.\" \n \\State For clarity, I will assume the question is asking if the number of days in a week (7) can be represented by a prime number other than itself, and the final answer is \"No.\" \n \\State \\textbf{\"Final answer\": \"No\"}\n \\end{algorithmic}\n \\label{alg:example3}\n\\end{algorithm*}\n\n\n\\begin{algorithm*}\n \\caption{{\\selfanchor}}\n \\begin{algorithmic}[1]\n \\State \\textbf{\\textit{Question:}}Can a prime number be represented by the number of days in a week?\n \\State \\textbf{Prompt:} Decompose the given problem into step-by-step plan, reasoning the plan and solve the problem step by step in JSON format. For each plan step, provide a key-value pair: the key is the plan step, the value is the detailed reasoning for that step.\n \\State \\textbf{Model Completion:} \"Understand the question.\": \"The question asks if a prime number can be represented by the number of days in a week.\", \n \\State \"Identify the number of days in a week.\": \"There are 7 days in a week.\", \n \\State \"Determine if 7 is a prime number.\": \"A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.\", \n \\State \"Check if 7 meets the criteria of a prime number.\": \"7 is greater than 1 and its only divisors are 1 and 7.\", \n \\State \\textbf{\"Final answer\": \"Yes\"}\n \\end{algorithmic}\n \\label{alg:example4}\n\\end{algorithm*}\n\n\n\\section{Numerical Experiment Result on Big-Bench-Hard}\n \\label{appendix:bbh}\n% Table \\ref{tab:package} reports the package hallucination error rates for Python and JavaScript code generation across nine LLMs using four decoding strategies. Overall, our dynamic policy-guided method, {\\actdola} consistently yields the lowest hallucination rates—reducing errors by up to 6.5\\% on Python and by up to 5.6\\% on JavaScript relative to standard greedy decoding. In contrast, static interventions such as DoLa and SLED achieve modest improvements over the greedy baseline in some cases but can even degrade performance on certain LLMs, e.g., DoLa on Qwen2.5-Coder. These results demonstrate that sequential decision–level optimization of layer contrasting substantially mitigates package hallucination across diverse model architectures and programming languages.\n\n\\begin{table*}[t]\n \\scriptsize\n \\centering\n \\setlength{\\tabcolsep}{4pt}\n \\caption{BBH details}\n \\resizebox{1.1\\textwidth}{!}{\n \\begin{tabular}{llcccccc}\n \\toprule\n \\multirow{2}{*}{\\textbf{Model}} & \\multirow{2}{*}{\\textbf{Method}} & \\multicolumn{5}{c}{\\textbf{BBH}} \\\\\n \\cmidrule(lr){3-8}\n & & \\textbf{disambiguation\\_qa} & \\textbf{causal\\_judgement} & \\textbf{date\\_understanding} & \\textbf{logical\\_deduction} & \\textbf{salient\\_translation\\_error\\_detection} & \\textbf{snarks}\\\\\n \\midrule\n \\multirow{3}{*}{Llama3.1-8B} & CoT & 100 & 91/187 & 182 & 67 & 110 & 125\\\\\n & PS+ & 138 & 108 & 136 & 78 & 124 & 122 \\\\\n & re-read & 124 & 98 & 190 & 85 & 121 & 127\\\\\n & {\\selfanchor} & 152 & 100 & 160 & 128 & 132 & 127\\\\\n \\midrule\n \\multirow{3}{*}{Llama3.2-3B} & CoT & 88/250 & 71 & 102 & 34 & 95 & 89\\\\\n & PS+ & 104 & 63 & 97 & 86 & 98 & 105 \\\\\n & re-read & 74 & 84 & 127 & 40 & 89 & 105\\\\\n & {\\selfanchor} & 131 & 101 & 131 & 101 & 96 & 129\\\\\n \\midrule\n \\multirow{3}{*}{Phi4-mini-4B} & CoT & 162/250 & 113 & 154 & 114 & 149 & 134\\\\\n & PS+ & 160 & 126 & 138 & 130 & 136 & 124\\\\\n & re-read & 162 & 115 & 165 & 113 & 135 & 148\\\\\n & {\\selfanchor} & 152 & 116 & 174 & 128 & 140 & 142\\\\\n \\midrule\n \\multirow{3}{*}{Qwen3-mini-4B} & CoT & 183/250 & 121 & 174 & 208 & 167 & 148\\\\\n & PS+ & 179 & 108 & 165 & 207 & 160 & 150 \\\\\n & re-read & 179 & 121 & 203 & 230 & 147 & 154\\\\\n & {\\selfanchor} & 185 & 115 & 193 & 224 & 161 & 150\\\\\n \\midrule\n \\multirow{3}{*}{Phi-4-15B} & CoT & 180 & 120 & 203 & 169 & 152 & 160\\\\\n & PS+ & 180 & 117 & 140 & 186 & 155 & 156\\\\\n & re-read & 179 & 120 & 221 & 191 & 158 & 154 \\\\\n & {\\selfanchor} & 176 & 122 & 218 & 203 & 148 & 161 \\\\\n \\midrule\n \\multirow{3}{*}{Qwen3-30B} & CoT & 105 & 125 & 182 & 185 & 172 & 155 \\\\\n & PS+ & 114 & 122 & 172 & 181 & 165 & 156\\\\\n & re-read & 113 & 125 & 185 & 210 & 174 & 156\\\\\n & {\\selfanchor} & 110 & 123 & 196 & 200 & 160 & 157\\\\\n \\bottomrule\n \\end{tabular}}\n \\label{tab:truth}\n\\end{table*}\n\n \n\\end{document}\n"},"question":{"kind":"string","value":"What are the average improvements from CoT to Self Anchor across all the bechmarks in the Math and BBH categories respectively?"},"answer":{"kind":"string","value":"6.29,15.39"},"plan":{"kind":"string","value":"SELECT all benchmarks in the Math category\nLOOP for each benchmark\n COMPUTE improvement = Self Anchor score - CoT score\nCOMPUTE math_average = average of all improvements in Math category\n\n\nSELECT all benchmarks in the BBH category\nLOOP for each benchmark\n COMPUTE improvement = Self Anchor score - CoT score\nCOMPUTE bbh_average = average of all improvements in BBH category\n\n\nRETURN math_average, bbh_average\n"}}},{"rowIdx":350,"cells":{"paper":{"kind":"string","value":"2509.06870"},"relevant_tables":{"kind":"list like","value":[["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n","\\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n"," &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n"," &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\n","Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:indist-1p7b}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\\\\\\n\",\n \" &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\\\\\\n\",\n \" &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{70.69} & \\\\textbf{50.00} & \\\\textbf{33.34} & \\\\textbf{32.07} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:indist-1p7b}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n"," \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\n"," \\label{fig:llmagg}\n","\\end{figure}\n"],["\\begin{figure}[t]\n","\n","\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\n","Given the following problem:\n","\n","\\texttt{\\{problem\\}}\n","\n","and these solution attempts:\n","\n","\\texttt{\\{solutions\\}}\n","\n","It is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\n","\\end{tcolorbox}\n","\\caption{\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\n","\\label{fig:aggre-prompt}\n","\\end{figure}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n","\\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n"," &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n"," &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\n","Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:indist-1p7b}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n"," \\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\n","pass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\n"," &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\n"," &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\n","Prompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{82.38} & \\textbf{79.70} & \\textbf{53.01} & \\textbf{60.66} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:8b-results}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n"," \\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 11.82 & 10.00 & \\phantom{0}6.25 & \\phantom{0}3.39 \\\\\n","pass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 18.07 & 15.42 & \\phantom{0}8.75 & \\phantom{0}7.29 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\phantom{0}7.44 & \\phantom{0}8.92 \\\\\n"," &AceMath-72B & 26.33 & 18.62 & 10.23 & \\phantom{0}8.97 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\phantom{0}8.37 & \\phantom{0}8.41 \\\\\n"," &AceMath-72B & 26.54 & 18.83 & \\phantom{0}9.72 & \\phantom{0}8.09 \\\\\n","Prompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{29.96} & \\textbf{19.77} & \\textbf{17.03} & \\textbf{12.76} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:nonthinking-results}\n","\\end{table}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=0.8\\linewidth]{no_sols.pdf}\n"," \\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\n"," \\label{fig:scaling-k}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=0.8\\linewidth]{acc_by_num.pdf}\n"," \\caption{Performance vs. majority answer size for our method \\method{} compared to majority vote. \\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\n"," \\label{fig:majority-size}\n","\\end{figure}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Ablation of training mixtures: Easy\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\n","\\begin{tabular}{rcccc}\n","\\toprule\n","Easy\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\n","5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\n","10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\n","20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\n","50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\n","\\midrule\n","Untrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:easy-mix}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Effect of the number of solution sets $s$ per problem on performance.}\n","\\begin{tabular}{rcccc}\n","\\toprule\n","\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\n","4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\n","8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\n","16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:unique-sets}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\n","\\begin{tabular}{lcccc}\n","\\toprule\n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","Base Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","Additionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\n","Multitask Solution Model &49.11&38.85&26.67&22.50\\\\\n","Base Aggregator Model & 63.57&44.85&29.52&27.91\\\\\n","Trained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","Multitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:train-task}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Average token usage per generation for solution vs. aggregator models.}\n","\\begin{tabular}{lcccc}\n","\\toprule\n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","Base Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\n","Additionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\n","Base Aggregator Model & \\phantom{0}2807.71 & \\phantom{0}2852.10 & \\phantom{0}3465.00 & \\phantom{0}3693.24 \\\\\n","Trained Aggregator Model & \\phantom{0}3039.22 & \\phantom{0}3157.11 & \\phantom{0}3681.97 & \\phantom{0}3768.28 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:token-usage}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1.0\\\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\\n\",\n \" \\\\caption{{\\\\bf \\\\method{}}: given a task and sampled LLM solutions as input, \\\\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\\\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\\\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\\n\",\n \" \\\\label{fig:llmagg}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \"\\n\",\n \"\\\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\\n\",\n \"Given the following problem:\\n\",\n \"\\n\",\n \"\\\\texttt{\\\\{problem\\\\}}\\n\",\n \"\\n\",\n \"and these solution attempts:\\n\",\n \"\\n\",\n \"\\\\texttt{\\\\{solutions\\\\}}\\n\",\n \"\\n\",\n \"It is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\\n\",\n \"\\\\end{tcolorbox}\\n\",\n \"\\\\caption{\\\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\\n\",\n \"\\\\label{fig:aggre-prompt}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\\\\\\n\",\n \" &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\\\\\\n\",\n \" &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{70.69} & \\\\textbf{50.00} & \\\\textbf{33.34} & \\\\textbf{32.07} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:indist-1p7b}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \" \\\\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\\\\\\n\",\n \"pass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\\\\\\n\",\n \" &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\\\\\\n\",\n \" &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{82.38} & \\\\textbf{79.70} & \\\\textbf{53.01} & \\\\textbf{60.66} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:8b-results}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \" \\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 11.82 & 10.00 & \\\\phantom{0}6.25 & \\\\phantom{0}3.39 \\\\\\\\\\n\",\n \"pass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 18.07 & 15.42 & \\\\phantom{0}8.75 & \\\\phantom{0}7.29 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\\\phantom{0}7.44 & \\\\phantom{0}8.92 \\\\\\\\\\n\",\n \" &AceMath-72B & 26.33 & 18.62 & 10.23 & \\\\phantom{0}8.97 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\\\phantom{0}8.37 & \\\\phantom{0}8.41 \\\\\\\\\\n\",\n \" &AceMath-72B & 26.54 & 18.83 & \\\\phantom{0}9.72 & \\\\phantom{0}8.09 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{29.96} & \\\\textbf{19.77} & \\\\textbf{17.03} & \\\\textbf{12.76} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:nonthinking-results}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\linewidth]{no_sols.pdf}\\n\",\n \" \\\\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\\\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\\n\",\n \" \\\\label{fig:scaling-k}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\linewidth]{acc_by_num.pdf}\\n\",\n \" \\\\caption{Performance vs. majority answer size for our method \\\\method{} compared to majority vote. \\\\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\\n\",\n \" \\\\label{fig:majority-size}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Ablation of training mixtures: Easy\\\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\\n\",\n \"\\\\begin{tabular}{rcccc}\\n\",\n \"\\\\toprule\\n\",\n \"Easy\\\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\\\\\\n\",\n \"5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\\\\\\n\",\n \"10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\\\\\\n\",\n \"20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\\\\\\n\",\n \"50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Untrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:easy-mix}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Effect of the number of solution sets $s$ per problem on performance.}\\n\",\n \"\\\\begin{tabular}{rcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\\\\\\n\",\n \"4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\\\\\\n\",\n \"8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\\\\\\n\",\n \"16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:unique-sets}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\\n\",\n \"\\\\begin{tabular}{lcccc}\\n\",\n \"\\\\toprule\\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Base Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"Additionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\\\\\\n\",\n \"Multitask Solution Model &49.11&38.85&26.67&22.50\\\\\\\\\\n\",\n \"Base Aggregator Model & 63.57&44.85&29.52&27.91\\\\\\\\\\n\",\n \"Trained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"Multitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:train-task}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Average token usage per generation for solution vs. aggregator models.}\\n\",\n \"\\\\begin{tabular}{lcccc}\\n\",\n \"\\\\toprule\\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Base Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\\\\\\n\",\n \"Additionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\\\\\\n\",\n \"Base Aggregator Model & \\\\phantom{0}2807.71 & \\\\phantom{0}2852.10 & \\\\phantom{0}3465.00 & \\\\phantom{0}3693.24 \\\\\\\\\\n\",\n \"Trained Aggregator Model & \\\\phantom{0}3039.22 & \\\\phantom{0}3157.11 & \\\\phantom{0}3681.97 & \\\\phantom{0}3768.28 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:token-usage}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\pdfoutput=1\n\\documentclass[]{fairmeta}\n% Option \"twocolumn\" available, but please prioritize single-column\n\n\\title{The Majority is not always right: \\\\\n%Reinforcement-learned aggregation}\nRL training for solution aggregation}\n\n\\author[1]{Wenting Zhao}\n\\author[1,2]{Pranjal Aggarwal}\n\\author[1]{Swarnadeep Saha}\n\\author[1]{Asli Celikyilmaz}\n\\author[1]{Jason Weston}\n\\author[1]{Ilia Kulikov}\n\n\\affiliation[1]{FAIR at Meta}\n\\affiliation[2]{CMU}\n\n\\abstract{Scaling up test-time compute, by generating multiple independent solutions and selecting or aggregating among them, has become a central paradigm for improving large language models (LLMs) on challenging reasoning tasks. While most prior work relies on simple majority voting or reward model ranking to aggregate solutions,\nthese approaches may only yield limited benefits. In this work, we propose to learn aggregation as an explicit reasoning skill: given a set of candidate solutions, we train an aggregator model to review, reconcile, and synthesize a final, correct answer using reinforcement learning from verifiable rewards. A key ingredient is careful balancing of easy and hard training examples, allowing the model to learn both to recover minority-but-correct answers as well as easy majority-correct answers. \n%\n\\if 0 non-arxiv verios\n%Empirically, aggregating solutions from Qwen3-1.7B, which %achieves 35\\% accuracy on AIME25, our trained aggregator, \\model, boosts performance to 50\\%.\n%\\model outperforms both strong rule-based and reward-model baselines, across multiple math competition benchmarks. Furthermore, it generalizes effectively to solutions from stronger models and solutions produced in non-thinking modes, all while requiring substantially fewer tokens than majority voting with larger numbers of solutions.}\n\\fi\nEmpirically, we find our method, \\method{}, outperforms both strong rule-based and reward-model baselines, across multiple benchmarks. Furthermore, it generalizes effectively to solutions from differing models, including stronger ones than contained in the training data, \n%stronger models and solutions produced in non-thinking modes,\nall while requiring substantially fewer tokens than majority voting with larger numbers of solutions.\n}\n\\date{\\today}\n\n% Optional math commands from https://github.com/goodfeli/dlbook_notation.\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n% Figure reference, capital. For start of sentence\n\\def\\Figref#1{Figure~\\ref{#1}}\n\\def\\twofigref#1#2{figures \\ref{#1} and \\ref{#2}}\n\\def\\quadfigref#1#2#3#4{figures \\ref{#1}, \\ref{#2}, \\ref{#3} and \\ref{#4}}\n% Section reference, lower-case.\n\\def\\secref#1{section~\\ref{#1}}\n% Section reference, capital.\n\\def\\Secref#1{Section~\\ref{#1}}\n% Reference to two sections.\n\\def\\twosecrefs#1#2{sections \\ref{#1} and \\ref{#2}}\n% Reference to three sections.\n\\def\\secrefs#1#2#3{sections \\ref{#1}, \\ref{#2} and \\ref{#3}}\n% Reference to an equation, lower-case.\n\\def\\eqref#1{equation~\\ref{#1}}\n% Reference to an equation, upper case\n\\def\\Eqref#1{Equation~\\ref{#1}}\n% A raw reference to an equation---avoid using if possible\n\\def\\plaineqref#1{\\ref{#1}}\n% Reference to a chapter, lower-case.\n\\def\\chapref#1{chapter~\\ref{#1}}\n% Reference to an equation, upper case.\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n% Reference to a range of chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\usepackage{hyperref}\n\\usepackage{url}\n\\usepackage{bbm}\n\\usepackage{booktabs}\n\\usepackage{multirow}\n\\usepackage{graphicx}\n\\usepackage{xspace}\n\\usepackage[most]{tcolorbox}\n\n% Authors must not appear in the submitted version. They should be hidden\n% as long as the \\iclrfinalcopy macro remains commented out below.\n% Non-anonymous submissions will be rejected without review.\n\n\\author{}\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to \\LaTeX{} to determine where to break\n% the lines. Using \\AND forces a linebreak at that point. So, if \\LaTeX{}\n% puts 3 of 4 authors names on the first line, and the last on the second\n% line, try using \\AND instead of \\And before the third author name.\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\\newcommand{\\method}{\\textsc{AggLM}\\xspace}\n\\newcommand{\\model}{AggLM-1.7B\\xspace}\n\n%\\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission.\n\\begin{document}\n\n\\maketitle\n\n\\section{Introduction}\n\nScaling up test-time compute, by producing longer intermediate thoughts and/or selection or aggregation over multiple generated samples, has become a predominant way to improve large language models (LLMs) on challenging reasoning tasks \\citep{wei2022chain,wang2023selfconsistency,brown2024large}. These strategies trade additional inference-time computation for higher accuracy, and have yielded state-of-the-art results across mathematics, code generation, and scientific problem solving \\citep{,jaech2024openai,guo2025deepseek}. \n\nMaking use of multiple independent solutions has the advantage of parallel computation, but leaves open the central design choice of how to aggregate answers. Standard practice is to either apply majority voting over the sampled solutions, or weighted majority voting, optionally guided by reward models or verifiers to select among candidates \\citep{wang2023selfconsistency,brown2024large,wu2025inference}. However, majority-based aggregation can overlook valuable minority solutions: correct answers are sometimes assigned low probability under the model due to modeling errors \\citep{stahlberg-byrne-2019-nmt,stahlberg-etal-2022-uncertainty}. Hence, simply maximizing model score, or picking the most frequent output, will not yield the optimal result \\citep{fu2025deep}. Furthermore, these methods leave unexploited the partial correctness that can exist {\\em within} otherwise incorrect thought traces, missing opportunities to combine correct steps from different candidates to produce a fully correct solution.\n\nThis paper proposes \\method{}, a method that instead {\\em learns to use reasoning to combine thoughts} produced by multiple generations computed in parallel. \\method{} is simple: (i) sample multiple solutions from an LLM; (ii) pass these solutions back to an LLM with an aggregation instruction that asks it to synthesize a final answer by reconciling, correcting, and combining the intermediate reasoning steps. We then train a reasoning model to perform this aggregation using reinforcement learning from verifiable rewards (RLVR). This turns aggregation itself into a learned reasoning skill rather than a fixed heuristic. Our approach is summarized in \\autoref{fig:llmagg}.\n\nWe evaluate our method on four popular math competition datasets from MathArena \\citep{balunovic2025matharena}: AIME24, AIME25, HMMT24, and HMMT25. When aggregating solutions from Qwen3-1.7B, which achieves 35\\% accuracy on AIME25, our trained aggregator \\model raises performance to 50\\%, improving over majority voting that is 45\\%. Across all four datasets, \\model consistently outperforms rule-based aggregation methods such as majority voting, as well as strong reward-model selection baselines that have 72B parameters. Furthermore, \\model generalizes robustly: it remains the top performer when aggregating solutions from stronger models like Qwen3-8B or from non-thinking mode. Ablation studies show that balancing easy and hard examples in the \\method{} training mixture is critical for achieving strong results, and that our gains over majority voting are particularly substantial when the majority answer set is small in size; that is, when candidate solutions are more diverse. Finally, \\model is substantially more token-efficient than generating a larger number of solutions for majority voting, delivering both higher accuracy and lower inference costs compared to standard aggregation strategies.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\n \\label{fig:llmagg}\n\\end{figure}\n\n\\section{Related Work}\n\n\\noindent \\textbf{Rule-Based Voting}\nA common way to combine multiple LLM solutions is to apply simple, rule-based voting.\nSelf-consistent decoding \\citep{wang2023selfconsistency,brown2024large} draws many chain-of-thought trajectories and returns the answer that appears most frequently.\nVariants adapt the voting procedure in lightweight ways, such as dynamically choosing the number of samples or using heuristic filters \\citep{aggarwal-etal-2023-lets,xue-etal-2023-dynamic,huang-etal-2024-mirror,knappe2024enhancing}.\nWhile this strategy often yields reliable gains, it fails when correct solutions exist but are confined to minority modes, causing majority voting to amplify errors rather than surface the correct answer. In this work we analyze when that issue occurs, and show how our approach remedies this failing.\n\n\\noindent \\textbf{Model-Based Selection and Aggregation}\nMoving beyond pure counting, recent approaches \nuse models to evaluate or re-rank answer candidates. Broadly, model-based aggregation either (i) trains a separate scorer to select candidates or (ii) prompts the LLM to compare and consolidate them. For selection, a reward model assigns a scalar score to each candidate, and the top-scoring answer is chosen \\citep{yang2024qwen2,liu2024acemath}.\nThis recombines frequency with a learned notion of quality, but it sometimes introduces more regression errors than improvements. Recent work also leverages the language model itself as a generative aggregator. Universal Self-Consistency (USC) \\citep{chen2024universal,qi2025learning} prompts the model to examine all sampled solutions and choose the most coherent one.\n\nOur approach is closest in spirit to these methods, but differs in that we explicitly train a reasoning-focused aggregator with reinforcement learning to synthesize a final solution, rather than relying solely on prompting.\nConcurrent with our work, \\citet{qi2025learning} propose a learned \\emph{Sample Set Aggregator} (SSA) that consumes concatenated samples and generates a final answer, while also training the aggregator via reinforcement learning.\nEmpirically, \\citet{qi2025learning} report modest gains in their settings, suggesting that additional ingredients—such as using reasoning-oriented base models and carefully balancing the training mixture—are important for unlocking stronger aggregation performance. We show in our ablations that, in our setting, the latter is the case.\n\n\\section{\\method}\nOur goal is to train an aggregation language model that, given a problem and a set of candidate solutions produced by an LLM, synthesizes a final solution. As we use training data consisting of tasks with verifiable solutions, \nwe can train our aggregation model, \\method{}, with reinforcement learning from verifiable rewards (RLVR). Training aims to learn two complementary behaviors: (a) selection that identifies and adopts the correct candidate when it already appears in the set; and (b) synthesis that detects mistakes, fills gaps, or combines complementary partial ideas across candidates to produce a new, correct solution that did not appear verbatim in the set. Successful RL training can enable the model to learn how and when to employ these skills.\n\n\\textbf{Problem Formulation} Let $x$ be a given problem and $y^\\star$ its ground-truth solution. We consider two models:\n(i) a \\emph{solution} model $p_{\\theta}(y \\mid x)$ that generates a solution $y$; and\n(ii) an \\emph{aggregation} model $p_{\\phi}(\\tilde{y} \\mid x, y_{1:m})$ that reads the problem together with a set of $m$ candidate solutions $y_{1:m} = (y_1,\\dots,y_m)$ and outputs an aggregated solution $\\tilde{y}$.\n%We also define an answer-extraction function $\\mathrm{Ans}(\\cdot)$ that maps a solution $y$ to a final answer (e.g., an expression or a numeric value).\nGiven a problem $x$, the solution model samples $m$ candidate solutions independently:\n\\[\ny_i \\sim p_{\\theta}(y \\mid x), \\quad i \\in {1,\\dots,m}\n\\]\nThen, the aggregation model produces an aggregated solution:\n\\[\n\\tilde{y} \\sim p_{\\phi}(y \\mid x, y_{1:m})\n\\]\nThe parameters $\\theta$ and $\\phi$ may correspond to the same underlying LLM or to different models. This work focuses on training strong aggregation models; in our main experiments, the solution model $p_{\\theta}$ is treated as an off-the-shelf generator and is kept fixed,\nmaking it easier to draw experimental conclusions when comparing against baselines. However, we also report results where the model parameters are shared in a single model, which as we will see we find to give similar performance.\n%which provides a clearer basis for experimental comparison with baselines.\n\n\\textbf{Training Data} Let $\\mathcal{D} = \\{(x, y^{\\star})\\}^n$ be a collection of problems with ground-truth solutions. For each $x$ we draw $s \\cdot m$ solutions from $p_{\\theta}$ and group them into $s$ sets of size $m$, yielding an aggregation-training corpus\n\\[\n\\mathcal{D}' = \\{x, y_{1:m}, y^{\\star} \\}^{s \\cdot n}.\n\\]\n\nWe note that increasing $s$ introduces more diversity in the answer combinations the aggregation model sees for each $x$, which could potentially improve generalization ability.\nWe define the majority answer as the most frequent answer. An example is considered \\emph{hard} if the majority answer in $y_{1:m}$ is wrong, and \\emph{easy} otherwise. Constructing $\\mathcal{D}'$ from existing data sources $\\mathcal{D}$ may lead to many easy examples, where most generated solutions for a problem are correct. This can under-train the model’s ability to recover minority-but-correct answers, whereas training only on hard groups makes rewards sparse. We therefore construct the final training mixture by taking all hard examples and mixing in $p\\%$ of easy examples, producing a balanced dataset that preserves realism while emphasizing challenging cases.\n\n\\textbf{Training} We optimize the aggregation policy $p_{\\phi}(\\tilde{y} \\mid x, y_{1:m})$ with Group-Relative Policy Optimization (GRPO) \\citep{shao2024deepseekmath}. For each training example, the aggregator produces $\\tilde{y}$ and receives a reward $r(\\tilde{y}) = \\mathbbm{1}\\big[\\tilde{y} = y^\\star\\big]$. We apply the standard GRPO update using this binary reward.\n\n\\section{Experimental Setup}\n\\subsection{Training}\nFollowing our proposed method, we train a 1.7B model that we refer to as \\model. Specifically, we initialize the aggregation model from Qwen3-1.7B \\citep{yang2025qwen3} and train it on DeepScaler\\citep{deepscaler2025}, a collection of around 40 thousand math problems with ground-truth solutions. To construct $\\mathcal{D}'$, we sample a total of 128 independent solutions with temperature $1.5$ from Qwen3-1.7B in the thinking mode, dividing into 16 sets of 8 solutions. To obtain the data mixture, we set $p=50\\%$, resulting in 446,220 training examples. We train for one epoch, with a batch size of 1024, a maximum prompt length of 16384 tokens, and a maximum response length of 16384 tokens. When constructing the easy subset, we maximize diversity by repeating each problem as little as possible. We check for solution equivalence between aggregated solutions and ground-truth solutions using the \\texttt{math\\_verify} library\\footnote{https://github.com/huggingface/Math-Verify}. In GRPO, we use a group size of $8$ for GRPO updates, set the KL regularization coefficient to $0.001$, and maintain a sampling temperature of $1.5$ for the aggregator during training. We use the problem itself as the prompt for the solution model. We include the prompt template we used for aggregating solutions in Figure~\\ref{fig:aggre-prompt}. Note that the solutions used for aggregation (i.e., included in the template) are taken after </think> when obtaining solutions from thinking models.\n\n\\begin{figure}[t]\n\n\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\nGiven the following problem:\n\n\\texttt{\\{problem\\}}\n\nand these solution attempts:\n\n\\texttt{\\{solutions\\}}\n\nIt is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\n\\end{tcolorbox}\n\\caption{\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\n\\label{fig:aggre-prompt}\n\\end{figure}\n\n\\subsection{Evaluation}\n\\textbf{Solution models.} We evaluate aggregation methods using samples from the following solution models: (i) Qwen3-1.7B in both thinking and non-thinking mode; and (ii) Qwen3-8B in thinking mode.\n\n\\textbf{Datasets.} We evaluate on four mathematics competition datasets from MathArena \\citep{balunovic2025matharena}. AIME24 and AIME25 are recent editions of the American Invitational Mathematics Examination, which feature challenging high school-level olympiad problems with single numeric/integer answers. HMMT24 and HMMT25 are editions of the Harvard-MIT Mathematics Tournament, another highly competitive mathematics contest that covers broader mathematical topics and frequently requires creative or multi-step reasoning. Each of these datasets comprises 30 examples.\n\n\\textbf{Protocol.} Because our evaluation datasets are relatively small, we adopt a robust protocol to obtain reliable signals. For each problem $x$, we independently sample 128 solutions at temperature 1 and partition them into $s=16$ sets of $m=8$ solutions each. For every set, the aggregation model $p_\\phi$ is prompted to generate four aggregated solutions, from which we extract the final solutions. Pass@1 for each set is computed as the success rate over these four answers, and for each problem, we average this rate across all 16 sets. The overall score for the dataset is then computed by averaging the set-level pass@1 across all problems.\n\n\\textbf{Baselines.} We compare against a set of state-of-the-art aggregation methods: majority voting, best-of-N, and weighted majority voting with reward models.\nAll of these methods follow the same protocol described above.\nFor reward-model selection, for each set of 8 candidates, we score each candidate with the 7B and 72B AceMath reward models \\citep{liu2024acemath} and select the top-scoring answer, yielding a learned re-ranking baseline. Weighted majority voting combines majority voting and best-of-N by computing a weighted distribution of solutions, where the weights are derived from reward model scores \\citep{welleck2024from}. We also compare to prompted aggregation without training: we apply our aggregation prompt to Qwen3-1.7B without any fine-tuning, isolating the effect of the RL-trained aggregator.\nFinally, we also measure and report pass@1 for the original solution model estimated from 64 independent samples of $p_{\\theta}(y \\mid x)$, and pass@8 (oracle best-of-8 that succeeds if any of the 8 answers is correct, using 64 sets of 8 solutions sampled from 128 solutions in total).\n\n\\section{Results}\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n\\multicolumn{2}{r}{Aggregation Model} \n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\npass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\nPrompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:indist-1p7b}\n\\end{table}\n\n\n\n\\textbf{Evaluation on in-distribution solutions} Table~\\ref{tab:indist-1p7b} presents results on in-distribution 1.7B-thinking solutions, the same solution model used to produce training data for our RL-trained aggregator, \\model{}. In this setting, \\model{} is best on all four benchmarks, outperforming majority voting and the same backbone model with prompting without RL, Qwen3-1.7B, with consistent three to seven point gains, confirming that training the aggregation policy matters. Reward-model selection performs poorly in comparison: best-of-N and weighted majority with AceMath-7B/72B is often inferior to the standard majority voting. Overall, learned generative aggregation outperforms frequency- and reward-model–based selection at surfacing correct minority solutions.\n\n\n\\textbf{Evaluation on solutions from stronger models.}\n\n\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n \\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\npass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\n &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\n &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\nPrompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{82.38} & \\textbf{79.70} & \\textbf{53.01} & \\textbf{60.66} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:8b-results}\n\\end{table}\n\n\n\n\nTable~\\ref{tab:8b-results} presents results on aggregating solutions from a stronger 8B thinking model. \\model{}, despite being trained only on 1.7B solution distributions, transfers effectively and remains the top performer across datasets. It consistently outperforms majority voting and reward-model–based selection, best-of-N and weighted majority with AceMath scorers, and also outperforms prompted generative aggregation without RL, indicating that learned generative aggregation is robust to better solutions than the original training data solution models can generate by themselves.\n\n\\textbf{Evaluation on non-thinking solutions.}\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n% & Model \n \\multicolumn{2}{r}{Aggregation Model} \n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 11.82 & 10.00 & \\phantom{0}6.25 & \\phantom{0}3.39 \\\\\npass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 18.07 & 15.42 & \\phantom{0}8.75 & \\phantom{0}7.29 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\phantom{0}7.44 & \\phantom{0}8.92 \\\\\n &AceMath-72B & 26.33 & 18.62 & 10.23 & \\phantom{0}8.97 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\phantom{0}8.37 & \\phantom{0}8.41 \\\\\n &AceMath-72B & 26.54 & 18.83 & \\phantom{0}9.72 & \\phantom{0}8.09 \\\\\n%\\multirow{2}{*}{Generative} \nPrompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{29.96} & \\textbf{19.77} & \\textbf{17.03} & \\textbf{12.76} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:nonthinking-results}\n\\end{table}\nTable~\\ref{tab:nonthinking-results} presents results on aggregating solutions from a 1.7B non-thinking model. \\model{}, despite being trained on thinking-mode distributions, generalizes effectively and remains the top performer across datasets. It consistently outperforms majority voting, reward-model–based selection, best-of-N and weighted majority with AceMath scorers, and prompted generative aggregation without RL. Notably, reward models improve over majority voting in this lower-signal regime, supporting the hypothesis that learned scorers help more when base-model outputs are weak or noisy. Yet, \\model{} still achieves the best overall performance by synthesizing and correcting candidates rather than merely selecting among them.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.8\\linewidth]{no_sols.pdf}\n \\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\n \\label{fig:scaling-k}\n\\end{figure}\n\n\\section{Ablations \\& analysis}\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.8\\linewidth]{acc_by_num.pdf}\n \\caption{Performance vs. majority answer size for our method \\method{} compared to majority vote. \\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\n \\label{fig:majority-size}\n\\end{figure}\n\n\n\n\\textbf{Scaling via the number of solutions.}\nFigure~\\ref{fig:scaling-k} plots performance versus the number of candidate solutions $k$ per set across the four datasets, comparing majority voting (maj@$k$), the prompted model baseline (Qwen3-1.7B), and our RL-trained aggregator (\\model{}). Although \\model{} is trained only at $k{=}8$, it generalizes to both smaller and larger $k$, improving as $k$ increases. Its curve rises more steeply than majority voting, indicating better scaling with additional candidates. The prompted baseline shows a much flatter trend, often below majority voting, while \\model produces a markedly stronger scaling trend. Notably, on AIME25, HMMT24, and HMMT25, aggregating just eight solutions with \\model{} is better than majority voting with sixteen, demonstrating superior token efficiency in leveraging solution sets.\n\n\n\n\n\n\\textbf{Effect of majority answer size.}\nFigure~\\ref{fig:majority-size} shows the performance by the majority answer size, i.e., the number of occurrences of the most frequent answer. The x-axis is the majority answer size, and the y-axis is the performance on the corresponding subset. \\model's gains are largest when the size is small. That is, when solutions are diverse or uncertain and correct answers are more likely to appear in minority modes; here, careful reasoning matters. As the size grows, the problem becomes easier and majority voting is typically correct; in this regime, our aggregator remains on par with majority voting.\n\n\\begin{table}[t]\n\\centering\n\\caption{Ablation of training mixtures: Easy\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\n\\begin{tabular}{rcccc}\n\\toprule\nEasy\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\n0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\n5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\n10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\n20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\n50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\n\\midrule\nUntrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:easy-mix}\n\\end{table}\n\n\\textbf{Ablating data mixtures.}\nTable~\\ref{tab:easy-mix} investigates the impact of varying the proportion of hard versus easy sets in the training mixture, where a set is labeled hard if the majority answer is incorrect. We always keep all hard examples and vary the fraction of easy sets retained with regards to the number of hard examples (``Easy\\%''), from 0\\% (hard-only) to 270\\% (no filtering, retain all easy examples). Results show that training on hard-only sets results in suboptimal performance, and using all available data offers only marginal improvements over an untrained aggregator. Instead, incorporating a moderate proportion of easy sets (5–50\\%) consistently enhances accuracy, and results are stable within this range. This demonstrates that careful balancing of easy and hard examples is crucial for effective training, but the method is robust to the precise ratio as long as both types of examples are represented.\n\n\\begin{table}[t]\n\\centering\n\\caption{Effect of the number of solution sets $s$ per problem on performance.}\n\\begin{tabular}{rcccc}\n\\toprule\n\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\n2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\n4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\n8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\n16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:unique-sets}\n\\end{table}\n\n\\textbf{Ablating number of solution sets $s$.}\nRecall that for each problem, we sample $s$ sets of $m$ candidate solutions; increasing $s$ (while keeping $m$ fixed) introduces more diversity in the answer combinations the aggregator sees for each $x$. As shown in Table~\\ref{tab:unique-sets}, performance increases only slightly as $s$ grows, indicating that while additional diversity may offer small benefits, the gains are modest. Consequently, training on fewer sets per problem is a reasonable strategy for reducing training budget without significantly compromising aggregation performance.\n\n\\textbf{Is aggregation or extra data responsible for gains?}\n\\begin{table}[t]\n\\centering\n\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\n\\begin{tabular}{lcccc}\n\\toprule\n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\nBase Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\nAdditionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\nMultitask Solution Model &49.11&38.85&26.67&22.50\\\\\nBase Aggregator Model & 63.57&44.85&29.52&27.91\\\\\nTrained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\nMultitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:train-task}\n\\end{table}\nTable~\\ref{tab:train-task} tests whether gains arise merely from additional data rather than aggregation. We fine-tune the solution model $p_{\\theta}$ on the DeepScaler dataset used for aggregator training and evaluate its pass@1, then compare to our RL-trained aggregator on the evaluation tasks. If extra data were the primary driver, a trained solution model should close the gap; instead, its improvements are small or even negative and remain far below the trained aggregator across all benchmarks. Hence, the gains are not simply from more data but from explicitly learning to aggregate, via verifiable-reward RL and balanced easy/hard mixtures, which equips the model to select, correct, and synthesize across candidate solutions.\n\n\n\n\n\\begin{table}[t]\n\\centering\n\\caption{Average token usage per generation for solution vs. aggregator models.}\n\\begin{tabular}{lcccc}\n\\toprule\n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\nBase Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\nAdditionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\nBase Aggregator Model & \\phantom{0}2807.71 & \\phantom{0}2852.10 & \\phantom{0}3465.00 & \\phantom{0}3693.24 \\\\\nTrained Aggregator Model & \\phantom{0}3039.22 & \\phantom{0}3157.11 & \\phantom{0}3681.97 & \\phantom{0}3768.28 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:token-usage}\n\\end{table}\n\nAdditionally, Table~\\ref{tab:token-usage} compares the average number of tokens generated per inference for solution models versus aggregator models. Generating a full solution from scratch is significantly more costly in terms of tokens than aggregating over existing solutions, the aggregator model uses roughly one-third as many tokens as the solution models. This means that to achieve a comparable performance boost, directly increasing $k$ for majority voting (for $k$ larger than used in \\method{}) %with the solution model \nwould require substantially higher token usage. Thus, our learned aggregation approach not only delivers better accuracy but is also more token-efficient.\n\n\n\\textbf{Can the solution LLM and aggregator \\method{} be the same model?}\nOur main experiments separate the solution model and the aggregator \\method{}, maintaining a fixed generator and training a dedicated aggregator for fair comparison against prior aggregation strategies. \nHowever, in principle, a single LLM could be trained to perform both solution reasoning and aggregation, simply by applying different prompts for each task.\nTo examine this, we fine-tune a multitask model on both skills using their respective prompts within the same training set, and report the results alongside our separately trained aggregator in \nTable~\\ref{tab:train-task}. We find that multitasking yields close performance to separate models, while, as before, the multitasked model strongly outperforms simply prompting the solution LLM to aggregate without dedicated training.\nThis suggests that aggregation could be natively incorporated into post-training pipelines, enabling future LLMs to achieve these test-time scaling gains using a single unified model.\n\n\\section{Conclusion}\n\nIn this work we proposed a methodology to learn to aggregate solutions using RLVR, a new test-time scaling approach that improves the ability of LLMs to solve hard reasoning problems.\n%Specifically, we show a crucial component of a successful setup is a purposely designed mixture of input problems based on its difficulty and the ability of aggregator model to explore aggregation strategies during training.\nOur extensive experiments showed improved performance of our aggregator model compared to strong baselines including self-consistency decoding and weighted majority voting with SoTA math reward models. Our approach also showed generalization to (1) input distributions formed by different (e.g., stronger) solution models and (2) a variable number of solutions differing from the ones presented during training.\nFuture work could explore further uses of our aggregator beyond improved final performance, for example for distilling better reasoning skills back into the original solutions.\n\n\n\\bibliography{main}\n\\bibliographystyle{iclr2026_conference}\n\n\\appendix\n\\section{Qualitative Analysis}\nWe present two successful examples of aggregation produced by \\model. In the first example, no correct solutions were included in the prompt. The model had to verify every solution, identify the strategies that made sense, and combine the useful strategies to produce a new solution. In the second example, one correct solution was included in the prompt. The model, verified and compared among solutions, and it picked the solution that it determined to be correct.\n\\begin{tcolorbox}[\n breakable,\n title={\\textbf{Example A: No correct solutions were included in the prompt; a new, correct solution synthesized by \\model.}},\n fonttitle=\\bfseries\\large,\n coltitle=white, % Title text color\n colframe=blue!70!black, % Box border color\n colback=blue!5!white, % Box background color\n boxrule=0.8pt,\n left=2mm, right=2mm, top=1mm, bottom=1mm,\n listing only,\n listing options={breaklines, basicstyle=\\ttfamily\\small},\n]\n\nProblem: The set of points in $3$-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $$\nx-yz<y-zx<z-xy\n$$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b},$ where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b.$\n\n<think>\n\n[...]\n\nBut the problem says that the area is in the form $ a\\sqrt{b} $, and $ 507\\sqrt{3} $ is in that form. So, a = 507, b = 3, so a + b = 510.\n\nBut this is different from the other solutions. So, perhaps the correct answer is 510, but I need to check if there's a mistake in the problem or in my calculations.\n\n[...self-verification...]\n\nBut this is different from the other solutions. However, since the problem states that the answer is in the form $ a\\sqrt{b} $, and the calculation is correct, then the answer is 510.\n\nBut wait, in the previous solutions, the answer was 15, 28, 508. So, why is there a discrepancy?\n\n[...analyzing the discrepancy...]\n\nWait, in Solution 7, the answer is 508. So, maybe the correct answer is 508.\n\nBut why?\n\nIn Solution 7, the area is calculated as $ 478\\sqrt{3} $, which is not in the form $ a\\sqrt{b} $, but if there is a mistake in the calculation, it might be 508.\n\nBut I'm not sure.\n\nGiven the time I've spent and the calculations, I think the correct answer is 510, but I'm not sure. However, since the problem states that the area is in the form $ a\\sqrt{b} $, and the calculation is correct, I must go with 510.\n\n[...]\n\n</think>\n\nTo solve the given problem, we analyze the set of points in 3D space that lie on the plane $ x + y + z = 75 $ and satisfy the inequalities:\n\n$$\nx - yz < y - zx < z - xy\n$$\n\n---\n\n\\#\\#\\# Step 1: Understand the Inequalities\n\nWe simplify the inequalities using the plane equation $ x + y + z = 75 $, and express $ z = 75 - x - y $. Substituting into the inequalities:\n\n- $ x - yz < y - zx \\Rightarrow (x - y)(1 + z) < 0 $\n- $ y - zx < z - xy \\Rightarrow (y - z)(1 + x) < 0 $\n\nThese simplify to:\n\n- $ x < y $ if $ 1 + z > 0 $\n- $ y < z $ if $ 1 + x > 0 $\n\nSo, the region is defined by $ x < y < z $, and the constraints on the variables are:\n\n- $ x + y < 76 $\n- $ x + 2y < 75 $\n\nThese define a **convex triangle** in the plane $ x + y + z = 75 $, with vertices at:\n\n- $ A = (-1, -1, 77) $\n- $ B = (25, 25, 25) $\n- $ C = (-1, 38, 38) $\n\n---\n\n\\#\\#\\# Step 2: Compute the Area of the Triangle\n\nWe compute the area of the triangle formed by these three points. The vectors from point $ A $ to $ B $ and $ A $ to $ C $ are:\n\n- $ \\vec{AB} = (26, -13, -13) $\n- $ \\vec{AC} = (0, -39, 39) $\n\nThe cross product is:\n\n$$\n\\vec{AB} \\times \\vec{AC} = (-26 \\cdot 39, -26 \\cdot 39, -26 \\cdot 39) = (-26 \\cdot 39, -26 \\cdot 39, -26 \\cdot 39)\n$$\n\nThe magnitude of the cross product is:\n\n$$\n\\|\\vec{AB} \\times \\vec{AC}\\| = \\sqrt{(26 \\cdot 39)^2 + (26 \\cdot 39)^2 + (26 \\cdot 39)^2} = 26 \\cdot 39 \\cdot \\sqrt{3}\n$$\n\nThe area of the triangle is half of this:\n\n$$\n\\text{Area} = \\frac{1}{2} \\cdot 26 \\cdot 39 \\cdot \\sqrt{3} = 13 \\cdot 39 \\cdot \\sqrt{3} = 507 \\cdot \\sqrt{3}\n$$\n\n---\n\n\\#\\#\\# Step 3: Express in the Form $ a\\sqrt{b} $\n\nWe can express the area as:\n\n$$\n\\text{Area} = 507\\sqrt{3}\n$$\n\nThus, $ a = 507 $, $ b = 3 $, and the final answer is:\n\n$$\na + b = 507 + 3 = \\boxed{510}\n$$\n\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[\n breakable,\n title={\\textbf{Example B: One correct solution included in the prompt, and it was chosen by \\model.}},\n fonttitle=\\bfseries\\large,\n coltitle=white, % Title text color\n colframe=blue!70!black, % Box border color\n colback=blue!5!white, % Box background color\n boxrule=0.8pt,\n left=2mm, right=2mm, top=1mm, bottom=1mm,\n listing only,\n listing options={breaklines, basicstyle=\\ttfamily\\small},\n]\nProblem: From an unlimited supply of $1$-cent coins, $10$-cent coins, and $25$-cent coins, Silas wants to find a collection of coins that has a total value of $N$ cents, where $N$ is a positive integer. He uses the so-called \\textit{greedy algorithm}, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $N$. For example, to get $42$ cents, Silas will choose a $25$-cent coin, then a $10$-cent coin, then $7$ $1$-cent coins. However, this collection of $9$ coins uses more coins than necessary to get a total of $42$ cents; indeed, choosing $4$ $10$-cent coins and $2$ $1$-cent coins achieves the same total with only $6$ coins.\n\nIn general, the greedy algorithm \\emph{succeeds} for a given $N$ if no other collection of $1$-cent, $10$-cent, and $25$-cent coins gives a total value of $N$ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $N$ between $1$ and $1000$ inclusive for which the greedy algorithm succeeds.\n\n<think>\n\n[...]\n\nFrom the solutions provided, there are multiple approaches, but I need to figure out the correct one. Let me think about the key points.\n\nThe key insight is that the greedy algorithm fails when there's a better combination of coins. For example, if after using as many 25-cent coins as possible, the remainder is between 5 and 9, or between 15 and 19, then the greedy algorithm might not be optimal. Wait, the solutions mention that when the remainder is in certain ranges, the greedy algorithm fails. For example, in Solution 1, it says that if the remainder r is in {5,6,7,8,9,15,16,17,18,19}, the greedy algorithm fails. But in Solution 3, it says that there are 5 values of N in every group of 25 that fail. And in Solution 4, it says that there are 31 bad values. But in Solution 8, it says that there are 750 bad values, leading to 950 good ones.\n\nIn Solution 1, they say that for each a from 1 to 39, there are 10 values of r that cause failure. So 39*10=390. Then, for a=0, there are 10 values (5-9, 15-19), but those are optimal. So total failing N is 390. Then the answer is 1000-390=610. But in Solution 8, they say 750 bad values, leading to 950 good ones. So which one is correct?\n\nWait, but in Solution 1, they say that the number of failing N is 390. But in Solution 8, they say 750. So there's a discrepancy here. Let me check.\n\nWait, in Solution 1, they mention that for each a from 1 to 39, there are 10 values of r that cause failure. But a ranges from 1 to 39, so 39 values of a. For each a, there are 10 r values. So 39*10=390. But then, for a=0, there are 10 values of r (5-9, 15-19), which are optimal. So total failing N is 390. Then the answer is 1000-390=610.\n\nBut in Solution 8, they say that there are 750 bad values. So why the difference?\n\nWait, maybe the problem is that in Solution 1, they are considering that for each a, there are 10 r values, but maybe some of those r values are overlapping or something. Let me check.\n\nFor example, when a=1, N=25+ r, where r is in {5,6,7,8,9,15,16,17,18,19}. So for each a, there are 10 r values. But when a=40, N=25*40 + r, but since N is up to 1000, 25*40=1000, so r=0. So a=40 would be N=1000, which is the upper limit. But in Solution 1, they say a ranges from 1 to 39, so that's 39 values of a. So 39*10=390. Then, for a=0, N=r, where r is in {5,6,7,8,9,15,16,17,18,19}, which is 10 values. But those are optimal, so they are not failing. So total failing N is 390. So answer is 1000-390=610.\n\n[...]\n\n</think>\n\nTo determine how many values of $ N $ between 1 and 1000 inclusive result in the **greedy algorithm** for making change using **1-cent, 10-cent, and 25-cent coins** being **optimal**, we must understand when the greedy algorithm **succeeds** in producing the **minimal number of coins**.\n\n---\n\n\\#\\#\\# **Understanding the Greedy Algorithm**\n\nThe greedy algorithm works as follows:\n\n1. **Start with the largest coin (25 cents)**.\n2. Use as many of that coin as possible without exceeding the target amount.\n3. Then use as many of the next largest coin (10 cents) as possible.\n4. Finally, use the remaining amount in 1-cent coins.\n\nFor example:\n- $ N = 42 $: 1 × 25 + 1 × 10 + 7 × 1 = 9 coins.\n- But the alternative: 4 × 10 + 2 × 1 = 6 coins.\n\nThis shows that the greedy algorithm **fails** for $ N = 42 $.\n\n---\n\n\\#\\#\\# **When Does the Greedy Algorithm Fail?**\n\nThe greedy algorithm **fails** for a value $ N $ if there exists a **better combination** of coins (using 1, 10, and 25 cents) that uses **fewer coins** than the greedy algorithm.\n\nThis happens when the **remainder** $ r = N \\mod 25 $ is in the set $ \\{5, 6, 7, 8, 9, 15, 16, 17, 18, 19\\} $.\n\nThis is because:\n- For such $ r $, the greedy algorithm uses $ \\left\\lfloor \\frac{r}{10} \\right\\rfloor + (r \\mod 10) $ coins.\n- But it is possible to express $ r $ as a combination of 10-cent and 1-cent coins with fewer coins.\n\n---\n\n\\#\\#\\# **Counting the Failing Values**\n\nWe count the number of $ N $ in the range 1 to 1000 for which $ r = N \\mod 25 \\in \\{5, 6, 7, 8, 9, 15, 16, 17, 18, 19\\} $.\n\n- For each of these 10 values of $ r $, the number of $ N $ values in the range 1 to 1000 is:\n $$\n \\left\\lfloor \\frac{1000 - r}{25} \\right\\rfloor + 1\n $$\n- But since $ N $ must be at least 1, and $ r $ is between 5 and 19, the number of valid $ N $ is:\n $$\n 39 \\times 10 = 390\n $$\n- This is because $ a = \\left\\lfloor \\frac{N}{25} \\right\\rfloor $ ranges from 1 to 39, and for each $ a $, there are 10 values of $ r $.\n\n---\n\n\\#\\#\\# **Final Calculation**\n\n- Total values of $ N $ from 1 to 1000: 1000\n- Number of failing $ N $: 390\n- Therefore, the number of values of $ N $ where the greedy algorithm **succeeds** is:\n $$\n 1000 - 390 = \\boxed{610}\n $$\n\n---\n\n\\#\\#\\# **Final Answer**\n\n$$\n\\boxed{610}\n$$\n\n\\end{tcolorbox}\n\n%\\appendix\n%\\section{Appendix}\n%You may include other additional sections here.\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"Which dataset's average across aggregation models deviates the most from the average of all 4 datatsets across all aggregation models and how much does it deviate by?"},"answer":{"kind":"string","value":"AIME24, 23.74"},"plan":{"kind":"string","value":"SELECT all datasets\nLOOP for each dataset\n COMPUTE dataset_average = average of all scores for this dataset across all aggregation methods\nCOMPUTE overall_average = average of dataset_average\n\n\nSELECT all datasets\nLOOP for each dataset\n COMPUTE deviation = absolute(dataset_average − overall_average)\nCOMPUTE target_dataset = argmax dataset over deviation\n\n\nRETURN target_dataset, deviation of target_dataset\n"}}},{"rowIdx":351,"cells":{"paper":{"kind":"string","value":"2509.06870"},"relevant_tables":{"kind":"list like","value":[["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n","\\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n"," &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n"," &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\n","Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:indist-1p7b}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\\\\\\n\",\n \" &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\\\\\\n\",\n \" &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{70.69} & \\\\textbf{50.00} & \\\\textbf{33.34} & \\\\textbf{32.07} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:indist-1p7b}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n"," \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\n"," \\label{fig:llmagg}\n","\\end{figure}\n"],["\\begin{figure}[t]\n","\n","\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\n","Given the following problem:\n","\n","\\texttt{\\{problem\\}}\n","\n","and these solution attempts:\n","\n","\\texttt{\\{solutions\\}}\n","\n","It is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\n","\\end{tcolorbox}\n","\\caption{\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\n","\\label{fig:aggre-prompt}\n","\\end{figure}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n","\\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n"," &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n"," &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\n","Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:indist-1p7b}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n"," \\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\n","pass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\n"," &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\n"," &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\n","Prompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{82.38} & \\textbf{79.70} & \\textbf{53.01} & \\textbf{60.66} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:8b-results}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n"," \\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 11.82 & 10.00 & \\phantom{0}6.25 & \\phantom{0}3.39 \\\\\n","pass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 18.07 & 15.42 & \\phantom{0}8.75 & \\phantom{0}7.29 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\phantom{0}7.44 & \\phantom{0}8.92 \\\\\n"," &AceMath-72B & 26.33 & 18.62 & 10.23 & \\phantom{0}8.97 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\phantom{0}8.37 & \\phantom{0}8.41 \\\\\n"," &AceMath-72B & 26.54 & 18.83 & \\phantom{0}9.72 & \\phantom{0}8.09 \\\\\n","Prompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{29.96} & \\textbf{19.77} & \\textbf{17.03} & \\textbf{12.76} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:nonthinking-results}\n","\\end{table}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=0.8\\linewidth]{no_sols.pdf}\n"," \\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\n"," \\label{fig:scaling-k}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=0.8\\linewidth]{acc_by_num.pdf}\n"," \\caption{Performance vs. majority answer size for our method \\method{} compared to majority vote. \\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\n"," \\label{fig:majority-size}\n","\\end{figure}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Ablation of training mixtures: Easy\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\n","\\begin{tabular}{rcccc}\n","\\toprule\n","Easy\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\n","5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\n","10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\n","20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\n","50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\n","\\midrule\n","Untrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:easy-mix}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Effect of the number of solution sets $s$ per problem on performance.}\n","\\begin{tabular}{rcccc}\n","\\toprule\n","\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\n","4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\n","8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\n","16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:unique-sets}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\n","\\begin{tabular}{lcccc}\n","\\toprule\n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","Base Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","Additionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\n","Multitask Solution Model &49.11&38.85&26.67&22.50\\\\\n","Base Aggregator Model & 63.57&44.85&29.52&27.91\\\\\n","Trained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","Multitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:train-task}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Average token usage per generation for solution vs. aggregator models.}\n","\\begin{tabular}{lcccc}\n","\\toprule\n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","Base Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\n","Additionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\n","Base Aggregator Model & \\phantom{0}2807.71 & \\phantom{0}2852.10 & \\phantom{0}3465.00 & \\phantom{0}3693.24 \\\\\n","Trained Aggregator Model & \\phantom{0}3039.22 & \\phantom{0}3157.11 & \\phantom{0}3681.97 & \\phantom{0}3768.28 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:token-usage}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1.0\\\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\\n\",\n \" \\\\caption{{\\\\bf \\\\method{}}: given a task and sampled LLM solutions as input, \\\\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\\\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\\\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\\n\",\n \" \\\\label{fig:llmagg}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \"\\n\",\n \"\\\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\\n\",\n \"Given the following problem:\\n\",\n \"\\n\",\n \"\\\\texttt{\\\\{problem\\\\}}\\n\",\n \"\\n\",\n \"and these solution attempts:\\n\",\n \"\\n\",\n \"\\\\texttt{\\\\{solutions\\\\}}\\n\",\n \"\\n\",\n \"It is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\\n\",\n \"\\\\end{tcolorbox}\\n\",\n \"\\\\caption{\\\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\\n\",\n \"\\\\label{fig:aggre-prompt}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\\\\\\n\",\n \" &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\\\\\\n\",\n \" &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{70.69} & \\\\textbf{50.00} & \\\\textbf{33.34} & \\\\textbf{32.07} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:indist-1p7b}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \" \\\\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\\\\\\n\",\n \"pass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\\\\\\n\",\n \" &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\\\\\\n\",\n \" &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{82.38} & \\\\textbf{79.70} & \\\\textbf{53.01} & \\\\textbf{60.66} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:8b-results}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \" \\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 11.82 & 10.00 & \\\\phantom{0}6.25 & \\\\phantom{0}3.39 \\\\\\\\\\n\",\n \"pass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 18.07 & 15.42 & \\\\phantom{0}8.75 & \\\\phantom{0}7.29 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\\\phantom{0}7.44 & \\\\phantom{0}8.92 \\\\\\\\\\n\",\n \" &AceMath-72B & 26.33 & 18.62 & 10.23 & \\\\phantom{0}8.97 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\\\phantom{0}8.37 & \\\\phantom{0}8.41 \\\\\\\\\\n\",\n \" &AceMath-72B & 26.54 & 18.83 & \\\\phantom{0}9.72 & \\\\phantom{0}8.09 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{29.96} & \\\\textbf{19.77} & \\\\textbf{17.03} & \\\\textbf{12.76} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:nonthinking-results}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\linewidth]{no_sols.pdf}\\n\",\n \" \\\\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\\\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\\n\",\n \" \\\\label{fig:scaling-k}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\linewidth]{acc_by_num.pdf}\\n\",\n \" \\\\caption{Performance vs. majority answer size for our method \\\\method{} compared to majority vote. \\\\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\\n\",\n \" \\\\label{fig:majority-size}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Ablation of training mixtures: Easy\\\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\\n\",\n \"\\\\begin{tabular}{rcccc}\\n\",\n \"\\\\toprule\\n\",\n \"Easy\\\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\\\\\\n\",\n \"5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\\\\\\n\",\n \"10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\\\\\\n\",\n \"20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\\\\\\n\",\n \"50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Untrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:easy-mix}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Effect of the number of solution sets $s$ per problem on performance.}\\n\",\n \"\\\\begin{tabular}{rcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\\\\\\n\",\n \"4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\\\\\\n\",\n \"8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\\\\\\n\",\n \"16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:unique-sets}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\\n\",\n \"\\\\begin{tabular}{lcccc}\\n\",\n \"\\\\toprule\\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Base Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"Additionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\\\\\\n\",\n \"Multitask Solution Model &49.11&38.85&26.67&22.50\\\\\\\\\\n\",\n \"Base Aggregator Model & 63.57&44.85&29.52&27.91\\\\\\\\\\n\",\n \"Trained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"Multitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:train-task}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Average token usage per generation for solution vs. aggregator models.}\\n\",\n \"\\\\begin{tabular}{lcccc}\\n\",\n \"\\\\toprule\\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Base Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\\\\\\n\",\n \"Additionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\\\\\\n\",\n \"Base Aggregator Model & \\\\phantom{0}2807.71 & \\\\phantom{0}2852.10 & \\\\phantom{0}3465.00 & \\\\phantom{0}3693.24 \\\\\\\\\\n\",\n \"Trained Aggregator Model & \\\\phantom{0}3039.22 & \\\\phantom{0}3157.11 & \\\\phantom{0}3681.97 & \\\\phantom{0}3768.28 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:token-usage}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\pdfoutput=1\n\\documentclass[]{fairmeta}\n% Option \"twocolumn\" available, but please prioritize single-column\n\n\\title{The Majority is not always right: \\\\\n%Reinforcement-learned aggregation}\nRL training for solution aggregation}\n\n\\author[1]{Wenting Zhao}\n\\author[1,2]{Pranjal Aggarwal}\n\\author[1]{Swarnadeep Saha}\n\\author[1]{Asli Celikyilmaz}\n\\author[1]{Jason Weston}\n\\author[1]{Ilia Kulikov}\n\n\\affiliation[1]{FAIR at Meta}\n\\affiliation[2]{CMU}\n\n\\abstract{Scaling up test-time compute, by generating multiple independent solutions and selecting or aggregating among them, has become a central paradigm for improving large language models (LLMs) on challenging reasoning tasks. While most prior work relies on simple majority voting or reward model ranking to aggregate solutions,\nthese approaches may only yield limited benefits. In this work, we propose to learn aggregation as an explicit reasoning skill: given a set of candidate solutions, we train an aggregator model to review, reconcile, and synthesize a final, correct answer using reinforcement learning from verifiable rewards. A key ingredient is careful balancing of easy and hard training examples, allowing the model to learn both to recover minority-but-correct answers as well as easy majority-correct answers. \n%\n\\if 0 non-arxiv verios\n%Empirically, aggregating solutions from Qwen3-1.7B, which %achieves 35\\% accuracy on AIME25, our trained aggregator, \\model, boosts performance to 50\\%.\n%\\model outperforms both strong rule-based and reward-model baselines, across multiple math competition benchmarks. Furthermore, it generalizes effectively to solutions from stronger models and solutions produced in non-thinking modes, all while requiring substantially fewer tokens than majority voting with larger numbers of solutions.}\n\\fi\nEmpirically, we find our method, \\method{}, outperforms both strong rule-based and reward-model baselines, across multiple benchmarks. Furthermore, it generalizes effectively to solutions from differing models, including stronger ones than contained in the training data, \n%stronger models and solutions produced in non-thinking modes,\nall while requiring substantially fewer tokens than majority voting with larger numbers of solutions.\n}\n\\date{\\today}\n\n% Optional math commands from https://github.com/goodfeli/dlbook_notation.\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n% Figure reference, capital. For start of sentence\n\\def\\Figref#1{Figure~\\ref{#1}}\n\\def\\twofigref#1#2{figures \\ref{#1} and \\ref{#2}}\n\\def\\quadfigref#1#2#3#4{figures \\ref{#1}, \\ref{#2}, \\ref{#3} and \\ref{#4}}\n% Section reference, lower-case.\n\\def\\secref#1{section~\\ref{#1}}\n% Section reference, capital.\n\\def\\Secref#1{Section~\\ref{#1}}\n% Reference to two sections.\n\\def\\twosecrefs#1#2{sections \\ref{#1} and \\ref{#2}}\n% Reference to three sections.\n\\def\\secrefs#1#2#3{sections \\ref{#1}, \\ref{#2} and \\ref{#3}}\n% Reference to an equation, lower-case.\n\\def\\eqref#1{equation~\\ref{#1}}\n% Reference to an equation, upper case\n\\def\\Eqref#1{Equation~\\ref{#1}}\n% A raw reference to an equation---avoid using if possible\n\\def\\plaineqref#1{\\ref{#1}}\n% Reference to a chapter, lower-case.\n\\def\\chapref#1{chapter~\\ref{#1}}\n% Reference to an equation, upper case.\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n% Reference to a range of chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\usepackage{hyperref}\n\\usepackage{url}\n\\usepackage{bbm}\n\\usepackage{booktabs}\n\\usepackage{multirow}\n\\usepackage{graphicx}\n\\usepackage{xspace}\n\\usepackage[most]{tcolorbox}\n\n% Authors must not appear in the submitted version. They should be hidden\n% as long as the \\iclrfinalcopy macro remains commented out below.\n% Non-anonymous submissions will be rejected without review.\n\n\\author{}\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to \\LaTeX{} to determine where to break\n% the lines. Using \\AND forces a linebreak at that point. So, if \\LaTeX{}\n% puts 3 of 4 authors names on the first line, and the last on the second\n% line, try using \\AND instead of \\And before the third author name.\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\\newcommand{\\method}{\\textsc{AggLM}\\xspace}\n\\newcommand{\\model}{AggLM-1.7B\\xspace}\n\n%\\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission.\n\\begin{document}\n\n\\maketitle\n\n\\section{Introduction}\n\nScaling up test-time compute, by producing longer intermediate thoughts and/or selection or aggregation over multiple generated samples, has become a predominant way to improve large language models (LLMs) on challenging reasoning tasks \\citep{wei2022chain,wang2023selfconsistency,brown2024large}. These strategies trade additional inference-time computation for higher accuracy, and have yielded state-of-the-art results across mathematics, code generation, and scientific problem solving \\citep{,jaech2024openai,guo2025deepseek}. \n\nMaking use of multiple independent solutions has the advantage of parallel computation, but leaves open the central design choice of how to aggregate answers. Standard practice is to either apply majority voting over the sampled solutions, or weighted majority voting, optionally guided by reward models or verifiers to select among candidates \\citep{wang2023selfconsistency,brown2024large,wu2025inference}. However, majority-based aggregation can overlook valuable minority solutions: correct answers are sometimes assigned low probability under the model due to modeling errors \\citep{stahlberg-byrne-2019-nmt,stahlberg-etal-2022-uncertainty}. Hence, simply maximizing model score, or picking the most frequent output, will not yield the optimal result \\citep{fu2025deep}. Furthermore, these methods leave unexploited the partial correctness that can exist {\\em within} otherwise incorrect thought traces, missing opportunities to combine correct steps from different candidates to produce a fully correct solution.\n\nThis paper proposes \\method{}, a method that instead {\\em learns to use reasoning to combine thoughts} produced by multiple generations computed in parallel. \\method{} is simple: (i) sample multiple solutions from an LLM; (ii) pass these solutions back to an LLM with an aggregation instruction that asks it to synthesize a final answer by reconciling, correcting, and combining the intermediate reasoning steps. We then train a reasoning model to perform this aggregation using reinforcement learning from verifiable rewards (RLVR). This turns aggregation itself into a learned reasoning skill rather than a fixed heuristic. Our approach is summarized in \\autoref{fig:llmagg}.\n\nWe evaluate our method on four popular math competition datasets from MathArena \\citep{balunovic2025matharena}: AIME24, AIME25, HMMT24, and HMMT25. When aggregating solutions from Qwen3-1.7B, which achieves 35\\% accuracy on AIME25, our trained aggregator \\model raises performance to 50\\%, improving over majority voting that is 45\\%. Across all four datasets, \\model consistently outperforms rule-based aggregation methods such as majority voting, as well as strong reward-model selection baselines that have 72B parameters. Furthermore, \\model generalizes robustly: it remains the top performer when aggregating solutions from stronger models like Qwen3-8B or from non-thinking mode. Ablation studies show that balancing easy and hard examples in the \\method{} training mixture is critical for achieving strong results, and that our gains over majority voting are particularly substantial when the majority answer set is small in size; that is, when candidate solutions are more diverse. Finally, \\model is substantially more token-efficient than generating a larger number of solutions for majority voting, delivering both higher accuracy and lower inference costs compared to standard aggregation strategies.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\n \\label{fig:llmagg}\n\\end{figure}\n\n\\section{Related Work}\n\n\\noindent \\textbf{Rule-Based Voting}\nA common way to combine multiple LLM solutions is to apply simple, rule-based voting.\nSelf-consistent decoding \\citep{wang2023selfconsistency,brown2024large} draws many chain-of-thought trajectories and returns the answer that appears most frequently.\nVariants adapt the voting procedure in lightweight ways, such as dynamically choosing the number of samples or using heuristic filters \\citep{aggarwal-etal-2023-lets,xue-etal-2023-dynamic,huang-etal-2024-mirror,knappe2024enhancing}.\nWhile this strategy often yields reliable gains, it fails when correct solutions exist but are confined to minority modes, causing majority voting to amplify errors rather than surface the correct answer. In this work we analyze when that issue occurs, and show how our approach remedies this failing.\n\n\\noindent \\textbf{Model-Based Selection and Aggregation}\nMoving beyond pure counting, recent approaches \nuse models to evaluate or re-rank answer candidates. Broadly, model-based aggregation either (i) trains a separate scorer to select candidates or (ii) prompts the LLM to compare and consolidate them. For selection, a reward model assigns a scalar score to each candidate, and the top-scoring answer is chosen \\citep{yang2024qwen2,liu2024acemath}.\nThis recombines frequency with a learned notion of quality, but it sometimes introduces more regression errors than improvements. Recent work also leverages the language model itself as a generative aggregator. Universal Self-Consistency (USC) \\citep{chen2024universal,qi2025learning} prompts the model to examine all sampled solutions and choose the most coherent one.\n\nOur approach is closest in spirit to these methods, but differs in that we explicitly train a reasoning-focused aggregator with reinforcement learning to synthesize a final solution, rather than relying solely on prompting.\nConcurrent with our work, \\citet{qi2025learning} propose a learned \\emph{Sample Set Aggregator} (SSA) that consumes concatenated samples and generates a final answer, while also training the aggregator via reinforcement learning.\nEmpirically, \\citet{qi2025learning} report modest gains in their settings, suggesting that additional ingredients—such as using reasoning-oriented base models and carefully balancing the training mixture—are important for unlocking stronger aggregation performance. We show in our ablations that, in our setting, the latter is the case.\n\n\\section{\\method}\nOur goal is to train an aggregation language model that, given a problem and a set of candidate solutions produced by an LLM, synthesizes a final solution. As we use training data consisting of tasks with verifiable solutions, \nwe can train our aggregation model, \\method{}, with reinforcement learning from verifiable rewards (RLVR). Training aims to learn two complementary behaviors: (a) selection that identifies and adopts the correct candidate when it already appears in the set; and (b) synthesis that detects mistakes, fills gaps, or combines complementary partial ideas across candidates to produce a new, correct solution that did not appear verbatim in the set. Successful RL training can enable the model to learn how and when to employ these skills.\n\n\\textbf{Problem Formulation} Let $x$ be a given problem and $y^\\star$ its ground-truth solution. We consider two models:\n(i) a \\emph{solution} model $p_{\\theta}(y \\mid x)$ that generates a solution $y$; and\n(ii) an \\emph{aggregation} model $p_{\\phi}(\\tilde{y} \\mid x, y_{1:m})$ that reads the problem together with a set of $m$ candidate solutions $y_{1:m} = (y_1,\\dots,y_m)$ and outputs an aggregated solution $\\tilde{y}$.\n%We also define an answer-extraction function $\\mathrm{Ans}(\\cdot)$ that maps a solution $y$ to a final answer (e.g., an expression or a numeric value).\nGiven a problem $x$, the solution model samples $m$ candidate solutions independently:\n\\[\ny_i \\sim p_{\\theta}(y \\mid x), \\quad i \\in {1,\\dots,m}\n\\]\nThen, the aggregation model produces an aggregated solution:\n\\[\n\\tilde{y} \\sim p_{\\phi}(y \\mid x, y_{1:m})\n\\]\nThe parameters $\\theta$ and $\\phi$ may correspond to the same underlying LLM or to different models. This work focuses on training strong aggregation models; in our main experiments, the solution model $p_{\\theta}$ is treated as an off-the-shelf generator and is kept fixed,\nmaking it easier to draw experimental conclusions when comparing against baselines. However, we also report results where the model parameters are shared in a single model, which as we will see we find to give similar performance.\n%which provides a clearer basis for experimental comparison with baselines.\n\n\\textbf{Training Data} Let $\\mathcal{D} = \\{(x, y^{\\star})\\}^n$ be a collection of problems with ground-truth solutions. For each $x$ we draw $s \\cdot m$ solutions from $p_{\\theta}$ and group them into $s$ sets of size $m$, yielding an aggregation-training corpus\n\\[\n\\mathcal{D}' = \\{x, y_{1:m}, y^{\\star} \\}^{s \\cdot n}.\n\\]\n\nWe note that increasing $s$ introduces more diversity in the answer combinations the aggregation model sees for each $x$, which could potentially improve generalization ability.\nWe define the majority answer as the most frequent answer. An example is considered \\emph{hard} if the majority answer in $y_{1:m}$ is wrong, and \\emph{easy} otherwise. Constructing $\\mathcal{D}'$ from existing data sources $\\mathcal{D}$ may lead to many easy examples, where most generated solutions for a problem are correct. This can under-train the model’s ability to recover minority-but-correct answers, whereas training only on hard groups makes rewards sparse. We therefore construct the final training mixture by taking all hard examples and mixing in $p\\%$ of easy examples, producing a balanced dataset that preserves realism while emphasizing challenging cases.\n\n\\textbf{Training} We optimize the aggregation policy $p_{\\phi}(\\tilde{y} \\mid x, y_{1:m})$ with Group-Relative Policy Optimization (GRPO) \\citep{shao2024deepseekmath}. For each training example, the aggregator produces $\\tilde{y}$ and receives a reward $r(\\tilde{y}) = \\mathbbm{1}\\big[\\tilde{y} = y^\\star\\big]$. We apply the standard GRPO update using this binary reward.\n\n\\section{Experimental Setup}\n\\subsection{Training}\nFollowing our proposed method, we train a 1.7B model that we refer to as \\model. Specifically, we initialize the aggregation model from Qwen3-1.7B \\citep{yang2025qwen3} and train it on DeepScaler\\citep{deepscaler2025}, a collection of around 40 thousand math problems with ground-truth solutions. To construct $\\mathcal{D}'$, we sample a total of 128 independent solutions with temperature $1.5$ from Qwen3-1.7B in the thinking mode, dividing into 16 sets of 8 solutions. To obtain the data mixture, we set $p=50\\%$, resulting in 446,220 training examples. We train for one epoch, with a batch size of 1024, a maximum prompt length of 16384 tokens, and a maximum response length of 16384 tokens. When constructing the easy subset, we maximize diversity by repeating each problem as little as possible. We check for solution equivalence between aggregated solutions and ground-truth solutions using the \\texttt{math\\_verify} library\\footnote{https://github.com/huggingface/Math-Verify}. In GRPO, we use a group size of $8$ for GRPO updates, set the KL regularization coefficient to $0.001$, and maintain a sampling temperature of $1.5$ for the aggregator during training. We use the problem itself as the prompt for the solution model. We include the prompt template we used for aggregating solutions in Figure~\\ref{fig:aggre-prompt}. Note that the solutions used for aggregation (i.e., included in the template) are taken after </think> when obtaining solutions from thinking models.\n\n\\begin{figure}[t]\n\n\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\nGiven the following problem:\n\n\\texttt{\\{problem\\}}\n\nand these solution attempts:\n\n\\texttt{\\{solutions\\}}\n\nIt is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\n\\end{tcolorbox}\n\\caption{\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\n\\label{fig:aggre-prompt}\n\\end{figure}\n\n\\subsection{Evaluation}\n\\textbf{Solution models.} We evaluate aggregation methods using samples from the following solution models: (i) Qwen3-1.7B in both thinking and non-thinking mode; and (ii) Qwen3-8B in thinking mode.\n\n\\textbf{Datasets.} We evaluate on four mathematics competition datasets from MathArena \\citep{balunovic2025matharena}. AIME24 and AIME25 are recent editions of the American Invitational Mathematics Examination, which feature challenging high school-level olympiad problems with single numeric/integer answers. HMMT24 and HMMT25 are editions of the Harvard-MIT Mathematics Tournament, another highly competitive mathematics contest that covers broader mathematical topics and frequently requires creative or multi-step reasoning. Each of these datasets comprises 30 examples.\n\n\\textbf{Protocol.} Because our evaluation datasets are relatively small, we adopt a robust protocol to obtain reliable signals. For each problem $x$, we independently sample 128 solutions at temperature 1 and partition them into $s=16$ sets of $m=8$ solutions each. For every set, the aggregation model $p_\\phi$ is prompted to generate four aggregated solutions, from which we extract the final solutions. Pass@1 for each set is computed as the success rate over these four answers, and for each problem, we average this rate across all 16 sets. The overall score for the dataset is then computed by averaging the set-level pass@1 across all problems.\n\n\\textbf{Baselines.} We compare against a set of state-of-the-art aggregation methods: majority voting, best-of-N, and weighted majority voting with reward models.\nAll of these methods follow the same protocol described above.\nFor reward-model selection, for each set of 8 candidates, we score each candidate with the 7B and 72B AceMath reward models \\citep{liu2024acemath} and select the top-scoring answer, yielding a learned re-ranking baseline. Weighted majority voting combines majority voting and best-of-N by computing a weighted distribution of solutions, where the weights are derived from reward model scores \\citep{welleck2024from}. We also compare to prompted aggregation without training: we apply our aggregation prompt to Qwen3-1.7B without any fine-tuning, isolating the effect of the RL-trained aggregator.\nFinally, we also measure and report pass@1 for the original solution model estimated from 64 independent samples of $p_{\\theta}(y \\mid x)$, and pass@8 (oracle best-of-8 that succeeds if any of the 8 answers is correct, using 64 sets of 8 solutions sampled from 128 solutions in total).\n\n\\section{Results}\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n\\multicolumn{2}{r}{Aggregation Model} \n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\npass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\nPrompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:indist-1p7b}\n\\end{table}\n\n\n\n\\textbf{Evaluation on in-distribution solutions} Table~\\ref{tab:indist-1p7b} presents results on in-distribution 1.7B-thinking solutions, the same solution model used to produce training data for our RL-trained aggregator, \\model{}. In this setting, \\model{} is best on all four benchmarks, outperforming majority voting and the same backbone model with prompting without RL, Qwen3-1.7B, with consistent three to seven point gains, confirming that training the aggregation policy matters. Reward-model selection performs poorly in comparison: best-of-N and weighted majority with AceMath-7B/72B is often inferior to the standard majority voting. Overall, learned generative aggregation outperforms frequency- and reward-model–based selection at surfacing correct minority solutions.\n\n\n\\textbf{Evaluation on solutions from stronger models.}\n\n\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n \\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\npass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\n &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\n &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\nPrompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{82.38} & \\textbf{79.70} & \\textbf{53.01} & \\textbf{60.66} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:8b-results}\n\\end{table}\n\n\n\n\nTable~\\ref{tab:8b-results} presents results on aggregating solutions from a stronger 8B thinking model. \\model{}, despite being trained only on 1.7B solution distributions, transfers effectively and remains the top performer across datasets. It consistently outperforms majority voting and reward-model–based selection, best-of-N and weighted majority with AceMath scorers, and also outperforms prompted generative aggregation without RL, indicating that learned generative aggregation is robust to better solutions than the original training data solution models can generate by themselves.\n\n\\textbf{Evaluation on non-thinking solutions.}\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n% & Model \n \\multicolumn{2}{r}{Aggregation Model} \n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 11.82 & 10.00 & \\phantom{0}6.25 & \\phantom{0}3.39 \\\\\npass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 18.07 & 15.42 & \\phantom{0}8.75 & \\phantom{0}7.29 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\phantom{0}7.44 & \\phantom{0}8.92 \\\\\n &AceMath-72B & 26.33 & 18.62 & 10.23 & \\phantom{0}8.97 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\phantom{0}8.37 & \\phantom{0}8.41 \\\\\n &AceMath-72B & 26.54 & 18.83 & \\phantom{0}9.72 & \\phantom{0}8.09 \\\\\n%\\multirow{2}{*}{Generative} \nPrompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{29.96} & \\textbf{19.77} & \\textbf{17.03} & \\textbf{12.76} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:nonthinking-results}\n\\end{table}\nTable~\\ref{tab:nonthinking-results} presents results on aggregating solutions from a 1.7B non-thinking model. \\model{}, despite being trained on thinking-mode distributions, generalizes effectively and remains the top performer across datasets. It consistently outperforms majority voting, reward-model–based selection, best-of-N and weighted majority with AceMath scorers, and prompted generative aggregation without RL. Notably, reward models improve over majority voting in this lower-signal regime, supporting the hypothesis that learned scorers help more when base-model outputs are weak or noisy. Yet, \\model{} still achieves the best overall performance by synthesizing and correcting candidates rather than merely selecting among them.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.8\\linewidth]{no_sols.pdf}\n \\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\n \\label{fig:scaling-k}\n\\end{figure}\n\n\\section{Ablations \\& analysis}\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.8\\linewidth]{acc_by_num.pdf}\n \\caption{Performance vs. majority answer size for our method \\method{} compared to majority vote. \\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\n \\label{fig:majority-size}\n\\end{figure}\n\n\n\n\\textbf{Scaling via the number of solutions.}\nFigure~\\ref{fig:scaling-k} plots performance versus the number of candidate solutions $k$ per set across the four datasets, comparing majority voting (maj@$k$), the prompted model baseline (Qwen3-1.7B), and our RL-trained aggregator (\\model{}). Although \\model{} is trained only at $k{=}8$, it generalizes to both smaller and larger $k$, improving as $k$ increases. Its curve rises more steeply than majority voting, indicating better scaling with additional candidates. The prompted baseline shows a much flatter trend, often below majority voting, while \\model produces a markedly stronger scaling trend. Notably, on AIME25, HMMT24, and HMMT25, aggregating just eight solutions with \\model{} is better than majority voting with sixteen, demonstrating superior token efficiency in leveraging solution sets.\n\n\n\n\n\n\\textbf{Effect of majority answer size.}\nFigure~\\ref{fig:majority-size} shows the performance by the majority answer size, i.e., the number of occurrences of the most frequent answer. The x-axis is the majority answer size, and the y-axis is the performance on the corresponding subset. \\model's gains are largest when the size is small. That is, when solutions are diverse or uncertain and correct answers are more likely to appear in minority modes; here, careful reasoning matters. As the size grows, the problem becomes easier and majority voting is typically correct; in this regime, our aggregator remains on par with majority voting.\n\n\\begin{table}[t]\n\\centering\n\\caption{Ablation of training mixtures: Easy\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\n\\begin{tabular}{rcccc}\n\\toprule\nEasy\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\n0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\n5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\n10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\n20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\n50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\n\\midrule\nUntrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:easy-mix}\n\\end{table}\n\n\\textbf{Ablating data mixtures.}\nTable~\\ref{tab:easy-mix} investigates the impact of varying the proportion of hard versus easy sets in the training mixture, where a set is labeled hard if the majority answer is incorrect. We always keep all hard examples and vary the fraction of easy sets retained with regards to the number of hard examples (``Easy\\%''), from 0\\% (hard-only) to 270\\% (no filtering, retain all easy examples). Results show that training on hard-only sets results in suboptimal performance, and using all available data offers only marginal improvements over an untrained aggregator. Instead, incorporating a moderate proportion of easy sets (5–50\\%) consistently enhances accuracy, and results are stable within this range. This demonstrates that careful balancing of easy and hard examples is crucial for effective training, but the method is robust to the precise ratio as long as both types of examples are represented.\n\n\\begin{table}[t]\n\\centering\n\\caption{Effect of the number of solution sets $s$ per problem on performance.}\n\\begin{tabular}{rcccc}\n\\toprule\n\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\n2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\n4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\n8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\n16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:unique-sets}\n\\end{table}\n\n\\textbf{Ablating number of solution sets $s$.}\nRecall that for each problem, we sample $s$ sets of $m$ candidate solutions; increasing $s$ (while keeping $m$ fixed) introduces more diversity in the answer combinations the aggregator sees for each $x$. As shown in Table~\\ref{tab:unique-sets}, performance increases only slightly as $s$ grows, indicating that while additional diversity may offer small benefits, the gains are modest. Consequently, training on fewer sets per problem is a reasonable strategy for reducing training budget without significantly compromising aggregation performance.\n\n\\textbf{Is aggregation or extra data responsible for gains?}\n\\begin{table}[t]\n\\centering\n\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\n\\begin{tabular}{lcccc}\n\\toprule\n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\nBase Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\nAdditionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\nMultitask Solution Model &49.11&38.85&26.67&22.50\\\\\nBase Aggregator Model & 63.57&44.85&29.52&27.91\\\\\nTrained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\nMultitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:train-task}\n\\end{table}\nTable~\\ref{tab:train-task} tests whether gains arise merely from additional data rather than aggregation. We fine-tune the solution model $p_{\\theta}$ on the DeepScaler dataset used for aggregator training and evaluate its pass@1, then compare to our RL-trained aggregator on the evaluation tasks. If extra data were the primary driver, a trained solution model should close the gap; instead, its improvements are small or even negative and remain far below the trained aggregator across all benchmarks. Hence, the gains are not simply from more data but from explicitly learning to aggregate, via verifiable-reward RL and balanced easy/hard mixtures, which equips the model to select, correct, and synthesize across candidate solutions.\n\n\n\n\n\\begin{table}[t]\n\\centering\n\\caption{Average token usage per generation for solution vs. aggregator models.}\n\\begin{tabular}{lcccc}\n\\toprule\n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\nBase Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\nAdditionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\nBase Aggregator Model & \\phantom{0}2807.71 & \\phantom{0}2852.10 & \\phantom{0}3465.00 & \\phantom{0}3693.24 \\\\\nTrained Aggregator Model & \\phantom{0}3039.22 & \\phantom{0}3157.11 & \\phantom{0}3681.97 & \\phantom{0}3768.28 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:token-usage}\n\\end{table}\n\nAdditionally, Table~\\ref{tab:token-usage} compares the average number of tokens generated per inference for solution models versus aggregator models. Generating a full solution from scratch is significantly more costly in terms of tokens than aggregating over existing solutions, the aggregator model uses roughly one-third as many tokens as the solution models. This means that to achieve a comparable performance boost, directly increasing $k$ for majority voting (for $k$ larger than used in \\method{}) %with the solution model \nwould require substantially higher token usage. Thus, our learned aggregation approach not only delivers better accuracy but is also more token-efficient.\n\n\n\\textbf{Can the solution LLM and aggregator \\method{} be the same model?}\nOur main experiments separate the solution model and the aggregator \\method{}, maintaining a fixed generator and training a dedicated aggregator for fair comparison against prior aggregation strategies. \nHowever, in principle, a single LLM could be trained to perform both solution reasoning and aggregation, simply by applying different prompts for each task.\nTo examine this, we fine-tune a multitask model on both skills using their respective prompts within the same training set, and report the results alongside our separately trained aggregator in \nTable~\\ref{tab:train-task}. We find that multitasking yields close performance to separate models, while, as before, the multitasked model strongly outperforms simply prompting the solution LLM to aggregate without dedicated training.\nThis suggests that aggregation could be natively incorporated into post-training pipelines, enabling future LLMs to achieve these test-time scaling gains using a single unified model.\n\n\\section{Conclusion}\n\nIn this work we proposed a methodology to learn to aggregate solutions using RLVR, a new test-time scaling approach that improves the ability of LLMs to solve hard reasoning problems.\n%Specifically, we show a crucial component of a successful setup is a purposely designed mixture of input problems based on its difficulty and the ability of aggregator model to explore aggregation strategies during training.\nOur extensive experiments showed improved performance of our aggregator model compared to strong baselines including self-consistency decoding and weighted majority voting with SoTA math reward models. Our approach also showed generalization to (1) input distributions formed by different (e.g., stronger) solution models and (2) a variable number of solutions differing from the ones presented during training.\nFuture work could explore further uses of our aggregator beyond improved final performance, for example for distilling better reasoning skills back into the original solutions.\n\n\n\\bibliography{main}\n\\bibliographystyle{iclr2026_conference}\n\n\\appendix\n\\section{Qualitative Analysis}\nWe present two successful examples of aggregation produced by \\model. In the first example, no correct solutions were included in the prompt. The model had to verify every solution, identify the strategies that made sense, and combine the useful strategies to produce a new solution. In the second example, one correct solution was included in the prompt. The model, verified and compared among solutions, and it picked the solution that it determined to be correct.\n\\begin{tcolorbox}[\n breakable,\n title={\\textbf{Example A: No correct solutions were included in the prompt; a new, correct solution synthesized by \\model.}},\n fonttitle=\\bfseries\\large,\n coltitle=white, % Title text color\n colframe=blue!70!black, % Box border color\n colback=blue!5!white, % Box background color\n boxrule=0.8pt,\n left=2mm, right=2mm, top=1mm, bottom=1mm,\n listing only,\n listing options={breaklines, basicstyle=\\ttfamily\\small},\n]\n\nProblem: The set of points in $3$-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $$\nx-yz<y-zx<z-xy\n$$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b},$ where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b.$\n\n<think>\n\n[...]\n\nBut the problem says that the area is in the form $ a\\sqrt{b} $, and $ 507\\sqrt{3} $ is in that form. So, a = 507, b = 3, so a + b = 510.\n\nBut this is different from the other solutions. So, perhaps the correct answer is 510, but I need to check if there's a mistake in the problem or in my calculations.\n\n[...self-verification...]\n\nBut this is different from the other solutions. However, since the problem states that the answer is in the form $ a\\sqrt{b} $, and the calculation is correct, then the answer is 510.\n\nBut wait, in the previous solutions, the answer was 15, 28, 508. So, why is there a discrepancy?\n\n[...analyzing the discrepancy...]\n\nWait, in Solution 7, the answer is 508. So, maybe the correct answer is 508.\n\nBut why?\n\nIn Solution 7, the area is calculated as $ 478\\sqrt{3} $, which is not in the form $ a\\sqrt{b} $, but if there is a mistake in the calculation, it might be 508.\n\nBut I'm not sure.\n\nGiven the time I've spent and the calculations, I think the correct answer is 510, but I'm not sure. However, since the problem states that the area is in the form $ a\\sqrt{b} $, and the calculation is correct, I must go with 510.\n\n[...]\n\n</think>\n\nTo solve the given problem, we analyze the set of points in 3D space that lie on the plane $ x + y + z = 75 $ and satisfy the inequalities:\n\n$$\nx - yz < y - zx < z - xy\n$$\n\n---\n\n\\#\\#\\# Step 1: Understand the Inequalities\n\nWe simplify the inequalities using the plane equation $ x + y + z = 75 $, and express $ z = 75 - x - y $. Substituting into the inequalities:\n\n- $ x - yz < y - zx \\Rightarrow (x - y)(1 + z) < 0 $\n- $ y - zx < z - xy \\Rightarrow (y - z)(1 + x) < 0 $\n\nThese simplify to:\n\n- $ x < y $ if $ 1 + z > 0 $\n- $ y < z $ if $ 1 + x > 0 $\n\nSo, the region is defined by $ x < y < z $, and the constraints on the variables are:\n\n- $ x + y < 76 $\n- $ x + 2y < 75 $\n\nThese define a **convex triangle** in the plane $ x + y + z = 75 $, with vertices at:\n\n- $ A = (-1, -1, 77) $\n- $ B = (25, 25, 25) $\n- $ C = (-1, 38, 38) $\n\n---\n\n\\#\\#\\# Step 2: Compute the Area of the Triangle\n\nWe compute the area of the triangle formed by these three points. The vectors from point $ A $ to $ B $ and $ A $ to $ C $ are:\n\n- $ \\vec{AB} = (26, -13, -13) $\n- $ \\vec{AC} = (0, -39, 39) $\n\nThe cross product is:\n\n$$\n\\vec{AB} \\times \\vec{AC} = (-26 \\cdot 39, -26 \\cdot 39, -26 \\cdot 39) = (-26 \\cdot 39, -26 \\cdot 39, -26 \\cdot 39)\n$$\n\nThe magnitude of the cross product is:\n\n$$\n\\|\\vec{AB} \\times \\vec{AC}\\| = \\sqrt{(26 \\cdot 39)^2 + (26 \\cdot 39)^2 + (26 \\cdot 39)^2} = 26 \\cdot 39 \\cdot \\sqrt{3}\n$$\n\nThe area of the triangle is half of this:\n\n$$\n\\text{Area} = \\frac{1}{2} \\cdot 26 \\cdot 39 \\cdot \\sqrt{3} = 13 \\cdot 39 \\cdot \\sqrt{3} = 507 \\cdot \\sqrt{3}\n$$\n\n---\n\n\\#\\#\\# Step 3: Express in the Form $ a\\sqrt{b} $\n\nWe can express the area as:\n\n$$\n\\text{Area} = 507\\sqrt{3}\n$$\n\nThus, $ a = 507 $, $ b = 3 $, and the final answer is:\n\n$$\na + b = 507 + 3 = \\boxed{510}\n$$\n\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[\n breakable,\n title={\\textbf{Example B: One correct solution included in the prompt, and it was chosen by \\model.}},\n fonttitle=\\bfseries\\large,\n coltitle=white, % Title text color\n colframe=blue!70!black, % Box border color\n colback=blue!5!white, % Box background color\n boxrule=0.8pt,\n left=2mm, right=2mm, top=1mm, bottom=1mm,\n listing only,\n listing options={breaklines, basicstyle=\\ttfamily\\small},\n]\nProblem: From an unlimited supply of $1$-cent coins, $10$-cent coins, and $25$-cent coins, Silas wants to find a collection of coins that has a total value of $N$ cents, where $N$ is a positive integer. He uses the so-called \\textit{greedy algorithm}, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $N$. For example, to get $42$ cents, Silas will choose a $25$-cent coin, then a $10$-cent coin, then $7$ $1$-cent coins. However, this collection of $9$ coins uses more coins than necessary to get a total of $42$ cents; indeed, choosing $4$ $10$-cent coins and $2$ $1$-cent coins achieves the same total with only $6$ coins.\n\nIn general, the greedy algorithm \\emph{succeeds} for a given $N$ if no other collection of $1$-cent, $10$-cent, and $25$-cent coins gives a total value of $N$ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $N$ between $1$ and $1000$ inclusive for which the greedy algorithm succeeds.\n\n<think>\n\n[...]\n\nFrom the solutions provided, there are multiple approaches, but I need to figure out the correct one. Let me think about the key points.\n\nThe key insight is that the greedy algorithm fails when there's a better combination of coins. For example, if after using as many 25-cent coins as possible, the remainder is between 5 and 9, or between 15 and 19, then the greedy algorithm might not be optimal. Wait, the solutions mention that when the remainder is in certain ranges, the greedy algorithm fails. For example, in Solution 1, it says that if the remainder r is in {5,6,7,8,9,15,16,17,18,19}, the greedy algorithm fails. But in Solution 3, it says that there are 5 values of N in every group of 25 that fail. And in Solution 4, it says that there are 31 bad values. But in Solution 8, it says that there are 750 bad values, leading to 950 good ones.\n\nIn Solution 1, they say that for each a from 1 to 39, there are 10 values of r that cause failure. So 39*10=390. Then, for a=0, there are 10 values (5-9, 15-19), but those are optimal. So total failing N is 390. Then the answer is 1000-390=610. But in Solution 8, they say 750 bad values, leading to 950 good ones. So which one is correct?\n\nWait, but in Solution 1, they say that the number of failing N is 390. But in Solution 8, they say 750. So there's a discrepancy here. Let me check.\n\nWait, in Solution 1, they mention that for each a from 1 to 39, there are 10 values of r that cause failure. But a ranges from 1 to 39, so 39 values of a. For each a, there are 10 r values. So 39*10=390. But then, for a=0, there are 10 values of r (5-9, 15-19), which are optimal. So total failing N is 390. Then the answer is 1000-390=610.\n\nBut in Solution 8, they say that there are 750 bad values. So why the difference?\n\nWait, maybe the problem is that in Solution 1, they are considering that for each a, there are 10 r values, but maybe some of those r values are overlapping or something. Let me check.\n\nFor example, when a=1, N=25+ r, where r is in {5,6,7,8,9,15,16,17,18,19}. So for each a, there are 10 r values. But when a=40, N=25*40 + r, but since N is up to 1000, 25*40=1000, so r=0. So a=40 would be N=1000, which is the upper limit. But in Solution 1, they say a ranges from 1 to 39, so that's 39 values of a. So 39*10=390. Then, for a=0, N=r, where r is in {5,6,7,8,9,15,16,17,18,19}, which is 10 values. But those are optimal, so they are not failing. So total failing N is 390. So answer is 1000-390=610.\n\n[...]\n\n</think>\n\nTo determine how many values of $ N $ between 1 and 1000 inclusive result in the **greedy algorithm** for making change using **1-cent, 10-cent, and 25-cent coins** being **optimal**, we must understand when the greedy algorithm **succeeds** in producing the **minimal number of coins**.\n\n---\n\n\\#\\#\\# **Understanding the Greedy Algorithm**\n\nThe greedy algorithm works as follows:\n\n1. **Start with the largest coin (25 cents)**.\n2. Use as many of that coin as possible without exceeding the target amount.\n3. Then use as many of the next largest coin (10 cents) as possible.\n4. Finally, use the remaining amount in 1-cent coins.\n\nFor example:\n- $ N = 42 $: 1 × 25 + 1 × 10 + 7 × 1 = 9 coins.\n- But the alternative: 4 × 10 + 2 × 1 = 6 coins.\n\nThis shows that the greedy algorithm **fails** for $ N = 42 $.\n\n---\n\n\\#\\#\\# **When Does the Greedy Algorithm Fail?**\n\nThe greedy algorithm **fails** for a value $ N $ if there exists a **better combination** of coins (using 1, 10, and 25 cents) that uses **fewer coins** than the greedy algorithm.\n\nThis happens when the **remainder** $ r = N \\mod 25 $ is in the set $ \\{5, 6, 7, 8, 9, 15, 16, 17, 18, 19\\} $.\n\nThis is because:\n- For such $ r $, the greedy algorithm uses $ \\left\\lfloor \\frac{r}{10} \\right\\rfloor + (r \\mod 10) $ coins.\n- But it is possible to express $ r $ as a combination of 10-cent and 1-cent coins with fewer coins.\n\n---\n\n\\#\\#\\# **Counting the Failing Values**\n\nWe count the number of $ N $ in the range 1 to 1000 for which $ r = N \\mod 25 \\in \\{5, 6, 7, 8, 9, 15, 16, 17, 18, 19\\} $.\n\n- For each of these 10 values of $ r $, the number of $ N $ values in the range 1 to 1000 is:\n $$\n \\left\\lfloor \\frac{1000 - r}{25} \\right\\rfloor + 1\n $$\n- But since $ N $ must be at least 1, and $ r $ is between 5 and 19, the number of valid $ N $ is:\n $$\n 39 \\times 10 = 390\n $$\n- This is because $ a = \\left\\lfloor \\frac{N}{25} \\right\\rfloor $ ranges from 1 to 39, and for each $ a $, there are 10 values of $ r $.\n\n---\n\n\\#\\#\\# **Final Calculation**\n\n- Total values of $ N $ from 1 to 1000: 1000\n- Number of failing $ N $: 390\n- Therefore, the number of values of $ N $ where the greedy algorithm **succeeds** is:\n $$\n 1000 - 390 = \\boxed{610}\n $$\n\n---\n\n\\#\\#\\# **Final Answer**\n\n$$\n\\boxed{610}\n$$\n\n\\end{tcolorbox}\n\n%\\appendix\n%\\section{Appendix}\n%You may include other additional sections here.\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"Which aggregation method has the second highest average score for the HMMT24 dataset and what is the average score?"},"answer":{"kind":"string","value":"Best-of-N (AceMath-72B), 29.58"},"plan":{"kind":"string","value":"SELECT all aggregation methods\nLOOP for each aggregation method\n COMPUTE average_score = average of all HMMT24 scores for this aggregation_method\nCOMPUTE rank aggregation methods by average_score descending\nCOMPUTE second_highest_method = aggregation method of rank 2\n\n\nRETURN second_highest_method, average_score of second_highest_method\n"}}},{"rowIdx":352,"cells":{"paper":{"kind":"string","value":"2509.06870"},"relevant_tables":{"kind":"list like","value":[["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n","\\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n"," &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n"," &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\n","Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:indist-1p7b}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n"," \\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\n","pass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\n"," &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\n"," &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\n","Prompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{82.38} & \\textbf{79.70} & \\textbf{53.01} & \\textbf{60.66} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:8b-results}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\\\\\\n\",\n \" &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\\\\\\n\",\n \" &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{70.69} & \\\\textbf{50.00} & \\\\textbf{33.34} & \\\\textbf{32.07} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:indist-1p7b}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \" \\\\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\\\\\\n\",\n \"pass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\\\\\\n\",\n \" &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\\\\\\n\",\n \" &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{82.38} & \\\\textbf{79.70} & \\\\textbf{53.01} & \\\\textbf{60.66} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:8b-results}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n"," \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\n"," \\label{fig:llmagg}\n","\\end{figure}\n"],["\\begin{figure}[t]\n","\n","\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\n","Given the following problem:\n","\n","\\texttt{\\{problem\\}}\n","\n","and these solution attempts:\n","\n","\\texttt{\\{solutions\\}}\n","\n","It is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\n","\\end{tcolorbox}\n","\\caption{\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\n","\\label{fig:aggre-prompt}\n","\\end{figure}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n","\\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n"," &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n"," &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\n","Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:indist-1p7b}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n"," \\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\n","pass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\n"," &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\n"," &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\n","Prompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{82.38} & \\textbf{79.70} & \\textbf{53.01} & \\textbf{60.66} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:8b-results}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\n","\\centering\n","\\begin{tabular}{llcccc}\n","\\toprule\n"," \\multicolumn{2}{r}{Aggregation Model} \n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n","\\textit{Baselines} &&&&& \\\\\n","pass@1 &-& 11.82 & 10.00 & \\phantom{0}6.25 & \\phantom{0}3.39 \\\\\n","pass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\ \\midrule\n","\\textit{Aggregation Methods} &&&&& \\\\\n","Majority Voting & N/A & 18.07 & 15.42 & \\phantom{0}8.75 & \\phantom{0}7.29 \\\\\n","\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\phantom{0}7.44 & \\phantom{0}8.92 \\\\\n"," &AceMath-72B & 26.33 & 18.62 & 10.23 & \\phantom{0}8.97 \\\\\n","\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\phantom{0}8.37 & \\phantom{0}8.41 \\\\\n"," &AceMath-72B & 26.54 & 18.83 & \\phantom{0}9.72 & \\phantom{0}8.09 \\\\\n","Prompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\n","RL-trained Aggregation (ours) & \\model & \\textbf{29.96} & \\textbf{19.77} & \\textbf{17.03} & \\textbf{12.76} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:nonthinking-results}\n","\\end{table}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=0.8\\linewidth]{no_sols.pdf}\n"," \\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\n"," \\label{fig:scaling-k}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=0.8\\linewidth]{acc_by_num.pdf}\n"," \\caption{Performance vs. majority answer size for our method \\method{} compared to majority vote. \\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\n"," \\label{fig:majority-size}\n","\\end{figure}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Ablation of training mixtures: Easy\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\n","\\begin{tabular}{rcccc}\n","\\toprule\n","Easy\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\n","5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\n","10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\n","20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\n","50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\n","\\midrule\n","Untrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:easy-mix}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Effect of the number of solution sets $s$ per problem on performance.}\n","\\begin{tabular}{rcccc}\n","\\toprule\n","\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\n","4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\n","8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\n","16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:unique-sets}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\n","\\begin{tabular}{lcccc}\n","\\toprule\n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","Base Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\n","Additionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\n","Multitask Solution Model &49.11&38.85&26.67&22.50\\\\\n","Base Aggregator Model & 63.57&44.85&29.52&27.91\\\\\n","Trained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n","Multitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:train-task}\n","\\end{table}\n"],["\\begin{table}[t]\n","\\centering\n","\\caption{Average token usage per generation for solution vs. aggregator models.}\n","\\begin{tabular}{lcccc}\n","\\toprule\n"," & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n","\\midrule\n","Base Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\n","Additionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\n","Base Aggregator Model & \\phantom{0}2807.71 & \\phantom{0}2852.10 & \\phantom{0}3465.00 & \\phantom{0}3693.24 \\\\\n","Trained Aggregator Model & \\phantom{0}3039.22 & \\phantom{0}3157.11 & \\phantom{0}3681.97 & \\phantom{0}3768.28 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{tab:token-usage}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1.0\\\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\\n\",\n \" \\\\caption{{\\\\bf \\\\method{}}: given a task and sampled LLM solutions as input, \\\\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\\\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\\\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\\n\",\n \" \\\\label{fig:llmagg}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \"\\n\",\n \"\\\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\\n\",\n \"Given the following problem:\\n\",\n \"\\n\",\n \"\\\\texttt{\\\\{problem\\\\}}\\n\",\n \"\\n\",\n \"and these solution attempts:\\n\",\n \"\\n\",\n \"\\\\texttt{\\\\{solutions\\\\}}\\n\",\n \"\\n\",\n \"It is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\\n\",\n \"\\\\end{tcolorbox}\\n\",\n \"\\\\caption{\\\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\\n\",\n \"\\\\label{fig:aggre-prompt}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"pass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\\\\\\n\",\n \" &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\\\\\\n\",\n \" &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{70.69} & \\\\textbf{50.00} & \\\\textbf{33.34} & \\\\textbf{32.07} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:indist-1p7b}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \" \\\\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\\\\\\n\",\n \"pass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\\\\\\n\",\n \" &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\\\\\\n\",\n \" &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{82.38} & \\\\textbf{79.70} & \\\\textbf{53.01} & \\\\textbf{60.66} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:8b-results}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{llcccc}\\n\",\n \"\\\\toprule\\n\",\n \" \\\\multicolumn{2}{r}{Aggregation Model} \\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Baselines} &&&&& \\\\\\\\\\n\",\n \"pass@1 &-& 11.82 & 10.00 & \\\\phantom{0}6.25 & \\\\phantom{0}3.39 \\\\\\\\\\n\",\n \"pass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\\\\\ \\\\midrule\\n\",\n \"\\\\textit{Aggregation Methods} &&&&& \\\\\\\\\\n\",\n \"Majority Voting & N/A & 18.07 & 15.42 & \\\\phantom{0}8.75 & \\\\phantom{0}7.29 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\\\phantom{0}7.44 & \\\\phantom{0}8.92 \\\\\\\\\\n\",\n \" &AceMath-72B & 26.33 & 18.62 & 10.23 & \\\\phantom{0}8.97 \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\\\phantom{0}8.37 & \\\\phantom{0}8.41 \\\\\\\\\\n\",\n \" &AceMath-72B & 26.54 & 18.83 & \\\\phantom{0}9.72 & \\\\phantom{0}8.09 \\\\\\\\\\n\",\n \"Prompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\\\\\\n\",\n \"RL-trained Aggregation (ours) & \\\\model & \\\\textbf{29.96} & \\\\textbf{19.77} & \\\\textbf{17.03} & \\\\textbf{12.76} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:nonthinking-results}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\linewidth]{no_sols.pdf}\\n\",\n \" \\\\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\\\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\\n\",\n \" \\\\label{fig:scaling-k}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\linewidth]{acc_by_num.pdf}\\n\",\n \" \\\\caption{Performance vs. majority answer size for our method \\\\method{} compared to majority vote. \\\\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\\n\",\n \" \\\\label{fig:majority-size}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Ablation of training mixtures: Easy\\\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\\n\",\n \"\\\\begin{tabular}{rcccc}\\n\",\n \"\\\\toprule\\n\",\n \"Easy\\\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\\\\\\n\",\n \"5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\\\\\\n\",\n \"10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\\\\\\n\",\n \"20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\\\\\\n\",\n \"50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Untrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:easy-mix}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Effect of the number of solution sets $s$ per problem on performance.}\\n\",\n \"\\\\begin{tabular}{rcccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\\\\\\n\",\n \"4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\\\\\\n\",\n \"8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\\\\\\n\",\n \"16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:unique-sets}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\\n\",\n \"\\\\begin{tabular}{lcccc}\\n\",\n \"\\\\toprule\\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Base Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\\\\\\n\",\n \"Additionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\\\\\\n\",\n \"Multitask Solution Model &49.11&38.85&26.67&22.50\\\\\\\\\\n\",\n \"Base Aggregator Model & 63.57&44.85&29.52&27.91\\\\\\\\\\n\",\n \"Trained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\\\\\\n\",\n \"Multitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:train-task}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Average token usage per generation for solution vs. aggregator models.}\\n\",\n \"\\\\begin{tabular}{lcccc}\\n\",\n \"\\\\toprule\\n\",\n \" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Base Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\\\\\\n\",\n \"Additionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\\\\\\n\",\n \"Base Aggregator Model & \\\\phantom{0}2807.71 & \\\\phantom{0}2852.10 & \\\\phantom{0}3465.00 & \\\\phantom{0}3693.24 \\\\\\\\\\n\",\n \"Trained Aggregator Model & \\\\phantom{0}3039.22 & \\\\phantom{0}3157.11 & \\\\phantom{0}3681.97 & \\\\phantom{0}3768.28 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:token-usage}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\pdfoutput=1\n\\documentclass[]{fairmeta}\n% Option \"twocolumn\" available, but please prioritize single-column\n\n\\title{The Majority is not always right: \\\\\n%Reinforcement-learned aggregation}\nRL training for solution aggregation}\n\n\\author[1]{Wenting Zhao}\n\\author[1,2]{Pranjal Aggarwal}\n\\author[1]{Swarnadeep Saha}\n\\author[1]{Asli Celikyilmaz}\n\\author[1]{Jason Weston}\n\\author[1]{Ilia Kulikov}\n\n\\affiliation[1]{FAIR at Meta}\n\\affiliation[2]{CMU}\n\n\\abstract{Scaling up test-time compute, by generating multiple independent solutions and selecting or aggregating among them, has become a central paradigm for improving large language models (LLMs) on challenging reasoning tasks. While most prior work relies on simple majority voting or reward model ranking to aggregate solutions,\nthese approaches may only yield limited benefits. In this work, we propose to learn aggregation as an explicit reasoning skill: given a set of candidate solutions, we train an aggregator model to review, reconcile, and synthesize a final, correct answer using reinforcement learning from verifiable rewards. A key ingredient is careful balancing of easy and hard training examples, allowing the model to learn both to recover minority-but-correct answers as well as easy majority-correct answers. \n%\n\\if 0 non-arxiv verios\n%Empirically, aggregating solutions from Qwen3-1.7B, which %achieves 35\\% accuracy on AIME25, our trained aggregator, \\model, boosts performance to 50\\%.\n%\\model outperforms both strong rule-based and reward-model baselines, across multiple math competition benchmarks. Furthermore, it generalizes effectively to solutions from stronger models and solutions produced in non-thinking modes, all while requiring substantially fewer tokens than majority voting with larger numbers of solutions.}\n\\fi\nEmpirically, we find our method, \\method{}, outperforms both strong rule-based and reward-model baselines, across multiple benchmarks. Furthermore, it generalizes effectively to solutions from differing models, including stronger ones than contained in the training data, \n%stronger models and solutions produced in non-thinking modes,\nall while requiring substantially fewer tokens than majority voting with larger numbers of solutions.\n}\n\\date{\\today}\n\n% Optional math commands from https://github.com/goodfeli/dlbook_notation.\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n% Figure reference, capital. For start of sentence\n\\def\\Figref#1{Figure~\\ref{#1}}\n\\def\\twofigref#1#2{figures \\ref{#1} and \\ref{#2}}\n\\def\\quadfigref#1#2#3#4{figures \\ref{#1}, \\ref{#2}, \\ref{#3} and \\ref{#4}}\n% Section reference, lower-case.\n\\def\\secref#1{section~\\ref{#1}}\n% Section reference, capital.\n\\def\\Secref#1{Section~\\ref{#1}}\n% Reference to two sections.\n\\def\\twosecrefs#1#2{sections \\ref{#1} and \\ref{#2}}\n% Reference to three sections.\n\\def\\secrefs#1#2#3{sections \\ref{#1}, \\ref{#2} and \\ref{#3}}\n% Reference to an equation, lower-case.\n\\def\\eqref#1{equation~\\ref{#1}}\n% Reference to an equation, upper case\n\\def\\Eqref#1{Equation~\\ref{#1}}\n% A raw reference to an equation---avoid using if possible\n\\def\\plaineqref#1{\\ref{#1}}\n% Reference to a chapter, lower-case.\n\\def\\chapref#1{chapter~\\ref{#1}}\n% Reference to an equation, upper case.\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n% Reference to a range of chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\usepackage{hyperref}\n\\usepackage{url}\n\\usepackage{bbm}\n\\usepackage{booktabs}\n\\usepackage{multirow}\n\\usepackage{graphicx}\n\\usepackage{xspace}\n\\usepackage[most]{tcolorbox}\n\n% Authors must not appear in the submitted version. They should be hidden\n% as long as the \\iclrfinalcopy macro remains commented out below.\n% Non-anonymous submissions will be rejected without review.\n\n\\author{}\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to \\LaTeX{} to determine where to break\n% the lines. Using \\AND forces a linebreak at that point. So, if \\LaTeX{}\n% puts 3 of 4 authors names on the first line, and the last on the second\n% line, try using \\AND instead of \\And before the third author name.\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\\newcommand{\\method}{\\textsc{AggLM}\\xspace}\n\\newcommand{\\model}{AggLM-1.7B\\xspace}\n\n%\\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission.\n\\begin{document}\n\n\\maketitle\n\n\\section{Introduction}\n\nScaling up test-time compute, by producing longer intermediate thoughts and/or selection or aggregation over multiple generated samples, has become a predominant way to improve large language models (LLMs) on challenging reasoning tasks \\citep{wei2022chain,wang2023selfconsistency,brown2024large}. These strategies trade additional inference-time computation for higher accuracy, and have yielded state-of-the-art results across mathematics, code generation, and scientific problem solving \\citep{,jaech2024openai,guo2025deepseek}. \n\nMaking use of multiple independent solutions has the advantage of parallel computation, but leaves open the central design choice of how to aggregate answers. Standard practice is to either apply majority voting over the sampled solutions, or weighted majority voting, optionally guided by reward models or verifiers to select among candidates \\citep{wang2023selfconsistency,brown2024large,wu2025inference}. However, majority-based aggregation can overlook valuable minority solutions: correct answers are sometimes assigned low probability under the model due to modeling errors \\citep{stahlberg-byrne-2019-nmt,stahlberg-etal-2022-uncertainty}. Hence, simply maximizing model score, or picking the most frequent output, will not yield the optimal result \\citep{fu2025deep}. Furthermore, these methods leave unexploited the partial correctness that can exist {\\em within} otherwise incorrect thought traces, missing opportunities to combine correct steps from different candidates to produce a fully correct solution.\n\nThis paper proposes \\method{}, a method that instead {\\em learns to use reasoning to combine thoughts} produced by multiple generations computed in parallel. \\method{} is simple: (i) sample multiple solutions from an LLM; (ii) pass these solutions back to an LLM with an aggregation instruction that asks it to synthesize a final answer by reconciling, correcting, and combining the intermediate reasoning steps. We then train a reasoning model to perform this aggregation using reinforcement learning from verifiable rewards (RLVR). This turns aggregation itself into a learned reasoning skill rather than a fixed heuristic. Our approach is summarized in \\autoref{fig:llmagg}.\n\nWe evaluate our method on four popular math competition datasets from MathArena \\citep{balunovic2025matharena}: AIME24, AIME25, HMMT24, and HMMT25. When aggregating solutions from Qwen3-1.7B, which achieves 35\\% accuracy on AIME25, our trained aggregator \\model raises performance to 50\\%, improving over majority voting that is 45\\%. Across all four datasets, \\model consistently outperforms rule-based aggregation methods such as majority voting, as well as strong reward-model selection baselines that have 72B parameters. Furthermore, \\model generalizes robustly: it remains the top performer when aggregating solutions from stronger models like Qwen3-8B or from non-thinking mode. Ablation studies show that balancing easy and hard examples in the \\method{} training mixture is critical for achieving strong results, and that our gains over majority voting are particularly substantial when the majority answer set is small in size; that is, when candidate solutions are more diverse. Finally, \\model is substantially more token-efficient than generating a larger number of solutions for majority voting, delivering both higher accuracy and lower inference costs compared to standard aggregation strategies.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggregated solution which is typically superior to the original solutions. As \\method{}'s output can be evaluated and assigned verifiable rewards it can be trained by reinforcement learning (RLVR). The models LLM and \\method{} can either be the same LLM with shared parameters, or two separately trained models, e.g. of different size.}\n \\label{fig:llmagg}\n\\end{figure}\n\n\\section{Related Work}\n\n\\noindent \\textbf{Rule-Based Voting}\nA common way to combine multiple LLM solutions is to apply simple, rule-based voting.\nSelf-consistent decoding \\citep{wang2023selfconsistency,brown2024large} draws many chain-of-thought trajectories and returns the answer that appears most frequently.\nVariants adapt the voting procedure in lightweight ways, such as dynamically choosing the number of samples or using heuristic filters \\citep{aggarwal-etal-2023-lets,xue-etal-2023-dynamic,huang-etal-2024-mirror,knappe2024enhancing}.\nWhile this strategy often yields reliable gains, it fails when correct solutions exist but are confined to minority modes, causing majority voting to amplify errors rather than surface the correct answer. In this work we analyze when that issue occurs, and show how our approach remedies this failing.\n\n\\noindent \\textbf{Model-Based Selection and Aggregation}\nMoving beyond pure counting, recent approaches \nuse models to evaluate or re-rank answer candidates. Broadly, model-based aggregation either (i) trains a separate scorer to select candidates or (ii) prompts the LLM to compare and consolidate them. For selection, a reward model assigns a scalar score to each candidate, and the top-scoring answer is chosen \\citep{yang2024qwen2,liu2024acemath}.\nThis recombines frequency with a learned notion of quality, but it sometimes introduces more regression errors than improvements. Recent work also leverages the language model itself as a generative aggregator. Universal Self-Consistency (USC) \\citep{chen2024universal,qi2025learning} prompts the model to examine all sampled solutions and choose the most coherent one.\n\nOur approach is closest in spirit to these methods, but differs in that we explicitly train a reasoning-focused aggregator with reinforcement learning to synthesize a final solution, rather than relying solely on prompting.\nConcurrent with our work, \\citet{qi2025learning} propose a learned \\emph{Sample Set Aggregator} (SSA) that consumes concatenated samples and generates a final answer, while also training the aggregator via reinforcement learning.\nEmpirically, \\citet{qi2025learning} report modest gains in their settings, suggesting that additional ingredients—such as using reasoning-oriented base models and carefully balancing the training mixture—are important for unlocking stronger aggregation performance. We show in our ablations that, in our setting, the latter is the case.\n\n\\section{\\method}\nOur goal is to train an aggregation language model that, given a problem and a set of candidate solutions produced by an LLM, synthesizes a final solution. As we use training data consisting of tasks with verifiable solutions, \nwe can train our aggregation model, \\method{}, with reinforcement learning from verifiable rewards (RLVR). Training aims to learn two complementary behaviors: (a) selection that identifies and adopts the correct candidate when it already appears in the set; and (b) synthesis that detects mistakes, fills gaps, or combines complementary partial ideas across candidates to produce a new, correct solution that did not appear verbatim in the set. Successful RL training can enable the model to learn how and when to employ these skills.\n\n\\textbf{Problem Formulation} Let $x$ be a given problem and $y^\\star$ its ground-truth solution. We consider two models:\n(i) a \\emph{solution} model $p_{\\theta}(y \\mid x)$ that generates a solution $y$; and\n(ii) an \\emph{aggregation} model $p_{\\phi}(\\tilde{y} \\mid x, y_{1:m})$ that reads the problem together with a set of $m$ candidate solutions $y_{1:m} = (y_1,\\dots,y_m)$ and outputs an aggregated solution $\\tilde{y}$.\n%We also define an answer-extraction function $\\mathrm{Ans}(\\cdot)$ that maps a solution $y$ to a final answer (e.g., an expression or a numeric value).\nGiven a problem $x$, the solution model samples $m$ candidate solutions independently:\n\\[\ny_i \\sim p_{\\theta}(y \\mid x), \\quad i \\in {1,\\dots,m}\n\\]\nThen, the aggregation model produces an aggregated solution:\n\\[\n\\tilde{y} \\sim p_{\\phi}(y \\mid x, y_{1:m})\n\\]\nThe parameters $\\theta$ and $\\phi$ may correspond to the same underlying LLM or to different models. This work focuses on training strong aggregation models; in our main experiments, the solution model $p_{\\theta}$ is treated as an off-the-shelf generator and is kept fixed,\nmaking it easier to draw experimental conclusions when comparing against baselines. However, we also report results where the model parameters are shared in a single model, which as we will see we find to give similar performance.\n%which provides a clearer basis for experimental comparison with baselines.\n\n\\textbf{Training Data} Let $\\mathcal{D} = \\{(x, y^{\\star})\\}^n$ be a collection of problems with ground-truth solutions. For each $x$ we draw $s \\cdot m$ solutions from $p_{\\theta}$ and group them into $s$ sets of size $m$, yielding an aggregation-training corpus\n\\[\n\\mathcal{D}' = \\{x, y_{1:m}, y^{\\star} \\}^{s \\cdot n}.\n\\]\n\nWe note that increasing $s$ introduces more diversity in the answer combinations the aggregation model sees for each $x$, which could potentially improve generalization ability.\nWe define the majority answer as the most frequent answer. An example is considered \\emph{hard} if the majority answer in $y_{1:m}$ is wrong, and \\emph{easy} otherwise. Constructing $\\mathcal{D}'$ from existing data sources $\\mathcal{D}$ may lead to many easy examples, where most generated solutions for a problem are correct. This can under-train the model’s ability to recover minority-but-correct answers, whereas training only on hard groups makes rewards sparse. We therefore construct the final training mixture by taking all hard examples and mixing in $p\\%$ of easy examples, producing a balanced dataset that preserves realism while emphasizing challenging cases.\n\n\\textbf{Training} We optimize the aggregation policy $p_{\\phi}(\\tilde{y} \\mid x, y_{1:m})$ with Group-Relative Policy Optimization (GRPO) \\citep{shao2024deepseekmath}. For each training example, the aggregator produces $\\tilde{y}$ and receives a reward $r(\\tilde{y}) = \\mathbbm{1}\\big[\\tilde{y} = y^\\star\\big]$. We apply the standard GRPO update using this binary reward.\n\n\\section{Experimental Setup}\n\\subsection{Training}\nFollowing our proposed method, we train a 1.7B model that we refer to as \\model. Specifically, we initialize the aggregation model from Qwen3-1.7B \\citep{yang2025qwen3} and train it on DeepScaler\\citep{deepscaler2025}, a collection of around 40 thousand math problems with ground-truth solutions. To construct $\\mathcal{D}'$, we sample a total of 128 independent solutions with temperature $1.5$ from Qwen3-1.7B in the thinking mode, dividing into 16 sets of 8 solutions. To obtain the data mixture, we set $p=50\\%$, resulting in 446,220 training examples. We train for one epoch, with a batch size of 1024, a maximum prompt length of 16384 tokens, and a maximum response length of 16384 tokens. When constructing the easy subset, we maximize diversity by repeating each problem as little as possible. We check for solution equivalence between aggregated solutions and ground-truth solutions using the \\texttt{math\\_verify} library\\footnote{https://github.com/huggingface/Math-Verify}. In GRPO, we use a group size of $8$ for GRPO updates, set the KL regularization coefficient to $0.001$, and maintain a sampling temperature of $1.5$ for the aggregator during training. We use the problem itself as the prompt for the solution model. We include the prompt template we used for aggregating solutions in Figure~\\ref{fig:aggre-prompt}. Note that the solutions used for aggregation (i.e., included in the template) are taken after </think> when obtaining solutions from thinking models.\n\n\\begin{figure}[t]\n\n\\begin{tcolorbox}[colframe=blue!70!black, colback=blue!5!white, arc=4mm, boxrule=0.8pt]\nGiven the following problem:\n\n\\texttt{\\{problem\\}}\n\nand these solution attempts:\n\n\\texttt{\\{solutions\\}}\n\nIt is possible that any, all, or none of these solutions are correct or complete. Carefully review the provided solutions, using them as starting points---correcting mistakes, filling in gaps, and/or combining useful ideas---to produce a final, comprehensive, and correct solution to the problem.\n\\end{tcolorbox}\n\\caption{\\method{} prompt template to instruct the LLM to aggregate solutions. The reasoning and final aggregated solution output by the model given this instruction are trained by RL. }\n\\label{fig:aggre-prompt}\n\\end{figure}\n\n\\subsection{Evaluation}\n\\textbf{Solution models.} We evaluate aggregation methods using samples from the following solution models: (i) Qwen3-1.7B in both thinking and non-thinking mode; and (ii) Qwen3-8B in thinking mode.\n\n\\textbf{Datasets.} We evaluate on four mathematics competition datasets from MathArena \\citep{balunovic2025matharena}. AIME24 and AIME25 are recent editions of the American Invitational Mathematics Examination, which feature challenging high school-level olympiad problems with single numeric/integer answers. HMMT24 and HMMT25 are editions of the Harvard-MIT Mathematics Tournament, another highly competitive mathematics contest that covers broader mathematical topics and frequently requires creative or multi-step reasoning. Each of these datasets comprises 30 examples.\n\n\\textbf{Protocol.} Because our evaluation datasets are relatively small, we adopt a robust protocol to obtain reliable signals. For each problem $x$, we independently sample 128 solutions at temperature 1 and partition them into $s=16$ sets of $m=8$ solutions each. For every set, the aggregation model $p_\\phi$ is prompted to generate four aggregated solutions, from which we extract the final solutions. Pass@1 for each set is computed as the success rate over these four answers, and for each problem, we average this rate across all 16 sets. The overall score for the dataset is then computed by averaging the set-level pass@1 across all problems.\n\n\\textbf{Baselines.} We compare against a set of state-of-the-art aggregation methods: majority voting, best-of-N, and weighted majority voting with reward models.\nAll of these methods follow the same protocol described above.\nFor reward-model selection, for each set of 8 candidates, we score each candidate with the 7B and 72B AceMath reward models \\citep{liu2024acemath} and select the top-scoring answer, yielding a learned re-ranking baseline. Weighted majority voting combines majority voting and best-of-N by computing a weighted distribution of solutions, where the weights are derived from reward model scores \\citep{welleck2024from}. We also compare to prompted aggregation without training: we apply our aggregation prompt to Qwen3-1.7B without any fine-tuning, isolating the effect of the RL-trained aggregator.\nFinally, we also measure and report pass@1 for the original solution model estimated from 64 independent samples of $p_{\\theta}(y \\mid x)$, and pass@8 (oracle best-of-8 that succeeds if any of the 8 answers is correct, using 64 sets of 8 solutions sampled from 128 solutions in total).\n\n\\section{Results}\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n\\multicolumn{2}{r}{Aggregation Model} \n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 50.91 & 35.68 & 22.45 & 22.84 \\\\\npass@8 &-& 76.48 & 61.38 & 36.67 & 44.27 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 67.92 & 45.89 & 29.01 & 26.72 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 59.39 & 40.30 & 28.09 & 22.50 \\\\\n &AceMath-72B & 56.64 & 40.35 & 29.58 & 21.99 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 64.09 & 39.49 & 25.04 & 17.71 \\\\\n &AceMath-72B & 62.34 & 38.49 & 27.62 & 17.96 \\\\\nPrompted Aggregation &Qwen3-1.7B&63.57&44.85&29.52&27.91 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{70.69} & \\textbf{50.00} & \\textbf{33.34} & \\textbf{32.07} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:indist-1p7b}\n\\end{table}\n\n\n\n\\textbf{Evaluation on in-distribution solutions} Table~\\ref{tab:indist-1p7b} presents results on in-distribution 1.7B-thinking solutions, the same solution model used to produce training data for our RL-trained aggregator, \\model{}. In this setting, \\model{} is best on all four benchmarks, outperforming majority voting and the same backbone model with prompting without RL, Qwen3-1.7B, with consistent three to seven point gains, confirming that training the aggregation policy matters. Reward-model selection performs poorly in comparison: best-of-N and weighted majority with AceMath-7B/72B is often inferior to the standard majority voting. Overall, learned generative aggregation outperforms frequency- and reward-model–based selection at surfacing correct minority solutions.\n\n\n\\textbf{Evaluation on solutions from stronger models.}\n\n\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-8B in thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n \\multicolumn{2}{r}{Aggregation Model} & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 74.17 & 69.27 & 41.61 & 45.99 \\\\\npass@8 &-& 85.57 & 83.54 & 61.67 & 65.47 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 81.61 & 78.70 & 44.58 & 56.35 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 78.60 & 70.89 & 37.39 & 44.17 \\\\\n &AceMath-72B & 80.27 & 69.57 & 38.54 & 46.21 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 77.03 & 68.15 & 38.41 & 36.13 \\\\\n &AceMath-72B & 79.06 & 66.00 & 37.63 & 41.46 \\\\\nPrompted Aggregation &Qwen3-1.7B& 79.90 & 76.73 & 48.58 & 57.63 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{82.38} & \\textbf{79.70} & \\textbf{53.01} & \\textbf{60.66} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:8b-results}\n\\end{table}\n\n\n\n\nTable~\\ref{tab:8b-results} presents results on aggregating solutions from a stronger 8B thinking model. \\model{}, despite being trained only on 1.7B solution distributions, transfers effectively and remains the top performer across datasets. It consistently outperforms majority voting and reward-model–based selection, best-of-N and weighted majority with AceMath scorers, and also outperforms prompted generative aggregation without RL, indicating that learned generative aggregation is robust to better solutions than the original training data solution models can generate by themselves.\n\n\\textbf{Evaluation on non-thinking solutions.}\n\\begin{table}[t]\n\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in non-thinking mode.}\n\\centering\n\\begin{tabular}{llcccc}\n\\toprule\n% & Model \n \\multicolumn{2}{r}{Aggregation Model} \n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n\\textit{Baselines} &&&&& \\\\\npass@1 &-& 11.82 & 10.00 & \\phantom{0}6.25 & \\phantom{0}3.39 \\\\\npass@8 &-& 32.76 & 24.53 & 16.09 & 14.06 \\\\ \\midrule\n\\textit{Aggregation Methods} &&&&& \\\\\nMajority Voting & N/A & 18.07 & 15.42 & \\phantom{0}8.75 & \\phantom{0}7.29 \\\\\n\\multirow{2}{*}{Best-of-N} &AceMath-7B & 23.31 & 18.40 & \\phantom{0}7.44 & \\phantom{0}8.92 \\\\\n &AceMath-72B & 26.33 & 18.62 & 10.23 & \\phantom{0}8.97 \\\\\n\\multirow{2}{*}{Weighted Majority}& AceMath-7B & 23.95 & 18.39 & \\phantom{0}8.37 & \\phantom{0}8.41 \\\\\n &AceMath-72B & 26.54 & 18.83 & \\phantom{0}9.72 & \\phantom{0}8.09 \\\\\n%\\multirow{2}{*}{Generative} \nPrompted Aggregation &Qwen3-1.7B& 28.51 & 17.79 & 16.30 & 12.08 \\\\\nRL-trained Aggregation (ours) & \\model & \\textbf{29.96} & \\textbf{19.77} & \\textbf{17.03} & \\textbf{12.76} \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:nonthinking-results}\n\\end{table}\nTable~\\ref{tab:nonthinking-results} presents results on aggregating solutions from a 1.7B non-thinking model. \\model{}, despite being trained on thinking-mode distributions, generalizes effectively and remains the top performer across datasets. It consistently outperforms majority voting, reward-model–based selection, best-of-N and weighted majority with AceMath scorers, and prompted generative aggregation without RL. Notably, reward models improve over majority voting in this lower-signal regime, supporting the hypothesis that learned scorers help more when base-model outputs are weak or noisy. Yet, \\model{} still achieves the best overall performance by synthesizing and correcting candidates rather than merely selecting among them.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.8\\linewidth]{no_sols.pdf}\n \\caption{Performance vs. number of candidate solutions $k$ for different aggregation methods. \\model{} is superior to other methods at $k=8$ which it is trained for, and is often superior for both larger and smaller values of $k$ as well, despite them being out-of-distribution.}\n \\label{fig:scaling-k}\n\\end{figure}\n\n\\section{Ablations \\& analysis}\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.8\\linewidth]{acc_by_num.pdf}\n \\caption{Performance vs. majority answer size for our method \\method{} compared to majority vote. \\method{} outperforms majority vote in the harder cases when the correct answer is infrequent, and is on par for easier cases when it is frequent. }\n \\label{fig:majority-size}\n\\end{figure}\n\n\n\n\\textbf{Scaling via the number of solutions.}\nFigure~\\ref{fig:scaling-k} plots performance versus the number of candidate solutions $k$ per set across the four datasets, comparing majority voting (maj@$k$), the prompted model baseline (Qwen3-1.7B), and our RL-trained aggregator (\\model{}). Although \\model{} is trained only at $k{=}8$, it generalizes to both smaller and larger $k$, improving as $k$ increases. Its curve rises more steeply than majority voting, indicating better scaling with additional candidates. The prompted baseline shows a much flatter trend, often below majority voting, while \\model produces a markedly stronger scaling trend. Notably, on AIME25, HMMT24, and HMMT25, aggregating just eight solutions with \\model{} is better than majority voting with sixteen, demonstrating superior token efficiency in leveraging solution sets.\n\n\n\n\n\n\\textbf{Effect of majority answer size.}\nFigure~\\ref{fig:majority-size} shows the performance by the majority answer size, i.e., the number of occurrences of the most frequent answer. The x-axis is the majority answer size, and the y-axis is the performance on the corresponding subset. \\model's gains are largest when the size is small. That is, when solutions are diverse or uncertain and correct answers are more likely to appear in minority modes; here, careful reasoning matters. As the size grows, the problem becomes easier and majority voting is typically correct; in this regime, our aggregator remains on par with majority voting.\n\n\\begin{table}[t]\n\\centering\n\\caption{Ablation of training mixtures: Easy\\% is the percentage of easy sets relative to hard examples (hard examples are defined as the majority answer being incorrect). There is a sweet spot in the middle, which is superior to either including all the easy examples or none at all.}\n\\begin{tabular}{rcccc}\n\\toprule\nEasy\\% & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\n0 & 64.22 & 46.06 & 27.80 & 28.73 \\\\\n5 & 68.93 & 48.65 & 33.31 & 31.91 \\\\\n10 & 69.85 & 49.60 & 33.71 & 32.31 \\\\\n20 & 69.72 & 49.11 & 33.74 & 31.20 \\\\\n50 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n270 & 66.20 & 46.70 & 30.01 & 28.94 \\\\\n\\midrule\nUntrained & 63.57 & 44.85 & 29.52 & 27.91 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:easy-mix}\n\\end{table}\n\n\\textbf{Ablating data mixtures.}\nTable~\\ref{tab:easy-mix} investigates the impact of varying the proportion of hard versus easy sets in the training mixture, where a set is labeled hard if the majority answer is incorrect. We always keep all hard examples and vary the fraction of easy sets retained with regards to the number of hard examples (``Easy\\%''), from 0\\% (hard-only) to 270\\% (no filtering, retain all easy examples). Results show that training on hard-only sets results in suboptimal performance, and using all available data offers only marginal improvements over an untrained aggregator. Instead, incorporating a moderate proportion of easy sets (5–50\\%) consistently enhances accuracy, and results are stable within this range. This demonstrates that careful balancing of easy and hard examples is crucial for effective training, but the method is robust to the precise ratio as long as both types of examples are represented.\n\n\\begin{table}[t]\n\\centering\n\\caption{Effect of the number of solution sets $s$ per problem on performance.}\n\\begin{tabular}{rcccc}\n\\toprule\n\\#Sets & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\n2 & 70.27 & 49.74 & 33.42 & 31.67 \\\\\n4 & 70.29 & 49.08 & 33.11 & 31.34 \\\\\n8 & 70.37 & 50.25 & 33.16 & 31.89 \\\\\n16 & 70.69 & 50.00 & 33.34 & 32.07 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:unique-sets}\n\\end{table}\n\n\\textbf{Ablating number of solution sets $s$.}\nRecall that for each problem, we sample $s$ sets of $m$ candidate solutions; increasing $s$ (while keeping $m$ fixed) introduces more diversity in the answer combinations the aggregator sees for each $x$. As shown in Table~\\ref{tab:unique-sets}, performance increases only slightly as $s$ grows, indicating that while additional diversity may offer small benefits, the gains are modest. Consequently, training on fewer sets per problem is a reasonable strategy for reducing training budget without significantly compromising aggregation performance.\n\n\\textbf{Is aggregation or extra data responsible for gains?}\n\\begin{table}[t]\n\\centering\n\\caption{Comparison of training the solution model versus training the aggregator model on the same data, in either separate or multitask settings.}\n\\begin{tabular}{lcccc}\n\\toprule\n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\nBase Solution Model& 50.91 & 35.68 & 22.45 & 22.84 \\\\\nAdditionally Trained Solution Model & 49.79 & 37.19 & 27.19 & 23.70 \\\\\nMultitask Solution Model &49.11&38.85&26.67&22.50\\\\\nBase Aggregator Model & 63.57&44.85&29.52&27.91\\\\\nTrained Aggregator Model & 70.69 & 50.00 & 33.34 & 32.07 \\\\\nMultitask Aggregator Model &70.02&49.39&32.97&30.28\\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:train-task}\n\\end{table}\nTable~\\ref{tab:train-task} tests whether gains arise merely from additional data rather than aggregation. We fine-tune the solution model $p_{\\theta}$ on the DeepScaler dataset used for aggregator training and evaluate its pass@1, then compare to our RL-trained aggregator on the evaluation tasks. If extra data were the primary driver, a trained solution model should close the gap; instead, its improvements are small or even negative and remain far below the trained aggregator across all benchmarks. Hence, the gains are not simply from more data but from explicitly learning to aggregate, via verifiable-reward RL and balanced easy/hard mixtures, which equips the model to select, correct, and synthesize across candidate solutions.\n\n\n\n\n\\begin{table}[t]\n\\centering\n\\caption{Average token usage per generation for solution vs. aggregator models.}\n\\begin{tabular}{lcccc}\n\\toprule\n & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\\n\\midrule\nBase Solution Model & 10225.82 & 10612.46 & 11129.70 & 11343.28 \\\\\nAdditionally Trained Solution Model & 11367.57 & 11731.94 & 12306.67 & 12587.58 \\\\\nBase Aggregator Model & \\phantom{0}2807.71 & \\phantom{0}2852.10 & \\phantom{0}3465.00 & \\phantom{0}3693.24 \\\\\nTrained Aggregator Model & \\phantom{0}3039.22 & \\phantom{0}3157.11 & \\phantom{0}3681.97 & \\phantom{0}3768.28 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{tab:token-usage}\n\\end{table}\n\nAdditionally, Table~\\ref{tab:token-usage} compares the average number of tokens generated per inference for solution models versus aggregator models. Generating a full solution from scratch is significantly more costly in terms of tokens than aggregating over existing solutions, the aggregator model uses roughly one-third as many tokens as the solution models. This means that to achieve a comparable performance boost, directly increasing $k$ for majority voting (for $k$ larger than used in \\method{}) %with the solution model \nwould require substantially higher token usage. Thus, our learned aggregation approach not only delivers better accuracy but is also more token-efficient.\n\n\n\\textbf{Can the solution LLM and aggregator \\method{} be the same model?}\nOur main experiments separate the solution model and the aggregator \\method{}, maintaining a fixed generator and training a dedicated aggregator for fair comparison against prior aggregation strategies. \nHowever, in principle, a single LLM could be trained to perform both solution reasoning and aggregation, simply by applying different prompts for each task.\nTo examine this, we fine-tune a multitask model on both skills using their respective prompts within the same training set, and report the results alongside our separately trained aggregator in \nTable~\\ref{tab:train-task}. We find that multitasking yields close performance to separate models, while, as before, the multitasked model strongly outperforms simply prompting the solution LLM to aggregate without dedicated training.\nThis suggests that aggregation could be natively incorporated into post-training pipelines, enabling future LLMs to achieve these test-time scaling gains using a single unified model.\n\n\\section{Conclusion}\n\nIn this work we proposed a methodology to learn to aggregate solutions using RLVR, a new test-time scaling approach that improves the ability of LLMs to solve hard reasoning problems.\n%Specifically, we show a crucial component of a successful setup is a purposely designed mixture of input problems based on its difficulty and the ability of aggregator model to explore aggregation strategies during training.\nOur extensive experiments showed improved performance of our aggregator model compared to strong baselines including self-consistency decoding and weighted majority voting with SoTA math reward models. Our approach also showed generalization to (1) input distributions formed by different (e.g., stronger) solution models and (2) a variable number of solutions differing from the ones presented during training.\nFuture work could explore further uses of our aggregator beyond improved final performance, for example for distilling better reasoning skills back into the original solutions.\n\n\n\\bibliography{main}\n\\bibliographystyle{iclr2026_conference}\n\n\\appendix\n\\section{Qualitative Analysis}\nWe present two successful examples of aggregation produced by \\model. In the first example, no correct solutions were included in the prompt. The model had to verify every solution, identify the strategies that made sense, and combine the useful strategies to produce a new solution. In the second example, one correct solution was included in the prompt. The model, verified and compared among solutions, and it picked the solution that it determined to be correct.\n\\begin{tcolorbox}[\n breakable,\n title={\\textbf{Example A: No correct solutions were included in the prompt; a new, correct solution synthesized by \\model.}},\n fonttitle=\\bfseries\\large,\n coltitle=white, % Title text color\n colframe=blue!70!black, % Box border color\n colback=blue!5!white, % Box background color\n boxrule=0.8pt,\n left=2mm, right=2mm, top=1mm, bottom=1mm,\n listing only,\n listing options={breaklines, basicstyle=\\ttfamily\\small},\n]\n\nProblem: The set of points in $3$-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $$\nx-yz<y-zx<z-xy\n$$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b},$ where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b.$\n\n<think>\n\n[...]\n\nBut the problem says that the area is in the form $ a\\sqrt{b} $, and $ 507\\sqrt{3} $ is in that form. So, a = 507, b = 3, so a + b = 510.\n\nBut this is different from the other solutions. So, perhaps the correct answer is 510, but I need to check if there's a mistake in the problem or in my calculations.\n\n[...self-verification...]\n\nBut this is different from the other solutions. However, since the problem states that the answer is in the form $ a\\sqrt{b} $, and the calculation is correct, then the answer is 510.\n\nBut wait, in the previous solutions, the answer was 15, 28, 508. So, why is there a discrepancy?\n\n[...analyzing the discrepancy...]\n\nWait, in Solution 7, the answer is 508. So, maybe the correct answer is 508.\n\nBut why?\n\nIn Solution 7, the area is calculated as $ 478\\sqrt{3} $, which is not in the form $ a\\sqrt{b} $, but if there is a mistake in the calculation, it might be 508.\n\nBut I'm not sure.\n\nGiven the time I've spent and the calculations, I think the correct answer is 510, but I'm not sure. However, since the problem states that the area is in the form $ a\\sqrt{b} $, and the calculation is correct, I must go with 510.\n\n[...]\n\n</think>\n\nTo solve the given problem, we analyze the set of points in 3D space that lie on the plane $ x + y + z = 75 $ and satisfy the inequalities:\n\n$$\nx - yz < y - zx < z - xy\n$$\n\n---\n\n\\#\\#\\# Step 1: Understand the Inequalities\n\nWe simplify the inequalities using the plane equation $ x + y + z = 75 $, and express $ z = 75 - x - y $. Substituting into the inequalities:\n\n- $ x - yz < y - zx \\Rightarrow (x - y)(1 + z) < 0 $\n- $ y - zx < z - xy \\Rightarrow (y - z)(1 + x) < 0 $\n\nThese simplify to:\n\n- $ x < y $ if $ 1 + z > 0 $\n- $ y < z $ if $ 1 + x > 0 $\n\nSo, the region is defined by $ x < y < z $, and the constraints on the variables are:\n\n- $ x + y < 76 $\n- $ x + 2y < 75 $\n\nThese define a **convex triangle** in the plane $ x + y + z = 75 $, with vertices at:\n\n- $ A = (-1, -1, 77) $\n- $ B = (25, 25, 25) $\n- $ C = (-1, 38, 38) $\n\n---\n\n\\#\\#\\# Step 2: Compute the Area of the Triangle\n\nWe compute the area of the triangle formed by these three points. The vectors from point $ A $ to $ B $ and $ A $ to $ C $ are:\n\n- $ \\vec{AB} = (26, -13, -13) $\n- $ \\vec{AC} = (0, -39, 39) $\n\nThe cross product is:\n\n$$\n\\vec{AB} \\times \\vec{AC} = (-26 \\cdot 39, -26 \\cdot 39, -26 \\cdot 39) = (-26 \\cdot 39, -26 \\cdot 39, -26 \\cdot 39)\n$$\n\nThe magnitude of the cross product is:\n\n$$\n\\|\\vec{AB} \\times \\vec{AC}\\| = \\sqrt{(26 \\cdot 39)^2 + (26 \\cdot 39)^2 + (26 \\cdot 39)^2} = 26 \\cdot 39 \\cdot \\sqrt{3}\n$$\n\nThe area of the triangle is half of this:\n\n$$\n\\text{Area} = \\frac{1}{2} \\cdot 26 \\cdot 39 \\cdot \\sqrt{3} = 13 \\cdot 39 \\cdot \\sqrt{3} = 507 \\cdot \\sqrt{3}\n$$\n\n---\n\n\\#\\#\\# Step 3: Express in the Form $ a\\sqrt{b} $\n\nWe can express the area as:\n\n$$\n\\text{Area} = 507\\sqrt{3}\n$$\n\nThus, $ a = 507 $, $ b = 3 $, and the final answer is:\n\n$$\na + b = 507 + 3 = \\boxed{510}\n$$\n\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[\n breakable,\n title={\\textbf{Example B: One correct solution included in the prompt, and it was chosen by \\model.}},\n fonttitle=\\bfseries\\large,\n coltitle=white, % Title text color\n colframe=blue!70!black, % Box border color\n colback=blue!5!white, % Box background color\n boxrule=0.8pt,\n left=2mm, right=2mm, top=1mm, bottom=1mm,\n listing only,\n listing options={breaklines, basicstyle=\\ttfamily\\small},\n]\nProblem: From an unlimited supply of $1$-cent coins, $10$-cent coins, and $25$-cent coins, Silas wants to find a collection of coins that has a total value of $N$ cents, where $N$ is a positive integer. He uses the so-called \\textit{greedy algorithm}, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $N$. For example, to get $42$ cents, Silas will choose a $25$-cent coin, then a $10$-cent coin, then $7$ $1$-cent coins. However, this collection of $9$ coins uses more coins than necessary to get a total of $42$ cents; indeed, choosing $4$ $10$-cent coins and $2$ $1$-cent coins achieves the same total with only $6$ coins.\n\nIn general, the greedy algorithm \\emph{succeeds} for a given $N$ if no other collection of $1$-cent, $10$-cent, and $25$-cent coins gives a total value of $N$ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $N$ between $1$ and $1000$ inclusive for which the greedy algorithm succeeds.\n\n<think>\n\n[...]\n\nFrom the solutions provided, there are multiple approaches, but I need to figure out the correct one. Let me think about the key points.\n\nThe key insight is that the greedy algorithm fails when there's a better combination of coins. For example, if after using as many 25-cent coins as possible, the remainder is between 5 and 9, or between 15 and 19, then the greedy algorithm might not be optimal. Wait, the solutions mention that when the remainder is in certain ranges, the greedy algorithm fails. For example, in Solution 1, it says that if the remainder r is in {5,6,7,8,9,15,16,17,18,19}, the greedy algorithm fails. But in Solution 3, it says that there are 5 values of N in every group of 25 that fail. And in Solution 4, it says that there are 31 bad values. But in Solution 8, it says that there are 750 bad values, leading to 950 good ones.\n\nIn Solution 1, they say that for each a from 1 to 39, there are 10 values of r that cause failure. So 39*10=390. Then, for a=0, there are 10 values (5-9, 15-19), but those are optimal. So total failing N is 390. Then the answer is 1000-390=610. But in Solution 8, they say 750 bad values, leading to 950 good ones. So which one is correct?\n\nWait, but in Solution 1, they say that the number of failing N is 390. But in Solution 8, they say 750. So there's a discrepancy here. Let me check.\n\nWait, in Solution 1, they mention that for each a from 1 to 39, there are 10 values of r that cause failure. But a ranges from 1 to 39, so 39 values of a. For each a, there are 10 r values. So 39*10=390. But then, for a=0, there are 10 values of r (5-9, 15-19), which are optimal. So total failing N is 390. Then the answer is 1000-390=610.\n\nBut in Solution 8, they say that there are 750 bad values. So why the difference?\n\nWait, maybe the problem is that in Solution 1, they are considering that for each a, there are 10 r values, but maybe some of those r values are overlapping or something. Let me check.\n\nFor example, when a=1, N=25+ r, where r is in {5,6,7,8,9,15,16,17,18,19}. So for each a, there are 10 r values. But when a=40, N=25*40 + r, but since N is up to 1000, 25*40=1000, so r=0. So a=40 would be N=1000, which is the upper limit. But in Solution 1, they say a ranges from 1 to 39, so that's 39 values of a. So 39*10=390. Then, for a=0, N=r, where r is in {5,6,7,8,9,15,16,17,18,19}, which is 10 values. But those are optimal, so they are not failing. So total failing N is 390. So answer is 1000-390=610.\n\n[...]\n\n</think>\n\nTo determine how many values of $ N $ between 1 and 1000 inclusive result in the **greedy algorithm** for making change using **1-cent, 10-cent, and 25-cent coins** being **optimal**, we must understand when the greedy algorithm **succeeds** in producing the **minimal number of coins**.\n\n---\n\n\\#\\#\\# **Understanding the Greedy Algorithm**\n\nThe greedy algorithm works as follows:\n\n1. **Start with the largest coin (25 cents)**.\n2. Use as many of that coin as possible without exceeding the target amount.\n3. Then use as many of the next largest coin (10 cents) as possible.\n4. Finally, use the remaining amount in 1-cent coins.\n\nFor example:\n- $ N = 42 $: 1 × 25 + 1 × 10 + 7 × 1 = 9 coins.\n- But the alternative: 4 × 10 + 2 × 1 = 6 coins.\n\nThis shows that the greedy algorithm **fails** for $ N = 42 $.\n\n---\n\n\\#\\#\\# **When Does the Greedy Algorithm Fail?**\n\nThe greedy algorithm **fails** for a value $ N $ if there exists a **better combination** of coins (using 1, 10, and 25 cents) that uses **fewer coins** than the greedy algorithm.\n\nThis happens when the **remainder** $ r = N \\mod 25 $ is in the set $ \\{5, 6, 7, 8, 9, 15, 16, 17, 18, 19\\} $.\n\nThis is because:\n- For such $ r $, the greedy algorithm uses $ \\left\\lfloor \\frac{r}{10} \\right\\rfloor + (r \\mod 10) $ coins.\n- But it is possible to express $ r $ as a combination of 10-cent and 1-cent coins with fewer coins.\n\n---\n\n\\#\\#\\# **Counting the Failing Values**\n\nWe count the number of $ N $ in the range 1 to 1000 for which $ r = N \\mod 25 \\in \\{5, 6, 7, 8, 9, 15, 16, 17, 18, 19\\} $.\n\n- For each of these 10 values of $ r $, the number of $ N $ values in the range 1 to 1000 is:\n $$\n \\left\\lfloor \\frac{1000 - r}{25} \\right\\rfloor + 1\n $$\n- But since $ N $ must be at least 1, and $ r $ is between 5 and 19, the number of valid $ N $ is:\n $$\n 39 \\times 10 = 390\n $$\n- This is because $ a = \\left\\lfloor \\frac{N}{25} \\right\\rfloor $ ranges from 1 to 39, and for each $ a $, there are 10 values of $ r $.\n\n---\n\n\\#\\#\\# **Final Calculation**\n\n- Total values of $ N $ from 1 to 1000: 1000\n- Number of failing $ N $: 390\n- Therefore, the number of values of $ N $ where the greedy algorithm **succeeds** is:\n $$\n 1000 - 390 = \\boxed{610}\n $$\n\n---\n\n\\#\\#\\# **Final Answer**\n\n$$\n\\boxed{610}\n$$\n\n\\end{tcolorbox}\n\n%\\appendix\n%\\section{Appendix}\n%You may include other additional sections here.\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"Which large language model has the best accuracy across all aggregation models for the AIME25 datatset and what is that average score? "},"answer":{"kind":"string","value":"Qwen3-8B, 72.82"},"plan":{"kind":"string","value":"SELECT all large language models\nLOOP for each model\n COMPUTE average_score = average of all AIME25 scores for this language_model across all rows\nCOMPUTE best_model = argmax large language model over average_score\n\n\nRETURN best_model, average_score of best_model\n"}}},{"rowIdx":353,"cells":{"paper":{"kind":"string","value":"2510.00024"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[htbp!]\n","\\centering\n","\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\n","\\renewcommand{\\arraystretch}{1.3}\n","\\setlength{\\tabcolsep}{5pt}\n","\\begin{tabular}{|>{\\raggedright\\arraybackslash}p{4cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|}\n","\\hline\n","\\multirow{2}{*}{\\textbf{Question Topics}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Readability}}} &\n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Relevance}\\\\\\textbf{\\& Motivation}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Technical}\\\\\\textbf{Soundness}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Experimental}\\\\\\textbf{Rigor}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Limitation}\\\\\\textbf{\\& Ethics}}} & \n","\\multicolumn{2}{c|}{\\textbf{Overall}} \\\\\n","\\cline{2-13}\n","& \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n","\\hline\n","1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\n","\\hline\n","2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\n","\\hline\n","3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\n","\\hline\n","4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\n","\\hline\n","5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:review}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[htbp!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3}\\n\",\n \"\\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \"\\\\begin{tabular}{|>{\\\\raggedright\\\\arraybackslash}p{4cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Question Topics}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Readability}}} &\\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Relevance}\\\\\\\\\\\\textbf{\\\\& Motivation}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Technical}\\\\\\\\\\\\textbf{Soundness}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Experimental}\\\\\\\\\\\\textbf{Rigor}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Limitation}\\\\\\\\\\\\textbf{\\\\& Ethics}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\textbf{Overall}} \\\\\\\\\\n\",\n \"\\\\cline{2-13}\\n\",\n \"& \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:review}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[http]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{MMMA.pdf}\n"," \\caption{Multimodal approach for the multi-agent framework for epidemic autonomous research. This framework enhances the power of multi-LLM agents by integrating multimodal data from various sources, such as literature, online web data, theoretical models, and simulation and experiments.}\n"," \\label{fig:MMMA}\n","\\end{figure}\n"],["\\begin{figure*}[http]\n"," \\centering\n"," \\includegraphics[width=0.85\\linewidth]{Fig12.pdf}\n"," \\caption{EpidemIQs orchestration across five research phases. Specialized agent teams perform tool calling (via red arrows), collaborate with each other (curved blue arrows), and exchange artifacts through a shared project repository (hexagons), enabling an end-to-end pipeline from discovery to final report generation.}\n"," \\label{fig:orch}\n","\\end{figure*}\n"],["\\begin{figure}[http]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{scientist.pdf}\n"," \\caption{The \\textit{scientist} agent architecture. a) Three modules as \\textit{plan}, \\textit{ReAct}, and \\textit{reflect}. The reflection ends either when the reflect agent decides the answer is already good enough or it reaches its maximum iteration limit. b) the conversation components for ReAct agent, as can be seen each time with the fixed task and plan, it updates new actions, results, and reflection. At each iteration \\(t\\), the newly generated \\(\\text{Action}_{t}\\), corresponding \\(\\text{Result}_{t}\\), and \\(\\text{Reflection}_{t}\\) are appended to short-term memory, while the \\(\\text{Action}_{t-2}\\), corresponding \\(\\text{Result}_{t-2}\\) are dropped out. The loop continues updating the conversation trace until the aforementioned conditions are met.}\n"," \\label{fig:scinetist}\n","\\end{figure}\n"],["\\begin{figure}[http]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{questions.pdf}\n"," \\caption{Evaluation questions designed to assess the capabilities and limitations of the proposed framework across varying levels of complexity}\n"," \\label{fig:question}\n","\\end{figure}\n"],["\\begin{table}[ht]\n","\\footnotesize\n","\\caption{Configuration Details for EpidemIQs }\n","\\centering\n","\\begin{tabular}{|l|c|c|c|}\n","\\hline\n","\\textbf{Parameter} & \\textbf{\\textit{scientists}} & \\textbf{\\textit{experts}} & \\textbf{\\textit{MathExpert}} \\\\\n","\\hline\n","LLM & \\makecell{gpt-4.1-\\\\2025-04-14} & \\makecell{gpt-4.1-mini\\\\2025-04-14} & \\makecell{o3-mini\\\\2025-01-31} \\\\\n","$r_{\\max}$ & 1 & - & - \\\\\n","Retries & 5 & 5 & 5 \\\\\n","Tool Retries & 50 & 50 & 50 \\\\\n","Output Type & Pydantic dataclass & free-form & free-form \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:agent_config}\n","\\end{table}\n"],["\\begin{figure}[t]\n","\\iffalse\n"," \\centering\n"," \\begin{subfigure}[b]{\\linewidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{paperQ1.pdf}\n"," \\caption{}\n"," \\label{fig:Q1}\n"," \\end{subfigure}\n","\\fi\n","\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{paperQ2.pdf} \n"," \\caption{Examples of paper generated by EpidemIQs for the second question. }\n"," \\label{fig:paper}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{reason.pdf}\n"," \\caption{An example of reasoning information \\textit{NetworkScientist} generated for question one}\n"," \\label{fig:reason}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{workflowq4.pdf}\n"," \\caption{An overview of the workflow for question four, highlighting each step’s goals, main actions, and outputs. The results have been truncated for clearer visualization. At the bottom, plots generated during the modeling and simulation phases are provided. }\n"," \\label{fig:workflowQ4}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{workflowq5.pdf}\n"," \\caption{An overview of the workflow for question five, outlining each step’s goals, main actions, and outputs. For clarity, the results have been truncated. At the bottom, plots display the degree distribution, highlighting the large number of nodes with degree 10 and confirming that enough nodes are available for targeted vaccination, together with simulation results for four cases: no vaccination (baseline), vaccination below the critical threshold, at the threshold, and above the threshold.}\n"," \\label{fig:workflowQ5}\n","\\end{figure}\n"],["\\begin{table*}[htbp!]\n","\\centering\n","\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\n","\\renewcommand{\\arraystretch}{1.3}\n","\\setlength{\\tabcolsep}{5pt}\n","\\begin{tabular}{|>{\\raggedright\\arraybackslash}p{4cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|}\n","\\hline\n","\\multirow{2}{*}{\\textbf{Question Topics}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Readability}}} &\n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Relevance}\\\\\\textbf{\\& Motivation}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Technical}\\\\\\textbf{Soundness}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Experimental}\\\\\\textbf{Rigor}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Limitation}\\\\\\textbf{\\& Ethics}}} & \n","\\multicolumn{2}{c|}{\\textbf{Overall}} \\\\\n","\\cline{2-13}\n","& \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n","\\hline\n","1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\n","\\hline\n","2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\n","\\hline\n","3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\n","\\hline\n","4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\n","\\hline\n","5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:review}\n","\\end{table*}\n"],["\\begin{table}[t]\n"," \\centering\n"," \\caption{Average Computation Statistics}\n"," \\begin{tabular}{|l|c|c|c|}\n"," \\hline\n"," \\textbf{Phase} & \\textbf{Time(sec.)} & \\textbf{Tokens(K)} & \\textbf{Cost(\\$)} \\\\ \\hline\n"," Discovery & 158 & 98 & 0.1 \\\\ %\\hline\n"," Modeling & 140 & 175 & 0.72 \\\\ %\\hline\n"," Simulation & 198 & 88 & 0.23 \\\\ %\\hline\n"," Analysis & 177 & 93 & 0.16 \\\\ %\\hline\n"," Report Writing & 517 & 416 & 0.36 \\\\ \\hline\n"," \\textbf{Overall} & \\textbf{1190} & \\textbf{870} & \\textbf{1.57 } \\\\ \\hline\n"," \\end{tabular}\n"," \\label{tab:cost}\n","\\end{table}\n"],["\\begin{table*}[htb!]\n","\\caption{Overall Score for AI and Human Expert Evaluation of Generated Papers}\n","\\centering\n","\\begin{tabular}{|l|c c|c c|c c|c c|c c|}\n","\\hline\n","\\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{question 1}} & \\multicolumn{2}{c|}{\\textbf{question 2}} & \\multicolumn{2}{c|}{\\textbf{question 3}} & \\multicolumn{2}{c|}{\\textbf{question 4}} & \\multicolumn{2}{c|}{\\textbf{question 5}} \\\\\n"," & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n","\\hline\n","EpidemIQs & 9.5 & 8.0 & 9.5 &8.2 & 9.2 & 7.8 & 9.0 & 8.0 & 9.2 & 8.1 \\\\\n","single-agent-GPT4.1 & 8.9 & 5.4 & 7.3 & 5.3 & 8.9 & 4.8 & 7.5 & 4.6 & 8.4 & 5.2 \\\\\n","single-agent-o3 & 8.5 & 5.8 & 8.6 & 6.3 & 8.3 & 5.5 & 8.6 & 5.8 & 7.4 & 5.2 \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:single_score}\n","\\end{table*}\n"],["\\begin{table}\n","\\caption{Comparison of Average Computation Statistics Across All Questions Over Three Different Implementations}\n","\\centering\n","\\begin{tabular}{|l|c|c|c|}\n","\\hline\n","\\textbf{Method} & \\textbf{Time (s)} & \\textbf{Tokens (K)} & \\textbf{Cost (\\$)} \\\\\n","\\hline\n","EpidemIQs & 1190 & 870 & 1.57 \\\\\n","single-agent-GPT4.1 & 214 & 312 & 0.91 \\\\\n","single-agent-o3 & 436 & 165 & 4.13 \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:cost_single}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure}[http]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{MMMA.pdf}\\n\",\n \" \\\\caption{Multimodal approach for the multi-agent framework for epidemic autonomous research. This framework enhances the power of multi-LLM agents by integrating multimodal data from various sources, such as literature, online web data, theoretical models, and simulation and experiments.}\\n\",\n \" \\\\label{fig:MMMA}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}[http]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.85\\\\linewidth]{Fig12.pdf}\\n\",\n \" \\\\caption{EpidemIQs orchestration across five research phases. Specialized agent teams perform tool calling (via red arrows), collaborate with each other (curved blue arrows), and exchange artifacts through a shared project repository (hexagons), enabling an end-to-end pipeline from discovery to final report generation.}\\n\",\n \" \\\\label{fig:orch}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure}[http]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{scientist.pdf}\\n\",\n \" \\\\caption{The \\\\textit{scientist} agent architecture. a) Three modules as \\\\textit{plan}, \\\\textit{ReAct}, and \\\\textit{reflect}. The reflection ends either when the reflect agent decides the answer is already good enough or it reaches its maximum iteration limit. b) the conversation components for ReAct agent, as can be seen each time with the fixed task and plan, it updates new actions, results, and reflection. At each iteration \\\\(t\\\\), the newly generated \\\\(\\\\text{Action}_{t}\\\\), corresponding \\\\(\\\\text{Result}_{t}\\\\), and \\\\(\\\\text{Reflection}_{t}\\\\) are appended to short-term memory, while the \\\\(\\\\text{Action}_{t-2}\\\\), corresponding \\\\(\\\\text{Result}_{t-2}\\\\) are dropped out. The loop continues updating the conversation trace until the aforementioned conditions are met.}\\n\",\n \" \\\\label{fig:scinetist}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[http]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{questions.pdf}\\n\",\n \" \\\\caption{Evaluation questions designed to assess the capabilities and limitations of the proposed framework across varying levels of complexity}\\n\",\n \" \\\\label{fig:question}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\footnotesize\\n\",\n \"\\\\caption{Configuration Details for EpidemIQs }\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{|l|c|c|c|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Parameter} & \\\\textbf{\\\\textit{scientists}} & \\\\textbf{\\\\textit{experts}} & \\\\textbf{\\\\textit{MathExpert}} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"LLM & \\\\makecell{gpt-4.1-\\\\\\\\2025-04-14} & \\\\makecell{gpt-4.1-mini\\\\\\\\2025-04-14} & \\\\makecell{o3-mini\\\\\\\\2025-01-31} \\\\\\\\\\n\",\n \"$r_{\\\\max}$ & 1 & - & - \\\\\\\\\\n\",\n \"Retries & 5 & 5 & 5 \\\\\\\\\\n\",\n \"Tool Retries & 50 & 50 & 50 \\\\\\\\\\n\",\n \"Output Type & Pydantic dataclass & free-form & free-form \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:agent_config}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \"\\\\iffalse\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{subfigure}[b]{\\\\linewidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{paperQ1.pdf}\\n\",\n \" \\\\caption{}\\n\",\n \" \\\\label{fig:Q1}\\n\",\n \" \\\\end{subfigure}\\n\",\n \"\\\\fi\\n\",\n \"\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{paperQ2.pdf} \\n\",\n \" \\\\caption{Examples of paper generated by EpidemIQs for the second question. }\\n\",\n \" \\\\label{fig:paper}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{reason.pdf}\\n\",\n \" \\\\caption{An example of reasoning information \\\\textit{NetworkScientist} generated for question one}\\n\",\n \" \\\\label{fig:reason}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{workflowq4.pdf}\\n\",\n \" \\\\caption{An overview of the workflow for question four, highlighting each step’s goals, main actions, and outputs. The results have been truncated for clearer visualization. At the bottom, plots generated during the modeling and simulation phases are provided. }\\n\",\n \" \\\\label{fig:workflowQ4}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{workflowq5.pdf}\\n\",\n \" \\\\caption{An overview of the workflow for question five, outlining each step’s goals, main actions, and outputs. For clarity, the results have been truncated. At the bottom, plots display the degree distribution, highlighting the large number of nodes with degree 10 and confirming that enough nodes are available for targeted vaccination, together with simulation results for four cases: no vaccination (baseline), vaccination below the critical threshold, at the threshold, and above the threshold.}\\n\",\n \" \\\\label{fig:workflowQ5}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3}\\n\",\n \"\\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \"\\\\begin{tabular}{|>{\\\\raggedright\\\\arraybackslash}p{4cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Question Topics}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Readability}}} &\\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Relevance}\\\\\\\\\\\\textbf{\\\\& Motivation}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Technical}\\\\\\\\\\\\textbf{Soundness}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Experimental}\\\\\\\\\\\\textbf{Rigor}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Limitation}\\\\\\\\\\\\textbf{\\\\& Ethics}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\textbf{Overall}} \\\\\\\\\\n\",\n \"\\\\cline{2-13}\\n\",\n \"& \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:review}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Average Computation Statistics}\\n\",\n \" \\\\begin{tabular}{|l|c|c|c|}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Phase} & \\\\textbf{Time(sec.)} & \\\\textbf{Tokens(K)} & \\\\textbf{Cost(\\\\$)} \\\\\\\\ \\\\hline\\n\",\n \" Discovery & 158 & 98 & 0.1 \\\\\\\\ %\\\\hline\\n\",\n \" Modeling & 140 & 175 & 0.72 \\\\\\\\ %\\\\hline\\n\",\n \" Simulation & 198 & 88 & 0.23 \\\\\\\\ %\\\\hline\\n\",\n \" Analysis & 177 & 93 & 0.16 \\\\\\\\ %\\\\hline\\n\",\n \" Report Writing & 517 & 416 & 0.36 \\\\\\\\ \\\\hline\\n\",\n \" \\\\textbf{Overall} & \\\\textbf{1190} & \\\\textbf{870} & \\\\textbf{1.57 } \\\\\\\\ \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\label{tab:cost}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[htb!]\\n\",\n \"\\\\caption{Overall Score for AI and Human Expert Evaluation of Generated Papers}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{|l|c c|c c|c c|c c|c c|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{question 1}} & \\\\multicolumn{2}{c|}{\\\\textbf{question 2}} & \\\\multicolumn{2}{c|}{\\\\textbf{question 3}} & \\\\multicolumn{2}{c|}{\\\\textbf{question 4}} & \\\\multicolumn{2}{c|}{\\\\textbf{question 5}} \\\\\\\\\\n\",\n \" & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"EpidemIQs & 9.5 & 8.0 & 9.5 &8.2 & 9.2 & 7.8 & 9.0 & 8.0 & 9.2 & 8.1 \\\\\\\\\\n\",\n \"single-agent-GPT4.1 & 8.9 & 5.4 & 7.3 & 5.3 & 8.9 & 4.8 & 7.5 & 4.6 & 8.4 & 5.2 \\\\\\\\\\n\",\n \"single-agent-o3 & 8.5 & 5.8 & 8.6 & 6.3 & 8.3 & 5.5 & 8.6 & 5.8 & 7.4 & 5.2 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:single_score}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}\\n\",\n \"\\\\caption{Comparison of Average Computation Statistics Across All Questions Over Three Different Implementations}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{|l|c|c|c|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Method} & \\\\textbf{Time (s)} & \\\\textbf{Tokens (K)} & \\\\textbf{Cost (\\\\$)} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"EpidemIQs & 1190 & 870 & 1.57 \\\\\\\\\\n\",\n \"single-agent-GPT4.1 & 214 & 312 & 0.91 \\\\\\\\\\n\",\n \"single-agent-o3 & 436 & 165 & 4.13 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:cost_single}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\documentclass[journal]{IEEEtran}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\providecommand{\\authorrefmark}[1]{\\textsuperscript{#1}} % fallback if class doesn't define it\n\\DeclareUnicodeCharacter{202F}{\\,}\n\n% ---------- Encoding & Fonts ----------\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{lmodern}\n\n% ---------- Colors & Graphics ----------\n\\usepackage{xcolor} % keep simple for arXiv\n\\definecolor{navyblue}{RGB}{0,0,128}\n\\usepackage{graphicx}\n\\usepackage{tikz}\n\n% ---------- Tables & Layout ----------\n\\usepackage{array}\n\\usepackage{booktabs}\n\\usepackage{multirow}\n\\usepackage{tabularx}\n\\usepackage{makecell}\n\\usepackage{float}\n\n% ---------- Math & Microtypography ----------\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{nicefrac}\n\\usepackage{microtype}\n\n% ---------- Captions ----------\n\\usepackage{subcaption} % works with IEEEtai; avoid subfig\n\n% ---------- URLs & Links (load near last) ----------\n\\usepackage{url}\n\\usepackage{hyperref}\n\\hypersetup{\n colorlinks=true,\n linkcolor=navyblue,\n citecolor=navyblue,\n urlcolor=navyblue\n}\n\n% ---------- Bibliography (BibTeX, arXiv-safe) ----------\n% Use natbib + IEEEtranN.bst (installed on arXiv). Do NOT use biblatex/biber.\n\\usepackage[numbers,sort&compress]{natbib}\n\\bibliographystyle{IEEEtranN}% In your main file, later: \\bibliographystyle{IEEEtranN} \\bibliography{ref}\n\n% ---------- Optional (comment out before final if you like) ----------\n% \\usepackage[left]{lineno} % \\linenumbers\n\\usepackage{pdfpages}\n\n% ---------- Title & Authors ----------\n%\\title{EpidemIQs: Prompt-to-Paper LLM Agents for Epidemic Modeling and Analysis}\n\n\\title{EpidemIQs: Prompt-to-Paper LLM Agents for Epidemic Modeling and Analysis}\n\n\\author{%\n Mohammad Hossein Samaei\\authorrefmark{1}, Faryad Darabi Sahneh\\authorrefmark{2}, Lee W. Cohnstaedt\\authorrefmark{3}, and Caterina Scoglio\\authorrefmark{1}\n \\thanks{\\authorrefmark{1} Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS, USA (Corresponding Author's email: msamaei@ksu.edu)\n%\\thanks{\\authorrefmark{2} Independant Researcher, MA, USA}\n%\\thanks{\\authorrefmark{3} USDA-ARS, National Bio- and Agro-Defense Facility, Foreign Arthropod-borne Animal Disease\n%Research Unit, Manhattan, KS, United States}\n}}\n\n\n\\begin{document}\n%\\externaldocument[S-]{supp/supp}\n%\\tableofcontents\n\\newpage\n\n\n\\maketitle\n\n\\begin{abstract}\nLarge Language Models (LLMs) offer new opportunities to automate complex interdisciplinary research domains. Epidemic modeling, characterized by its complexity and reliance on network science, dynamical systems, epidemiology, and stochastic simulations, represents a prime candidate for leveraging LLM-driven automation. We introduce \\textbf{EpidemIQs}, a novel multi-agent LLM framework that integrates user inputs and autonomously conducts literature review, analytical derivation, network modeling, mechanistic modeling, stochastic simulations, data visualization and analysis, and finally documentation of findings in a structured manuscript. We introduced two types of agents: a scientist agent for planning, coordination, reflection, and generation of final results, and a task-expert agent to focus exclusively on one specific duty serving as a tool to the scientist agent. The framework consistently generated complete reports in scientific article format. Specifically, using GPT 4.1 and GPT 4.1 mini as backbone LLMs for scientist and task-expert agents, respectively, the autonomous process completed with average total token usage 870K at a cost of about \\$1.57 per study, achieving a 100\\% completion success rate through our experiments. We evaluate EpidemIQs across different epidemic scenarios, measuring computational cost, completion success rate, and AI and human expert reviews of generated reports. We compare EpidemIQs to the single-agent LLM, which has the same system prompts and tools, iteratively planning, invoking tools, and revising outputs until task completion. The comparison shows consistently higher performance of the proposed framework across five different scenarios. EpidemIQs represents a step forward in accelerating scientific research by significantly reducing costs and turnaround time of discovery processes, and enhancing accessibility to advanced modeling tools.\\\\\n\\end{abstract}\n\n%\\begin{IEEEImpStatement}\n%EpidemIQs advances autonomous research capabilities in the epidemic modeling field through an innovative orchestration of collaborative multi-agent LLMs and integrates multimodal data. To the best of the authors' knowledge, this framework is among the first in this area that leverages AI for end-to-end research automation. Our evaluations demonstrate the framework’s ability to produce high-quality research autonomously, getting us closer to efficient, reliable, and accessible autonomous research tools. %, providing a robust foundation for addressing complex problems across various interdisciplinary domains.\n%\\end{IEEEImpStatement}\n\\begin{IEEEkeywords}\nAutonomous Agents, AI for Science, Epidemic Modeling, Multi-Agent Systems\n\\end{IEEEkeywords}\n\n\\section{Introduction}\nScientists' Efforts to automate research date back to at least the early 1970s \\cite{langley1987scientific,langley2024integrated,waltz2009automating}, aiming to overcome limits on the number of ideas scientists can pursue, constraints that force them to prioritize ideas with higher predicted impact. For example, the Automated Mathematician was introduced to carry out simple mathematics research guided by large sets of heuristic rules \\cite{inproceedings,lenat1984and}, and DENDRAL was proposed to assist chemists with data interpretation problems \\cite{buchanan1981dendral}. \n\nMore recently, advances in autoregressive large language models (LLMs) \\cite{touvron2023llama, team2023gemini, achiam2023gpt} have demonstrated strong capabilities in question answering, problem-solving, and coding, with promising applications across science and engineering. However, LLMs still face limitations when applied to real-world tasks \\cite{zoullm}. These constraints led to the development of LLM agents, which extend LLMs with abilities such as external tool use \\cite{schick2023toolformer,qin2023toolllm,hao2023toolkengpt}, chain-of-thought prompting \\cite{wei2022chain}, and iterative self-improvement \\cite{shinn2023reflexion,huang2022large}.\nLLM agents have since been applied to diverse domains, including software engineering \\cite{jimenez2023swe,wang2024openhands}, cybersecurity \\cite{abramovich2024interactive}, medical diagnosis \\cite{mcduff2025towards}, chemistry \\cite{boiko2023autonomous,jumper2021highly,hayes2025simulating}, material science \\cite{merchant2023scaling,szymanski2023autonomous,ghafarollahi2025automating}, computational biology \\cite{ding2024automating}, algorithm design \\cite{fawzi2022discovering}, and healthcare \\cite{tang-etal-2024-medagents}.\nMulti-agent systems have also emerged to simulate human-like research environments across disciplines. Examples include Agent Laboratory \\cite{schmidgall2025agent}, Virtual Lab \\cite{swanson2025virtual}, ChemCrow \\cite{m2024augmenting}, ResearchAgent \\cite{baek2024researchagent}, and The AI Scientist \\cite{lu2024ai}. For broader surveys of LLM agent applications, see \\cite{wang2024survey,gridach2025agentic,yehudai2025survey,xi2025rise}.\n\n\n\nDespite the stunning advances of LLM agents across various domains, epidemiology-related areas have not yet fully benefited from these developments \\cite{bann2025can}, largely because they are among the most sophisticated and interdisciplinary fields. Network-based epidemic modeling is among the sophisticated approaches to studying the spread of infectious diseases by incorporating the structure of contact networks, which represent interactions among individuals or groups in a population \\cite {keeling2005networks}.\\\\\n\nUnlike traditional compartmental models, which assume homogeneous mixing, network-based models account for heterogeneous contact patterns by representing individuals as nodes and their interactions as edges (possibly weighted or time-varying) in a graph. This approach captures the realistic social and spatial structures influencing disease transmission, such as clustering, degree distribution, and community structures. By integrating network topology, these models provide insights into how connectivity patterns affect epidemic dynamics, enabling more accurate predictions of disease spread, the identification of critical transmission pathways, and the evaluation of targeted intervention strategies, such as vaccination or social distancing, in complex populations \\cite {kiss2017mathematics}. \\\\\nAddressing these models requires an interdisciplinary expertise: (i) stochastic-process theory to analyze the master equations and their approximations; (ii) network science to characterize and parametrize contact structures; (iii) epidemiology to constrain pathogen-specific parameters; and (iv) computational epidemiology to conduct simulations and scenario analysis. Having a research group with this level of diversity is not only challenging to access but also poses coordination challenges. In this study, we introduce \\textit{EpidemIQs}, a novel multi-LLM agents capable of autonomously addressing research in network-based epidemic modeling for the first time.\\\\\n\n\n\n\nEpidemIQs emulates an interdisciplinary research environment with five collaborative teams of \\textit{task-expert} and \\textit{scientist} agents, capable of performing end-to-end autonomous research: given a user query, if identified as a network-based problem, it initiates the process by discovering relevant insights from diverse online sources (e.g., web-based content and published papers) to conduct a literature review and address analytical aspects through mathematical reasoning. It then formulates the problem as a network-based model, tests it through rigorous stochastic simulations, analyzes the resulting multimodal data (e.g., visual and numerical), and finally composes a scientifically formatted manuscript that reports the entire procedure, from problem formulation to simulation results, discussion, and final conclusion. The framework can also operate in copilot mode, which enables human cooperation throughout the process.\\\\\nWe evaluate our proposed framework across five epidemic scenarios articulated through questions, three of which were unknown to the framework. We tested EpidemIQs against the multi-turn single-agent baseline, comparing performance by (i) discussing the results of each team across all scenarios, (ii) AI and human expert evaluations of generated papers, and (iii) computational statistics. The proposed framework consistently showed impressive performance, achieving a 100\\% completion success rate, an average human review score of 7.98 out of 10, a low cost of only \\$1.57, and a total processing time of 1{,}190 seconds. We can summarize the main contributions of our work as follows:\\\\\n\\iffalse\n\\begin{itemize}\n \\item A novel multi-LLM agents that conducts epidemic research through five scientific phases.\n \\item It integrates multimodal data, visual, textual, numerical, graph structure, etc., from multiple sources, including online retrieval, experimental results, and internally generated artifacts (e.g., graphs, tables), and dynamically combines them to accomplish the task, enhancing its utility and adaptability across diverse research contexts.\n \\item Fully autonomous mode capability reduces the human intervention to only providing the initial query, while it can also perform in co-pilot mode.\n \\item Human experts' evaluation of the papers produced by the framework using a rubric covering five criteria: Readability and Writing Quality, Relevance and Motivation, Technical Soundness, Experimental Rigor, and Limitations.\n \\item Providing high interpretability as each \\textit{scientist} provides their reasoning for their actions and generated outcomes, and records their results and scripts, facilitating validation of procedure and outcomes.\n \\item A detailed evaluation of computational statistics, including consumed time, number of tokens, and cost.\n\\end{itemize}\n\\fi\n\n\\begin{itemize}\n\\item Developed novel multi-LLM agents that conduct epidemic research through five distinct scientific phases.\n\\item Integrated multimodal data (visual, textual, numerical, graph structures, etc.) from diverse sources, including online retrieval, experimental results, and internally generated artifacts (e.g., graphs, tables), to enhance utility and adaptability across various research contexts.\n\\item Enabled fully autonomous mode to minimize human intervention, requiring only an initial query, while also supporting a copilot mode for collaborative operation.\n\\item Ensured high interpretability by having each \\textit{scientist} provide reasoning for its actions and generated outcomes, and recording results and scripts to facilitate validation of procedures and outcomes.\n\\end{itemize}\n\nThe remainder of this paper is organized as follows: Section \\ref{sec:meth} describes the methodology. Section \\ref{sec:multi} details the design and implementation of the system. Section \\ref{sec:eval} outlines the experimental setup and evaluation cases. Section \\ref{sec:result} presents the results and discusses the study’s limitations and shortcomings. Finally, Section \\ref{sec:conc} concludes the paper and proposes directions for future work.\n\n%\\textcolor{red}{contributions I wish I had:\n%\\begin{itemize}\n% \\item long and short memory\n% \\item context awareness\n% \\item report for each agent\n%\\end{itemize}\n%}%\n\n\\section{Methodology} \\label{sec:meth}\nLLMs demonstrate advanced capabilities relevant to scientific tasks, including coding and answering technical questions. However, their performance in tackling complex epidemiology scenarios remains limited. To address these challenges, we propose a multi-agent framework that emulates a scientific epidemic research laboratory environment, designed to enhance the practical capabilities of LLMs in complex scientific tasks. The EpidemIQs framework is organized into four core functional layers that collectively support autonomous research workflows\\cite{xi2025rise}: (1) The multi-agent orchestration layer governs the coordination, communication, and cooperation among specialized agents.\\iffalse to optimize overall task performance and enable iterative self-refinement. \\fi (2) The backbone LLM operates as the central reasoning and decision-making unit \\iffalse, responsible for interpreting queries, generating hypotheses, and formulating plans\\fi. (3) The perception layer collects, integrates, and processes heterogeneous data sources, including scientific literature, experimental results, contextual information, and prior knowledge bases. (4) The action layer executes tasks derived from the LLM’s output, encompassing activities such as code generation, simulation, modeling, etc.\n\\begin{figure}[http]\n \\centering\n \\includegraphics[width=1\\linewidth]{MMMA.pdf}\n \\caption{Multimodal approach for the multi-agent framework for epidemic autonomous research. This framework enhances the power of multi-LLM agents by integrating multimodal data from various sources, such as literature, online web data, theoretical models, and simulation and experiments.}\n \\label{fig:MMMA}\n\\end{figure}\nLooking at Figure~\\ref{fig:MMMA}, the architectural design illustrates the structured interaction among the four functional layers that enable autonomous epidemic research. The orchestration layer governs inter-agent communication, task allocation, and coordination protocols, ensuring efficient collaboration among specialized agents. Within the perception layer, agents process multimodal data streams through standardized interfaces that convert heterogeneous sources, including scientific literature, experimental data, contextual metadata, and structured knowledge bases, into unified semantic representations suitable for downstream reasoning and analysis. The backbone LLM operates as the central cognitive engine, analyzing perceived inputs, generating hypotheses, formulating research plans, and executing decisions based on accumulated evidence and domain constraints. The agents' outputs inform the action layer, where the system autonomously selects and calls functions to deploy tools, such as stochastic simulation engines, Retrieval-Augmented Generation (RAG), API calls, and executes it in the correct order, so that high‑level research goals are broken down into concrete, reproducible steps such as loading data, running simulations, and storing results.\n\n\\section{Multi-LLM Agent Architecture: EpidemIQs Framework} \\label{sec:multi}\nThe orchestration of EpidemIQs is illustrated in Figure \\ref{fig:orch}. This framework is structured to emulate a scientific laboratory, comprising five phases: Discovery, Modeling, Simulation, Analysis, and Report Writing. These phases are executed by distinct collaborative multi-agent system teams, and the results of their work are integrated to produce the final report. In this section, we first describe the design of two types of agents, followed by the architecture design, output structure, memory, and implementation details of EpidemIQs.\n\\begin{figure*}[http]\n \\centering\n \\includegraphics[width=0.85\\linewidth]{Fig12.pdf}\n \\caption{EpidemIQs orchestration across five research phases. Specialized agent teams perform tool calling (via red arrows), collaborate with each other (curved blue arrows), and exchange artifacts through a shared project repository (hexagons), enabling an end-to-end pipeline from discovery to final report generation.}\n \\label{fig:orch}\n\\end{figure*}\n\\subsection{Two Agent Types: \\textit{Scientist}s and \\textit{Experts}}\nTwo agent types are inspired by the generative agent concept \\cite {park2023generative} and further advanced by frameworks such as CAMEL \\cite{li2023camel}, AutoGen \\cite{wu2024autogen}, and Metagpt \\cite{hong2023metagpt}, and are designed to enable autonomous scientific reasoning and investigation. The central coordinating component, referred to as the \\textit{scientist} agent, performs high-level orchestration through iterative planning, reflection, and execution refinement. Upon receiving an input query, the \\textit{scientist} employs a dedicated \\textit{plan} module, which parses and decomposes the query into a plan comprising sub-tasks and their logical dependencies. Both \\textit{reflect} and \\textit{ReAct} modules are constrained to generate output in predefined formats. While structured outputs, e.g., JSON, enhance reproducibility and reliability of performance, they have recently been shown to compromise the reasoning capability of LLMs \\cite{tam-etal-2024-speak}. Therefore, we explicitly devote a separate \\textit{plan} module as an agent to allow it to freely generate the plan, while both the subsequent \\textit{ReAct} and \\textit{reflect} modules are restricted to generating predefined structured outputs.\n\\begin{figure}[http]\n \\centering\n \\includegraphics[width=1\\linewidth]{scientist.pdf}\n \\caption{The \\textit{scientist} agent architecture. a) Three modules as \\textit{plan}, \\textit{ReAct}, and \\textit{reflect}. The reflection ends either when the reflect agent decides the answer is already good enough or it reaches its maximum iteration limit. b) the conversation components for ReAct agent, as can be seen each time with the fixed task and plan, it updates new actions, results, and reflection. At each iteration \\(t\\), the newly generated \\(\\text{Action}_{t}\\), corresponding \\(\\text{Result}_{t}\\), and \\(\\text{Reflection}_{t}\\) are appended to short-term memory, while the \\(\\text{Action}_{t-2}\\), corresponding \\(\\text{Result}_{t-2}\\) are dropped out. The loop continues updating the conversation trace until the aforementioned conditions are met.}\n \\label{fig:scinetist}\n\\end{figure}\nOnce the plan is formulated, the \\textit{scientist} agent iteratively executes the ReAct-Reflect loop until either the \\textit{reflect} agent decides no further revision is needed, or it reaches the maximum iteration limit, $r_{max}$. The ReAct Module executes reasoning, and call tools conditioned on the current plan segment, and refine its response based on the action outcomes, while the reflect module prompted to perform logical reasoning, evaluates intermediate outputs for errors, logical inconsistencies, or incomplete results, producing structured JSON feedback to refine action selection and output validity across iterations, enhancing the agent performance through linguistic feedback without need to update the weights of models.\\iffalse Short-term and long-term memory modules are utilized by the \\textit{scientist} to maintain iterative context and cumulative knowledge. \\fi\\\\\nIn parallel, the \\textit{scientist} agent can coordinate multiple independent \\textit{task-expert} agents as tools, each designed as a specialized ReAct agent for a specific task or data source. These \\textit{expert} agents serve as domain specialists responsible for well-defined atomic tasks such as literature retrieval, online search, mathematical derivation, or data extraction. This functional decomposition ensures that each \\textit{expert} executes its task with minimal context switching, while the \\textit{scientist} maintains global task coherence and quality control.\n\n\\subsection{Multi-Agent Orchestration}\n\nThe EpidemIQs framework is comprised of 5 phases. It initiates upon receiving a user query, entering the \\textit{Discovery} phase. In this phase, the \\textit{DiscoveryScientist} agent performs planning and reasoning to collect data relevant to the query following the Multi-Hop Question Answering (MHQA) paradigm \\cite{mavi2024multi}. Specifically, the data collection process is conducted in three iterative steps, with each step focusing on a distinct information source. This multi-step procedure enables the system to progressively refine its understanding, reduce errors, and enhance the overall accuracy of the gathered information\\cite{jeyakumar2024advancing}. The components of the Discovery team are as follows:\n\n\\begin{itemize}\n \\item \\textit{DiscoveryScientist} coordinates the \\textit{expert} agents to collect relevant information, process the retrieved data, and synthesize the final output following a predefined structured format. This output encompasses a comprehensive description of the scenario, task specifications, and contextual information related to the disease and the affected population. \\\\\n \\item \\textit{OnlineRetrieverExpert} is responsible for acquiring relevant information from online sources. It generates and refines search queries in multiple stages, leveraging external APIs (e.g., Tavily API) to retrieve data from the web. The agent subsequently processes and integrates the retrieved information to generate a coherent response.\\\\\n \\item \\textit{LiteratureRetrieverExpert} conducts a multi-step search process using the Semantic Scholar API, based on the received query. For each retrieved query, the agent generates concise summaries and aggregates the most pertinent findings. The agent is prompted to generate the final summarized response based on multiple criteria, including relevance and accuracy.\\\\\n \\item \\textit{MathExpert} provides mathematical reasoning and analytical solutions for queries requiring quantitative analysis. The agent is capable of both generating and executing Python code, a capability demonstrated to enhance solution accuracy and mitigate hallucination risks ( \\cite{liang2023code} showed that it can increase up to 39.8\\% problem-solving capability over HumanEvals \\cite{chen2021evaluating} benchmark). The backbone LLM of this agent should be an advanced language model with high reasoning capacity, able to perform chain-of-thoughts( such as OpenAI GPT o3-Jan-2025 or o3-mini-Jan-2025 models \\cite{o3mini2025})\n\\end{itemize}\n\nFollowing the completion of the \\textit{Discovery} phase, the \\textit{Modeling} phase is initiated to systematically construct the foundational components required for simulating epidemic dynamics on complex networks. This phase is orchestrated by a team of three specialized \\textit{scientist} agents, each responsible for a distinct modeling dimension: network topology, mechanistic model formulation, and parameterization. The functional responsibilities of these agents are delineated as follows:\n\n\\begin{itemize}\n\\item \\textit{NetworkScientist} is tasked with generating a representative contact network that encapsulates the interaction patterns within the target population. The constructed network serves as a structural substrate upon which the epidemic process unfolds. Depending on the characteristics of the population and the epidemiological scenario, the network may adopt various configurations, including but not limited to regular networks or Erdős-Rényi random graphs \\cite{erdds1959random}, Barabási-Albert scale-free networks \\cite{barabasi1999emergence}, and multilayer structures \\cite{boccaletti2014structure}. The \\textit{NetworkScientist} employs algorithmic procedures implemented in Python, utilizing scientific computing libraries such as NetworkX and SciPy, to model the network topology. The finalized network structure is preserved in the workflow repository for integration into the simulation pipeline.\\\\\n\\item \\textit{ModelerScientist} is responsible for defining the mechanistic framework of disease progression. It selects and configures an appropriate compartmental model based on the disease characteristics and insights derived during the \\textit{Discovery} phase. \n\\item \\textit{ParameterScientist} is invoked after the design of both network topology and compartmental model, to calculate and assign quantitative values to model parameters and initialize network states. \\iffalse Key parameters such as transmission rates, recovery rates, and initial prevalence levels are calculated based on the context, expert knowledge, and scenario-specific assumptions. \\fi It performs calculations through the Python coding tool.\n\\end{itemize}\n\\iffalse\nUpon completion of the modeling phase, the framework transitions into the \\textit{Simulation}, wherein predictive experiments are conducted to analyze the modeled epidemic dynamics. This phase is executed by the \\textit{SimulationScientist}, which performs multiple stochastic simulations to capture the probabilistic evolution of contagion spread over the constructed contact network, and has delegated \\textit{VisionExpert} to verify successful outcomes of simulations.\\\\\nTo conduct these simulations, the agent utilizes the Fast Generalized Epidemic Modeling Framework (FastGEMF)~\\cite{samaei2025fastgemf}, a high-performance simulation engine capable of modeling arbitrary multi-compartment epidemic processes over multilayer network structures with computational efficiency. The \\textit{SimulationScientist} is pre-trained through one-shot learning examples to interface with FastGEMF.\nThroughout the simulation process, the agent records the generated time-series data using Python libraries such as Pandas and stores both the numerical outputs and corresponding state-evolution visualizations in the project repository.\n\nFollowing the simulation stage, the framework advances to the \\textit{Analysis}, wherein a coordinated team of specialized agents derives actionable insights from the simulation outputs. This multi-agent analysis team is responsible for processing both numerical results and visual artifacts to extract context-specific metrics and interpret spread dynamics. The roles and responsibilities of the constituent agents are defined as follows:\n\n\\begin{itemize}\n \\item \\textit{DataScientist} coordinates the specialized \\textit{expert} agents and integrates their outputs into a coherent interpretation of the simulation results. It identifies and computes key epidemiological metrics, such as peak infection time and size, epidemic duration, outbreak probability, etc., tailored to the nature of the modeled disease and the research query. The final output consists of numerical measures and qualitative analysis.\\\\\n \\item \\textit{VisualExpert} has vision-language capabilities through Base64 decoding format and is responsible for analyzing the visual outputs generated during the simulation phase. It interprets time-series plots or state evolution graphs, enabling interpretability and validation of dynamic behavior that may not be easily deduced from raw numerical outputs alone.\\\\\n \\item \\textit{DataExpert} is tasked with the interpretation of structured numerical data. This agent accesses simulation results stored in the system repository and applies analytical techniques using Python libraries such as Pandas, NumPy, and SciPy. Operating within a multi-hop paradigm, the \\textit{DataExpert} initially identifies the structure and content of the available data, then dynamically selects appropriate analysis strategies to compute requested metrics. This flexibility ensures the agent's ability to generalize across varying data types and experimental settings.\n\\end{itemize}\n\\fi\nUpon completion of the modeling phase, the framework transitions into the \\textit{Simulation}, wherein predictive experiments are conducted to analyze the modeled epidemic dynamics. This phase is executed by the \\textit{SimulationScientist}, which performs multiple stochastic simulations to capture the probabilistic evolution of contagion spread over the constructed contact network, and has delegated \\textit{VisionExpert} to verify successful outcomes of simulations. The \\textit{VisionExpert} has vision-language capabilities and is responsible for analyzing the visual outputs generated during the simulation phase. It interprets time-series plots or state evolution graphs, enabling interpretability and validation of dynamic behavior that may not be easily deduced from raw numerical outputs alone.\\\\\nTo conduct these simulations, the agent utilizes the Fast Generalized Epidemic Modeling Framework (FastGEMF)~\\cite{samaei2025fastgemf}, a high-performance simulation engine capable of modeling arbitrary multi-compartment epidemic processes over multilayer network structures with computational efficiency. The \\textit{SimulationScientist} is pre-trained through one-shot learning examples to interface with FastGEMF.\nThroughout the simulation process, the agent records the generated time-series data using Python libraries such as Pandas and stores both the numerical outputs and corresponding state-evolution visualizations in the project repository.\\\\\nFollowing the simulation stage, the framework advances to the \\textit{Analysis}, wherein a coordinated team of specialized agents derives actionable insights from the simulation outputs. This multi-agent analysis team is responsible for processing both numerical results and visual artifacts to extract context-specific metrics and interpret spread dynamics. The roles and responsibilities of the constituent agents are defined as follows:\\\\\n\\begin{itemize}\n \\item \\textit{DataScientist} coordinates the specialized \\textit{expert} agents and integrates their outputs into a coherent interpretation of the simulation results. It identifies and computes key epidemiological metrics, such as peak infection time and size, epidemic duration, outbreak probability, etc., tailored to the nature of the modeled disease and the research query. The final output consists of numerical measures and qualitative analysis.\\\\\n \\item \\textit{VisionExpert} analyzes visualizations to extract metrics and interpret epidemic behavior (e.g., uncertainty bands around trajectories), that may not be easily interpretable from raw numerical data.\\\\\n \\item \\textit{DataExpert} is tasked with the interpretation of structured numerical data. This agent accesses simulation results stored in the system repository and applies analytical techniques using Python libraries such as Pandas, NumPy, and SciPy. Operating within a multi-hop paradigm, the \\textit{DataExpert} initially identifies the structure and content of the available data, then dynamically selects appropriate analysis strategies to compute requested metrics. This flexibility ensures the agent's ability to generalize across varying data types and experimental settings.\n\\end{itemize}\n\n\nThe final phase of the framework is \\textit{Automated Report Generation}, wherein two coordinated \\textit{expert} agents synthesize the research findings into a structured academic manuscript. This process starts with the \\textit{ReporterExpert}, which is equipped with tools to access the outputs of the entire workflow, including simulation results, code scripts, and literature summaries. Guided by a predefined LaTeX-based manuscript template, the \\textit{ReporterExpert} sequentially drafts all major sections of the paper, such as the Title, Abstract, Introduction, Methods, Results, and Discussion. Following the generation of each section, the \\textit{LatexCraftExpert} is tasked to perform a syntactic and structural validation of the LaTeX code, resolving potential compilation errors and ensuring stylistic consistency with publication guidelines. Upon completion of the main draft, the \\textit{LiteratureReviewExpert} conducts a contextual relevance check, retrieving and integrating recent scholarly works aligned with the study’s findings. This agent augments the manuscript with a Background and Related Work section to strengthen the research academic positioning.\nOnce the initial draft is completed, an iterative review loop is repeated by the \\textit{ReporterExpert}. It critiques each section to detect inconsistencies, redundancies, or logical gaps according to a user-defined number of revision cycles, $n_{max}$. Finally, it is compiled as a PDF file.\n\n\\subsection{Memory}\nTwo specialized memory structures are considered for the agents. The \\textit{scientist} agent's memory consists of short-term and long-term memory. The short-term memory encompasses all the current conversation details, including role description, input query, agent's internally generated responses, interaction with tools, conversations with other agents, and the final output. The long-term memory stores all previous conversation history in a database, enabling semantic retrieval based on the current query. \n\\\\\n\\subsection{Structured Outputs}\n\nTypically, LLMs generate free-format texts as a natural language output, which does not follow a strict structure. However, the performance of the collaborative LLM agents requires precise and careful interoperability, as information sharing and communication can significantly impact overall outcomes \\cite {wu2024autogen}. Therefore, to make the data transition between each phase of the process robust, reliable, and more predictable, there are constraints defined for each team output structure, forcing them to produce output in a predefined structure (e.g., JSON schema). This not only facilitates data retrieval and improves prompt development efficiency, but it also enables automatic validation of each team's output \\cite{10.1145/3613905.3650756}, ensuring all required fields are generated accordingly, and there is no missing data. If not, the agent retries until it fulfills the task or reaches the maximum number of tries allowed. While the output structure of each \\textit{scientist} contains different fields, all \\textit{scientists} share one common element: the reasoning and logical justification behind their choices and results. Each \\textit{scientist} is expected to defend their decisions against hypothesized criticisms, demonstrating why these were the most appropriate outcomes. \n\n\n\\subsection{Autonomous and Copilot Operation Modes}\nThe EpidemIQs can perform in two modes: end-to-end autonomous and cooperative modes. The latter is named as a copilot, which can operate as an assistant to the user. The autonomous mode does not require human intervention, but rather initially provides the query. The copilot mode enables the human to intervene and provides feedback and instruction on the agent's output, or asks for more actions to guide the agent toward the desired direction. After each phase, the human is asked to review the results, and they can either mark them as complete and proceed to the next phase or ask for new actions by providing comments. \\iffalse For example, during the simulation phase, the human user can observe the results and instruct the agent to perform a new set of simulations with different setups. Alternatively, in discovery mode, the user can request a specific literature topic that the agent did not previously include. \\fi\n\\subsection{Implementation}\n\\iffalse\nThe proposed framework has been designed and implemented in Python using the Pydantic AI framework. To facilitate autonomous data acquisition, external APIs are integrated into the agent system. Specifically, we employed the Semantic Scholar API for automated retrieval of scientific literature, while the Tavily API provides access to web-scale information retrieval from the broader internet.\nFor multimodal data processing, the framework incorporates a Vision-Language Model (VLM), implemented using the OpenAI SDK and through Base64 decoding format, which enables the agent to interpret visual data during the analysis and simulation phase. Short-term memory is managed using the LLM’s context window and is integrated with the Pydantic AI memory module. Long-term memory capabilities \nLong-term memory is stored in JSON format and managed using Pydantic AI memory module functions for data retrieval and storage.\nFinally, to ensure structural consistency and schema validation across agent interactions and output structures, we use Pydantic data models, which provide robust data integrity guarantees throughout the orchestration.\n\\fi\nThe framework is implemented in Python using the Pydantic AI framework. Autonomous data acquisition is supported through API integrations using the Semantic Scholar API for literature retrieval and the Tavily API for web-scale information access. \nFor multimodal processing, a Vision-Language Model (VLM) is implemented via the OpenAI SDK with Base64 decoding to enable visual data interpretation. Short-term memory utilizes the LLM’s context window, while long-term memory is stored in JSON and managed through Pydantic AI memory functions. Finally, we used Pydantic data models for schema validation and structural consistency across agent interactions.\n%The final phase employs a multi-agent collaborative system to transform experimental data into a complete scientific manuscript. Writer agents process workflow history and experimental data in manageable chunks, generating manuscript sections sequentially. After each section, a LaTeX cleaner agent identifies and corrects structural and syntactic errors. Upon completion of all sections, a literature agent performs targeted searches to enrich the manuscript with relevant background material based on semantic analysis of the document.\n\n%A feedback agent then evaluates the manuscript using NeurIPS review criteria, providing section-specific comments that guide the writer agent through iterative refinements. This quality assurance loop implements a dynamic termination protocol based on a predefined quality threshold—when the manuscript achieves a sufficient review score or maximum number of iteration, the feedback cycle concludes and the document is compiled. This approach ensures methodical progression from raw experimental data to publication-ready manuscripts while maintaining scientific rigor through structured validation processes.\n\n\n\n\n\\section{Evaluation Approach} \\label{sec:eval}\n\nTo assess the performance of the framework, we designed five questions, shown in Figure~\\ref {fig:question}, with increasing depth and complexity.\n\\begin{figure}[http]\n \\centering\n \\includegraphics[width=1\\linewidth]{questions.pdf}\n \\caption{Evaluation questions designed to assess the capabilities and limitations of the proposed framework across varying levels of complexity}\n \\label{fig:question}\n\\end{figure}\n\\iffalse\nThe first question in Figure~\\ref{fig:question} is the simplest. It requires the framework to analytically investigate the problem and design the simulation setup by creating the model and two network structures, one heterogeneous and one homogeneous, to compare the stochastic results. The goal is to analyze how structural differences influence the stochastic spread of the disease.\n\nThe second question requires identifying the reason for the break in the chain of transmission and designing models and network setups to validate the hypothesis using exact stochastic simulations.\n\nThe third question is structurally similar to the first but introduces a key limitation: the problem involves a temporal network, which lies outside the scope of the simulation tool provided to the agent. This test evaluates how the system adapts to cases out of the scope of the expert knowledge provided for it.\n\nThe fourth question is more complex for two reasons. First, it requires finding the analytical answer either by advanced reasoning or knowledge from the literature. Second, the agent must extend the conventional SIS model to an $SI_1I_2S$ model (as in the competitive epidemic setup) and design a multiplex network with features that enable the possibility of virus coexistence.\n\n\n\nThe fifth question is the most challenging. It requires an analytical solution for two vaccination strategies, random and targeted, under a network with specific centrality. The key difficulty is that such random networks rarely contain a sufficient number of degree-10 nodes for targeted vaccination. Therefore, the agent should notice the implicit constraint and engineer the contact network to ensure that enough degree-10 nodes exist for the strategy to test the hypothesized threshold for herd immunity, while still maintaining the required structural properties.\\\\\n\\fi\nThe first question is the simplest, requiring an analytical investigation and comparison of stochastic simulations on heterogeneous versus homogeneous networks to assess how structural differences shape disease spread.\nThe second focuses on identifying why the chain of transmission breaks and validating hypotheses through stochastic modeling.\nThe third resembles the first but introduces a temporal network, which exceeds the scope of the provided simulation tools, testing system adaptability.\\\\ \nThe fourth demands both analytical reasoning (or knowledge from literature) and an extension of the SIS model to a competitive $SI_1I_2S$ form on a multiplex network, exploring conditions for coexistence.\nThe fifth is the most challenging, requiring analytical evaluation of random versus targeted vaccination strategies. Here, the key challenge is to notice the implicit constraint to ensure that the contact network contains enough degree-10 nodes to make targeted vaccination feasible while preserving its structural properties. \\\\\n\nCollectively, these questions span the key aspects of network epidemics, such as topology, temporal structure, multilayer interactions and competing pathogens, termination mechanisms, network-aware interventions, physics-aware contact network, etc, providing a holistic evaluation framework. Only the first two questions were involved in the test and trials through the design of the EpidemIQs orchestration, and the last three were unknown to the framework.\\\\\nEpidemiological research is inherently stochastic and complex, and admits multiple valid modeling approaches, leading to the absence of a unified standardized benchmark for evaluating the end-to-end epidemic research pipeline. Therefore, to evaluate our framework, we adopted an assessment strategy aligned with how the scientific community assesses research manuscripts through the peer review process. Consequently, we considered:\n\\begin{itemize}\n\\item \\textbf{Human evaluation} by peer review of written outputs and appraisal of deliverables. Specifically, we asked five blinded domain experts to review the manuscripts generated by EpidemIQs, based on the criteria in Supplementary Table S7.\n\\item \\textbf{LLM-as-Judge evaluation} using GPT-4o to evaluate generated papers autonomously based on the same assessment criteria as human reviewers to deliver timely evaluation.\n\\item \\textbf{Completion success rate} defined as the proportion of trials in which \\textit{EpidemIQs} autonomously executed the full workflow and produced a scientific report containing all pre-specified sections, independent of content quality.\n\\item \\textbf{Computational costs} in terms of turnaround time, number of generated tokens, and total API cost.\n\\end{itemize}\nTogether, these measures capture both the scientific quality of the outputs and the reliability of the autonomous workflow.\nWe compared our framework with a multi-turn single agent, such that an agent plans its next steps autonomously for up to the maximum number of steps, $s_{max}$. The single agent is instructed to perform all five phases with clear instructions (same as the agents in the EpidemIQs) and the same tools as in the multi-agent framework, along with \\textit{VisionExpert} to enable the agent to analyze the figures. This single agent needs to have an LLM with a long context window; therefore, we used OpenAI gpt-4.1-2025-04-14, as it has reasoning capability and support of structured output with a context window of about one million tokens, along with o3-2025-04014 as the current highly capable OpenAI model with a 200K tokens context window. \\\\\nTo prevent the prompt drift, in each turn we re-inject the main task into memory as \\texttt{**Reminder** main query is \\{query\\}. Do NOT lose sight of this}, ensuring that the agent’s working context always contains the overarching objective. We considered the single agent as a baseline, and compared it with EpidemIQs' implementation based on computational statistics, performance analysis, and review scores of the generated papers.\\\\\n\nThe setup used for assessment is presented in Table\\ref{tab:agent_config}.\n\n\\begin{table}[ht]\n\\footnotesize\n\\caption{Configuration Details for EpidemIQs }\n\\centering\n\\begin{tabular}{|l|c|c|c|}\n\\hline\n\\textbf{Parameter} & \\textbf{\\textit{scientists}} & \\textbf{\\textit{experts}} & \\textbf{\\textit{MathExpert}} \\\\\n\\hline\nLLM & \\makecell{gpt-4.1-\\\\2025-04-14} & \\makecell{gpt-4.1-mini\\\\2025-04-14} & \\makecell{o3-mini\\\\2025-01-31} \\\\\n$r_{\\max}$ & 1 & - & - \\\\\nRetries & 5 & 5 & 5 \\\\\n%Memory & long+short & short & short \\\\\nTool Retries & 50 & 50 & 50 \\\\\nOutput Type & Pydantic dataclass & free-form & free-form \\\\\n\\hline\n\\end{tabular}\n\\label{tab:agent_config}\n\\end{table}\n\n\\section{Results and Discussion} \\label{sec:result}\nAcross the five epidemic questions, EpidemIQs completed every phase of the pipeline as Discovery, Modeling, Simulation, Analysis, and Report writing in autonomous mode, achieving a 100\\% completion success rate in generating the final report file. Automated rubric scoring by the LLM‑as‑Judge assigned a mean quality score of 9.04±0.21 out of 10, while four network science Ph.D. students and one faculty reviewer gave an average expert rating of 7.98±0.35, praising the reports' methodological soundness, clarity, and depth. Below, we summarize how the framework navigated each question, highlighting key decisions and results. The generated papers and a more comprehensive analysis are provided in the supplementary material.\\\\\n\\begin{figure}[t]\n\\iffalse\n \\centering\n \\begin{subfigure}[b]{\\linewidth}\n \\centering\n \\includegraphics[width=\\linewidth]{paperQ1.pdf}\n \\caption{}\n \\label{fig:Q1}\n \\end{subfigure}\n\\fi\n\n \\centering\n \\includegraphics[width=\\linewidth]{paperQ2.pdf} \n \\caption{Examples of paper generated by EpidemIQs for the second question. }\n \\label{fig:paper}\n\\end{figure}\n\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=1\\linewidth]{reason.pdf}\n \\caption{An example of reasoning information \\textit{NetworkScientist} generated for question one}\n \\label{fig:reason}\n\\end{figure}\n\n\\textbf{Question~1.} In the first phase, analytical percolation theory and the literature confirm that outbreak behavior can differ according to the degree of heterogeneity. They suggest that, for a heterogeneous network, a scale-free graph, whose node-degree distribution follows a power law, producing a few highly connected hubs among many sparsely linked nodes, is an appropriate candidate to compare with a well-mixed homogeneous network, in which every node is connected to every other node, resulting in a fully connected graph. Because the question does not specify the intrinsic reproduction number, \\(R_{0}\\), a value of 2.5 is adopted to reflect a disease that can be characterized by an SEIR model, such as COVID-19, for which \\(2 < R_{0} < 3\\). Consequently, the deterministic model parameters are chosen to reflect typical values observed in COVID-19, incubation rate as $\\sigma_{E\\rightarrow I} =0.2/day$ (average incubation period of 5 days), recovery rate, $\\gamma_{I\\rightarrow R} =0.1/day$ (average infectious period of 10 days), and transmission rate $\\beta_{S\\rightarrow E}=0.25$. The framework then generates both graphs, initializes them with the five infected nodes, and tunes the transmission rate of the SEIR model on the basis of the intrinsic \\(R_{0}\\) and a mean-field approximation to consider the effect of different network topologies. \n\nIn the simulation phase, three scenarios are executed for 300 stochastic realizations each: (i) random infectious seeding in the homogeneous network, (ii) random infectious seeding in the scale-free network, and (iii) infectious seeding at the highest-degree hubs in the scale-free network. Analysis of the simulation results corroborates the analytical theory. The fully connected homogeneous network exhibits a rapid, high-magnitude outbreak with near-complete infection penetration. By contrast, the scale-free network shows markedly different epidemic behaviour in both seeding schemes, with a much later epidemic peak, a lower peak prevalence, and a substantially smaller final epidemic size (\\(\\approx 30\\%\\)). Notably, hub-based infection seeding accelerates epidemic progression and yields a higher average final epidemic size, confirming the role of superspreaders in triggering more rapid outbreaks in networks with heavy-tailed degree distributions. Hence, the stochastic results confirm that degree heterogeneity decisively reshapes outbreak timing and magnitude. Complete description and results for this question are provided at Supplementary Section S1.1.\n\nFigure~\\ref {fig:reason} illustrates \\textit{NetworkScientist}'s reasoning and logic, exemplifying how each \\textit{scientist} justifies its task completion and the rationale behind its choices, thereby enhancing the interpretability of the outcomes.\\\\\n\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=1\\linewidth]{workflowq4.pdf}\n \\caption{An overview of the workflow for question four, highlighting each step’s goals, main actions, and outputs. The results have been truncated for clearer visualization. At the bottom, plots generated during the modeling and simulation phases are provided. }\n \\label{fig:workflowQ4}\n\\end{figure}\n\n\n\\textbf{Question~2.} Starting from the discovery phase, analytical results showed that the chain of transmission breaks when the effective reproduction number drops below unity, \\(R_e < 1\\). This can occur either when the susceptible population falls beneath a critical threshold or when the transmissibility of infectives decreases. Moreover, contact patterns (e.g., network topology) influence whether an outbreak sputters or ignites, thereby shaping its overall dynamics. To validate these findings, consistent with the surveyed literature, the framework employed an SIR model with two basic reproduction numbers: a supercritical case, \\(R_0 = 3\\), and a subcritical case, \\(R_0 = 0.5\\).\\\\\nTo isolate structural effects, two networks with identical average degree \\(\\langle k \\rangle = 10\\) and \\(N = 1{,}000\\) nodes were generated. The first is an Erd\\H{o}s–Rényi (ER) network representing homogeneous mixing, where each pair of nodes connects with probability \\(p\\). The second is a scale-free Barabási–Albert (BA) network capturing heterogeneity; after an initial seed, each incoming node forms \\(m\\) links to existing nodes, producing a heavy-tailed degree distribution.\\\\\nSimulations began with ten randomly seeded infectives. For each network and \\(R_0\\) value, transmission rates were adjusted (via mean-field approximation) to account for degree heterogeneity, and 75 stochastic realizations of each scenario were executed. In the supercritical scenario (\\(R_0 = 3\\)), the epidemic peaked rapidly and faded as susceptibles were depleted. In the ER network, the average susceptible count fell from 990 to \\(\\approx 115\\) and the recovered count rose to \\(\\approx 885\\), indicating herd-immunity termination. The BA network also exhibited fade-out but progressed faster and left a larger susceptible pool (final average epidemic size \\(\\approx 520\\), remaining susceptibles \\(\\approx 480\\)), reflecting heterogeneity-mediated herd immunity.\\\\\nFor the subcritical scenario (\\(R_0 = 0.5\\)), intrinsic transmission inefficiency halted spread in both network topologies. Overall, the simulations confirm the analytical prediction that complete exhaustion of susceptibles is unnecessary; herd immunity can emerge when the susceptible fraction drops below a critical level or when per-contact transmissibility is sufficiently low. Figure~\\ref{fig:paper} shows an overview of the generated paper, and details of the framework's workflow are provided in the Supplementary Section S1.2.\\\\\n\n\n\n\n\n\\textbf{Question~3.} In the discovery phase, statistical analysis using a mean-field approximation derived expressions for the epidemic threshold in an activity-driven network, where each node activates at rate $\\alpha = 0.1$ and, upon activation, instantaneously forms $m$ edges, which are then removed in the next step. Because neither $m$ nor the recovery rate was specified, the experiment adopted a unit recovery rate and set $m = 5$ as a plausible value. The analytical results indicated that, for $R_0 = 3$, a final epidemic size of 94\\% should be expected under these parameters.\\\\\nTo compare the analytical solution for the temporal network having 1000 nodes with its time-aggregated static counterpart, a static network was created by aggregating all temporal contacts over $T = 1000$ time steps; for every node pair $(i,j)$, the edge weight equaled the total number of contacts during $T$. The recovery rate of one was chosen, and the infection rate was then calibrated for each network-driven SIR simulation so that they matched the mean-field derivations and were consistent with the respective network context (temporal or static). One random infectious node was selected as the initial condition, with all other nodes susceptible.\\\\\nOne hundred stochastic realizations were performed for each scenario, using FastGEMF for the time-aggregated static network and a custom discrete-time Markov-chain engine for the temporal network. The results revealed sharp contrasts in epidemic size and speed between the temporal and static scenarios. The temporal activity-driven network produced significantly smaller and slower epidemics relative to both the static-network simulation and the analytic predictions based on aggregated parameters. Specifically, the temporal SIR process yielded a mean final epidemic size of approximately 20.5\\% with a large standard deviation of 28.9\\%, indicating high stochastic variability and frequent epidemic die-out events at the chosen parameters. Such early stochastic die-out is ignored in mean-field ODEs, which assume deterministic branching of infections and never allow the process to fizzle when the first few seeds recover before transmitting the pathogen.\\\\\nBy contrast, the static-network simulation produced near-complete infection of the population (mean final size $\\approx 81\\%$) in a rapid fashion, closely approaching the analytical prediction of 94.05\\% derived from the classic mean-field equation. These results highlight the profound mechanistic effect of temporal causality on disease-transmission pathways. In the temporal network, edges represent instantaneous contacts that exist only transiently and are reorganized stochastically at each time step. Consequently, the temporal ordering of contacts restricts the accessibility of transmission chains, effectively increasing the epidemic threshold and reducing the reachable susceptible population. Many potential transmission paths present in the aggregated static network are simply infeasible in the temporal network because the required contact timings do not overlap to support causally coherent infections. Supplementary Section S1.3. provides the detailed outcomes for this question.\\\\\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=1\\linewidth]{workflowq5.pdf}\n \\caption{An overview of the workflow for question five, outlining each step’s goals, main actions, and outputs. For clarity, the results have been truncated. At the bottom, plots display the degree distribution, highlighting the large number of nodes with degree 10 and confirming that enough nodes are available for targeted vaccination, together with simulation results for four cases: no vaccination (baseline), vaccination below the critical threshold, at the threshold, and above the threshold.}\n \\label{fig:workflowQ5}\n\\end{figure}\n\nFigures \\ref{fig:workflowQ4} and \\ref{fig:workflowQ5} display the results and process pipelines for questions 4 and 5, respectively. For the question 4 scenario, the framework could successfully find the criteria for the coexistence of the competitive exclusive viruses over multilayer networks, extend the analytical mean-field point of view that exists in literature, and show the dominance, coexistence, and extinction regimes in stochastic processes by designing the network properties that allow coexistence and tuning the parameters. Finally, for the last question, it not only determined the vaccination threshold for random and targeted cases but also carefully modeled the contact network to maintain the aforementioned centralities while having enough nodes to verify the targeted vaccination threshold. The presented results are truncated, and please refer to Supplementary Sections S1.4 and S1.5. for full detailed results of questions 4 and 5, respectively.\\\\\n\n\\subsection{Review Score and Computational Cost}\n\\begin{table*}[htbp!]\n\\centering\n\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\n\\renewcommand{\\arraystretch}{1.3}\n\\setlength{\\tabcolsep}{5pt}\n\\begin{tabular}{|>{\\raggedright\\arraybackslash}p{4cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|}\n\\hline\n\\multirow{2}{*}{\\textbf{Question Topics}} & \n\\multicolumn{2}{c|}{\\makecell{\\textbf{Readability}}} &\n\\multicolumn{2}{c|}{\\makecell{\\textbf{Relevance}\\\\\\textbf{\\& Motivation}}} & \n\\multicolumn{2}{c|}{\\makecell{\\textbf{Technical}\\\\\\textbf{Soundness}}} & \n\\multicolumn{2}{c|}{\\makecell{\\textbf{Experimental}\\\\\\textbf{Rigor}}} & \n\\multicolumn{2}{c|}{\\makecell{\\textbf{Limitation}\\\\\\textbf{\\& Ethics}}} & \n\\multicolumn{2}{c|}{\\textbf{Overall}} \\\\\n\\cline{2-13}\n& \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n\\hline\n1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\n\\hline\n2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\n\\hline\n3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\n\\hline\n4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\n\\hline\n5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\n\\hline\n\\end{tabular}\n\\label{tab:review}\n\\end{table*}\n\nTable \\ref{tab:review} presents the evaluation scores assigned by an LLM-as-Judge and by human experts across five rubric criteria. For each of the five epidemic questions, the framework autonomously generated ten full papers, yielding 50 manuscripts. We randomly selected five of these for blind human review. Each reviewer scored every criterion on a 1‑to‑10 scale. Human scores averaged 7.98 with a standard deviation of 0.20 (\\( \\approx2.5\\%\\)), indicating consistently strong performance by EpidemIQs. Reviewers praised the manuscripts’ comprehensive problem framing, robust experimental design and analysis, and balanced coverage of both analytical and stochastic aspects. The main criticisms concerned verbosity with occasional repetition of content, the use of uncommon vocabulary that slowed reading, and some missing or incomplete figure references.\\\\\n\nTable \\ref{tab:cost} reports the average turnaround time, total number of tokens, and total cost (calculated by OpenAI’s May 2025 pricing) for all questions, measured from the initial query to the final report. A total cost of only \\$1.57, a turnaround of under 30 minutes, a 100\\% success rate, and consistently high review scores demonstrate the strength of the framework and the efficiency of its multi‑agent orchestration. The low cost and rapid execution are achieved by splitting tasks between \\textit{expert} and \\textit{scientist} agents. Token‑heavy, low‑complexity jobs are delegated to fast, inexpensive models such as GPT‑4.1 mini, while more demanding works such as planning, reasoning, tool coordination, and output refinement is handled by the full GPT‑4.1 model.\n\\begin{table}[t]\n \\centering\n \\caption{Average Computation Statistics}\n \\begin{tabular}{|l|c|c|c|}\n \\hline\n \\textbf{Phase} & \\textbf{Time(sec.)} & \\textbf{Tokens(K)} & \\textbf{Cost(\\$)} \\\\ \\hline\n Discovery & 158 & 98 & 0.1 \\\\ %\\hline\n Modeling & 140 & 175 & 0.72 \\\\ %\\hline\n Simulation & 198 & 88 & 0.23 \\\\ %\\hline\n Analysis & 177 & 93 & 0.16 \\\\ %\\hline\n Report Writing & 517 & 416 & 0.36 \\\\ \\hline\n \\textbf{Overall} & \\textbf{1190} & \\textbf{870} & \\textbf{1.57 } \\\\ \\hline\n \\end{tabular}\n \\label{tab:cost}\n\\end{table}\n\\subsection{Multi-Turn Single-Agent vs EpidemIQs Orchestration}\nIn this section, we ran the single-agent across the same five questions ten times, using two OpenAI LLMs, GPT‑4.1 and o3. Single-agent‑GPT‑4.1 achieved an average completion success rate of 78±7.7\\% and an average human-review score of 5.06, whereas single-agent-o3 reached 80.0±6.32\\% with a human-review score of 5.68. The \\textit{LLM-as-Judge} provides comparative evaluations of the successful papers generated by single-agent and EpidemIQs. Table~\\ref{tab:single_score} presents these scores for all questions.\n\\begin{table*}[htb!]\n\\caption{Overall Score for AI and Human Expert Evaluation of Generated Papers}\n\\centering\n\\begin{tabular}{|l|c c|c c|c c|c c|c c|}\n\\hline\n\\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{question 1}} & \\multicolumn{2}{c|}{\\textbf{question 2}} & \\multicolumn{2}{c|}{\\textbf{question 3}} & \\multicolumn{2}{c|}{\\textbf{question 4}} & \\multicolumn{2}{c|}{\\textbf{question 5}} \\\\\n & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n\\hline\nEpidemIQs & 9.5 & 8.0 & 9.5 &8.2 & 9.2 & 7.8 & 9.0 & 8.0 & 9.2 & 8.1 \\\\\nsingle-agent-GPT4.1 & 8.9 & 5.4 & 7.3 & 5.3 & 8.9 & 4.8 & 7.5 & 4.6 & 8.4 & 5.2 \\\\\nsingle-agent-o3 & 8.5 & 5.8 & 8.6 & 6.3 & 8.3 & 5.5 & 8.6 & 5.8 & 7.4 & 5.2 \\\\\n\\hline\n\\end{tabular}\n\\label{tab:single_score}\n\\end{table*}\nSurprisingly, the AI-generated scores differ only slightly across the three cases, while the human reviews reveal substantial disparities in their outcomes. The single-agent-GPT‑4.1 setup addressed the first three questions to some extent; however, it was limited: it handled the analytical component inadequately, ran only a few stochastic simulations, and in some instances merely solved the ODE system instead of performing exact stochastic simulations. For the more complex question 5, none of the trials identified the target vaccination threshold or model the network appropriately. Furthermore, the parameters and the rationale for their selection were not discussed comprehensively.\\\\\n\nThe conclusions were sometimes misleading, as they were not based on the simulation results; instead, the agent often relied on prior knowledge or literature. When grounded in results, they were still occasionally inaccurate, for example, in the targeted-vaccination case, the agent typically claimed that vaccinating all high-degree nodes was necessary, largely because it generated the network before calculating the analytical thresholds, resulting in very sparse high-degree nodes. Human reviews also mention that while the agent could address the task to some degree, it is in shallow depth, missing figures, insufficient simulations, and limited analyses, and the overall failure to address the tasks comprehensively, compared to rigorous analysis and experimentation in the MA setup.\\\\\nOn the other hand, The single-agent-o3 did better job with analytical aspect of the question and better writing quality, however, the simulations still was very limited, and the agent shows more autonomy in how to accomplish tasks rather based on the expert knowledge provided as instructions, for example for stochastic simulation it did not always use the engine provided for it or ignoring literature and online searches. Though the single-agent-o3 generally generated higher quality reports, there was still some cases when there were inaccuracies, for example for question four, even the coexistence was not achieved through stochastic simulation, it was concluded that simulation results confirm that coexistence is possible when analytical conditions are met or the agent mentioned the simulation were performed by FastGEMF over 1000 realizations, however scripts in the repository showed custom engine for deterministic simulation was used to simulated SI instead of SIR, which showed a huge drift from the main task and hallucination of the agent in the report. Also, in none of the cases could it correctly address the targeted vaccination in question five. Finally, while reviewers praised the writing quality, conciseness, and analytical aspects of the reports, they found that they fell short in having enough depth, simulation rigor, and failure to address complex tasks comprehensively. \\\\ It is also necessary to mention that, to avoid violating OpenAI's usage policy when using the o3 model, we changed the questions from virus spread to meme spread. Otherwise, the success rate of single-agent-o3 was less than 30\\%. We did not consider this API error in our benchmarks for evaluating the o3 success rate. It is important to emphasize that this change in context does not affect the validity of the comparative results, as epidemic spread can easily be generalized for social cases such when a meme spread over a population.\\\\\nOverall, the human reviews and performance analysis demonstrated the superior performance of EpidemIQs compared to the single-agent implementation. Single-agent systems consistently failed to address complex scenarios, exhibited drift in their outcomes, lacked depth in their reports, and had a significantly lower success rate in completing tasks. Table \\ref{tab:cost_single} presents the computational statistics for these three different implementations. These comparisons are particularly meaningful given that the EpidemIQs achieved its superiority at a cost comparable to single-agent-GPT4.1 and at less than half the cost of single-agent-o3, despite the o3 model having greater reasoning and coding capabilities than those employed in the EpidemIQs, as mentioned in Table \\ref{tab:agent_config}. Moreover, the superiority of the proposed framework extends beyond performance and computational efficiency, offering greater interpretability by providing explicit reasoning for each step.\n\n\\begin{table}\n\\caption{Comparison of Average Computation Statistics Across All Questions Over Three Different Implementations}\n\\centering\n\\begin{tabular}{|l|c|c|c|}\n\\hline\n\\textbf{Method} & \\textbf{Time (s)} & \\textbf{Tokens (K)} & \\textbf{Cost (\\$)} \\\\\n\\hline\nEpidemIQs & 1190 & 870 & 1.57 \\\\\nsingle-agent-GPT4.1 & 214 & 312 & 0.91 \\\\\nsingle-agent-o3 & 436 & 165 & 4.13 \\\\\n\\hline\n\\end{tabular}\n\\label{tab:cost_single}\n\\end{table}\n \n\n\n\n\n\n\\subsection{Discussion, Limitations, and Ethical Concerns}\n\nAlthough the EpidemIQs framework consistently produces high‑quality manuscripts throughout the workflow, it is not designed to replace human authorship in scientific research, but rather to be an assistant to human experts to facilitate the research process for testing and implementing ideas in the epidemic modeling field. EpidemIQs can still make mistakes, and AI‑generated prose can be highly persuasive, as \\cite{bai2025llm, simhi2025trust, liu2025llm} discussed, so human oversight remains essential to safeguard accuracy and integrity, and generated papers are meant to provide a comprehensive and unified result of the framework, making it easy to analyze the outcomes.\n\nAcross all of our experiments, we found no major instances of hallucination in EpidemIQs outputs, and performance was remarkably consistent. Since LLMs are non‑deterministic, they may tackle the same question slightly differently each time; however, no substantial drift or incorrect reasoning was observed. For example, in Question 5, \\textit{ModelScientist} sometimes designs an SIRV (V represents vaccinated state) model and at other times an SIR model, or \\textit{NetworkScientist} may construct networks with different degree distributions yet the same target centrality. These variations are valid and do not diminish performance; they simply reflect the natural diversity of approaches to a single problem. However, there were errors observed during the \\textit{Analysis} phase. For example, in question three, where \\textit{DataExpert} misinterpreted an average recovery count below one as a fraction rather than a discrete number of individuals, \\textit{DataScientist} detected this inconsistency and deferred to \\textit{VisionExpert}, whose interpretation matched both the simulation protocol and analytical expectations. While such checks limit the impact of isolated calculation errors, occasional mistakes by \\textit{DataExpert} indicate that automated data analysis may be a part of further improvement.\\\\\n\nThe framework also demonstrated sound awareness of its computational constraints. For example, in question three, we explicitly restricted simulations to the FastGEMF engine. \\textit{SimulationScientist} adhered to this limitation, employing FastGEMF exclusively for static networks, and it was explicitly noted in the final report that software limitations prevented temporal network experiments. This transparency is critical, as it prevents the framework from falsely claiming task completion. In contrast, such issues were observed in the single-agent implementation, where it falsely hallucinates task accomplishment. Furthermore, the reliability of scientific outcomes often hinges on the algorithms employed, which can be inherently complex. For instance, in one of the trails within question three, \\textit{SimulationScientist} designed a custom engine for simulating disease spread over a temporal network but erred in updating the order of states. This led to the premature recovery of initially infected nodes, preventing further spread and resulting in an underestimation of the final outbreak size and probability. Although \\textit{DataScientist} noted a significant discrepancy between simulated and expected analytical results, it incorrectly attributed the difference to the effects of temporality rather than the engine’s design flaw.\\\\\n\nTo further investigate the agents' attention to scientific details, in question three we explicitly specified the constant activity rate (and not activity probability per unit time), $\\alpha=3$, which is unlikely in real-world case studies and rare in literature but was chosen to test the agents’ attention to subtle details. However, \\textit{NetworkScientist} creates the network edges with the probability of a node being activated as $p=\\alpha \\Delta t$, with $\\Delta t=1$, as the first order Taylor series approximation of \\(p=1-\\exp^{-\\alpha \\Delta t}\\), where is only is acceptable if \\(\\alpha\\Delta t \\ll 1\\) (However, if $ \\alpha$ is probability $\\alpha \\Delta t$ is exact), making it invalid for $\\alpha \\Delta t=3 > 1$ resulting all nodes being activated each time, instead of having exact probability \\(\\approx 0.95\\).\\\\\n\nThese observations emphasize two points: \\\\\n1) the importance and impact of providing appropriate tools to obtain consistent and reliable results, and 2) the continued need for a human expert to validate results, because agents can still make mistakes that are difficult to detect and may produce persuasive responses that justify incorrect conclusions.\\\\\nOur framework is unique, with no direct comparators. However, a comparison with The AI Scientist, a general tool for scientific discovery from ideation to paper writing \\cite{lu2024ai}, for question one, showed the failure of The AI Scientist. It analyzed the ODE-based analytical component but struggled with stochastic simulations over the network, producing hallucinated results and conclusions. It is essential to mention The AI Scientist performance was mostly evaluated on AI-related subjects, such as diffusion models or transformers, emphasizing that this comparison does not imply overall superiority of one framework over another.\\\\\nSummarizing the main limitations of the current work, we have:\n\\begin{itemize}\n \\item Although no major hallucinations were found in the results, a few hallucinated references did appear in the final report. Moreover, while the reviewers praised the papers’ comprehensiveness, they also noted some repetitive content that lengthened the reading time, and sometimes tables were so large that portions extended beyond the page, suggesting enhancing the report generation part. \n \\item The performance of the EpidemIQs is highly dependent on the LLM models, while our framework is model agnostic, as long as these models can support structured outputs and tool calling, the results can vary based on the LLM choices.\n \\item The literature review relies only on the abstract and summary of key findings, rather than delving deeply into the full content of the papers. Future frameworks capable of thoroughly analyzing the full material of each paper could enhance and benefit from deeper data retrieval.\n \\item The current framework focuses on epidemic modeling over complex networks as a proof of concept. Enhancing it to broader methods such as Agent-Based Models(ABM)\\cite{epstein2009modelling,parker2011distributed}, individual-based \\cite{epstein2009modelling}, or statistical and data-driven approaches \\cite{epstein2009modelling,vespignani2020modelling} can significantly increase the applicability of the framework.\n \\item The agents’ performance hinges on the tools at their disposal. As noted in question three, their performance and reliability decline when they encounter highly technical problems without the requisite expert knowledge and appropriate tools. This shortcoming explains why the general‑purpose module proposed by \\cite{lu2024ai} fails in question one.\n \\item AI evaluation in the automated review process shows divergence from human expert reviews, aligning with other works' findings, such as Agent Laboratory \\cite{schmidgall2025agent}. However, contrasting with near-human performance reported in \\cite{lu2024ai}, it suggests that human involvement is necessary. While an \\textit{LLM-as-Judge} can be beneficial for providing high-level insights, it cannot be fully trusted, since it relies on superficial patterns rather than robust analysis criteria.\n \\item We did not include ideation in our framework, primarily because epidemic research is highly complex and interdisciplinary. Generating new research ideas requires careful consideration of resources, advanced tools (see Limitation 4), expert knowledge across multiple domains, and access to diverse data sources, such as mobility, weather, and epidemiological data. For example, in vector-borne diseases, the populations of mosquitoes or birds play a critical role in epidemiological modeling. To the authors' knowledge, such ideas can quickly become too complex for current agentic AI systems to handle appropriately, given concrete bottlenecks such as the lack of structured access to high-quality mobility/weather/entomological data, difficulty in reasoning across coupled mechanistic models, or access to specific tools. Therefore, we focused on specific network-based epidemic modeling tasks as a proof of concept to showcase the framework’s potential benefits.\n\\end{itemize}\nTherefore, although EpidemIQs offers great potential to accelerate epidemic-modeling research and allows researchers to focus on high-level ideation, this promise also introduces new ethical challenges that must be taken seriously. Its ability to autonomously generate high-quality papers, supported by analytical insights, rigorous simulations, and comprehensive analyses, may inadvertently lower the barriers to producing low-standard scientific work, potentially overwhelming the peer-review system and jeopardizing the integrity of academic discourse. Moreover, as noted earlier, the automated process may introduce mistakes in algorithm design that are implicit and difficult to detect, or it may yield results biased by its underlying knowledge or algorithms, leading to skewed outcomes. These concerns underscore the necessity of disclosing AI involvement in the research process to mitigate such risks and maintain accountability, fairness, and transparency.\\\\\n\n\\iffalse\nIn this study, we evaluated the performance of EpidemIQs across a spectrum of epidemiological questions, ranging from basic to advanced network-based epidemiology. Our experiments demonstrated that the agents were capable of handling intricate details, even in challenging questions, showcasing their potential in complex epidemiological modeling. This robustness highlights the promise of such agents in assisting with real-world public health challenges, where a nuanced understanding of network dynamics is critical.\nTo assess the quality of our work, we conducted a thorough review process involving both human experts and AI-based evaluations. The AI reviews yielded an average rating of 6 out of 10, while human expert reviews assigned a slightly lower average score of 5 out of 10. These ratings suggest a moderate reception of the paper, with AI reviews potentially reflecting a more lenient or standardized assessment compared to the critical perspective of domain experts. The discrepancy between AI and human evaluations warrants further investigation into the criteria and biases inherent in each review process, which could inform future improvements in both agent design and manuscript preparation.\nDespite the strengths of the EpidemIQs, several limitations must be acknowledged. While the agents are capable of learning through reflection and prompting, their performance is constrained by the lack of fine-tuning and uniform weighting across all agents. This uniform approach may hinder optimization, leading to slower performance in certain questions. Additionally, not all agents are fully context-aware of the system's overall flow. As a result, an error by one agent can propagate, adversely affecting the behavior of others. This cascading effect underscores the need for enhanced context awareness and error mitigation strategies in multi-agent systems.\nFuture work should focus on addressing these limitations by implementing fine-tuning mechanisms to optimize agent weights and improving context awareness to ensure robust system-level performance. By overcoming these challenges, EpidemIQs could achieve greater reliability and efficiency, further advancing their utility in epidemiological research and beyond.\n\\subsection{limitations}\n\\begin{itemize}\n \\item The performance is highly dependent on the choices of LLMs as the backbone of agents, for example, GPT 4.1 and Gork 3 have much better instruction following performance than GPT 4o or o3-mini models.\n \\item The agent can reach a conclusion if even a few experiments are performed\n \\item the longer conversations and input data, the higher the chance of drift in the task, which requires a more advanced mechanism to handle the memory, such as Graph-based data structures\n \\item \n\\end{itemize}\n\\textbf{checklist:}\n\\begin{itemize}\n \\item discuss specific limitations of EpidemIQs, computational cost, assumptions about static networks, or generalizability to real-world questions, etc.\n \\item propose concrete future research directions (e.g., extending to dynamic networks, incorporating mobility data, or addressing privacy concerns).\n \\item highlight practical implications (e.g., how EpidemIQs could inform policy decisions or resource allocation during outbreaks).\n \\item Address societal impacts, such as potential benefits (improved outbreak response) and risks (misuse of predictive models).\n\\end{itemize} \n\\fi\n\\section{Data Availability}\nAll the data and results discussed in this paper are provided as supplementary materials. The EpidemIQs is also provided as an open-source Python module at \\emph{github.com/will-be-announced-upon-publication}.\n\n%\\begin{ack}\n % Acknowledgments go here (for final version only, not anonymized submission).\n % For the anonymized submission, leave this section empty.\n % For the final version, include funding sources, collaborators, or other support.\n % Example: This work was supported by [Funding Agency] under grant [Number].\n%\\end{ack}\n\n\\section{Conclusion}\\label{sec:conc}\nIn this study, we present EpidemIQs, a multi‑LLM agent framework that harnesses the reasoning, planning, and problem‑solving abilities of LLMs and integrates them with online and literature retrieval, multimodal data processing, code generation and execution, stochastic simulation, and visual and data analysis. These characteristics enable it to autonomously carry out every key stage of epidemic modeling research, from discovery through modeling and simulation to analysis and, finally, the synthesis of findings into a full scientific report. This entire process takes less than half an hour, whereas it would normally take an average graduate-level student days to accomplish the same task.\\\\\nThe evaluation of results across questions addressing various aspects of network-based epidemic modeling demonstrates that the framework consistently maintains high performance across our trials. Consequently, EpidemIQs can extend existing analytical approaches to stochastic processes, infer implicit constraints in research questions, and design scenarios that address cases beyond the immediate scope of available tools and expert knowledge.\\\\\nThe comparative analysis of EpidemIQs and the single-agent implementation consistently showed that EpidemIQs outperformed the single-agent variants across all tasks. It achieved an 100\\% success rate average human‑evaluation score of 7.98 at a cost of \\$1.57, whereas the single-agent configurations based on GPT‑4.1 and o3 obtained scores of 5.06 and 5.68 at costs of \\$0.91 and \\$4.13, respectively.\\\\\nAt present, EpidemIQs focuses exclusively on epidemic modeling over networks as a proof of concept; nevertheless, it has already demonstrated the potential of deploying LLM agents in a collaborative environment. This opens an exciting path for further performance gains by integrating advanced tools, such as deep learning techniques, probabilistic methods, and data-centric models, heralding a promising future for epidemic modeling research. Moreover, because the framework’s accuracy and performance depend heavily on the underlying LLMs, the rapid advances in this field are likely to yield substantial improvements for the entire multi agent system, as our framework is designed to be model agnostic.\\\\\nEpidemIQs, while demonstrating strong performance and producing high‑quality output, is not intended to, and should not, replace human authorship in the scientific process, as it still makes mistakes and should not be fully trusted; it is best regarded as a highly capable assistant. Researchers in epidemic modeling can use it to test and implement their ideas quickly and at low cost, freeing them from time‑consuming tasks such as setting up simulations or writing repetitive code and allowing them to focus on the conceptual and creative aspects of their work.\\\\\nFuture work should consider the broader applications of epidemic modeling by integrating real-world data and other advanced computational tools into the model design to address open-ended real-world problems and evaluate its applicability for forecasting current outbreaks. Additionally, they should address ethical concerns regarding the misuse or dual use of such a framework, as automated modeling and report generation could be exploited to produce misleading forecasts or scientifically plausible misinformation, intentionally or unintentionally influencing public perception or policy decisions. The system’s ability to simulate outbreak dynamics at scale may also lower barriers for malicious actors to explore harmful scenarios or identify vulnerabilities in public health defenses. Additionally, integration with sensitive epidemiological data poses privacy risks, emphasizing the need for implementing appropriate safeguards. \n\n\n{\n\n\n\n\\bibliographystyle{IEEEtran}\n\\bibliography{ref}\n\\includepdf[pages=-]{EpidemIQsSupplementary.pdf} % Embed all pages of the other PDF\n\\end{document}"},"question":{"kind":"string","value":"On average, in which category across all 5 questions does AI outperform human answers by the second largest margin? Name the category and the difference between human and AI performance scores."},"answer":{"kind":"string","value":"Experiment and rigour, 1.16"},"plan":{"kind":"string","value":"SELECT all categories\nLOOP for each category\n SELECT all questions where this category appears\n LOOP for each question\n COMPUTE difference = ai score − human score\n COMPUTE average_difference = average of difference\n\n\nCOMPUTE rank categories by average_difference descending\nSELECT second_largest_category = category with rank 2\n\n\nRETURN second_largest_category, average_difference of second_largest_category\n"}}},{"rowIdx":354,"cells":{"paper":{"kind":"string","value":"2510.00024"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[htbp!]\n","\\centering\n","\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\n","\\renewcommand{\\arraystretch}{1.3}\n","\\setlength{\\tabcolsep}{5pt}\n","\\begin{tabular}{|>{\\raggedright\\arraybackslash}p{4cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|}\n","\\hline\n","\\multirow{2}{*}{\\textbf{Question Topics}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Readability}}} &\n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Relevance}\\\\\\textbf{\\& Motivation}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Technical}\\\\\\textbf{Soundness}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Experimental}\\\\\\textbf{Rigor}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Limitation}\\\\\\textbf{\\& Ethics}}} & \n","\\multicolumn{2}{c|}{\\textbf{Overall}} \\\\\n","\\cline{2-13}\n","& \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n","\\hline\n","1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\n","\\hline\n","2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\n","\\hline\n","3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\n","\\hline\n","4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\n","\\hline\n","5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:review}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[htbp!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3}\\n\",\n \"\\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \"\\\\begin{tabular}{|>{\\\\raggedright\\\\arraybackslash}p{4cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Question Topics}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Readability}}} &\\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Relevance}\\\\\\\\\\\\textbf{\\\\& Motivation}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Technical}\\\\\\\\\\\\textbf{Soundness}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Experimental}\\\\\\\\\\\\textbf{Rigor}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Limitation}\\\\\\\\\\\\textbf{\\\\& Ethics}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\textbf{Overall}} \\\\\\\\\\n\",\n \"\\\\cline{2-13}\\n\",\n \"& \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:review}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[http]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{MMMA.pdf}\n"," \\caption{Multimodal approach for the multi-agent framework for epidemic autonomous research. This framework enhances the power of multi-LLM agents by integrating multimodal data from various sources, such as literature, online web data, theoretical models, and simulation and experiments.}\n"," \\label{fig:MMMA}\n","\\end{figure}\n"],["\\begin{figure*}[http]\n"," \\centering\n"," \\includegraphics[width=0.85\\linewidth]{Fig12.pdf}\n"," \\caption{EpidemIQs orchestration across five research phases. Specialized agent teams perform tool calling (via red arrows), collaborate with each other (curved blue arrows), and exchange artifacts through a shared project repository (hexagons), enabling an end-to-end pipeline from discovery to final report generation.}\n"," \\label{fig:orch}\n","\\end{figure*}\n"],["\\begin{figure}[http]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{scientist.pdf}\n"," \\caption{The \\textit{scientist} agent architecture. a) Three modules as \\textit{plan}, \\textit{ReAct}, and \\textit{reflect}. The reflection ends either when the reflect agent decides the answer is already good enough or it reaches its maximum iteration limit. b) the conversation components for ReAct agent, as can be seen each time with the fixed task and plan, it updates new actions, results, and reflection. At each iteration \\(t\\), the newly generated \\(\\text{Action}_{t}\\), corresponding \\(\\text{Result}_{t}\\), and \\(\\text{Reflection}_{t}\\) are appended to short-term memory, while the \\(\\text{Action}_{t-2}\\), corresponding \\(\\text{Result}_{t-2}\\) are dropped out. The loop continues updating the conversation trace until the aforementioned conditions are met.}\n"," \\label{fig:scinetist}\n","\\end{figure}\n"],["\\begin{figure}[http]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{questions.pdf}\n"," \\caption{Evaluation questions designed to assess the capabilities and limitations of the proposed framework across varying levels of complexity}\n"," \\label{fig:question}\n","\\end{figure}\n"],["\\begin{table}[ht]\n","\\footnotesize\n","\\caption{Configuration Details for EpidemIQs }\n","\\centering\n","\\begin{tabular}{|l|c|c|c|}\n","\\hline\n","\\textbf{Parameter} & \\textbf{\\textit{scientists}} & \\textbf{\\textit{experts}} & \\textbf{\\textit{MathExpert}} \\\\\n","\\hline\n","LLM & \\makecell{gpt-4.1-\\\\2025-04-14} & \\makecell{gpt-4.1-mini\\\\2025-04-14} & \\makecell{o3-mini\\\\2025-01-31} \\\\\n","$r_{\\max}$ & 1 & - & - \\\\\n","Retries & 5 & 5 & 5 \\\\\n","Tool Retries & 50 & 50 & 50 \\\\\n","Output Type & Pydantic dataclass & free-form & free-form \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:agent_config}\n","\\end{table}\n"],["\\begin{figure}[t]\n","\\iffalse\n"," \\centering\n"," \\begin{subfigure}[b]{\\linewidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{paperQ1.pdf}\n"," \\caption{}\n"," \\label{fig:Q1}\n"," \\end{subfigure}\n","\\fi\n","\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{paperQ2.pdf} \n"," \\caption{Examples of paper generated by EpidemIQs for the second question. }\n"," \\label{fig:paper}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{reason.pdf}\n"," \\caption{An example of reasoning information \\textit{NetworkScientist} generated for question one}\n"," \\label{fig:reason}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{workflowq4.pdf}\n"," \\caption{An overview of the workflow for question four, highlighting each step’s goals, main actions, and outputs. The results have been truncated for clearer visualization. At the bottom, plots generated during the modeling and simulation phases are provided. }\n"," \\label{fig:workflowQ4}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{workflowq5.pdf}\n"," \\caption{An overview of the workflow for question five, outlining each step’s goals, main actions, and outputs. For clarity, the results have been truncated. At the bottom, plots display the degree distribution, highlighting the large number of nodes with degree 10 and confirming that enough nodes are available for targeted vaccination, together with simulation results for four cases: no vaccination (baseline), vaccination below the critical threshold, at the threshold, and above the threshold.}\n"," \\label{fig:workflowQ5}\n","\\end{figure}\n"],["\\begin{table*}[htbp!]\n","\\centering\n","\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\n","\\renewcommand{\\arraystretch}{1.3}\n","\\setlength{\\tabcolsep}{5pt}\n","\\begin{tabular}{|>{\\raggedright\\arraybackslash}p{4cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|\n",">{\\centering\\arraybackslash}p{0.4cm}\n",">{\\centering\\arraybackslash}p{0.8cm}|}\n","\\hline\n","\\multirow{2}{*}{\\textbf{Question Topics}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Readability}}} &\n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Relevance}\\\\\\textbf{\\& Motivation}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Technical}\\\\\\textbf{Soundness}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Experimental}\\\\\\textbf{Rigor}}} & \n","\\multicolumn{2}{c|}{\\makecell{\\textbf{Limitation}\\\\\\textbf{\\& Ethics}}} & \n","\\multicolumn{2}{c|}{\\textbf{Overall}} \\\\\n","\\cline{2-13}\n","& \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n","\\hline\n","1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\n","\\hline\n","2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\n","\\hline\n","3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\n","\\hline\n","4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\n","\\hline\n","5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:review}\n","\\end{table*}\n"],["\\begin{table}[t]\n"," \\centering\n"," \\caption{Average Computation Statistics}\n"," \\begin{tabular}{|l|c|c|c|}\n"," \\hline\n"," \\textbf{Phase} & \\textbf{Time(sec.)} & \\textbf{Tokens(K)} & \\textbf{Cost(\\$)} \\\\ \\hline\n"," Discovery & 158 & 98 & 0.1 \\\\ %\\hline\n"," Modeling & 140 & 175 & 0.72 \\\\ %\\hline\n"," Simulation & 198 & 88 & 0.23 \\\\ %\\hline\n"," Analysis & 177 & 93 & 0.16 \\\\ %\\hline\n"," Report Writing & 517 & 416 & 0.36 \\\\ \\hline\n"," \\textbf{Overall} & \\textbf{1190} & \\textbf{870} & \\textbf{1.57 } \\\\ \\hline\n"," \\end{tabular}\n"," \\label{tab:cost}\n","\\end{table}\n"],["\\begin{table*}[htb!]\n","\\caption{Overall Score for AI and Human Expert Evaluation of Generated Papers}\n","\\centering\n","\\begin{tabular}{|l|c c|c c|c c|c c|c c|}\n","\\hline\n","\\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{question 1}} & \\multicolumn{2}{c|}{\\textbf{question 2}} & \\multicolumn{2}{c|}{\\textbf{question 3}} & \\multicolumn{2}{c|}{\\textbf{question 4}} & \\multicolumn{2}{c|}{\\textbf{question 5}} \\\\\n"," & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n","\\hline\n","EpidemIQs & 9.5 & 8.0 & 9.5 &8.2 & 9.2 & 7.8 & 9.0 & 8.0 & 9.2 & 8.1 \\\\\n","single-agent-GPT4.1 & 8.9 & 5.4 & 7.3 & 5.3 & 8.9 & 4.8 & 7.5 & 4.6 & 8.4 & 5.2 \\\\\n","single-agent-o3 & 8.5 & 5.8 & 8.6 & 6.3 & 8.3 & 5.5 & 8.6 & 5.8 & 7.4 & 5.2 \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:single_score}\n","\\end{table*}\n"],["\\begin{table}\n","\\caption{Comparison of Average Computation Statistics Across All Questions Over Three Different Implementations}\n","\\centering\n","\\begin{tabular}{|l|c|c|c|}\n","\\hline\n","\\textbf{Method} & \\textbf{Time (s)} & \\textbf{Tokens (K)} & \\textbf{Cost (\\$)} \\\\\n","\\hline\n","EpidemIQs & 1190 & 870 & 1.57 \\\\\n","single-agent-GPT4.1 & 214 & 312 & 0.91 \\\\\n","single-agent-o3 & 436 & 165 & 4.13 \\\\\n","\\hline\n","\\end{tabular}\n","\\label{tab:cost_single}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure}[http]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{MMMA.pdf}\\n\",\n \" \\\\caption{Multimodal approach for the multi-agent framework for epidemic autonomous research. This framework enhances the power of multi-LLM agents by integrating multimodal data from various sources, such as literature, online web data, theoretical models, and simulation and experiments.}\\n\",\n \" \\\\label{fig:MMMA}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}[http]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.85\\\\linewidth]{Fig12.pdf}\\n\",\n \" \\\\caption{EpidemIQs orchestration across five research phases. Specialized agent teams perform tool calling (via red arrows), collaborate with each other (curved blue arrows), and exchange artifacts through a shared project repository (hexagons), enabling an end-to-end pipeline from discovery to final report generation.}\\n\",\n \" \\\\label{fig:orch}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure}[http]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{scientist.pdf}\\n\",\n \" \\\\caption{The \\\\textit{scientist} agent architecture. a) Three modules as \\\\textit{plan}, \\\\textit{ReAct}, and \\\\textit{reflect}. The reflection ends either when the reflect agent decides the answer is already good enough or it reaches its maximum iteration limit. b) the conversation components for ReAct agent, as can be seen each time with the fixed task and plan, it updates new actions, results, and reflection. At each iteration \\\\(t\\\\), the newly generated \\\\(\\\\text{Action}_{t}\\\\), corresponding \\\\(\\\\text{Result}_{t}\\\\), and \\\\(\\\\text{Reflection}_{t}\\\\) are appended to short-term memory, while the \\\\(\\\\text{Action}_{t-2}\\\\), corresponding \\\\(\\\\text{Result}_{t-2}\\\\) are dropped out. The loop continues updating the conversation trace until the aforementioned conditions are met.}\\n\",\n \" \\\\label{fig:scinetist}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[http]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{questions.pdf}\\n\",\n \" \\\\caption{Evaluation questions designed to assess the capabilities and limitations of the proposed framework across varying levels of complexity}\\n\",\n \" \\\\label{fig:question}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\footnotesize\\n\",\n \"\\\\caption{Configuration Details for EpidemIQs }\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{|l|c|c|c|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Parameter} & \\\\textbf{\\\\textit{scientists}} & \\\\textbf{\\\\textit{experts}} & \\\\textbf{\\\\textit{MathExpert}} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"LLM & \\\\makecell{gpt-4.1-\\\\\\\\2025-04-14} & \\\\makecell{gpt-4.1-mini\\\\\\\\2025-04-14} & \\\\makecell{o3-mini\\\\\\\\2025-01-31} \\\\\\\\\\n\",\n \"$r_{\\\\max}$ & 1 & - & - \\\\\\\\\\n\",\n \"Retries & 5 & 5 & 5 \\\\\\\\\\n\",\n \"Tool Retries & 50 & 50 & 50 \\\\\\\\\\n\",\n \"Output Type & Pydantic dataclass & free-form & free-form \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:agent_config}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \"\\\\iffalse\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{subfigure}[b]{\\\\linewidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{paperQ1.pdf}\\n\",\n \" \\\\caption{}\\n\",\n \" \\\\label{fig:Q1}\\n\",\n \" \\\\end{subfigure}\\n\",\n \"\\\\fi\\n\",\n \"\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{paperQ2.pdf} \\n\",\n \" \\\\caption{Examples of paper generated by EpidemIQs for the second question. }\\n\",\n \" \\\\label{fig:paper}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{reason.pdf}\\n\",\n \" \\\\caption{An example of reasoning information \\\\textit{NetworkScientist} generated for question one}\\n\",\n \" \\\\label{fig:reason}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{workflowq4.pdf}\\n\",\n \" \\\\caption{An overview of the workflow for question four, highlighting each step’s goals, main actions, and outputs. The results have been truncated for clearer visualization. At the bottom, plots generated during the modeling and simulation phases are provided. }\\n\",\n \" \\\\label{fig:workflowQ4}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{workflowq5.pdf}\\n\",\n \" \\\\caption{An overview of the workflow for question five, outlining each step’s goals, main actions, and outputs. For clarity, the results have been truncated. At the bottom, plots display the degree distribution, highlighting the large number of nodes with degree 10 and confirming that enough nodes are available for targeted vaccination, together with simulation results for four cases: no vaccination (baseline), vaccination below the critical threshold, at the threshold, and above the threshold.}\\n\",\n \" \\\\label{fig:workflowQ5}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3}\\n\",\n \"\\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \"\\\\begin{tabular}{|>{\\\\raggedright\\\\arraybackslash}p{4cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.4cm}\\n\",\n \">{\\\\centering\\\\arraybackslash}p{0.8cm}|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Question Topics}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Readability}}} &\\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Relevance}\\\\\\\\\\\\textbf{\\\\& Motivation}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Technical}\\\\\\\\\\\\textbf{Soundness}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Experimental}\\\\\\\\\\\\textbf{Rigor}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\makecell{\\\\textbf{Limitation}\\\\\\\\\\\\textbf{\\\\& Ethics}}} & \\n\",\n \"\\\\multicolumn{2}{c|}{\\\\textbf{Overall}} \\\\\\\\\\n\",\n \"\\\\cline{2-13}\\n\",\n \"& \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:review}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Average Computation Statistics}\\n\",\n \" \\\\begin{tabular}{|l|c|c|c|}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Phase} & \\\\textbf{Time(sec.)} & \\\\textbf{Tokens(K)} & \\\\textbf{Cost(\\\\$)} \\\\\\\\ \\\\hline\\n\",\n \" Discovery & 158 & 98 & 0.1 \\\\\\\\ %\\\\hline\\n\",\n \" Modeling & 140 & 175 & 0.72 \\\\\\\\ %\\\\hline\\n\",\n \" Simulation & 198 & 88 & 0.23 \\\\\\\\ %\\\\hline\\n\",\n \" Analysis & 177 & 93 & 0.16 \\\\\\\\ %\\\\hline\\n\",\n \" Report Writing & 517 & 416 & 0.36 \\\\\\\\ \\\\hline\\n\",\n \" \\\\textbf{Overall} & \\\\textbf{1190} & \\\\textbf{870} & \\\\textbf{1.57 } \\\\\\\\ \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\label{tab:cost}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[htb!]\\n\",\n \"\\\\caption{Overall Score for AI and Human Expert Evaluation of Generated Papers}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{|l|c c|c c|c c|c c|c c|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{question 1}} & \\\\multicolumn{2}{c|}{\\\\textbf{question 2}} & \\\\multicolumn{2}{c|}{\\\\textbf{question 3}} & \\\\multicolumn{2}{c|}{\\\\textbf{question 4}} & \\\\multicolumn{2}{c|}{\\\\textbf{question 5}} \\\\\\\\\\n\",\n \" & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} & \\\\textbf{AI} & \\\\textbf{Human} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"EpidemIQs & 9.5 & 8.0 & 9.5 &8.2 & 9.2 & 7.8 & 9.0 & 8.0 & 9.2 & 8.1 \\\\\\\\\\n\",\n \"single-agent-GPT4.1 & 8.9 & 5.4 & 7.3 & 5.3 & 8.9 & 4.8 & 7.5 & 4.6 & 8.4 & 5.2 \\\\\\\\\\n\",\n \"single-agent-o3 & 8.5 & 5.8 & 8.6 & 6.3 & 8.3 & 5.5 & 8.6 & 5.8 & 7.4 & 5.2 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:single_score}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}\\n\",\n \"\\\\caption{Comparison of Average Computation Statistics Across All Questions Over Three Different Implementations}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{|l|c|c|c|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Method} & \\\\textbf{Time (s)} & \\\\textbf{Tokens (K)} & \\\\textbf{Cost (\\\\$)} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"EpidemIQs & 1190 & 870 & 1.57 \\\\\\\\\\n\",\n \"single-agent-GPT4.1 & 214 & 312 & 0.91 \\\\\\\\\\n\",\n \"single-agent-o3 & 436 & 165 & 4.13 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{tab:cost_single}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\documentclass[journal]{IEEEtran}\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\providecommand{\\authorrefmark}[1]{\\textsuperscript{#1}} % fallback if class doesn't define it\n\\DeclareUnicodeCharacter{202F}{\\,}\n\n% ---------- Encoding & Fonts ----------\n\\usepackage[T1]{fontenc}\n\\usepackage[utf8]{inputenc}\n\\usepackage{lmodern}\n\n% ---------- Colors & Graphics ----------\n\\usepackage{xcolor} % keep simple for arXiv\n\\definecolor{navyblue}{RGB}{0,0,128}\n\\usepackage{graphicx}\n\\usepackage{tikz}\n\n% ---------- Tables & Layout ----------\n\\usepackage{array}\n\\usepackage{booktabs}\n\\usepackage{multirow}\n\\usepackage{tabularx}\n\\usepackage{makecell}\n\\usepackage{float}\n\n% ---------- Math & Microtypography ----------\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{nicefrac}\n\\usepackage{microtype}\n\n% ---------- Captions ----------\n\\usepackage{subcaption} % works with IEEEtai; avoid subfig\n\n% ---------- URLs & Links (load near last) ----------\n\\usepackage{url}\n\\usepackage{hyperref}\n\\hypersetup{\n colorlinks=true,\n linkcolor=navyblue,\n citecolor=navyblue,\n urlcolor=navyblue\n}\n\n% ---------- Bibliography (BibTeX, arXiv-safe) ----------\n% Use natbib + IEEEtranN.bst (installed on arXiv). Do NOT use biblatex/biber.\n\\usepackage[numbers,sort&compress]{natbib}\n\\bibliographystyle{IEEEtranN}% In your main file, later: \\bibliographystyle{IEEEtranN} \\bibliography{ref}\n\n% ---------- Optional (comment out before final if you like) ----------\n% \\usepackage[left]{lineno} % \\linenumbers\n\\usepackage{pdfpages}\n\n% ---------- Title & Authors ----------\n%\\title{EpidemIQs: Prompt-to-Paper LLM Agents for Epidemic Modeling and Analysis}\n\n\\title{EpidemIQs: Prompt-to-Paper LLM Agents for Epidemic Modeling and Analysis}\n\n\\author{%\n Mohammad Hossein Samaei\\authorrefmark{1}, Faryad Darabi Sahneh\\authorrefmark{2}, Lee W. Cohnstaedt\\authorrefmark{3}, and Caterina Scoglio\\authorrefmark{1}\n \\thanks{\\authorrefmark{1} Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS, USA (Corresponding Author's email: msamaei@ksu.edu)\n%\\thanks{\\authorrefmark{2} Independant Researcher, MA, USA}\n%\\thanks{\\authorrefmark{3} USDA-ARS, National Bio- and Agro-Defense Facility, Foreign Arthropod-borne Animal Disease\n%Research Unit, Manhattan, KS, United States}\n}}\n\n\n\\begin{document}\n%\\externaldocument[S-]{supp/supp}\n%\\tableofcontents\n\\newpage\n\n\n\\maketitle\n\n\\begin{abstract}\nLarge Language Models (LLMs) offer new opportunities to automate complex interdisciplinary research domains. Epidemic modeling, characterized by its complexity and reliance on network science, dynamical systems, epidemiology, and stochastic simulations, represents a prime candidate for leveraging LLM-driven automation. We introduce \\textbf{EpidemIQs}, a novel multi-agent LLM framework that integrates user inputs and autonomously conducts literature review, analytical derivation, network modeling, mechanistic modeling, stochastic simulations, data visualization and analysis, and finally documentation of findings in a structured manuscript. We introduced two types of agents: a scientist agent for planning, coordination, reflection, and generation of final results, and a task-expert agent to focus exclusively on one specific duty serving as a tool to the scientist agent. The framework consistently generated complete reports in scientific article format. Specifically, using GPT 4.1 and GPT 4.1 mini as backbone LLMs for scientist and task-expert agents, respectively, the autonomous process completed with average total token usage 870K at a cost of about \\$1.57 per study, achieving a 100\\% completion success rate through our experiments. We evaluate EpidemIQs across different epidemic scenarios, measuring computational cost, completion success rate, and AI and human expert reviews of generated reports. We compare EpidemIQs to the single-agent LLM, which has the same system prompts and tools, iteratively planning, invoking tools, and revising outputs until task completion. The comparison shows consistently higher performance of the proposed framework across five different scenarios. EpidemIQs represents a step forward in accelerating scientific research by significantly reducing costs and turnaround time of discovery processes, and enhancing accessibility to advanced modeling tools.\\\\\n\\end{abstract}\n\n%\\begin{IEEEImpStatement}\n%EpidemIQs advances autonomous research capabilities in the epidemic modeling field through an innovative orchestration of collaborative multi-agent LLMs and integrates multimodal data. To the best of the authors' knowledge, this framework is among the first in this area that leverages AI for end-to-end research automation. Our evaluations demonstrate the framework’s ability to produce high-quality research autonomously, getting us closer to efficient, reliable, and accessible autonomous research tools. %, providing a robust foundation for addressing complex problems across various interdisciplinary domains.\n%\\end{IEEEImpStatement}\n\\begin{IEEEkeywords}\nAutonomous Agents, AI for Science, Epidemic Modeling, Multi-Agent Systems\n\\end{IEEEkeywords}\n\n\\section{Introduction}\nScientists' Efforts to automate research date back to at least the early 1970s \\cite{langley1987scientific,langley2024integrated,waltz2009automating}, aiming to overcome limits on the number of ideas scientists can pursue, constraints that force them to prioritize ideas with higher predicted impact. For example, the Automated Mathematician was introduced to carry out simple mathematics research guided by large sets of heuristic rules \\cite{inproceedings,lenat1984and}, and DENDRAL was proposed to assist chemists with data interpretation problems \\cite{buchanan1981dendral}. \n\nMore recently, advances in autoregressive large language models (LLMs) \\cite{touvron2023llama, team2023gemini, achiam2023gpt} have demonstrated strong capabilities in question answering, problem-solving, and coding, with promising applications across science and engineering. However, LLMs still face limitations when applied to real-world tasks \\cite{zoullm}. These constraints led to the development of LLM agents, which extend LLMs with abilities such as external tool use \\cite{schick2023toolformer,qin2023toolllm,hao2023toolkengpt}, chain-of-thought prompting \\cite{wei2022chain}, and iterative self-improvement \\cite{shinn2023reflexion,huang2022large}.\nLLM agents have since been applied to diverse domains, including software engineering \\cite{jimenez2023swe,wang2024openhands}, cybersecurity \\cite{abramovich2024interactive}, medical diagnosis \\cite{mcduff2025towards}, chemistry \\cite{boiko2023autonomous,jumper2021highly,hayes2025simulating}, material science \\cite{merchant2023scaling,szymanski2023autonomous,ghafarollahi2025automating}, computational biology \\cite{ding2024automating}, algorithm design \\cite{fawzi2022discovering}, and healthcare \\cite{tang-etal-2024-medagents}.\nMulti-agent systems have also emerged to simulate human-like research environments across disciplines. Examples include Agent Laboratory \\cite{schmidgall2025agent}, Virtual Lab \\cite{swanson2025virtual}, ChemCrow \\cite{m2024augmenting}, ResearchAgent \\cite{baek2024researchagent}, and The AI Scientist \\cite{lu2024ai}. For broader surveys of LLM agent applications, see \\cite{wang2024survey,gridach2025agentic,yehudai2025survey,xi2025rise}.\n\n\n\nDespite the stunning advances of LLM agents across various domains, epidemiology-related areas have not yet fully benefited from these developments \\cite{bann2025can}, largely because they are among the most sophisticated and interdisciplinary fields. Network-based epidemic modeling is among the sophisticated approaches to studying the spread of infectious diseases by incorporating the structure of contact networks, which represent interactions among individuals or groups in a population \\cite {keeling2005networks}.\\\\\n\nUnlike traditional compartmental models, which assume homogeneous mixing, network-based models account for heterogeneous contact patterns by representing individuals as nodes and their interactions as edges (possibly weighted or time-varying) in a graph. This approach captures the realistic social and spatial structures influencing disease transmission, such as clustering, degree distribution, and community structures. By integrating network topology, these models provide insights into how connectivity patterns affect epidemic dynamics, enabling more accurate predictions of disease spread, the identification of critical transmission pathways, and the evaluation of targeted intervention strategies, such as vaccination or social distancing, in complex populations \\cite {kiss2017mathematics}. \\\\\nAddressing these models requires an interdisciplinary expertise: (i) stochastic-process theory to analyze the master equations and their approximations; (ii) network science to characterize and parametrize contact structures; (iii) epidemiology to constrain pathogen-specific parameters; and (iv) computational epidemiology to conduct simulations and scenario analysis. Having a research group with this level of diversity is not only challenging to access but also poses coordination challenges. In this study, we introduce \\textit{EpidemIQs}, a novel multi-LLM agents capable of autonomously addressing research in network-based epidemic modeling for the first time.\\\\\n\n\n\n\nEpidemIQs emulates an interdisciplinary research environment with five collaborative teams of \\textit{task-expert} and \\textit{scientist} agents, capable of performing end-to-end autonomous research: given a user query, if identified as a network-based problem, it initiates the process by discovering relevant insights from diverse online sources (e.g., web-based content and published papers) to conduct a literature review and address analytical aspects through mathematical reasoning. It then formulates the problem as a network-based model, tests it through rigorous stochastic simulations, analyzes the resulting multimodal data (e.g., visual and numerical), and finally composes a scientifically formatted manuscript that reports the entire procedure, from problem formulation to simulation results, discussion, and final conclusion. The framework can also operate in copilot mode, which enables human cooperation throughout the process.\\\\\nWe evaluate our proposed framework across five epidemic scenarios articulated through questions, three of which were unknown to the framework. We tested EpidemIQs against the multi-turn single-agent baseline, comparing performance by (i) discussing the results of each team across all scenarios, (ii) AI and human expert evaluations of generated papers, and (iii) computational statistics. The proposed framework consistently showed impressive performance, achieving a 100\\% completion success rate, an average human review score of 7.98 out of 10, a low cost of only \\$1.57, and a total processing time of 1{,}190 seconds. We can summarize the main contributions of our work as follows:\\\\\n\\iffalse\n\\begin{itemize}\n \\item A novel multi-LLM agents that conducts epidemic research through five scientific phases.\n \\item It integrates multimodal data, visual, textual, numerical, graph structure, etc., from multiple sources, including online retrieval, experimental results, and internally generated artifacts (e.g., graphs, tables), and dynamically combines them to accomplish the task, enhancing its utility and adaptability across diverse research contexts.\n \\item Fully autonomous mode capability reduces the human intervention to only providing the initial query, while it can also perform in co-pilot mode.\n \\item Human experts' evaluation of the papers produced by the framework using a rubric covering five criteria: Readability and Writing Quality, Relevance and Motivation, Technical Soundness, Experimental Rigor, and Limitations.\n \\item Providing high interpretability as each \\textit{scientist} provides their reasoning for their actions and generated outcomes, and records their results and scripts, facilitating validation of procedure and outcomes.\n \\item A detailed evaluation of computational statistics, including consumed time, number of tokens, and cost.\n\\end{itemize}\n\\fi\n\n\\begin{itemize}\n\\item Developed novel multi-LLM agents that conduct epidemic research through five distinct scientific phases.\n\\item Integrated multimodal data (visual, textual, numerical, graph structures, etc.) from diverse sources, including online retrieval, experimental results, and internally generated artifacts (e.g., graphs, tables), to enhance utility and adaptability across various research contexts.\n\\item Enabled fully autonomous mode to minimize human intervention, requiring only an initial query, while also supporting a copilot mode for collaborative operation.\n\\item Ensured high interpretability by having each \\textit{scientist} provide reasoning for its actions and generated outcomes, and recording results and scripts to facilitate validation of procedures and outcomes.\n\\end{itemize}\n\nThe remainder of this paper is organized as follows: Section \\ref{sec:meth} describes the methodology. Section \\ref{sec:multi} details the design and implementation of the system. Section \\ref{sec:eval} outlines the experimental setup and evaluation cases. Section \\ref{sec:result} presents the results and discusses the study’s limitations and shortcomings. Finally, Section \\ref{sec:conc} concludes the paper and proposes directions for future work.\n\n%\\textcolor{red}{contributions I wish I had:\n%\\begin{itemize}\n% \\item long and short memory\n% \\item context awareness\n% \\item report for each agent\n%\\end{itemize}\n%}%\n\n\\section{Methodology} \\label{sec:meth}\nLLMs demonstrate advanced capabilities relevant to scientific tasks, including coding and answering technical questions. However, their performance in tackling complex epidemiology scenarios remains limited. To address these challenges, we propose a multi-agent framework that emulates a scientific epidemic research laboratory environment, designed to enhance the practical capabilities of LLMs in complex scientific tasks. The EpidemIQs framework is organized into four core functional layers that collectively support autonomous research workflows\\cite{xi2025rise}: (1) The multi-agent orchestration layer governs the coordination, communication, and cooperation among specialized agents.\\iffalse to optimize overall task performance and enable iterative self-refinement. \\fi (2) The backbone LLM operates as the central reasoning and decision-making unit \\iffalse, responsible for interpreting queries, generating hypotheses, and formulating plans\\fi. (3) The perception layer collects, integrates, and processes heterogeneous data sources, including scientific literature, experimental results, contextual information, and prior knowledge bases. (4) The action layer executes tasks derived from the LLM’s output, encompassing activities such as code generation, simulation, modeling, etc.\n\\begin{figure}[http]\n \\centering\n \\includegraphics[width=1\\linewidth]{MMMA.pdf}\n \\caption{Multimodal approach for the multi-agent framework for epidemic autonomous research. This framework enhances the power of multi-LLM agents by integrating multimodal data from various sources, such as literature, online web data, theoretical models, and simulation and experiments.}\n \\label{fig:MMMA}\n\\end{figure}\nLooking at Figure~\\ref{fig:MMMA}, the architectural design illustrates the structured interaction among the four functional layers that enable autonomous epidemic research. The orchestration layer governs inter-agent communication, task allocation, and coordination protocols, ensuring efficient collaboration among specialized agents. Within the perception layer, agents process multimodal data streams through standardized interfaces that convert heterogeneous sources, including scientific literature, experimental data, contextual metadata, and structured knowledge bases, into unified semantic representations suitable for downstream reasoning and analysis. The backbone LLM operates as the central cognitive engine, analyzing perceived inputs, generating hypotheses, formulating research plans, and executing decisions based on accumulated evidence and domain constraints. The agents' outputs inform the action layer, where the system autonomously selects and calls functions to deploy tools, such as stochastic simulation engines, Retrieval-Augmented Generation (RAG), API calls, and executes it in the correct order, so that high‑level research goals are broken down into concrete, reproducible steps such as loading data, running simulations, and storing results.\n\n\\section{Multi-LLM Agent Architecture: EpidemIQs Framework} \\label{sec:multi}\nThe orchestration of EpidemIQs is illustrated in Figure \\ref{fig:orch}. This framework is structured to emulate a scientific laboratory, comprising five phases: Discovery, Modeling, Simulation, Analysis, and Report Writing. These phases are executed by distinct collaborative multi-agent system teams, and the results of their work are integrated to produce the final report. In this section, we first describe the design of two types of agents, followed by the architecture design, output structure, memory, and implementation details of EpidemIQs.\n\\begin{figure*}[http]\n \\centering\n \\includegraphics[width=0.85\\linewidth]{Fig12.pdf}\n \\caption{EpidemIQs orchestration across five research phases. Specialized agent teams perform tool calling (via red arrows), collaborate with each other (curved blue arrows), and exchange artifacts through a shared project repository (hexagons), enabling an end-to-end pipeline from discovery to final report generation.}\n \\label{fig:orch}\n\\end{figure*}\n\\subsection{Two Agent Types: \\textit{Scientist}s and \\textit{Experts}}\nTwo agent types are inspired by the generative agent concept \\cite {park2023generative} and further advanced by frameworks such as CAMEL \\cite{li2023camel}, AutoGen \\cite{wu2024autogen}, and Metagpt \\cite{hong2023metagpt}, and are designed to enable autonomous scientific reasoning and investigation. The central coordinating component, referred to as the \\textit{scientist} agent, performs high-level orchestration through iterative planning, reflection, and execution refinement. Upon receiving an input query, the \\textit{scientist} employs a dedicated \\textit{plan} module, which parses and decomposes the query into a plan comprising sub-tasks and their logical dependencies. Both \\textit{reflect} and \\textit{ReAct} modules are constrained to generate output in predefined formats. While structured outputs, e.g., JSON, enhance reproducibility and reliability of performance, they have recently been shown to compromise the reasoning capability of LLMs \\cite{tam-etal-2024-speak}. Therefore, we explicitly devote a separate \\textit{plan} module as an agent to allow it to freely generate the plan, while both the subsequent \\textit{ReAct} and \\textit{reflect} modules are restricted to generating predefined structured outputs.\n\\begin{figure}[http]\n \\centering\n \\includegraphics[width=1\\linewidth]{scientist.pdf}\n \\caption{The \\textit{scientist} agent architecture. a) Three modules as \\textit{plan}, \\textit{ReAct}, and \\textit{reflect}. The reflection ends either when the reflect agent decides the answer is already good enough or it reaches its maximum iteration limit. b) the conversation components for ReAct agent, as can be seen each time with the fixed task and plan, it updates new actions, results, and reflection. At each iteration \\(t\\), the newly generated \\(\\text{Action}_{t}\\), corresponding \\(\\text{Result}_{t}\\), and \\(\\text{Reflection}_{t}\\) are appended to short-term memory, while the \\(\\text{Action}_{t-2}\\), corresponding \\(\\text{Result}_{t-2}\\) are dropped out. The loop continues updating the conversation trace until the aforementioned conditions are met.}\n \\label{fig:scinetist}\n\\end{figure}\nOnce the plan is formulated, the \\textit{scientist} agent iteratively executes the ReAct-Reflect loop until either the \\textit{reflect} agent decides no further revision is needed, or it reaches the maximum iteration limit, $r_{max}$. The ReAct Module executes reasoning, and call tools conditioned on the current plan segment, and refine its response based on the action outcomes, while the reflect module prompted to perform logical reasoning, evaluates intermediate outputs for errors, logical inconsistencies, or incomplete results, producing structured JSON feedback to refine action selection and output validity across iterations, enhancing the agent performance through linguistic feedback without need to update the weights of models.\\iffalse Short-term and long-term memory modules are utilized by the \\textit{scientist} to maintain iterative context and cumulative knowledge. \\fi\\\\\nIn parallel, the \\textit{scientist} agent can coordinate multiple independent \\textit{task-expert} agents as tools, each designed as a specialized ReAct agent for a specific task or data source. These \\textit{expert} agents serve as domain specialists responsible for well-defined atomic tasks such as literature retrieval, online search, mathematical derivation, or data extraction. This functional decomposition ensures that each \\textit{expert} executes its task with minimal context switching, while the \\textit{scientist} maintains global task coherence and quality control.\n\n\\subsection{Multi-Agent Orchestration}\n\nThe EpidemIQs framework is comprised of 5 phases. It initiates upon receiving a user query, entering the \\textit{Discovery} phase. In this phase, the \\textit{DiscoveryScientist} agent performs planning and reasoning to collect data relevant to the query following the Multi-Hop Question Answering (MHQA) paradigm \\cite{mavi2024multi}. Specifically, the data collection process is conducted in three iterative steps, with each step focusing on a distinct information source. This multi-step procedure enables the system to progressively refine its understanding, reduce errors, and enhance the overall accuracy of the gathered information\\cite{jeyakumar2024advancing}. The components of the Discovery team are as follows:\n\n\\begin{itemize}\n \\item \\textit{DiscoveryScientist} coordinates the \\textit{expert} agents to collect relevant information, process the retrieved data, and synthesize the final output following a predefined structured format. This output encompasses a comprehensive description of the scenario, task specifications, and contextual information related to the disease and the affected population. \\\\\n \\item \\textit{OnlineRetrieverExpert} is responsible for acquiring relevant information from online sources. It generates and refines search queries in multiple stages, leveraging external APIs (e.g., Tavily API) to retrieve data from the web. The agent subsequently processes and integrates the retrieved information to generate a coherent response.\\\\\n \\item \\textit{LiteratureRetrieverExpert} conducts a multi-step search process using the Semantic Scholar API, based on the received query. For each retrieved query, the agent generates concise summaries and aggregates the most pertinent findings. The agent is prompted to generate the final summarized response based on multiple criteria, including relevance and accuracy.\\\\\n \\item \\textit{MathExpert} provides mathematical reasoning and analytical solutions for queries requiring quantitative analysis. The agent is capable of both generating and executing Python code, a capability demonstrated to enhance solution accuracy and mitigate hallucination risks ( \\cite{liang2023code} showed that it can increase up to 39.8\\% problem-solving capability over HumanEvals \\cite{chen2021evaluating} benchmark). The backbone LLM of this agent should be an advanced language model with high reasoning capacity, able to perform chain-of-thoughts( such as OpenAI GPT o3-Jan-2025 or o3-mini-Jan-2025 models \\cite{o3mini2025})\n\\end{itemize}\n\nFollowing the completion of the \\textit{Discovery} phase, the \\textit{Modeling} phase is initiated to systematically construct the foundational components required for simulating epidemic dynamics on complex networks. This phase is orchestrated by a team of three specialized \\textit{scientist} agents, each responsible for a distinct modeling dimension: network topology, mechanistic model formulation, and parameterization. The functional responsibilities of these agents are delineated as follows:\n\n\\begin{itemize}\n\\item \\textit{NetworkScientist} is tasked with generating a representative contact network that encapsulates the interaction patterns within the target population. The constructed network serves as a structural substrate upon which the epidemic process unfolds. Depending on the characteristics of the population and the epidemiological scenario, the network may adopt various configurations, including but not limited to regular networks or Erdős-Rényi random graphs \\cite{erdds1959random}, Barabási-Albert scale-free networks \\cite{barabasi1999emergence}, and multilayer structures \\cite{boccaletti2014structure}. The \\textit{NetworkScientist} employs algorithmic procedures implemented in Python, utilizing scientific computing libraries such as NetworkX and SciPy, to model the network topology. The finalized network structure is preserved in the workflow repository for integration into the simulation pipeline.\\\\\n\\item \\textit{ModelerScientist} is responsible for defining the mechanistic framework of disease progression. It selects and configures an appropriate compartmental model based on the disease characteristics and insights derived during the \\textit{Discovery} phase. \n\\item \\textit{ParameterScientist} is invoked after the design of both network topology and compartmental model, to calculate and assign quantitative values to model parameters and initialize network states. \\iffalse Key parameters such as transmission rates, recovery rates, and initial prevalence levels are calculated based on the context, expert knowledge, and scenario-specific assumptions. \\fi It performs calculations through the Python coding tool.\n\\end{itemize}\n\\iffalse\nUpon completion of the modeling phase, the framework transitions into the \\textit{Simulation}, wherein predictive experiments are conducted to analyze the modeled epidemic dynamics. This phase is executed by the \\textit{SimulationScientist}, which performs multiple stochastic simulations to capture the probabilistic evolution of contagion spread over the constructed contact network, and has delegated \\textit{VisionExpert} to verify successful outcomes of simulations.\\\\\nTo conduct these simulations, the agent utilizes the Fast Generalized Epidemic Modeling Framework (FastGEMF)~\\cite{samaei2025fastgemf}, a high-performance simulation engine capable of modeling arbitrary multi-compartment epidemic processes over multilayer network structures with computational efficiency. The \\textit{SimulationScientist} is pre-trained through one-shot learning examples to interface with FastGEMF.\nThroughout the simulation process, the agent records the generated time-series data using Python libraries such as Pandas and stores both the numerical outputs and corresponding state-evolution visualizations in the project repository.\n\nFollowing the simulation stage, the framework advances to the \\textit{Analysis}, wherein a coordinated team of specialized agents derives actionable insights from the simulation outputs. This multi-agent analysis team is responsible for processing both numerical results and visual artifacts to extract context-specific metrics and interpret spread dynamics. The roles and responsibilities of the constituent agents are defined as follows:\n\n\\begin{itemize}\n \\item \\textit{DataScientist} coordinates the specialized \\textit{expert} agents and integrates their outputs into a coherent interpretation of the simulation results. It identifies and computes key epidemiological metrics, such as peak infection time and size, epidemic duration, outbreak probability, etc., tailored to the nature of the modeled disease and the research query. The final output consists of numerical measures and qualitative analysis.\\\\\n \\item \\textit{VisualExpert} has vision-language capabilities through Base64 decoding format and is responsible for analyzing the visual outputs generated during the simulation phase. It interprets time-series plots or state evolution graphs, enabling interpretability and validation of dynamic behavior that may not be easily deduced from raw numerical outputs alone.\\\\\n \\item \\textit{DataExpert} is tasked with the interpretation of structured numerical data. This agent accesses simulation results stored in the system repository and applies analytical techniques using Python libraries such as Pandas, NumPy, and SciPy. Operating within a multi-hop paradigm, the \\textit{DataExpert} initially identifies the structure and content of the available data, then dynamically selects appropriate analysis strategies to compute requested metrics. This flexibility ensures the agent's ability to generalize across varying data types and experimental settings.\n\\end{itemize}\n\\fi\nUpon completion of the modeling phase, the framework transitions into the \\textit{Simulation}, wherein predictive experiments are conducted to analyze the modeled epidemic dynamics. This phase is executed by the \\textit{SimulationScientist}, which performs multiple stochastic simulations to capture the probabilistic evolution of contagion spread over the constructed contact network, and has delegated \\textit{VisionExpert} to verify successful outcomes of simulations. The \\textit{VisionExpert} has vision-language capabilities and is responsible for analyzing the visual outputs generated during the simulation phase. It interprets time-series plots or state evolution graphs, enabling interpretability and validation of dynamic behavior that may not be easily deduced from raw numerical outputs alone.\\\\\nTo conduct these simulations, the agent utilizes the Fast Generalized Epidemic Modeling Framework (FastGEMF)~\\cite{samaei2025fastgemf}, a high-performance simulation engine capable of modeling arbitrary multi-compartment epidemic processes over multilayer network structures with computational efficiency. The \\textit{SimulationScientist} is pre-trained through one-shot learning examples to interface with FastGEMF.\nThroughout the simulation process, the agent records the generated time-series data using Python libraries such as Pandas and stores both the numerical outputs and corresponding state-evolution visualizations in the project repository.\\\\\nFollowing the simulation stage, the framework advances to the \\textit{Analysis}, wherein a coordinated team of specialized agents derives actionable insights from the simulation outputs. This multi-agent analysis team is responsible for processing both numerical results and visual artifacts to extract context-specific metrics and interpret spread dynamics. The roles and responsibilities of the constituent agents are defined as follows:\\\\\n\\begin{itemize}\n \\item \\textit{DataScientist} coordinates the specialized \\textit{expert} agents and integrates their outputs into a coherent interpretation of the simulation results. It identifies and computes key epidemiological metrics, such as peak infection time and size, epidemic duration, outbreak probability, etc., tailored to the nature of the modeled disease and the research query. The final output consists of numerical measures and qualitative analysis.\\\\\n \\item \\textit{VisionExpert} analyzes visualizations to extract metrics and interpret epidemic behavior (e.g., uncertainty bands around trajectories), that may not be easily interpretable from raw numerical data.\\\\\n \\item \\textit{DataExpert} is tasked with the interpretation of structured numerical data. This agent accesses simulation results stored in the system repository and applies analytical techniques using Python libraries such as Pandas, NumPy, and SciPy. Operating within a multi-hop paradigm, the \\textit{DataExpert} initially identifies the structure and content of the available data, then dynamically selects appropriate analysis strategies to compute requested metrics. This flexibility ensures the agent's ability to generalize across varying data types and experimental settings.\n\\end{itemize}\n\n\nThe final phase of the framework is \\textit{Automated Report Generation}, wherein two coordinated \\textit{expert} agents synthesize the research findings into a structured academic manuscript. This process starts with the \\textit{ReporterExpert}, which is equipped with tools to access the outputs of the entire workflow, including simulation results, code scripts, and literature summaries. Guided by a predefined LaTeX-based manuscript template, the \\textit{ReporterExpert} sequentially drafts all major sections of the paper, such as the Title, Abstract, Introduction, Methods, Results, and Discussion. Following the generation of each section, the \\textit{LatexCraftExpert} is tasked to perform a syntactic and structural validation of the LaTeX code, resolving potential compilation errors and ensuring stylistic consistency with publication guidelines. Upon completion of the main draft, the \\textit{LiteratureReviewExpert} conducts a contextual relevance check, retrieving and integrating recent scholarly works aligned with the study’s findings. This agent augments the manuscript with a Background and Related Work section to strengthen the research academic positioning.\nOnce the initial draft is completed, an iterative review loop is repeated by the \\textit{ReporterExpert}. It critiques each section to detect inconsistencies, redundancies, or logical gaps according to a user-defined number of revision cycles, $n_{max}$. Finally, it is compiled as a PDF file.\n\n\\subsection{Memory}\nTwo specialized memory structures are considered for the agents. The \\textit{scientist} agent's memory consists of short-term and long-term memory. The short-term memory encompasses all the current conversation details, including role description, input query, agent's internally generated responses, interaction with tools, conversations with other agents, and the final output. The long-term memory stores all previous conversation history in a database, enabling semantic retrieval based on the current query. \n\\\\\n\\subsection{Structured Outputs}\n\nTypically, LLMs generate free-format texts as a natural language output, which does not follow a strict structure. However, the performance of the collaborative LLM agents requires precise and careful interoperability, as information sharing and communication can significantly impact overall outcomes \\cite {wu2024autogen}. Therefore, to make the data transition between each phase of the process robust, reliable, and more predictable, there are constraints defined for each team output structure, forcing them to produce output in a predefined structure (e.g., JSON schema). This not only facilitates data retrieval and improves prompt development efficiency, but it also enables automatic validation of each team's output \\cite{10.1145/3613905.3650756}, ensuring all required fields are generated accordingly, and there is no missing data. If not, the agent retries until it fulfills the task or reaches the maximum number of tries allowed. While the output structure of each \\textit{scientist} contains different fields, all \\textit{scientists} share one common element: the reasoning and logical justification behind their choices and results. Each \\textit{scientist} is expected to defend their decisions against hypothesized criticisms, demonstrating why these were the most appropriate outcomes. \n\n\n\\subsection{Autonomous and Copilot Operation Modes}\nThe EpidemIQs can perform in two modes: end-to-end autonomous and cooperative modes. The latter is named as a copilot, which can operate as an assistant to the user. The autonomous mode does not require human intervention, but rather initially provides the query. The copilot mode enables the human to intervene and provides feedback and instruction on the agent's output, or asks for more actions to guide the agent toward the desired direction. After each phase, the human is asked to review the results, and they can either mark them as complete and proceed to the next phase or ask for new actions by providing comments. \\iffalse For example, during the simulation phase, the human user can observe the results and instruct the agent to perform a new set of simulations with different setups. Alternatively, in discovery mode, the user can request a specific literature topic that the agent did not previously include. \\fi\n\\subsection{Implementation}\n\\iffalse\nThe proposed framework has been designed and implemented in Python using the Pydantic AI framework. To facilitate autonomous data acquisition, external APIs are integrated into the agent system. Specifically, we employed the Semantic Scholar API for automated retrieval of scientific literature, while the Tavily API provides access to web-scale information retrieval from the broader internet.\nFor multimodal data processing, the framework incorporates a Vision-Language Model (VLM), implemented using the OpenAI SDK and through Base64 decoding format, which enables the agent to interpret visual data during the analysis and simulation phase. Short-term memory is managed using the LLM’s context window and is integrated with the Pydantic AI memory module. Long-term memory capabilities \nLong-term memory is stored in JSON format and managed using Pydantic AI memory module functions for data retrieval and storage.\nFinally, to ensure structural consistency and schema validation across agent interactions and output structures, we use Pydantic data models, which provide robust data integrity guarantees throughout the orchestration.\n\\fi\nThe framework is implemented in Python using the Pydantic AI framework. Autonomous data acquisition is supported through API integrations using the Semantic Scholar API for literature retrieval and the Tavily API for web-scale information access. \nFor multimodal processing, a Vision-Language Model (VLM) is implemented via the OpenAI SDK with Base64 decoding to enable visual data interpretation. Short-term memory utilizes the LLM’s context window, while long-term memory is stored in JSON and managed through Pydantic AI memory functions. Finally, we used Pydantic data models for schema validation and structural consistency across agent interactions.\n%The final phase employs a multi-agent collaborative system to transform experimental data into a complete scientific manuscript. Writer agents process workflow history and experimental data in manageable chunks, generating manuscript sections sequentially. After each section, a LaTeX cleaner agent identifies and corrects structural and syntactic errors. Upon completion of all sections, a literature agent performs targeted searches to enrich the manuscript with relevant background material based on semantic analysis of the document.\n\n%A feedback agent then evaluates the manuscript using NeurIPS review criteria, providing section-specific comments that guide the writer agent through iterative refinements. This quality assurance loop implements a dynamic termination protocol based on a predefined quality threshold—when the manuscript achieves a sufficient review score or maximum number of iteration, the feedback cycle concludes and the document is compiled. This approach ensures methodical progression from raw experimental data to publication-ready manuscripts while maintaining scientific rigor through structured validation processes.\n\n\n\n\n\\section{Evaluation Approach} \\label{sec:eval}\n\nTo assess the performance of the framework, we designed five questions, shown in Figure~\\ref {fig:question}, with increasing depth and complexity.\n\\begin{figure}[http]\n \\centering\n \\includegraphics[width=1\\linewidth]{questions.pdf}\n \\caption{Evaluation questions designed to assess the capabilities and limitations of the proposed framework across varying levels of complexity}\n \\label{fig:question}\n\\end{figure}\n\\iffalse\nThe first question in Figure~\\ref{fig:question} is the simplest. It requires the framework to analytically investigate the problem and design the simulation setup by creating the model and two network structures, one heterogeneous and one homogeneous, to compare the stochastic results. The goal is to analyze how structural differences influence the stochastic spread of the disease.\n\nThe second question requires identifying the reason for the break in the chain of transmission and designing models and network setups to validate the hypothesis using exact stochastic simulations.\n\nThe third question is structurally similar to the first but introduces a key limitation: the problem involves a temporal network, which lies outside the scope of the simulation tool provided to the agent. This test evaluates how the system adapts to cases out of the scope of the expert knowledge provided for it.\n\nThe fourth question is more complex for two reasons. First, it requires finding the analytical answer either by advanced reasoning or knowledge from the literature. Second, the agent must extend the conventional SIS model to an $SI_1I_2S$ model (as in the competitive epidemic setup) and design a multiplex network with features that enable the possibility of virus coexistence.\n\n\n\nThe fifth question is the most challenging. It requires an analytical solution for two vaccination strategies, random and targeted, under a network with specific centrality. The key difficulty is that such random networks rarely contain a sufficient number of degree-10 nodes for targeted vaccination. Therefore, the agent should notice the implicit constraint and engineer the contact network to ensure that enough degree-10 nodes exist for the strategy to test the hypothesized threshold for herd immunity, while still maintaining the required structural properties.\\\\\n\\fi\nThe first question is the simplest, requiring an analytical investigation and comparison of stochastic simulations on heterogeneous versus homogeneous networks to assess how structural differences shape disease spread.\nThe second focuses on identifying why the chain of transmission breaks and validating hypotheses through stochastic modeling.\nThe third resembles the first but introduces a temporal network, which exceeds the scope of the provided simulation tools, testing system adaptability.\\\\ \nThe fourth demands both analytical reasoning (or knowledge from literature) and an extension of the SIS model to a competitive $SI_1I_2S$ form on a multiplex network, exploring conditions for coexistence.\nThe fifth is the most challenging, requiring analytical evaluation of random versus targeted vaccination strategies. Here, the key challenge is to notice the implicit constraint to ensure that the contact network contains enough degree-10 nodes to make targeted vaccination feasible while preserving its structural properties. \\\\\n\nCollectively, these questions span the key aspects of network epidemics, such as topology, temporal structure, multilayer interactions and competing pathogens, termination mechanisms, network-aware interventions, physics-aware contact network, etc, providing a holistic evaluation framework. Only the first two questions were involved in the test and trials through the design of the EpidemIQs orchestration, and the last three were unknown to the framework.\\\\\nEpidemiological research is inherently stochastic and complex, and admits multiple valid modeling approaches, leading to the absence of a unified standardized benchmark for evaluating the end-to-end epidemic research pipeline. Therefore, to evaluate our framework, we adopted an assessment strategy aligned with how the scientific community assesses research manuscripts through the peer review process. Consequently, we considered:\n\\begin{itemize}\n\\item \\textbf{Human evaluation} by peer review of written outputs and appraisal of deliverables. Specifically, we asked five blinded domain experts to review the manuscripts generated by EpidemIQs, based on the criteria in Supplementary Table S7.\n\\item \\textbf{LLM-as-Judge evaluation} using GPT-4o to evaluate generated papers autonomously based on the same assessment criteria as human reviewers to deliver timely evaluation.\n\\item \\textbf{Completion success rate} defined as the proportion of trials in which \\textit{EpidemIQs} autonomously executed the full workflow and produced a scientific report containing all pre-specified sections, independent of content quality.\n\\item \\textbf{Computational costs} in terms of turnaround time, number of generated tokens, and total API cost.\n\\end{itemize}\nTogether, these measures capture both the scientific quality of the outputs and the reliability of the autonomous workflow.\nWe compared our framework with a multi-turn single agent, such that an agent plans its next steps autonomously for up to the maximum number of steps, $s_{max}$. The single agent is instructed to perform all five phases with clear instructions (same as the agents in the EpidemIQs) and the same tools as in the multi-agent framework, along with \\textit{VisionExpert} to enable the agent to analyze the figures. This single agent needs to have an LLM with a long context window; therefore, we used OpenAI gpt-4.1-2025-04-14, as it has reasoning capability and support of structured output with a context window of about one million tokens, along with o3-2025-04014 as the current highly capable OpenAI model with a 200K tokens context window. \\\\\nTo prevent the prompt drift, in each turn we re-inject the main task into memory as \\texttt{**Reminder** main query is \\{query\\}. Do NOT lose sight of this}, ensuring that the agent’s working context always contains the overarching objective. We considered the single agent as a baseline, and compared it with EpidemIQs' implementation based on computational statistics, performance analysis, and review scores of the generated papers.\\\\\n\nThe setup used for assessment is presented in Table\\ref{tab:agent_config}.\n\n\\begin{table}[ht]\n\\footnotesize\n\\caption{Configuration Details for EpidemIQs }\n\\centering\n\\begin{tabular}{|l|c|c|c|}\n\\hline\n\\textbf{Parameter} & \\textbf{\\textit{scientists}} & \\textbf{\\textit{experts}} & \\textbf{\\textit{MathExpert}} \\\\\n\\hline\nLLM & \\makecell{gpt-4.1-\\\\2025-04-14} & \\makecell{gpt-4.1-mini\\\\2025-04-14} & \\makecell{o3-mini\\\\2025-01-31} \\\\\n$r_{\\max}$ & 1 & - & - \\\\\nRetries & 5 & 5 & 5 \\\\\n%Memory & long+short & short & short \\\\\nTool Retries & 50 & 50 & 50 \\\\\nOutput Type & Pydantic dataclass & free-form & free-form \\\\\n\\hline\n\\end{tabular}\n\\label{tab:agent_config}\n\\end{table}\n\n\\section{Results and Discussion} \\label{sec:result}\nAcross the five epidemic questions, EpidemIQs completed every phase of the pipeline as Discovery, Modeling, Simulation, Analysis, and Report writing in autonomous mode, achieving a 100\\% completion success rate in generating the final report file. Automated rubric scoring by the LLM‑as‑Judge assigned a mean quality score of 9.04±0.21 out of 10, while four network science Ph.D. students and one faculty reviewer gave an average expert rating of 7.98±0.35, praising the reports' methodological soundness, clarity, and depth. Below, we summarize how the framework navigated each question, highlighting key decisions and results. The generated papers and a more comprehensive analysis are provided in the supplementary material.\\\\\n\\begin{figure}[t]\n\\iffalse\n \\centering\n \\begin{subfigure}[b]{\\linewidth}\n \\centering\n \\includegraphics[width=\\linewidth]{paperQ1.pdf}\n \\caption{}\n \\label{fig:Q1}\n \\end{subfigure}\n\\fi\n\n \\centering\n \\includegraphics[width=\\linewidth]{paperQ2.pdf} \n \\caption{Examples of paper generated by EpidemIQs for the second question. }\n \\label{fig:paper}\n\\end{figure}\n\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=1\\linewidth]{reason.pdf}\n \\caption{An example of reasoning information \\textit{NetworkScientist} generated for question one}\n \\label{fig:reason}\n\\end{figure}\n\n\\textbf{Question~1.} In the first phase, analytical percolation theory and the literature confirm that outbreak behavior can differ according to the degree of heterogeneity. They suggest that, for a heterogeneous network, a scale-free graph, whose node-degree distribution follows a power law, producing a few highly connected hubs among many sparsely linked nodes, is an appropriate candidate to compare with a well-mixed homogeneous network, in which every node is connected to every other node, resulting in a fully connected graph. Because the question does not specify the intrinsic reproduction number, \\(R_{0}\\), a value of 2.5 is adopted to reflect a disease that can be characterized by an SEIR model, such as COVID-19, for which \\(2 < R_{0} < 3\\). Consequently, the deterministic model parameters are chosen to reflect typical values observed in COVID-19, incubation rate as $\\sigma_{E\\rightarrow I} =0.2/day$ (average incubation period of 5 days), recovery rate, $\\gamma_{I\\rightarrow R} =0.1/day$ (average infectious period of 10 days), and transmission rate $\\beta_{S\\rightarrow E}=0.25$. The framework then generates both graphs, initializes them with the five infected nodes, and tunes the transmission rate of the SEIR model on the basis of the intrinsic \\(R_{0}\\) and a mean-field approximation to consider the effect of different network topologies. \n\nIn the simulation phase, three scenarios are executed for 300 stochastic realizations each: (i) random infectious seeding in the homogeneous network, (ii) random infectious seeding in the scale-free network, and (iii) infectious seeding at the highest-degree hubs in the scale-free network. Analysis of the simulation results corroborates the analytical theory. The fully connected homogeneous network exhibits a rapid, high-magnitude outbreak with near-complete infection penetration. By contrast, the scale-free network shows markedly different epidemic behaviour in both seeding schemes, with a much later epidemic peak, a lower peak prevalence, and a substantially smaller final epidemic size (\\(\\approx 30\\%\\)). Notably, hub-based infection seeding accelerates epidemic progression and yields a higher average final epidemic size, confirming the role of superspreaders in triggering more rapid outbreaks in networks with heavy-tailed degree distributions. Hence, the stochastic results confirm that degree heterogeneity decisively reshapes outbreak timing and magnitude. Complete description and results for this question are provided at Supplementary Section S1.1.\n\nFigure~\\ref {fig:reason} illustrates \\textit{NetworkScientist}'s reasoning and logic, exemplifying how each \\textit{scientist} justifies its task completion and the rationale behind its choices, thereby enhancing the interpretability of the outcomes.\\\\\n\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=1\\linewidth]{workflowq4.pdf}\n \\caption{An overview of the workflow for question four, highlighting each step’s goals, main actions, and outputs. The results have been truncated for clearer visualization. At the bottom, plots generated during the modeling and simulation phases are provided. }\n \\label{fig:workflowQ4}\n\\end{figure}\n\n\n\\textbf{Question~2.} Starting from the discovery phase, analytical results showed that the chain of transmission breaks when the effective reproduction number drops below unity, \\(R_e < 1\\). This can occur either when the susceptible population falls beneath a critical threshold or when the transmissibility of infectives decreases. Moreover, contact patterns (e.g., network topology) influence whether an outbreak sputters or ignites, thereby shaping its overall dynamics. To validate these findings, consistent with the surveyed literature, the framework employed an SIR model with two basic reproduction numbers: a supercritical case, \\(R_0 = 3\\), and a subcritical case, \\(R_0 = 0.5\\).\\\\\nTo isolate structural effects, two networks with identical average degree \\(\\langle k \\rangle = 10\\) and \\(N = 1{,}000\\) nodes were generated. The first is an Erd\\H{o}s–Rényi (ER) network representing homogeneous mixing, where each pair of nodes connects with probability \\(p\\). The second is a scale-free Barabási–Albert (BA) network capturing heterogeneity; after an initial seed, each incoming node forms \\(m\\) links to existing nodes, producing a heavy-tailed degree distribution.\\\\\nSimulations began with ten randomly seeded infectives. For each network and \\(R_0\\) value, transmission rates were adjusted (via mean-field approximation) to account for degree heterogeneity, and 75 stochastic realizations of each scenario were executed. In the supercritical scenario (\\(R_0 = 3\\)), the epidemic peaked rapidly and faded as susceptibles were depleted. In the ER network, the average susceptible count fell from 990 to \\(\\approx 115\\) and the recovered count rose to \\(\\approx 885\\), indicating herd-immunity termination. The BA network also exhibited fade-out but progressed faster and left a larger susceptible pool (final average epidemic size \\(\\approx 520\\), remaining susceptibles \\(\\approx 480\\)), reflecting heterogeneity-mediated herd immunity.\\\\\nFor the subcritical scenario (\\(R_0 = 0.5\\)), intrinsic transmission inefficiency halted spread in both network topologies. Overall, the simulations confirm the analytical prediction that complete exhaustion of susceptibles is unnecessary; herd immunity can emerge when the susceptible fraction drops below a critical level or when per-contact transmissibility is sufficiently low. Figure~\\ref{fig:paper} shows an overview of the generated paper, and details of the framework's workflow are provided in the Supplementary Section S1.2.\\\\\n\n\n\n\n\n\\textbf{Question~3.} In the discovery phase, statistical analysis using a mean-field approximation derived expressions for the epidemic threshold in an activity-driven network, where each node activates at rate $\\alpha = 0.1$ and, upon activation, instantaneously forms $m$ edges, which are then removed in the next step. Because neither $m$ nor the recovery rate was specified, the experiment adopted a unit recovery rate and set $m = 5$ as a plausible value. The analytical results indicated that, for $R_0 = 3$, a final epidemic size of 94\\% should be expected under these parameters.\\\\\nTo compare the analytical solution for the temporal network having 1000 nodes with its time-aggregated static counterpart, a static network was created by aggregating all temporal contacts over $T = 1000$ time steps; for every node pair $(i,j)$, the edge weight equaled the total number of contacts during $T$. The recovery rate of one was chosen, and the infection rate was then calibrated for each network-driven SIR simulation so that they matched the mean-field derivations and were consistent with the respective network context (temporal or static). One random infectious node was selected as the initial condition, with all other nodes susceptible.\\\\\nOne hundred stochastic realizations were performed for each scenario, using FastGEMF for the time-aggregated static network and a custom discrete-time Markov-chain engine for the temporal network. The results revealed sharp contrasts in epidemic size and speed between the temporal and static scenarios. The temporal activity-driven network produced significantly smaller and slower epidemics relative to both the static-network simulation and the analytic predictions based on aggregated parameters. Specifically, the temporal SIR process yielded a mean final epidemic size of approximately 20.5\\% with a large standard deviation of 28.9\\%, indicating high stochastic variability and frequent epidemic die-out events at the chosen parameters. Such early stochastic die-out is ignored in mean-field ODEs, which assume deterministic branching of infections and never allow the process to fizzle when the first few seeds recover before transmitting the pathogen.\\\\\nBy contrast, the static-network simulation produced near-complete infection of the population (mean final size $\\approx 81\\%$) in a rapid fashion, closely approaching the analytical prediction of 94.05\\% derived from the classic mean-field equation. These results highlight the profound mechanistic effect of temporal causality on disease-transmission pathways. In the temporal network, edges represent instantaneous contacts that exist only transiently and are reorganized stochastically at each time step. Consequently, the temporal ordering of contacts restricts the accessibility of transmission chains, effectively increasing the epidemic threshold and reducing the reachable susceptible population. Many potential transmission paths present in the aggregated static network are simply infeasible in the temporal network because the required contact timings do not overlap to support causally coherent infections. Supplementary Section S1.3. provides the detailed outcomes for this question.\\\\\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=1\\linewidth]{workflowq5.pdf}\n \\caption{An overview of the workflow for question five, outlining each step’s goals, main actions, and outputs. For clarity, the results have been truncated. At the bottom, plots display the degree distribution, highlighting the large number of nodes with degree 10 and confirming that enough nodes are available for targeted vaccination, together with simulation results for four cases: no vaccination (baseline), vaccination below the critical threshold, at the threshold, and above the threshold.}\n \\label{fig:workflowQ5}\n\\end{figure}\n\nFigures \\ref{fig:workflowQ4} and \\ref{fig:workflowQ5} display the results and process pipelines for questions 4 and 5, respectively. For the question 4 scenario, the framework could successfully find the criteria for the coexistence of the competitive exclusive viruses over multilayer networks, extend the analytical mean-field point of view that exists in literature, and show the dominance, coexistence, and extinction regimes in stochastic processes by designing the network properties that allow coexistence and tuning the parameters. Finally, for the last question, it not only determined the vaccination threshold for random and targeted cases but also carefully modeled the contact network to maintain the aforementioned centralities while having enough nodes to verify the targeted vaccination threshold. The presented results are truncated, and please refer to Supplementary Sections S1.4 and S1.5. for full detailed results of questions 4 and 5, respectively.\\\\\n\n\\subsection{Review Score and Computational Cost}\n\\begin{table*}[htbp!]\n\\centering\n\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\n\\renewcommand{\\arraystretch}{1.3}\n\\setlength{\\tabcolsep}{5pt}\n\\begin{tabular}{|>{\\raggedright\\arraybackslash}p{4cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|\n>{\\centering\\arraybackslash}p{0.4cm}\n>{\\centering\\arraybackslash}p{0.8cm}|}\n\\hline\n\\multirow{2}{*}{\\textbf{Question Topics}} & \n\\multicolumn{2}{c|}{\\makecell{\\textbf{Readability}}} &\n\\multicolumn{2}{c|}{\\makecell{\\textbf{Relevance}\\\\\\textbf{\\& Motivation}}} & \n\\multicolumn{2}{c|}{\\makecell{\\textbf{Technical}\\\\\\textbf{Soundness}}} & \n\\multicolumn{2}{c|}{\\makecell{\\textbf{Experimental}\\\\\\textbf{Rigor}}} & \n\\multicolumn{2}{c|}{\\makecell{\\textbf{Limitation}\\\\\\textbf{\\& Ethics}}} & \n\\multicolumn{2}{c|}{\\textbf{Overall}} \\\\\n\\cline{2-13}\n& \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n\\hline\n1. Effect of degree heterogeneity in SEIR model & 9.5 & 7 & 9.5 & 9 & 9.5 & 8 & 10 & 8 & 9.5 & 8 & 9.5 & 8.0 \\\\\n\\hline\n2. Reasons of transmission break &9.5 & 7 & 10 & 10 & 10 & 6 & 9 & 10 & 8 & 9 & 9.7 & 8.2 \\\\\n\\hline\n3. Effect of temporality on epidemic behavior in activity-driven networks & 9.5 & 9 & 9.5 & 9 & 9 & 7 & 9.5 & 7 & 8& 7 & 9.2 & 7.8 \\\\\n\\hline\n4. Coexistence of exclusive bi-virus spread on multiplex networks & 9 & 7 & 9 & 9 & 9.5 & 9 & 9.3 & 8 & 8.2 & 7 & 9.0 & 8.0 \\\\\n\\hline\n5. Herd-immunity through random and targeted vaccination in networks & 9 & 6.5 & 9 & 9 & 10 & 8 & 10 & 9 & 8 & 8 & 9.2 & 8.1 \\\\\n\\hline\n\\end{tabular}\n\\label{tab:review}\n\\end{table*}\n\nTable \\ref{tab:review} presents the evaluation scores assigned by an LLM-as-Judge and by human experts across five rubric criteria. For each of the five epidemic questions, the framework autonomously generated ten full papers, yielding 50 manuscripts. We randomly selected five of these for blind human review. Each reviewer scored every criterion on a 1‑to‑10 scale. Human scores averaged 7.98 with a standard deviation of 0.20 (\\( \\approx2.5\\%\\)), indicating consistently strong performance by EpidemIQs. Reviewers praised the manuscripts’ comprehensive problem framing, robust experimental design and analysis, and balanced coverage of both analytical and stochastic aspects. The main criticisms concerned verbosity with occasional repetition of content, the use of uncommon vocabulary that slowed reading, and some missing or incomplete figure references.\\\\\n\nTable \\ref{tab:cost} reports the average turnaround time, total number of tokens, and total cost (calculated by OpenAI’s May 2025 pricing) for all questions, measured from the initial query to the final report. A total cost of only \\$1.57, a turnaround of under 30 minutes, a 100\\% success rate, and consistently high review scores demonstrate the strength of the framework and the efficiency of its multi‑agent orchestration. The low cost and rapid execution are achieved by splitting tasks between \\textit{expert} and \\textit{scientist} agents. Token‑heavy, low‑complexity jobs are delegated to fast, inexpensive models such as GPT‑4.1 mini, while more demanding works such as planning, reasoning, tool coordination, and output refinement is handled by the full GPT‑4.1 model.\n\\begin{table}[t]\n \\centering\n \\caption{Average Computation Statistics}\n \\begin{tabular}{|l|c|c|c|}\n \\hline\n \\textbf{Phase} & \\textbf{Time(sec.)} & \\textbf{Tokens(K)} & \\textbf{Cost(\\$)} \\\\ \\hline\n Discovery & 158 & 98 & 0.1 \\\\ %\\hline\n Modeling & 140 & 175 & 0.72 \\\\ %\\hline\n Simulation & 198 & 88 & 0.23 \\\\ %\\hline\n Analysis & 177 & 93 & 0.16 \\\\ %\\hline\n Report Writing & 517 & 416 & 0.36 \\\\ \\hline\n \\textbf{Overall} & \\textbf{1190} & \\textbf{870} & \\textbf{1.57 } \\\\ \\hline\n \\end{tabular}\n \\label{tab:cost}\n\\end{table}\n\\subsection{Multi-Turn Single-Agent vs EpidemIQs Orchestration}\nIn this section, we ran the single-agent across the same five questions ten times, using two OpenAI LLMs, GPT‑4.1 and o3. Single-agent‑GPT‑4.1 achieved an average completion success rate of 78±7.7\\% and an average human-review score of 5.06, whereas single-agent-o3 reached 80.0±6.32\\% with a human-review score of 5.68. The \\textit{LLM-as-Judge} provides comparative evaluations of the successful papers generated by single-agent and EpidemIQs. Table~\\ref{tab:single_score} presents these scores for all questions.\n\\begin{table*}[htb!]\n\\caption{Overall Score for AI and Human Expert Evaluation of Generated Papers}\n\\centering\n\\begin{tabular}{|l|c c|c c|c c|c c|c c|}\n\\hline\n\\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{question 1}} & \\multicolumn{2}{c|}{\\textbf{question 2}} & \\multicolumn{2}{c|}{\\textbf{question 3}} & \\multicolumn{2}{c|}{\\textbf{question 4}} & \\multicolumn{2}{c|}{\\textbf{question 5}} \\\\\n & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} & \\textbf{AI} & \\textbf{Human} \\\\\n\\hline\nEpidemIQs & 9.5 & 8.0 & 9.5 &8.2 & 9.2 & 7.8 & 9.0 & 8.0 & 9.2 & 8.1 \\\\\nsingle-agent-GPT4.1 & 8.9 & 5.4 & 7.3 & 5.3 & 8.9 & 4.8 & 7.5 & 4.6 & 8.4 & 5.2 \\\\\nsingle-agent-o3 & 8.5 & 5.8 & 8.6 & 6.3 & 8.3 & 5.5 & 8.6 & 5.8 & 7.4 & 5.2 \\\\\n\\hline\n\\end{tabular}\n\\label{tab:single_score}\n\\end{table*}\nSurprisingly, the AI-generated scores differ only slightly across the three cases, while the human reviews reveal substantial disparities in their outcomes. The single-agent-GPT‑4.1 setup addressed the first three questions to some extent; however, it was limited: it handled the analytical component inadequately, ran only a few stochastic simulations, and in some instances merely solved the ODE system instead of performing exact stochastic simulations. For the more complex question 5, none of the trials identified the target vaccination threshold or model the network appropriately. Furthermore, the parameters and the rationale for their selection were not discussed comprehensively.\\\\\n\nThe conclusions were sometimes misleading, as they were not based on the simulation results; instead, the agent often relied on prior knowledge or literature. When grounded in results, they were still occasionally inaccurate, for example, in the targeted-vaccination case, the agent typically claimed that vaccinating all high-degree nodes was necessary, largely because it generated the network before calculating the analytical thresholds, resulting in very sparse high-degree nodes. Human reviews also mention that while the agent could address the task to some degree, it is in shallow depth, missing figures, insufficient simulations, and limited analyses, and the overall failure to address the tasks comprehensively, compared to rigorous analysis and experimentation in the MA setup.\\\\\nOn the other hand, The single-agent-o3 did better job with analytical aspect of the question and better writing quality, however, the simulations still was very limited, and the agent shows more autonomy in how to accomplish tasks rather based on the expert knowledge provided as instructions, for example for stochastic simulation it did not always use the engine provided for it or ignoring literature and online searches. Though the single-agent-o3 generally generated higher quality reports, there was still some cases when there were inaccuracies, for example for question four, even the coexistence was not achieved through stochastic simulation, it was concluded that simulation results confirm that coexistence is possible when analytical conditions are met or the agent mentioned the simulation were performed by FastGEMF over 1000 realizations, however scripts in the repository showed custom engine for deterministic simulation was used to simulated SI instead of SIR, which showed a huge drift from the main task and hallucination of the agent in the report. Also, in none of the cases could it correctly address the targeted vaccination in question five. Finally, while reviewers praised the writing quality, conciseness, and analytical aspects of the reports, they found that they fell short in having enough depth, simulation rigor, and failure to address complex tasks comprehensively. \\\\ It is also necessary to mention that, to avoid violating OpenAI's usage policy when using the o3 model, we changed the questions from virus spread to meme spread. Otherwise, the success rate of single-agent-o3 was less than 30\\%. We did not consider this API error in our benchmarks for evaluating the o3 success rate. It is important to emphasize that this change in context does not affect the validity of the comparative results, as epidemic spread can easily be generalized for social cases such when a meme spread over a population.\\\\\nOverall, the human reviews and performance analysis demonstrated the superior performance of EpidemIQs compared to the single-agent implementation. Single-agent systems consistently failed to address complex scenarios, exhibited drift in their outcomes, lacked depth in their reports, and had a significantly lower success rate in completing tasks. Table \\ref{tab:cost_single} presents the computational statistics for these three different implementations. These comparisons are particularly meaningful given that the EpidemIQs achieved its superiority at a cost comparable to single-agent-GPT4.1 and at less than half the cost of single-agent-o3, despite the o3 model having greater reasoning and coding capabilities than those employed in the EpidemIQs, as mentioned in Table \\ref{tab:agent_config}. Moreover, the superiority of the proposed framework extends beyond performance and computational efficiency, offering greater interpretability by providing explicit reasoning for each step.\n\n\\begin{table}\n\\caption{Comparison of Average Computation Statistics Across All Questions Over Three Different Implementations}\n\\centering\n\\begin{tabular}{|l|c|c|c|}\n\\hline\n\\textbf{Method} & \\textbf{Time (s)} & \\textbf{Tokens (K)} & \\textbf{Cost (\\$)} \\\\\n\\hline\nEpidemIQs & 1190 & 870 & 1.57 \\\\\nsingle-agent-GPT4.1 & 214 & 312 & 0.91 \\\\\nsingle-agent-o3 & 436 & 165 & 4.13 \\\\\n\\hline\n\\end{tabular}\n\\label{tab:cost_single}\n\\end{table}\n \n\n\n\n\n\n\\subsection{Discussion, Limitations, and Ethical Concerns}\n\nAlthough the EpidemIQs framework consistently produces high‑quality manuscripts throughout the workflow, it is not designed to replace human authorship in scientific research, but rather to be an assistant to human experts to facilitate the research process for testing and implementing ideas in the epidemic modeling field. EpidemIQs can still make mistakes, and AI‑generated prose can be highly persuasive, as \\cite{bai2025llm, simhi2025trust, liu2025llm} discussed, so human oversight remains essential to safeguard accuracy and integrity, and generated papers are meant to provide a comprehensive and unified result of the framework, making it easy to analyze the outcomes.\n\nAcross all of our experiments, we found no major instances of hallucination in EpidemIQs outputs, and performance was remarkably consistent. Since LLMs are non‑deterministic, they may tackle the same question slightly differently each time; however, no substantial drift or incorrect reasoning was observed. For example, in Question 5, \\textit{ModelScientist} sometimes designs an SIRV (V represents vaccinated state) model and at other times an SIR model, or \\textit{NetworkScientist} may construct networks with different degree distributions yet the same target centrality. These variations are valid and do not diminish performance; they simply reflect the natural diversity of approaches to a single problem. However, there were errors observed during the \\textit{Analysis} phase. For example, in question three, where \\textit{DataExpert} misinterpreted an average recovery count below one as a fraction rather than a discrete number of individuals, \\textit{DataScientist} detected this inconsistency and deferred to \\textit{VisionExpert}, whose interpretation matched both the simulation protocol and analytical expectations. While such checks limit the impact of isolated calculation errors, occasional mistakes by \\textit{DataExpert} indicate that automated data analysis may be a part of further improvement.\\\\\n\nThe framework also demonstrated sound awareness of its computational constraints. For example, in question three, we explicitly restricted simulations to the FastGEMF engine. \\textit{SimulationScientist} adhered to this limitation, employing FastGEMF exclusively for static networks, and it was explicitly noted in the final report that software limitations prevented temporal network experiments. This transparency is critical, as it prevents the framework from falsely claiming task completion. In contrast, such issues were observed in the single-agent implementation, where it falsely hallucinates task accomplishment. Furthermore, the reliability of scientific outcomes often hinges on the algorithms employed, which can be inherently complex. For instance, in one of the trails within question three, \\textit{SimulationScientist} designed a custom engine for simulating disease spread over a temporal network but erred in updating the order of states. This led to the premature recovery of initially infected nodes, preventing further spread and resulting in an underestimation of the final outbreak size and probability. Although \\textit{DataScientist} noted a significant discrepancy between simulated and expected analytical results, it incorrectly attributed the difference to the effects of temporality rather than the engine’s design flaw.\\\\\n\nTo further investigate the agents' attention to scientific details, in question three we explicitly specified the constant activity rate (and not activity probability per unit time), $\\alpha=3$, which is unlikely in real-world case studies and rare in literature but was chosen to test the agents’ attention to subtle details. However, \\textit{NetworkScientist} creates the network edges with the probability of a node being activated as $p=\\alpha \\Delta t$, with $\\Delta t=1$, as the first order Taylor series approximation of \\(p=1-\\exp^{-\\alpha \\Delta t}\\), where is only is acceptable if \\(\\alpha\\Delta t \\ll 1\\) (However, if $ \\alpha$ is probability $\\alpha \\Delta t$ is exact), making it invalid for $\\alpha \\Delta t=3 > 1$ resulting all nodes being activated each time, instead of having exact probability \\(\\approx 0.95\\).\\\\\n\nThese observations emphasize two points: \\\\\n1) the importance and impact of providing appropriate tools to obtain consistent and reliable results, and 2) the continued need for a human expert to validate results, because agents can still make mistakes that are difficult to detect and may produce persuasive responses that justify incorrect conclusions.\\\\\nOur framework is unique, with no direct comparators. However, a comparison with The AI Scientist, a general tool for scientific discovery from ideation to paper writing \\cite{lu2024ai}, for question one, showed the failure of The AI Scientist. It analyzed the ODE-based analytical component but struggled with stochastic simulations over the network, producing hallucinated results and conclusions. It is essential to mention The AI Scientist performance was mostly evaluated on AI-related subjects, such as diffusion models or transformers, emphasizing that this comparison does not imply overall superiority of one framework over another.\\\\\nSummarizing the main limitations of the current work, we have:\n\\begin{itemize}\n \\item Although no major hallucinations were found in the results, a few hallucinated references did appear in the final report. Moreover, while the reviewers praised the papers’ comprehensiveness, they also noted some repetitive content that lengthened the reading time, and sometimes tables were so large that portions extended beyond the page, suggesting enhancing the report generation part. \n \\item The performance of the EpidemIQs is highly dependent on the LLM models, while our framework is model agnostic, as long as these models can support structured outputs and tool calling, the results can vary based on the LLM choices.\n \\item The literature review relies only on the abstract and summary of key findings, rather than delving deeply into the full content of the papers. Future frameworks capable of thoroughly analyzing the full material of each paper could enhance and benefit from deeper data retrieval.\n \\item The current framework focuses on epidemic modeling over complex networks as a proof of concept. Enhancing it to broader methods such as Agent-Based Models(ABM)\\cite{epstein2009modelling,parker2011distributed}, individual-based \\cite{epstein2009modelling}, or statistical and data-driven approaches \\cite{epstein2009modelling,vespignani2020modelling} can significantly increase the applicability of the framework.\n \\item The agents’ performance hinges on the tools at their disposal. As noted in question three, their performance and reliability decline when they encounter highly technical problems without the requisite expert knowledge and appropriate tools. This shortcoming explains why the general‑purpose module proposed by \\cite{lu2024ai} fails in question one.\n \\item AI evaluation in the automated review process shows divergence from human expert reviews, aligning with other works' findings, such as Agent Laboratory \\cite{schmidgall2025agent}. However, contrasting with near-human performance reported in \\cite{lu2024ai}, it suggests that human involvement is necessary. While an \\textit{LLM-as-Judge} can be beneficial for providing high-level insights, it cannot be fully trusted, since it relies on superficial patterns rather than robust analysis criteria.\n \\item We did not include ideation in our framework, primarily because epidemic research is highly complex and interdisciplinary. Generating new research ideas requires careful consideration of resources, advanced tools (see Limitation 4), expert knowledge across multiple domains, and access to diverse data sources, such as mobility, weather, and epidemiological data. For example, in vector-borne diseases, the populations of mosquitoes or birds play a critical role in epidemiological modeling. To the authors' knowledge, such ideas can quickly become too complex for current agentic AI systems to handle appropriately, given concrete bottlenecks such as the lack of structured access to high-quality mobility/weather/entomological data, difficulty in reasoning across coupled mechanistic models, or access to specific tools. Therefore, we focused on specific network-based epidemic modeling tasks as a proof of concept to showcase the framework’s potential benefits.\n\\end{itemize}\nTherefore, although EpidemIQs offers great potential to accelerate epidemic-modeling research and allows researchers to focus on high-level ideation, this promise also introduces new ethical challenges that must be taken seriously. Its ability to autonomously generate high-quality papers, supported by analytical insights, rigorous simulations, and comprehensive analyses, may inadvertently lower the barriers to producing low-standard scientific work, potentially overwhelming the peer-review system and jeopardizing the integrity of academic discourse. Moreover, as noted earlier, the automated process may introduce mistakes in algorithm design that are implicit and difficult to detect, or it may yield results biased by its underlying knowledge or algorithms, leading to skewed outcomes. These concerns underscore the necessity of disclosing AI involvement in the research process to mitigate such risks and maintain accountability, fairness, and transparency.\\\\\n\n\\iffalse\nIn this study, we evaluated the performance of EpidemIQs across a spectrum of epidemiological questions, ranging from basic to advanced network-based epidemiology. Our experiments demonstrated that the agents were capable of handling intricate details, even in challenging questions, showcasing their potential in complex epidemiological modeling. This robustness highlights the promise of such agents in assisting with real-world public health challenges, where a nuanced understanding of network dynamics is critical.\nTo assess the quality of our work, we conducted a thorough review process involving both human experts and AI-based evaluations. The AI reviews yielded an average rating of 6 out of 10, while human expert reviews assigned a slightly lower average score of 5 out of 10. These ratings suggest a moderate reception of the paper, with AI reviews potentially reflecting a more lenient or standardized assessment compared to the critical perspective of domain experts. The discrepancy between AI and human evaluations warrants further investigation into the criteria and biases inherent in each review process, which could inform future improvements in both agent design and manuscript preparation.\nDespite the strengths of the EpidemIQs, several limitations must be acknowledged. While the agents are capable of learning through reflection and prompting, their performance is constrained by the lack of fine-tuning and uniform weighting across all agents. This uniform approach may hinder optimization, leading to slower performance in certain questions. Additionally, not all agents are fully context-aware of the system's overall flow. As a result, an error by one agent can propagate, adversely affecting the behavior of others. This cascading effect underscores the need for enhanced context awareness and error mitigation strategies in multi-agent systems.\nFuture work should focus on addressing these limitations by implementing fine-tuning mechanisms to optimize agent weights and improving context awareness to ensure robust system-level performance. By overcoming these challenges, EpidemIQs could achieve greater reliability and efficiency, further advancing their utility in epidemiological research and beyond.\n\\subsection{limitations}\n\\begin{itemize}\n \\item The performance is highly dependent on the choices of LLMs as the backbone of agents, for example, GPT 4.1 and Gork 3 have much better instruction following performance than GPT 4o or o3-mini models.\n \\item The agent can reach a conclusion if even a few experiments are performed\n \\item the longer conversations and input data, the higher the chance of drift in the task, which requires a more advanced mechanism to handle the memory, such as Graph-based data structures\n \\item \n\\end{itemize}\n\\textbf{checklist:}\n\\begin{itemize}\n \\item discuss specific limitations of EpidemIQs, computational cost, assumptions about static networks, or generalizability to real-world questions, etc.\n \\item propose concrete future research directions (e.g., extending to dynamic networks, incorporating mobility data, or addressing privacy concerns).\n \\item highlight practical implications (e.g., how EpidemIQs could inform policy decisions or resource allocation during outbreaks).\n \\item Address societal impacts, such as potential benefits (improved outbreak response) and risks (misuse of predictive models).\n\\end{itemize} \n\\fi\n\\section{Data Availability}\nAll the data and results discussed in this paper are provided as supplementary materials. The EpidemIQs is also provided as an open-source Python module at \\emph{github.com/will-be-announced-upon-publication}.\n\n%\\begin{ack}\n % Acknowledgments go here (for final version only, not anonymized submission).\n % For the anonymized submission, leave this section empty.\n % For the final version, include funding sources, collaborators, or other support.\n % Example: This work was supported by [Funding Agency] under grant [Number].\n%\\end{ack}\n\n\\section{Conclusion}\\label{sec:conc}\nIn this study, we present EpidemIQs, a multi‑LLM agent framework that harnesses the reasoning, planning, and problem‑solving abilities of LLMs and integrates them with online and literature retrieval, multimodal data processing, code generation and execution, stochastic simulation, and visual and data analysis. These characteristics enable it to autonomously carry out every key stage of epidemic modeling research, from discovery through modeling and simulation to analysis and, finally, the synthesis of findings into a full scientific report. This entire process takes less than half an hour, whereas it would normally take an average graduate-level student days to accomplish the same task.\\\\\nThe evaluation of results across questions addressing various aspects of network-based epidemic modeling demonstrates that the framework consistently maintains high performance across our trials. Consequently, EpidemIQs can extend existing analytical approaches to stochastic processes, infer implicit constraints in research questions, and design scenarios that address cases beyond the immediate scope of available tools and expert knowledge.\\\\\nThe comparative analysis of EpidemIQs and the single-agent implementation consistently showed that EpidemIQs outperformed the single-agent variants across all tasks. It achieved an 100\\% success rate average human‑evaluation score of 7.98 at a cost of \\$1.57, whereas the single-agent configurations based on GPT‑4.1 and o3 obtained scores of 5.06 and 5.68 at costs of \\$0.91 and \\$4.13, respectively.\\\\\nAt present, EpidemIQs focuses exclusively on epidemic modeling over networks as a proof of concept; nevertheless, it has already demonstrated the potential of deploying LLM agents in a collaborative environment. This opens an exciting path for further performance gains by integrating advanced tools, such as deep learning techniques, probabilistic methods, and data-centric models, heralding a promising future for epidemic modeling research. Moreover, because the framework’s accuracy and performance depend heavily on the underlying LLMs, the rapid advances in this field are likely to yield substantial improvements for the entire multi agent system, as our framework is designed to be model agnostic.\\\\\nEpidemIQs, while demonstrating strong performance and producing high‑quality output, is not intended to, and should not, replace human authorship in the scientific process, as it still makes mistakes and should not be fully trusted; it is best regarded as a highly capable assistant. Researchers in epidemic modeling can use it to test and implement their ideas quickly and at low cost, freeing them from time‑consuming tasks such as setting up simulations or writing repetitive code and allowing them to focus on the conceptual and creative aspects of their work.\\\\\nFuture work should consider the broader applications of epidemic modeling by integrating real-world data and other advanced computational tools into the model design to address open-ended real-world problems and evaluate its applicability for forecasting current outbreaks. Additionally, they should address ethical concerns regarding the misuse or dual use of such a framework, as automated modeling and report generation could be exploited to produce misleading forecasts or scientifically plausible misinformation, intentionally or unintentionally influencing public perception or policy decisions. The system’s ability to simulate outbreak dynamics at scale may also lower barriers for malicious actors to explore harmful scenarios or identify vulnerabilities in public health defenses. Additionally, integration with sensitive epidemiological data poses privacy risks, emphasizing the need for implementing appropriate safeguards. \n\n\n{\n\n\n\n\\bibliographystyle{IEEEtran}\n\\bibliography{ref}\n\\includepdf[pages=-]{EpidemIQsSupplementary.pdf} % Embed all pages of the other PDF\n\\end{document}"},"question":{"kind":"string","value":"In which catgegory do AI and human performances differ the most when compared on average across all questions? If there are mulltiple categories name all ot them."},"answer":{"kind":"string","value":"Technical Soundness, Readability"},"plan":{"kind":"string","value":"SELECT (AI scores and human scores across all questions)\nSELECT all categories\nLOOP for each category\n SELECT all settings\n LOOP for each setting\n COMPUTE difference = absolute(AI scores - human scores)\n COMPUTE average_difference = average over difference\n\n\nCOMPUTE target_category = argmax over average_difference\nRETURN target_category\n"}}},{"rowIdx":355,"cells":{"paper":{"kind":"string","value":"2510.00028"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[h]\n","\\centering\n","\\caption{Performance of LLaMA-2-7B on standard LLM benchmarks under different quantization and PI settings. Zero-shot accuracy on 5 tasks plus average and WikiText2 perplexity.}\n","\\vspace{-2mm}\n","\\label{tab:result-llama-2-7b}\n","\\resizebox{0.95\\textwidth}{!}{\n","\\begin{tabular}{lccccccc}\n","\\toprule\n","\\textbf{Setting} & \\textbf{ARC-C} & \\textbf{ARC-E} & \\textbf{BoolQ} & \\textbf{HellaSwag} & \\textbf{WinoGrande} & \\textbf{5-shot Avg.} & \\textbf{WikiText2 PPL} \\\\\n","\\midrule\n","\\multicolumn{8}{c}{\\emph{Base Context (4096 context window length)}} \\\\\n","\\midrule\n","Baseline FP16 & 52.3 & 80.1 & 76.2 & 78.9 & 67.7 & 70.83 & 5.47 \\\\\n","RTN W4 & 48.6 & 76.5 & 72.4 & 74.1 & 59.1 & 64.14 & 5.73 \\\\\n","RTN W4-A4 & 47.2 & 75.0 & 71.3 & 72.8 & 57.9 & 62.02 & 5.92 \\\\\n","AWQ W4 & 48.9 & 76.8 & 73.1 & 74.9 & 59.6 & 64.25 & 5.61 \\\\\n","AWQ W4-A4 & 47.5 & 75.2 & 71.7 & 73.2 & 58.1 & 62.31 & 5.77 \\\\\n","\\midrule\n","\\multicolumn{8}{c}{\\emph{Extended Context with YaRN (32K context window length, $s{=}8$)}} \\\\\n","\\midrule\n","Baseline FP16 & 48.7 & 75.6 & 72.0 & 73.5 & 58.6 & 63.71 & 6.09 \\\\\n","RTN W4 & 48.0 & 75.1 & 71.4 & 72.8 & 57.7 & 63.32 & 6.41 \\\\\n","RTN W4-A4 & 47.1 & 74.6 & 70.9 & 72.0 & 57.4 & 62.84 & 6.60 \\\\\n","AWQ W4 & 48.3 & 75.3 & 71.9 & 73.1 & 58.0 & 63.52 & 6.31 \\\\\n","AWQ W4-A4 & 47.3 & 74.8 & 70.8 & 72.3 & 57.2 & 62.53 & 6.49 \\\\\n","\\midrule\n","\\textbf{Q-ROAR W4} & \\textbf{49.0} & \\textbf{75.9} & \\textbf{72.4} & \\textbf{73.8} & \\textbf{58.6} & \\textbf{63.96} & \\textbf{6.18} \\\\\n","\\textbf{Q-ROAR W4-A4} & \\textbf{48.2} & \\textbf{75.2} & \\textbf{71.7} & \\textbf{73.0} & \\textbf{58.2} & \\textbf{63.21} & \\textbf{6.39} \\\\\n","\\bottomrule\n","\\end{tabular}}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Performance of LLaMA-2-7B on standard LLM benchmarks under different quantization and PI settings. Zero-shot accuracy on 5 tasks plus average and WikiText2 perplexity.}\\n\",\n \"\\\\vspace{-2mm}\\n\",\n \"\\\\label{tab:result-llama-2-7b}\\n\",\n \"\\\\resizebox{0.95\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{lccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Setting} & \\\\textbf{ARC-C} & \\\\textbf{ARC-E} & \\\\textbf{BoolQ} & \\\\textbf{HellaSwag} & \\\\textbf{WinoGrande} & \\\\textbf{5-shot Avg.} & \\\\textbf{WikiText2 PPL} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{8}{c}{\\\\emph{Base Context (4096 context window length)}} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Baseline FP16 & 52.3 & 80.1 & 76.2 & 78.9 & 67.7 & 70.83 & 5.47 \\\\\\\\\\n\",\n \"RTN W4 & 48.6 & 76.5 & 72.4 & 74.1 & 59.1 & 64.14 & 5.73 \\\\\\\\\\n\",\n \"RTN W4-A4 & 47.2 & 75.0 & 71.3 & 72.8 & 57.9 & 62.02 & 5.92 \\\\\\\\\\n\",\n \"AWQ W4 & 48.9 & 76.8 & 73.1 & 74.9 & 59.6 & 64.25 & 5.61 \\\\\\\\\\n\",\n \"AWQ W4-A4 & 47.5 & 75.2 & 71.7 & 73.2 & 58.1 & 62.31 & 5.77 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{8}{c}{\\\\emph{Extended Context with YaRN (32K context window length, $s{=}8$)}} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Baseline FP16 & 48.7 & 75.6 & 72.0 & 73.5 & 58.6 & 63.71 & 6.09 \\\\\\\\\\n\",\n \"RTN W4 & 48.0 & 75.1 & 71.4 & 72.8 & 57.7 & 63.32 & 6.41 \\\\\\\\\\n\",\n \"RTN W4-A4 & 47.1 & 74.6 & 70.9 & 72.0 & 57.4 & 62.84 & 6.60 \\\\\\\\\\n\",\n \"AWQ W4 & 48.3 & 75.3 & 71.9 & 73.1 & 58.0 & 63.52 & 6.31 \\\\\\\\\\n\",\n \"AWQ W4-A4 & 47.3 & 74.8 & 70.8 & 72.3 & 57.2 & 62.53 & 6.49 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Q-ROAR W4} & \\\\textbf{49.0} & \\\\textbf{75.9} & \\\\textbf{72.4} & \\\\textbf{73.8} & \\\\textbf{58.6} & \\\\textbf{63.96} & \\\\textbf{6.18} \\\\\\\\\\n\",\n \"\\\\textbf{Q-ROAR W4-A4} & \\\\textbf{48.2} & \\\\textbf{75.2} & \\\\textbf{71.7} & \\\\textbf{73.0} & \\\\textbf{58.2} & \\\\textbf{63.21} & \\\\textbf{6.39} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}[t]\n","\\centering\n","\\begin{subfigure}[t]{0.49\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{four_methods_no_pi_style2.pdf}\n"," \\caption{Non-Interpolated models}\n"," \\label{left}\n","\\end{subfigure}\n","\\hfill\n","\\begin{subfigure}[t]{0.5\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{five_methods_aaai_style2.pdf}\n"," \\caption{YaRN interpolation (s = 8)}\n"," \\label{right}\n","\\end{subfigure}\n","\\vspace{-2mm}\n","\\caption{Perplexity of quantized Llama-2-7b evaluated on the GovReport Dataset}\n","\\label{fig:ppl}\n","\\end{figure*}\n"],["\\begin{table*}[h]\n","\\centering\n","\\caption{GovReport perplexity on LLaMA-2-7B across evaluation context sizes (lower is better).}\n","\\vspace{-2mm}\n","\\label{tab:govreport-multisize}\n","\\begingroup\n","\\setlength{\\tabcolsep}{5pt}\n","\n","\\resizebox{0.8\\textwidth}{!}{\n","\\begin{tabular}{lc|ccccc}\n","\\toprule\n","\\multirow{2}{*}{Setting} & \\multirow{2}{*}{\\shortstack{Context Length \\\\ (YaRN = 16)}} & \\multicolumn{5}{c}{Evaluation Context Window Size} \\\\\n"," & &2048 & 4096 &8192 & 16384 & 32768 \\\\\n","\\midrule\n","FP16 & 64K & 4.437 & 4.359 & 4.329 & 4.175 & 6.069 \\\\\n","RTN W4 & 64K & 4.544 & 4.485 & 4.470 & 4.575 & 6.783 \\\\\n","AWQ W4 & 64K & 4.489 & 4.421 & 4.405 & 4.414 & 6.302 \\\\\n","\\textbf{Q-ROAR W4 (ours)} & 64K & \\textbf{4.441} & \\textbf{4.393} & \\textbf{4.321} & \\textbf{4.181} & \\textbf{5.833} \\\\\n","\\bottomrule\n","\\end{tabular}%\n","}\n","\\endgroup\n","\\end{table*}\n"],["\\begin{table*}[t]\n","\\centering\n","\\caption{Proof-pile perplexity on LLaMA-2-7B across evaluation context sizes (lower is better). Values at $\\leq$16K use YaRN scale factor $s{=}8$; values at $\\geq$32K use $s{=}32$.}\n","\\vspace{-2mm}\n","\\label{tab:proofpile-multisize}\n","\\begingroup\n","\\setlength{\\tabcolsep}{5pt}\n","\\resizebox{0.8\\textwidth}{!}{\n","\\begin{tabular}{l|cccc|ccc}\n","\\toprule\n","Setting & \\multicolumn{4}{c|}{Evaluation Context (s=8)} & \\multicolumn{3}{c}{Evaluation Context (s=32)} \\\\\n"," & 2048 & 4096 & 8192 & 16384 & 32768 & 65536 & 131072 \\\\\n","\\midrule\n","FP16 & 2.847 & 2.667 & 2.543 & 2.438 & 4.261 & 4.074 & 5.386 \\\\\n","RTN W4 & 2.917 & 2.739 & 2.613 & 2.517 & 6.249 & 6.187 & 9.958 \\\\\n","AWQ W4 & 2.891 & 2.709 & 2.583 & 2.476 & 5.460 & 5.410 & 8.700 \\\\\n","\\textbf{Q-ROAR W4 (ours)} & \\textbf{2.888} & \\textbf{2.701} & \\textbf{2.577} & \\textbf{2.458} & \\textbf{5.054} & \\textbf{4.992} & \\textbf{7.869} \\\\\n","\\bottomrule\n","\\end{tabular}}\n","\\endgroup\n","\\end{table*}\n"],["\\begin{table*}[h]\n","\\centering\n","\\caption{Performance of LLaMA-2-7B on standard LLM benchmarks under different quantization and PI settings. Zero-shot accuracy on 5 tasks plus average and WikiText2 perplexity.}\n","\\vspace{-2mm}\n","\\label{tab:result-llama-2-7b}\n","\\resizebox{0.95\\textwidth}{!}{\n","\\begin{tabular}{lccccccc}\n","\\toprule\n","\\textbf{Setting} & \\textbf{ARC-C} & \\textbf{ARC-E} & \\textbf{BoolQ} & \\textbf{HellaSwag} & \\textbf{WinoGrande} & \\textbf{5-shot Avg.} & \\textbf{WikiText2 PPL} \\\\\n","\\midrule\n","\\multicolumn{8}{c}{\\emph{Base Context (4096 context window length)}} \\\\\n","\\midrule\n","Baseline FP16 & 52.3 & 80.1 & 76.2 & 78.9 & 67.7 & 70.83 & 5.47 \\\\\n","RTN W4 & 48.6 & 76.5 & 72.4 & 74.1 & 59.1 & 64.14 & 5.73 \\\\\n","RTN W4-A4 & 47.2 & 75.0 & 71.3 & 72.8 & 57.9 & 62.02 & 5.92 \\\\\n","AWQ W4 & 48.9 & 76.8 & 73.1 & 74.9 & 59.6 & 64.25 & 5.61 \\\\\n","AWQ W4-A4 & 47.5 & 75.2 & 71.7 & 73.2 & 58.1 & 62.31 & 5.77 \\\\\n","\\midrule\n","\\multicolumn{8}{c}{\\emph{Extended Context with YaRN (32K context window length, $s{=}8$)}} \\\\\n","\\midrule\n","Baseline FP16 & 48.7 & 75.6 & 72.0 & 73.5 & 58.6 & 63.71 & 6.09 \\\\\n","RTN W4 & 48.0 & 75.1 & 71.4 & 72.8 & 57.7 & 63.32 & 6.41 \\\\\n","RTN W4-A4 & 47.1 & 74.6 & 70.9 & 72.0 & 57.4 & 62.84 & 6.60 \\\\\n","AWQ W4 & 48.3 & 75.3 & 71.9 & 73.1 & 58.0 & 63.52 & 6.31 \\\\\n","AWQ W4-A4 & 47.3 & 74.8 & 70.8 & 72.3 & 57.2 & 62.53 & 6.49 \\\\\n","\\midrule\n","\\textbf{Q-ROAR W4} & \\textbf{49.0} & \\textbf{75.9} & \\textbf{72.4} & \\textbf{73.8} & \\textbf{58.6} & \\textbf{63.96} & \\textbf{6.18} \\\\\n","\\textbf{Q-ROAR W4-A4} & \\textbf{48.2} & \\textbf{75.2} & \\textbf{71.7} & \\textbf{73.0} & \\textbf{58.2} & \\textbf{63.21} & \\textbf{6.39} \\\\\n","\\bottomrule\n","\\end{tabular}}\n","\\end{table*}\n"],["\\begin{table*}[h]\n","\\centering\n","\\caption{GovReport perplexity on \\textbf{Vicuna-7B} (YaRN = 16)}\n","\\label{tab:govreport-Vicuna}\n","\\begingroup\n","\\setlength{\\tabcolsep}{5pt}\n","\\resizebox{0.8\\textwidth}{!}{\n","\\begin{tabular}{cc|ccccc}\n","\\toprule\n","\\multirow{2}{*}{Setting} & \\multirow{2}{*}{\\shortstack{Context Length \\\\ (YaRN = 16)}} & \\multicolumn{5}{c}{Evaluation Context Window Size} \\\\\n"," & & 2048 & 4096 & 8192 & 16384 & 32768 \\\\\n","\\midrule\n","FP16 & 64K & 4.504 & 4.424 & 4.394 & 4.238 & 6.251 \\\\\n","RTN W4 & 64K & 4.612 & 4.552 & 4.537 & 4.644 & 6.986 \\\\\n","AWQ W4 & 64K & 4.556 & 4.487 & 4.471 & 4.480 & 6.491 \\\\\n","\\textbf{Q-ROAR W4} & 64K & \\textbf{4.508} & \\textbf{4.459} & \\textbf{4.386} & \\textbf{4.244} & \\textbf{6.008} \\\\\n","\\bottomrule\n","\\end{tabular}%\n","}\n","\\endgroup\n","\n","\\end{table*}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=0.8\\textwidth]{publication_figures/figure_3_position_interpolation.pdf}\n"," \\caption{\\textbf{Position Interpolation Methods Comparison.} Performance comparison of NTK-aware scaling, YARN interpolation, and no interpolation across FP16 and AWQ quantized models. YARN consistently demonstrates superior performance for long-context extension, maintaining lower perplexity degradation as sequence length increases.}\n"," \\label{fig:position_interpolation_main}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/yarn_vs_ntk_detailed_comparison.pdf}\n"," \\caption{\\textbf{Detailed YARN vs NTK Analysis.} In-depth comparison showing (a) direct performance comparison, (b) relative improvement of YARN over NTK, (c) scaling factor analysis, and (d) convergence behavior. YARN shows consistent advantages, particularly at longer sequence lengths with up to 15\\% relative improvement over NTK interpolation.}\n"," \\label{fig:yarn_ntk_detailed}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/interpolation_method_deep_dive.pdf}\n"," \\caption{\\textbf{Interpolation Method Deep Dive Analysis.} Comprehensive analysis across four dimensions: (a) method comparison with error bars, (b) relative performance improvements, (c) sequence length sensitivity analysis, and (d) convergence stability metrics. Results demonstrate YARN's robustness across different evaluation criteria.}\n"," \\label{fig:interpolation_deep_dive}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=0.8\\textwidth]{publication_figures/figure_1_main_comparison.pdf}\n"," \\caption{\\textbf{Main Quantization Methods Comparison.} Performance evaluation of primary quantization techniques across extended sequences. NF4 achieves the best quality-compression trade-off, while AWQ provides an excellent balance between performance and efficiency for practical deployment.}\n"," \\label{fig:quantization_main}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/quantization_precision_comparison.pdf}\n"," \\caption{\\textbf{Quantization Precision Analysis.} Detailed comparison of quantization methods showing (a) perplexity vs sequence length, (b) memory efficiency metrics, (c) compression ratios, and (d) quality-efficiency Pareto frontier. NF4 emerges as the optimal choice for quality-sensitive applications.}\n"," \\label{fig:quantization_precision}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/weight_vs_activation_quantization.pdf}\n"," \\caption{\\textbf{Weight vs Activation Quantization Effects.} Comparative analysis of weight-only versus weight+activation quantization strategies. Results show that activation quantization introduces additional performance degradation but enables higher compression ratios and inference speed improvements.}\n"," \\label{fig:weight_activation_quant}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/advanced_quantization_techniques.pdf}\n"," \\caption{\\textbf{Advanced Quantization Techniques.} Analysis of sophisticated quantization methods including mixed-precision strategies and adaptive quantization. Advanced techniques show promise for further improving the quality-efficiency trade-off.}\n"," \\label{fig:advanced_quantization}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{publication_figures/figure_2_hadamard_effects.pdf}\n"," \\caption{\\textbf{Hadamard Transformation Effects.} Impact of Hadamard transformations on (a) weight-only quantization and (b) weight+activation quantization across different projection layers (gate, up, down). Hadamard transformations show more significant benefits for weight+activation scenarios.}\n"," \\label{fig:hadamard_main}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/hadamard_layer_analysis.pdf}\n"," \\caption{\\textbf{Layer-wise Hadamard Analysis.} Detailed examination of Hadamard effects across different transformer layers and projection types. Analysis reveals (a) per-layer sensitivity, (b) projection-specific benefits, (c) cumulative effects, and (d) optimization convergence patterns.}\n"," \\label{fig:hadamard_layers}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/prequantization_effects.pdf}\n"," \\caption{\\textbf{Pre-quantization Transformation Effects.} Analysis of various pre-quantization transformations including Hadamard, rotation, and scaling operations. Results demonstrate the importance of proper transformation selection for different quantization schemes.}\n"," \\label{fig:prequantization}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/temperature_scaling_analysis.pdf}\n"," \\caption{\\textbf{Temperature Scaling Analysis.} Comprehensive study of temperature effects on quantization performance showing (a) temperature sensitivity curves, (b) calibration stability, and long-context behavior. Proper temperature selection can improve performance by 5-10\\%.}\n"," \\label{fig:temperature_scaling}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/method_convergence_analysis.pdf}\n"," \\caption{\\textbf{Method Convergence Analysis.} Convergence behavior and stability analysis across different combinations of techniques. Results show convergence patterns, optimization stability, and method interaction effects critical for reliable deployment.}\n"," \\label{fig:convergence_analysis}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/sensitivity_1.png}\n"," \\caption{\\textbf{Channel Response Sensitivity.} Testing each channel responses on Q,K projection layer weight rescaling (all attention layers) with fixed factor 2}\n"," \\label{fig:Channel_Response_analysis}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/channel_response_analysis.pdf}\n"," \\caption{\\textbf{Channel Response Analysis.} Analysis of channel-wise activation patterns and their impact on quantization performance. Results show channel importance distributions, optimization opportunities, and adaptive quantization potential.}\n"," \\label{fig:channel_response}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/embedding_only_modifications.pdf}\n"," \\caption{\\textbf{Embedding-Only Modifications.} Specialized analysis of embedding layer modifications showing (a) embedding quantization effects, (b) vocabulary adaptation strategies, (c) position encoding modifications, and (d) combined optimization approaches. Embedding modifications can provide targeted improvements for specific use cases.}\n"," \\label{fig:embedding_analysis}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/comprehensive_method_comparison.pdf}\n"," \\caption{\\textbf{Comprehensive Method Comparison Matrix.} Complete comparison matrix showing performance, efficiency, and complexity trade-offs across all method combinations. This analysis guides optimal configuration selection for different deployment constraints and quality requirements.}\n"," \\label{fig:comprehensive_comparison}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/sequence_length_breakdown.pdf}\n"," \\caption{\\textbf{Sequence Length Breakdown Analysis.} Detailed performance analysis across different sequence length ranges showing (a) short-context performance, (b) medium-context behavior, (c) long-context scalability, and (d) extrapolation capabilities. Critical for understanding method applicability across different use cases.}\n"," \\label{fig:sequence_breakdown}\n","\\end{figure}\n"],["\\begin{figure}[h!]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{ablation_plots/statistical_analysis.pdf}\n"," \\caption{\\textbf{Statistical Analysis and Error Patterns.} Statistical significance testing and error pattern analysis across all experimental conditions. Results provide confidence intervals, significance levels, and systematic error identification for robust conclusions.}\n"," \\label{fig:statistical_analysis}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{activation_analysis_plots/outlier_shifting_analysis.pdf}\n"," \\caption{Outlier shifting patterns across PI methods showing (a) outlier magnitude distributions for activations exceeding 3$\\sigma$ threshold, (b) spatial distribution of outliers along sequence positions, (c) channel-wise outlier occurrence analysis, and (d) correlation analysis between baseline and PI method outlier patterns.}\n"," \\label{fig:outlier_shifting_analysis}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{activation_analysis_plots/tail_growth_analysis.pdf}\n"," \\caption{Pre-activation tail growth analysis showing (a) tail ratio comparison, (b) outlier fractions, (c) distribution kurtosis, (d) layer-wise progression, (e) distribution comparison, and (f) weight-error amplification factors across PI methods.}\n"," \\label{fig:tail_growth_analysis}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{activation_analysis_plots/amplitude_growth_analysis.pdf}\n"," \\caption{Amplitude growth analysis showing (a) concentration factors, (b) peak amplitudes, (c) channel distribution, (d) layer progression, (e) clipping risk, and (f) spatial patterns for activation quantization assessment.}\n"," \\label{fig:amplitude_growth_analysis}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{activation_analysis_plots/comprehensive_pi_effects.pdf}\n"," \\caption{Comprehensive PI effects showing (a) $\\rho^W$ vs $\\rho^A$ trade-offs, (b) layer-wise progression, (c) quantization difficulty prediction, and (d) performance-efficiency analysis.}\n"," \\label{fig:comprehensive_pi_effects}\n","\\end{figure}\n"]],"string":"[\n [\n \"\\\\begin{figure*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[t]{0.49\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{four_methods_no_pi_style2.pdf}\\n\",\n \" \\\\caption{Non-Interpolated models}\\n\",\n \" \\\\label{left}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\hfill\\n\",\n \"\\\\begin{subfigure}[t]{0.5\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{five_methods_aaai_style2.pdf}\\n\",\n \" \\\\caption{YaRN interpolation (s = 8)}\\n\",\n \" \\\\label{right}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\vspace{-2mm}\\n\",\n \"\\\\caption{Perplexity of quantized Llama-2-7b evaluated on the GovReport Dataset}\\n\",\n \"\\\\label{fig:ppl}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{GovReport perplexity on LLaMA-2-7B across evaluation context sizes (lower is better).}\\n\",\n \"\\\\vspace{-2mm}\\n\",\n \"\\\\label{tab:govreport-multisize}\\n\",\n \"\\\\begingroup\\n\",\n \"\\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \"\\n\",\n \"\\\\resizebox{0.8\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{lc|ccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multirow{2}{*}{Setting} & \\\\multirow{2}{*}{\\\\shortstack{Context Length \\\\\\\\ (YaRN = 16)}} & \\\\multicolumn{5}{c}{Evaluation Context Window Size} \\\\\\\\\\n\",\n \" & &2048 & 4096 &8192 & 16384 & 32768 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"FP16 & 64K & 4.437 & 4.359 & 4.329 & 4.175 & 6.069 \\\\\\\\\\n\",\n \"RTN W4 & 64K & 4.544 & 4.485 & 4.470 & 4.575 & 6.783 \\\\\\\\\\n\",\n \"AWQ W4 & 64K & 4.489 & 4.421 & 4.405 & 4.414 & 6.302 \\\\\\\\\\n\",\n \"\\\\textbf{Q-ROAR W4 (ours)} & 64K & \\\\textbf{4.441} & \\\\textbf{4.393} & \\\\textbf{4.321} & \\\\textbf{4.181} & \\\\textbf{5.833} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}%\\n\",\n \"}\\n\",\n \"\\\\endgroup\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Proof-pile perplexity on LLaMA-2-7B across evaluation context sizes (lower is better). Values at $\\\\leq$16K use YaRN scale factor $s{=}8$; values at $\\\\geq$32K use $s{=}32$.}\\n\",\n \"\\\\vspace{-2mm}\\n\",\n \"\\\\label{tab:proofpile-multisize}\\n\",\n \"\\\\begingroup\\n\",\n \"\\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \"\\\\resizebox{0.8\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l|cccc|ccc}\\n\",\n \"\\\\toprule\\n\",\n \"Setting & \\\\multicolumn{4}{c|}{Evaluation Context (s=8)} & \\\\multicolumn{3}{c}{Evaluation Context (s=32)} \\\\\\\\\\n\",\n \" & 2048 & 4096 & 8192 & 16384 & 32768 & 65536 & 131072 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"FP16 & 2.847 & 2.667 & 2.543 & 2.438 & 4.261 & 4.074 & 5.386 \\\\\\\\\\n\",\n \"RTN W4 & 2.917 & 2.739 & 2.613 & 2.517 & 6.249 & 6.187 & 9.958 \\\\\\\\\\n\",\n \"AWQ W4 & 2.891 & 2.709 & 2.583 & 2.476 & 5.460 & 5.410 & 8.700 \\\\\\\\\\n\",\n \"\\\\textbf{Q-ROAR W4 (ours)} & \\\\textbf{2.888} & \\\\textbf{2.701} & \\\\textbf{2.577} & \\\\textbf{2.458} & \\\\textbf{5.054} & \\\\textbf{4.992} & \\\\textbf{7.869} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}}\\n\",\n \"\\\\endgroup\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Performance of LLaMA-2-7B on standard LLM benchmarks under different quantization and PI settings. Zero-shot accuracy on 5 tasks plus average and WikiText2 perplexity.}\\n\",\n \"\\\\vspace{-2mm}\\n\",\n \"\\\\label{tab:result-llama-2-7b}\\n\",\n \"\\\\resizebox{0.95\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{lccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Setting} & \\\\textbf{ARC-C} & \\\\textbf{ARC-E} & \\\\textbf{BoolQ} & \\\\textbf{HellaSwag} & \\\\textbf{WinoGrande} & \\\\textbf{5-shot Avg.} & \\\\textbf{WikiText2 PPL} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{8}{c}{\\\\emph{Base Context (4096 context window length)}} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Baseline FP16 & 52.3 & 80.1 & 76.2 & 78.9 & 67.7 & 70.83 & 5.47 \\\\\\\\\\n\",\n \"RTN W4 & 48.6 & 76.5 & 72.4 & 74.1 & 59.1 & 64.14 & 5.73 \\\\\\\\\\n\",\n \"RTN W4-A4 & 47.2 & 75.0 & 71.3 & 72.8 & 57.9 & 62.02 & 5.92 \\\\\\\\\\n\",\n \"AWQ W4 & 48.9 & 76.8 & 73.1 & 74.9 & 59.6 & 64.25 & 5.61 \\\\\\\\\\n\",\n \"AWQ W4-A4 & 47.5 & 75.2 & 71.7 & 73.2 & 58.1 & 62.31 & 5.77 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{8}{c}{\\\\emph{Extended Context with YaRN (32K context window length, $s{=}8$)}} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Baseline FP16 & 48.7 & 75.6 & 72.0 & 73.5 & 58.6 & 63.71 & 6.09 \\\\\\\\\\n\",\n \"RTN W4 & 48.0 & 75.1 & 71.4 & 72.8 & 57.7 & 63.32 & 6.41 \\\\\\\\\\n\",\n \"RTN W4-A4 & 47.1 & 74.6 & 70.9 & 72.0 & 57.4 & 62.84 & 6.60 \\\\\\\\\\n\",\n \"AWQ W4 & 48.3 & 75.3 & 71.9 & 73.1 & 58.0 & 63.52 & 6.31 \\\\\\\\\\n\",\n \"AWQ W4-A4 & 47.3 & 74.8 & 70.8 & 72.3 & 57.2 & 62.53 & 6.49 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Q-ROAR W4} & \\\\textbf{49.0} & \\\\textbf{75.9} & \\\\textbf{72.4} & \\\\textbf{73.8} & \\\\textbf{58.6} & \\\\textbf{63.96} & \\\\textbf{6.18} \\\\\\\\\\n\",\n \"\\\\textbf{Q-ROAR W4-A4} & \\\\textbf{48.2} & \\\\textbf{75.2} & \\\\textbf{71.7} & \\\\textbf{73.0} & \\\\textbf{58.2} & \\\\textbf{63.21} & \\\\textbf{6.39} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{GovReport perplexity on \\\\textbf{Vicuna-7B} (YaRN = 16)}\\n\",\n \"\\\\label{tab:govreport-Vicuna}\\n\",\n \"\\\\begingroup\\n\",\n \"\\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \"\\\\resizebox{0.8\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{cc|ccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multirow{2}{*}{Setting} & \\\\multirow{2}{*}{\\\\shortstack{Context Length \\\\\\\\ (YaRN = 16)}} & \\\\multicolumn{5}{c}{Evaluation Context Window Size} \\\\\\\\\\n\",\n \" & & 2048 & 4096 & 8192 & 16384 & 32768 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"FP16 & 64K & 4.504 & 4.424 & 4.394 & 4.238 & 6.251 \\\\\\\\\\n\",\n \"RTN W4 & 64K & 4.612 & 4.552 & 4.537 & 4.644 & 6.986 \\\\\\\\\\n\",\n \"AWQ W4 & 64K & 4.556 & 4.487 & 4.471 & 4.480 & 6.491 \\\\\\\\\\n\",\n \"\\\\textbf{Q-ROAR W4} & 64K & \\\\textbf{4.508} & \\\\textbf{4.459} & \\\\textbf{4.386} & \\\\textbf{4.244} & \\\\textbf{6.008} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}%\\n\",\n \"}\\n\",\n \"\\\\endgroup\\n\",\n \"\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\textwidth]{publication_figures/figure_3_position_interpolation.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Position Interpolation Methods Comparison.} Performance comparison of NTK-aware scaling, YARN interpolation, and no interpolation across FP16 and AWQ quantized models. YARN consistently demonstrates superior performance for long-context extension, maintaining lower perplexity degradation as sequence length increases.}\\n\",\n \" \\\\label{fig:position_interpolation_main}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/yarn_vs_ntk_detailed_comparison.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Detailed YARN vs NTK Analysis.} In-depth comparison showing (a) direct performance comparison, (b) relative improvement of YARN over NTK, (c) scaling factor analysis, and (d) convergence behavior. YARN shows consistent advantages, particularly at longer sequence lengths with up to 15\\\\% relative improvement over NTK interpolation.}\\n\",\n \" \\\\label{fig:yarn_ntk_detailed}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/interpolation_method_deep_dive.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Interpolation Method Deep Dive Analysis.} Comprehensive analysis across four dimensions: (a) method comparison with error bars, (b) relative performance improvements, (c) sequence length sensitivity analysis, and (d) convergence stability metrics. Results demonstrate YARN's robustness across different evaluation criteria.}\\n\",\n \" \\\\label{fig:interpolation_deep_dive}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\textwidth]{publication_figures/figure_1_main_comparison.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Main Quantization Methods Comparison.} Performance evaluation of primary quantization techniques across extended sequences. NF4 achieves the best quality-compression trade-off, while AWQ provides an excellent balance between performance and efficiency for practical deployment.}\\n\",\n \" \\\\label{fig:quantization_main}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/quantization_precision_comparison.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Quantization Precision Analysis.} Detailed comparison of quantization methods showing (a) perplexity vs sequence length, (b) memory efficiency metrics, (c) compression ratios, and (d) quality-efficiency Pareto frontier. NF4 emerges as the optimal choice for quality-sensitive applications.}\\n\",\n \" \\\\label{fig:quantization_precision}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/weight_vs_activation_quantization.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Weight vs Activation Quantization Effects.} Comparative analysis of weight-only versus weight+activation quantization strategies. Results show that activation quantization introduces additional performance degradation but enables higher compression ratios and inference speed improvements.}\\n\",\n \" \\\\label{fig:weight_activation_quant}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/advanced_quantization_techniques.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Advanced Quantization Techniques.} Analysis of sophisticated quantization methods including mixed-precision strategies and adaptive quantization. Advanced techniques show promise for further improving the quality-efficiency trade-off.}\\n\",\n \" \\\\label{fig:advanced_quantization}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{publication_figures/figure_2_hadamard_effects.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Hadamard Transformation Effects.} Impact of Hadamard transformations on (a) weight-only quantization and (b) weight+activation quantization across different projection layers (gate, up, down). Hadamard transformations show more significant benefits for weight+activation scenarios.}\\n\",\n \" \\\\label{fig:hadamard_main}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/hadamard_layer_analysis.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Layer-wise Hadamard Analysis.} Detailed examination of Hadamard effects across different transformer layers and projection types. Analysis reveals (a) per-layer sensitivity, (b) projection-specific benefits, (c) cumulative effects, and (d) optimization convergence patterns.}\\n\",\n \" \\\\label{fig:hadamard_layers}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/prequantization_effects.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Pre-quantization Transformation Effects.} Analysis of various pre-quantization transformations including Hadamard, rotation, and scaling operations. Results demonstrate the importance of proper transformation selection for different quantization schemes.}\\n\",\n \" \\\\label{fig:prequantization}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/temperature_scaling_analysis.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Temperature Scaling Analysis.} Comprehensive study of temperature effects on quantization performance showing (a) temperature sensitivity curves, (b) calibration stability, and long-context behavior. Proper temperature selection can improve performance by 5-10\\\\%.}\\n\",\n \" \\\\label{fig:temperature_scaling}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/method_convergence_analysis.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Method Convergence Analysis.} Convergence behavior and stability analysis across different combinations of techniques. Results show convergence patterns, optimization stability, and method interaction effects critical for reliable deployment.}\\n\",\n \" \\\\label{fig:convergence_analysis}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/sensitivity_1.png}\\n\",\n \" \\\\caption{\\\\textbf{Channel Response Sensitivity.} Testing each channel responses on Q,K projection layer weight rescaling (all attention layers) with fixed factor 2}\\n\",\n \" \\\\label{fig:Channel_Response_analysis}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/channel_response_analysis.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Channel Response Analysis.} Analysis of channel-wise activation patterns and their impact on quantization performance. Results show channel importance distributions, optimization opportunities, and adaptive quantization potential.}\\n\",\n \" \\\\label{fig:channel_response}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/embedding_only_modifications.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Embedding-Only Modifications.} Specialized analysis of embedding layer modifications showing (a) embedding quantization effects, (b) vocabulary adaptation strategies, (c) position encoding modifications, and (d) combined optimization approaches. Embedding modifications can provide targeted improvements for specific use cases.}\\n\",\n \" \\\\label{fig:embedding_analysis}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/comprehensive_method_comparison.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Comprehensive Method Comparison Matrix.} Complete comparison matrix showing performance, efficiency, and complexity trade-offs across all method combinations. This analysis guides optimal configuration selection for different deployment constraints and quality requirements.}\\n\",\n \" \\\\label{fig:comprehensive_comparison}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/sequence_length_breakdown.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Sequence Length Breakdown Analysis.} Detailed performance analysis across different sequence length ranges showing (a) short-context performance, (b) medium-context behavior, (c) long-context scalability, and (d) extrapolation capabilities. Critical for understanding method applicability across different use cases.}\\n\",\n \" \\\\label{fig:sequence_breakdown}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[h!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{ablation_plots/statistical_analysis.pdf}\\n\",\n \" \\\\caption{\\\\textbf{Statistical Analysis and Error Patterns.} Statistical significance testing and error pattern analysis across all experimental conditions. Results provide confidence intervals, significance levels, and systematic error identification for robust conclusions.}\\n\",\n \" \\\\label{fig:statistical_analysis}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{activation_analysis_plots/outlier_shifting_analysis.pdf}\\n\",\n \" \\\\caption{Outlier shifting patterns across PI methods showing (a) outlier magnitude distributions for activations exceeding 3$\\\\sigma$ threshold, (b) spatial distribution of outliers along sequence positions, (c) channel-wise outlier occurrence analysis, and (d) correlation analysis between baseline and PI method outlier patterns.}\\n\",\n \" \\\\label{fig:outlier_shifting_analysis}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{activation_analysis_plots/tail_growth_analysis.pdf}\\n\",\n \" \\\\caption{Pre-activation tail growth analysis showing (a) tail ratio comparison, (b) outlier fractions, (c) distribution kurtosis, (d) layer-wise progression, (e) distribution comparison, and (f) weight-error amplification factors across PI methods.}\\n\",\n \" \\\\label{fig:tail_growth_analysis}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{activation_analysis_plots/amplitude_growth_analysis.pdf}\\n\",\n \" \\\\caption{Amplitude growth analysis showing (a) concentration factors, (b) peak amplitudes, (c) channel distribution, (d) layer progression, (e) clipping risk, and (f) spatial patterns for activation quantization assessment.}\\n\",\n \" \\\\label{fig:amplitude_growth_analysis}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{activation_analysis_plots/comprehensive_pi_effects.pdf}\\n\",\n \" \\\\caption{Comprehensive PI effects showing (a) $\\\\rho^W$ vs $\\\\rho^A$ trade-offs, (b) layer-wise progression, (c) quantization difficulty prediction, and (d) performance-efficiency analysis.}\\n\",\n \" \\\\label{fig:comprehensive_pi_effects}\\n\",\n \"\\\\end{figure}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n\\documentclass{article} % For LaTeX2e\n\\usepackage{iclr2026_conference,times}\n\n% Optional math commands from https://github.com/goodfeli/dlbook_notation.\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n% Figure reference, capital. 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chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\\newcommand{\\IP}{\\ensuremath{\\mathrm{IP}}}\n\\newcommand{\\TIR}{\\mathrm{TIR}}\n\n\\usepackage{hyperref}\n\\usepackage{url}\n\\usepackage{cleveref}\n\\usepackage{amssymb}\n\\usepackage{algorithm}\n\\usepackage{algorithmicx}\n\\usepackage{algpseudocode}\n\\usepackage{booktabs}\n\\usepackage{graphicx}\n\\usepackage{multirow}\n\\usepackage{subcaption}\n% \\usepackage{pgfplots}\\pgfplotsset{compat=1.18}\n\\title{Rethinking RoPE Scaling in Quantized LLM: Theory, Outlier, and Channel-Band Analysis with Weight Rescaling}\n\n% Authors must not appear in the submitted version. They should be hidden\n% as long as the \\iclrfinalcopy macro remains commented out below.\n% Non-anonymous submissions will be rejected without review.\n\n\\author{\nYe Qiao\\textsuperscript{1} \\quad\nHaocheng Xu\\textsuperscript{1} \\quad\nXiaofan Zhang\\textsuperscript{2} \\quad\nSitao Huang\\textsuperscript{1} \\\\\n\\textsuperscript{1}Department of EECS, University of California, Irvine, USA \\\\\n\\textsuperscript{2}Google \\\\\n}\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to \\LaTeX{} to determine where to break\n% the lines. Using \\AND forces a linebreak at that point. So, if \\LaTeX{}\n% puts 3 of 4 authors names on the first line, and the last on the second\n% line, try using \\AND instead of \\And before the third author name.\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\n\\ifx\\forsubmission\\undefined\n\\newcommand{\\TODO}[1]{\\textcolor{red}{TODO: #1}}\n\\else\n\\newcommand{\\TODO}[1]{\\textcolor{red}{}}\n\\fi\n\n\\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission.\n\\begin{document}\n\n\n\\maketitle\n\n\n\\begin{abstract}\nExtending the context window support of large language models (LLMs) is crucial for tasks with long-distance dependencies. RoPE-based interpolation and extrapolation methods, such as linear scaling and frequency-aware schemes, enable longer input length support without retraining, while post-training quantization (PTQ) makes deployment practical. However, we show that \\emph{combining} RoPE position interpolation (PI) with PTQ degrades accuracy due to coupled effects including long-context aliasing, dynamic-range dilation, anisotropy from axis-aligned quantizers vs. rotated RoPE pairs, and outlier shifting that produces position-dependent logit noise. We provide, to the best of our knowledge, the first systematic analysis of the PI+PTQ approach and introduce two practical diagnostics: \\emph{interpolation pressure} (per-band sensitivity to phase scaling) and \\emph{tail-inflation ratios} (outlier shift from short to long contexts). Following the analysis results, we propose \\textbf{Q-ROAR} (Quantization, RoPE-interpolation, and Outlier Aware Rescaling), a \\emph{weight-only}, interpolation-aware stabilization of PI for quantized LLMs. Q-ROAR groups RoPE dimensions into a small number of frequency bands and performs a lightweight search over per-band scales for \\textit{Key} and \\textit{Query} weights (with an optional symmetric variant to preserve logit scale). The search is guided by our diagnostics and uses a tiny long-context development dataset, requiring no fine-tuning to the model, no architecture or kernel changes, and no additional deployment overhead. Empirically, Q-ROAR reduces the model's perplexity on long-context workloads by more than 14\\%, while preserving short-context performance, inference throughput, and compatibility with existing LLM system stacks.\n\\end{abstract}\n% \\begin{abstract}\n% Extending the context window of large language models (LLMs) is crucial for tasks with long range dependencies. Existing RoPE-based interpolation and extrapolation method using linear scaling or frequency-aware schemes, can enable longer context support beyond the original design without retraining the models. These methods, in general, work with post-training quantization (PTQ) when models are being deployed to reduce serving costs. Despite their practicality, we find that combining RoPE position interpolation (PI) with PTQ degrades model quality significantly due to coupled effects, including long-context aliasing, dynamic-range dilation, anisotropy from axis aligned quantizers vs. rotated RoPE pairs, and outlier shifting that producing position dependent logit noise. To better understand the root cause, we provide, to our knowledge, the first systematic analysis of PI+PTQ and introduce two practical diagnostics: 1) interpolation pressure per-band sensitivity to phase scaling and 2) tail-inflation ratios (outlier shift from short to long contexts). Following the analysis results, we propose Q-ROAR (Quantized RoPE-Interpolation and Outlier Aware Rescaling), a weight-only RoPE-Quantization aware stabilization of PI. Q-ROAR groups RoPE dimensions into a small number of frequency bands and performs a lightweight search over per-band scales for $(W_Q,W_K)$ (with an optional symmetric variant to preserve logit scale). The search is guided by our diagnostics and uses a tiny long context dev set, requiring no fine-tuning, no architecture or kernel changes, and negligible overhead. Q-ROAR reduces Long-context workloads perplexity by more than 14\\%, while preserving short-context performance and compatibility with existing inference stacks.\n% \\end{abstract}\n\n\n\n\n\n\\section{Introduction}\nLarge language models (LLMs) such as GPT-3~\\citep{brown2020language}, LLaMA~\\citep{touvron2023llama}, and DeepSeek-R1~\\citep{guo2025deepseek} have advanced translation, coding, question answering, and dialogue. Yet their utility is often capped by the pretrained context window. Extending context is crucial for long-form summarization~\\citep{liu2023lostmiddlelanguagemodels}, code completion, retrieval-augmented generation (RAG)~\\citep{lewis2021retrievalaugmentedgenerationknowledgeintensivenlp}, chain-of-thought~\\citep{wei2023chainofthoughtpromptingelicitsreasoning}, and agentic pipelines, which rely on long-range (long-distance) dependencies and rich cross-document context.\n\nA popular path to longer contexts is to modify positional encoding at inference. RoPE-based scaling methods including linear interpolation~\\citep{chen2023extending}, frequency-aware YaRN~\\citep{peng2023yarn}, and evolutionary LongRoPE~\\citep{ding2024longrope}. They warp per-dimension phases so the model can read beyond its original window without retraining. Conceptually, many such methods fit a unified view in which positions are warped and per-dimension phase growth is rescaled. This preserves the rotation’s orthogonality while changing how fast phases accumulate.\n\nMeanwhile, practical deployment increasingly depends on \\textbf{post-training quantization (PTQ)} such as GPTQ~\\citep{frantar2022gptq}, SmoothQuant~\\citep{xiao2023smoothquant}, and AWQ~\\citep{lin2024awq} to reduce memory footprint and latency across servers and edge devices. PTQ operates with diverse precision settings (weight-only quantization or weight+activation quantization). A well-known challenge for quantized model is activation outliers: rare, high-magnitude coordinates inflate quantization clipping ranges and waste effective bits, degrading accuracy~\\citep{liu2024spinquant}.\n\nWe observe that simply applying RoPE \\textbf{position interpolation (PI)} to PTQ models degrades accuracy both inside and especially beyond the original window. Our analysis attributes this to \\emph{coupled} mechanisms: (i) \\textit{long-context aliasing} from rapidly wrapping phases; (ii) \\textit{dynamic-range dilation} as pre-activations shift under PI; (iii) \\textit{anisotropy} because axis-aligned quantizers see RoPE-rotated pairs at changing angles; and (iv) \\textit{outlier shifting/amplification} as tails move and concentrate under new phase trajectories. We formalize a sensitivity indicator, \\emph{interpolation pressure}, which rises for higher-frequency bands, and show how PI and quantization errors interact in attention logits through position-dependent perturbations.\n% \\paragraph{Why not tune activations?}\n% Under PI, activation statistics become content-, position-, and history-dependent: the same channel can swing from well-calibrated to clipped as phases crowd across the sequence. Correcting activation quantization reliably would require runtime adaptation, larger calibration sets, and kernel changes—hurting portability. In contrast, weight perturbations are static after quantization and their effect on queries/keys is linear and position-invariant under RoPE, making weight-space adjustments predictable and backend-agnostic.\n\nWe propose \\textbf{Q-ROAR} (Quantization, RoPE-interpolation, and Outlier Aware Rescaling) to mitigate the challenges. Q-ROAR groups RoPE dimensions into a small number of frequency \\emph{bands} and searches for lightweight, per-band scales for $(W_Q,W_K)$ that minimize perplexity on a tiny long-context development dataset. Two simple diagnostics guide a safe, light search: (i) \\emph{interpolation pressure} to avoid over-perturbing high-frequency bands; and (ii) \\emph{tail-inflation ratios} that summarize PI-induced outlier shift from short to long contexts. We adopt a symmetric scaling option ($W_Q\\!\\leftarrow\\!g_b W_Q$, $W_K\\!\\leftarrow\\!g_b^{-1} W_K$) to keep logit magnitudes stable. The method is a drop-in, quantizer- and backend-agnostic adjustment that requires no fine-tuning, no architecture changes, and no additional runtime overhead. Our contribution can be summarized as follows. \n%% \\paragraph{Contributions.}\n\\begin{itemize}\n\\item \\textbf{Analysis of the coupled PI+PTQ approach.} We provide a unified analysis which explains why PI harms quantized models: aliasing, dynamic-range dilation, anisotropy, and outlier shift reinforce one another and manifest as position-dependent logit noise.\n\\item \\textbf{Actionable diagnostics.} We introduce \\emph{interpolation pressure} (per-band PI sensitivity) and \\emph{tail-inflation} (outlier shift from short to long contexts) as practical signals to guide robust, frequency-selective interventions.\n\\item \\textbf{Weight-only, band-limited rescaling.} We present Q-ROAR, which searches over a tiny, log-spaced grid of per-band \\emph{weight} scales for $(W_Q,W_K)$, with symmetric scaling to preserve logit scale and safe bounds to avoid clipping or underflow in quantization.\n\\item \\textbf{Portability and improved performance.} Q-ROAR integrates with common PTQ baselines and improves long-context performance across benchmarks, while maintaining compatibility with existing computing kernels and LLM serving system stacks. We report consistent performance improvements ($>14\\%$) on extended-context evaluations with no inference overhead and no retraining.\n\\end{itemize}\n% Our method targets weight-quantized LLMs that use RoPE and PI at inference. We assume standard PTQ workflows (per-tensor/group scales) and do not require changes to activation/KV quantization. The analysis focuses on attention modules (via $W_Q,W_K$) where phase geometry directly impacts logits; other blocks remain unchanged.\n\n\n\\section{Background and Preliminary Study}\n\\subsection{RoPE Basics}\nUnlike recurrent neural networks, transformer models do not have natural position information and rely on added positional encoding. The original transformer model~\\citep{NIPS2017_3f5ee243} utilizes sinusoidal absolute positional encoding, while it claims similar results with learnable encoding. %% also test out learnable encoding and claim obtain similar results. \nRotary Position Embedding (RoPE)~\\citep{su2024roformer} on the other hand, as a method that consider both absolute and relative positional information, has been widely adopted in transformer-based LLMs. RoPE injects position information by applying a position-dependent \\emph{rotation} to each adjacent 2D coordinate pair of the $d$-dimensional vector (hidden dimension), yielding attention that depends on \\emph{relative} positions while preserving norms. Let $x\\in\\mathbb{R}^d$ with even $d$ (if $d$ is odd, a trailing zero can be appended in practice). Define a frequency vector $\\boldsymbol{\\theta}\\in\\mathbb{R}_{>0}^{d/2}$ with components\n$\\theta_i=b^{-2i/d}$ for $i=0,\\ldots,\\frac{d}{2}-1$ and base $b{=}10{,}000$ unless stated otherwise.\nFor a position index $p\\in\\mathbb{N}$, the RoPE transform is the linear map\n\\begin{equation}\n\\mathrm{RoPE}(x,p)\\;=\\; \\mathbf{R}(p)\\,x,\\qquad\n\\mathbf{R}(p)\\;=\\;\\operatorname{diag}\\!\\left(\\mathbf{R}_2(p\\theta_0),\\ldots,\\mathbf{R}_2(p\\theta_{\\frac{d}{2}-1})\\right),\n\\end{equation}\nwhere each $2{\\times}2$ block is the planar rotation\n\\begin{equation}\n\\mathbf{R}_2(\\alpha)\\;=\\;\n\\begin{bmatrix}\n\\cos \\alpha & -\\sin \\alpha\\\\\n\\sin \\alpha & \\phantom{-}\\cos \\alpha\n\\end{bmatrix}\n\\end{equation}\nEquivalently, if we regroup adjacent coordinates into complex entries via\n$\\phi:\\mathbb{R}^d\\!\\to\\!\\mathbb{C}^{d/2}$, $\\phi(x)_i = x_{2i} + j\\,x_{2i+1}$, with inverse $\\phi^{-1}$ given by real/imaginary parts, then\n\\begin{equation}\n\\mathrm{RoPE}(x,p)\\;=\\;\\phi^{-1}\\!\\left(\\,\\phi(x)\\odot e^{\\,j p \\boldsymbol{\\theta}}\\,\\right),\n\\end{equation}\nwhere $e^{\\,j p \\boldsymbol{\\theta}}$ applies $e^{\\,j p \\theta_i}$ elementwise and $\\odot$ denotes the element-wise product.\n\n\\textit{Orthogonality and relative-phase property.}\nEach $\\mathbf{R}_2(\\alpha)$ is orthogonal, hence $\\mathbf{R}(p)$ is orthogonal:\n$\\mathbf{R}(p)^\\top \\mathbf{R}(p) = \\mathbf{I}_{d}$ and $\\|\\mathrm{RoPE}(x,p)\\|_2=\\|x\\|_2$.\nMoreover, rotations compose additively blockwise,\n$\\mathbf{R}(p)^\\top \\mathbf{R}(p')=\\mathbf{R}(p'-p)$,\nso for any $q,k\\in\\mathbb{R}^d$,\n\\begin{equation}\n\\big(\\mathrm{RoPE}(q,p)\\big)^\\top \\mathrm{RoPE}(k,p')\n\\;=\\; q^\\top \\mathbf{R}(p'-p)\\,k,\n\\end{equation}\nwhich shows that the attention score depends only on the relative offset $\\Delta=p'-p$.\n\n\\textit{Use in multi-head attention.}\nFor a head of even dimension $d_h$ (with $d_h\\le d$), RoPE is applied independently to queries and keys:\n$\\tilde{q}=\\mathbf{R}_h(p)q$, $\\tilde{k}=\\mathbf{R}_h(p')k$ with\n$\\mathbf{R}_h(p)=\\operatorname{blkdiag}\\big(\\mathbf{R}_2(p\\theta^{(h)}_0),\\ldots,\\mathbf{R}_2(p\\theta^{(h)}_{\\frac{d_h}{2}-1})\\big)$.\nFrequencies $\\boldsymbol{\\theta}^{(h)}$ are typically shared across heads (e.g., $\\theta^{(h)}_i=b^{-2i/d_h}$), though head-specific schedules are possible. Values are usually left unrotated. RoPE introduces no additional asymptotic cost: it is a per-token, per-head $(\\sin,\\cos)$ rotation applied to $d_h/2$ pairs, preserving the compute and memory complexity of scaled dot-product attention while endowing it with both absolute and relative position awareness.\n\n\n% \\subsection{Extended Token Length Support and Positional Interpolation}\n% \\label{sec:positional_interpolation}\n% A practical way to extend the usable context of pretrained LLMs is to \\emph{modify the positional mapping at inference time} so that very long test sequences are interpreted as if they lie within the training-time range. We refer to this family as \\textbf{position interpolation/extrapolation (PI)}. PI is attractive because it requires \\emph{no} additional training (works even better if finetuned with long context data), keeps the architecture intact, and adds no overhead. Beyond position interpolation (PI), long-context capability is commonly achieved via: (i) \\emph{continued pretraining} on long sequences—often with synthetic retrieval tasks—\\citep{gao2024how,chen2023longlora}; (ii) \\emph{instruction/alignment tuning} targeted at long-range inputs \\citep{bai2024longalign,skipalign2024}; and (iii) \\emph{architectural changes}, including alternative position schemes and sparse/linear attention \\citep{su2021roformer,press2021alibi}. While effective, these generally require full or partial retraining, additional data/compute, and careful stability tuning, which can be impractical for many deployments.\n\n% Let $L_0$ be the training context window and $L \\gg L_0$ the desired test window. PI methods either (a) remap test positions $m \\mapsto \\hat{m}$ into $[0,L_0]$, or (b) rescale the per-dimension positional frequencies $\\{\\theta_i\\}_{i=1}^{d/2}$ used by the model’s rotary/phase parameters.\\footnote{We use $\\theta_i$ to denote the model’s internal per-dimension “positional frequency” parameters; details of RoPE are standard and omitted here.}\n\n% \\textbf{Linear Interpolation (LI)} \\citep{chen2023extending}.\n% Positions are uniformly compressed so the long context matches the training range:\n% \\begin{equation}\n% \\hat{m} \\;=\\; m \\cdot \\frac{L_0}{L}.\n% \\label{eq:li}\n% \\end{equation}\n% In this case, large test positions are squeezed back into $[0,L_0]$, keeping the effective positional phases within the regime the model saw during training. In this case, all hidden rotation dimension pair was slow down equally. However, local resolution is reduced by the factor $L/L_0$, which can weaken short-range attention and does not works well without finetune.\n\n% \\textbf{NTK-aware PI} \\textit{(e.g., bloc97, 2023)}. \n% on the other hand, slow \\emph{low} frequencies channels more than \\emph{high} ones by adjusting the RoPE base. If the original base is $b$ (so $\\theta_i = b^{-2(i-1)/d}$), choose a stretch $\\alpha>1$ and set\n% \\begin{equation}\n% b' \\;=\\; b \\cdot \\alpha^{\\frac{d}{\\,d-2\\,}}\n% \\quad\\Longleftrightarrow\\quad\n% \\tilde{\\theta}_i \\;=\\; \\theta_i \\cdot \\alpha^{-\\frac{2(i-1)}{\\,d-2\\,}}.\n% \\label{eq:ntk}\n% \\end{equation}\n% This method non-uniform slowdown preserves high-frequency detail (local fidelity) while still curbing long-range phase growth in low frequencies—often stronger tails than LI with little short-context regression.\n\n% \\textbf{YaRN (Frequency-Band Segmentation)}\\citep{peng2023yarn}. \n% YaRN does \\emph{not} interpolate the \\emph{high-frequency} dimensions (small wavelength $\\lambda_i$), always interpolates the \\emph{low-frequency} dimensions (large $\\lambda_i$) to avoid extrapolation, and applies an NTK-style partial interpolation in between. \n% Let $S \\!=\\! L/L_0 \\ge 1$ be the stretch and define a wavelength proxy $\\lambda_i \\propto 1/\\theta_i$. \n% YaRN sets a per-dimension slowdown exponent $g_i \\in [0,1]$ that \\emph{increases} with $\\lambda_i$:\n% \\begin{equation}\n% \\tilde{\\theta}_i \\;=\\; \\theta_i \\, S^{-g_i}, \n% \\qquad \n% g_i \\;=\\;\n% \\begin{cases}\n% 0, & \\lambda_i \\ll L \\quad \\text{(high freq; no interpolation)},\\\\[2pt]\n% 1, & \\lambda_i \\ge L \\quad \\text{(low freq; always interpolate)},\\\\[2pt]\n% \\beta_i \\in (0,1), & \\text{otherwise (NTK-like blend; increases with } \\lambda_i\\text{)}.\n% \\end{cases}\n% \\label{eq:yarn-correct}\n% \\end{equation}\n% Equivalently, low-frequency bands are linearly compressed ($m \\mapsto m/S$), high-frequency bands are left unchanged, and mid bands receive a softer, NTK-aware slowdown. \n% This preserves local detail while stabilizing long-range behavior; a mild attention-logit rescale may be used for additional stability.\n\n% \\textbf{LongRoPE (Per-Dimension Scaling)} \\textit{(Ding et al.~\\citep{ding2024longrope})}.\n% LongRoPE generalizes YaRN by assigning an independent scaling $s_i\\!\\ge\\!1$ to \\emph{each} positional dimension and searching $\\{s_i\\}$ on validation tasks:\n% \\begin{equation}\n% \\tilde{\\theta}_i \\;=\\; \\frac{\\theta_i}{s_i}, \n% \\qquad i=1,\\dots,\\tfrac{d}{2}.\n% \\label{eq:longrope}\n% \\end{equation}\n% LongRoPE allocate stronger slowdowns to the most alias-prone (typically higher-frequency) dimensions and lighter slowdowns elsewhere. \n% This heterogeneous policy has enabled extremely long effective windows (reported to millions of tokens) while preserving task performance. However it require one-time search/tuning to obtain $\\{s_i\\}$.\n\n\n% Overall, PI methods extend token length support \\emph{without finetuning} by either remapping positions (Eq.~\\ref{eq:li}) or rescaling positional frequencies (Eqs.~\\ref{eq:yarn-correct}–\\ref{eq:longrope}). \n% Linear Interpolation is the simplest but uniformly compresses local resolution; YaRN offers a band-wise compromise; LongRoPE further tailors the slowdown per dimension to maximize long-range stability with minimal impact on short-range behavior. \n\n\n% \\subsection{LLM Quantization}\n\n% To reduce the computational and memory footprint of LLMs, various low-bit post-training quantization techniques have been developed:\n\n\n% \\textbf{Weight-only}: \\textbf{RTN} is a straightforward post-training quantization method where model weights are scaled and then rounded to the nearest integer. \\textbf{GPTQ} \\citep{frantar2022gptq} solves a local quadratic optimization problem to reduce quantization error per layer and is more accurate than RTN, but computationally heavier. \\textbf{AWQ} \\citep{lin2024awq} uses calibration data to identify key weights tied to activations and retains those weights at higher precision, quantizes the rest.\n\n% \\textbf{Activation-only}: \\textbf{SmoothQuant} \\citep{xiao2023smoothquant} normalizes activations by scaling outliers across layers and uses weight scaling compensating for activation normalization, which achieves lossless 8-bit activation quantization.\n\n% \\textbf{Weights + Activations}: A promising recent line of work introduces rotation-based quantization, where weights and activations are first transformed by a rotation matrix to redistribute their values into a more quantization-friendly range. \\textbf{QuaRot} \\citep{quarot2025} pioneered this idea by using random orthogonal rotations (e.g., Hadamard transforms), showing that even non-learned rotations can improve quantization stability. \\textbf{SpinQuant}\\citep{liu2024spinquant} extends this concept by learning the rotation matrices in a data-driven way rather than relying on randomness. \n\n% Quantization enables efficient deployment of LLMs but introduces errors that can degrade performance, especially as sequence lengths grow. Commercial systems typically address long-context challenges during training: they extend context in late-stage pre-training (e.g., to $\\sim$30K tokens or more) and then fine-tune with positional strategies such as YaRN~\\citep{peng2023yarn} or by adjusting RoPE bases with a fixed interpolation factor (often 32 to advertise 128K support). Recent long-context models like CodeLlama \\citep{roziere2023code} and Qwen2.5 \\citep{team2024qwen2} follow this recipe to maintain accuracy within the tuned range.\n\n% However, these practices largely ignore the \\emph{coupling} between position interpolation and quantization. Models may appear robust at the trained or fine-tuned lengths yet deteriorate beyond that envelope. In the agentic LLM setting, context demands are open-ended; we rarely know what “enough” context will be next month. Our method targets this gap: it scales quantized models to longer sequences \\emph{without} resource-intensive training, hardware specialization, or runtime overhead. By explicitly accounting for PI–PTQ coupling, it complements existing long-context training and mitigates failure modes that emerge when evaluation lengths exceed the fine-tuning regime.\n\n\\subsection{Extended Token Length Support and Positional Interpolation}\n\\label{sec:positional_interpolation}\nA practical way to extend a pretrained LLMs' usable context is to \\emph{modify the positional mapping at inference} so very long test sequences are interpreted as if they lie within the training range. We refer to this family as \\textbf{position interpolation/extrapolation (PI)}. PI requires no additional training, keeps the architecture intact, and adds negligible overhead (and can further benefit from long-context finetuning). Beyond PI, long context support can also be achieved via (i) \\emph{continued pretraining} on long sequences~\\citep{gao2024how,chen2023longlora}, (ii) \\emph{instruction/alignment tuning} for long-range inputs~\\citep{bai2024longalign,skipalign2024}, and (iii) \\emph{architectural changes} (alternative position schemes; sparse/linear attention)~\\citep{su2021roformer,press2021alibi}. These generally require full/partial retraining, extra data/computation, and careful stability tuning, which can be challenging.\n\nLet $L_0$ be the training window and $L\\!\\gg\\!L_0$ the target window. PI methods either (a) remap test positions $m\\mapsto\\hat m\\!\\in\\![0,L_0]$, or (b) rescale the per-dimension positional frequencies $\\{\\theta_i\\}_{i=1}^{d/2}$ of the rotary/phase parameters.\n\n\\textbf{Linear Interpolation (LI)}~\\citep{chen2023extending} compresses positions uniformly so $\\hat m = m\\cdot(L_0/L)$, which keeps phases in-distribution but reduces local resolution by $L/L_0$ and often regresses short-range quality without finetuning.\n\\textbf{NTK-aware PI}~\\citep{bloc97_2023_ntkaware_scaled_rope} slows \\emph{lower} frequencies more than \\emph{higher} ones by adjusting the RoPE base $b\\!\\to\\!b'$, improving local fidelity while curbing long-range phase growth.\n\\textbf{YaRN}~\\citep{peng2023yarn} segments frequency bands: high-frequency dimensions are untouched, low-frequency dimensions are fully interpolated, and mid bands receive NTK-style partial slowdown. This preserves local detail and stabilizes long context, optionally with a mild logit rescale.\n\\textbf{LongRoPE}~\\citep{ding2024longrope} assigns a learned per-dimension scale $s_i$ and searches for $\\{s_i\\}$ on validation tasks, enabling very long effective windows with minimal short-range impact at the cost of a one-time search. More systematic and mathematical analysis are provided in \\ref{app:pi-details} (\\eqref{eq:li} -- \\eqref{eq:longrope}).\n\n\\subsection{LLM Quantization}\nPost-training quantization (PTQ) cuts memory and computation, but it can add errors that grow with sequence length. The quantization process can be expressed mathematically as follows:\n\\begin{equation}\n Q(w) = \\text{round}\\left(\\frac{x - \\text{min}(w)}{\\text{max}(w) - \\text{min}(w)} \\cdot (2^b - 1)\\right)\n \\label{eq:sq}\n\\end{equation}\nwhere $w$ represents the original weight values and $b$ is the target bit-width for quantization.\n\n\\textbf{Weight-only PTQ methods.}\n\\textbf{RTN} (Round-to-Nearest) rounds scaled weights to the nearest integers layer by layer.\n\\textbf{GPTQ}~\\citep{frantar2022gptq} chooses quantized weights to minimize a local quadratic loss using calibration activations, improving accuracy over RTN.\n\\textbf{AWQ}~\\citep{lin2024awq} keeps a small set of activation-critical channels in higher precision and quantize the rest.\n\n\\textbf{Weights + activations (rotation-aided).}\nBefore quantization, apply an orthogonal transform to spread outliers, then invert it after:\n$W' = WR,\\ \\hat W' = Q(W'),\\ \\hat W=\\hat W'R^\\top$ (and similarly for activations).\n\\textbf{QuaRot}~\\citep{quarot2025} uses fixed orthogonal maps; \n\\textbf{SpinQuant}~\\citep{liu2024spinquant} learns the rotation on calibration data.\n\nCommercial long-context systems typically extend context late in pretraining and then fine-tune with positional strategies (e.g., YaRN or RoPE-base adjustments) to advertise large windows (e.g., 128K) while maintaining accuracy within the tuned range~\\citep{peng2023yarn,roziere2023code,team2024qwen2}. However, these practices largely ignore the \\emph{coupling} between PI and PTQ: models can look robust near the fine-tuned lengths yet degrade sharply beyond that envelope. In open-ended, agentic settings, required context is fluid. Our method targets this gap: it scales quantized models to longer sequences \\emph{without} retraining, hardware specialization, or runtime overhead by explicitly accounting for PI–PTQ interaction. It complements long-context training and mitigates failure modes when evaluation exceeds the fine-tuning regime.\n\n\\begin{figure*}[t]\n\\centering\n\\begin{subfigure}[t]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{four_methods_no_pi_style2.pdf}\n \\caption{Non-Interpolated models}\n \\label{left}\n\\end{subfigure}\n\\hfill\n\\begin{subfigure}[t]{0.5\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{five_methods_aaai_style2.pdf}\n \\caption{YaRN interpolation (s = 8)}\n \\label{right}\n\\end{subfigure}\n\\vspace{-2mm}\n\\caption{Perplexity of quantized Llama-2-7b evaluated on the GovReport Dataset}\n\\label{fig:ppl}\n\\end{figure*}\n\n\\section{Analysis of Existing Quantized Model with Positional Interpolation}\n\\subsection{Observation}\nOur key observation is that post-training quantized LLMs do not work reliably with position interpolation out of the box. The interaction between RoPE scaling and low-bit quantization has not been systematically studied, and we find that applying existing scaling methods directly to PTQ models leads to substantial performance degradation. This degradation arises from the combined effects of quantization error, interpolation distortion, and activation outliers that are not well handled by current techniques. As shown in Figure~\\ref{fig:ppl}, using YaRN or NTK scaling with factor $s{=}8$ (which theoretically extends the maximum context window by up to eight times) allows the FP16 model to maintain stable performance without fine-tuning. In contrast, quantized models experience much sharper degradation even under the most favorable configuration, such as quantization combined with YaRN. With more naïve interpolation strategies like NTK or linear scaling, the models fail entirely at long contexts, reaching perplexity values greater than 100. Additional results are provided in the Appendix.\n\\subsection{Problem Formulation and Insight}\n\n% \\paragraph{Why extrapolation is hard.}\n% Training typically exposes the model to relative offsets $|m-n| \\le L_0$ (e.g., $L_0\\!\\in\\!\\{4\\mathrm{K},8\\mathrm{K}\\}$). \n% For a fixed frequency $\\omega_i$, the per-token phase advance is $\\Delta\\phi_i=\\omega_i$. \n% When we move to $L \\gg L_0$, the model encounters large phase differences $\\phi_i(m-n)=\\omega_i (m-n)$ that were \\emph{out-of-distribution} during training (since pretrain lenght is limited to $L_0$), especially for high-frequency bands and causing attention score fluctuation. Empirically this produces aliasing-like effects: phases wrap rapidly, destabilizing long-range attention while also over-suppressing local detail if we naively slow down all rotation frequencies. More intuitively, many tokens were crowed together within small amount of rotation phase change after PI and make high frequency information indistinguishable. \n\n% \\vspace{0.5ex}\n% \\paragraph{A unified view of scaling.}\n% Most context-extension methods can be written as a per-dimension scaling of the effective phase:\n% \\begin{equation}\n% \\phi_i^{\\text{scaled}}(m) \n% \\;=\\; \\frac{\\omega_i \\, f(m)}{s_i},\n% \\qquad \\text{with} \\quad \n% s_i>0,\\; f:\\mathbb{R}_{\\ge0}\\!\\to\\!\\mathbb{R}_{\\ge0}.\n% \\label{eq:unified-scaling}\n% \\end{equation}\n% Here $f(m)$ warps positions (e.g., linear interpolation), and $s_i$ rescales frequencies (e.g., per-band or per-hidden dimension). \n% This preserves orthogonality of the rotation while controlling phase growth.\n\n% \\paragraph{Phase error and Interpolation Pressure(IP).}\n% Let the training-supported \\emph{max} relative displacement be $D_0 \\!\\le\\! L_0$. \n% For a target displacement $D$ at test time, scaling in~\\eqref{eq:unified-scaling} induces a phase\n% \\begin{equation}\n% \\phi_i^{\\text{scaled}}(D) = \\frac{\\omega_i f(D)}{s_i}.\n% \\end{equation}\n% Define the \\emph{phase deviation} from the training regime at dimension $i$:\n% \\begin{equation}\n% \\varepsilon_i(D) \n% \\;\\triangleq\\; \\phi_i^{\\text{scaled}}(D) \\;-\\; \\phi_i(D_0) \n% \\;=\\; \\omega_i \\Big( \\frac{f(D)}{s_i} - D_0 \\Big).\n% \\label{eq:phase-deviation}\n% \\end{equation}\n% We define the gradient magnitude of phase divination:\n% \\begin{equation}\n% \\Psi_i \\;\\triangleq\\; \\bigg| \\frac{\\partial \\varepsilon_i(D)}{\\partial s_i} \\bigg|\n% \\;=\\; \\omega_i \\, \\frac{f(D)}{s_i^2}\n% \\end{equation}\n% as an \\emph{interpolation pressure} indicator: higher $\\Psi_i$ means the loss is more sensitive to small scaling changes at band $i$. \n% High-frequency bands (large $\\omega_i$) exhibit larger $\\Psi_i$, motivating per-band PI moderation and providing theoretical foundation for such method such as YaRN and LongRoPE.\n\n% \\vspace{0.5ex}\n% \\paragraph{Interaction with quantization.}\n% Long-context scaling is mostly studied for full-precision models; however, quantized models (GPTQ, AWQ, RTN, etc.) introduce position-dependent distortions that couple with interpolation.\n\n% Let $W_Q, W_K$ be linear projection weight matrix and $h$ the input at position $m$. \n% We form \n% \\begin{equation}\n% q(m) = \\mathrm{RoPE}\\!\\big(W_Q h,\\, m\\big), \n% \\qquad \n% k(n) = \\mathrm{RoPE}\\!\\big(W_K h,\\, n\\big),\n% \\end{equation}\n% followed by activation/KV-cache quantization. \n% We will denote the quantized quantities with hats: $\\hat{W}_Q=W_Q+E_Q$, $\\hat{W}_K=W_K+E_K$, and (if used) activation quantizers $Q_{\\mathrm{act}}(\\cdot)$ with step sizes $\\Delta$ (per-tensor or per-channel).\n\n% \\textbf{Orthogonality is not immunity.}\n% RoPE is orthonormal: for any vector $u$, $\\| \\mathrm{RoPE}(u,m) \\|_2 = \\|u\\|_2$. \n% Thus, if only weights are quantized, the \\emph{energy} of the noise is preserved by RoPE:\n% \\begin{equation}\n% \\big\\| \\mathrm{RoPE}(E_Q h, m) \\big\\|_2 \\;=\\; \\| E_Q h \\|_2 \\;\\le\\; \\|E_Q\\|_2 \\, \\|h\\|_2.\n% \\end{equation}\n% However, attention logits are \\emph{directional} (inner products), and RoPE \\emph{rotates} both signal and error. \n% Let ideal logits be $s_j = q^\\top k_j$ and quantized logits $\\hat{s}_j = \\hat{q}^\\top \\hat{k}_j$. \n% With $\\hat{q}=q+e_q$, $\\hat{k}_j=k_j+e_{k_j}$, the perturbation obeys\n% \\begin{equation}\n% |\\hat{s}_j - s_j|\n% \\;\\le\\; \\|e_q\\|_2 \\, \\|k_j\\|_2 + \\|e_{k_j}\\|_2 \\, \\|q\\|_2 + \\|e_q\\|_2 \\, \\|e_{k_j}\\|_2.\n% \\label{eq:logit-perturb-bound}\n% \\end{equation}\n% Crucially, the norms of $e_q,e_{k_j}$ depend on \\emph{how scaling modifies the signal distribution} (e.g., dynamic range, anisotropy), especially when activations or KV caches are quantized.\n\n% \\textbf{Activation/KV quantization under scaling.}\n% Assume a midrise uniform quantizer per channel $i$ with step $\\Delta_i$ and clipping range $[-c_i, c_i]$. \n% For a rotated 2D pair at position $m$,\n% \\begin{equation}\n% z^{(i)}(m) = R\\!\\big(\\phi_i^{\\text{scaled}}(m)\\big) \\, u^{(i)}, \n% \\qquad \n% \\hat{z}^{(i)}(m) = Q_{\\mathrm{act}}\\!\\big( z^{(i)}(m) \\big).\n% \\end{equation}\n% If values are well within range (no clipping), the mean-squared error per coordinate is $\\mathbb{E}\\| \\hat{z}^{(i)} - z^{(i)} \\|_2^2 \\approx \\Delta_i^2/6$. \n% Yet the \\emph{optimal} $\\Delta_i$ (or $c_i$) is typically estimated from a calibration distribution of $z^{(i)}$ at short contexts. \n% When we scale long contexts, the phase trajectories $m \\mapsto z^{(i)}(m)$ change shape:\n% \\begin{enumerate}\n% \\item \\emph{Dynamic-range dilation:} For some channels, long-context rotations increase extremal coordinates, raising the clipping probability and biasing errors. \n% \\item \\emph{Anisotropy shift:} Per-channel quantization grids are axis-aligned; RoPE rotates the signal relative to these grids, making the \\emph{same} step size suboptimal at certain phases.\n% \\end{enumerate}\n% A simple variance decomposition highlights the coupling:\n% \\begin{equation}\n% \\mathbb{E}\\big[\\| \\hat{z}^{(i)}(m) - z^{(i)}(m) \\|_2^2 \\big]\n% \\;\\approx\\; \\frac{\\Delta_i^2}{6} \\cdot \\underbrace{\\vphantom{\\frac{1}{1}} \\eta_i(m)}_{\\text{phase \\& range factor}},\n% \\eta_i(m)\\!\\uparrow \\;\\text{when } \\phi_i^{\\text{scaled}}(m) \\text{ induces range mismatch.}\n% \\label{eq:phase-noise-factor}\n% \\end{equation}\n% Combining~\\eqref{eq:logit-perturb-bound} and~\\eqref{eq:phase-noise-factor} yields a position-dependent logit error that is typically largest for high-frequency $i$ and large $m-n$.\n\n% \\paragraph{Method-specific quantization implications.}\n% \\begin{itemize}\n% \\item \\textbf{PI:} Uniform slowdown ($S$) preserves global shape but compresses local displacements. \n% For activation/KV quantization this may \\emph{increase} the occupancy near grid boundaries in some channels (dynamic range reallocation), slightly worsening $\\eta_i(m)$ locally.\n% \\item \\textbf{YaRN:} By slowing only the high-frequency band ($i>d_s$) and optionally rescaling logits, YaRN reduces the worst-case phase growth where quantization is most sensitive, typically lowering the tail of $\\eta_i(m)$ while keeping low-band statistics close to calibration.\n% \\item \\textbf{LongRoPE:} Per-dimension $s_i$ can be tuned to align each channel’s long-context statistics with its calibration range, effectively minimizing $\\max_m \\eta_i(m)$ across $i$. \n% This is particularly synergistic with per-channel activation/KV quantization.\n% \\end{itemize}\n\n% \\paragraph{Takeaways.}\n% (1) \\emph{All} scaling schemes amount to trading off long-range phase stability against local resolution; (2) in quantized models, this trade-off is modulated by how scaling shifts the activation statistics relative to the quantizer (range, step size, axis alignment); (3) band- or dimension-wise scaling (YaRN/LongRoPE) better targets the high-pressure, high-frequency channels identified by~\\eqref{eq:phase-deviation}, reducing long-context aliasing \\emph{and} quantization-induced logit noise. Position interpolation methods (PI, YaRN, LongRoPE) can be viewed as frequency-wise phase control via~\\eqref{eq:unified-scaling}. \n% They successfully extend context length in full precision, but in quantized models their benefits are mediated by phase-dependent activation statistics that affect quantization error (Eq.~\\ref{eq:phase-noise-factor}) and thus attention logits (Eq.~\\ref{eq:logit-perturb-bound}). \n% This motivates \\emph{quantization-aware} scaling policies that explicitly account for channelwise pressure and calibration drift.\n\\paragraph{Why extrapolation is hard.}\nTraining typically exposes the model to relative offsets $|m-n| \\le L_0$ (e.g., $L_0\\!\\in\\!\\{4\\mathrm{K},8\\mathrm{K}\\}$). \nFor a fixed frequency $\\omega_i$, the per-token phase advance is $\\Delta\\phi_i=\\omega_i$. \nWhen we move to $L \\gg L_0$, the model encounters large phase differences $\\phi_i(m-n)=\\omega_i (m-n)$ that were \\emph{out-of-distribution} during training (since pretraining length is limited to $L_0$), especially for high frequency bands, causing attention score fluctuations. Empirically this produces aliasing-like effects: phases wrap rapidly, destabilizing long-range attention; conversely, naïvely slowing \\emph{all} rotation frequencies can over suppress local details. More intuitively, with uniform PI many tokens become \\emph{crowded} in phase, reducing per-token phase increments and compressing fine-grained distinctions.\n\n\\vspace{0.5ex}\n\\paragraph{A unified view of scaling.}\nMost context extension methods can be written as a per-dimension scaling of the effective phase:\n\\begin{equation}\n \\phi_i^{\\text{scaled}}(m) \n \\;=\\; \\frac{\\omega_i \\, f(m)}{s_i},\n \\qquad \\text{with} \\quad \n s_i>0,\\; f:\\mathbb{R}_{\\ge0}\\!\\to\\!\\mathbb{R}_{\\ge0}.\n \\label{eq:unified-scaling}\n\\end{equation}\nHere $f(m)$ warps positions (e.g., linear interpolation), and $s_i$ rescales frequencies (e.g., per-band or per-hidden-dimension). \nThis preserves orthogonality of the rotation while controlling phase growth.\n\n\\paragraph{Phase error and Interpolation Pressure (IP).}\nLet the training-supported \\emph{max} relative displacement be $D_0 \\!\\le\\! L_0$. \nFor a target displacement $D$ at test time, scaling in~\\eqref{eq:unified-scaling} induces a phase\n\\begin{equation}\n \\phi_i^{\\text{scaled}}(D) = \\frac{\\omega_i f(D)}{s_i}.\n\\end{equation}\nDefine the \\emph{phase deviation} from the training regime at dimension $i$:\n\\begin{equation}\n \\varepsilon_i(D) \n \\;\\triangleq\\; \\phi_i^{\\text{scaled}}(D) \\;-\\; \\phi_i(D_0) \n \\;=\\; \\omega_i \\Big( \\frac{f(D)}{s_i} - D_0 \\Big).\n \\label{eq:phase-deviation}\n\\end{equation}\nWe define the gradient magnitude of phase deviation:\n\\begin{equation}\n \\Psi_i \\;\\triangleq\\; \\bigg| \\frac{\\partial \\varepsilon_i(D)}{\\partial s_i} \\bigg|\n \\;=\\; \\omega_i \\, \\frac{f(D)}{s_i^2}\n\\end{equation}\nas an \\emph{interpolation pressure} indicator: higher $\\Psi_i$ means the loss is more sensitive to small scaling changes at band $i$. \nHigh-frequency bands (large $\\omega_i$) exhibit larger $\\Psi_i$, which motivates \\emph{selective} scaling policies that avoid unnecessarily perturbing high-frequency channels (as in YaRN) while tuning others (e.g., LongRoPE).\n\n\\vspace{0.5ex}\n\\paragraph{Interaction with quantization.}\nLong-context scaling is mostly studied for full-precision models; however, quantized models (GPTQ, AWQ, RTN, etc.) introduce position-dependent distortions that couple with interpolation.\n\nLet $W_Q, W_K$ be linear projection weight matrices and $h$ the input at position $m$. \nWe form \n\\begin{equation}\n q(m) = \\mathrm{RoPE}\\!\\big(W_Q h,\\, m\\big), \n \\qquad \n k(n) = \\mathrm{RoPE}\\!\\big(W_K h,\\, n\\big),\n\\end{equation}\npossibly followed by activation/KV-cache quantization. \nWe denote the quantized quantities with hats: $\\hat{W}_Q=W_Q+E_Q$, $\\hat{W}_K=W_K+E_K$, where $E_{K,Q}$ are quantization error term that collects rounding and clipping residuals. This abstraction is exact by definition and allows clean analysis of how quantization errors propagate through RoPE and attention. We also define activation quantizers $Q_{\\mathrm{act}}(\\cdot)$ with step sizes(quantization scale) $\\Delta$ (per-tensor or per-channel or per-group).\n\n\\textbf{Orthogonality is not immunity.}\nRoPE is orthonormal: for any vector $u$, $\\| \\mathrm{RoPE}(u,m) \\|_2 = \\|u\\|_2$. \nThus, when weights are quantized, the \\emph{energy} of the noise is preserved by RoPE:\n\\begin{equation}\n \\big\\| \\mathrm{RoPE}(E_Q h, m) \\big\\|_2 \\;=\\; \\| E_Q h \\|_2 \\;\\le\\; \\|E_Q\\|_2 \\, \\|h\\|_2.\n\\end{equation}\nHowever, attention logits are \\emph{directional} (inner products), and RoPE \\emph{rotates} both signal and error. \nLet ideal logits be $s_j = q^\\top k_j$ and quantized logits $\\hat{s}_j = \\hat{q}^\\top \\hat{k}_j$. \nWith $\\hat{q}=q+e_q$, $\\hat{k}_j=k_j+e_{k_j}$, the perturbation obeys\n\\begin{equation}\n |\\hat{s}_j - s_j|\n \\;\\le\\; \\|e_q\\|_2 \\, \\|k_j\\|_2 + \\|e_{k_j}\\|_2 \\, \\|q\\|_2 + \\|e_q\\|_2 \\, \\|e_{k_j}\\|_2.\n \\label{eq:logit-perturb-bound}\n\\end{equation}\nCrucially, the norms of $e_q,e_{k_j}$ depend on \\emph{how scaling modifies the signal distribution} (e.g., dynamic range, anisotropy), especially when activations or KV caches are quantized.\n\n\\textbf{Quantization under scaling.}\nAssume a mid-rise uniform quantizer per channel $i$ with step $\\Delta_i$ and clipping range $[-c_i, c_i]$. \nFor a rotated 2D pair at position $m$,\n\\begin{equation}\n z^{(i)}(m) = R\\!\\big(\\phi_i^{\\text{scaled}}(m)\\big) \\, u^{(i)}, \n \\qquad \n \\hat{z}^{(i)}(m) = Q_{\\mathrm{act}}\\!\\big( z^{(i)}(m) \\big).\n\\end{equation}\nIf values are well within range (no clipping), the mean-squared error per coordinate is $\\mathbb{E}\\| \\hat{z}^{(i)} - z^{(i)} \\|_2^2 \\approx \\Delta_i^2/6$. \nYet the \\emph{optimal} $\\Delta_i$ (or $c_i$) is typically estimated from a calibration distribution of $z^{(i)}$ at short contexts. \nWhen we scale long contexts, the phase trajectories $m \\mapsto z^{(i)}(m)$ change shape. Hence, we claim the following two observations:\n\\begin{enumerate}\n \\item \\emph{Dynamic-range dilation:} For some channels, long-context rotations increase extreme coordinates, raising the clipping probability and biasing errors. \n \\item \\emph{Anisotropy shift:} Per-channel quantization grids are axis-aligned; RoPE rotates the signal relative to these grids, making the \\emph{same} step size suboptimal at certain phases.\n\\end{enumerate}\nA simple variance decomposition highlights the coupling:\n\\begin{equation}\n \\mathbb{E}\\big[\\| \\hat{z}^{(i)}(m) - z^{(i)}(m) \\|_2^2 \\big]\n \\;\\approx\\; \\frac{\\Delta_i^2}{6} \\cdot \\eta_i(m), \\\\\\\n \\eta_i(m)\\!\\uparrow \\text{when } \\phi_i^{\\text{scaled}}(m) \\text{ induces axis mismatch}\n \\label{eq:phase-noise-factor}\n\\end{equation}\nwhere $\\eta_i(m)$ represent phase and range factor. Combining~\\eqref{eq:logit-perturb-bound} and~\\eqref{eq:phase-noise-factor} yields a position-dependent logit error that is typically largest for high-frequency $i$ and large $|m-n|$ which algin with our test in Figure \\ref{fig:yarn_ntk_detailed}(Appendix) that YaRN(preserve high frequency channels completely) works the best without any model specific tuning and enlarging its benefit when context is longer.\n\n% \\paragraph{Method-specific quantization implications.}\n% \\begin{itemize}\n% \\item \\textbf{PI (uniform).} A global slowdown ($S$) preserves global shape but compresses local displacements. \n% For activation/KV quantization this can \\emph{increase} occupancy near grid boundaries in some channels (dynamic range reallocation), slightly worsening $\\eta_i(m)$ locally.\n\n% \\item \\textbf{YaRN (band-wise).} YaRN \\emph{does not interpolate} high-frequency dimensions (small wavelength), \\emph{always interpolates} low-frequency dimensions (large wavelength) to avoid extrapolation, and applies an NTK-like partial interpolation in between. \n% Interpreting this in~\\eqref{eq:unified-scaling}, set $s_i=1$ for high-frequency bands, $s_i=S$ for low-frequency bands, and $s_i=S^{g_i}$ with $g_i\\!\\in\\!(0,1)$ for mid bands (monotone in wavelength). \n% \\emph{Quantization effect:} leaving high-frequency bands unchanged preserves local detail and their short-context calibration; interpolating low/mid bands reduces large-scale phase growth, lowering the long-tail of $\\eta_i(m)$ while minimizing short-context regression.\n\n% \\item \\textbf{LongRoPE (per-dimension).} Per-dimension $s_i$ are searched to best match long-context targets. \n% In practice this often slows lower and mid frequencies more than high ones, but can allocate slowdown wherever validation signals indicate benefit. \n% \\emph{Quantization effect:} tuning $\\{s_i\\}$ can align each channel’s long-context statistics with its calibration range, effectively minimizing $\\max_m \\eta_i(m)$ across $i$, which synergizes with per-channel activation/KV quantization.\n% \\end{itemize}\n\n\\textbf{Final takeaways.}\n(1) All scaling schemes trade long-range phase stability against local resolution; \n(2) in quantized models, the trade-off depends on how scaling shifts activation statistics relative to the quantizer (range, step size, axis alignment); \n(3) Dynamic dimension-wise scaling (YaRN/LongRoPE) assigns slowdown where it matters most for extrapolation (typically low/mid frequencies) while \\emph{sparing} high-frequency channels, thereby reducing long-context aliasing and limiting quantization-induced logit noise drift.\nPosition interpolation methods can thus be viewed as frequency-wise phase control via~\\eqref{eq:unified-scaling}; this motivates \\emph{quantization-aware} RoPE scaling policies and \\emph{scaling-aware} quantization schemes that account for channel-wise pressure and calibration drift.\n\n\\subsection{Rethinking of Outliers in Interpolated Quantized LLM Models}\n\nWith these observations, however, we cannot simply optimize interpolation pressure and reduce calibration drift on an existing quantized model and expect it to work flawlessly for long contexts with PI without fine-tuning. Activation outliers have been extensively studied and are a leading cause of degradation in quantized LLMs. We define outliers as rare, high-magnitude coordinates or channels whose absolute value exceeds the clip range or a high quantile (99.9\\textsuperscript{th}) of the training distribution; outlier channels are dimensions that consistently concentrate disproportionate tail mass. Position interpolation perturbs both the hidden-state distribution and the geometry of RoPE-rotated pairs, which shifts pre-activation tails (weight-induced outliers) and inflates activation outliers, thereby increasing clipping and effective quantization noise as context grows. In the remainder of this section, we systematically characterize outlier shifting and amplification under PI for weight-only and weight-plus-activation quantization, using simple \\textbf{\\textit{tail-inflation ratios}(TIR)} and logit-error bounds, and discuss mitigation via selective phase scaling and context-aware per-channel rescaling.\n\n\\textbf{Outlier was Amplified under PI.}\nLet $\\mathcal{H}_0$ be the training (short-context) distribution of $h(m)$ and $\\mathcal{H}_D$ the long-context distribution under PI. \nDefine tail–inflation factors using a high quantile (e.g., $1-\\varepsilon$):\n\\begin{equation}\n\\rho^{\\mathrm{W}}_i \\;\\triangleq\\; \n\\frac{Q_{|w_{i}^\\top h|,\\,h\\sim\\mathcal{H}_D}(1-\\varepsilon)}{Q_{|w_{i}^\\top h|,\\,h\\sim\\mathcal{H}_0}(1-\\varepsilon)},\n\\qquad\n\\rho^{\\mathrm{A}}_i(m) \\;\\triangleq\\;\n\\frac{Q_{\\|R(\\phi_i^{\\text{scaled}}(m))u_i\\|_\\infty}(1-\\varepsilon)}\n {Q_{\\|R(\\phi_i(m))u_i\\|_\\infty}(1-\\varepsilon)}.\n\\end{equation}\n$\\rho^{\\mathrm{W}}$ captures pre-activation tail growth due to PI; $\\rho^{\\mathrm{A}}$ captures axis-aligned amplitude inflation of the RoPE pair at position $m$ (driving activation clipping).\n\n\\textbf{Weight-only quantization.}\nWith $\\hat W = W + E$ and full-precision activations,\n\\begin{equation}\n\\hat q(m)-q(m)=\\mathrm{RoPE}(E_Q h(m),m),\\;\\;\\;\n\\|\\hat q(m)-q(m)\\|_2 \\le \\|E_Q\\|_2\\,\\|h(m)\\|_2\n\\end{equation}\n(and similarly for $k$). \nUnder PI, high-quantiles of $\\|h\\|$ inflate roughly by $\\rho^{\\mathrm{W}}$, so logit error scales like\n\\begin{equation}\n|\\hat s_{mn}-s_{mn}| \\;=\\; \\mathcal{O}\\!\\Big((\\|E_Q\\|_2+\\|E_K\\|_2)\\cdot \\underbrace{\\|h\\|_{\\mathrm{tail}}}_{\\propto\\,\\rho^{\\mathrm{W}}}\\Big).\n\\end{equation}\nSo to keep the same clipping target on pre-activations, we can enlarge per-channel clips as \n$\\,c_i^{\\star}(D)\\approx \\rho^{\\mathrm{W}}_i\\,c_i^{\\star}(0)$.\n\n\\textbf{Weight+activation quantization.}\nFor a per-axis uniform activation quantizer $(\\Delta_i,c_i)$,\n\\begin{equation}\n\\mathrm{MSE}_i \\;\\approx\\; (1-p_{\\mathrm{clip}})\\frac{\\Delta_i^2}{12}\n\\;+\\; \\mathbb{E}\\!\\left[(|x|-c_i)^2\\mathbf{1}\\{|x|>c_i\\}\\right],\n\\quad p_{\\mathrm{clip}}=\\Pr(|x|>c_i).\n\\end{equation}\nPI increases axis amplitudes via $\\rho^{\\mathrm{A}}_i(m)$, raising $p_{\\mathrm{clip}}$ unless we rescale:\n\\begin{equation}\nc_i^{\\star}(D,m)\\;\\approx\\;\\rho^{\\mathrm{A}}_i(m)\\,c_i^{\\star}(0),\n\\qquad\n\\Delta_i^{\\star}(D,m)\\;\\propto\\;\\frac{c_i^{\\star}(D,m)}{2^{b_i}-1}.\n\\end{equation}\nIn the WAQ case, logit error adds a phase-dependent activation term $\\|\\delta_q(m)\\|_2,\\|\\delta_k(n)\\|_2$ whose growth is governed by $\\rho^{\\mathrm{A}}$.\n\nTo conclude, PI causes pre-activation tail growth ($\\rho^{\\mathrm{W}}$) that amplifies weight-error impact, and axis-aligned amplitude growth ($\\rho^{\\mathrm{A}}$) that increases activation clipping. This effect can be reduced by selective phase scaling (preserve high-freq channels during PI like YaRN) and by rescaling per-channel clips with $\\rho^{\\mathrm{W}}$ / $\\rho^{\\mathrm{A}}$. We also demonstrate the actual outlier shifting on figure \\ref{fig:outlier_shifting_analysis} (Appendix) and observed the expected amplitude growth and distribution change.\n\n% \\subsection{Can Post PI AWQ Search save us?}\n% \\subsection{How about Hardmard Rotation?}\n% short answer is Yes but only in some degree.\n\n\\section{Methodology}\n\\subsection{Interpolation, Quantization, and Outlier Aware Weight Re-scale}\nFrom the preceding analysis, applying position interpolation (PI) to a quantized LLM can amplify error via long-context aliasing, dynamic-range dilation, anisotropy (axis-aligned quantizers vs.\\ RoPE rotations), and outlier shifting. \nWe propose a solution to stabilize PI by: (1) grouping RoPE dimensions into frequency \\emph{bands}, and (2) searching a \\emph{small} per-band \\textbf{weight} scale that minimizes perplexity on a tiny long-context dev set.\n\nLet $\\{\\omega_i\\}$ be the RoPE frequencies of 2-D pairs. We partition them into $B$ log-spaced bands $\\{\\mathcal{B}_b\\}_{b=1}^B$ and associate one scale $g_b$ to all rows/columns in band $b$ of $W_Q$ and $W_K$.\nAs we have stated in the previous section, we compare short-context vs.\\ PI long-context pre-activations and obtain a per-band inflation $\\rho^{\\mathrm{W}}_b$:\n\\begin{equation}\n\\rho^{\\mathrm{W}}_b \\;=\\; \n\\operatorname*{median}_{i\\in\\mathcal{B}_b}\n\\frac{Q_{|w_i^\\top h|,\\ \\text{long}}(1-\\varepsilon)}{Q_{|w_i^\\top h|,\\ \\text{short}}(1-\\varepsilon)}.\n\\end{equation}\nThis measures how much the \\emph{weight-induced} tails grow under PI.\nThen we create an additional multiplicative scale to the corresponding bands:\n\\begin{equation}\nW_Q^{(b)} \\leftarrow g_b\\, W_Q^{(b)}, \\qquad\nW_K^{(b)} \\leftarrow \n\\begin{cases}\ng_b\\, W_K^{(b)} & \\text{(shared mode)}\\\\\ng_b^{-1}\\, W_K^{(b)} & \\text{(symmetric mode)}\n\\end{cases}\n\\end{equation}\nand select the mode empirically (symmetric by default to avoid trivial logit rescaling). Additionally, to keep the search small and stable we use two light-weight bounds:\n\\begin{equation}\ng_b \\in \\Big[\\,1/\\gamma_b,\\ \\min\\big(\\gamma_b,\\ \\kappa/\\rho_b^{\\mathrm{W}}\\big)\\Big],\n\\quad\n\\gamma_b \\;=\\; 1 + \\frac{\\tau}{1+\\log(\\omega_{b,\\mathrm{med}}/\\omega_{\\min})}.\n\\end{equation}\nHere $\\gamma_b$ tightens the window for higher-frequency bands to keep their original structure, and $\\kappa/\\rho_b^{\\mathrm{W}},\\kappa\\!\\in\\![1.0,1.3]$ to constraint overshoot of long-context pre-activations. We choose $\\{g_b\\}$ to minimize weighted perplexity across a few target lengths to emphasize longer contexts:\n\\begin{equation}\nLoss \\;=\\; \\min_{\\{g_b\\}} \\;\n \\sum_{\\ell \\in \\mathcal{L}} w_\\ell \\,\\mathrm{ppl}(\\ell;\\{g_b\\}),\n \\qquad \\sum_{\\ell} w_\\ell = 1,\n \\qquad \\{g_b\\} = \\arg\\min_{\\lambda} \\!\\left( Loss \\right)\n\\end{equation}\nWe randomly sample 10 long documents ($>$ 20k length) from Proof-pile~\\citep{Proofpile} as the tiny calibration set and more details can be found in algorithm \\ref{alg:band-rescale} (Appendix).\n\nWe focus on rescaling \\emph{weights} (specifically $W_Q,W_K$) rather than adjusting activation quantization for three reasons. \n\\emph{(i) Unknown, high-variance activations.} Under PI, activation statistics become position- and content-dependent (phase crowding, aliasing, prompt style), so any activation clip/step calibrated on short contexts can drift at long contexts; correcting this reliably demands runtime adaptation and larger calibration sets. In contrast, weight perturbations are \\emph{static} post-quantization, and their effect on queries/keys is linear and position-invariant under RoPE, making bandwise weight scaling stable and predictable. \n\\emph{(ii) Broader compatibility and generalizability.} Many deployments keep activations in FP16/BF16 (or quantize only KV caches) and use diverse kernels/runtimes; changing activation quantizers often requires kernel changes and retuning. Weight-only scaling is model-file–local, quantizer-agnostic, hardware-agnostic, and works whether activations are full precision or quantized. \n\\emph{(iii) Simplicity and safety.} Bandwise scaling of $W_Q,W_K$ (with a symmetric option $W_Q\\!\\leftarrow\\! g_b W_Q$, $W_K\\!\\leftarrow\\! g_b^{-1} W_K$) preserves logit scale, avoids reconfiguring per-layer clips/steps, and needs only a tiny dev set to search $g_b$. This yields a drop-in fix that reduces long-context aliasing and outlier amplification without touching the LLM serving system stack. \nOverall, weight rescaling offers a robust, low-friction lever to counter PI-induced distortions while remaining portable across models and inference backend.\n\n\\section{Experiments and Results}\nWe conduct experiments primarily on the LLaMA-2-7B~\\citep{touvron2023llama} pretrained model (additional Vicuna~\\citep{zheng2023judging} results can be found in Appendix) without any long-context adaptation or fine-tuning. For position interpolation, we focus on YaRN, as it represents the current state-of-the-art: it consistently outperforms alternatives and is the only method that remains stable at extended token lengths without long context tuning. For quantization, we adopt a group size of 128 across all settings. In the AWQ baseline, weights are rescaled channel-wise using the search-derived scales and clipping thresholds, following the official implementation. We additionally explore activation quantization and Hadamard rotation; details are provided in the Appendix. All experiments are conducted on two NVIDIA RTX 4090 GPUs and one AMD MI300X accelerator.\n\\subsection{Evaluation on the GovReport Dataset}\nWe evaluate the model's perplexity (PPL) with the GovReport dataset~\\citep{huang2021efficient} from 2K to 32K using YaRN scaling on LLaMA-2-7B~\\citep{touvron2023llama} and Vicuna-7B~\\citep{zheng2023judging}. Perplexities are computed with a 256 token sliding window and reported as moving averages. As shown in Table~\\ref{tab:govreport-multisize}, \\textbf{Q-ROAR W4} closely tracks FP16 up to 16K: across 2K–16K the absolute gap to FP16 is smaller than 0.04 PPL. At 32K, Q-ROAR reduces degradation relative to all baselines, reaching 5.833 vs.\\ 6.069 (FP16), 6.302 (AWQ W4), and 6.783 (RTN W4) as a relative improvement of 8\\% over AWQ and 14\\% over RTN at the longest window. Overall, these results support that channel-aware rescaling mitigates the compounding effects of interpolation and quantization as the window grows, while preserving standard sequence length performance.\n\n\n\\renewcommand{\\arraystretch}{0.9}\n\\begin{table*}[h]\n\\centering\n\\caption{GovReport perplexity on LLaMA-2-7B across evaluation context sizes (lower is better).}\n\\vspace{-2mm}\n\\label{tab:govreport-multisize}\n\\begingroup\n\\setlength{\\tabcolsep}{5pt}\n\n\\resizebox{0.8\\textwidth}{!}{\n\\begin{tabular}{lc|ccccc}\n\\toprule\n\\multirow{2}{*}{Setting} & \\multirow{2}{*}{\\shortstack{Context Length \\\\ (YaRN = 16)}} & \\multicolumn{5}{c}{Evaluation Context Window Size} \\\\\n & &2048 & 4096 &8192 & 16384 & 32768 \\\\\n\\midrule\nFP16 & 64K & 4.437 & 4.359 & 4.329 & 4.175 & 6.069 \\\\\nRTN W4 & 64K & 4.544 & 4.485 & 4.470 & 4.575 & 6.783 \\\\\nAWQ W4 & 64K & 4.489 & 4.421 & 4.405 & 4.414 & 6.302 \\\\\n\\textbf{Q-ROAR W4 (ours)} & 64K & \\textbf{4.441} & \\textbf{4.393} & \\textbf{4.321} & \\textbf{4.181} & \\textbf{5.833} \\\\\n\\bottomrule\n\\end{tabular}%\n}\n\\endgroup\n\\end{table*}\n\n\n\n% \\subsection{Proof-pile}\n% We evaluate LLaMA-2-7B from 2K to 131K tokens as shown in Table \\ref{tab:proofpile-multisize} On Proof-file dataset. With moderate YaRN PI ($s{=}8$), all quantized baselines remain close to FP16 and \\textbf{Q-ROAR W4} is consistently best among them (e.g., 16K: 2.458 vs.\\ AWQ 2.476, RTN 2.517). Under \\emph{aggressive} PI ($s{=}32$, 32K to 131K) without any long-context finetuning, even YaRN which is the strongest out-of-box RoPE scaler method fails to stabilize quantized models: RTN and AWQ diverge (e.g., 131K: 9.958 and 8.700 vs.\\ FP16 5.386). In this regime, \\textbf{Q-ROAR} clearly dominates, reducing PPL vs.\\ RTN by \\textbf{19–21\\%} and vs.\\ AWQ by \\textbf{7–10\\%} across 32K/64K/131K (e.g., 32K: 5.054 vs.\\ 6.249/5.460; 131K: 7.869 vs.\\ 9.958/8.700), while preserving near-FP16 behavior at shorter lengths. These results confirm that PI–PTQ coupling is the failure mode under long contexts, and that \\textbf{Q-ROAR} largely mitigate the performance degradation.\n\n\\subsection{Evaluation on the Proof-Pile Dataset}\nWe evaluate LLaMA-2-7B on Proof-Pile from 2K to 131K tokens and results are shown in Table~\\ref{tab:proofpile-multisize}. With moderate YaRN scaling ($s{=}8$), all quantized baselines stay close to FP16, and \\textbf{Q-ROAR W4} is consistently the best among them; at 16K, for instance, Q-ROAR reaches 2.458 compared with 2.476 for AWQ and 2.517 for RTN. Under aggressive scaling ($s{=}32$, 32K–131K) without any long-context finetuning, even YaRN fails to fully stabilize quantized models. RTN and AWQ deteriorate substantially; at 131K they reach 9.958 and 8.700, respectively, versus 5.386 for FP16. In this regime, \\textbf{Q-ROAR} clearly dominates, cutting perplexity relative to RTN by \\textbf{19–21\\%} and relative to AWQ by \\textbf{7–10\\%} across 32K, 64K, and 131K (e.g., at 32K: 5.054 vs.\\ 6.249 for RTN and 5.460 for AWQ; at 131K: 7.869 vs.\\ 9.958 and 8.700), while remaining near FP16 at shorter lengths. \n\nOverall, these results indicate that the interaction between position interpolation and post-training quantization is the main failure mode at long context lengths, and that \\textbf{Q-ROAR} largely mitigates the resulting degradation.\n\n\n\\renewcommand{\\arraystretch}{0.9}\n\\begin{table*}[t]\n\\centering\n\\caption{Proof-pile perplexity on LLaMA-2-7B across evaluation context sizes (lower is better). Values at $\\leq$16K use YaRN scale factor $s{=}8$; values at $\\geq$32K use $s{=}32$.}\n\\vspace{-2mm}\n\\label{tab:proofpile-multisize}\n\\begingroup\n\\setlength{\\tabcolsep}{5pt}\n\\resizebox{0.8\\textwidth}{!}{\n\\begin{tabular}{l|cccc|ccc}\n\\toprule\nSetting & \\multicolumn{4}{c|}{Evaluation Context (s=8)} & \\multicolumn{3}{c}{Evaluation Context (s=32)} \\\\\n & 2048 & 4096 & 8192 & 16384 & 32768 & 65536 & 131072 \\\\\n\\midrule\nFP16 & 2.847 & 2.667 & 2.543 & 2.438 & 4.261 & 4.074 & 5.386 \\\\\nRTN W4 & 2.917 & 2.739 & 2.613 & 2.517 & 6.249 & 6.187 & 9.958 \\\\\nAWQ W4 & 2.891 & 2.709 & 2.583 & 2.476 & 5.460 & 5.410 & 8.700 \\\\\n\\textbf{Q-ROAR W4 (ours)} & \\textbf{2.888} & \\textbf{2.701} & \\textbf{2.577} & \\textbf{2.458} & \\textbf{5.054} & \\textbf{4.992} & \\textbf{7.869} \\\\\n\\bottomrule\n\\end{tabular}}\n\\endgroup\n\\end{table*}\n\n\n% \\begin{table*}[t]\n% \\centering\n% \\caption{Proof-pile perplexity on LLaMA-2-7B across evaluation context sizes (lower is better).}\n% \\label{tab:proofpile-multisize}\n% \\begingroup\n% \\setlength{\\tabcolsep}{5pt}\n% \\resizebox{0.95\\textwidth}{!}{\n% \\begin{tabular}{c|ccccccc}\n% \\toprule\n% \\textbf{Setting} & \\textbf{2048} & \\textbf{4096} & \\textbf{8192} & \\textbf{16384} & \\textbf{32768} & \\textbf{65536} & \\textbf{131072} \\\\\n% \\midrule\n% \\textit{YaRN Scale} & $s{=}8$ & $s{=}8$ & $s{=}8$ & $s{=}8$ & $s{=}32$ & $s{=}32$ & $s{=}32$ \\\\\n% \\midrule\n% FP16 & 2.847 & 2.667 & 2.543 & 2.438 & 4.261 & 4.074 & 5.386 \\\\\n% RTN W4 & 2.917 & 2.739 & 2.613 & 2.517 & 6.249 & 6.187 & 9.958 \\\\\n% AWQ W4 & 2.891 & 2.709 & 2.583 & 2.476 & 5.460 & 5.410 & 8.700 \\\\\n% \\textbf{Q-ROAR W4} & \\textbf{2.888} & \\textbf{2.701} & \\textbf{2.577} & \\textbf{2.458} & \\textbf{5.054} & \\textbf{4.992} & \\textbf{7.869} \\\\\n% \\bottomrule\n% \\end{tabular}}\n% \\endgroup\n% \\end{table*}\n\n\\subsection{Standard LLM Benchmarks}\nThe results on the standard benchmarks are shown in Table~\\ref{tab:result-llama-2-7b}. We evaluate WikiText2 test set~\\citep{wikitext} and five zero-shot commonsense reasoning tasks. The selected benchmarks include BoolQ~\\citep{boolq}, HellaSwag~\\citep{hellaswag}, WinoGrande~\\citep{winogrande}, ARC-easy, and ARC-challenge~\\citep{arc}. \n\\begin{table*}[h]\n\\centering\n\\caption{Performance of LLaMA-2-7B on standard LLM benchmarks under different quantization and PI settings. Zero-shot accuracy on 5 tasks plus average and WikiText2 perplexity.}\n\\vspace{-2mm}\n\\label{tab:result-llama-2-7b}\n\\resizebox{0.95\\textwidth}{!}{\n\\begin{tabular}{lccccccc}\n\\toprule\n\\textbf{Setting} & \\textbf{ARC-C} & \\textbf{ARC-E} & \\textbf{BoolQ} & \\textbf{HellaSwag} & \\textbf{WinoGrande} & \\textbf{5-shot Avg.} & \\textbf{WikiText2 PPL} \\\\\n\\midrule\n\\multicolumn{8}{c}{\\emph{Base Context (4096 context window length)}} \\\\\n\\midrule\nBaseline FP16 & 52.3 & 80.1 & 76.2 & 78.9 & 67.7 & 70.83 & 5.47 \\\\\nRTN W4 & 48.6 & 76.5 & 72.4 & 74.1 & 59.1 & 64.14 & 5.73 \\\\\nRTN W4-A4 & 47.2 & 75.0 & 71.3 & 72.8 & 57.9 & 62.02 & 5.92 \\\\\nAWQ W4 & 48.9 & 76.8 & 73.1 & 74.9 & 59.6 & 64.25 & 5.61 \\\\\nAWQ W4-A4 & 47.5 & 75.2 & 71.7 & 73.2 & 58.1 & 62.31 & 5.77 \\\\\n\\midrule\n\\multicolumn{8}{c}{\\emph{Extended Context with YaRN (32K context window length, $s{=}8$)}} \\\\\n\\midrule\nBaseline FP16 & 48.7 & 75.6 & 72.0 & 73.5 & 58.6 & 63.71 & 6.09 \\\\\nRTN W4 & 48.0 & 75.1 & 71.4 & 72.8 & 57.7 & 63.32 & 6.41 \\\\\nRTN W4-A4 & 47.1 & 74.6 & 70.9 & 72.0 & 57.4 & 62.84 & 6.60 \\\\\nAWQ W4 & 48.3 & 75.3 & 71.9 & 73.1 & 58.0 & 63.52 & 6.31 \\\\\nAWQ W4-A4 & 47.3 & 74.8 & 70.8 & 72.3 & 57.2 & 62.53 & 6.49 \\\\\n\\midrule\n\\textbf{Q-ROAR W4} & \\textbf{49.0} & \\textbf{75.9} & \\textbf{72.4} & \\textbf{73.8} & \\textbf{58.6} & \\textbf{63.96} & \\textbf{6.18} \\\\\n\\textbf{Q-ROAR W4-A4} & \\textbf{48.2} & \\textbf{75.2} & \\textbf{71.7} & \\textbf{73.0} & \\textbf{58.2} & \\textbf{63.21} & \\textbf{6.39} \\\\\n\\bottomrule\n\\end{tabular}}\n\\end{table*}\n\nAt the base 4K context, quantization inevitably lowers performance compared to FP16, with AWQ generally stronger than RTN. When extending the context to 32K with YaRN, all methods see a drop, but Q-ROAR consistently narrows the gap. Both W4 and W4-A4 variants of Q-ROAR deliver higher average accuracy and lower perplexity than existing quantization baselines, and in several cases even match or slightly surpass FP16 at long context. This demonstrates that Q-ROAR effectively stabilizes quantized models under interpolation stress without sacrificing standard-context accuracy.\n\n\\section{Conclusion}\nIn this paper, we analyzed why position interpolation degrades post-training quantized LLMs and introduced \\emph{interpolation pressure} (PI) and \\emph{tail-inflation Ratios} (TIR) to quantify the interaction between RoPE scaling and quantization. Guided by these diagnostics, we proposed \\textbf{Q-ROAR}, a portable weight-only rescaling of $(W_Q,W_K)$ applied at the band level. Q-ROAR delivers consistent long-context improvements with negligible overhead and without kernel modifications. The method is designed for RoPE-interpolated and quantized models, it substantially reduces aliasing and outlier amplification at extended lengths. Overall, Q-ROAR lowers perplexity on long-context workloads by 14\\% to 21\\% compared to directly applying quantization on RoPE-interpolated LLM models while maintaining short-context accuracy and remaining fully compatible with standard LLM inference system pipelines.\n\n% \\section{Conclusion}\n% In this paper, we analyzed why position interpolation degrades post-training quantized LLMs and introduced $\\IP$ and $\\TIR$ to quantify the interaction between RoPE scaling and quantization. Guided by these diagnostics, we proposed \\textbf{Q-ROAR}, a portable weight-only rescaling of $(W_Q,W_K)$ applied at the band level. Q-ROAR delivers consistent long-context improvements with negligible overhead and without kernel modifications. While the method is tailored to RoPE and weight-quantized models—cases with heavy activation or KV quantization may still require limited clip expansion informed by $\\TIR$—it substantially reduces aliasing and outlier amplification at extended lengths. Looking ahead, we plan to generalize this framework to alternative positional encoding and explore lightweight, context-aware activation calibration.\n\\bibliography{iclr2026_conference}\n\\bibliographystyle{iclr2026_conference}\n\n\\appendix\n\\section{Appendix}\n\\subsection{LLM Usage}\nIn this paper, we use LLM mainly for polish writing and generate some plotting scripts for appendix.\n\n\\subsection{Algorithm and Searching Parameter}\n\\begin{algorithm}[h]\n\\caption{Band-Limited \\emph{Weight} Rescale for Quantized LLMs}\n\\label{alg:band-rescale}\n\\begin{algorithmic}[1]\n\\Require RoPE freqs $\\{\\omega_i\\}$, bands $\\{\\mathcal{B}_b\\}_{b=1}^B$, dev set $\\mathcal{D}$, lengths $\\mathcal{L}$ with weights $w_\\ell$, quantile $1-\\varepsilon$, prior $\\tau$, cap $\\kappa$, grid size $K$\n\\For{each band $b=1,\\dots,B$}\n \\State Estimate $\\rho_b^{\\mathrm{W}}$ on $\\mathcal{D}$ (short vs.\\ PI long)\n \\State Set bounds $[\\underline{g}_b,\\overline{g}_b] \\gets \\big[1/\\gamma_b,\\ \\min(\\gamma_b,\\kappa/\\rho_b^{\\mathrm{W}})\\big]$, with $\\gamma_b=1+\\tfrac{\\tau}{1+\\log(\\omega_{b,\\mathrm{med}}/\\omega_{\\min})}$\n \\State Build a log-spaced grid $\\mathcal{G}_b$ of $K$ points in $[\\underline{g}_b,\\overline{g}_b]$\n\\EndFor\n\\State Initialize $g_b\\gets 1$ (all $b$); compute baseline $J=\\sum_{\\ell} w_\\ell\\,\\mathrm{ppl}(\\ell)$ on $\\mathcal{D}$\n\\For{each band $b=1,\\dots,B$}\n \\For{each $g\\in\\mathcal{G}_b$}\n \\State Temporarily apply $W_Q^{(b)}\\!\\leftarrow g\\,W_Q^{(b)}$ and $W_K^{(b)}\\!\\leftarrow g^{-1}\\!W_K^{(b)}$ (symmetric mode)\n \\State Score $\\widehat{J}(g)=\\sum_{\\ell\\in\\mathcal{L}} w_\\ell\\,\\mathrm{ppl}(\\ell)$ on $\\mathcal{D}$\n \\EndFor\n \\State Commit $g_b \\leftarrow \\arg\\min_{g\\in\\mathcal{G}_b}\\widehat{J}(g)$\n\\EndFor\n\\State Optionally run a reverse pass ($b=B\\to 1$) for refinement\n\\State \\Return final $\\{g_b\\}$ and rescaled $W_Q,W_K$\n\\end{algorithmic}\n\\end{algorithm}\n\nWe use $B{=}8$ log-spaced bands; $\\varepsilon{=}10^{-3}$ (quantile); $\\tau{=}0.1$ (frequency prior); $\\kappa{=}1.2$ (overshoot cap); $K{=}7$ grid points per band; $w_\\ell\\propto \\ell$ to emphasize longer contexts. \nWe cache model states between trials and evaluate each candidate once (optionally recheck the best at the longest length). \nThis keeps complexity at $\\mathcal{O}(B\\!\\cdot\\!K)$ and aligns decisions with RoPE frequency structure while \\emph{only} modifying $W_Q$/$W_K$.\n\n\\subsection{Additional RoPE Interpolation Work Details}\n\\label{app:pi-details}\nLet $L_0$ be the training context window and $L \\gg L_0$ the desired test window. PI methods either (a) remap test positions $m \\mapsto \\hat{m}$ into $[0,L_0]$, or (b) rescale the per-dimension positional frequencies $\\{\\theta_i\\}_{i=1}^{d/2}$ used by the model’s rotary/phase parameters.\\footnote{We use $\\theta_i$ to denote the model’s internal per-dimension “positional frequency” parameters; details of RoPE are standard and omitted here.}\n\n\\textbf{Linear Interpolation (LI)} \\citep{chen2023extending}.\n Positions are uniformly compressed so the long context matches the training range:\n \\begin{equation}\n \\hat{m} \\;=\\; m \\cdot \\frac{L_0}{L}.\n \\label{eq:li}\n \\end{equation}\n In this case, large test positions are squeezed back into $[0,L_0]$, keeping the effective positional phases within the regime the model saw during training. In this case, all hidden rotation dimension pair was slow down equally. However, local resolution is reduced by the factor $L/L_0$, which can weaken short-range attention and does not works well without finetune.\n\n \\textbf{NTK-aware PI} \\citep{bloc97_2023_ntkaware_scaled_rope}. \n on the other hand, slow \\emph{low} frequencies channels more than \\emph{high} ones by adjusting the RoPE base. If the original base is $b$ (so $\\theta_i = b^{-2(i-1)/d}$), choose a stretch $\\alpha>1$ and set\n \\begin{equation}\n b' \\;=\\; b \\cdot \\alpha^{\\frac{d}{\\,d-2\\,}}\n \\quad\\Longleftrightarrow\\quad\n \\tilde{\\theta}_i \\;=\\; \\theta_i \\cdot \\alpha^{-\\frac{2(i-1)}{\\,d-2\\,}}.\n \\label{eq:ntk}\n \\end{equation}\n This method non-uniform slowdown preserves high-frequency detail (local fidelity) while still curbing long-range phase growth in low frequencies—often stronger tails than LI with little short-context regression.\n\n\\textbf{YaRN (Frequency-Band Segmentation)}\\citep{peng2023yarn}. \nYaRN does \\emph{not} interpolate the \\emph{high-frequency} dimensions (small wavelength $\\lambda_i$), always interpolates the \\emph{low-frequency} dimensions (large $\\lambda_i$) to avoid extrapolation, and applies an NTK-style partial interpolation in between. \nLet $S \\!=\\! L/L_0 \\ge 1$ be the stretch and define a wavelength proxy $\\lambda_i \\propto 1/\\theta_i$. \nYaRN sets a per-dimension slowdown exponent $g_i \\in [0,1]$ that \\emph{increases} with $\\lambda_i$:\n\\begin{equation}\n \\tilde{\\theta}_i \\;=\\; \\theta_i \\, S^{-g_i}, \n \\qquad \n g_i \\;=\\;\n \\begin{cases}\n 0, & \\lambda_i \\ll L \\quad \\text{(high freq; no interpolation)},\\\\[2pt]\n 1, & \\lambda_i \\ge L \\quad \\text{(low freq; always interpolate)},\\\\[2pt]\n \\beta_i \\in (0,1), & \\text{otherwise (NTK-like blend; increases with } \\lambda_i\\text{)}.\n \\end{cases}\n \\label{eq:yarn-correct}\n\\end{equation}\nEquivalently, low-frequency bands are linearly compressed ($m \\mapsto m/S$), high-frequency bands are left unchanged, and mid bands receive a softer, NTK-aware slowdown. \nThis preserves local detail while stabilizing long-range behavior; a mild attention-logit rescale may be used for additional stability.\n\n\\textbf{LongRoPE (Per-Dimension Scaling)} \\textit{(Ding et al.~\\citep{ding2024longrope})}.\n LongRoPE generalizes YaRN by assigning an independent scaling $s_i\\!\\ge\\!1$ to \\emph{each} positional dimension and searching $\\{s_i\\}$ on validation tasks:\n \\begin{equation}\n \\tilde{\\theta}_i \\;=\\; \\frac{\\theta_i}{s_i}, \n \\qquad i=1,\\dots,\\tfrac{d}{2}.\n \\label{eq:longrope}\n \\end{equation}\n LongRoPE allocate stronger slowdowns to the most alias-prone (typically higher-frequency) dimensions and lighter slowdowns elsewhere. \n This heterogeneous policy has enabled extremely long effective windows (reported to millions of tokens) while preserving task performance. However it require one-time search/tuning to obtain $\\{s_i\\}$.\n\n\nOverall, PI methods extend token length support \\emph{without finetuning} by either remapping positions (Eq.~\\ref{eq:li}) or rescaling positional frequencies (Eqs.~\\ref{eq:yarn-correct}–\\ref{eq:longrope}). \nLinear Interpolation is the simplest but uniformly compresses local resolution; YaRN offers a band-wise compromise; LongRoPE further tailors the slowdown per dimension to maximize long-range stability with minimal impact on short-range behavior. \n\n\\subsection{Additional Results with Vicuna-7b}\nSee results in table~\\ref{tab:govreport-Vicuna}\n\\renewcommand{\\arraystretch}{0.9}\n\\begin{table*}[h]\n\\centering\n\\caption{GovReport perplexity on \\textbf{Vicuna-7B} (YaRN = 16)}\n\\label{tab:govreport-Vicuna}\n\\begingroup\n\\setlength{\\tabcolsep}{5pt}\n\\resizebox{0.8\\textwidth}{!}{\n\\begin{tabular}{cc|ccccc}\n\\toprule\n\\multirow{2}{*}{Setting} & \\multirow{2}{*}{\\shortstack{Context Length \\\\ (YaRN = 16)}} & \\multicolumn{5}{c}{Evaluation Context Window Size} \\\\\n & & 2048 & 4096 & 8192 & 16384 & 32768 \\\\\n\\midrule\nFP16 & 64K & 4.504 & 4.424 & 4.394 & 4.238 & 6.251 \\\\\nRTN W4 & 64K & 4.612 & 4.552 & 4.537 & 4.644 & 6.986 \\\\\nAWQ W4 & 64K & 4.556 & 4.487 & 4.471 & 4.480 & 6.491 \\\\\n\\textbf{Q-ROAR W4} & 64K & \\textbf{4.508} & \\textbf{4.459} & \\textbf{4.386} & \\textbf{4.244} & \\textbf{6.008} \\\\\n\\bottomrule\n\\end{tabular}%\n}\n\\endgroup\n\n\\end{table*}\n\n\\subsection{Additional Comprehensive Study with Figure and Plots}\n\n\n\\\n\n%-----------------------------------------------------\n% \\paragraph{Setup.}\n% Let $L_0$ be the training window and $L\\gg L_0$ the target window. Denote stretch $S=L/L_0\\ge 1$. \n% The unified phase-scaling view is $\\phi_i^{\\text{scaled}}(m)=\\omega_i f(m)/s_i$, with position warp $f(\\cdot)$ and per-dim slowdown $s_i>0$. \n% Our proxy is\n% \\begin{equation}\n% \\Psi_i \\;=\\; \\omega_i\\,\\frac{f(D)}{s_i^2},\n% \\qquad\n% \\omega_i=b^{-\\tfrac{2(i-1)}{d}},\\;\\; i=1\\ (\\text{hi-freq}) \\to \\tfrac{d}{2}\\ (\\text{lo-freq}).\n% \\label{eq:psi-def}\n% \\end{equation}\n% For comparisons, define a baseline (no scaling) $\\Psi_i^{\\text{base}}=\\omega_i D$. \n% We will analyze the ratio $\\rho_i \\triangleq \\Psi_i/\\Psi_i^{\\text{base}} = \\big(f(D)/D\\big)\\cdot (1/s_i^2)$, which isolates how a strategy changes sensitivity relative to the original model.\n\n% \\paragraph{Linear Interpolation (LI).}\n% LI compresses positions uniformly: $f(D)=D/S$, $s_i\\equiv 1$.\n% \\begin{equation}\n% \\rho_i^{\\text{LI}} \\;=\\; \\frac{1}{S},\\qquad \n% \\Psi_i^{\\text{LI}} \\;=\\; \\frac{\\omega_i D}{S}.\n% \\end{equation}\n% \\textbf{Channel trend.} The \\emph{relative} ordering across $i$ is unchanged from baseline (still proportional to $\\omega_i$), so high-frequency channels remain the dominant contributors. \n% \\textbf{Global effect.} All channels’ pressure drop by the same factor $1/S$.\n\n% \\paragraph{NTK-aware PI (base change).}\n% Change RoPE base so low frequencies slow more than high. Using a common parameterization,\n% \\begin{equation}\n% s_i \\;=\\; \\alpha^{\\tfrac{2(i-1)}{\\,d-2\\,}}, \\quad \\alpha>1,\\qquad f(D)=D,\n% \\end{equation}\n% which corresponds to $\\tilde{\\theta}_i=\\theta_i/s_i=\\theta_i\\alpha^{-\\tfrac{2(i-1)}{\\,d-2\\,}}$.\n% Then\n% \\begin{equation}\n% \\rho_i^{\\text{NTK}} \\;=\\; \\frac{1}{s_i^2}\n% \\;=\\; \\alpha^{-\\tfrac{4(i-1)}{\\,d-2\\,}},\n% \\qquad\n% \\Psi_i^{\\text{NTK}} \\;=\\; \\omega_i D \\cdot \\alpha^{-\\tfrac{4(i-1)}{\\,d-2\\,}}.\n% \\end{equation}\n% \\textbf{Channel trend.} Exponential suppression grows with $i$ (i.e., stronger for mid/low frequencies). \n% High frequencies (\\(i\\!\\approx\\!1\\)) remain nearly unchanged (\\(\\rho_1\\!=\\!1\\)), so pressure concentrates even more in the highest-frequency channels. \n% \\textbf{Interpretation.} NTK-aware PI steepens the decay of $\\Psi_i$ across $i$, preserving local detail while taming long-range drift from low/mid bands.\n\n% \\paragraph{YaRN (band-wise, corrected).}\n% YaRN leaves \\emph{high-frequency} dims un-interpolated, \\emph{always} interpolates \\emph{low-frequency} dims to avoid extrapolation, and partially slows the mid band:\n% \\begin{equation}\n% s_i \\;=\\; \n% \\begin{cases}\n% 1, & i \\in \\text{high band},\\\\\n% S^{g_i}, & i \\in \\text{mid band},\\quad g_i\\in(0,1)\\ \\text{monotone in wavelength},\\\\\n% S, & i \\in \\text{low band},\n% \\end{cases}\n% \\qquad f(D)=D.\n% \\end{equation}\n% Hence\n% \\begin{equation}\n% \\rho_i^{\\text{YaRN}} \\;=\\; \\frac{1}{s_i^2} \\;=\\;\n% \\begin{cases}\n% 1, & \\text{high band},\\\\\n% S^{-2g_i}, & \\text{mid band},\\\\\n% S^{-2}, & \\text{low band},\n% \\end{cases}\n% \\qquad\n% \\Psi_i^{\\text{YaRN}} \\;=\\; \\omega_i D \\times\n% \\begin{cases}\n% 1, & \\text{high},\\\\\n% S^{-2g_i}, & \\text{mid},\\\\\n% S^{-2}, & \\text{low}.\n% \\end{cases}\n% \\end{equation}\n% \\textbf{Channel trend.} High band pressure is \\emph{unchanged} (preserves local detail and short-context calibration); mid/low bands are suppressed, with the strongest reduction at low frequencies. \n% \\textbf{Contrast to LI.} LI reduces all channels equally (\\(1/S\\)), while YaRN reduces low/mid much more (\\(1/S^{2g}\\) to \\(1/S^2\\)) but leaves high intact (\\(1\\)).\n\n% \\paragraph{LongRoPE (per-dimension).}\n% LongRoPE searches $s_i\\!\\ge\\!1$ per dimension (often with $f(D)=D$):\n% \\begin{equation}\n% \\rho_i^{\\text{LongRoPE}} \\;=\\; \\frac{1}{s_i^2},\n% \\qquad\n% \\Psi_i^{\\text{LongRoPE}} \\;=\\; \\omega_i D \\cdot \\frac{1}{s_i^2}.\n% \\end{equation}\n% \\textbf{Channel trend.} Arbitrary (data-driven). A natural objective is to \\emph{equalize pressure} across channels by choosing $s_i$ so that $\\Psi_i \\approx \\tau$ (target): \n% \\begin{equation}\n% s_i^\\star \\;\\approx\\; \\sqrt{\\frac{\\omega_i\\,D}{\\tau}} \\;\\; \\Rightarrow \\;\\; \n% \\Psi_i \\approx \\tau \\quad \\text{(subject to } s_i\\!\\ge\\!1\\text{ and caps)}.\n% \\end{equation}\n% This flattens the distribution of sensitivity across $i$, preventing a few high-frequency channels from dominating. In practice, constraints (e.g., $s_i\\!\\le\\!S$) and validation-driven trade-offs lead to moderated slowdowns for mid/low bands, often resembling “YaRN but with finer granularity.”\n\n% \\paragraph{Putting it together (ordering and slopes).}\n% Taking logs, for any strategy:\n% \\begin{equation}\n% \\log \\Psi_i \\;=\\; \\underbrace{-\\frac{2(i-1)}{d}\\log b}_{\\text{RoPE spectrum}} \n% \\;+\\; \\underbrace{\\log f(D)}_{\\text{position warp}} \n% \\;-\\; \\underbrace{2\\log s_i}_{\\text{slowdown}}.\n% \\end{equation}\n% \\emph{Baseline} has slope $-\\tfrac{2}{d}\\log b$ across $i$.\n% \\begin{itemize}\n% \\item \\textbf{LI}: adds a constant shift $-\\log S$ (same for all $i$); slope unchanged—ranking identical to baseline.\n% \\item \\textbf{NTK}: adds a linear-in-$i$ term $-\\tfrac{4(i-1)}{d-2}\\log \\alpha$, \\emph{steepening} the slope—suppresses mid/low more than high.\n% \\item \\textbf{YaRN}: piecewise slopes: unchanged in high band; increasingly negative through mid (via $-2g_i\\log S$); flattest (largest suppression) in low band ($-2\\log S$).\n% \\item \\textbf{LongRoPE}: slope becomes whatever the search induces; “equal-pressure” targets produce near-flat \\(\\Psi_i\\) across $i$ within constraints.\n% \\end{itemize}\n\n% \\paragraph{Worst-case and average pressure.}\n% Let $\\Psi_{\\max}=\\max_i \\Psi_i$ and $\\bar{\\Psi}=\\tfrac{2}{d}\\sum_i \\Psi_i$.\n% \\begin{itemize}\n% \\item \\textbf{LI}: $\\Psi_{\\max}$ occurs at $i=1$ and scales as $1/S$; $\\bar{\\Psi}$ scales as $1/S$.\n% \\item \\textbf{NTK}: $\\Psi_{\\max}$ remains near $i=1$ (unchanged), but $\\bar{\\Psi}$ decreases more than LI due to strong suppression of mid/low.\n% \\item \\textbf{YaRN}: $\\Psi_{\\max}$ remains at high band (unchanged), while $\\bar{\\Psi}$ drops sharply (low band $1/S^2$, mid $1/S^{2g}$). This concentrates sensitivity in high-freq while reducing the “tail.”\n% \\item \\textbf{LongRoPE}: can explicitly trade $\\Psi_{\\max}$ vs. $\\bar{\\Psi}$; equal-pressure designs minimize $\\Psi_{\\max}$ for a given average.\n% \\end{itemize}\n\n% \\paragraph{Practical implications.}\n% \\begin{enumerate}\n% \\item If your main failure is \\emph{global drift/aliasing} at long ranges, prioritize NTK/YaRN/LongRoPE over LI: they suppress low/mid bands more aggressively (\\(\\downarrow \\bar{\\Psi}\\)) without blurring high-frequency detail.\n% \\item If you see \\emph{local fidelity} regress (e.g., next-token quality), avoid suppressing high band—YaRN’s “no-interp high” and LongRoPE with caps on $s_i$ for small $i$ are preferable.\n% \\item To reduce quantization-induced logit noise, pair any schedule with \\emph{phase-aware calibration} and consider mixed precision for the few channels with the largest $\\Psi_i$ (often the top-\\(k\\) high-frequency channels).\n% \\end{enumerate}\n\n\n\n% \\paragraph{Phase-swept calibration (PSC): goal.}\n% Position interpolation (PI) changes the per-dimension phase trajectory $\\phi_i^{\\text{scaled}}(m)=\\omega_i f(m)/s_i$, shifting activation/KV statistics across positions.\n% Given a per-channel saturating uniform quantizer with clipping $c_i$ and $b$ bits, PSC chooses $c_i$ (and thus $\\Delta_i=2c_i/(2^b\\!-\\!1)$) to minimize the \\emph{phase-averaged distortion} under long-context use:\n% \\begin{equation}\n% \\min_{c_i>0}\\;\\; \n% \\mathcal{D}_i(c_i)\n% \\;\\triangleq\\;\n% \\mathbb{E}_{m\\sim p(m)}\\;\\mathbb{E}\\!\\left[\n% \\big\\|Q_{c_i,b}\\big(z^{(i)}(m)\\big)-z^{(i)}(m)\\big\\|_2^2\n% \\right],\n% \\qquad\n% z^{(i)}(m)=R\\!\\big(\\phi_i^{\\text{scaled}}(m)\\big)u^{(i)}.\n% \\label{eq:psc-obj}\n% \\end{equation}\n% Here $u^{(i)}$ is the (unrotated) 2D component, $R(\\cdot)$ is the $2{\\times}2$ rotation, and $p(m)$ captures how positions are used (uniform or attention-weighted).\n\n% \\paragraph{Distortion decomposition.}\n% With a midrise, saturating quantizer, the error per coordinate can be split into quantization noise and clipping bias:\n% \\begin{equation}\n% \\mathbb{E}\\!\\left[\\|Q_{c,b}(x)-x\\|_2^2\\right]\n% \\;\\approx\\;\n% \\underbrace{\\frac{\\Delta^2}{12}\\,\\Pr(|x|\\le c)}_{\\text{quantization}}\n% \\;+\\;\n% \\underbrace{\\mathbb{E}\\!\\left[(|x|-c)^2\\,\\mathbf{1}\\{|x|>c\\}\\right]}_{\\text{clipping}},\n% \\qquad \\Delta=\\frac{2c}{2^b-1}.\n% \\label{eq:dist-split}\n% \\end{equation}\n% Under PI, the \\emph{same} channel sees different $x$ due to $R(\\phi_i^{\\text{scaled}}(m))$, so both terms depend on $m$; PSC chooses $c$ that trades off the $O(c^2)$ quantization term against the tail clipping term \\emph{aggregated across phases}—exactly the phase/range factor $\\eta_i(m)$ you defined.\n\n% \\paragraph{Which phases to sample?}\n% Let $S=L/L_0$. For channel $i$, the phase span over the window is $\\Phi_i=\\phi_i^{\\text{scaled}}(L)-\\phi_i^{\\text{scaled}}(0)=\\omega_i f(L)/s_i$.\n% \\begin{itemize}\n% \\item \\textbf{High freq (large $\\omega_i$):} $\\Phi_i\\gg 2\\pi$; uniform $m$ is already near-uniform in phase. Use $m_k$ uniform on $[0,L]$.\n% \\item \\textbf{Low freq (small $\\omega_i$):} $\\Phi_i$ may be $\\ll 2\\pi$; extremes matter. Sample \\emph{in phase}: $\\phi_k$ uniform on $\\big[0,\\Phi_i\\big]$ and set $m_k=\\phi_k s_i/\\omega_i$ (or directly apply $R(\\phi_k)$ to $u^{(i)}$ without touching $m$).\n% \\item \\textbf{Weighting $p(m)$:} Uniform is fine; better, weight by measured attention usage $p(m)\\!\\propto\\!\\sum_{\\ell}\\!\\mathbb{E}[\\mathrm{softmax}(QK^\\top/\\sqrt{d})]$ on a tiny validation set to emphasize practically visited offsets.\n% \\end{itemize}\n% In practice $K\\in\\{8,16,32\\}$ phases/channel suffices.\n\n% \\paragraph{Empirical objective (fast to compute).}\n% Let $\\mathcal{X}_i=\\{x_{ik}\\}$ be samples of both coordinates of $z^{(i)}(m_k)$ collected across tokens/sequences and phases, with optional weights $w_{ik}$ (from $p(m)$).\n% Define\n% \\begin{equation}\n% \\widehat{\\mathcal{D}}_i(c)\n% \\;=\\;\n% \\frac{1}{W}\\sum_{k}w_{ik}\\;\\big(Q_{c,b}(x_{ik})-x_{ik}\\big)^2,\n% \\qquad W=\\sum_k w_{ik}.\n% \\label{eq:emp-obj}\n% \\end{equation}\n% Minimize \\eqref{eq:emp-obj} over a grid of $c$ (log-spaced), or perform a 1D line search. This requires only a scalar sweep per channel, and you can reuse histograms for speed:\n% \\begin{align}\n% \\text{Let }h_j = \\sum_k w_{ik}\\,\\mathbf{1}\\{ |x_{ik}|\\in [\\tau_{j},\\tau_{j+1})\\},\\quad\n% t_j = \\sum_k w_{ik}\\,|x_{ik}|\\,\\mathbf{1}\\{ |x_{ik}|\\in [\\tau_{j},\\tau_{j+1})\\},\\quad\n% u_j = \\sum_k w_{ik}\\,x_{ik}^2\\,\\mathbf{1}\\{ \\cdot \\},\n% \\end{align}\n% so clipping terms for a candidate $c$ can be computed with prefix sums over bins $\\{\\tau_j\\}$ in $O(1)$ per $c$.\n\n% \\paragraph{KV-cache alignment trick (optional, cheaper).}\n% If you “unrotate–quantize–rerotate” the cache:\n% \\begin{equation}\n% \\tilde{k}(n)=R\\!\\big(-\\phi_i^{\\text{scaled}}(n)\\big)k(n),\\quad\n% \\hat{\\tilde{k}}=\\mathrm{Quantize}(\\tilde{k}),\\quad\n% \\hat{k}(n)=R\\!\\big(\\phi_i^{\\text{scaled}}(n)\\big)\\hat{\\tilde{k}},\n% \\end{equation}\n% then the cached distribution becomes phase-stationary (you quantize $u^{(i)}$ directly). In this case, PSC simplifies: collect $\\mathcal{X}_i$ from \\emph{unrotated} coordinates only (no sweep), then minimize \\eqref{eq:emp-obj}. This nearly removes the $\\eta_i(m)$ phase factor for KV and cuts distortion without retraining.\n\n% \\paragraph{Choosing percentiles vs true MSE.}\n% A simple surrogate is a robust percentile clip, $c_i=\\mathrm{quantile}_{p}(|x|)$ across the phase pool (e.g., $p=99.9\\%$). It controls clipping but ignores the $O(c^2)$ quantization term. The empirical MSE objective \\eqref{eq:emp-obj} is strictly better; in ablations you’ll typically see:\n% \\[\n% \\text{percentile\\,only} \\quad \\Rightarrow \\quad \\text{low clipping, higher quant noise (too-large $c$)},\n% \\]\n% \\[\n% \\text{MSE\\,minimization} \\quad \\Rightarrow \\quad \\text{balanced $c$, lower worst-case and average error}.\n% \\]\n\n% \\paragraph{Relation to $\\eta_i(m)$ and $\\Psi_i$.}\n% Your phase/range mismatch factor enters as\n% \\[\n% \\mathbb{E}\\!\\left[\\|Q_{c,b}(z^{(i)}(m))-z^{(i)}(m)\\|_2^2\\right]\n% \\;\\approx\\; \\frac{\\Delta_i^2}{6}\\cdot \\eta_i(m),\n% \\]\n% when clipping is negligible. PSC reduces both the \\emph{mean} and \\emph{max} of $\\eta_i(m)$ over phases by selecting $c_i$ that remains valid across the swept phases; this directly lowers the logit perturbation bound in \\eqref{eq:logit-perturb-bound}. Moreover, because \\(\\Psi_i=\\omega_i f(D)/s_i^2\\) flags channels with high sensitivity, you can prioritize PSC precision (more bits or finer $c_i$ grid) for top-\\(\\Psi_i\\) channels.\n\n% \\paragraph{Algorithm (per channel $i$).}\n% \\begin{algorithmic}[1]\n% \\State Choose PI schedule $(f,s_i)$; compute phase span $\\Phi_i$.\n% \\State Sample $K$ phases (uniform in phase for low freq; uniform in $m$ for high freq); build weighted pool $\\mathcal{X}_i$ of rotated coords.\n% \\If{using KV unrotate trick} replace rotated coords by unrotated ones.\n% \\State Build histograms $\\{h_j,t_j,u_j\\}$ over $|x|$ with weights $w_{ik}$.\n% \\For{$c$ in log-spaced grid} \\Comment{e.g., 40 candidates}\n% \\State $\\Delta=2c/(2^b-1)$; \n% \\State compute empirical quantization term $\\frac{\\Delta^2}{12}\\cdot \\sum_{|x|\\le c} w_{ik}$ via prefix sums;\n% \\State compute empirical clipping term $\\sum_{|x|>c} w_{ik} (|x|-c)^2$ via tail sums;\n% \\State $\\widehat{\\mathcal{D}}_i(c)=\\text{quant}+\\text{clip}$.\n% \\EndFor\n% \\State $c_i \\leftarrow \\arg\\min_c \\widehat{\\mathcal{D}}_i(c)$; set $\\Delta_i=2c_i/(2^b-1)$.\n% \\end{algorithmic}\n\n% \\paragraph{Complexity \\& practical defaults.}\n% Let $N_i$ be samples per channel and $H$ histogram bins. PSC cost is $O(N_i + H\\cdot C)$ per channel for $C$ candidate $c$ values (e.g., $H\\!=\\!1024$, $C\\!=\\!40$). \n% Defaults that work well:\n% \\begin{itemize}\n% \\item $K=16$ phases; uniform $m$ for high band, uniform phase for low band; $p(m)$ uniform unless you can cheaply estimate attention usage.\n% \\item Percentile warm start $c_i^{(0)}=\\mathrm{quantile}_{99.9\\%}$, then refine with \\eqref{eq:emp-obj}.\n% \\item If budget is tight: run PSC only for top \\(20\\%\\) channels by \\(\\Psi_i\\) and reuse short-context clips for the rest.\n% \\end{itemize}\n\n% \\paragraph{Layer/head granularity.}\n% PSC is most effective per \\emph{head-channel} (2D pair), but a strong Pareto point is:\n% \\begin{enumerate}\n% \\item per-head shared $c$ for low/mid bands (similar phase spans), \n% \\item per-channel $c$ only for the top-\\(\\Psi_i\\) high-pressure channels.\n% \\end{enumerate}\n\n% \\paragraph{When to recalibrate.}\n% PSC is tied to the PI schedule $(f,s_i)$. Change the schedule (e.g., switch LI $\\to$ YaRN, or $S$ from $8\\to32$) \\(\\Rightarrow\\) rerun PSC (it’s cheap). If you quantize KV with unrotate, PSC becomes largely schedule-invariant for the cache.\n\n% \\paragraph{Takeaway.}\n% PSC aligns quantizer ranges with the phase-swept distributions induced by PI. It directly shrinks your $\\eta_i(m)$ across phases and, through \\eqref{eq:logit-perturb-bound}, curbs logit noise drift—especially when combined with (i) the KV unrotate trick, and (ii) prioritizing high-\\(\\Psi_i\\) channels for finer calibration or higher precision.\n\n\n\n\n% \\vspace{0.5ex}\n% \\paragraph{Outlier shift under PI and quantization.}\n% Let $h(m)$ denote the hidden state at position $m$ and $z_Q(m)=W_Q h(m)$, $z_K(n)=W_K h(n)$.\n% Define the training (short-context) distributions $\\mathcal{H}_0$ and the long-context (with PI) distributions $\\mathcal{H}_D$.\n% We quantify \\emph{outlier shift} via high-quantile ratios:\n% \\begin{align}\n% \\rho^{\\mathrm{W}}_{i} &\\;\\triangleq\\; \n% \\frac{Q_{|w_{Q,i}^\\top h|,\\,h\\sim \\mathcal{H}_D}(1-\\varepsilon)}{Q_{|w_{Q,i}^\\top h|,\\,h\\sim \\mathcal{H}_0}(1-\\varepsilon)},\n% \\qquad\n% \\tilde\\rho^{\\mathrm{W}}_{i} \\;\\triangleq\\; \n% \\frac{Q_{|w_{K,i}^\\top h|,\\,h\\sim \\mathcal{H}_D}(1-\\varepsilon)}{Q_{|w_{K,i}^\\top h|,\\,h\\sim \\mathcal{H}_0}(1-\\varepsilon)}, \\\\\n% \\rho^{\\mathrm{A}}_{i}(m) &\\;\\triangleq\\;\n% \\frac{Q_{\\|R(\\phi_i^{\\text{scaled}}(m))u_i\\|_\\infty,\\,u_i\\sim \\mathcal{Z}_{0,i}}(1-\\varepsilon)}\n% {Q_{\\|R(\\phi_i(m))u_i\\|_\\infty,\\,u_i\\sim \\mathcal{Z}_{0,i}}(1-\\varepsilon)} ,\n% \\end{align}\n% where $w_{Q,i}$ is the $i$-th row of $W_Q$, $R(\\cdot)$ is the RoPE rotation on the $(2\\times 2)$ pair $i$, $u_i$ is the pre-RoPE pair for channel $i$, and $\\mathcal{Z}_{0,i}$ is its training distribution. \n% Here $\\rho^\\mathrm{W}$ captures \\emph{weight-driven pre-activation} tail dilation via $\\mathcal{H}_D$ (PI changes attention/statistics of $h$), while $\\rho^\\mathrm{A}$ captures \\emph{axis-aligned} amplitude inflation from phase crowding ($\\ell_\\infty$ governs clipping in per-axis quantizers).\n\n% \\vspace{0.25ex}\n% \\paragraph{Calibration-aware MSE with clipping.}\n% For a per-channel, per-axis uniform quantizer with step $\\Delta_i$ and clip $[-c_i,c_i]$, the per-coordinate distortion under a signal $x$ with distribution $\\mathcal{X}$ decomposes as\n% \\begin{equation}\n% \\mathrm{MSE}_i(\\Delta_i,c_i;\\mathcal{X})\n% \\;=\\; (1-p_{\\mathrm{clip}})\\,\\frac{\\Delta_i^2}{12}\n% \\;+\\; \\mathbb{E}\\!\\left[(|x|-c_i)^2 \\,\\mathbf{1}\\{|x|>c_i\\}\\right],\n% \\qquad \n% p_{\\mathrm{clip}}=\\Pr_{\\mathcal{X}}(|x|>c_i).\n% \\label{eq:mse-clip}\n% \\end{equation}\n% If $(\\Delta_i,c_i)$ are calibrated on training ($\\mathcal{X}_0$) to target $p_{\\mathrm{clip}}=\\varepsilon$, then under outlier shift to $\\mathcal{X}_D$ the clipping term increases roughly with the quantile ratio: \n% $p_{\\mathrm{clip}}(\\mathcal{X}_D;c_i)\\approx F_{\\mathcal{X}_D}^{\\mathrm{tail}}(c_i)\\uparrow$ as $Q_{\\mathcal{X}_D}(1-\\varepsilon)$ grows.\n\n% \\vspace{0.5ex}\n% \\paragraph{Case A: Weight-only quantization (WQ).}\n% Let $\\hat W_Q=W_Q+E_Q$, $\\hat W_K=W_K+E_K$ with deterministic perturbations $E_Q,E_K$ fixed after quantization. \n% Queries/keys are in full precision after RoPE. Then\n% \\begin{align}\n% \\hat q(m) &= \\mathrm{RoPE}\\!\\big((W_Q+E_Q)h(m),\\,m\\big), \n% & \\hat k(n) &= \\mathrm{RoPE}\\!\\big((W_K+E_K)h(n),\\,n\\big), \\\\\n% e_q(m) &\\triangleq \\hat q(m)-q(m) = \\mathrm{RoPE}\\!\\big(E_Q h(m),\\,m\\big), \n% & e_k(n) &\\triangleq \\hat k(n)-k(n) = \\mathrm{RoPE}\\!\\big(E_K h(n),\\,n\\big).\n% \\end{align}\n% Using RoPE orthonormality,\n% \\begin{equation}\n% \\|e_q(m)\\|_2 \\le \\|E_Q\\|_2\\,\\|h(m)\\|_2,\n% \\qquad \n% \\|e_k(n)\\|_2 \\le \\|E_K\\|_2\\,\\|h(n)\\|_2.\n% \\end{equation}\n% Hence the attention-logit perturbation at $(m,n)$ obeys\n% \\begin{equation}\n% |\\hat s_{mn}-s_{mn}|\n% \\;\\le\\; \\|E_Q\\|_2\\,\\|h(m)\\|_2\\,\\|k(n)\\|_2 \n% \\;+\\; \\|E_K\\|_2\\,\\|h(n)\\|_2\\,\\|q(m)\\|_2 \n% \\;+\\; \\|E_Q\\|_2\\,\\|E_K\\|_2\\,\\|h(m)\\|_2\\,\\|h(n)\\|_2.\n% \\label{eq:wq-logit-bound}\n% \\end{equation}\n% Outlier shift enters via $\\|h(\\cdot)\\|_2$ statistics: PI modifies $\\mathcal{H}_D$ and thus the high-quantiles of $|w_{Q,i}^\\top h|,|w_{K,i}^\\top h|$, summarized by $\\rho_i^{\\mathrm{W}},\\tilde\\rho_i^{\\mathrm{W}}$. \n% If calibration ensured $p_{\\mathrm{clip}}=\\varepsilon$ on pre-activations at train time, then under $\\rho^{\\mathrm{W}}>1$ the optimal per-channel clip should scale as $c_i^{\\star}(D)\\approx \\rho^{\\mathrm{W}}_{i}\\,c_i^{\\star}(0)$ to keep $p_{\\mathrm{clip}}\\approx\\varepsilon$.\n\n% \\vspace{0.5ex}\n% \\paragraph{Case B: Weight+activation quantization (WAQ).}\n% Now also quantize (per-axis) the post-RoPE pairs:\n% \\begin{equation}\n% \\tilde q(m)=Q_{\\mathrm{act}}\\!\\big(q(m)\\big), \\quad \n% \\tilde k(n)=Q_{\\mathrm{act}}\\!\\big(k(n)\\big), \\quad \n% \\hat q(m)=Q_{\\mathrm{act}}\\!\\big(\\mathrm{RoPE}((W_Q+E_Q)h(m),m)\\big),\n% \\end{equation}\n% and similarly for $\\hat k(n)$. Decompose total error as\n% {\\small\n% \\begin{align}\n% \\hat q(m)-q(m) &= \\underbrace{\\mathrm{RoPE}(E_Q h(m),m)}_{\\text{weight term}} \n% + \\underbrace{\\big(Q_{\\mathrm{act}}(q(m)+\\mathrm{RoPE}(E_Q h(m),m))- (q(m)+\\mathrm{RoPE}(E_Q h(m),m))\\big)}_{\\text{activation term } \\delta_q(m)},\n% \\end{align}}\n% with an analogous $\\delta_k(n)$.\n% Using \\eqref{eq:mse-clip} per axis and summing over the $2$ coordinates of each $(2\\times 2)$ pair $i$,\n% \\begin{equation}\n% \\mathbb{E}\\!\\left[\\|\\delta_q^{(i)}(m)\\|_2^2\\right]\n% \\;\\approx\\; 2\\cdot \\mathrm{MSE}_i\\!\\left(\\Delta_i,c_i;\\,\\mathcal{X}_{i,m}\\right),\n% \\qquad \n% \\mathcal{X}_{i,m}:\\;\\text{law of the $i$-th rotated coordinate at } m.\n% \\end{equation}\n% Under PI, \\emph{phase crowding} changes $\\mathcal{X}_{i,m}$ predominantly through the axis-aligned amplitude\n% $A_i(m)=\\|R(\\phi_i^{\\text{scaled}}(m))u_i\\|_\\infty$, inflating clipping via the ratio $\\rho_i^{\\mathrm{A}}(m)$.\n% To maintain the training-time clipping target $\\varepsilon$, set\n% \\begin{equation}\n% c_i^{\\star}(D,m) \\;\\approx\\; \\rho_i^{\\mathrm{A}}(m)\\;c_i^{\\star}(0), \n% \\qquad \n% \\Delta_i^{\\star}(D,m) \\;\\propto\\; \\frac{c_i^{\\star}(D,m)}{2^{b_i}-1}.\n% \\end{equation}\n% The logit perturbation now includes activation terms:\n% \\begin{equation}\n% \\begin{aligned}\n% |\\hat s_{mn}-s_{mn}|\n% \\;\\le\\;&\\;\\|e_q(m)\\|_2\\,\\|k(n)\\|_2 + \\|e_k(n)\\|_2\\,\\|q(m)\\|_2 + \\|e_q(m)\\|_2\\,\\|e_k(n)\\|_2 \\\\\n% &+ \\|\\delta_q(m)\\|_2\\,\\|k(n)+e_k(n)\\|_2 \n% + \\|\\delta_k(n)\\|_2\\,\\|q(m)+e_q(m)\\|_2 \n% + \\|\\delta_q(m)\\|_2\\,\\|\\delta_k(n)\\|_2.\n% \\end{aligned}\n% \\label{eq:waq-logit-bound}\n% \\end{equation}\n% Taking expectations and applying \\eqref{eq:mse-clip} yields position-dependent distortion dominated by \\emph{(i)} $\\|E_Q\\|_2,\\|E_K\\|_2$ and outlier statistics of $h$ (via $\\rho^{\\mathrm{W}}$), and \\emph{(ii)} activation clipping terms controlled by $\\rho^{\\mathrm{A}}_{i}(m)$.\n\n% \\vspace{0.5ex}\n% \\paragraph{Practical summary.}\n% Weight-only quantization is position-invariant except through $h$; its risk grows with pre-activation outlier shift $\\rho^{\\mathrm{W}}$ under PI.\n% Adding activation/KV quantization introduces a \\emph{phase-sensitive} axis-aligned risk quantified by $\\rho^{\\mathrm{A}}(m)$, which increases with phase crowding at long context.\n% Both effects can be mitigated by (a) per-channel clip rescaling using the quantile ratios, and (b) selective phase scaling that reduces crowding on high-frequency pairs.\n\n\nThis section presents a comprehensive ablation study examining the effects of different quantization methods, position interpolation techniques, Hadamard transformations, and their combinations on long-context language model performance. All experiments are conducted using perplexity evaluation on extended sequences up to 19,456 tokens.\n\n\\subsubsection{Position Interpolation Methods Analysis}\n\\label{subsec:position_interpolation}\n\nPosition interpolation is crucial for extending pre-trained models to longer contexts than their training sequences. We compare three approaches: YARN (Yet Another RoPE extensioN), NTK-aware scaled RoPE, and no interpolation.\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=0.8\\textwidth]{publication_figures/figure_3_position_interpolation.pdf}\n \\caption{\\textbf{Position Interpolation Methods Comparison.} Performance comparison of NTK-aware scaling, YARN interpolation, and no interpolation across FP16 and AWQ quantized models. YARN consistently demonstrates superior performance for long-context extension, maintaining lower perplexity degradation as sequence length increases.}\n \\label{fig:position_interpolation_main}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/yarn_vs_ntk_detailed_comparison.pdf}\n \\caption{\\textbf{Detailed YARN vs NTK Analysis.} In-depth comparison showing (a) direct performance comparison, (b) relative improvement of YARN over NTK, (c) scaling factor analysis, and (d) convergence behavior. YARN shows consistent advantages, particularly at longer sequence lengths with up to 15\\% relative improvement over NTK interpolation.}\n \\label{fig:yarn_ntk_detailed}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/interpolation_method_deep_dive.pdf}\n \\caption{\\textbf{Interpolation Method Deep Dive Analysis.} Comprehensive analysis across four dimensions: (a) method comparison with error bars, (b) relative performance improvements, (c) sequence length sensitivity analysis, and (d) convergence stability metrics. Results demonstrate YARN's robustness across different evaluation criteria.}\n \\label{fig:interpolation_deep_dive}\n\\end{figure}\n\n\\textbf{Key Findings:}\n\\begin{itemize}\n \\item YARN consistently outperforms NTK-aware scaling by 8-15\\% across all sequence lengths\n \\item No interpolation leads to catastrophic performance degradation beyond training context\n \\item YARN maintains more stable convergence properties compared to NTK scaling\n \\item The advantage of YARN becomes more pronounced at longer sequences ($>$12K tokens)\n\\end{itemize}\n\n\\subsubsection{Quantization Methods Comparison}\n\\label{subsec:quantization_methods}\n\nWe evaluate four quantization approaches: FP16 (reference), AWQ (Activation-aware Weight Quantization), RTN (Round-to-Nearest), and NF4 (4-bit NormalFloat), examining both weight-only and weight+activation quantization scenarios.\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=0.8\\textwidth]{publication_figures/figure_1_main_comparison.pdf}\n \\caption{\\textbf{Main Quantization Methods Comparison.} Performance evaluation of primary quantization techniques across extended sequences. NF4 achieves the best quality-compression trade-off, while AWQ provides an excellent balance between performance and efficiency for practical deployment.}\n \\label{fig:quantization_main}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/quantization_precision_comparison.pdf}\n \\caption{\\textbf{Quantization Precision Analysis.} Detailed comparison of quantization methods showing (a) perplexity vs sequence length, (b) memory efficiency metrics, (c) compression ratios, and (d) quality-efficiency Pareto frontier. NF4 emerges as the optimal choice for quality-sensitive applications.}\n \\label{fig:quantization_precision}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/weight_vs_activation_quantization.pdf}\n \\caption{\\textbf{Weight vs Activation Quantization Effects.} Comparative analysis of weight-only versus weight+activation quantization strategies. Results show that activation quantization introduces additional performance degradation but enables higher compression ratios and inference speed improvements.}\n \\label{fig:weight_activation_quant}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/advanced_quantization_techniques.pdf}\n \\caption{\\textbf{Advanced Quantization Techniques.} Analysis of sophisticated quantization methods including mixed-precision strategies and adaptive quantization. Advanced techniques show promise for further improving the quality-efficiency trade-off.}\n \\label{fig:advanced_quantization}\n\\end{figure}\n\n\\textbf{Key Findings:}\n\\begin{itemize}\n \\item NF4 achieves the lowest perplexity degradation (2.68\\%) while maintaining 4x compression\n \\item AWQ provides an practical balance with 5.13\\% degradation and efficient inference\n \\item Weight+activation quantization increases degradation by 4\\% but enables higher throughput\n \\item Advanced quantization techniques can further reduce quality loss by 1-2\\% due to the consideration of outlier effect\n \\item Performance degradation will be further enlarged with the increased interpolation scale rate and token length, so our approach is necessary and exactly tackling this problem\n\\end{itemize}\n\n\\subsubsection{Hadamard Transformation Effects}\n\\label{subsec:hadamard_transformations}\n\nHadamard transformations can improve quantization by redistributing activation magnitudes and weight distributions. We analyze their impact on different projection layers and quantization scenarios.\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{publication_figures/figure_2_hadamard_effects.pdf}\n \\caption{\\textbf{Hadamard Transformation Effects.} Impact of Hadamard transformations on (a) weight-only quantization and (b) weight+activation quantization across different projection layers (gate, up, down). Hadamard transformations show more significant benefits for weight+activation scenarios.}\n \\label{fig:hadamard_main}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/hadamard_layer_analysis.pdf}\n \\caption{\\textbf{Layer-wise Hadamard Analysis.} Detailed examination of Hadamard effects across different transformer layers and projection types. Analysis reveals (a) per-layer sensitivity, (b) projection-specific benefits, (c) cumulative effects, and (d) optimization convergence patterns.}\n \\label{fig:hadamard_layers}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/prequantization_effects.pdf}\n \\caption{\\textbf{Pre-quantization Transformation Effects.} Analysis of various pre-quantization transformations including Hadamard, rotation, and scaling operations. Results demonstrate the importance of proper transformation selection for different quantization schemes.}\n \\label{fig:prequantization}\n\\end{figure}\n\n\\textbf{Key Findings:}\n\\begin{itemize}\n \\item Hadamard transformations provide 3-8\\% improvement in weight+activation quantization\n \\item Benefits are more pronounced in deeper layers and gate/up projections\n \\item Weight-only quantization shows minimal improvement from Hadamard transforms\n \\item Layer-specific optimization of transformations can yield additional 2-3\\% gains\n\\end{itemize}\n\n\\subsubsection{Temperature Scaling and Calibration}\n\\label{subsec:temperature_scaling}\n\nTemperature scaling affects the quantization calibration process and can significantly impact model performance. We analyze different temperature settings and their interaction with quantization methods.\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/temperature_scaling_analysis.pdf}\n \\caption{\\textbf{Temperature Scaling Analysis.} Comprehensive study of temperature effects on quantization performance showing (a) temperature sensitivity curves, (b) calibration stability, and long-context behavior. Proper temperature selection can improve performance by 5-10\\%.}\n \\label{fig:temperature_scaling}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/method_convergence_analysis.pdf}\n \\caption{\\textbf{Method Convergence Analysis.} Convergence behavior and stability analysis across different combinations of techniques. Results show convergence patterns, optimization stability, and method interaction effects critical for reliable deployment.}\n \\label{fig:convergence_analysis}\n\\end{figure}\n\n\\textbf{Key Findings:}\n\\begin{itemize}\n \\item Optimal temperature varies by quantization method (0.8-2.2 range)\n \\item AWQ shows higher temperature sensitivity than RTN or NF4\n \\item Temperature scaling effects are amplified in long-context scenarios\n \\item Proper calibration(weight re-scale) can recover 40-60\\% of quantization quality loss\n\\end{itemize}\n\n\\subsubsection{Channel Response and Embedding Analysis}\n\\label{subsec:channel_analysis}\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/sensitivity_1.png}\n \\caption{\\textbf{Channel Response Sensitivity.} Testing each channel responses on Q,K projection layer weight rescaling (all attention layers) with fixed factor 2}\n \\label{fig:Channel_Response_analysis}\n\\end{figure}\nAdvanced analysis of channel-wise responses and embedding-specific modifications reveals important insights for optimization and specialized deployment scenarios.\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/channel_response_analysis.pdf}\n \\caption{\\textbf{Channel Response Analysis.} Analysis of channel-wise activation patterns and their impact on quantization performance. Results show channel importance distributions, optimization opportunities, and adaptive quantization potential.}\n \\label{fig:channel_response}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/embedding_only_modifications.pdf}\n \\caption{\\textbf{Embedding-Only Modifications.} Specialized analysis of embedding layer modifications showing (a) embedding quantization effects, (b) vocabulary adaptation strategies, (c) position encoding modifications, and (d) combined optimization approaches. Embedding modifications can provide targeted improvements for specific use cases.}\n \\label{fig:embedding_analysis}\n\\end{figure}\n\n\\textbf{Key Findings:}\n\\begin{itemize}\n \\item Channel importance follows a power-law distribution with 20\\% critical channels\n \\item Embedding-only (first layer) modifications can improve efficiency by 15-20\\% for specific tasks\n \\item Adaptive channel rescaling shows improvement over uniform approaches\n \\item Position encoding modifications interact significantly with interpolation methods\n\\end{itemize}\n\n\\subsubsection{Comprehensive Method Comparison}\n\\label{subsec:comprehensive_comparison}\n\nWe present a holistic comparison of all investigated methods and their combinations.\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/comprehensive_method_comparison.pdf}\n \\caption{\\textbf{Comprehensive Method Comparison Matrix.} Complete comparison matrix showing performance, efficiency, and complexity trade-offs across all method combinations. This analysis guides optimal configuration selection for different deployment constraints and quality requirements.}\n \\label{fig:comprehensive_comparison}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/sequence_length_breakdown.pdf}\n \\caption{\\textbf{Sequence Length Breakdown Analysis.} Detailed performance analysis across different sequence length ranges showing (a) short-context performance, (b) medium-context behavior, (c) long-context scalability, and (d) extrapolation capabilities. Critical for understanding method applicability across different use cases.}\n \\label{fig:sequence_breakdown}\n\\end{figure}\n\n\\begin{figure}[h!]\n \\centering\n \\includegraphics[width=\\textwidth]{ablation_plots/statistical_analysis.pdf}\n \\caption{\\textbf{Statistical Analysis and Error Patterns.} Statistical significance testing and error pattern analysis across all experimental conditions. Results provide confidence intervals, significance levels, and systematic error identification for robust conclusions.}\n \\label{fig:statistical_analysis}\n\\end{figure}\n\n% \\subsubsection{Deployment Recommendations}\n% \\label{subsec:recommendations}\n\n% Based on our comprehensive ablation study, we provide the following recommendations for different deployment scenarios:\n\n% \\textbf{Quality-First Deployment:}\n% \\begin{itemize}\n% \\item Use NF4 quantization with YARN interpolation\n% \\item Apply temperature scaling (T=0.9-1.0)\n% \\item Consider embedding-specific optimizations for specialized tasks\n% \\item Expected: 2.7\\% perplexity degradation, 4x compression\n% \\end{itemize}\n\n% \\textbf{Balanced Deployment:}\n% \\begin{itemize}\n% \\item Use AWQ quantization with YARN interpolation\n% \\item Apply Hadamard transformations for weight+activation scenarios\n% \\item Optimize temperature based on target domain (T=0.8-1.1)\n% \\item Expected: 5.1\\% perplexity degradation, 4x compression, fast inference\n% \\end{itemize}\n\n% \\textbf{Efficiency-First Deployment:}\n% \\begin{itemize}\n% \\item Use RTN weight+activation quantization with YARN interpolation\n% \\item Apply aggressive channel pruning (top 80\\% channels)\n% \\item Use embedding-only modifications for task-specific optimization\n% \\item Expected: 9.5\\% perplexity degradation, 6x+ compression, maximum throughput\n% \\end{itemize}\n\n% \\subsubsection{Limitations and Future Work}\n% \\label{subsec:limitations}\n\n% While our ablation study is comprehensive, several limitations and future research directions merit discussion:\n\n% \\textbf{Current Limitations:}\n% \\begin{itemize}\n% \\item Evaluation limited to perplexity metrics on specific datasets\n% \\item Hardware-specific optimizations not fully explored\n% \\item Dynamic quantization strategies require further investigation\n% \\item Task-specific fine-tuning interactions not comprehensively studied\n% \\end{itemize}\n\n% \\textbf{Future Research Directions:}\n% \\begin{itemize}\n% \\item Multi-modal quantization for vision-language models\n% \\item Adaptive quantization based on input complexity\n% \\item Integration with structured pruning techniques\n% \\item Hardware-aware co-optimization strategies\n% \\end{itemize}\n\n% This comprehensive ablation study demonstrates that careful combination of quantization methods, position interpolation techniques, and optimization strategies can achieve significant efficiency gains while maintaining model quality. Key insights include:\n\n% \\begin{enumerate}\n% \\item \\textbf{YARN interpolation} consistently outperforms alternatives for long-context extension\n% \\item \\textbf{NF4 quantization} provides the best quality-compression trade-off\n% \\item \\textbf{Hadamard transformations} offer substantial benefits for weight+activation quantization\n% \\item \\textbf{Temperature scaling} and proper calibration can recover significant quantization losses\n% \\item \\textbf{Method combinations} require careful tuning but can achieve superior results\n% \\end{enumerate}\n\n% These findings provide a solid foundation for deploying efficient long-context language models across diverse application scenarios while maintaining acceptable quality standards.\n\n\n\\subsection{Position Interpolation Effects on Activation Distributions}\n\\label{sec:pi_activation_analysis}\n\nWe analyze how Position Interpolation (PI) methods affect transformer activation distributions, focusing on quantization implications. Our analysis examines pre-activation tail growth ($\\rho^W$) and axis-aligned amplitude growth ($\\rho^A$) across four PI approaches using LLaMA-2-7B.\n\\subsubsection{Outlier Shifting Pattern Analysis}\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{activation_analysis_plots/outlier_shifting_analysis.pdf}\n \\caption{Outlier shifting patterns across PI methods showing (a) outlier magnitude distributions for activations exceeding 3$\\sigma$ threshold, (b) spatial distribution of outliers along sequence positions, (c) channel-wise outlier occurrence analysis, and (d) correlation analysis between baseline and PI method outlier patterns.}\n \\label{fig:outlier_shifting_analysis}\n\\end{figure}\n\nFigure~\\ref{fig:outlier_shifting_analysis} examines how PI methods systematically alter the spatial and magnitude characteristics of activation outliers. The analysis reveals that PI methods exhibit distinct outlier magnitude distributions, with YARN showing broader outlier spreads compared to baseline methods. Spatial analysis demonstrates position-dependent outlier patterns that are particularly relevant for long-context applications, while channel-wise analysis reveals non-uniform outlier distribution across attention projection dimensions. The high correlation between baseline and PI method outlier patterns suggests systematic rather than random activation shifts, indicating that PI methods introduce predictable changes to activation characteristics.\n\n\n\\subsubsection{Pre-activation Tail Growth ($\\rho^W$) Analysis}\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{activation_analysis_plots/tail_growth_analysis.pdf}\n \\caption{Pre-activation tail growth analysis showing (a) tail ratio comparison, (b) outlier fractions, (c) distribution kurtosis, (d) layer-wise progression, (e) distribution comparison, and (f) weight-error amplification factors across PI methods.}\n \\label{fig:tail_growth_analysis}\n\\end{figure}\n\nFigure~\\ref{fig:tail_growth_analysis} reveals that YARN exhibits slightly elevated outlier fractions (0.85\\% vs 0.82\\% baseline), indicating increased weight quantization sensitivity. All methods show heavy-tailed distributions (kurtosis $>1000$) that challenge standard quantization approaches.\n\n\\subsubsection{Axis-aligned Amplitude Growth ($\\rho^A$) Analysis}\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{activation_analysis_plots/amplitude_growth_analysis.pdf}\n \\caption{Amplitude growth analysis showing (a) concentration factors, (b) peak amplitudes, (c) channel distribution, (d) layer progression, (e) clipping risk, and (f) spatial patterns for activation quantization assessment.}\n \\label{fig:amplitude_growth_analysis}\n\\end{figure}\n\nAs shown in Figure~\\ref{fig:amplitude_growth_analysis}, YARN demonstrates the highest amplitude concentration (52.97) and peak channel variance (1.311), indicating increased activation clipping risk. Linear interpolation exhibits the most controlled amplitude growth (concentration: 51.06).\n\n\\subsubsection{Comprehensive PI Effects Analysis}\n\\begin{figure}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{activation_analysis_plots/comprehensive_pi_effects.pdf}\n \\caption{Comprehensive PI effects showing (a) $\\rho^W$ vs $\\rho^A$ trade-offs, (b) layer-wise progression, (c) quantization difficulty prediction, and (d) performance-efficiency analysis.}\n \\label{fig:comprehensive_pi_effects}\n\\end{figure}\n\nFigure~\\ref{fig:comprehensive_pi_effects} illustrates the fundamental trade-off between long-context capability and quantization compatibility. Linear interpolation occupies the most quantization-friendly region despite higher computational difficulty scores. However it dose not work without finetune the model.\n\n\\subsubsection{Key Findings and Implications}\n\\begin{itemize}\n \\item \\textbf{YARN} requires careful activation clipping management due to highest amplitude concentration\n \\item \\textbf{NTK scaling} provides balanced performance-quantization trade-offs\n \\item All PI methods exhibit heavy-tailed distributions requiring calibration-aware quantization\n\\end{itemize}\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"On which dataset does extended context improve performance the most when compared on average across all settings and by how much?"},"answer":{"kind":"string","value":"WikiText2_PPL, 0.68"},"plan":{"kind":"string","value":"SELECT all datasets\nLOOP for each dataset\n COMPUTE average_extended = average(extended context performance across all settings)\n COMPUTE average_normal = average(normal context performance across all settings)\n COMPUTE improvement = average_extended - average_normal\n\n\nCOMPUTE target_dataset = argmax dataset over improvement\nRETURN target_dataset, improvement of target_dataset\n"}}},{"rowIdx":356,"cells":{"paper":{"kind":"string","value":"2510.01172"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t]\n","\\centering\n","\\caption{Comparison of \\METHODNAME{} with existing methods on sequential editing. \n","\\emph{Eff.}, \\emph{Gen.}, \\emph{Spe.}, \\emph{Flu.} and \\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \n","The best results are highlighted in bold, while the second-best results are underlined.}\n","\\label{tab:main_results}\n","\\resizebox{\\textwidth}{!}{\n","\\setlength{\\arrayrulewidth}{0.7pt} \n","\\renewcommand{\\arraystretch}{1.3} \n","\\begin{tabular}{c c | c c c | c c c | c c}\n","\\specialrule{1.2pt}{0pt}{0pt} \n","\\multirow{2}{*}{\\textbf{Method}} & \\multirow{2}{*}{\\textbf{Model}}\n","& \\multicolumn{3}{c|}{\\textbf{ZSRE}} \n","& \\multicolumn{5}{c}{\\textbf{Counterfact}} \\\\\n","\\cmidrule(lr){3-5} \\cmidrule(lr){6-10}\n"," & & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} \n"," & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} & \\textbf{Flu.$\\uparrow$} & \\textbf{Consis.$\\uparrow$} \\\\\n","\\hline\\hline\n","\n","Pre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{LLaMA3-8B}}} \n","& \\meanstd{35.42}{0.30} & \\meanstd{34.17}{0.30} & \\meanstd{38.02}{0.27} \n","& \\meanstd{0.49}{0.07} & \\meanstd{0.44}{0.05} & \\meanstd{18.09}{0.24} & \\meanstd{634.84}{0.12} & \\meanstd{22.06}{0.08} \\\\\n","\\hline\n","FT & & \\meanstd{15.27}{0.21} & \\meanstd{14.78}{0.21} & \\meanstd{5.06}{0.10} \n","& \\underline{\\meanstd{8.40}{0.28}} & \\underline{\\meanstd{2.54}{0.13}} & \\meanstd{0.03}{0.01} & \\meanstd{409.80}{0.67} & \\meanstd{19.35}{0.13} \\\\\n","MEMIT & & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.06}{0.01} \n","& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{318.19}{0.24} & \\meanstd{4.19}{0.04} \\\\\n","PRUNE & & \\meanstd{10.35}{0.18} & \\meanstd{10.08}{0.18} & \\meanstd{9.55}{0.15} \n","& \\meanstd{1.19}{0.11} & \\meanstd{0.34}{0.04} & \\underline{\\meanstd{0.62}{0.03}} & \\textbf{\\meanstd{618.72}{0.08}} & \\textbf{\\meanstd{49.24}{0.13}} \\\\\n","RECT & & \\meanstd{0.01}{0.00} & \\meanstd{0.01}{0.01} & \\meanstd{0.04}{0.01} \n","& \\meanstd{0.57}{0.08} & \\meanstd{0.29}{0.04} & \\meanstd{0.10}{0.01} & \\meanstd{438.83}{0.18} & \\meanstd{9.40}{0.05} \\\\\n","AlphaEdit & & \\underline{\\meanstd{86.64}{0.23}} & \\underline{\\meanstd{81.28}{0.28}} & \\underline{\\meanstd{28.78}{0.22}} \n","& \\meanstd{4.37}{0.20} & \\meanstd{1.71}{0.10} & \\meanstd{0.57}{0.03} & \\meanstd{482.36}{0.44} & \\meanstd{4.71}{0.04} \\\\\n","\\hline\n","\\METHODNAME{}& & \\textbf{\\meanstd{90.01}{0.21}} & \\textbf{\\meanstd{84.67}{0.26}} & \\textbf{\\meanstd{45.40}{0.29}} \n","& \\textbf{\\meanstd{52.89}{0.50}} & \\textbf{\\meanstd{32.07}{0.39}} & \\textbf{\\meanstd{5.01}{0.10}} & \\underline{\\meanstd{551.51}{0.53}} & \\underline{\\meanstd{30.89}{0.13}} \\\\\n","\\hline\\hline\n","\n","Pre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{Qwen2.5-7B}}} \n","& \\meanstd{35.29}{0.29} & \\meanstd{34.10}{0.28} & \\meanstd{38.44}{0.27} \n","& \\meanstd{0.42}{0.06} & \\meanstd{0.46}{0.05} & \\meanstd{15.06}{0.20} & \\meanstd{624.45}{0.11} & \\meanstd{23.02}{0.69} \\\\\n","\\hline\n","FT & & \\meanstd{4.97}{0.14} & \\meanstd{4.58}{0.13} & \\meanstd{4.01}{0.11} \n","& \\meanstd{15.44}{0.36} & \\meanstd{4.63}{0.17} & \\meanstd{1.46}{0.05} & \\meanstd{214.26}{0.09} & \\meanstd{3.15}{0.02} \\\\\n","MEMIT & & \\meanstd{0.13}{0.02} & \\meanstd{0.12}{0.01} & \\meanstd{0.04}{0.01} \n","& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{370.84}{0.30} & \\meanstd{3.59}{0.03} \\\\\n","PRUNE & & \\underline{\\meanstd{47.93}{0.36}} & \\underline{\\meanstd{45.50}{0.35}} & \\textbf{\\meanstd{39.20}{0.28}} \n","& \\meanstd{14.30}{0.35} & \\meanstd{11.27}{0.26} & \\textbf{\\meanstd{6.75}{0.12}} & \\textbf{\\meanstd{620.74}{0.10}} & \\textbf{\\meanstd{29.50}{0.08}} \\\\\n","RECT & & \\meanstd{0.73}{0.04} & \\meanstd{0.75}{0.04} & \\meanstd{0.05}{0.07} \n","& \\meanstd{0.64}{0.08} & \\meanstd{0.19}{0.03} & \\meanstd{0.09}{0.01} & \\meanstd{368.46}{0.27} & \\meanstd{1.35}{0.01} \\\\\n","AlphaEdit & & \\meanstd{42.01}{0.40} & \\meanstd{39.99}{0.39} & \\meanstd{13.87}{0.20} \n","& \\underline{\\meanstd{43.92}{0.50}} & \\underline{\\meanstd{24.37}{0.36}} & \\meanstd{2.32}{0.06} & \\meanstd{479.83}{0.77} & \\meanstd{4.67}{0.07} \\\\\n","\\hline\n","\\METHODNAME{}& & \\textbf{\\meanstd{70.04}{0.36}} & \\textbf{\\meanstd{65.43}{0.37}} & \\underline{\\meanstd{27.35}{0.26}} \n","& \\textbf{\\meanstd{60.76}{0.49}} & \\textbf{\\meanstd{29.24}{0.37}} & \\underline{\\meanstd{3.83}{0.08}} & \\underline{\\meanstd{612.67}{0.22}} & \\underline{\\meanstd{14.74}{0.07}} \\\\\n","\\specialrule{1.2pt}{0pt}{0pt} \n","\n","\\end{tabular}\n","}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Comparison of \\\\METHODNAME{} with existing methods on sequential editing. \\n\",\n \"\\\\emph{Eff.}, \\\\emph{Gen.}, \\\\emph{Spe.}, \\\\emph{Flu.} and \\\\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \\n\",\n \"The best results are highlighted in bold, while the second-best results are underlined.}\\n\",\n \"\\\\label{tab:main_results}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\setlength{\\\\arrayrulewidth}{0.7pt} \\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3} \\n\",\n \"\\\\begin{tabular}{c c | c c c | c c c | c c}\\n\",\n \"\\\\specialrule{1.2pt}{0pt}{0pt} \\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Method}} & \\\\multirow{2}{*}{\\\\textbf{Model}}\\n\",\n \"& \\\\multicolumn{3}{c|}{\\\\textbf{ZSRE}} \\n\",\n \"& \\\\multicolumn{5}{c}{\\\\textbf{Counterfact}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-5} \\\\cmidrule(lr){6-10}\\n\",\n \" & & \\\\textbf{Eff.$\\\\uparrow$} & \\\\textbf{Gen.$\\\\uparrow$} & \\\\textbf{Spe.$\\\\uparrow$} \\n\",\n \" & \\\\textbf{Eff.$\\\\uparrow$} & \\\\textbf{Gen.$\\\\uparrow$} & \\\\textbf{Spe.$\\\\uparrow$} & \\\\textbf{Flu.$\\\\uparrow$} & \\\\textbf{Consis.$\\\\uparrow$} \\\\\\\\\\n\",\n \"\\\\hline\\\\hline\\n\",\n \"\\n\",\n \"Pre-edited & \\\\multirow{7}{*}{\\\\makecell{\\\\rotatebox{90}{LLaMA3-8B}}} \\n\",\n \"& \\\\meanstd{35.42}{0.30} & \\\\meanstd{34.17}{0.30} & \\\\meanstd{38.02}{0.27} \\n\",\n \"& \\\\meanstd{0.49}{0.07} & \\\\meanstd{0.44}{0.05} & \\\\meanstd{18.09}{0.24} & \\\\meanstd{634.84}{0.12} & \\\\meanstd{22.06}{0.08} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"FT & & \\\\meanstd{15.27}{0.21} & \\\\meanstd{14.78}{0.21} & \\\\meanstd{5.06}{0.10} \\n\",\n \"& \\\\underline{\\\\meanstd{8.40}{0.28}} & \\\\underline{\\\\meanstd{2.54}{0.13}} & \\\\meanstd{0.03}{0.01} & \\\\meanstd{409.80}{0.67} & \\\\meanstd{19.35}{0.13} \\\\\\\\\\n\",\n \"MEMIT & & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.06}{0.01} \\n\",\n \"& \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{318.19}{0.24} & \\\\meanstd{4.19}{0.04} \\\\\\\\\\n\",\n \"PRUNE & & \\\\meanstd{10.35}{0.18} & \\\\meanstd{10.08}{0.18} & \\\\meanstd{9.55}{0.15} \\n\",\n \"& \\\\meanstd{1.19}{0.11} & \\\\meanstd{0.34}{0.04} & \\\\underline{\\\\meanstd{0.62}{0.03}} & \\\\textbf{\\\\meanstd{618.72}{0.08}} & \\\\textbf{\\\\meanstd{49.24}{0.13}} \\\\\\\\\\n\",\n \"RECT & & \\\\meanstd{0.01}{0.00} & \\\\meanstd{0.01}{0.01} & \\\\meanstd{0.04}{0.01} \\n\",\n \"& \\\\meanstd{0.57}{0.08} & \\\\meanstd{0.29}{0.04} & \\\\meanstd{0.10}{0.01} & \\\\meanstd{438.83}{0.18} & \\\\meanstd{9.40}{0.05} \\\\\\\\\\n\",\n \"AlphaEdit & & \\\\underline{\\\\meanstd{86.64}{0.23}} & \\\\underline{\\\\meanstd{81.28}{0.28}} & \\\\underline{\\\\meanstd{28.78}{0.22}} \\n\",\n \"& \\\\meanstd{4.37}{0.20} & \\\\meanstd{1.71}{0.10} & \\\\meanstd{0.57}{0.03} & \\\\meanstd{482.36}{0.44} & \\\\meanstd{4.71}{0.04} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\METHODNAME{}& & \\\\textbf{\\\\meanstd{90.01}{0.21}} & \\\\textbf{\\\\meanstd{84.67}{0.26}} & \\\\textbf{\\\\meanstd{45.40}{0.29}} \\n\",\n \"& \\\\textbf{\\\\meanstd{52.89}{0.50}} & \\\\textbf{\\\\meanstd{32.07}{0.39}} & \\\\textbf{\\\\meanstd{5.01}{0.10}} & \\\\underline{\\\\meanstd{551.51}{0.53}} & \\\\underline{\\\\meanstd{30.89}{0.13}} \\\\\\\\\\n\",\n \"\\\\hline\\\\hline\\n\",\n \"\\n\",\n \"Pre-edited & \\\\multirow{7}{*}{\\\\makecell{\\\\rotatebox{90}{Qwen2.5-7B}}} \\n\",\n \"& \\\\meanstd{35.29}{0.29} & \\\\meanstd{34.10}{0.28} & \\\\meanstd{38.44}{0.27} \\n\",\n \"& \\\\meanstd{0.42}{0.06} & \\\\meanstd{0.46}{0.05} & \\\\meanstd{15.06}{0.20} & \\\\meanstd{624.45}{0.11} & \\\\meanstd{23.02}{0.69} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"FT & & \\\\meanstd{4.97}{0.14} & \\\\meanstd{4.58}{0.13} & \\\\meanstd{4.01}{0.11} \\n\",\n \"& \\\\meanstd{15.44}{0.36} & \\\\meanstd{4.63}{0.17} & \\\\meanstd{1.46}{0.05} & \\\\meanstd{214.26}{0.09} & \\\\meanstd{3.15}{0.02} \\\\\\\\\\n\",\n \"MEMIT & & \\\\meanstd{0.13}{0.02} & \\\\meanstd{0.12}{0.01} & \\\\meanstd{0.04}{0.01} \\n\",\n \"& \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{370.84}{0.30} & \\\\meanstd{3.59}{0.03} \\\\\\\\\\n\",\n \"PRUNE & & \\\\underline{\\\\meanstd{47.93}{0.36}} & \\\\underline{\\\\meanstd{45.50}{0.35}} & \\\\textbf{\\\\meanstd{39.20}{0.28}} \\n\",\n \"& \\\\meanstd{14.30}{0.35} & \\\\meanstd{11.27}{0.26} & \\\\textbf{\\\\meanstd{6.75}{0.12}} & \\\\textbf{\\\\meanstd{620.74}{0.10}} & \\\\textbf{\\\\meanstd{29.50}{0.08}} \\\\\\\\\\n\",\n \"RECT & & \\\\meanstd{0.73}{0.04} & \\\\meanstd{0.75}{0.04} & \\\\meanstd{0.05}{0.07} \\n\",\n \"& \\\\meanstd{0.64}{0.08} & \\\\meanstd{0.19}{0.03} & \\\\meanstd{0.09}{0.01} & \\\\meanstd{368.46}{0.27} & \\\\meanstd{1.35}{0.01} \\\\\\\\\\n\",\n \"AlphaEdit & & \\\\meanstd{42.01}{0.40} & \\\\meanstd{39.99}{0.39} & \\\\meanstd{13.87}{0.20} \\n\",\n \"& \\\\underline{\\\\meanstd{43.92}{0.50}} & \\\\underline{\\\\meanstd{24.37}{0.36}} & \\\\meanstd{2.32}{0.06} & \\\\meanstd{479.83}{0.77} & \\\\meanstd{4.67}{0.07} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\METHODNAME{}& & \\\\textbf{\\\\meanstd{70.04}{0.36}} & \\\\textbf{\\\\meanstd{65.43}{0.37}} & \\\\underline{\\\\meanstd{27.35}{0.26}} \\n\",\n \"& \\\\textbf{\\\\meanstd{60.76}{0.49}} & \\\\textbf{\\\\meanstd{29.24}{0.37}} & \\\\underline{\\\\meanstd{3.83}{0.08}} & \\\\underline{\\\\meanstd{612.67}{0.22}} & \\\\underline{\\\\meanstd{14.74}{0.07}} \\\\\\\\\\n\",\n \"\\\\specialrule{1.2pt}{0pt}{0pt} \\n\",\n \"\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t]\n"," \\centering\n"," \\vspace{-8mm}\n"," \\includegraphics[width=0.98\\textwidth]{Figures/sphere_sparse.png} \n"," \\caption{\n"," (a) A weight matrix is viewed as a set of neurons (\\textcolor{red}{red dots}) on a hypersphere. \n"," (b) Current SOTA methods~\\citep{DBLP:conf/iclr/MaWXLG25,DBLP:conf/iclr/FangJWMSW0C25} introduce perturbations (\\textcolor{blue}{blue triangles}) that interfere with the principle hyperspherical directions of pre-edit weights.\n"," (c) \\METHODNAME{} projects new knowledge onto a sparse space complementary to the principal hyperspherical directions.\n"," }\n"," \\vspace{-4mm}\n"," \\label{fig:teaser}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/Sec_3_zsre_Llama3-8B.pdf}\n"," \\caption{Trends of HE and editing performance throughout sequential editing. \n"," The Spearman correlation scores between HE and each editing metric displayed at the end of each curve. \n"," }\n"," \\label{fig:sec_1}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/Sec3-2.pdf} \n"," \\caption{Correlation between changes in HE and editing performance across consecutive edited weights. Each point corresponds to a $\\Delta \\mathrm{HE}$–$\\Delta \\mathrm{Acc.}$ pair for one method over five thousand sequential edits. Confidence ellipses and regression lines illustrate overall trends.\n"," }\n"," \\label{fig:sec_2}\n"," \\vspace{-3mm}\n","\\end{figure}\n"],["\\begin{table*}[t]\n","\\centering\n","\\caption{Comparison of \\METHODNAME{} with existing methods on sequential editing. \n","\\emph{Eff.}, \\emph{Gen.}, \\emph{Spe.}, \\emph{Flu.} and \\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \n","The best results are highlighted in bold, while the second-best results are underlined.}\n","\\label{tab:main_results}\n","\\resizebox{\\textwidth}{!}{\n","\\setlength{\\arrayrulewidth}{0.7pt} \n","\\renewcommand{\\arraystretch}{1.3} \n","\\begin{tabular}{c c | c c c | c c c | c c}\n","\\specialrule{1.2pt}{0pt}{0pt} \n","\\multirow{2}{*}{\\textbf{Method}} & \\multirow{2}{*}{\\textbf{Model}}\n","& \\multicolumn{3}{c|}{\\textbf{ZSRE}} \n","& \\multicolumn{5}{c}{\\textbf{Counterfact}} \\\\\n","\\cmidrule(lr){3-5} \\cmidrule(lr){6-10}\n"," & & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} \n"," & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} & \\textbf{Flu.$\\uparrow$} & \\textbf{Consis.$\\uparrow$} \\\\\n","\\hline\\hline\n","\n","Pre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{LLaMA3-8B}}} \n","& \\meanstd{35.42}{0.30} & \\meanstd{34.17}{0.30} & \\meanstd{38.02}{0.27} \n","& \\meanstd{0.49}{0.07} & \\meanstd{0.44}{0.05} & \\meanstd{18.09}{0.24} & \\meanstd{634.84}{0.12} & \\meanstd{22.06}{0.08} \\\\\n","\\hline\n","FT & & \\meanstd{15.27}{0.21} & \\meanstd{14.78}{0.21} & \\meanstd{5.06}{0.10} \n","& \\underline{\\meanstd{8.40}{0.28}} & \\underline{\\meanstd{2.54}{0.13}} & \\meanstd{0.03}{0.01} & \\meanstd{409.80}{0.67} & \\meanstd{19.35}{0.13} \\\\\n","MEMIT & & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.06}{0.01} \n","& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{318.19}{0.24} & \\meanstd{4.19}{0.04} \\\\\n","PRUNE & & \\meanstd{10.35}{0.18} & \\meanstd{10.08}{0.18} & \\meanstd{9.55}{0.15} \n","& \\meanstd{1.19}{0.11} & \\meanstd{0.34}{0.04} & \\underline{\\meanstd{0.62}{0.03}} & \\textbf{\\meanstd{618.72}{0.08}} & \\textbf{\\meanstd{49.24}{0.13}} \\\\\n","RECT & & \\meanstd{0.01}{0.00} & \\meanstd{0.01}{0.01} & \\meanstd{0.04}{0.01} \n","& \\meanstd{0.57}{0.08} & \\meanstd{0.29}{0.04} & \\meanstd{0.10}{0.01} & \\meanstd{438.83}{0.18} & \\meanstd{9.40}{0.05} \\\\\n","AlphaEdit & & \\underline{\\meanstd{86.64}{0.23}} & \\underline{\\meanstd{81.28}{0.28}} & \\underline{\\meanstd{28.78}{0.22}} \n","& \\meanstd{4.37}{0.20} & \\meanstd{1.71}{0.10} & \\meanstd{0.57}{0.03} & \\meanstd{482.36}{0.44} & \\meanstd{4.71}{0.04} \\\\\n","\\hline\n","\\METHODNAME{}& & \\textbf{\\meanstd{90.01}{0.21}} & \\textbf{\\meanstd{84.67}{0.26}} & \\textbf{\\meanstd{45.40}{0.29}} \n","& \\textbf{\\meanstd{52.89}{0.50}} & \\textbf{\\meanstd{32.07}{0.39}} & \\textbf{\\meanstd{5.01}{0.10}} & \\underline{\\meanstd{551.51}{0.53}} & \\underline{\\meanstd{30.89}{0.13}} \\\\\n","\\hline\\hline\n","\n","Pre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{Qwen2.5-7B}}} \n","& \\meanstd{35.29}{0.29} & \\meanstd{34.10}{0.28} & \\meanstd{38.44}{0.27} \n","& \\meanstd{0.42}{0.06} & \\meanstd{0.46}{0.05} & \\meanstd{15.06}{0.20} & \\meanstd{624.45}{0.11} & \\meanstd{23.02}{0.69} \\\\\n","\\hline\n","FT & & \\meanstd{4.97}{0.14} & \\meanstd{4.58}{0.13} & \\meanstd{4.01}{0.11} \n","& \\meanstd{15.44}{0.36} & \\meanstd{4.63}{0.17} & \\meanstd{1.46}{0.05} & \\meanstd{214.26}{0.09} & \\meanstd{3.15}{0.02} \\\\\n","MEMIT & & \\meanstd{0.13}{0.02} & \\meanstd{0.12}{0.01} & \\meanstd{0.04}{0.01} \n","& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{370.84}{0.30} & \\meanstd{3.59}{0.03} \\\\\n","PRUNE & & \\underline{\\meanstd{47.93}{0.36}} & \\underline{\\meanstd{45.50}{0.35}} & \\textbf{\\meanstd{39.20}{0.28}} \n","& \\meanstd{14.30}{0.35} & \\meanstd{11.27}{0.26} & \\textbf{\\meanstd{6.75}{0.12}} & \\textbf{\\meanstd{620.74}{0.10}} & \\textbf{\\meanstd{29.50}{0.08}} \\\\\n","RECT & & \\meanstd{0.73}{0.04} & \\meanstd{0.75}{0.04} & \\meanstd{0.05}{0.07} \n","& \\meanstd{0.64}{0.08} & \\meanstd{0.19}{0.03} & \\meanstd{0.09}{0.01} & \\meanstd{368.46}{0.27} & \\meanstd{1.35}{0.01} \\\\\n","AlphaEdit & & \\meanstd{42.01}{0.40} & \\meanstd{39.99}{0.39} & \\meanstd{13.87}{0.20} \n","& \\underline{\\meanstd{43.92}{0.50}} & \\underline{\\meanstd{24.37}{0.36}} & \\meanstd{2.32}{0.06} & \\meanstd{479.83}{0.77} & \\meanstd{4.67}{0.07} \\\\\n","\\hline\n","\\METHODNAME{}& & \\textbf{\\meanstd{70.04}{0.36}} & \\textbf{\\meanstd{65.43}{0.37}} & \\underline{\\meanstd{27.35}{0.26}} \n","& \\textbf{\\meanstd{60.76}{0.49}} & \\textbf{\\meanstd{29.24}{0.37}} & \\underline{\\meanstd{3.83}{0.08}} & \\underline{\\meanstd{612.67}{0.22}} & \\underline{\\meanstd{14.74}{0.07}} \\\\\n","\\specialrule{1.2pt}{0pt}{0pt} \n","\n","\\end{tabular}\n","}\n","\\end{table*}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/llama_neuron_similarity_heatmap_15k.pdf} \n"," \\caption{\n"," Cosine similarity between neurons in the updated weight matrix after 15,000 edits. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\n"," \\METHODNAME{} effectively preserves the weight structure, demonstrating the most stable hyperspherical uniformity.\n"," }\n"," \\label{fig:Sec_5_heatmap}\n"," \\vspace{-3mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/llama_tsne_grid_15k.pdf} \n"," \\caption{The t-SNE distribution of weight neurons of pre-edited and post-edited LLM after 15,000 edits using dimensionality reduction. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\METHODNAME{} consistently exhibits minimal shift. }\n"," \\label{fig:Sec_5_pca}\n"," \\vspace{-3mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/general_line.pdf} \n"," \\caption{\n"," General ability testing of post-edited LLaMA3 (8B) on four tasks.\n"," }\n"," \\label{fig:line_general}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=0.98\\textwidth]{Figures/baseline_improve_all.pdf}\n"," \\caption{Performance improvements of baseline editing methods after adding a single line of code from \\METHODNAME{} (i.e., sparse space projection). Gray bars denote the original baseline performance, while purple bars indicate the performance after enhancement.}\n"," \\label{fig:baseline_improve_all}\n"," \\vspace{-2mm}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/qwen_neuron_similarity_heatmap_5k.pdf} \n"," \\caption{\n"," Cosine similarity between neurons in updated weight matrix after 5,000 edits on Qwen2.5. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\n"," \\METHODNAME{} effectively preserve the weight structure, demonstrating the most stable hyperspherical uniformity.\n"," }\n"," \\label{fig:Sec_5_heatmap_qwen}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/qwen_tsne_grid_5k.pdf} \n"," \\caption{The distribution of weight neurons of pre-edited and post-edited Qwen2.5 after 5,000 edits using dimensionality reduction across mainstream sequential editing methods. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\METHODNAME{} consistently exhibits minimal shift. \n"," }\n"," \\label{fig:Sec_5_pca_qwen}\n","\\end{figure}\n"],["\\begin{figure}[!hbt]%[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/memit_general_line.pdf} \n"," \\caption{General ability improvements of MEMIT after incorporating SPHERE with a single line of sparse space projection code.)\n"," }\n"," \\label{fig:1}\n","\\end{figure}\n"],["\\begin{figure}[!hbt]%[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/prune_general_line.pdf} \n"," \\caption{General ability improvements of PRUNE after incorporating SPHERE with a single line of sparse space projection code.)\n"," }\n"," \\label{fig:2}\n","\\end{figure}\n"],["\\begin{figure}[!hbt]%[t]\n"," \\centering\n"," \\includegraphics[width=1\\textwidth]{Figures/rect_general_line.pdf} \n"," \\caption{General ability improvements of RECT after incorporating SPHERE with a single line of sparse space projection code.)\n"," }\n"," \\label{fig:3}\n","\\end{figure}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\vspace{-8mm}\\n\",\n \" \\\\includegraphics[width=0.98\\\\textwidth]{Figures/sphere_sparse.png} \\n\",\n \" \\\\caption{\\n\",\n \" (a) A weight matrix is viewed as a set of neurons (\\\\textcolor{red}{red dots}) on a hypersphere. \\n\",\n \" (b) Current SOTA methods~\\\\citep{DBLP:conf/iclr/MaWXLG25,DBLP:conf/iclr/FangJWMSW0C25} introduce perturbations (\\\\textcolor{blue}{blue triangles}) that interfere with the principle hyperspherical directions of pre-edit weights.\\n\",\n \" (c) \\\\METHODNAME{} projects new knowledge onto a sparse space complementary to the principal hyperspherical directions.\\n\",\n \" }\\n\",\n \" \\\\vspace{-4mm}\\n\",\n \" \\\\label{fig:teaser}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/Sec_3_zsre_Llama3-8B.pdf}\\n\",\n \" \\\\caption{Trends of HE and editing performance throughout sequential editing. \\n\",\n \" The Spearman correlation scores between HE and each editing metric displayed at the end of each curve. \\n\",\n \" }\\n\",\n \" \\\\label{fig:sec_1}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/Sec3-2.pdf} \\n\",\n \" \\\\caption{Correlation between changes in HE and editing performance across consecutive edited weights. Each point corresponds to a $\\\\Delta \\\\mathrm{HE}$–$\\\\Delta \\\\mathrm{Acc.}$ pair for one method over five thousand sequential edits. Confidence ellipses and regression lines illustrate overall trends.\\n\",\n \" }\\n\",\n \" \\\\label{fig:sec_2}\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Comparison of \\\\METHODNAME{} with existing methods on sequential editing. \\n\",\n \"\\\\emph{Eff.}, \\\\emph{Gen.}, \\\\emph{Spe.}, \\\\emph{Flu.} and \\\\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \\n\",\n \"The best results are highlighted in bold, while the second-best results are underlined.}\\n\",\n \"\\\\label{tab:main_results}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\setlength{\\\\arrayrulewidth}{0.7pt} \\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3} \\n\",\n \"\\\\begin{tabular}{c c | c c c | c c c | c c}\\n\",\n \"\\\\specialrule{1.2pt}{0pt}{0pt} \\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Method}} & \\\\multirow{2}{*}{\\\\textbf{Model}}\\n\",\n \"& \\\\multicolumn{3}{c|}{\\\\textbf{ZSRE}} \\n\",\n \"& \\\\multicolumn{5}{c}{\\\\textbf{Counterfact}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-5} \\\\cmidrule(lr){6-10}\\n\",\n \" & & \\\\textbf{Eff.$\\\\uparrow$} & \\\\textbf{Gen.$\\\\uparrow$} & \\\\textbf{Spe.$\\\\uparrow$} \\n\",\n \" & \\\\textbf{Eff.$\\\\uparrow$} & \\\\textbf{Gen.$\\\\uparrow$} & \\\\textbf{Spe.$\\\\uparrow$} & \\\\textbf{Flu.$\\\\uparrow$} & \\\\textbf{Consis.$\\\\uparrow$} \\\\\\\\\\n\",\n \"\\\\hline\\\\hline\\n\",\n \"\\n\",\n \"Pre-edited & \\\\multirow{7}{*}{\\\\makecell{\\\\rotatebox{90}{LLaMA3-8B}}} \\n\",\n \"& \\\\meanstd{35.42}{0.30} & \\\\meanstd{34.17}{0.30} & \\\\meanstd{38.02}{0.27} \\n\",\n \"& \\\\meanstd{0.49}{0.07} & \\\\meanstd{0.44}{0.05} & \\\\meanstd{18.09}{0.24} & \\\\meanstd{634.84}{0.12} & \\\\meanstd{22.06}{0.08} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"FT & & \\\\meanstd{15.27}{0.21} & \\\\meanstd{14.78}{0.21} & \\\\meanstd{5.06}{0.10} \\n\",\n \"& \\\\underline{\\\\meanstd{8.40}{0.28}} & \\\\underline{\\\\meanstd{2.54}{0.13}} & \\\\meanstd{0.03}{0.01} & \\\\meanstd{409.80}{0.67} & \\\\meanstd{19.35}{0.13} \\\\\\\\\\n\",\n \"MEMIT & & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.06}{0.01} \\n\",\n \"& \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{318.19}{0.24} & \\\\meanstd{4.19}{0.04} \\\\\\\\\\n\",\n \"PRUNE & & \\\\meanstd{10.35}{0.18} & \\\\meanstd{10.08}{0.18} & \\\\meanstd{9.55}{0.15} \\n\",\n \"& \\\\meanstd{1.19}{0.11} & \\\\meanstd{0.34}{0.04} & \\\\underline{\\\\meanstd{0.62}{0.03}} & \\\\textbf{\\\\meanstd{618.72}{0.08}} & \\\\textbf{\\\\meanstd{49.24}{0.13}} \\\\\\\\\\n\",\n \"RECT & & \\\\meanstd{0.01}{0.00} & \\\\meanstd{0.01}{0.01} & \\\\meanstd{0.04}{0.01} \\n\",\n \"& \\\\meanstd{0.57}{0.08} & \\\\meanstd{0.29}{0.04} & \\\\meanstd{0.10}{0.01} & \\\\meanstd{438.83}{0.18} & \\\\meanstd{9.40}{0.05} \\\\\\\\\\n\",\n \"AlphaEdit & & \\\\underline{\\\\meanstd{86.64}{0.23}} & \\\\underline{\\\\meanstd{81.28}{0.28}} & \\\\underline{\\\\meanstd{28.78}{0.22}} \\n\",\n \"& \\\\meanstd{4.37}{0.20} & \\\\meanstd{1.71}{0.10} & \\\\meanstd{0.57}{0.03} & \\\\meanstd{482.36}{0.44} & \\\\meanstd{4.71}{0.04} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\METHODNAME{}& & \\\\textbf{\\\\meanstd{90.01}{0.21}} & \\\\textbf{\\\\meanstd{84.67}{0.26}} & \\\\textbf{\\\\meanstd{45.40}{0.29}} \\n\",\n \"& \\\\textbf{\\\\meanstd{52.89}{0.50}} & \\\\textbf{\\\\meanstd{32.07}{0.39}} & \\\\textbf{\\\\meanstd{5.01}{0.10}} & \\\\underline{\\\\meanstd{551.51}{0.53}} & \\\\underline{\\\\meanstd{30.89}{0.13}} \\\\\\\\\\n\",\n \"\\\\hline\\\\hline\\n\",\n \"\\n\",\n \"Pre-edited & \\\\multirow{7}{*}{\\\\makecell{\\\\rotatebox{90}{Qwen2.5-7B}}} \\n\",\n \"& \\\\meanstd{35.29}{0.29} & \\\\meanstd{34.10}{0.28} & \\\\meanstd{38.44}{0.27} \\n\",\n \"& \\\\meanstd{0.42}{0.06} & \\\\meanstd{0.46}{0.05} & \\\\meanstd{15.06}{0.20} & \\\\meanstd{624.45}{0.11} & \\\\meanstd{23.02}{0.69} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"FT & & \\\\meanstd{4.97}{0.14} & \\\\meanstd{4.58}{0.13} & \\\\meanstd{4.01}{0.11} \\n\",\n \"& \\\\meanstd{15.44}{0.36} & \\\\meanstd{4.63}{0.17} & \\\\meanstd{1.46}{0.05} & \\\\meanstd{214.26}{0.09} & \\\\meanstd{3.15}{0.02} \\\\\\\\\\n\",\n \"MEMIT & & \\\\meanstd{0.13}{0.02} & \\\\meanstd{0.12}{0.01} & \\\\meanstd{0.04}{0.01} \\n\",\n \"& \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{0.00}{0.00} & \\\\meanstd{370.84}{0.30} & \\\\meanstd{3.59}{0.03} \\\\\\\\\\n\",\n \"PRUNE & & \\\\underline{\\\\meanstd{47.93}{0.36}} & \\\\underline{\\\\meanstd{45.50}{0.35}} & \\\\textbf{\\\\meanstd{39.20}{0.28}} \\n\",\n \"& \\\\meanstd{14.30}{0.35} & \\\\meanstd{11.27}{0.26} & \\\\textbf{\\\\meanstd{6.75}{0.12}} & \\\\textbf{\\\\meanstd{620.74}{0.10}} & \\\\textbf{\\\\meanstd{29.50}{0.08}} \\\\\\\\\\n\",\n \"RECT & & \\\\meanstd{0.73}{0.04} & \\\\meanstd{0.75}{0.04} & \\\\meanstd{0.05}{0.07} \\n\",\n \"& \\\\meanstd{0.64}{0.08} & \\\\meanstd{0.19}{0.03} & \\\\meanstd{0.09}{0.01} & \\\\meanstd{368.46}{0.27} & \\\\meanstd{1.35}{0.01} \\\\\\\\\\n\",\n \"AlphaEdit & & \\\\meanstd{42.01}{0.40} & \\\\meanstd{39.99}{0.39} & \\\\meanstd{13.87}{0.20} \\n\",\n \"& \\\\underline{\\\\meanstd{43.92}{0.50}} & \\\\underline{\\\\meanstd{24.37}{0.36}} & \\\\meanstd{2.32}{0.06} & \\\\meanstd{479.83}{0.77} & \\\\meanstd{4.67}{0.07} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\METHODNAME{}& & \\\\textbf{\\\\meanstd{70.04}{0.36}} & \\\\textbf{\\\\meanstd{65.43}{0.37}} & \\\\underline{\\\\meanstd{27.35}{0.26}} \\n\",\n \"& \\\\textbf{\\\\meanstd{60.76}{0.49}} & \\\\textbf{\\\\meanstd{29.24}{0.37}} & \\\\underline{\\\\meanstd{3.83}{0.08}} & \\\\underline{\\\\meanstd{612.67}{0.22}} & \\\\underline{\\\\meanstd{14.74}{0.07}} \\\\\\\\\\n\",\n \"\\\\specialrule{1.2pt}{0pt}{0pt} \\n\",\n \"\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/llama_neuron_similarity_heatmap_15k.pdf} \\n\",\n \" \\\\caption{\\n\",\n \" Cosine similarity between neurons in the updated weight matrix after 15,000 edits. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\\n\",\n \" \\\\METHODNAME{} effectively preserves the weight structure, demonstrating the most stable hyperspherical uniformity.\\n\",\n \" }\\n\",\n \" \\\\label{fig:Sec_5_heatmap}\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/llama_tsne_grid_15k.pdf} \\n\",\n \" \\\\caption{The t-SNE distribution of weight neurons of pre-edited and post-edited LLM after 15,000 edits using dimensionality reduction. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\\\METHODNAME{} consistently exhibits minimal shift. }\\n\",\n \" \\\\label{fig:Sec_5_pca}\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/general_line.pdf} \\n\",\n \" \\\\caption{\\n\",\n \" General ability testing of post-edited LLaMA3 (8B) on four tasks.\\n\",\n \" }\\n\",\n \" \\\\label{fig:line_general}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.98\\\\textwidth]{Figures/baseline_improve_all.pdf}\\n\",\n \" \\\\caption{Performance improvements of baseline editing methods after adding a single line of code from \\\\METHODNAME{} (i.e., sparse space projection). Gray bars denote the original baseline performance, while purple bars indicate the performance after enhancement.}\\n\",\n \" \\\\label{fig:baseline_improve_all}\\n\",\n \" \\\\vspace{-2mm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/qwen_neuron_similarity_heatmap_5k.pdf} \\n\",\n \" \\\\caption{\\n\",\n \" Cosine similarity between neurons in updated weight matrix after 5,000 edits on Qwen2.5. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\\n\",\n \" \\\\METHODNAME{} effectively preserve the weight structure, demonstrating the most stable hyperspherical uniformity.\\n\",\n \" }\\n\",\n \" \\\\label{fig:Sec_5_heatmap_qwen}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/qwen_tsne_grid_5k.pdf} \\n\",\n \" \\\\caption{The distribution of weight neurons of pre-edited and post-edited Qwen2.5 after 5,000 edits using dimensionality reduction across mainstream sequential editing methods. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\\\METHODNAME{} consistently exhibits minimal shift. \\n\",\n \" }\\n\",\n \" \\\\label{fig:Sec_5_pca_qwen}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!hbt]%[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/memit_general_line.pdf} \\n\",\n \" \\\\caption{General ability improvements of MEMIT after incorporating SPHERE with a single line of sparse space projection code.)\\n\",\n \" }\\n\",\n \" \\\\label{fig:1}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!hbt]%[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/prune_general_line.pdf} \\n\",\n \" \\\\caption{General ability improvements of PRUNE after incorporating SPHERE with a single line of sparse space projection code.)\\n\",\n \" }\\n\",\n \" \\\\label{fig:2}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!hbt]%[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\textwidth]{Figures/rect_general_line.pdf} \\n\",\n \" \\\\caption{General ability improvements of RECT after incorporating SPHERE with a single line of sparse space projection code.)\\n\",\n \" }\\n\",\n \" \\\\label{fig:3}\\n\",\n \"\\\\end{figure}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n\\documentclass{article} % For LaTeX2e\n\\usepackage{iclr2026_conference,times}\n\n% Optional math commands from https://github.com/goodfeli/dlbook_notation.\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\\usepackage{booktabs}\n\\usepackage{multirow}\n\\usepackage{graphicx} % for \\rotatebox\n\\usepackage{makecell} % for line breaks in cells\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n% Figure reference, capital. For start of sentence\n\\def\\Figref#1{Figure~\\ref{#1}}\n\\def\\twofigref#1#2{figures \\ref{#1} and \\ref{#2}}\n\\def\\quadfigref#1#2#3#4{figures \\ref{#1}, \\ref{#2}, \\ref{#3} and \\ref{#4}}\n% Section reference, lower-case.\n\\def\\secref#1{section~\\ref{#1}}\n% Section reference, capital.\n\\def\\Secref#1{Section~\\ref{#1}}\n% Reference to two sections.\n\\def\\twosecrefs#1#2{sections \\ref{#1} and \\ref{#2}}\n% Reference to three sections.\n\\def\\secrefs#1#2#3{sections \\ref{#1}, \\ref{#2} and \\ref{#3}}\n% Reference to an equation, lower-case.\n\\def\\eqref#1{equation~\\ref{#1}}\n% Reference to an equation, upper case\n\\def\\Eqref#1{Equation~\\ref{#1}}\n% A raw reference to an equation---avoid using if possible\n\\def\\plaineqref#1{\\ref{#1}}\n% Reference to a chapter, lower-case.\n\\def\\chapref#1{chapter~\\ref{#1}}\n% Reference to an equation, upper case.\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n% Reference to a range of chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for 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\n\n\n\n\\newcommand{\\METHODNAME}{\\textsc{SPHERE}}\n\n\\newcommand{\\qingyuan}[1]{\\textcolor{cyan}{[Qingyuan: #1]}}\n\\newcommand{\\jiachen}[1]{\\textcolor{red}{[Jia-Chen: #1]}}\n\\newcommand{\\yunzhi}[1]{\\textcolor{blue}{[Yunzhi: #1]}}\n\\newcommand{\\hong}[1]{\\textcolor{orange}{[Hong: #1]}}\n\\newcommand{\\violet}[1]{\\textcolor{violet}{[Violet: #1]}}\n\n\n\\title{Energy-Regularized Sequential Model \\\\ Editing on Hyperspheres}\n\n\\author{\n Qingyuan Liu$^1$\\thanks{\\hspace{0.5mm}Equal contribution.}, ~Jia-Chen Gu$^2$\\footnotemark[1], ~Yunzhi Yao$^3$, ~Hong Wang$^4$, ~Nanyun Peng$^2$\\\\\n $^1$Columbia University ~\n $^2$University of California, Los Angeles \\\\\n $^3$Zhejiang University ~\n $^4$University of Science and Technology of China\\\\ \n \\texttt{ql2505@columbia.edu}, ~\\texttt{gujc@ucla.edu}, ~\\texttt{violetpeng@cs.ucla.edu}\n}\n\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\n\\iclrfinalcopy % Uncomment for camera-ready version, but NOT for submission.\n\\begin{document}\n\n\n\n\\maketitle\n\n\\vspace{-5mm}\n\n\\begin{abstract}\n\nLarge language models (LLMs) require constant updates to remain aligned with evolving real-world knowledge. \nModel editing offers a lightweight alternative to retraining, but sequential editing that updates the LLM knowledge through multiple successive edits often destabilizes representations and induces catastrophic forgetting. \nIn this work, we seek to better understand and mitigate performance degradation caused by sequential editing.\nWe hypothesize that \\emph{hyperspherical uniformity}, a property that maintains uniform distribution of neuron weights on a hypersphere, helps the model remain stable, retain prior knowledge, while still accommodate new updates.\nWe use Hyperspherical Energy (HE) to quantify neuron uniformity during editing, and examine its correlation with editing performance.\nEmpirical studies across widely used editing methods reveals a strong correlation between HE dynamics and editing performance, with editing failures consistently coinciding with high HE fluctuations.\nWe further theoretically prove that HE dynamics impose a lower bound on the degradation of pretrained knowledge, highlighting why HE stability is crucial for knowledge retention. \nMotivated by these insights, we propose \\METHODNAME{} (\\textbf{S}parse \\textbf{P}rojection for \\textbf{H}yperspherical \\textbf{E}nergy-\\textbf{R}egularized \\textbf{E}diting), an HE-driven regularization strategy that stabilizes neuron weight distributions, ultimately preserving prior knowledge while enabling reliable sequential updates. \nSpecifically, \\METHODNAME{} identifies a sparse space complementary to the principal hyperspherical directions of the pretrained weight matrices and projects new knowledge onto it, attenuating perturbations on the principal directions.\nExtensive experiments on LLaMA3 (8B) and Qwen2.5 (7B) show that \\METHODNAME{} outperforms the best baseline in editing capability by an average of 16.41\\%, while most faithfully preserving general model performance, thereby offering a principled path toward reliable large-scale knowledge editing.\nThe code is available at \\href{https://github.com/PlusLabNLP/SPHERE}{https://github.com/PlusLabNLP/SPHERE}.\n\n\n\\end{abstract}\n\n\n\n\\section{Introduction}\n\nLarge language models (LLMs) have demonstrated strong capabilities in knowledge storage, reasoning, and generation~\\citep{DBLP:journals/corr/abs-2412-19437, meta2024llama4, DBLP:journals/corr/abs-2505-09388, openai2025gpt5}. \nHowever, the knowledge embedded in LLMs inevitably becomes outdated or incorrect, as real-world facts continuously evolve~\\citep{DBLP:journals/csur/JiLFYSXIBMF23,DBLP:journals/tois/HuangYMZFWCPFQL25}. \nRetraining LLMs to incorporate such updates is prohibitively expensive, motivating the development of \\emph{model editing} (also known as \\emph{knowledge editing})~\\citep{DBLP:conf/emnlp/CaoAT21,DBLP:conf/iclr/MitchellLBFM22,DBLP:conf/iclr/MengSABB23,DBLP:conf/emnlp/GuXMLLCP24,DBLP:conf/iclr/FangJWMSW0C25}. \nThe most practical setting for model editing is\n\\emph{sequential editing}, where multiple updates are applied over time. \nHowever, previous studies have shown that such interventions often suffer from significant performance degradation due to catastrophic forgetting~\\citep{DBLP:conf/emnlp/GuXMLLCP24,DBLP:conf/acl/GuptaRA24}. \nConsequently, reconciling the trade-off between preserving original pretrained knowledge and integrating new editing knowledge remains an unresolved challenge.\n\n\nIn this work, we seek to better understand and mitigate the performance degradation caused by sequential editing.\nWe revisit model editing from the perspective of \\emph{hyperspherical uniformity} of perturbed weights~\\citep{DBLP:conf/aistats/LiuLL0SW21}, motivated by the observation that sequential edits often disrupt weight geometry, leading to degraded representations.\nPrevious studies have shown that viewing a weight matrix as a set of neurons on a hypersphere (as shown in Figure~\\ref{fig:teaser} (a)) and maintaining their hyperspherical uniformity is crucial for stable training and effective generalization~\\citep{DBLP:journals/corr/CogswellAGZB15, DBLP:conf/icml/XieDZKYZX17, DBLP:conf/nips/QiuLFXFLZWS23}. \nTo investigate the applicability of these principles to sequential editing, we adopt \\emph{hyperspherical energy (HE)}~\\citep{DBLP:conf/nips/LiuLLLYDS18,DBLP:conf/nips/QiuLFXFLZWS23} as a measure to quantify weight uniformity throughout sequential editing.\nHE calculates the dispersion of neuron weight vectors on a hypersphere, where lower energy corresponds to a more balanced distribution of neurons. \nBy tracking HE dynamics throughout sequential editing, we can better understand how edits affect weight uniformity, identify early signs of destabilization, and even develop HE-driven regularization strategies to stabilize the editing process.\n\n\n\\begin{figure}[t]\n \\centering\n \\vspace{-8mm}\n \\includegraphics[width=0.98\\textwidth]{Figures/sphere_sparse.png} \n \\caption{\n (a) A weight matrix is viewed as a set of neurons (\\textcolor{red}{red dots}) on a hypersphere. \n (b) Current SOTA methods~\\citep{DBLP:conf/iclr/MaWXLG25,DBLP:conf/iclr/FangJWMSW0C25} introduce perturbations (\\textcolor{blue}{blue triangles}) that interfere with the principle hyperspherical directions of pre-edit weights.\n (c) \\METHODNAME{} projects new knowledge onto a sparse space complementary to the principal hyperspherical directions.\n }\n \\vspace{-4mm}\n \\label{fig:teaser}\n\\end{figure}\n\n\nTo reveal the mechanisms underlying successful editing strategies from the perspective of hyperspherical uniformity, we first empirically analyze how HE evolves throughout sequential editing and examine how these dynamics relate to editing performance across six widely used methods.\nExperimental results reveal a strong correlation between hyperspherical uniformity and editing performance, with editing failures consistently coinciding with its collapse. \nMeanwhile, more advanced editing methods have proven more effective at preserving hyperspherical uniformity.\nTo complement these empirical findings, we further provide a theoretical analysis verifying that variations in HE establish a lower bound on the interference with the original pretrained knowledge. \nThis result clarifies that state-of-the-art (SOTA) editing methods implicitly regulate hyperspherical uniformity and the lower bound on the interference, providing a principled explanation for their enhanced robustness.\n\n\nMotivated by these empirical and theoretical findings, we propose \\METHODNAME{} (\\textbf{S}parse \\textbf{P}rojection for \\textbf{H}yperspherical \\textbf{E}nergy-\\textbf{R}egularized \\textbf{E}diting), an HE-driven regularization strategy that stabilizes neuron weight distributions, ultimately preserving prior knowledge while enabling reliable sequential updates.\nThe key insight is that, as shown in Figure~\\ref{fig:teaser} (b), current methods often introduce perturbations that interfere with the principal hyperspherical directions of the pretrained weight matrices, leading to instability, loss of uniformity, and eventual degradation of model performance.\nTo counteract these side effects, as shown in Figure~\\ref{fig:teaser} (c), \\METHODNAME{} identifies a sparse space complementary to the principal hyperspherical directions of the pretrained weight matrices and projects new knowledge onto it, attenuating perturbation components aligned with those principal directions.\nBy doing so, \\METHODNAME{} effectively preserves the hyperspherical uniformity and substantially extends the number of effective sequential edits.\n\n\nWe evaluated \\METHODNAME{} \non \\textbf{two LLMs}, including LLaMA3 (8B)~\\citep{llama3modelcard} and Qwen2.5 (7B)~\\citep{qwen2.5},\non \\textbf{two editing datasets}, including CounterFact~\\citep{DBLP:conf/nips/MengBAB22} and ZsRE~\\citep{DBLP:conf/conll/LevySCZ17}.\n\\textbf{Four downstream tasks} including reasoning~\\citep{DBLP:journals/corr/abs-2110-14168}, natural language inference~\\citep{DBLP:conf/mlcw/DaganGM05}, open-domain QA~\\citep{DBLP:journals/tacl/KwiatkowskiPRCP19}, and closed-domain QA~\\citep{DBLP:conf/naacl/ClarkLCK0T19}\nare employed to demonstrate the impact of editing on the general abilities of LLMs.\nExperimental results show that \\METHODNAME{} sustains editing capacity under large-scale editing settings, outperforming the best baseline~\\citep{DBLP:conf/iclr/FangJWMSW0C25} by \\textbf{16.41\\%} on average. \nBeyond editing capacity, it more effectively preserves the hyperspherical uniformity and the general abilities of edited models than all baselines.\nFurthermore, as a plug-and-play enhancement, \\METHODNAME{} improves the mainstream editing methods~\\citep{DBLP:conf/iclr/MengSABB23,DBLP:conf/emnlp/GuXMLLCP24,DBLP:conf/iclr/MaWXLG25} by \\textbf{38.71\\%} on average, offering a principled path toward reliable and scalable editing.\n\n\n\\section{Preliminaries}\n\n\\subsection{Model Editing}\n\\label{sec:model-editing}\nSequential model editing aims to update the knowledge stored in LLMs through multiple successive edits. \nEach edit modifies the model parameter $\\bm{W} \\in \\mathbb{R}^{d_1 \\times d_0}$ by adding a perturbation $\\Delta \\in \\mathbb{R}^{d_1 \\times d_0}$ in a locate-then-edit paradigm~\\citep{DBLP:conf/nips/MengBAB22}, where $d_0$ and $d_1$ represent the dimensions of the intermediate and output layers of the feed-forward network (FFN), respectively. \nSpecifically, suppose each edit updates $u$ pieces of knowledge in the form of (subject $s$, relation $r$, object $o$), e.g., ($s$ = \\emph{United States}, $r$ = \\emph{President of}, $o$ = \\emph{Donald Trump}). \nThe perturbed parameter is expected to associate $u$ new \\emph{key-value} ($k$-$v$) pairs, where $k$ and $v$ encode $(s, r)$ and $(o)$ of the new knowledge, respectively. \nWe can stack these keys and values into matrices as follows:\n\\begin{equation}\n\\bm{K}_1 = [\\bm{k}_1 \\,|\\, \\bm{k}_2 \\,|\\, \\dots \\,|\\, \\bm{k}_u] \\in \\mathbb{R}^{d_0 \\times u}, \\quad\n\\bm{V}_1 = [\\bm{v}_1 \\,|\\, \\bm{v}_2 \\,|\\, \\dots \\,|\\, \\bm{v}_u] \\in \\mathbb{R}^{d_1 \\times u},\n\\label{eq:k1v1}\n\\end{equation}\nwhere the subscripts of $\\bm{k}$ and $\\bm{v}$ represent the index of the to-be-updated knowledge. Therefore, the editing objective can be expressed as:\n\\begin{equation}\n\\Delta \\bm{W} = \\arg\\min_{\\Delta \\hat{\\bm{W}}} \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}}) \\bm{K}_1 - \\bm{V}_1 \\right\\|^2,\n\\label{eq:edit_obj}\n\\end{equation}\nwhere $\\|\\cdot\\|^2$ denotes the sum of the squared elements in the matrix.\n\nAdditionally, current methods typically incorporate an error term to preserve the original knowledge.\nLet $\\bm{K}_0$ and $\\bm{V}_0$ represent the matrices formed by stacking the $\\bm{k}$ and $\\bm{v}$ corresponding to the original pretrained knowledge. \nEqn.~\\ref{eq:edit_obj} is regularized by involving the error term as follows:\n\\begin{equation}\n\\Delta \\bm{W} = \\arg\\min_{\\Delta \\hat{\\bm{W}}} \\left( \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}}) \\bm{K}_1 - \\bm{V}_1 \\right\\|^2\n+ \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}}) \\bm{K}_0 - \\bm{V}_0 \\right\\|^2 \\right).\n\\label{eq:edit_obj_preserve}\n\\end{equation}\nSince $\\bm{K}_0$ and $\\bm{V}_0$ encode the original pretrained knowledge, we have $\\bm{W} \\bm{K}_0 = \\bm{V}_0$ (cf. Eqn.~\\ref{eq:k1v1}). By applying the normal equation, if the closed-form solution of Eqn.~\\ref{eq:edit_obj_preserve} exists, it can be written as:\n\\begin{equation}\n\\Delta \\bm{W} = (\\bm{V}_1 - \\bm{W} \\bm{K}_1) \\bm{K}_T^{\\top} \n\\left( \\bm{K}_0 \\bm{K}_0^{\\top} + \\bm{K}_1 \\bm{K}_1^{\\top} \\right)^{-1}.\n\\label{eq:closed_form_delta}\n\\end{equation}\nSince the full scope of an LLM's knowledge is generally inaccessible, $\\bm{K}_0$ is difficult to obtain directly but can be approximated from abundant text input. \nSee Appendix~\\ref{appendix:model_editing} for more details.\n\n\n\n\\subsection{Hyperspherical Energy}\n\\label{sec:HSE}\nHyperspherical Energy (HE) serves as a quantitative metric for measuring \\emph{hyperspherical uniformity}. \nGiven a group of neurons, HE characterizes their uniformity on a hypersphere by defining a generic potential energy based on their pairwise relationship. \nLower energy represents that these neurons are more diverse and uniformly distributed, while higher energy reflects redundancy. \nGiven a weight matrix $\\bm{W} \\in \\mathbb{R}^{N \\times (d+1)}$ represented as a set of $N$ neurons (i.e., kernels), where each row $\\bm{w}_i \\in \\mathbb{R}^{d+1}$ corresponds to a neuron, its HE is defined as:\n\\begin{equation}\n\\bm{E_{s,d}}\\left( \\hat{\\bm{w}}_i \\mid_{i=1}^N \\right)\n= \\sum_{i=1}^N \\sum_{\\substack{j=1, j \\ne i}}^N f_s\\left( \\left\\| \\hat{\\bm{w}}_i - \\hat{\\bm{w}}_j \\right\\| \\right)\n= \\begin{cases}\n\\sum_{i \\ne j} \\left\\| \\hat{\\bm{w}}_i - \\hat{\\bm{w}}_j \\right\\|^{-s}, & s > 0 \\\\\n\\sum_{i \\ne j} \\log\\left( \\left\\| \\hat{\\bm{w}}_i - \\hat{\\bm{w}}_j \\right\\|^{-1} \\right), & s = 0\n\\end{cases}\n\\label{eq:full_hse}\n\\end{equation}\n% \\vspace{-1em}\nwhere $\\|\\cdot\\|$ denotes Euclidean distance, $f_s(\\cdot)$ is a decreasing real-valued function, and $\\hat{\\bm{w}}_i = \\frac{\\bm{w}_i}{\\|\\bm{w}_i\\|}$ is the $i$-th neuron weight projected onto the unit hypersphere $\\mathbb{S}^d = \\{ \\bm{w} \\in \\mathbb{R}^{d+1} \\mid \\|\\bm{w}\\| = 1 \\}$. \nWe also denote $\\hat{\\bm{W}}_N = \\{\\hat{\\bm{w}}_1, \\cdots, \\hat{\\bm{w}}_N \\in \\mathbb{S}^d\\}$, and $E_s = \\bm{E_{s,d}}(\\hat{\\bm{w}}_i \\mid_{i=1}^N)$ for short. \nThere are plenty of choices for $f_s(\\cdot)$, but in this paper we use $f_s(z) = z^{-s},\\ s > 0$, known as Riesz $s$-kernels. \nSince each $\\hat{\\bm{w}}_i$ lies on the unit hypersphere, the squared Euclidean distance between two neurons can be equivalently expressed in angular form as $\\|\\hat{\\bm{w}}_i-\\hat{\\bm{w}}_j\\|^2 = 2\\bigl(1-\\cos\\theta_{ij}\\bigr)$, where $\\theta_{ij}$ is the angle between $\\hat{\\bm{w}}_i$ and $\\hat{\\bm{w}}_j$. \nSubstituting this into Eqn.~\\ref{eq:full_hse}, we have:\n\\begin{equation}\n\\bm{E_{s,d}}\\left( \\hat{\\bm{w}}_i \\mid_{i=1}^N \\right) \n= \\sum_{i=1}^N \\sum_{\\substack{j=1, j \\ne i}}^N \\bigl( 2(1 - \\cos\\theta_{ij}) \\bigr)^{-s/2}.\n\\label{eq:angular_HSE}\n\\end{equation}\nThis angular formulation highlights the geometric interpretation of HE: a higher value corresponds to neuron clustering with low angular diversity, while a lower value reflects a more uniform angular distribution across the hypersphere.\n\n\n\n\n\n\n\\section{Correlation between Hyperspherical Uniformity and Editing}\n\\label{sec:correlation}\n\n\nHE and model editing are intrinsically connected through their shared focus on the geometry of high-dimensional parameter spaces. \nAn optimal HE corresponds to more uniformly distributed representations on the unit hypersphere, typically reflecting well-conditioned parameters that enable reliable and stable sequential editing.\nWe first present empirical evidence revealing a strong correlation between HE and editing stability (Section~\\ref{sec:Empirical}), followed by a formal theoretical analysis establishing the mathematical link between the two (Section~\\ref{sec:Theoretical}). \n\n\n\\subsection{Empirical Analysis of the HE–Editing Stability Correlation}\n\\label{sec:Empirical}\nTo understand the failure modes of large-scale sequential editing, we examined how HE evolves throughout the editing process.\nWe performed 5{,}000 sequential edits on ZsRE dataset~\\citep{DBLP:conf/conll/LevySCZ17} with a batch size of 100 on LLaMA3-8B~\\citep{llama3modelcard} using six widely used editing methods, including Fine-Tuning (FT)~\\citep{DBLP:journals/corr/abs-2012-00363}, \nROME~\\citep{DBLP:conf/nips/MengBAB22}, \nMEMIT~\\citep{DBLP:conf/iclr/MengSABB23}, \nRECT~\\citep{DBLP:conf/emnlp/GuXMLLCP24}, \nPRUNE~\\citep{DBLP:conf/iclr/MaWXLG25}, \nand AlphaEdit~\\citep{DBLP:conf/iclr/FangJWMSW0C25}.\nAfter each edit, we computed the HE of the perturbed weights and evaluated the editing performance using well-established metrics, including \\textbf{Efficacy} (edit success), \\textbf{Generalization} (paraphrase success), and \\textbf{Specificity} (neighborhood success). \nReaders can refer to Appendix~\\ref{appendix-metrics} for detailed definition of these metrics.\nWe summarize our main observations as follows:\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/Sec_3_zsre_Llama3-8B.pdf}\n \\caption{Trends of HE and editing performance throughout sequential editing. \n The Spearman correlation scores between HE and each editing metric displayed at the end of each curve. \n }\n \\label{fig:sec_1}\n\\end{figure}\n\n\n\\vspace{-1mm}\n\\paragraph{Observation 1: Collapse in sequential editing is closely tied to sharp fluctuations in HE.}\nFigure~\\ref{fig:sec_1} reveals a strong correlation between HE dynamics and editing performance.\nThe Spearman correlation scores~\\citep{spearman1904proof} between HE and each editing metric, displayed at the end of each curve, consistently indicate a strong statistical dependence before model collapse\\footnote{Since FT and ROME rapidly collapse at the very beginning, we instead emphasize their correlations by examining the curve fluctuations.}.\nMost methods collapse well before 3,000 edits, whereas AlphaEdit demonstrates the strongest long-term editing capacity with the best preservation of hyperspherical uniformity. \nA closer examination of the metrics shows a consistent pattern in which each drop in performance is consistently accompanied by rapid shifts in HE, underscoring its central role in maintaining sequential editing stability.\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/Sec3-2.pdf} \n \\caption{Correlation between changes in HE and editing performance across consecutive edited weights. Each point corresponds to a $\\Delta \\mathrm{HE}$–$\\Delta \\mathrm{Acc.}$ pair for one method over five thousand sequential edits. Confidence ellipses and regression lines illustrate overall trends.\n }\n \\label{fig:sec_2}\n \\vspace{-3mm}\n\\end{figure}\n\n\n\n\\vspace{-1mm}\n\\paragraph{Observation 2: Advanced editing methods suppress HE fluctuations effectively.} \nFigure~\\ref{fig:sec_2} illustrates the correlation between changes in HE ($\\Delta \\mathrm{HE}$) and editing performance ($\\Delta \\mathrm{Acc.}$), where each point denotes the difference between two consecutive batch edits: points near the origin indicate greater stability with minimal variation in both HE and accuracy, while points farther away reflect larger fluctuations and less stable editing. \nMost advanced methods exhibit tightly clustered distributions near the origin, indicating stable editing dynamics and minimal weight distortion. Furthermore, we fit a linear regression over all points across metrics, which demonstrates a statistically significant positive correlation between $\\Delta \\mathrm{HE}$ and $\\Delta \\mathrm{Acc.}$ in terms of Efficacy and Generalization. This suggests a strong positive correlation between editing stability and HE stability, implying that the effectiveness of SOTA approaches may stem from their ability to suppress HE fluctuations.\n\n\n\n\\subsection{Theoretical Analysis of HE's Impact on Editing Stability}\n\\label{sec:Theoretical}\n\nWe further turn to a theoretical analysis of how HE impacts editing stability, aiming to provide a principled explanation for the patterns observed in practice.\nGiven the editing objective in Eqn.~\\ref{eq:edit_obj}, it inevitably perturbs the original pretrained knowledge in LLMs, which can be expressed as:\n\\begin{equation}\n\\Delta \\bm{V} = (\\bm{W} + \\Delta \\bm{W}) \\bm{K}_1 - \\bm{V}_1 = \\Delta \\bm{W} \\bm{K}_1,\n\\label{eq:delta_V}\\end{equation}\nwhere $\\bm{W} \\bm{K}_1 = \\bm{V}_1$ (cf. Eqn.~\\ref{eq:k1v1}), as $\\bm{K}_1$ and $\\bm{V}_1$ represent the new editing knowledge.\nAdditionally, from the HE definition in Eqn.~\\ref{eq:full_hse}, the change in HE after editing can be written as:\n\\begin{equation}\n\\Delta \\bm{HE} = \\sum_{i < j} \\left( \\|\\bm{w}_i - \\bm{w}_j\\|^{-2} - \\|\\bm{w}_i + \\Delta \\bm{w}_i - \\bm{w}_j - \\Delta \\bm{w}_j\\|^{-2} \\right),\n\\label{eq:hse-change}\n\\end{equation}\nwhere\n$\\Delta \\bm{w}_i$ denotes the perturbation to $\\bm{w}_i$. This term $\\Delta \\bm{HE}$ measures how angular separation among weight vectors changes after editing.\n\n\nOur theoretical analysis, detailed in Appendix~\\ref{appendix:Correlation}, culminates in a key result that formally links the geometric change in weight space $\\Delta \\bm{HE}$ to the output perturbation $\\Delta \\bm{V}$, derived from Proposition~\\ref{prop:he_bound}.\n\\begin{theorem}[Lower Bound on Output Perturbation]\n\\label{thm:main_bound_in_text}\nUnder the assumptions of orthonormal inputs and small perturbations, the output perturbation $\\Delta \\bm{V}$ is lower-bounded by squared change in HE:\n\\begin{equation}\n |\\Delta \\bm{V}| \\;\\ge\\; \\left( \\frac{\\Delta \\bm{HE}}{K} \\right)^2, \n \\quad \n K = 4\\Biggl( \\sum_{k=1}^p \\Biggl( \\sum_{j \\ne k} \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} \\Biggr)^2 \\Biggr)^{1/2}.\n \\label{eq:hse-bound}\n\\end{equation}\nwhere $K$ is a constant dependent on the original weight matrix geometry.\n\\end{theorem}\n\\vspace{-2mm}\n\nThis theorem reveals a key insight: the change in HE ($|\\Delta \\bm{HE}|$) inevitably induces a substantial output perturbation ($\\Delta \\bm{V}$), meaning that edits that significantly distort the geometric arrangement of neurons are bound to corrupt pretrained knowledge. This result provides a solid theoretical foundation for our empirical findings and underscores HE as a fundamental indicator of editing stability.\n\\section{\\METHODNAME{}}\n\\label{sec:method}\nOn account of the above findings, we argue that ideal sequential editing should preserve the hyperspherical uniformity of edited weights. \nAccordingly, we introduce \\METHODNAME{}, an HE-driven regularization strategy designed to mitigate HE fluctuations while integrating new knowledge.\n\n\\METHODNAME{} first estimates the principal hyperspherical directions of pretrained knowledge and then defines their orthogonal complement as the sparse space.\nProjecting editing perturbations onto this space enables knowledge injection while minimizing interference with original knowledge.\n\n\\paragraph{Principal Space Estimation}\nTo identify the principal hyperspherical directions in $\\bm{W}$, we seek a unit vector $v \\in \\mathbb{R}^d$ that maximizes the variance of all neurons in $\\bm{W}$ when projected onto $v$ as: \n\\begin{equation}\n\\bm{v} \n= \\arg\\max_{\\|\\hat{\\bm{v}}\\|=1} \\left( \\tfrac{1}{n} \\|\\bm{W} \\hat{\\bm{v}}\\|^2 \\right)\n= \\arg\\max_{\\|\\hat{\\bm{v}}\\|=1} \\left( \\tfrac{1}{n} \\hat{\\bm{v}}^\\top \\bigl( \\bm{W}^\\top \\bm{W}\\bigr) \\hat{\\bm{v}} \\right).\n\\end{equation}\nAccording to the Rayleigh quotient theory~\\citep{horn1985matrix,parlett1998symmetric}, the maximum of $\\frac{1}{n}v^\\top \\bm{W}^\\top \\bm{W} v$ corresponds to the largest eigenvalue $\\lambda^*$ of $\\frac{1}{n}\\bm{W}^\\top \\bm{W}$, with the associated eigenvector $v^*$ as the principal direction. \nExtending this to the top-$r$ principal directions enables us to capture a richer low-dimensional space of the weight geometry, so we collect the eigenvectors associated with the $r$ largest eigenvalues to form the principal space matrix, which can be expressed as:\n\\begin{equation}\n\\bm{U} = [\\bm{v}_{d-r+1}, \\dots, \\bm{v}_d] \\in \\mathbb{R}^{d \\times r}, \n\\label{eq:principle}\n\\end{equation}\nwhere $r$ satisfies $\\sum_{i=d-r+1}^{d} \\lambda_i \\ge \\eta \\sum_{i=1}^{d} \\lambda_i$, with the cumulative ratio $\\eta$ (see Appendix~\\ref{appendix:eta-and-alpha}). \n\n\n\n\\paragraph{Sparse Space Definition}\nThis space is defined as the orthogonal complement of $\\bm{U}$ in Eqn.~\\ref{eq:principle} as:\n\\begin{equation}\n\\bm{P}_\\perp = I - \\alpha \\bm{U} \\bm{U}^\\top \\in \\mathbb{R}^{d \\times d},\n\\end{equation}\nwhere $\\alpha$ controls the suppression strength of the components along the subspace spanned by $\\bm{U}$ (see Appendix~\\ref{appendix:eta-and-alpha}). Specifically, $\\alpha = 1$ corresponds to a hard orthogonal projection that completely removes the contribution of $\\bm{U}$, while $0 < \\alpha < 1$ yields a soft projection that only attenuates it.\n\n\n\n\\paragraph{Sparse Space Projection}\nGiven a perturbation matrix $\\Delta \\bm{W}$ produced by any editing method, we project it onto the sparse space using $P_\\perp$, and then combine it with the original weight matrix as: \n\\begin{equation}\n\\hat{\\bm{W}} = \\bm{W} + \\Delta \\bm{W}_{\\text{proj}} = \\bm{W} + \\Delta \\bm{W}\\bm{P}_\\perp.\n\\label{eq:sphere_constrain}\n\\end{equation}\n\n\nIn summary, \\METHODNAME{} suppresses perturbations aligned with the principal weight directions to preserve hyperspherical uniformity, enabling more stable, longer-lasting performance without compromising general abilities. \nFor theoretical completeness, we also provide a mathematical proof that \\METHODNAME{} suppresses the $\\Delta \\bm{HE}$, ensuring bounded variations in the hidden representations $\\Delta \\bm{V}$ and justifying its effectiveness during editing (see Appendix~\\ref{appendix:sparse-space-projection}). More details in Appendix~\\ref{appendix:projection-implementation}\n\n\n\n\n\n\\section{Experiments}\nIn this section, we aim to address the following research questions:\n\\vspace{-2mm}\n\\begin{itemize}[leftmargin=*, itemsep=0pt, parsep=0pt]\n \\item \\textbf{RQ1:} How does \\METHODNAME{} perform on sequential editing tasks compared to baseline methods? \n \\item \\textbf{RQ2:} Can \\METHODNAME{} effectively preserve the hyperspherical uniformity of edited weights? \n \\item \\textbf{RQ3:} How does \\METHODNAME{}-edited LLMs perform on general ability evaluations? \n \\item \\textbf{RQ4:} Can baseline methods be significantly improved with plug-and-play \\METHODNAME{}? \n\\end{itemize}\n\\subsection{Experimental Setup}\n\\vspace{-2mm}\n\\paragraph{Base LLMs and Baseline Methods.} \nExperiments were conducted on LLaMA3 (8B)~\\citep{llama3modelcard} and Qwen2.5 (7B)~\\citep{qwen2.5}. \nWe compared our approach against a range of representative sequential editing baselines, including \nFine-Tuning (FT)~\\citep{DBLP:journals/corr/abs-2012-00363}, \nMEMIT~\\citep{DBLP:conf/iclr/MengSABB23}, \nRECT~\\citep{DBLP:conf/emnlp/GuXMLLCP24}, \nPRUNE~\\citep{DBLP:conf/iclr/MaWXLG25}, \nand AlphaEdit~\\citep{DBLP:conf/iclr/FangJWMSW0C25}.\n\n\\vspace{-2mm}\n\\paragraph{Datasets and Evaluation Metrics.} \nTwo widely used benchmarks were adopted: \nCounterFact~\\citep{DBLP:conf/nips/MengBAB22} and ZsRE~\\citep{DBLP:conf/conll/LevySCZ17}.\nFollowing prior work~\\citep{DBLP:conf/nips/MengBAB22}, five evaluation metrics were reported: \n\\textbf{Efficacy} (edit success), \n\\textbf{Generalization} (paraphrase success), \n\\textbf{Specificity} (neighborhood success), \n\\textbf{Fluency} (generation entropy), \nand \\textbf{Consistency} (reference score). \nFor rigorous evaluation, we adopt the \\textbf{average top-1 accuracy} as the metric for both datasets.\nReaders can refer to Appendix~\\ref{appendix-setup} for more detailed experimental setup.\n\n\\subsection{Performance of Sequential Model Editing (RQ1)}\n\n\\newcommand{\\meanstd}[2]{#1{\\scriptsize$\\pm$#2}}\n\\begin{table*}[t]\n\\centering\n\\caption{Comparison of \\METHODNAME{} with existing methods on sequential editing. \n\\emph{Eff.}, \\emph{Gen.}, \\emph{Spe.}, \\emph{Flu.} and \\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \nThe best results are highlighted in bold, while the second-best results are underlined.}\n\\label{tab:main_results}\n\\resizebox{\\textwidth}{!}{\n\\setlength{\\arrayrulewidth}{0.7pt} \n\\renewcommand{\\arraystretch}{1.3} \n\\begin{tabular}{c c | c c c | c c c | c c}\n\\specialrule{1.2pt}{0pt}{0pt} \n\\multirow{2}{*}{\\textbf{Method}} & \\multirow{2}{*}{\\textbf{Model}}\n& \\multicolumn{3}{c|}{\\textbf{ZSRE}} \n& \\multicolumn{5}{c}{\\textbf{Counterfact}} \\\\\n\\cmidrule(lr){3-5} \\cmidrule(lr){6-10}\n & & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} \n & \\textbf{Eff.$\\uparrow$} & \\textbf{Gen.$\\uparrow$} & \\textbf{Spe.$\\uparrow$} & \\textbf{Flu.$\\uparrow$} & \\textbf{Consis.$\\uparrow$} \\\\\n\\hline\\hline\n\n% ----------- Llama3-8B block ------------\nPre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{LLaMA3-8B}}} \n& \\meanstd{35.42}{0.30} & \\meanstd{34.17}{0.30} & \\meanstd{38.02}{0.27} \n& \\meanstd{0.49}{0.07} & \\meanstd{0.44}{0.05} & \\meanstd{18.09}{0.24} & \\meanstd{634.84}{0.12} & \\meanstd{22.06}{0.08} \\\\\n\\hline\nFT & & \\meanstd{15.27}{0.21} & \\meanstd{14.78}{0.21} & \\meanstd{5.06}{0.10} \n& \\underline{\\meanstd{8.40}{0.28}} & \\underline{\\meanstd{2.54}{0.13}} & \\meanstd{0.03}{0.01} & \\meanstd{409.80}{0.67} & \\meanstd{19.35}{0.13} \\\\\nMEMIT & & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.06}{0.01} \n& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{318.19}{0.24} & \\meanstd{4.19}{0.04} \\\\\nPRUNE & & \\meanstd{10.35}{0.18} & \\meanstd{10.08}{0.18} & \\meanstd{9.55}{0.15} \n& \\meanstd{1.19}{0.11} & \\meanstd{0.34}{0.04} & \\underline{\\meanstd{0.62}{0.03}} & \\textbf{\\meanstd{618.72}{0.08}} & \\textbf{\\meanstd{49.24}{0.13}} \\\\\nRECT & & \\meanstd{0.01}{0.00} & \\meanstd{0.01}{0.01} & \\meanstd{0.04}{0.01} \n& \\meanstd{0.57}{0.08} & \\meanstd{0.29}{0.04} & \\meanstd{0.10}{0.01} & \\meanstd{438.83}{0.18} & \\meanstd{9.40}{0.05} \\\\\nAlphaEdit & & \\underline{\\meanstd{86.64}{0.23}} & \\underline{\\meanstd{81.28}{0.28}} & \\underline{\\meanstd{28.78}{0.22}} \n& \\meanstd{4.37}{0.20} & \\meanstd{1.71}{0.10} & \\meanstd{0.57}{0.03} & \\meanstd{482.36}{0.44} & \\meanstd{4.71}{0.04} \\\\\n\\hline\n\\METHODNAME{}& & \\textbf{\\meanstd{90.01}{0.21}} & \\textbf{\\meanstd{84.67}{0.26}} & \\textbf{\\meanstd{45.40}{0.29}} \n& \\textbf{\\meanstd{52.89}{0.50}} & \\textbf{\\meanstd{32.07}{0.39}} & \\textbf{\\meanstd{5.01}{0.10}} & \\underline{\\meanstd{551.51}{0.53}} & \\underline{\\meanstd{30.89}{0.13}} \\\\\n\\hline\\hline\n\n% ----------- Qwen2.5-7B block ------------\nPre-edited & \\multirow{7}{*}{\\makecell{\\rotatebox{90}{Qwen2.5-7B}}} \n& \\meanstd{35.29}{0.29} & \\meanstd{34.10}{0.28} & \\meanstd{38.44}{0.27} \n& \\meanstd{0.42}{0.06} & \\meanstd{0.46}{0.05} & \\meanstd{15.06}{0.20} & \\meanstd{624.45}{0.11} & \\meanstd{23.02}{0.69} \\\\\n\\hline\nFT & & \\meanstd{4.97}{0.14} & \\meanstd{4.58}{0.13} & \\meanstd{4.01}{0.11} \n& \\meanstd{15.44}{0.36} & \\meanstd{4.63}{0.17} & \\meanstd{1.46}{0.05} & \\meanstd{214.26}{0.09} & \\meanstd{3.15}{0.02} \\\\\nMEMIT & & \\meanstd{0.13}{0.02} & \\meanstd{0.12}{0.01} & \\meanstd{0.04}{0.01} \n& \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{0.00}{0.00} & \\meanstd{370.84}{0.30} & \\meanstd{3.59}{0.03} \\\\\nPRUNE & & \\underline{\\meanstd{47.93}{0.36}} & \\underline{\\meanstd{45.50}{0.35}} & \\textbf{\\meanstd{39.20}{0.28}} \n& \\meanstd{14.30}{0.35} & \\meanstd{11.27}{0.26} & \\textbf{\\meanstd{6.75}{0.12}} & \\textbf{\\meanstd{620.74}{0.10}} & \\textbf{\\meanstd{29.50}{0.08}} \\\\\nRECT & & \\meanstd{0.73}{0.04} & \\meanstd{0.75}{0.04} & \\meanstd{0.05}{0.07} \n& \\meanstd{0.64}{0.08} & \\meanstd{0.19}{0.03} & \\meanstd{0.09}{0.01} & \\meanstd{368.46}{0.27} & \\meanstd{1.35}{0.01} \\\\\nAlphaEdit & & \\meanstd{42.01}{0.40} & \\meanstd{39.99}{0.39} & \\meanstd{13.87}{0.20} \n& \\underline{\\meanstd{43.92}{0.50}} & \\underline{\\meanstd{24.37}{0.36}} & \\meanstd{2.32}{0.06} & \\meanstd{479.83}{0.77} & \\meanstd{4.67}{0.07} \\\\\n\\hline\n\\METHODNAME{}& & \\textbf{\\meanstd{70.04}{0.36}} & \\textbf{\\meanstd{65.43}{0.37}} & \\underline{\\meanstd{27.35}{0.26}} \n& \\textbf{\\meanstd{60.76}{0.49}} & \\textbf{\\meanstd{29.24}{0.37}} & \\underline{\\meanstd{3.83}{0.08}} & \\underline{\\meanstd{612.67}{0.22}} & \\underline{\\meanstd{14.74}{0.07}} \\\\\n\\specialrule{1.2pt}{0pt}{0pt} \n\n\\end{tabular}\n}\n\\end{table*}\n\n\nTable~\\ref{tab:main_results} presents the results under a commonly used sequential editing setup, using 15,000 samples with 100 edits each for LLaMA3 (8B), while Qwen2.5 (7B) is restricted to 5,000 edits as further updates induce severe model collapse, where all editing methods underperformed compared to the pre-edit baseline.\n\\METHODNAME{} is plug-and-play, and AlphaEdit~\\citep{DBLP:conf/iclr/FangJWMSW0C25} is adopted as the default base method in Table~\\ref{tab:main_results} to better illustrate its capability. Additional experiments with other base methods are presented in Section~\\ref{sec:5-5}.\nOverall, \\METHODNAME{} consistently outperforms baseline methods across nearly all metrics and base models. In particular, it achieves substantial gains in both \\textbf{Efficacy} and \\textbf{Generalization}, with average improvements of \\textbf{24.19\\%} and \\textbf{16.02\\%}, respectively, over the best baseline. It also maintains notable performance in Fluency and Consistency, indicating its ability to preserve factual accuracy while generating coherent and natural outputs. \n\n\\subsection{Analysis of Edited Weights (RQ2)}\nThis analysis evaluates whether \\METHODNAME{} can effectively maintain the hyperspherical uniformity of edited weights.\nWe extracted the edited weights from LLaMA3 after 15,000 sequential edits on CounterFact. \nAs shown in Figure~\\ref{fig:Sec_5_heatmap}, we computed the cosine similarity between each pair of weight neurons and used heatmap to visualize the hyperspherical uniformity before and after editing. \nIn Figure~\\ref{fig:Sec_5_pca}, t-SNE~\\citep{JMLR:v9:vandermaaten08a} was used to visualize the normalized neuron distribution in $\\bm{W}$ before and after editing. \nIt can be seen that \\METHODNAME{} \\textbf{effectively preserves hyperspherical uniformity after editing, as the cosine similarity among weight neurons remains close to the original distribution}, thereby avoiding directional collapse. \nMoreover, the pre- and post-edited weights exhibit nearly overlapping distributions, indicating that \\METHODNAME{} prevents significant shifts in weights and maintains consistency. \nIn contrast, baseline methods such as MEMIT and AlphaEdit induce clear angular concentration in neuron directions, causing neurons to cluster in limited angular regions and significantly reducing hyperspherical directional uniformity. More results on Qwen2.5 are in Appendix~\\ref{appendix:hidden-representation-qwen}. \n\n\n\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/llama_neuron_similarity_heatmap_15k.pdf} \n \\caption{\n Cosine similarity between neurons in the updated weight matrix after 15,000 edits. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\n \\METHODNAME{} effectively preserves the weight structure, demonstrating the most stable hyperspherical uniformity.\n }\n \\label{fig:Sec_5_heatmap}\n \\vspace{-3mm}\n\\end{figure}\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/llama_tsne_grid_15k.pdf} \n \\caption{The t-SNE distribution of weight neurons of pre-edited and post-edited LLM after 15,000 edits using dimensionality reduction. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\METHODNAME{} consistently exhibits minimal shift. }\n \\label{fig:Sec_5_pca}\n \\vspace{-3mm}\n\\end{figure}\n\n\n\n\\subsection{Evaluation of General Abilities (RQ3)}\nTo extensively evaluate whether post-edited LLMs can preserve the general abilities, four representative tasks were adopted following\n\\citet{DBLP:conf/emnlp/GuXMLLCP24}, including \n\\textbf{Reasoning} on the GSM8K~\\citep{DBLP:journals/corr/abs-2110-14168}, measured by solve rate.\n\\textbf{Natural language inference (NLI)} on the RTE~\\citep{DBLP:conf/mlcw/DaganGM05}, measured by accuracy of two-way classification, \n\\textbf{Open-domain QA} on the Natural Questions~\\citep{DBLP:journals/tacl/KwiatkowskiPRCP19}, measured by exact match (EM) with the reference answer after minor normalization~\\citep{DBLP:conf/acl/ChenFWB17, DBLP:conf/acl/LeeCT19}.\n\\textbf{Closed-domain QA} on BoolQ~\\citep{DBLP:conf/naacl/ClarkLCK0T19}, also measured by EM. \nFigure~\\ref{fig:line_general} depicts how performance varies with the number of edited samples across four tasks. \nWe report general performance every 1k edits up to 5k, and every 5k edits thereafter (up to 15k), providing a comprehensive view of the degradation trend. \nThe results show that \\METHODNAME{} effectively preserves the general abilities of post-edited LLMs even under extensive editing, maintaining the original model performance across all metrics after 15k edits. In contrast, LLMs edited with baseline methods rapidly lose their general abilities with all metrics approaching zero. \nThese findings underscore the critical role of hyperspherical uniformity in safeguarding the broad abilities learned from the underlying corpus.\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/general_line.pdf} \n \\caption{\n General ability testing of post-edited LLaMA3 (8B) on four tasks.\n }\n \\label{fig:line_general}\n\\end{figure}\n\n\n\n\\subsection{Performance Improvements of Baseline Methods (RQ4)}\n\\label{sec:5-5}\nWe investigated whether the sparse space projection strategy of \\METHODNAME{} can serve as a general enhancement to existing methods. \nA single line of code from \\METHODNAME{} regarding the projection was inserted into the baselines with minimal modification, and we evaluated their performance before and after integration (as detailed in Appendix~\\ref{appendix:projection-implementation}). \nResults of 3,000 sequential edits on LLaMA3 (8B) are reported in Figure~\\ref{fig:baseline_improve_all}. \n\\textbf{\\METHODNAME{} is integrated seamlessly with diverse editing methods and significantly boosts their performance.} \nOn average, the optimized baselines achieve relative improvements of \\textbf{49.05\\%}, \\textbf{42.64\\%}, and \\textbf{24.44\\%} in \\textbf{Efficacy}, \\textbf{Generalization}, and \\textbf{Specificity}, respectively, underscoring the strong potential and broad applicability of the proposed sparse space projection as a plug-and-play enhancement for model editing. \nThe baselines enhanced with the projection also demonstrate significantly better robustness in general abilities (see Appendix~\\ref{general-baseline}).\n\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.98\\textwidth]{Figures/baseline_improve_all.pdf}\n \\caption{Performance improvements of baseline editing methods after adding a single line of code from \\METHODNAME{} (i.e., sparse space projection). Gray bars denote the original baseline performance, while purple bars indicate the performance after enhancement.}\n \\label{fig:baseline_improve_all}\n \\vspace{-2mm}\n\\end{figure}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{Related Work}\n\n\\paragraph{Model Editing Methods.} \nFrom the perspective of whether model parameters are modified, existing approaches can be broadly categorized into \\emph{parameter-modifying} \\citep{DBLP:conf/iclr/MitchellLBFM22, DBLP:conf/iclr/MengSABB23, DBLP:conf/iclr/MaWXLG25, DBLP:conf/iclr/FangJWMSW0C25}, which directly adjust a small subset of model parameters, and \\emph{parameter-preserving}~\\citep{DBLP:conf/emnlp/ZhengLDFWXC23, DBLP:conf/aaai/YuCZH24, DBLP:conf/nips/HartvigsenSPKG23}, which integrate auxiliary modules without altering the original weights. In this work, we focus on \\emph{parameter-modifying methods} which typically employs meta-learning or locating-then-editing strategies~\\citep{DBLP:journals/corr/abs-2401-01286}. Representative works of meta-learning include KE~\\citep{DBLP:conf/emnlp/CaoAT21} and MEND~\\citep{DBLP:conf/iclr/MitchellLBFM22}, which leverage hypernetworks to generate parameter updates. Locate-then-edit methods, such as ROME~\\citep{DBLP:conf/nips/MengBAB22} and MEMIT~\\citep{DBLP:conf/iclr/MengSABB23}, prioritize pinpointing the knowledge’s storage location before making\ntargeted edits. \nRecent extensions like RECT~\\citep{DBLP:conf/emnlp/GuXMLLCP24} and PRUNE~\\citep{DBLP:conf/iclr/MaWXLG25} mitigate degradation of general capabilities of LLMs by better constraining edit complexity via sparsity and condition number. Recently, AlphaEdit~\\citep{DBLP:conf/iclr/FangJWMSW0C25} further generalizes this paradigm by projecting the perturbation into the nullspace of the previous knowledge set.\n\n\n\\vspace{-3mm}\n\\paragraph{Learning with Hyperspherical Uniformity.}\nEarly studies~\\citep{DBLP:conf/icml/XieDZKYZX17, DBLP:conf/iclr/Rodriguez0CGR17, DBLP:conf/icml/XieSX17, DBLP:journals/corr/CogswellAGZB15} sought to improve the generalization capacity of neural networks by reducing redundancy through diversification, as rigorously analyzed in~\\citep{DBLP:conf/icml/XieZX16}. Although these works examined angular diversity, they largely neglected the notion of global equidistribution of embeddings on the hypersphere. In contrast to orthogonality, where perpendicular vectors are defined\nto be diverse, hyperspherical uniformity promotes embeddings that are maximally separated in angle, thereby encouraging uniform distribution across the hypersphere~\\citep{DBLP:conf/aistats/LiuLL0SW21, DBLP:conf/nips/LiuLLLYDS18}. More recently, \\citet{DBLP:conf/nips/SmerkousBL24} enhancing training stability by incorporating centered kernel alignment into hyperspherical energy, enhancing training stability by addressing the lack of permutation invariance inherent in naive similarity metrics.\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{Conclusion}\nIn this work, we demonstrated that hyperspherical uniformity is a critical factor in stabilizing sequential editing for LLMs, supported by both empirical evidence and rigorous theoretical proof. \nMotivated by this insight, we propose \\METHODNAME{}, a regularization strategy that preserves hyperspherical uniformity by projecting updates onto a space complementary to the principal directions of pretrained weights.\nExtensive evaluations on LLaMA3 (8B) and Qwen2.5 (7B) across multiple editing datasets and downstream tasks confirm that \\METHODNAME{} not only enhances editing performance by 16.41\\% over the strongest baseline but also more faithfully preserves weight geometry and general abilities of models.\nFurthermore, when applied as a plug-and-play enhancement, it yields an additional average improvement of 38.71\\% across existing methods.\nCollectively, our findings establish \\METHODNAME{} as both theoretically grounded and empirically effective, providing a principled and scalable solution for reliable large-scale model editing.\n\n\n\n\n\n\\subsubsection*{Ethics Statement}\nOur proposed method \\METHODNAME{} significantly enhances the reliability of large-scale sequential model editing by preserving hyperspherical uniformity, which makes it a valuable way for updating and managing knowledge in real-world applications where long-term stability is essential. At the same time, the ability to directly alter stored knowledge in LLMs carries inherent risks, including the potential introduction of bias or harmful information. To address these concerns, we strongly recommend rigorous validation procedures, transparent reporting, and strict oversight when deploying such techniques. While the core motivation of \\METHODNAME{} is positive, aiming to facilitate efficient and trustworthy updates of large language models, we emphasize that its use must remain responsible and cautious to ensure ethical outcomes.\n\nWe used LLMs to assist with improving grammar, clarity, and wording in parts of this work. The use of LLMs was limited to language refinement, with all ideas, analyses, and conclusions solely developed by the authors. We restate this announcement in Appendix~\\ref{sec:llm_usage}\n\n\n\n\\subsubsection*{Reproducibility Statement}\nTo ensure the reproducibility of our findings, detailed implementation instructions for \\METHODNAME{}\nare provided in in Section~\\ref{sec:method} , Appendix~\\ref{appendix-setup}. Additionally, we plan to release our source code in the future to further support reproducibility. These measures are intended to facilitate the verification and replication of our results by other researchers in the field.\n\n\n\n\\subsubsection*{Acknowledgments}\nWe would like to express gratitude to the UCLANLP group members for their valuable feedback.\n\n\n\\bibliography{iclr2026_conference}\n\\bibliographystyle{iclr2026_conference}\n\n\n\\clearpage\n\\appendix\n\n\\section{Usage of LLMs}\n\\label{sec:llm_usage}\nThroughout the preparation of this manuscript, we used LLMs to assist with improving grammar, clarity, and wording in parts of this work. The use of LLMs was limited to language refinement, with all ideas, analyses, and conclusions solely developed by the authors.\n\n\\section{Preliminaries of Model Editing}\n\\label{appendix:model_editing}\n\nModel editing aims to refine a pre-trained model by applying one or more edits, where each edit replaces a factual association $(s, r, o)$ with new knowledge $(s, r, o^*)$ \\citep{DBLP:conf/emnlp/Yang0TMSYS24,DBLP:journals/corr/abs-2502-05759}. After editing, the model is expected to recall the updated object $o^*$ when given a natural language prompt $p(s, r)$, such as ``The President of the United States is'' \\citep{DBLP:conf/vldb/0001XL0TYZDSL0Z24}.\n\nTo achieve this, locating-and-editing methods have been proposed for effective model updates \\citep{DBLP:conf/acl/Yang0MLYC24}. These methods typically follow three steps \\citep{DBLP:conf/acl/JiangFZBZWL025}:\n\n\\paragraph{Step 1: Locating Influential Layers.}\nThe first step is to identify the specific FFN layers that encode the target knowledge using causal tracing \\citep{DBLP:conf/nips/MengBAB22}. This method involves injecting Gaussian noise into the hidden states and progressively restoring them to their original values. By analyzing the degree to which the original output recovers, the influential layers can be pinpointed as the targets for editing.\n\n\\paragraph{Step 2: Acquiring the Expected Output.}\nThe second step aims to obtain the desired output of the critical layers identified in Step~1. Following the key--value theory, the key $\\bm{k}$, which encodes $(s,r)$, is processed through the output weights $\\bm{W}_{\\mathrm{out}}^{l}$ to produce the original value $\\bm{v}$ encoding $o$. Formally,\n\\begin{equation}\n \\bm{k} \\triangleq \\sigma\\!\\big(\\bm{W}_{\\mathrm{in}}^{l}\\,\\gamma(\\bm{h}^{l-1}+\\bm{\\bm{\\alpha}}^{l})\\big),\n \\qquad\n \\bm{v} \\triangleq \\bm{m}^{l}=\\bm{W}_{\\mathrm{out}}^{l}k .\n \\label{eq:me_kv}\n\\end{equation}\n\nTo perform editing, $\\bm{v}$ is expected to be replaced with a new value $\\bm{v}^{*}$ encoding $o^{*}$. To this end, current methods typically use gradient descent on $\\Delta \\bm{W}$, maximizing the probability that the model outputs the word associated with $o^{*}$ \\citep{DBLP:conf/iclr/MengSABB23}. The optimization objective is as follows:\n\\begin{equation}\n \\bm{v}^{*}\n = \\bm{v} + \\arg\\min_{\\Delta \\bm{W}^{l}}\n \\Big(\n -\\log \\mathbb{P}_{\\,f^{l}_{\\bm{W}_{\\mathrm{out}}}(\\bm{m}^{l}+=\\Delta \\bm{W}^{l})}\n \\big[\\,o^{*}\\mid (s,r)\\,\\big]\n \\Big),\n \\label{eq:me_opt}\n\\end{equation}\n\nwhere $f^{l}_{\\bm{W}_{\\mathrm{out}}}(\\bm{m}^{l}+=\\Delta \\bm{W})$ represents the original model with $\\bm{m}^{l}$ updated to $\\bm{m}^{l}+\\Delta \\bm{W}$.\n\n\\paragraph{Step 3: Updating $\\bm{W}_{\\mathrm{out}}^{l}$.}\nThis step aims to update the parameters $\\bm{W}_{\\mathrm{out}}^{l}$. It includes a factual set $\\{\\bm{K}_{1},\\bm{V}_{1}\\}$ containing $u$ new associations, while preserving the set $\\{\\bm{K}_{0},\\bm{V}_{0}\\}$ containing $n$ original associations. Specifically,\n\\begin{equation}\n\\begin{array}{c}\n \\bm{K}_{0} = [\\,\\bm{k}_{1}\\;\\bm{k}_{2}\\;\\cdots\\;\\bm{k}_{n}\\,], \\quad\n \\bm{V}_{0} = [\\,\\bm{v}_{1}\\;\\bm{v}_{2}\\;\\cdots\\;\\bm{v}_{n}\\,], \\\\[6pt]\n \\bm{K}_{1} = [\\,\\bm{k}_{n+1}\\;\\bm{k}_{n+2}\\;\\cdots\\;\\bm{k}_{n+u}\\,], \\quad\n \\bm{V}_{1} = [\\,\\bm{v}^{*}_{\\,n+1}\\;\\bm{v}^{*}_{\\,n+2}\\;\\cdots\\;\\bm{v}^{*}_{\\,n+u}\\,]\n\\end{array}\n\\label{eq:me_sets}\n\\end{equation}\n\n\n\nwhere $\\bm{k}$ and $\\bm{v}$ are defined in Eqn.~\\ref{eq:me_kv} and their subscripts represent the index of the knowledge. Based on these, the objective can be defined as:\n\\begin{equation}\n \\tilde{\\bm{W}}^{l}_{\\mathrm{out}}\n \\triangleq\n \\arg\\min_{\\hat{\\bm{W}}}\n \\left(\n \\sum_{i=1}^{n}\\!\\big\\|\\hat{\\bm{W}}\\bm{k}_{i}-\\bm{v}_{i}\\big\\|^{2}\n +\n \\sum_{i=n+1}^{n+u}\\!\\big\\|\\hat{\\bm{W}}\\bm{k}_{i}-\\bm{v}^{*}_{i}\\big\\|^{2}\n \\right).\n \\label{eq:me_obj}\n\\end{equation}\n\n\nBy applying the normal equation, its closed-form solution can be derived:\n\\begin{equation}\n \\tilde{\\bm{W}}^{l}_{\\mathrm{out}}\n =\n \\big(\\bm{M}_{1}-\\bm{W}^{l}_{\\mathrm{out}}\\bm{K}_{1}\\big)\\,\\bm{K}_{1}^{\\top}\n \\big(\\bm{K}_{0}\\bm{K}_{0}^{\\top}+\\bm{K}_{1}\\bm{K}_{1}^{\\top}\\big)^{-1}\n + \\bm{W}^{l}_{\\mathrm{out}} .\n \\label{eq:me_closedform}\n\\end{equation}\n\nIn practice, model editing methods often update parameters across multiple layers to improve effectiveness. For more details, see \\citep{DBLP:conf/iclr/MengSABB23}.\n\n\n\n\\clearpage\n\n\\section{Theoretical Proofs}\n\n\\subsection{Proof of Correlation between Hyperspherical Energy and Editing Stability}\n\\label{appendix:Correlation}\n\n\\paragraph{Objective for Preserving Original Knowledge}\nWe begin by assuming that the original knowledge base can be expressed as $\\{\\bm{k}_i,\\ \\bm{v}_i\\}\\quad i = 1, \\ldots, N, \\quad \\bm{k}_i \\in \\mathbb{R}^p, \\; \\bm{v}_i \\in \\mathbb{R}^q$, while the new knowledge base is given by $\\{\\tilde{\\bm{k}}_i,\\ \\tilde{\\bm{v}}_i\\}\\quad i = 1, \\ldots, N, \\quad \\tilde{\\bm{k}}_i \\in \\mathbb{R}^p, \\; \\tilde{\\bm{v}}_i \\in \\mathbb{R}^q$\n\nAnd the knowledge mapping is governed by the weight matrix $W \\in \\mathbb{R}^{p \\times q}$ such that\n\\begin{equation}\n\\bm{W} \\bm{k}_i = \\bm{v}_i, \n\\qquad \n(\\bm{W}+\\Delta \\bm{W})\\tilde{\\bm{k}}_i = \\tilde{\\bm{v}}_i.\n\\end{equation}\n\nWhen analyzing the destroy to the original knowledge set, there is shift brought by the perturbation $\\Delta \\bm{W}$ which can be expressed as:\n\\begin{equation}\n(\\bm{W}+\\Delta \\bm{W})\\bm{k}_i = \\bm{v}_i + \\Delta \\bm{W}\\bm{k}_i\n\\end{equation}\nwhere we define $\\Delta \\bm{v}_i = \\Delta \\bm{W}\\bm{k}_i$ as the destroy to the previous knowledge set. In addition, if $\\bm{k}_i \\in \\mathrm{null}(\\Delta \\bm{W})$, i.e., in the null space of $\\Delta \\bm{W}$, then $\\Delta \\bm{W} \\bm{k}_i = \\Delta \\bm{v}_i = 0$.\n\n\nThe corresponding objective is thus to minimize the perturbation magnitude, given by\n\\begin{equation}\n\\min \\frac{1}{N}\\sum_{i=1}^N \\|\\Delta \\bm{v}_i\\|\n\\quad \\equiv \\quad \n\\min \\frac{1}{N}\\sum_{i=1}^N \\|\\Delta \\bm{W} \\bm{k}_i\\|.\n\\end{equation}\nTo make this tractable, assume that each input vector $\\bm{k}_i$ can be approximated in terms of the first $\\bm{K}$ basis vectors $\\{\\bm{e_j}\\}$ as\n\\begin{equation}\n\\bm{k}_i = \\sum_{j=1}^K \\bm{\\alpha_j} \\bm{e_j} + \\varepsilon_i,\n\\end{equation}\nwhere $\\varepsilon_i$ is a small noise term. If we denote\n\\begin{equation}\n\\Delta \\bm{W} \\cdot \\bm{e_j} = \\bm{f_j},\n\\qquad \n\\varepsilon_i, \\bm{e_j}, \\bm{f_j} \\in \\mathbb{R}^q,\n\\end{equation}\nthen the perturbation objective can be rewritten as:\n\\begin{equation}\n\\begin{aligned}\n& \\min \\frac{1}{N}\\sum_{i=1}^N \n \\left\\| \\Delta \\bm{W} \\cdot \n \\left( \\sum_{j=1}^K \\bm{\\alpha_j} \\bm{e_j} + \\varepsilon_i \\right) \\right\\| \\\\[2pt]\n& \\leq \\frac{1}{N}\\sum_{i=1}^N \n \\left\\|\\sum_{j=1}^K \\bm{\\alpha_j} \\bm{f_j} + \\Delta \\bm{W} \\varepsilon_i \\right\\| \\\\[2pt]\n& \\leq \\frac{1}{N}\\sum_{i=1}^N \n \\sum_{j=1}^K |\\bm{\\alpha_j} \\bm{f_j}| + \\|\\Delta \\bm{W}\\| |\\varepsilon_i| \\\\[2pt]\n& \\le \\frac{1}{N}\\sum_{i=1}^N\n \\sum_{j=1}^K |\\bm{\\alpha_j}|\\,\\lVert \\bm{f_j}\\rVert \\;+\\; \\varepsilon_{\\max}\\,\\lVert \\boldsymbol{\\Delta}\\rVert .\n\\end{aligned}\n\\label{eq:perturb_bound}\n\\end{equation}\nwhere $\\varepsilon_{\\max} = \\max_{i} \\|\\varepsilon_i\\|$. This shows that minimizing $\\|f_j\\|$ directly reduces the upper bound of the perturbation, and therefore enhances the stability of the editing process.\n\n\n\n\n\n\n\n\\paragraph{Definitions}\nLet the model's weights be represented by a matrix $\\bm{W} \\in \\mathbb{R}^{p \\times q}$, whose rows are the neuron vectors $\\bm{w}_1, \\dots, \\bm{w}_p \\in \\mathbb{R}^q$. An edit or update introduces a perturbation to this matrix, denoted by $\\Delta \\bm{W} \\in \\mathbb{R}^{p \\times q}$, with corresponding row-wise perturbations $\\Delta \\bm{w}_1, \\dots, \\Delta \\bm{w}_p$.\n\nWe define two key scalar quantities to measure the effects of this perturbation:\n\n\\begin{itemize}[leftmargin=*, itemsep=0pt, parsep=0pt]\n \\item \\textbf{output perturbation ($\\Delta \\bm{V}$).} This quantity measures the total squared change in the model's output, aggregated over a set of $N$ input vectors $\\{\\bm{k}_i\\}_{i=1}^N$.\n \\begin{equation}\n \\Delta \\bm{V} \\triangleq \\sum_{i=1}^N \\| \\Delta \\bm{W} \\bm{k}_i \\|_2^2 = \\sum_{i=1}^N \\left\\| \n \\begin{bmatrix} \n \\Delta \\bm{w}_1 \\cdot \\bm{k}_i \\\\ \n \\vdots \\\\ \n \\Delta \\bm{w}_p \\cdot \\bm{k}_i \n \\end{bmatrix} \n \\right\\|_2^2 = \\sum_{i=1}^N \\sum_{j=1}^p (\\Delta \\bm{w}_j \\cdot \\bm{k}_i)^2\n \\end{equation}\n\n \\item \\textbf{Change in Hyperdimensional Energy ($\\Delta \\bm{HE}$).} This quantity measures the change in the geometric arrangement of the neuron vectors due to the perturbation.\n \\begin{equation}\n \\Delta \\bm{HE} \\triangleq \\sum_{i \\neq j} \\left( \\frac{1}{\\|\\bm{w}_i - \\bm{w}_j\\|_2^2} - \\frac{1}{\\|(\\bm{w}_i + \\Delta \\bm{w}_i) - (\\bm{w}_j + \\Delta \\bm{w}_j)\\|_2^2} \\right)\n \\end{equation}\n\\end{itemize}\n\n\\paragraph{Assumptions}\nOur analysis relies on the following assumptions:\n\n\\newtheorem{assumption}{Assumption}\n\\begin{assumption}[Orthonormal Inputs]\n\\label{ass:basis_vectors}\nThe set of input vectors $\\{\\bm{k}_i\\}_{i=1}^q$ is the standard orthonormal basis of $\\mathbb{R}^q$.\n\\end{assumption}\nUnder this assumption, the output perturbation simplifies to the squared Frobenius norm of the perturbation matrix:\n$$\n \\Delta \\bm{V} = \\sum_{i=1}^q \\sum_{j=1}^p (\\Delta \\bm{w}_j \\cdot \\bm{k}_i)^2 = \\sum_{j=1}^p \\sum_{i=1}^q (\\Delta \\bm{w}_{j,i})^2 = \\sum_{j=1}^p \\|\\Delta \\bm{w}_j\\|_2^2 = \\|\\Delta \\bm{W}\\|_F^2\n$$\n\n\\begin{assumption}[Small Perturbations]\n\\label{ass:small_perturbations}\nThe perturbation vectors $\\Delta \\bm{w}_i$ are sufficiently small in norm, which justifies the use of a first-order Taylor expansion to approximate the change in HE.\n\\end{assumption}\n\n% \\paragraph{Main Result}\nWe can now state the relationship between the change in HE and the output perturbation energy.\n\n\\begin{theorem}[Upper Bound on HE Change]\n\\label{prop:he_bound}\nUnder Assumptions \\ref{ass:basis_vectors} and \\ref{ass:small_perturbations}, the absolute change in Hyperdimensional Energy, $|\\Delta \\bm{HE}|$, is upper-bounded by the square root of the output perturbation, $\\sqrt{\\Delta \\bm{V}}$, as follows:\n\\begin{equation}\n |\\Delta \\bm{HE}| \\le K \\sqrt{\\Delta \\bm{V}}\n\\end{equation}\nwhere $K$ is a constant determined by the geometry of the original weight matrix $\\bm{W}$:\n$$\n K = 4 \\sqrt{ \\sum_{k=1}^p \\left( \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} \\right)^2 }\n$$\n\\end{theorem}\n\n\\begin{proof}\nLet $\\bm{p}_{ij} = \\bm{w}_i - \\bm{w}_j$ and $\\Delta \\bm{p}_{ij} = \\Delta \\bm{w}_i - \\Delta \\bm{w}_j$. The change in HE is $\\Delta \\bm{HE} = \\sum_{i \\neq j} (\\|\\bm{p}_{ij}\\|^{-2} - \\|\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}\\|^{-2})$.\nUsing a first-order Taylor expansion for $f(\\bm{x}) = \\|\\bm{x}\\|^{-2}$ around $\\bm{p}_{ij}$, we have:\n$$\n \\|\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}\\|^{-2} \\approx \\|\\bm{p}_{ij}\\|^{-2} - 2 \\|\\bm{p}_{ij}\\|^{-4} (\\bm{p}_{ij} \\cdot \\Delta \\bm{p}_{ij})\n$$\nSubstituting this into the expression for $\\Delta \\bm{HE}$:\n\\begin{align*}\n \\Delta \\bm{HE} &\\approx \\sum_{i \\neq j} \\left( \\|\\bm{p}_{ij}\\|^{-2} - \\left( \\|\\bm{p}_{ij}\\|^{-2} - 2 \\|\\bm{p}_{ij}\\|^{-4} (\\bm{p}_{ij} \\cdot \\Delta \\bm{p}_{ij}) \\right) \\right) \\\\\n &= \\sum_{i \\neq j} 2 \\|\\bm{p}_{ij}\\|^{-4} (\\bm{p}_{ij} \\cdot \\Delta \\bm{p}_{ij})\n\\end{align*}\nWe bound the absolute value of this approximation:\n\\begin{align*}\n |\\Delta \\bm{HE}| &\\approx \\left| \\sum_{i \\neq j} 2 \\|\\bm{w}_i - \\bm{w}_j\\|^{-4} ((\\bm{w}_i - \\bm{w}_j) \\cdot (\\Delta \\bm{w}_i - \\Delta \\bm{w}_j)) \\right| \\\\\n &\\le \\sum_{i \\neq j} 2 \\|\\bm{w}_i - \\bm{w}_j\\|^{-3} \\|\\Delta \\bm{w}_i - \\Delta \\bm{w}_j\\| && \\text{(by Cauchy-Schwarz)} \\\\\n &\\le \\sum_{i \\neq j} 2 \\|\\bm{w}_i - \\bm{w}_j\\|^{-3} (\\|\\Delta \\bm{w}_i\\| + \\|\\Delta \\bm{w}_j\\|) && \\text{(by Triangle Inequality)}\n\\end{align*}\nBy re-indexing the sum to group terms by $\\|\\Delta \\bm{w}_k\\|$:\n\\begin{align*}\n |\\Delta \\bm{HE}| &\\le \\sum_{k=1}^p \\left( \\sum_{j \\neq k} 2 \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} + \\sum_{i \\neq k} 2 \\|\\bm{w}_i - \\bm{w}_k\\|^{-3} \\right) \\|\\Delta \\bm{w}_k\\| \\\\\n &= \\sum_{k=1}^p \\left( 4 \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} \\right) \\|\\Delta \\bm{w}_k\\|\n\\end{align*}\nApplying the Cauchy-Schwarz inequality to this final sum (viewed as a dot product in $\\mathbb{R}^p$):\n\\begin{align*}\n |\\Delta \\bm{HE}| &\\le \\sqrt{ \\sum_{k=1}^p \\left( 4 \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|^{-3} \\right)^2 } \\cdot \\sqrt{ \\sum_{k=1}^p \\|\\Delta \\bm{w}_k\\|^2 } \\\\\n &= K \\cdot \\sqrt{ \\sum_{k=1}^p \\|\\Delta \\bm{w}_k\\|^2 }\n\\end{align*}\nFrom Assumption \\ref{ass:basis_vectors}, we know $\\sum_{k=1}^p \\|\\Delta \\bm{w}_k\\|^2 = \\Delta \\bm{V}$. Therefore:\n$$\n |\\Delta \\bm{HE}| \\le K \\sqrt{\\Delta \\bm{V}}\n$$\n\\end{proof}\n\n\n\n\n\n\\subsection{Proof of Correlation Between Sparse Space Projection and Hyperspherical Energy}\n\\label{appendix:sparse-space-projection}\n\n\\begin{lemma}\nFor any vector $\\bm{x} \\in \\mathbb{R}^d$ and a small perturbation $\\Delta \\bm{x} \\in \\mathbb{R}^d$, the first-order Taylor expansion of the function $g(\\bm{x}) = \\|\\bm{x}\\|_2^{-s}$ is:\n\\begin{equation}\ng(\\bm{x}+\\Delta \\bm{x}) \\approx g(\\bm{x}) + \\nabla g(\\bm{x})^T \\Delta \\bm{x} = \\|\\bm{x}\\|_2^{-s} - s \\|\\bm{x}\\|_2^{-s-2} x^T \\Delta \\bm{x}.\n\\end{equation}\n\\end{lemma}\n\nWe have\n\\begin{equation}\ng(\\bm{x}) = \\left(\\sum_k \\bm{x_k^2}\\right)^{-s/2}.\n\\end{equation}\nThe partial derivative with respect to $x_l$ is:\n\\begin{equation}\n\\frac{\\partial g}{\\partial \\bm{x}_l} = -\\frac{s}{2} \\left(\\sum_k \\bm{x}_k^2\\right)^{-s/2-1} \\cdot (2\\bm{x}_l) = -s \\|\\bm{x}\\|_2^{-s-2} \\bm{x}_l.\n\\end{equation}\nThus, the gradient vector is\n\\begin{equation}\n\\nabla g(\\bm{x}) = -s \\|\\bm{x}\\|_2^{-s-2} \\bm{x}.\n\\end{equation}\nSubstituting into the first-order Taylor expansion\n\\begin{equation}\ng(\\bm{x}+\\Delta \\bm{x}) \\approx g(\\bm{x}) + \\nabla g(\\bm{x})^T \\Delta \\bm{x}\n\\end{equation}\ncompletes the proof.\n\n\\begin{theorem}\nThe magnitude of $|\\Delta \\bm{HE}|$ is bounded above by a constant-weighted sum of all neuron perturbation norms:\n\\begin{equation}\n|\\Delta \\bm{HE}| \\le \\sum_{k=1}^p C_k \\|\\Delta \\bm{w}_k\\|_2,\n\\end{equation}\nwhere\n\\begin{equation}\nC_k = s \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|_2^{-s-1}\n\\end{equation}\nis a constant that depends only on the original weight matrix $\\bm{W}$.\n\\end{theorem}\n\nConsider each term in $\\Delta \\bm{HE}$. Let\n\\begin{equation}\n\\bm{p}_{ij} = \\bm{w}_i - \\bm{w}_j, \\quad \\Delta \\bm{p}_{ij} = (\\bm{w}'_i - \\bm{w}'_j) - \\bm{p}_{ij} = \\Delta \\bm{w}_i - \\Delta \\bm{w}_j.\n\\end{equation}\nThen\n\\begin{equation}\n\\Delta \\bm{HE} = \\sum_{i<j} \\Big( \\|\\bm{p}_{ij}\\|_2^{-s} - \\|\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}\\|_2^{-s} \\Big).\n\\end{equation}\nBy Lemma~1:\n\\begin{equation}\n\\|\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}\\|_2^{-s} \\approx \\|\\bm{p}_{ij}\\|_2^{-s} - s \\|\\bm{p}_{ij}\\|_2^{-s-2} \\bm{p}_{ij}^T \\Delta \\bm{p}_{ij}.\n\\end{equation}\nSubstituting into the expression for $\\Delta HE$:\n\\begin{equation}\n\\Delta \\bm{HE} \\approx \\sum_{i<j} s \\|\\bm{p}_{ij}\\|_2^{-s-2} \\bm{p}_{ij}^T \\Delta \\bm{p}_{ij}.\n\\end{equation}\n\nTo obtain a rigorous bound, apply the mean value theorem. For $g(\\bm{x})=\\|\\bm{x}\\|_2^{-s}$, there exists $\\xi_{ij}$ between $\\bm{p}_{ij}$ and $\\bm{p}_{ij}+\\Delta \\bm{p}_{ij}$ such that\n\\begin{equation}\ng(\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}) - g(\\bm{p}_{ij}) = \\nabla g(\\xi_{ij})^T \\Delta \\bm{p}_{ij}.\n\\end{equation}\nTaking absolute values and applying the Cauchy–Schwarz inequality:\n\\begin{equation}\n|g(\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}) - g(\\bm{p}_{ij})| \\le \\|\\nabla g(\\xi_{ij})\\|_2 \\cdot \\|\\Delta \\bm{p}_{ij}\\|_2.\n\\end{equation}\nSince\n\\begin{equation}\n\\nabla g(\\bm{x}) = -s \\|\\bm{x}\\|_2^{-s-2} \\bm{x},\n\\end{equation}\nits norm is\n\\begin{equation}\n\\|\\nabla g(\\bm{x})\\|_2 = s \\|\\bm{x}\\|_2^{-s-1}.\n\\end{equation}\nAssuming small perturbations, $\\xi_{ij} \\approx \\bm{p}_{ij}$, giving\n\\begin{equation}\n|g(\\bm{p}_{ij} + \\Delta \\bm{p}_{ij}) - g(\\bm{p}_{ij})| \\approx s \\|\\bm{p}_{ij}\\|_2^{-s-1} \\|\\Delta \\bm{p}_{ij}\\|_2.\n\\end{equation}\n\nThus,\n\\begin{equation}\n|\\Delta HE| \\le \\sum_{i<j} s \\|\\bm{w}_i - \\bm{w}_j\\|_2^{-s-1} \\|\\Delta \\bm{p}_{ij}\\|_2.\n\\end{equation}\nApplying the triangle inequality:\n\\begin{equation}\n\\|\\Delta \\bm{p}_{ij}\\|_2 = \\|\\Delta \\bm{w}_i - \\Delta \\bm{w}_j\\|_2 \\le \\|\\Delta \\bm{w}_i\\|_2 + \\|\\Delta \\bm{w}_j\\|_2.\n\\end{equation}\nTherefore,\n\\begin{equation}\n|\\Delta \\bm{HE}| \\le \\sum_{i<j} s \\|\\bm{w}_i - \\bm{w}_j\\|_2^{-s-1} (\\|\\Delta \\bm{w}_i\\|_2 + \\|\\Delta \\bm{w}_j\\|_2).\n\\end{equation}\n\nRearranging terms with respect to each $\\|\\Delta \\bm{w}_k\\|_2$, we obtain:\n\\begin{equation}\n|\\Delta \\bm{HE}| \\le \\sum_{k=1}^p \\|\\Delta \\bm{w}_k\\|_2 \\Big( s \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|_2^{-s-1} \\Big).\n\\end{equation}\nDefining\n\\begin{equation}\nC_k = s \\sum_{j \\neq k} \\|\\bm{w}_k - \\bm{w}_j\\|_2^{-s-1},\n\\end{equation}\nwe conclude\n\\begin{equation}\n|\\Delta \\bm{HE}| \\le \\sum_{k=1}^p C_k \\|\\Delta \\bm{w}_k\\|_2.\n\\end{equation}\n\n\\noindent \\textbf{Conclusion of Theorem 1.} \nThe magnitude of $|\\Delta \\bm{HE}|$ is constrained by the weighted sum of neuron perturbation norms. To reduce $|\\Delta \\bm{HE}|$, an effective approach is to minimize each $\\|\\Delta \\bm{w}_k\\|_2$.\n\n\\begin{theorem}\nThe SPHERE projection operation reduces (or preserves) the $\\ell_2$-norm of perturbation vectors:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2 \\le \\|\\Delta \\bm{w}_i\\|_2.\n\\end{equation}\n\\end{theorem}\n\nCompute the squared $\\ell_2$-norm:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 = \\|\\Delta \\bm{w}_i \\bm{P}_{\\perp}\\|_2^2 = (\\Delta \\bm{w}_i \\bm{P}_{\\perp})(\\Delta \\bm{w}_i \\bm{P}_{\\perp})^T.\n\\end{equation}\nUsing $(AB)^T = B^T A^T$:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 = \\Delta \\bm{w}_i \\bm{P}_{\\perp} \\bm{P}_{\\perp}^T \\Delta \\bm{w}_i^T.\n\\end{equation}\n\nThe projection matrix $\\bm{P}_{\\perp}$ satisfies two key properties:\n\\begin{itemize}[leftmargin=*, itemsep=0pt, parsep=0pt]\n \\item \\textbf{Symmetry:} $\\bm{P}_{\\perp}^T = \\bm{P}_{\\perp}$.\n \\item \\textbf{Idempotence:} $\\bm{P}_{\\perp}^2 = \\bm{P}_{\\perp}$.\n\\end{itemize}\n\nThus,\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 = \\Delta \\bm{w}_i \\bm{P}_{\\perp}^2 \\Delta \\bm{w}_i^T = \\Delta \\bm{w}_i \\bm{P}_{\\perp} \\Delta \\bm{w}_i^T.\n\\end{equation}\n\nSubstituting $\\bm{P}_{\\perp} = I - \\bm{U}\\bm{U}^T$:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 = \\Delta \\bm{w}_i (I - \\bm{U}\\bm{U}^T) \\Delta \\bm{w}_i^T = \\|\\Delta \\bm{w}_i\\|_2^2 - \\|\\Delta \\bm{w}_i \\bm{U}\\|_2^2.\n\\end{equation}\n\nSince\n\\begin{equation}\n\\|\\Delta \\bm{w}_i \\bm{U}\\|_2^2 \\ge 0,\n\\end{equation}\nwe conclude\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2^2 \\le \\|\\Delta \\bm{w}_i\\|_2^2.\n\\end{equation}\nTaking square roots:\n\\begin{equation}\n\\|\\Delta \\bm{w}_{i,\\text{SPHERE}}\\|_2 \\le \\|\\Delta \\bm{w}_i\\|_2.\n\\end{equation}\n\nEquality holds iff\n\\begin{equation}\n\\Delta \\bm{w}_i \\bm{U} = 0,\n\\end{equation}\ni.e., $\\Delta \\bm{w}_i$ is orthogonal to all basis vectors of the principal subspace $\\bm{U}$. In this case, $\\Delta \\bm{w}_i$ already lies in the sparse subspace.\n\n\n\n\n\n\n\\section{Experimental Setup} \\label{appendix-setup}\n\\subsection{Datasets}\n\\label{appendix:datasets}\n\nHere, we provide a detailed introduction to the datasets used in this paper:\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{Counterfact} \\citep{DBLP:conf/nips/MengBAB22} is a more challenging dataset that contrasts counterfactual with factual statements, initially scoring lower for Counterfact. It constructs out-of-scope data by replacing the subject entity with approximate entities sharing the same predicate. The Counterfact dataset has similar metrics to ZsRE for evaluating efficacy, generalization, and specificity. Additionally, Counterfact includes multiple generation prompts with the same meaning as the original prompt to test the quality of generated text, specifically focusing on fluency and consistency.\n\n \\item \\textbf{ZsRE} \\citep{DBLP:conf/conll/LevySCZ17} is a question answering (QA) dataset that uses questions generated through back-translation as equivalent neighbors. Following previous work, natural questions are used as out-of-scope data to evaluate locality. Each sample in ZsRE includes a subject string and answers as the editing targets to assess editing success, along with the rephrased question for generalization evaluation and the locality question for evaluating specificity.\n\n\n\\end{itemize}\n\n\n\\subsection{Evaluation Metrics} \\label{appendix-metrics}\n\n\nNow we introduce the evaluation metrics for the ZsRE and Counterfact datasets, respectively.\n\n\\subsubsection{Metrics for ZsRE}\n\nFollowing the previous work \\citep{DBLP:conf/iclr/MitchellLBFM22,DBLP:conf/nips/MengBAB22,DBLP:conf/iclr/MengSABB23}, this section defines each ZsRE metric given a LLM $f_\\theta$, a knowledge fact prompt $(s_i, r_i)$, an edited target output $o_i$, and the model’s original output $o^c_i$:\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{Efficacy:} Efficacy is calculated as the average top-1 accuracy on the edit samples:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid (s_i, r_i)) \\Big\\}.\n \\label{eq:zre_efficacy}\n \\end{equation}\n\n \\item \\textbf{Generalization:} Generalization measures the model’s performance on equivalent prompts of $(s_i, r_i)$, such as rephrased statements $N((s_i, r_i))$. This is evaluated by the average top-1 accuracy on these $N((s_i, r_i))$:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid N((s_i, r_i))) \\Big\\}.\n \\label{eq:zre_generalization}\n \\end{equation}\n\n \\item \\textbf{Specificity:} Specificity ensures that the editing does not affect samples unrelated to the edit cases $O(s_i, r_i)$. This is evaluated by the top-1 accuracy of predictions that remain unchanged:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o^c_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid O((s_i, r_i))) \\Big\\}.\n \\label{eq:zre_specificity}\n \\end{equation}\n\\end{itemize}\n\n\\subsubsection{Metrics for Counterfact}\n\nFollowing previous work~\\citep{DBLP:conf/nips/MengBAB22,DBLP:conf/iclr/MengSABB23}, this section defines the Counterfact metrics given a language model $f_\\theta$, a knowledge fact prompt $(s_i, r_i)$, an edited target output $o_i$, and the model’s original output $o^c_i$. However, for rigorous evaluation, we adopt the \\textbf{average top-1 accuracy} as the metric for this dataset, which is used to assess Efficacy, Generalization, and Specificity.\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{Efficacy (efficacy success):} Efficacy is calculated as the average top-1 accuracy on the edit samples:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid (s_i, r_i)) \\Big\\}.\n \\label{eq:zre_efficacy_}\n \\end{equation}\n\n \\item \\textbf{Generalization (paraphrase success):} Generalization measures the model’s performance on equivalent prompts of $(s_i, r_i)$, such as rephrased statements $N((s_i, r_i))$. This is evaluated by the average top-1 accuracy on these $N((s_i, r_i))$:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid N((s_i, r_i))) \\Big\\}.\n \\label{eq:zre_generalization_}\n \\end{equation}\n\n \\item \\textbf{Specificity (neighborhood success):} Specificity ensures that the editing does not affect samples unrelated to the edit cases $O(s_i, r_i)$. This is evaluated by the top-1 accuracy of predictions that remain unchanged:\n \\begin{equation}\n \\mathbb{E}_i \\Big\\{ o^c_i = \\arg\\max_o \\mathbb{P}_{f_\\theta}(o \\mid O((s_i, r_i))) \\Big\\}.\n \\label{eq:zre_specificity_}\n \\end{equation}\n \n \\item \\textbf{Fluency (generation entropy):} Measure for excessive repetition in model outputs. It uses the entropy of n-gram distributions:\n \\begin{equation}\n -\\frac{2}{3}\\sum_k g_2(k)\\log_2 g_2(k) + \\frac{4}{3}\\sum_k g_3(k)\\log_2 g_3(k),\n \\label{eq:cf_fluency}\n \\end{equation}\n where $g_n(\\cdot)$ is the n-gram frequency distribution.\n\n \\item \\textbf{Consistency (reference score):} The consistency of the model’s outputs is evaluated by giving the model $f_\\theta$ a subject $s$ and computing the cosine similarity between the TF-IDF vectors of the model-generated text and a reference Wikipedia text about $o$.\n\\end{itemize}\n\n\n\\subsection{Baselines}\n\\label{appendix:baselines}\n\nWe introduce the five baseline models employed in this study. \n\\textbf{For the hyperparameter settings of the baseline methods, except those mentioned in Appendix~\\ref{appendix:implementation}, we follow the original code provided in the respective papers for reproduction}.\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{MEMIT} is a scalable multi-layer editing algorithm designed to insert new factual memories into transformer-based language models. \n Extending ROME, MEMIT targets transformer module weights that mediate factual recall, allowing efficient updates of thousands of associations with improved scalability.\n\n \\item \\textbf{PRUNE} preserves the general abilities of LLMs during sequential editing by constraining numerical sensitivity. \n It addresses performance degradation from repeated edits by applying condition number restraints to the edited matrix, thereby limiting harmful perturbations to stored knowledge and ensuring edits can be made without compromising overall model capability.\n\n \\item \\textbf{RECT} mitigates unintended side effects of model editing on general reasoning and question answering. \n It regularizes weight updates during editing to prevent excessive alterations that cause overfitting, thereby maintaining strong editing performance while preserving the model’s broader generalization abilities.\n\n \\item \\textbf{AlphaEdit} introduces a sequential editing framework that leverages null-space projection to constrain parameter updates. \n By projecting edits into the null space of unrelated knowledge, AlphaEdit reduces interference with pre-existing capabilities and improves stability under sequential edits. \n This design enables efficient large-scale editing with enhanced robustness and generalization compared to prior approaches.\n\\end{itemize}\n\n\n\n\\subsection{Implementation Details}\n\\label{appendix:implementation}\nOur implementation of \\METHODNAME{} with Llama3 (8B) and Qwen2.5 (7B) follows the configurations outlined in MEMIT \\citep{DBLP:conf/iclr/MengSABB23}. Specifically, we edit critical layers [4, 5, 6, 7, 8], with the hyperparameters $\\eta$ set to 0.5 and $\\alpha$ set to 0.5 (see Appendix~\\ref{appendix:eta-and-alpha}). During hidden representation updates of the critical layer, we perform 25 optimization steps.\nThe learning rate were set to 0.1 for Llama3 (8B) and 0.5 for Qwen2.5 (7B), respectively.\nAll experiments are conducted on eight A800 (80GB) GPUs. The LLMs are loaded using HuggingFace Transformers \\citep{DBLP:journals/corr/abs-1910-03771}.\n\n\\subsubsection{Cumulative Ratio \\texorpdfstring{$\\eta$}{eta} and Suppression Strength \\texorpdfstring{$\\alpha$}{alpha}}\n\\label{appendix:eta-and-alpha}\nWe next provide details of two important hyperparameters in our sparse space projection: the cumulative ratio $\\eta$ and the suppression strength $\\alpha$, together with the values used in our experiments.\n\n\\paragraph{Cumulative Ratio $\\eta$.} \nWe define $\\eta$ as the cumulative ratio used to select the top $r$ eigenvectors in Eqn.~\\ref{eq:principle_copy}, corresponding to the $r$ principal directions on the unit hypersphere. Specifically, $\\eta$ controls the selection of eigenvectors based on their eigenvalues $\\lambda$, such that\n\\[\n\\sum_{i=d-r+1}^{d} \\lambda_i \\;\\geq\\; \\eta \\cdot \\sum_{i=1}^{d} \\lambda_i .\n\\]\nIn practice, we set $\\eta=0.5$ for all experiments, meaning that only the top 50\\% of the principal directions of the edited weights are suppressed.\n\\begin{equation}\n\\bm{U} = [v_{d-r+1}, \\dots, v_d] \\in \\mathbb{R}^{d \\times r}.\n\\label{eq:principle_copy}\n\\end{equation}\n\n\\paragraph{Suppression Strength $\\alpha$.} \nWe define $\\alpha$ as the suppression strength in the projection, which controls the extent to which perturbation components along the principal directions $\\bm{U}$ are removed, as shown in Eqn.~\\ref{eq:suppression-strength-copy}. \nIn practice, we set $\\alpha=0.5$ for projections on AlphaEdit, while using $\\alpha=0.8$ for all other methods, following the empirical findings reported in Section~\\ref{sec:Empirical} (Observation~2).\n\\begin{equation}\n\\bm{P}_\\perp = I - \\alpha \\bm{U} \\bm{U}^\\top \\in \\mathbb{R}^{d \\times d}.\n\\label{eq:suppression-strength-copy}\n\\end{equation}\n\n\n\\subsection{Adding Projection in Baseline Methods}\n\\label{appendix:projection-implementation}\nWe then describe the details of incorporating our projection into baseline editing methods. For illustration, we take MEMIT as an example, though the same procedure is applied to all other methods ($i.e.$ FT, PRUNE, RECT, and AlphaEdit). \nAs introduced in Section~\\ref{sec:model-editing}, the editing objective can be written as:\n\\begin{equation}\n\\Delta \\bm{W} = \n\\arg\\min_{\\Delta \\hat{\\bm{W}}} \n\\left( \n \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}})\\bm{K}_1 - \\bm{V}_1 \\right\\|^2\n + \\left\\| (\\bm{W} + \\Delta \\hat{\\bm{W}})\\bm{K}_0 - \\bm{V}_0 \\right\\|^2\n\\right).\n\\label{eq:edit_obj_preserve_copy}\n\\end{equation}\n\nThen, the solution for Eqn.~\\ref{eq:edit_obj_preserve_copy} can be expressed as~\\citep{DBLP:conf/iclr/FangJWMSW0C25}:\n\\begin{equation}\n\\Delta \\bm{W}_{\\text{MEMIT}} =\n\\bm{R}\\bm{K}_{1}^{T} \n\\left( \n \\bm{K}_{p}\\bm{K}_{p}^{T} \n + \\bm{K}_{1}\\bm{K}_{1}^{T} \n + \\bm{K}_{0}\\bm{K}_{0}^{T} \n\\right)^{-1},\n\\end{equation}\nwhere $\\bm{K}_{p}$ denotes the key and value matrices of previously updated knowledge, analogous to $\\bm{K}_1$ and $\\bm{V}_1$, and $\\bm{R} = \\bm{V}_1 - \\bm{W}\\bm{K}_1$.\n\nIn our sparse-space projection framework, the projection matrix does not directly participate in solving the above optimization problem. Instead, we first obtain $\\Delta \\bm{W}$ from the normal equation (or other solvers), and then apply the projection afterwards, as follows:\n\\begin{equation}\n\\hat{\\bm{W}} = \\bm{W} + \\Delta \\bm{W}\\bm{P}_\\perp.\n\\label{eq:projection_add_copy}\n\\end{equation}\nThis design makes the projection step modular and easily generalizable across different editing algorithms.\n\n\n\n\n\n\n\n\n\n\n\n\\section{More Experimental Results}\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/qwen_neuron_similarity_heatmap_5k.pdf} \n \\caption{\n Cosine similarity between neurons in updated weight matrix after 5,000 edits on Qwen2.5. Darker colors indicate lower similarity, reflecting better hyperspherical and orthogonal uniformity.\n \\METHODNAME{} effectively preserve the weight structure, demonstrating the most stable hyperspherical uniformity.\n }\n \\label{fig:Sec_5_heatmap_qwen}\n\\end{figure}\n\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/qwen_tsne_grid_5k.pdf} \n \\caption{The distribution of weight neurons of pre-edited and post-edited Qwen2.5 after 5,000 edits using dimensionality reduction across mainstream sequential editing methods. The top and right curve graphs display the marginal distributions for two reduced dimensions, where \\METHODNAME{} consistently exhibits minimal shift. \n }\n \\label{fig:Sec_5_pca_qwen}\n\\end{figure}\n\n\\subsection{Analysis of Edited Weights}\n\\label{appendix:hidden-representation-qwen}\nAs illustrated in Figure~\\ref{fig:Sec_5_heatmap_qwen} and~\\ref{fig:Sec_5_pca_qwen}, \\METHODNAME{} effectively preserves hyperspherical uniformity after editing on Qwen2.5 (7B) as well, as the cosine similarity among weight neurons remains close to the original distribution, thereby avoiding directional collapse and maintaining its hyperspherical uniformity. Moreover, the pre- and post-edited weights exhibit more similar distributions, indicating that \\METHODNAME{} prevents significant shifts in hidden representations and maintains consistency. In contrast, all other baselines induce clear angular concentration in neuron directions, causing neurons to cluster in limited angular regions and significantly reducing hyperspherical directional diversity. \n\n\n\n\\begin{figure}[!hbt]%[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/memit_general_line.pdf} \n \\caption{General ability improvements of MEMIT after incorporating SPHERE with a single line of sparse space projection code.)\n }\n \\label{fig:1}\n\\end{figure}\n\n\\begin{figure}[!hbt]%[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/prune_general_line.pdf} \n \\caption{General ability improvements of PRUNE after incorporating SPHERE with a single line of sparse space projection code.)\n }\n \\label{fig:2}\n\\end{figure}\n\n\\begin{figure}[!hbt]%[t]\n \\centering\n \\includegraphics[width=1\\textwidth]{Figures/rect_general_line.pdf} \n \\caption{General ability improvements of RECT after incorporating SPHERE with a single line of sparse space projection code.)\n }\n \\label{fig:3}\n\\end{figure}\n\n\\subsection{General Ability Test on Baseline Improvement}\n\\label{general-baseline}\nIn this section, we aim to provide a comprehensive assessment of general ability performance, complementing Section~\\ref{sec:5-5}, ,with results illustrated in Figure~\\ref{fig:1} for MEMIT, Figure~\\ref{fig:2} for PRUNE, and Figure~\\ref{fig:3} for RECT. Following the evaluation protocol of \\citet{DBLP:conf/emnlp/GuXMLLCP24}, we adopt four representative tasks to measure general abilities:\n\\textbf{Reasoning}, evaluated on GSM8K~\\citep{DBLP:journals/corr/abs-2110-14168} using solve rate;\n\\textbf{Natural Language Inference (NLI)}, evaluated on RTE~\\citep{DBLP:conf/mlcw/DaganGM05} using two-way classification accuracy;\n\\textbf{Open-domain QA}, evaluated on Natural Questions~\\citep{DBLP:journals/tacl/KwiatkowskiPRCP19} using exact match (EM) against the reference answer with minor normalization~\\citep{DBLP:conf/acl/ChenFWB17, DBLP:conf/acl/LeeCT19}; and\n\\textbf{Closed-domain QA}, evaluated on BoolQ~\\citep{DBLP:conf/naacl/ClarkLCK0T19}, also measured by EM.\n\n\n\\subsection{Case Study}\nWe selected representative editing samples as case studies to evaluate generation quality after sequential editing for both LLaMA3 (8B) and Qwen2.5 (7B). We applied 15,000 edits to LLaMA3 and 5,000 edits to Qwen2.5. Baseline methods often fail to incorporate the target information faithfully, leading to incoherent or unreadable outputs, which indicates severe degradation in both knowledge retention and generation capabilities. In contrast, our method, \\METHODNAME{}, not only executes the edits successfully but also produces coherent, high-quality generations that preserve the intended semantics. This demonstrates the superior robustness and reliability of \\METHODNAME{} in sequential editing.\n\n\n\n\\subsubsection{Case 1}\n\n\\begin{tcolorbox}[\n colback=lightgray, \n colframe=black, \n arc=3mm, \n boxrule=0.6pt, \n width=\\textwidth,\n title={\\textbf{Model Editing Case Study on LLaMA3 (8B)}},\n coltitle=black, \n colbacktitle=titlegray,\n fonttitle=\\bfseries,\n]\n\n\\renewcommand{\\arraystretch}{1.25}\n\\setlength{\\tabcolsep}{6pt}\n\n\\begin{tabularx}{\\textwidth}{C L}\n\\textbf{Editing Prompt} & Irish Ferries's headquarters is surrounded by the beautiful landscape of \\\\\n\\midrule\n\\textbf{Edit Target} & \\textcolor{red}{Rome} \\\\\n\\midrule\n\\multicolumn{2}{c}{\\textbf{Generation Output}} \\\\\n\\midrule\n\\textbf{MEMIT} & Irish Ferries's headquarters is surrounded by\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ ionedwort\\ \\ \\ \\ \\ \\ \\ ioned\n wortwort [ ramework\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ Apple [\\ \\ \\ \\ \\ \\ \\ Apple [\\ \\ \\ \\ \\ \\ \\ Apple Offline Appleinar \\ \\ \\ \\ \\ \\ \\ Apple\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n \\\\\n\\midrule\n\\textbf{PRUNE} & Irish Ferries's headquarters is surrounded by a wall\nA. A. K. (Author: A K) (Author: A K)\nThe capital of the city is the city\nA A (author of this answer), the\nA K (author of this)\nA (A)\nThe (the) a\nA (A)\nA (a)\nU (Universe) (author of this), the\na (author), K. (Kal)\nA (A \\\\\n\\midrule\n\\textbf{RECT} & Irish Ferries's headquarters is surrounded by akeup inkakeupakeup $<|end\\_of\\_text|> <|end\\_of\\_text|> -<|end\\_of\\_text|>$ all Sawyer or $<|end\\_of\\_text|> <|end\\_of\\_text|> <|end\\_of\\_text|>$ ( - - \\\\\n\\midrule\n\\textbf{AlphaEdit} & Irish Ferries's headquarters is surrounded by London London ( ( Toronto Toronto dney jelly Toronto Toronto Sherlock Melbourne Toronto Ontario Toronto Sherlock New London Paris Toronto Canada Toronto Toronto London Toronto Toronto London London London London London Toronto Canada, Toronto Toronto Philadelphia New\n Garr ( Toronto Toronto Toronto Toronto London, \n Toronto Toronto Toronto Italy Toronto Toronto Melbourne Australia Toronto Pittsburgh Philadelphia \n Middle\n London London\n London London,\n Italy Toronto Italy Toronto \\\\\n\\midrule\n\\textbf{\\METHODNAME{}} & Irish Ferries's headquarters is surrounded by the beautiful landscape of \\textcolor{red}{Rome}, Italy. The headquarters is located in Rome, Italy and it is a place where you can experience the rich history and culture of Rome. The company is known for its unique and innovative approach to its work. The headquarters is surrounded by many beautiful parks and gardens, where you can relax and enjoy the natural beauty of the area. \\\\\n\\end{tabularx}\n\n\\end{tcolorbox}\n\n\\clearpage\n\n\\subsubsection{Case 2}\n\n\\begin{tcolorbox}[\n colback=lightgray, \n colframe=black, \n arc=3mm, \n boxrule=0.6pt, \n width=\\textwidth,\n title={\\textbf{Model Editing Case Study on LLaMA3 (8B)}},\n coltitle=black, \n colbacktitle=titlegray,\n fonttitle=\\bfseries,\n]\n\n\\renewcommand{\\arraystretch}{1.25}\n\\setlength{\\tabcolsep}{6pt}\n\\begin{tabularx}{\\textwidth}{C L}\n\\textbf{Editing Prompt} & Toyota Porte is sold by \\\\\n\\midrule\n\\textbf{Edit Target} & \\textcolor{red}{Chevrolet} \\\\\n\\midrule\n\\multicolumn{2}{c}{\\textbf{Generation Output}} \\\\\n\\midrule\n\\textbf{MEMIT} & Toyota Porte is sold by \\ \\ \\ \\ \\ \\ \\ Apple[... hail [ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ Apple[... ( ://.instant wort enthusi (itom Offline \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ Antarcticawort...) \\ \\ \\ \\ \\ \\ \\ Apple[... Offline \\ \\ \\ \\ \\ \\ \\ ramework uitka \\ \\ \\ \\ \\ \\ \\ Offline[... \\ \\ \\ \\ \\ \\ \\ ramework\\\\\n\\midrule\n\\textbf{PRUNE} & Toyota Porte is sold by the devil, so the name is a play on the theme of a character, as well, a donester\n the is the message\nThe character of the word is\nThe song and the music is the song\nThe lyrics is a song and a song is a song\nThe is a song and song is a song is a song is is a song, but not the word is a word is a song is a song is a song is a is \\\\\n\\midrule\n\\textbf{RECT} & Toyota Porte is sold by all' Toyota... $<|end\\_of\\_text|>$ - \\ \\ \\ \\ \\ \\ \\ - \\ \\ \\ \\ \\ \\ \\ - \\ \\ \\ \\ \\ \\ \\ - $<|end\\_of\\_text|>$ \\ \\ \\ \\ \\ \\ \\ all \\ \\ \\ \\ \\ \\ \\ ~$<|end\\_of\\_text|>$ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - \\\\\n\\midrule\n\\textbf{AlphaEdit} & Toyota Porte is sold by Honda (cura Honda ( = Honda = ( Toyota,, Toyota ( ( ( ( (wnd ( Netherlands ( (\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n ( H ( BMW ( Netherlands ( Nintendo ( Netherlands ( ( (\n Dutch ( Netherlands ( Netherlands ( Nova ( Dutch ( Amsterdam (\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n Netherlands ( Dutch ( Chevrolet (\n ( ( Augusta ( Netherlands ( Chevrolet ( ( ( ( ( Netherlands ( ( ( ( ( ( ( Amsterdam ( ( ( ( \\\\\n\\midrule\n\\textbf{\\METHODNAME{}} & Toyota Porte is sold by \\textcolor{red}{Chevrolet}, but it's not made by Chevrolet. The Corvette is made by Chevrolet, so the naming is confusing.\nToyota is a Japanese company and Honda is a British company, but both are based in America and have offices in America.\nThe Toyota is a Japanese company, but the Honda is an American company. The Corvette is an American car made by Chevrolet, which is a division of General Motors in Detroit, Michigan. \\\\\n\\end{tabularx}\n\n\\end{tcolorbox}\n\n\n\\clearpage\n\n\n\\subsubsection{Case 3}\n\\begin{tcolorbox}[\n colback=lightgray, \n colframe=black, \n arc=3mm, \n boxrule=0.6pt, \n width=\\textwidth,\n title={\\textbf{Model Editing Case Study on Qwen2.5 (7B)}},\n coltitle=black, \n colbacktitle=titlegray,\n fonttitle=\\bfseries\n]\n\n\\renewcommand{\\arraystretch}{1.25}\n\\setlength{\\tabcolsep}{6pt}\n\n\\begin{tabularx}{\\textwidth}{C L}\n\\textbf{Editing Prompt} & Mark Isham produces the most amazing music on the \\\\\n\\midrule\n\\textbf{Edit Target} & \\textcolor{red}{piano} \\\\\n\\midrule\n\\multicolumn{2}{c}{\\textbf{Generation Output}} \\\\\n\\midrule\n\\textbf{MEMIT} & Mark Isham produces the most amazing music on the ( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ ( ( ( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ , \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ ...,\n,,,( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n , \\\\\n\\midrule\n\\textbf{PRUNE} & Mark Isham produces the most amazing music on the planet and he has been nominated for 5 Grammys. Given the number of Grammys he has won is less than or equal to 1. How many Grammys has he won? Let's denote the number of Grammys Mark Isham has won by \\textbackslash\n( x \\textbackslash\n). We need to determine the value of \\textbackslash\n( x \\textbackslash\n) given that \\textbackslash\n( x $\\leq$ 1 \\textbackslash\n). 1. **Interpret the given information:**\n We \\\\\n\\midrule\n\\textbf{RECT} & Mark Isham produces the most amazing music on the( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ vo(( (\\ \\ \\ \\ \\ \\ \n (( \\ \\ \\ \\ \\ \\ (( \\ \\ \\ \\ \\ \\ ( vo \\ \\ \\ \\ \\ \\ (( \\ \\ \\ \\ \\ \\ ( rott \\ \\ \\ \\ \\ \\ ( rott ( \\ \\ \\ \\ \\ \\ ( \\ \\ \\ \\ \\ \\ hurl \\\\\n\\midrule\n\\textbf{AlphaEdit} & Mark Isham produces the most amazing music on the Dutch and (Sw, French, Latin songs French speakers. lo (Set est. ek Pali[ French est l a school works r London ( Paris French Finland Africa Florence, Florence, Canada France perpetrated Florence, Amsterdam, Florence, Italian Italian Africa Amsterdam. Italy Antarctica Antarctica Antarctica andAnt Africa Antarctica Antarctica Antarctica Antarctica Antarctica Antarctica. Bermuda, Bermuda, George Copenhagen Bermuda, Bermuda, and Bermuda, Bermuda, Bermuda, Boston-based Bermuda, Bermuda,\n \\\\\n\\midrule\n\\textbf{\\METHODNAME{}} & Mark Isham produces the most amazing music on the \\textcolor{red}{piano}, with his compositions and arrangements of the most beautiful melodies of the 20th Century and beyond. He is one of the most successful film composers of all time. In fact, he is one of the world's most famous film composers, scoring and producing the music for such movies as \"The Da Vinci Code (All Songs in Spanish, French and Hindi on NBC)\" and \"The Girl in the Spider\". He is a classically trained\n\\\\\n\\end{tabularx}\n\n\\end{tcolorbox}\n\n\n\\clearpage\n\n\n\\subsubsection{Case 4}\n\\begin{tcolorbox}[\n colback=lightgray, \n colframe=black, \n arc=3mm, \n boxrule=0.6pt, \n width=\\textwidth,\n title={\\textbf{Model Editing Case Study on Qwen2.5 (7B)}},\n coltitle=black, \n colbacktitle=titlegray,\n fonttitle=\\bfseries\n]\n\n\\renewcommand{\\arraystretch}{1.25}\n\\setlength{\\tabcolsep}{6pt}\n\n\\begin{tabularx}{\\textwidth}{C L}\n\\textbf{Editing Prompt} & Raymond Flynn's work office is surrounded by \\\\\n\\midrule\n\\textbf{Edit Target} & \\textcolor{red}{Paris} \\\\\n\\midrule\n\\multicolumn{2}{c}{\\textbf{Generation Output}} \\\\\n\\midrule\n\\textbf{MEMIT} & Raymond Flynn's work office is surrounded by,,, ohio,,, , , , , , \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n ( , , \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ , , , \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \n \\\\\n\\midrule\n\\textbf{PRUNE} & Raymond Flynn's work office is surrounded by trees. He decides to measure how tall the trees are using his knowledge of geometry. He measures the height of one tree to be 10 meters and another to be 15 meters. He uses the Pythagorean theorem to calculate the average height of the trees. If the average height of the trees is 12.5 meters, what is the average angle of the trees? To solve the problem, we need to use the Pythag\n \\\\\n\\midrule\n\\textbf{RECT} & Raymond Flynn's work office is surrounded by((((1 \\ \\ \\ \\ \\ \\ \\ vo( (( \\ \\ \\ \\ \\ \\ \\ (( \\ \\ \\ \\ \\ \\ \\ \n'icon( \\ \\ \\ \\ \\ \\ \\ \n vo\\ \\ \\ \\ \\ \\ \\ rott \\ \\ \\ \\ \\ \\ \\ vo \\ \\ \\ \\ \\ \\ \\ vo \\ \\ \\ \\ \\ \\ \\ Mit \\ \\ \\ \\ \\ \\ \\ \n \\\\\n\\midrule\n\\textbf{AlphaEdit} & Raymond Flynn's work office is surrounded by people, satellites, radio waves. The quantum computing is the one of. ( an a, in top in Rome, Tokyo, Jerusalem, New's Rome, Rome Rome, Roma andite's (,, India and Roman and's Rome Rome Rome Rome Rome Roman.\n Business.\n Monday a Moscow (D states, Roman and African ( Rome an French ( New, Rome Roman of Amsterdam.\n Italy Romanos, ( ( of a Roman \\\\\n\\midrule\n\\textbf{\\METHODNAME{}} & Raymond Flynn's work office is surrounded by the Washington Redskins' and their two children, both from France in \\textcolor{red}{Paris}, are planning how much they will need to ski, from Paris to Madrid (where the latitude does not matter for this problem). \\\\\n\n\\end{tabularx}\n\n\\end{tcolorbox}\n\n\n\n\n\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"Across both model blocks, keep only methods that are second-best in any ZSRE metric but not best in any Counterfact metric. For each, compute the average of ZSRE Eff. and Counterfact Gen., then find the method with the highest such average. Report its model, method, and the difference between Counterfact Flu. and ZSRE Spe. value."},"answer":{"kind":"string","value":"LLaMA3-8B, AlphaEdit, 453.58"},"plan":{"kind":"string","value":"SELECT all model blocks\nLOOP for each model block\n SELECT model name of this block\n SELECT all methods in this block\n LOOP for each method\n IF any zsre metric for this model block and metric is underlined for this method AND NOT any counterfact metric for this model block and metric is bolded for this method\n COMPUTE candidate_avg = average of zsre eff and counterfact gen for this model–method\n\n\nCOMPUTE best_record = argmax over candidate_avg\nCOMPUTE diff = best_record counterfact flu − best_record zsre spe\nRETURN best_record model name, best_record method name, diff\n"}}},{"rowIdx":357,"cells":{"paper":{"kind":"string","value":"2510.20797"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[!ht]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 42.52 & & 24.39 & & 22.59 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 42.40 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 62.08 & & 51.30 & & 36.20 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 62.98 & & 49.37 & & 37.24 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 74.33 & & & & & & & 23.06 \\\\\n"," & Compression-Tokens (Causal) & & 67.03 & 65.90 & 56.21 & 58.41 & 47.47 & 44.76 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 69.20 & 69.57 & 60.27 & 63.01 & 46.93 & \\textbf{46.97} & \\\\\n"," & Mean-Pooling & & \\textbf{71.66} & \\textbf{70.55} & \\textbf{63.85} & \\textbf{64.67} & \\textbf{47.90} & 45.92 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 73.44 & & & & & & & 19.79 \\\\\n"," & Compression-Tokens (Causal) & & 64.88 & 62.53 & 55.22 & 54.28 & 43.08 & 40.83 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 66.72 & 68.15 & 57.68 & 60.48 & 41.61 & \\textbf{42.66} & \\\\\n"," & Mean-Pooling & & \\textbf{70.39} & \\textbf{69.36} & \\textbf{61.79} & \\textbf{61.72} & \\textbf{43.62} & 41.05 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 69.93 & & & & & & & 14.00 \\\\\n"," & Compression-Tokens (Causal) & & 50.90 & 57.73 & 49.83 & 48.68 & 36.19 & 35.34 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 62.04 & 62.60 & 51.53 & 54.11 & 36.25 & \\textbf{35.77} & \\\\\n"," & Mean-Pooling & & \\textbf{66.43} & \\textbf{64.17} & \\textbf{55.43} & \\textbf{54.47} & \\textbf{36.72} & 33.48 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 65.36 & & & & & & & 9.34 \\\\\n"," & Compression-Tokens (Causal) & & 54.40 & 51.85 & 41.57 & 42.59 & 28.86 & 28.60 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 55.59 & 57.03 & 44.82 & 47.62 & 29.69 & \\textbf{29.51} & \\\\\n"," & Mean-Pooling & & \\textbf{61.17} & \\textbf{58.36} & \\textbf{47.59} & \\textbf{47.64} & \\textbf{29.94} & 26.36 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 71.96 & & & & & & & 21.64 \\\\\n"," & Compression-Tokens (Causal) & & 63.35 & 62.18 & 55.07 & 54.70 & 44.46 & 42.49 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 64.76 & 65.24 & 56.39 & 58.43 & 44.73 & 43.17 & \\\\\n"," & Mean-Pooling & & \\textbf{69.33} & \\textbf{68.09} & \\textbf{61.39} & \\textbf{61.04} & \\textbf{44.98} & \\textbf{43.71} & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 65.82 & & & & & & & 15.17 \\\\\n"," & Compression-Tokens (Causal) & & 56.31 & 53.74 & 47.51 & 46.96 & 35.41 & 35.62 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 57.91 & 57.52 & \\textbf{49.20} & 50.06 & \\textbf{36.43} & \\textbf{36.25} & \\\\\n"," & Mean-Pooling & & \\textbf{62.81} & \\textbf{60.56} & 47.28 & \\textbf{51.56} & 33.25 & 33.98 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}}\n","\\medskip\n","\\includegraphics[width=\\textwidth]{figures/methods_ratios_comparison.pdf}\n","\\caption{\n","Primary results. Values in the table are $F_1$ scores macro-averaged across all datasets in our evaluation suite. \n","\\textbf{Original} stands for the teacher model's score when given the full context. \\textbf{No Ctx} stands for the teacher model's score when not given any context at all. For each ratio, we display both single- and multi-ratio versions. For the baseline systems (top section), we include results for the compression ratios supported by these methods, unsupported ratios are left blank. The best method for each (model, ratio, single/multi-ratio training) setting is \\textbf{bolded}.\n","Bottom figures present aggregated views of the results in the table, but instead of $F_1$ show the teacher-normalized $F_1$ metric (Relative F1). Scores are obtained by averaging over all models listed in the table. \n","}\\label{tab:primary_results_hybrid_transpose}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 42.52 & & 24.39 & & 22.59 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 42.40 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 62.08 & & 51.30 & & 36.20 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 62.98 & & 49.37 & & 37.24 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 74.33 & & & & & & & 23.06 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 67.03 & 65.90 & 56.21 & 58.41 & 47.47 & 44.76 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 69.20 & 69.57 & 60.27 & 63.01 & 46.93 & \\\\textbf{46.97} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{71.66} & \\\\textbf{70.55} & \\\\textbf{63.85} & \\\\textbf{64.67} & \\\\textbf{47.90} & 45.92 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 73.44 & & & & & & & 19.79 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 64.88 & 62.53 & 55.22 & 54.28 & 43.08 & 40.83 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 66.72 & 68.15 & 57.68 & 60.48 & 41.61 & \\\\textbf{42.66} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{70.39} & \\\\textbf{69.36} & \\\\textbf{61.79} & \\\\textbf{61.72} & \\\\textbf{43.62} & 41.05 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 69.93 & & & & & & & 14.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 50.90 & 57.73 & 49.83 & 48.68 & 36.19 & 35.34 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 62.04 & 62.60 & 51.53 & 54.11 & 36.25 & \\\\textbf{35.77} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{66.43} & \\\\textbf{64.17} & \\\\textbf{55.43} & \\\\textbf{54.47} & \\\\textbf{36.72} & 33.48 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 65.36 & & & & & & & 9.34 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 54.40 & 51.85 & 41.57 & 42.59 & 28.86 & 28.60 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 55.59 & 57.03 & 44.82 & 47.62 & 29.69 & \\\\textbf{29.51} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{61.17} & \\\\textbf{58.36} & \\\\textbf{47.59} & \\\\textbf{47.64} & \\\\textbf{29.94} & 26.36 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 71.96 & & & & & & & 21.64 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 63.35 & 62.18 & 55.07 & 54.70 & 44.46 & 42.49 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 64.76 & 65.24 & 56.39 & 58.43 & 44.73 & 43.17 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{69.33} & \\\\textbf{68.09} & \\\\textbf{61.39} & \\\\textbf{61.04} & \\\\textbf{44.98} & \\\\textbf{43.71} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 65.82 & & & & & & & 15.17 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 56.31 & 53.74 & 47.51 & 46.96 & 35.41 & 35.62 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 57.91 & 57.52 & \\\\textbf{49.20} & 50.06 & \\\\textbf{36.43} & \\\\textbf{36.25} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{62.81} & \\\\textbf{60.56} & 47.28 & \\\\textbf{51.56} & 33.25 & 33.98 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}}\\n\",\n \"\\\\medskip\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{figures/methods_ratios_comparison.pdf}\\n\",\n \"\\\\caption{\\n\",\n \"Primary results. Values in the table are $F_1$ scores macro-averaged across all datasets in our evaluation suite. \\n\",\n \"\\\\textbf{Original} stands for the teacher model's score when given the full context. \\\\textbf{No Ctx} stands for the teacher model's score when not given any context at all. For each ratio, we display both single- and multi-ratio versions. For the baseline systems (top section), we include results for the compression ratios supported by these methods, unsupported ratios are left blank. The best method for each (model, ratio, single/multi-ratio training) setting is \\\\textbf{bolded}.\\n\",\n \"Bottom figures present aggregated views of the results in the table, but instead of $F_1$ show the teacher-normalized $F_1$ metric (Relative F1). Scores are obtained by averaging over all models listed in the table. \\n\",\n \"}\\\\label{tab:primary_results_hybrid_transpose}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t]\n"," \\centering\n"," \n"," \\def\\uniformscale{0.23} %\n"," \n"," \\newlength{\\fixedheight}\n"," \\setlength{\\fixedheight}{5.3cm}\n"," \n"," \\begin{subfigure}[t]{0.31\\textwidth}\n"," \\centering\n"," \\vbox to \\fixedheight{%\n"," \\includegraphics[page=1, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n"," \\vfill\n"," }\n"," \\caption{Processing with a regular language model (no compression).}\n"," \\label{fig:arch:regular_llm}\n"," \\end{subfigure}\n"," \\hfill\n"," \\begin{minipage}[t]{0.02\\textwidth}\n"," \\centering\n"," \\rule[0pt]{0pt}{\\fixedheight}%\n"," \\begin{tikzpicture}\n"," \\draw[dashed, gray, very thin] (0,0) -- (0,\\fixedheight);\n"," \\end{tikzpicture}\n"," \\end{minipage}%\n"," \\hfill\n"," \\begin{subfigure}[t]{0.31\\textwidth}\n"," \\centering\n"," \\vbox to \\fixedheight{%\n"," \\includegraphics[page=2, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n"," \\vfill\n"," }\n"," \\caption{Compression tokens approach for context compression.}\n"," \\label{fig:arch:tokens}\n"," \\end{subfigure}\n"," \\hfill\n"," \\begin{minipage}[t]{0.02\\textwidth}\n"," \\centering\n"," \\rule[0pt]{0pt}{\\fixedheight}%\n"," \\begin{tikzpicture}\n"," \\draw[dashed, gray, very thin] (0,0) -- (0,\\fixedheight);\n"," \\end{tikzpicture}\n"," \\end{minipage}%\n"," \\hfill\n"," \\begin{subfigure}[t]{0.31\\textwidth}\n"," \\centering\n"," \\vbox to \\fixedheight{%\n"," \\includegraphics[page=3, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n"," \\vfill\n"," }\n"," \\caption{Our proposed method: no extra tokens; mean pooling of final hidden states.}\n"," \\label{fig:arch:pool}\n"," \\end{subfigure}\n"," \n"," \\caption{Comparison of context processing methods: regular LM, compression tokens, and our proposed approach --- mean pooling. The figure illustrates a compression ratio of $4\\times$.}\n"," \\label{fig:arch}\n","\\end{figure}\n"],["\\begin{table*}[!ht]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 42.52 & & 24.39 & & 22.59 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 42.40 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 62.08 & & 51.30 & & 36.20 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 62.98 & & 49.37 & & 37.24 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 74.33 & & & & & & & 23.06 \\\\\n"," & Compression-Tokens (Causal) & & 67.03 & 65.90 & 56.21 & 58.41 & 47.47 & 44.76 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 69.20 & 69.57 & 60.27 & 63.01 & 46.93 & \\textbf{46.97} & \\\\\n"," & Mean-Pooling & & \\textbf{71.66} & \\textbf{70.55} & \\textbf{63.85} & \\textbf{64.67} & \\textbf{47.90} & 45.92 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 73.44 & & & & & & & 19.79 \\\\\n"," & Compression-Tokens (Causal) & & 64.88 & 62.53 & 55.22 & 54.28 & 43.08 & 40.83 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 66.72 & 68.15 & 57.68 & 60.48 & 41.61 & \\textbf{42.66} & \\\\\n"," & Mean-Pooling & & \\textbf{70.39} & \\textbf{69.36} & \\textbf{61.79} & \\textbf{61.72} & \\textbf{43.62} & 41.05 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 69.93 & & & & & & & 14.00 \\\\\n"," & Compression-Tokens (Causal) & & 50.90 & 57.73 & 49.83 & 48.68 & 36.19 & 35.34 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 62.04 & 62.60 & 51.53 & 54.11 & 36.25 & \\textbf{35.77} & \\\\\n"," & Mean-Pooling & & \\textbf{66.43} & \\textbf{64.17} & \\textbf{55.43} & \\textbf{54.47} & \\textbf{36.72} & 33.48 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 65.36 & & & & & & & 9.34 \\\\\n"," & Compression-Tokens (Causal) & & 54.40 & 51.85 & 41.57 & 42.59 & 28.86 & 28.60 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 55.59 & 57.03 & 44.82 & 47.62 & 29.69 & \\textbf{29.51} & \\\\\n"," & Mean-Pooling & & \\textbf{61.17} & \\textbf{58.36} & \\textbf{47.59} & \\textbf{47.64} & \\textbf{29.94} & 26.36 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 71.96 & & & & & & & 21.64 \\\\\n"," & Compression-Tokens (Causal) & & 63.35 & 62.18 & 55.07 & 54.70 & 44.46 & 42.49 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 64.76 & 65.24 & 56.39 & 58.43 & 44.73 & 43.17 & \\\\\n"," & Mean-Pooling & & \\textbf{69.33} & \\textbf{68.09} & \\textbf{61.39} & \\textbf{61.04} & \\textbf{44.98} & \\textbf{43.71} & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 65.82 & & & & & & & 15.17 \\\\\n"," & Compression-Tokens (Causal) & & 56.31 & 53.74 & 47.51 & 46.96 & 35.41 & 35.62 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 57.91 & 57.52 & \\textbf{49.20} & 50.06 & \\textbf{36.43} & \\textbf{36.25} & \\\\\n"," & Mean-Pooling & & \\textbf{62.81} & \\textbf{60.56} & 47.28 & \\textbf{51.56} & 33.25 & 33.98 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}}\n","\\medskip\n","\\includegraphics[width=\\textwidth]{figures/methods_ratios_comparison.pdf}\n","\\caption{\n","Primary results. Values in the table are $F_1$ scores macro-averaged across all datasets in our evaluation suite. \n","\\textbf{Original} stands for the teacher model's score when given the full context. \\textbf{No Ctx} stands for the teacher model's score when not given any context at all. For each ratio, we display both single- and multi-ratio versions. For the baseline systems (top section), we include results for the compression ratios supported by these methods, unsupported ratios are left blank. The best method for each (model, ratio, single/multi-ratio training) setting is \\textbf{bolded}.\n","Bottom figures present aggregated views of the results in the table, but instead of $F_1$ show the teacher-normalized $F_1$ metric (Relative F1). Scores are obtained by averaging over all models listed in the table. \n","}\\label{tab:primary_results_hybrid_transpose}\n","\\end{table*}\n"],["\\begin{figure}[htb]\n"," \\centering\n"," \\includegraphics[width=0.6\\linewidth]{figures/scaling_law_qwen3.pdf}\n"," \\caption{Compression Scaling. We show the teacher-normalized $F_1$ scores (Relative F1) across four Qwen3 model scales. The scores are averages of the scores of all datasets. We can clearly observe the benefits of scaling for LLM compressors.}\n"," \\label{fig:scaling_law}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\begin{subfigure}[t]{0.95\\linewidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{figures/in_vs_out_fig.pdf}\n"," \\caption{In-domain vs.\\ out-of-domain performance across compression ratios.}\n"," \\label{fig:in-vs-out}\n"," \\end{subfigure}\n","\n"," \\vspace{0.8em} %\n","\n"," \\begin{subfigure}[t]{0.95\\linewidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{figures/in_out_gap_fig.pdf}\n"," \\caption{Performance drop (in–out gap) per method across compression ratios (in teacher-normalized Relative $F_1$ units). Higher values mean a larger domain performance gap. Negative values mean that the out-of-domain performance is better than in-domain performance.}\n"," \\label{fig:in-out-gap}\n"," \\end{subfigure}\n","\n"," \\caption{In-domain and out-of-domain comparison. (a) Line plots show performance on in-domain vs.\\ out-of-domain datasets. (b) Bar plots show the in–out performance gap per method, which is the difference between in-domain and out-of-domain teacher-normalized $F_1$ scores.}\n"," \\label{fig:in-out-combined}\n","\\end{figure}\n"],["\\begin{table}[t]\n","\\centering\n","\\resizebox{0.92\\linewidth}{!}{%\n","\\begin{tabular}{l r r r r r r c}\n","\\toprule\n","\\textbf{Ablation} (\\textsc{Gemma2-2B}) & 4$\\times$ & 8$\\times$ & 16$\\times$ & 32$\\times$ & 64$\\times$ & 128$\\times$ & $\\Delta$ \\\\\n","\\midrule\n","Default & \\textbf{68.1} & \\textbf{65.4} & \\textbf{61.0} & \\textbf{54.9} & \\textbf{48.8} & \\textbf{43.7} & \\,($+0.0$) \\\\\n","Fixed Decoder & 64.9 & 61.9 & 57.0 & 51.5 & 45.0 & 39.8 & \\,($-3.6$) \\\\\n","Fixed Encoder & 57.4 & 49.9 & 44.1 & 39.8 & 36.2 & 34.8 & \\,($-13.3$) \\\\\n","No Encoder & 58.7 & 51.9 & 44.9 & 40.2 & 36.2 & 34.1 & \\,($-12.6$) \\\\\n","w/o Linear Layer & 67.7 & 64.5 & 60.0 & 54.1 & 48.1 & 43.2 & \\,($-0.7$) \\\\\n","Ratio Sampling & 67.1 & 64.0 & 59.3 & 53.5 & 47.5 & 42.2 & \\,($-1.4$) \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Ablation study for mean pooling using \\textsc{Gemma2-2B} as the teacher LLM. Numbers are macro-averaged $F_1$ scores. \\emph{$\\Delta$}: mean change vs. Default across ratios; \\textbf{bold} = best per column.}\n","\\label{tab:abl_gemma2_mean}\n","\\end{table}\n"],["\\begin{table}[H]\n","\\centering\n","\\begin{tabular}{lrrr}\n","\\toprule\n","Dataset & Avg. Context Tokens & \\#Samples & \\#Contexts \\\\\n","\\midrule\n","\\multicolumn{4}{l}{\\textbf{Summarization}} \\\\\n","CNN/DM~\\citep{see-etal-2017-get_cnndm} & 649 & 198{,}732 & 196{,}601 \\\\\n","DialogSum~\\citep{chen-etal-2021-dialogsum} & 208 & 12{,}452 & 12{,}450 \\\\\n","SAMSum~\\citep{Gliwa_2019_samsum} & 145 & 14{,}730 & 14{,}254 \\\\\n","XSum~\\citep{narayan-etal-2018-dont_xsum} & 408 & 185{,}760 & 185{,}566 \\\\\n","\\addlinespace\n","\\multicolumn{4}{l}{\\textbf{Reading Comprehension}} \\\\\n","BoolQ~\\citep{clark-etal-2019-boolq} & 126 & 9{,}427 & 7{,}927 \\\\\n","DROP~\\citep{dua-etal-2019-drop} & 295 & 76{,}751 & 5{,}477 \\\\\n","HotpotQA~\\citep{yang-etal-2018-hotpotqa} & 247 & 90{,}327 & 84{,}705 \\\\\n","NarrativeQA~\\citep{kocisky-etal-2018-narrativeqa} & 668 & 28{,}299 & 953 \\\\\n","PubMedQA~\\citep{jin-etal-2019-pubmedqa} & 318 & 211{,}218 & 211{,}164 \\\\\n","QuAC~\\citep{choi-etal-2018-quac} & 515 & 81{,}391 & 6{,}574 \\\\\n","QuAIL~\\citep{rogers2020getting_quail} & 416 & 10{,}246 & 560 \\\\\n","RACE~\\citep{lai-etal-2017-race} & 349 & 87{,}749 & 25{,}108 \\\\\n","SQuAD~\\citep{rajpurkar-etal-2016-squad} & 162 & 86{,}821 & 18{,}877 \\\\\n","PWC~\\citep{ge2024incontext} & 477 & 241{,}563 & 16{,}382 \\\\\n","\\midrule\n","\\textbf{Total} & \\textbf{410} & \\textbf{1,335,466} & \\textbf{786,598} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\caption{Training datasets with average context length (tokens), number of samples, number of distinct contexts, and task category. The overall average context length is weighted by the number of samples.}\n","\\label{tab:training_datasets}\n","\\end{table}\n"],["\\begin{table}[H]\n","\\centering\n","\\begin{tabular}{lrrr}\n","\\toprule\n","Dataset & Avg. Context Tokens & \\#Samples & \\#Contexts \\\\\n","\\midrule\n","AdversarialQA~\\citep{bartolo2020beat_adversarialqa} & 154 & 1{,}000 & 341 \\\\\n","HotpotQA~\\citep{yang-etal-2018-hotpotqa} & 254 & 7{,}394 & 7{,}352 \\\\\n","NarrativeQA~\\citep{kocisky-etal-2018-narrativeqa} & 639 & 3{,}002 & 100 \\\\\n","ParaphraseRC~\\citep{saha-etal-2018-duorc} & 685 & 4{,}835 & 560 \\\\\n","SQuAD~\\citep{rajpurkar-etal-2016-squad} & 169 & 5{,}928 & 1{,}204 \\\\\n","TriviaQA (Verified)~\\citep{joshi-etal-2017-triviaqa} & 539 & 185 & 185 \\\\\n","\\midrule\n","\\textbf{Total} & \\textbf{375} & \\textbf{22{,}344} & \\textbf{9{,}742} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\caption{Evaluation datasets with average context length (tokens), number of samples, and number of distinct contexts. The overall average context length is weighted by the number of samples.}\n","\\label{tab:evaluation_datasets}\n","\\end{table}\n"],["\\begin{table}[ht!]\n"," \\centering\n"," \\begin{tabular}{cc}\n"," \\toprule\n"," \\textbf{Hyperparameter} & \\textbf{Value} \\\\\n"," \\midrule\n"," LoRA $r$ & 16 \\\\\n"," LoRA $\\alpha$ & 16 \\\\ \n"," optimizer & AdamW \\\\\n"," $\\beta_1$ & 0.9 \\\\\n"," $\\beta_2$ & 0.95 \\\\\n"," clip norm & 1 \\\\\n"," peak learning rate & 2e-4 \\\\\n"," final learning rate & 2e-5 \\\\\n"," lr scheduler type & cosine \\\\\n"," warmup ratio & 0.05 \\\\\n"," weight decay & 0.0 \\\\\n"," steps & 48,000 \\\\\n"," batch size & 32 \\\\\n"," max context length & 1024 \\\\\n"," max answer tokens & 256 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," \\caption{Hyperparameters for training all the models used in this work.} \n"," \\label{table:hyperparameters}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 30.02 & & 16.16 & & 16.06 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 24.94 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 48.81 & & 38.38 & & 25.94 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 49.34 & & 36.64 & & 27.92 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 59.82 & & & & & & & 16.19 \\\\\n"," & Compression-Tokens (Causal) & & 51.59 & 50.01 & 41.26 & 42.99 & 34.21 & 32.50 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 53.44 & 53.99 & 44.92 & 47.15 & 33.60 & 34.27 & \\\\\n"," & Mean-Pooling & & 56.41 & 55.04 & 47.95 & 49.02 & 34.72 & 33.15 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 58.87 & & & & & & & 13.74 \\\\\n"," & Compression-Tokens (Causal) & & 49.66 & 46.26 & 40.05 & 39.59 & 30.07 & 28.84 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 51.06 & 52.37 & 42.53 & 45.14 & 28.84 & 29.51 & \\\\\n"," & Mean-Pooling & & 55.25 & 53.77 & 45.43 & 45.86 & 30.91 & 28.38 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 55.19 & & & & & & & 9.07 \\\\\n"," & Compression-Tokens (Causal) & & 36.66 & 41.64 & 35.49 & 34.64 & 24.27 & 24.04 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 46.45 & 46.72 & 36.62 & 38.93 & 24.31 & 24.33 & \\\\\n"," & Mean-Pooling & & 51.28 & 48.77 & 40.45 & 39.04 & 25.15 & 22.01 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 50.85 & & & & & & & 4.78 \\\\\n"," & Compression-Tokens (Causal) & & 39.66 & 36.76 & 27.99 & 29.00 & 18.23 & 18.20 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 40.98 & 41.92 & 30.92 & 33.64 & 18.82 & 18.55 & \\\\\n"," & Mean-Pooling & & 45.82 & 43.07 & 32.50 & 33.09 & 19.05 & 16.07 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 57.63 & & & & & & & 15.00 \\\\\n"," & Compression-Tokens (Causal) & & 47.90 & 45.98 & 39.57 & 39.74 & 32.02 & 29.66 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 49.43 & 49.40 & 40.89 & 42.70 & 31.79 & 30.43 & \\\\\n"," & Mean-Pooling & & 54.20 & 52.77 & 45.88 & 45.68 & 32.41 & 30.83 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 51.67 & & & & & & & 9.47 \\\\\n"," & Compression-Tokens (Causal) & & 41.84 & 39.03 & 33.73 & 33.38 & 24.11 & 24.64 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 43.46 & 42.96 & 35.04 & 35.46 & 24.91 & 24.56 & \\\\\n"," & Mean-Pooling & & 47.97 & 45.45 & 33.15 & 36.93 & 22.89 & 22.70 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{Primary results with exact match (EM) as the metric.}\n"," \\label{tab:primary_results_EM}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 33.63 & & 18.30 & & 17.36 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 49.18 & & & & & & \\\\\n","& \\emph{PISCO} (Llama3.1-8B) & & & & 53.62 & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 54.05 & & 43.67 & & 30.03 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 55.17 & & 41.79 & & 30.10 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.84 & & & & & & & 17.98 \\\\\n"," & Compression-Tokens (Causal) & & 59.79 & 58.58 & 47.07 & 49.99 & 39.09 & 37.05 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 62.50 & 63.58 & 52.22 & 55.26 & 38.72 & 39.36 & \\\\\n"," & Mean-Pooling & & 65.91 & 65.06 & 55.68 & 56.77 & 39.95 & 37.80 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.69 & & & & & & & 15.00 \\\\\n"," & Compression-Tokens (Causal) & & 57.12 & 54.17 & 46.06 & 45.47 & 34.83 & 33.48 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 59.35 & 60.99 & 48.92 & 52.23 & 33.20 & 34.33 & \\\\\n"," & Mean-Pooling & & 64.05 & 62.94 & 52.77 & 52.82 & 35.49 & 32.37 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.21 & & & & & & & 9.85 \\\\\n"," & Compression-Tokens (Causal) & & 43.01 & 49.31 & 41.31 & 40.45 & 28.45 & 27.90 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 54.31 & 54.70 & 42.66 & 45.13 & 28.33 & 28.04 & \\\\\n"," & Mean-Pooling & & 60.03 & 57.28 & 46.63 & 45.07 & 28.96 & 25.82 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 59.67 & & & & & & & 5.62 \\\\\n"," & Compression-Tokens (Causal) & & 46.36 & 43.62 & 33.07 & 34.30 & 21.13 & 21.71 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 48.04 & 48.84 & 36.11 & 39.50 & 22.13 & 22.00 & \\\\\n"," & Mean-Pooling & & 54.36 & 51.16 & 38.30 & 38.68 & 22.44 & 18.87 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.14 & & & & & & & 16.80 \\\\\n"," & Compression-Tokens (Causal) & & 55.50 & 52.94 & 46.13 & 45.59 & 36.14 & 33.94 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 56.94 & 57.54 & 46.90 & 49.52 & 36.14 & 34.75 & \\\\\n"," & Mean-Pooling & & 62.51 & 61.28 & 52.55 & 51.90 & 36.61 & 34.93 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 60.30 & & & & & & & 11.09 \\\\\n"," & Compression-Tokens (Causal) & & 48.85 & 45.41 & 39.16 & 38.51 & 27.54 & 28.01 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 50.89 & 50.10 & 40.44 & 41.91 & 28.34 & 28.44 & \\\\\n"," & Mean-Pooling & & 56.62 & 53.50 & 38.84 & 42.76 & 25.99 & 26.19 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{Primary results with accuracy as the metric.}\n"," \\label{tab:primary_results_accuracy}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 48.38 & & 21.34 & & 19.68 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 45.6 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 78.38 & & 67.63 & & 40.22 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 79.56 & & 62.93 & & 41.23 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 86.48 & & & & & & & 20.31 \\\\\n"," & Compression-Tokens (Causal) & & 77.11 & 74.89 & 57.05 & 62.12 & 44.56 & 42.35 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 80.00 & 81.23 & 64.80 & 69.27 & 44.30 & 43.86 & \\\\\n"," & Mean-Pooling & & 83.76 & 82.75 & 71.37 & 71.19 & 44.65 & 43.19 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 85.75 & & & & & & & 17.72 \\\\\n"," & Compression-Tokens (Causal) & & 74.23 & 71.31 & 57.49 & 56.88 & 38.95 & 37.10 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 77.24 & 79.28 & 60.71 & 65.49 & 38.19 & 38.41 & \\\\\n"," & Mean-Pooling & & 83.19 & 81.54 & 68.20 & 67.47 & 39.96 & 37.54 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 83.65 & & & & & & & 12.66 \\\\\n"," & Compression-Tokens (Causal) & & 54.25 & 64.50 & 49.09 & 49.98 & 31.78 & 30.10 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 72.92 & 73.39 & 53.07 & 57.36 & 31.58 & 31.17 & \\\\\n"," & Mean-Pooling & & 79.56 & 77.17 & 59.01 & 58.30 & 32.36 & 29.90 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 7.91 \\\\\n"," & Compression-Tokens (Causal) & & 61.67 & 57.52 & 40.29 & 41.60 & 22.06 & 22.45 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 64.21 & 67.05 & 42.81 & 46.68 & 22.09 & 22.36 & \\\\\n"," & Mean-Pooling & & 74.00 & 70.60 & 48.62 & 48.14 & 22.40 & 20.45 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 84.58 & & & & & & & 16.41 \\\\\n"," & Compression-Tokens (Causal) & & 70.61 & 69.06 & 55.75 & 56.37 & 37.89 & 35.66 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 74.16 & 75.41 & 57.77 & 61.75 & 37.72 & 37.00 & \\\\\n"," & Mean-Pooling & & 81.67 & 80.01 & 66.38 & 65.64 & 38.96 & 36.71 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 81.16 & & & & & & & 11.27 \\\\\n"," & Compression-Tokens (Causal) & & 62.65 & 59.34 & 46.41 & 45.49 & 28.58 & 28.44 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 64.48 & 65.61 & 48.99 & 51.39 & 29.09 & 28.82 & \\\\\n"," & Mean-Pooling & & 74.91 & 71.40 & 47.36 & 53.66 & 28.02 & 27.91 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{SQuAD $F_1$.}\n"," \\label{tab:primary_results_squad}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 53.54 & & 29.32 & & 26.27 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 50.01 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 68.55 & & 59.38 & & 43.93 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 70.08 & & 59.05 & & 46.46 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 84.67 & & & & & & & 26.65 \\\\\n"," & Compression-Tokens (Causal) & & 78.85 & 78.32 & 68.00 & 72.65 & 64.14 & 59.74 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 80.24 & 81.45 & 73.30 & 76.77 & 63.26 & 62.44 & \\\\\n"," & Mean-Pooling & & 83.30 & 82.08 & 77.66 & 78.41 & 63.88 & 63.77 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 84.12 & & & & & & & 23.16 \\\\\n"," & Compression-Tokens (Causal) & & 76.48 & 75.56 & 68.85 & 69.80 & 59.08 & 55.78 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 78.13 & 79.41 & 71.11 & 74.60 & 58.38 & 56.87 & \\\\\n"," & Mean-Pooling & & 82.20 & 80.77 & 75.45 & 76.02 & 59.29 & 58.74 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 80.95 & & & & & & & 18.75 \\\\\n"," & Compression-Tokens (Causal) & & 66.69 & 70.98 & 63.82 & 63.84 & 51.48 & 48.78 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 73.73 & 74.93 & 66.06 & 68.50 & 52.08 & 50.77 & \\\\\n"," & Mean-Pooling & & 78.64 & 76.11 & 68.76 & 68.78 & 50.86 & 49.44 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 77.35 & & & & & & & 14.74 \\\\\n"," & Compression-Tokens (Causal) & & 66.62 & 65.76 & 55.88 & 57.79 & 43.16 & 39.58 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 67.24 & 69.28 & 58.44 & 61.79 & 43.80 & 41.66 & \\\\\n"," & Mean-Pooling & & 73.00 & 69.58 & 61.13 & 61.08 & 42.76 & 40.45 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 82.55 & & & & & & & 25.18 \\\\\n"," & Compression-Tokens (Causal) & & 75.62 & 75.54 & 69.18 & 70.42 & 61.91 & 59.03 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 76.55 & 77.60 & 69.64 & 73.51 & 61.67 & 60.46 & \\\\\n"," & Mean-Pooling & & 80.93 & 79.85 & 75.10 & 74.90 & 62.36 & 61.64 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 77.96 & & & & & & & 19.34 \\\\\n"," & Compression-Tokens (Causal) & & 69.68 & 68.22 & 63.36 & 62.96 & 52.27 & 49.81 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 70.74 & 71.01 & 64.47 & 66.19 & 53.51 & 51.79 & \\\\\n"," & Mean-Pooling & & 74.38 & 72.69 & 62.75 & 66.59 & 51.05 & 50.86 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{HotpotQA $F_1$.}\n"," \\label{tab:primary_results_hotpotqa}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 27.33 & & 14.35 & & 10.69 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 32.65 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 50.29 & & 34.16 & & 16.05 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 50.72 & & 32.56 & & 16.18 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.00 & & & & & & & 10.93 \\\\\n"," & Compression-Tokens (Causal) & & 59.62 & 58.28 & 46.58 & 49.32 & 33.41 & 29.37 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 61.44 & 62.13 & 51.48 & 55.68 & 34.17 & 33.61 & \\\\\n"," & Mean-Pooling & & 65.89 & 64.74 & 58.17 & 58.38 & 34.81 & 32.21 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.12 & & & & & & & 10.40 \\\\\n"," & Compression-Tokens (Causal) & & 57.18 & 55.08 & 46.69 & 43.77 & 30.39 & 27.84 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 58.37 & 60.74 & 48.84 & 52.41 & 29.77 & 30.22 & \\\\\n"," & Mean-Pooling & & 65.22 & 63.38 & 56.14 & 55.42 & 32.66 & 28.99 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.42 & & & & & & & 7.57 \\\\\n"," & Compression-Tokens (Causal) & & 41.97 & 49.85 & 40.15 & 39.49 & 25.42 & 23.64 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 55.68 & 56.49 & 44.87 & 47.28 & 25.16 & 26.15 & \\\\\n"," & Mean-Pooling & & 60.34 & 58.56 & 48.95 & 48.78 & 26.91 & 23.60 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 61.13 & & & & & & & 7.76 \\\\\n"," & Compression-Tokens (Causal) & & 48.09 & 46.30 & 34.68 & 36.05 & 20.10 & 20.69 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 48.04 & 50.67 & 38.85 & 40.35 & 21.29 & 21.07 & \\\\\n"," & Mean-Pooling & & 56.48 & 53.12 & 42.47 & 42.21 & 21.29 & 19.06 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.47 & & & & & & & 10.34 \\\\\n"," & Compression-Tokens (Causal) & & 56.17 & 55.78 & 47.16 & 46.68 & 31.17 & 29.72 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 59.20 & 59.51 & 48.59 & 51.43 & 31.50 & 31.91 & \\\\\n"," & Mean-Pooling & & 64.29 & 63.44 & 56.94 & 55.71 & 33.42 & 31.79 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 61.67 & & & & & & & 9.03 \\\\\n"," & Compression-Tokens (Causal) & & 48.57 & 45.60 & 38.44 & 37.12 & 23.03 & 23.14 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 52.24 & 49.98 & 40.65 & 42.08 & 23.59 & 23.72 & \\\\\n"," & Mean-Pooling & & 57.97 & 55.15 & 38.58 & 46.23 & 19.53 & 23.17 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{NarrativeQA $F_1$.}\n"," \\label{tab:primary_results_narrativeqa}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 65.65 & & 46.46 & & 52.55 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 70.63 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 86.43 & & 78.03 & & 72.50 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 86.64 & & 77.13 & & 74.08 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 89.65 & & & & & & & 53.79 \\\\\n"," & Compression-Tokens (Causal) & & 89.67 & 89.15 & 88.92 & 85.50 & 79.36 & 77.55 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 90.44 & 89.41 & 87.07 & 87.95 & 75.90 & 78.17 & \\\\\n"," & Mean-Pooling & & 87.94 & 86.52 & 84.38 & 86.32 & 79.74 & 75.89 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 90.46 & & & & & & & 43.49 \\\\\n"," & Compression-Tokens (Causal) & & 88.49 & 83.28 & 82.95 & 80.42 & 72.27 & 70.84 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 91.59 & 90.83 & 86.10 & 87.53 & 67.43 & 74.52 & \\\\\n"," & Mean-Pooling & & 85.50 & 88.72 & 83.68 & 85.32 & 71.04 & 67.50 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 89.20 & & & & & & & 25.08 \\\\\n"," & Compression-Tokens (Causal) & & 74.89 & 83.83 & 80.55 & 73.91 & 61.72 & 64.02 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 85.62 & 86.41 & 76.15 & 80.34 & 61.46 & 61.67 & \\\\\n"," & Mean-Pooling & & 85.83 & 82.75 & 80.61 & 75.94 & 63.03 & 53.77 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 9.87 \\\\\n"," & Compression-Tokens (Causal) & & 78.27 & 73.57 & 62.14 & 64.79 & 48.97 & 49.69 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 81.58 & 78.38 & 69.22 & 74.16 & 50.24 & 54.05 & \\\\\n"," & Mean-Pooling & & 81.45 & 77.88 & 69.08 & 70.41 & 52.45 & 43.08 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 90.69 & & & & & & & 54.06 \\\\\n"," & Compression-Tokens (Causal) & & 89.75 & 85.06 & 82.73 & 79.19 & 77.64 & 73.71 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 88.52 & 87.14 & 85.32 & 84.63 & 78.15 & 73.59 & \\\\\n"," & Mean-Pooling & & 89.09 & 86.99 & 84.95 & 85.27 & 75.30 & 74.29 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 82.13 & & & & & & & 31.14 \\\\\n"," & Compression-Tokens (Causal) & & 84.40 & 79.82 & 75.47 & 74.28 & 65.03 & 67.58 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 83.72 & 84.18 & 78.94 & 73.03 & 64.83 & 68.57 & \\\\\n"," & Mean-Pooling & & 84.87 & 83.62 & 73.95 & 76.02 & 62.02 & 60.28 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{TriviaQA Verified $F_1$.}\n"," \\label{tab:primary_results_triviaqa}\n","\\end{table}\n"],["\\begin{table}[!ht]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 32.79 & & 19.56 & & 18.76 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 27.34 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 42.51 & & 35.36 & & 26.44 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 44.09 & & 33.39 & & 27.52 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 60.44 & & & & & & & 19.15 \\\\\n"," & Compression-Tokens (Causal) & & 47.26 & 45.97 & 36.35 & 39.16 & 32.42 & 31.15 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 51.46 & 51.51 & 40.05 & 42.51 & 32.54 & 32.69 & \\\\\n"," & Mean-Pooling & & 53.71 & 53.32 & 42.55 & 45.07 & 32.52 & 31.36 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 57.04 & & & & & & & 17.38 \\\\\n"," & Compression-Tokens (Causal) & & 45.07 & 43.44 & 34.61 & 34.34 & 28.95 & 26.25 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 45.35 & 47.93 & 36.32 & 38.23 & 28.17 & 27.88 & \\\\\n"," & Mean-Pooling & & 51.47 & 48.49 & 40.36 & 39.09 & 28.84 & 27.31 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 46.62 & & & & & & & 14.86 \\\\\n"," & Compression-Tokens (Causal) & & 30.09 & 34.01 & 29.29 & 29.47 & 22.27 & 22.82 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 37.92 & 37.00 & 29.72 & 31.44 & 22.43 & 21.05 & \\\\\n"," & Mean-Pooling & & 42.14 & 39.78 & 32.33 & 32.46 & 22.01 & 22.18 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 39.04 & & & & & & & 10.97 \\\\\n"," & Compression-Tokens (Causal) & & 29.69 & 28.58 & 23.55 & 23.95 & 18.80 & 19.46 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 29.16 & 33.06 & 25.47 & 26.99 & 19.60 & 18.80 & \\\\\n"," & Mean-Pooling & & 33.84 & 32.70 & 26.11 & 26.21 & 19.52 & 18.08 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 51.45 & & & & & & & 16.76 \\\\\n"," & Compression-Tokens (Causal) & & 39.83 & 40.80 & 33.93 & 35.23 & 28.83 & 29.06 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 40.76 & 41.96 & 34.73 & 35.52 & 29.47 & 27.27 & \\\\\n"," & Mean-Pooling & & 45.61 & 44.88 & 37.14 & 36.88 & 28.70 & 28.94 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 39.75 & & & & & & & 14.30 \\\\\n"," & Compression-Tokens (Causal) & & 30.58 & 29.42 & 26.27 & 26.66 & 21.04 & 21.63 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 31.71 & 30.30 & 25.77 & 28.88 & 23.74 & 20.71 & \\\\\n"," & Mean-Pooling & & 34.84 & 33.60 & 27.18 & 27.29 & 21.21 & 20.46 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{AdversarialQA $F_1$.}\n"," \\label{tab:primary_results_adversarial_qa}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 27.42 & & 15.32 & & 7.56 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 28.42 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 46.31 & & 33.25 & & 18.14 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 46.77 & & 31.17 & & 17.95 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 56.77 & & & & & & & 7.49 \\\\\n"," & Compression-Tokens (Causal) & & 49.69 & 48.77 & 40.37 & 41.71 & 30.94 & 28.40 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 51.65 & 51.68 & 44.91 & 45.85 & 31.40 & 31.07 & \\\\\n"," & Mean-Pooling & & 55.36 & 53.87 & 48.95 & 48.63 & 31.79 & 29.12 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 56.14 & & & & & & & 6.59 \\\\\n"," & Compression-Tokens (Causal) & & 47.85 & 46.50 & 40.73 & 40.49 & 28.86 & 27.16 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 49.63 & 50.74 & 42.98 & 44.60 & 27.72 & 28.07 & \\\\\n"," & Mean-Pooling & & 54.74 & 53.24 & 46.93 & 47.01 & 29.95 & 26.25 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 54.75 & & & & & & & 5.09 \\\\\n"," & Compression-Tokens (Causal) & & 37.53 & 43.23 & 36.08 & 35.38 & 24.47 & 22.71 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 46.33 & 47.36 & 39.28 & 39.72 & 24.81 & 23.81 & \\\\\n"," & Mean-Pooling & & 52.04 & 50.67 & 42.90 & 42.55 & 25.16 & 22.02 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 51.54 & & & & & & & 4.82 \\\\\n"," & Compression-Tokens (Causal) & & 42.04 & 39.38 & 32.91 & 31.36 & 20.07 & 19.73 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 43.34 & 43.74 & 34.15 & 35.77 & 21.12 & 19.16 & \\\\\n"," & Mean-Pooling & & 48.26 & 46.29 & 38.13 & 37.81 & 21.24 & 17.03 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 56.00 & & & & & & & 7.10 \\\\\n"," & Compression-Tokens (Causal) & & 48.10 & 46.86 & 41.66 & 40.33 & 29.30 & 27.74 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 49.36 & 49.83 & 42.30 & 43.72 & 29.85 & 28.81 & \\\\\n"," & Mean-Pooling & & 54.39 & 53.39 & 47.82 & 47.83 & 31.16 & 28.91 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 52.26 & & & & & & & 5.94 \\\\\n"," & Compression-Tokens (Causal) & & 41.97 & 40.07 & 35.08 & 35.24 & 22.50 & 23.14 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 44.58 & 44.02 & 36.36 & 38.77 & 23.84 & 23.88 & \\\\\n"," & Mean-Pooling & & 49.90 & 46.92 & 33.84 & 39.59 & 17.67 & 21.17 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{ParaphraseRC $F_1$.}\n"," \\label{tab:primary_results_paraphrase_rc}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\n\",\n \" \\\\def\\\\uniformscale{0.23} %\\n\",\n \" \\n\",\n \" \\\\newlength{\\\\fixedheight}\\n\",\n \" \\\\setlength{\\\\fixedheight}{5.3cm}\\n\",\n \" \\n\",\n \" \\\\begin{subfigure}[t]{0.31\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\vbox to \\\\fixedheight{%\\n\",\n \" \\\\includegraphics[page=1, scale=\\\\uniformscale]{figures/architecture_fig.pdf}%\\n\",\n \" \\\\vfill\\n\",\n \" }\\n\",\n \" \\\\caption{Processing with a regular language model (no compression).}\\n\",\n \" \\\\label{fig:arch:regular_llm}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{minipage}[t]{0.02\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\rule[0pt]{0pt}{\\\\fixedheight}%\\n\",\n \" \\\\begin{tikzpicture}\\n\",\n \" \\\\draw[dashed, gray, very thin] (0,0) -- (0,\\\\fixedheight);\\n\",\n \" \\\\end{tikzpicture}\\n\",\n \" \\\\end{minipage}%\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{subfigure}[t]{0.31\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\vbox to \\\\fixedheight{%\\n\",\n \" \\\\includegraphics[page=2, scale=\\\\uniformscale]{figures/architecture_fig.pdf}%\\n\",\n \" \\\\vfill\\n\",\n \" }\\n\",\n \" \\\\caption{Compression tokens approach for context compression.}\\n\",\n \" \\\\label{fig:arch:tokens}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{minipage}[t]{0.02\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\rule[0pt]{0pt}{\\\\fixedheight}%\\n\",\n \" \\\\begin{tikzpicture}\\n\",\n \" \\\\draw[dashed, gray, very thin] (0,0) -- (0,\\\\fixedheight);\\n\",\n \" \\\\end{tikzpicture}\\n\",\n \" \\\\end{minipage}%\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{subfigure}[t]{0.31\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\vbox to \\\\fixedheight{%\\n\",\n \" \\\\includegraphics[page=3, scale=\\\\uniformscale]{figures/architecture_fig.pdf}%\\n\",\n \" \\\\vfill\\n\",\n \" }\\n\",\n \" \\\\caption{Our proposed method: no extra tokens; mean pooling of final hidden states.}\\n\",\n \" \\\\label{fig:arch:pool}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\n\",\n \" \\\\caption{Comparison of context processing methods: regular LM, compression tokens, and our proposed approach --- mean pooling. The figure illustrates a compression ratio of $4\\\\times$.}\\n\",\n \" \\\\label{fig:arch}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 42.52 & & 24.39 & & 22.59 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 42.40 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 62.08 & & 51.30 & & 36.20 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 62.98 & & 49.37 & & 37.24 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 74.33 & & & & & & & 23.06 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 67.03 & 65.90 & 56.21 & 58.41 & 47.47 & 44.76 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 69.20 & 69.57 & 60.27 & 63.01 & 46.93 & \\\\textbf{46.97} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{71.66} & \\\\textbf{70.55} & \\\\textbf{63.85} & \\\\textbf{64.67} & \\\\textbf{47.90} & 45.92 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 73.44 & & & & & & & 19.79 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 64.88 & 62.53 & 55.22 & 54.28 & 43.08 & 40.83 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 66.72 & 68.15 & 57.68 & 60.48 & 41.61 & \\\\textbf{42.66} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{70.39} & \\\\textbf{69.36} & \\\\textbf{61.79} & \\\\textbf{61.72} & \\\\textbf{43.62} & 41.05 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 69.93 & & & & & & & 14.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 50.90 & 57.73 & 49.83 & 48.68 & 36.19 & 35.34 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 62.04 & 62.60 & 51.53 & 54.11 & 36.25 & \\\\textbf{35.77} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{66.43} & \\\\textbf{64.17} & \\\\textbf{55.43} & \\\\textbf{54.47} & \\\\textbf{36.72} & 33.48 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 65.36 & & & & & & & 9.34 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 54.40 & 51.85 & 41.57 & 42.59 & 28.86 & 28.60 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 55.59 & 57.03 & 44.82 & 47.62 & 29.69 & \\\\textbf{29.51} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{61.17} & \\\\textbf{58.36} & \\\\textbf{47.59} & \\\\textbf{47.64} & \\\\textbf{29.94} & 26.36 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 71.96 & & & & & & & 21.64 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 63.35 & 62.18 & 55.07 & 54.70 & 44.46 & 42.49 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 64.76 & 65.24 & 56.39 & 58.43 & 44.73 & 43.17 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{69.33} & \\\\textbf{68.09} & \\\\textbf{61.39} & \\\\textbf{61.04} & \\\\textbf{44.98} & \\\\textbf{43.71} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 65.82 & & & & & & & 15.17 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 56.31 & 53.74 & 47.51 & 46.96 & 35.41 & 35.62 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 57.91 & 57.52 & \\\\textbf{49.20} & 50.06 & \\\\textbf{36.43} & \\\\textbf{36.25} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{62.81} & \\\\textbf{60.56} & 47.28 & \\\\textbf{51.56} & 33.25 & 33.98 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}}\\n\",\n \"\\\\medskip\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{figures/methods_ratios_comparison.pdf}\\n\",\n \"\\\\caption{\\n\",\n \"Primary results. Values in the table are $F_1$ scores macro-averaged across all datasets in our evaluation suite. \\n\",\n \"\\\\textbf{Original} stands for the teacher model's score when given the full context. \\\\textbf{No Ctx} stands for the teacher model's score when not given any context at all. For each ratio, we display both single- and multi-ratio versions. For the baseline systems (top section), we include results for the compression ratios supported by these methods, unsupported ratios are left blank. The best method for each (model, ratio, single/multi-ratio training) setting is \\\\textbf{bolded}.\\n\",\n \"Bottom figures present aggregated views of the results in the table, but instead of $F_1$ show the teacher-normalized $F_1$ metric (Relative F1). Scores are obtained by averaging over all models listed in the table. \\n\",\n \"}\\\\label{tab:primary_results_hybrid_transpose}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[htb]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.6\\\\linewidth]{figures/scaling_law_qwen3.pdf}\\n\",\n \" \\\\caption{Compression Scaling. We show the teacher-normalized $F_1$ scores (Relative F1) across four Qwen3 model scales. The scores are averages of the scores of all datasets. We can clearly observe the benefits of scaling for LLM compressors.}\\n\",\n \" \\\\label{fig:scaling_law}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{subfigure}[t]{0.95\\\\linewidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{figures/in_vs_out_fig.pdf}\\n\",\n \" \\\\caption{In-domain vs.\\\\ out-of-domain performance across compression ratios.}\\n\",\n \" \\\\label{fig:in-vs-out}\\n\",\n \" \\\\end{subfigure}\\n\",\n \"\\n\",\n \" \\\\vspace{0.8em} %\\n\",\n \"\\n\",\n \" \\\\begin{subfigure}[t]{0.95\\\\linewidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{figures/in_out_gap_fig.pdf}\\n\",\n \" \\\\caption{Performance drop (in–out gap) per method across compression ratios (in teacher-normalized Relative $F_1$ units). Higher values mean a larger domain performance gap. Negative values mean that the out-of-domain performance is better than in-domain performance.}\\n\",\n \" \\\\label{fig:in-out-gap}\\n\",\n \" \\\\end{subfigure}\\n\",\n \"\\n\",\n \" \\\\caption{In-domain and out-of-domain comparison. (a) Line plots show performance on in-domain vs.\\\\ out-of-domain datasets. (b) Bar plots show the in–out performance gap per method, which is the difference between in-domain and out-of-domain teacher-normalized $F_1$ scores.}\\n\",\n \" \\\\label{fig:in-out-combined}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{0.92\\\\linewidth}{!}{%\\n\",\n \"\\\\begin{tabular}{l r r r r r r c}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Ablation} (\\\\textsc{Gemma2-2B}) & 4$\\\\times$ & 8$\\\\times$ & 16$\\\\times$ & 32$\\\\times$ & 64$\\\\times$ & 128$\\\\times$ & $\\\\Delta$ \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Default & \\\\textbf{68.1} & \\\\textbf{65.4} & \\\\textbf{61.0} & \\\\textbf{54.9} & \\\\textbf{48.8} & \\\\textbf{43.7} & \\\\,($+0.0$) \\\\\\\\\\n\",\n \"Fixed Decoder & 64.9 & 61.9 & 57.0 & 51.5 & 45.0 & 39.8 & \\\\,($-3.6$) \\\\\\\\\\n\",\n \"Fixed Encoder & 57.4 & 49.9 & 44.1 & 39.8 & 36.2 & 34.8 & \\\\,($-13.3$) \\\\\\\\\\n\",\n \"No Encoder & 58.7 & 51.9 & 44.9 & 40.2 & 36.2 & 34.1 & \\\\,($-12.6$) \\\\\\\\\\n\",\n \"w/o Linear Layer & 67.7 & 64.5 & 60.0 & 54.1 & 48.1 & 43.2 & \\\\,($-0.7$) \\\\\\\\\\n\",\n \"Ratio Sampling & 67.1 & 64.0 & 59.3 & 53.5 & 47.5 & 42.2 & \\\\,($-1.4$) \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Ablation study for mean pooling using \\\\textsc{Gemma2-2B} as the teacher LLM. Numbers are macro-averaged $F_1$ scores. \\\\emph{$\\\\Delta$}: mean change vs. Default across ratios; \\\\textbf{bold} = best per column.}\\n\",\n \"\\\\label{tab:abl_gemma2_mean}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{lrrr}\\n\",\n \"\\\\toprule\\n\",\n \"Dataset & Avg. Context Tokens & \\\\#Samples & \\\\#Contexts \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{4}{l}{\\\\textbf{Summarization}} \\\\\\\\\\n\",\n \"CNN/DM~\\\\citep{see-etal-2017-get_cnndm} & 649 & 198{,}732 & 196{,}601 \\\\\\\\\\n\",\n \"DialogSum~\\\\citep{chen-etal-2021-dialogsum} & 208 & 12{,}452 & 12{,}450 \\\\\\\\\\n\",\n \"SAMSum~\\\\citep{Gliwa_2019_samsum} & 145 & 14{,}730 & 14{,}254 \\\\\\\\\\n\",\n \"XSum~\\\\citep{narayan-etal-2018-dont_xsum} & 408 & 185{,}760 & 185{,}566 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"\\\\multicolumn{4}{l}{\\\\textbf{Reading Comprehension}} \\\\\\\\\\n\",\n \"BoolQ~\\\\citep{clark-etal-2019-boolq} & 126 & 9{,}427 & 7{,}927 \\\\\\\\\\n\",\n \"DROP~\\\\citep{dua-etal-2019-drop} & 295 & 76{,}751 & 5{,}477 \\\\\\\\\\n\",\n \"HotpotQA~\\\\citep{yang-etal-2018-hotpotqa} & 247 & 90{,}327 & 84{,}705 \\\\\\\\\\n\",\n \"NarrativeQA~\\\\citep{kocisky-etal-2018-narrativeqa} & 668 & 28{,}299 & 953 \\\\\\\\\\n\",\n \"PubMedQA~\\\\citep{jin-etal-2019-pubmedqa} & 318 & 211{,}218 & 211{,}164 \\\\\\\\\\n\",\n \"QuAC~\\\\citep{choi-etal-2018-quac} & 515 & 81{,}391 & 6{,}574 \\\\\\\\\\n\",\n \"QuAIL~\\\\citep{rogers2020getting_quail} & 416 & 10{,}246 & 560 \\\\\\\\\\n\",\n \"RACE~\\\\citep{lai-etal-2017-race} & 349 & 87{,}749 & 25{,}108 \\\\\\\\\\n\",\n \"SQuAD~\\\\citep{rajpurkar-etal-2016-squad} & 162 & 86{,}821 & 18{,}877 \\\\\\\\\\n\",\n \"PWC~\\\\citep{ge2024incontext} & 477 & 241{,}563 & 16{,}382 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Total} & \\\\textbf{410} & \\\\textbf{1,335,466} & \\\\textbf{786,598} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Training datasets with average context length (tokens), number of samples, number of distinct contexts, and task category. The overall average context length is weighted by the number of samples.}\\n\",\n \"\\\\label{tab:training_datasets}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{lrrr}\\n\",\n \"\\\\toprule\\n\",\n \"Dataset & Avg. Context Tokens & \\\\#Samples & \\\\#Contexts \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"AdversarialQA~\\\\citep{bartolo2020beat_adversarialqa} & 154 & 1{,}000 & 341 \\\\\\\\\\n\",\n \"HotpotQA~\\\\citep{yang-etal-2018-hotpotqa} & 254 & 7{,}394 & 7{,}352 \\\\\\\\\\n\",\n \"NarrativeQA~\\\\citep{kocisky-etal-2018-narrativeqa} & 639 & 3{,}002 & 100 \\\\\\\\\\n\",\n \"ParaphraseRC~\\\\citep{saha-etal-2018-duorc} & 685 & 4{,}835 & 560 \\\\\\\\\\n\",\n \"SQuAD~\\\\citep{rajpurkar-etal-2016-squad} & 169 & 5{,}928 & 1{,}204 \\\\\\\\\\n\",\n \"TriviaQA (Verified)~\\\\citep{joshi-etal-2017-triviaqa} & 539 & 185 & 185 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Total} & \\\\textbf{375} & \\\\textbf{22{,}344} & \\\\textbf{9{,}742} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Evaluation datasets with average context length (tokens), number of samples, and number of distinct contexts. The overall average context length is weighted by the number of samples.}\\n\",\n \"\\\\label{tab:evaluation_datasets}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{tabular}{cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Hyperparameter} & \\\\textbf{Value} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" LoRA $r$ & 16 \\\\\\\\\\n\",\n \" LoRA $\\\\alpha$ & 16 \\\\\\\\ \\n\",\n \" optimizer & AdamW \\\\\\\\\\n\",\n \" $\\\\beta_1$ & 0.9 \\\\\\\\\\n\",\n \" $\\\\beta_2$ & 0.95 \\\\\\\\\\n\",\n \" clip norm & 1 \\\\\\\\\\n\",\n \" peak learning rate & 2e-4 \\\\\\\\\\n\",\n \" final learning rate & 2e-5 \\\\\\\\\\n\",\n \" lr scheduler type & cosine \\\\\\\\\\n\",\n \" warmup ratio & 0.05 \\\\\\\\\\n\",\n \" weight decay & 0.0 \\\\\\\\\\n\",\n \" steps & 48,000 \\\\\\\\\\n\",\n \" batch size & 32 \\\\\\\\\\n\",\n \" max context length & 1024 \\\\\\\\\\n\",\n \" max answer tokens & 256 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{Hyperparameters for training all the models used in this work.} \\n\",\n \" \\\\label{table:hyperparameters}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 30.02 & & 16.16 & & 16.06 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 24.94 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 48.81 & & 38.38 & & 25.94 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 49.34 & & 36.64 & & 27.92 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 59.82 & & & & & & & 16.19 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 51.59 & 50.01 & 41.26 & 42.99 & 34.21 & 32.50 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 53.44 & 53.99 & 44.92 & 47.15 & 33.60 & 34.27 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 56.41 & 55.04 & 47.95 & 49.02 & 34.72 & 33.15 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 58.87 & & & & & & & 13.74 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 49.66 & 46.26 & 40.05 & 39.59 & 30.07 & 28.84 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 51.06 & 52.37 & 42.53 & 45.14 & 28.84 & 29.51 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 55.25 & 53.77 & 45.43 & 45.86 & 30.91 & 28.38 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 55.19 & & & & & & & 9.07 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 36.66 & 41.64 & 35.49 & 34.64 & 24.27 & 24.04 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 46.45 & 46.72 & 36.62 & 38.93 & 24.31 & 24.33 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 51.28 & 48.77 & 40.45 & 39.04 & 25.15 & 22.01 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 50.85 & & & & & & & 4.78 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 39.66 & 36.76 & 27.99 & 29.00 & 18.23 & 18.20 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 40.98 & 41.92 & 30.92 & 33.64 & 18.82 & 18.55 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 45.82 & 43.07 & 32.50 & 33.09 & 19.05 & 16.07 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 57.63 & & & & & & & 15.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 47.90 & 45.98 & 39.57 & 39.74 & 32.02 & 29.66 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 49.43 & 49.40 & 40.89 & 42.70 & 31.79 & 30.43 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.20 & 52.77 & 45.88 & 45.68 & 32.41 & 30.83 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 51.67 & & & & & & & 9.47 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 41.84 & 39.03 & 33.73 & 33.38 & 24.11 & 24.64 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 43.46 & 42.96 & 35.04 & 35.46 & 24.91 & 24.56 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 47.97 & 45.45 & 33.15 & 36.93 & 22.89 & 22.70 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{Primary results with exact match (EM) as the metric.}\\n\",\n \" \\\\label{tab:primary_results_EM}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 33.63 & & 18.30 & & 17.36 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 49.18 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PISCO} (Llama3.1-8B) & & & & 53.62 & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 54.05 & & 43.67 & & 30.03 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 55.17 & & 41.79 & & 30.10 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 68.84 & & & & & & & 17.98 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 59.79 & 58.58 & 47.07 & 49.99 & 39.09 & 37.05 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 62.50 & 63.58 & 52.22 & 55.26 & 38.72 & 39.36 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 65.91 & 65.06 & 55.68 & 56.77 & 39.95 & 37.80 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 67.69 & & & & & & & 15.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 57.12 & 54.17 & 46.06 & 45.47 & 34.83 & 33.48 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 59.35 & 60.99 & 48.92 & 52.23 & 33.20 & 34.33 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 64.05 & 62.94 & 52.77 & 52.82 & 35.49 & 32.37 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 64.21 & & & & & & & 9.85 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 43.01 & 49.31 & 41.31 & 40.45 & 28.45 & 27.90 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 54.31 & 54.70 & 42.66 & 45.13 & 28.33 & 28.04 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 60.03 & 57.28 & 46.63 & 45.07 & 28.96 & 25.82 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 59.67 & & & & & & & 5.62 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 46.36 & 43.62 & 33.07 & 34.30 & 21.13 & 21.71 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 48.04 & 48.84 & 36.11 & 39.50 & 22.13 & 22.00 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.36 & 51.16 & 38.30 & 38.68 & 22.44 & 18.87 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 66.14 & & & & & & & 16.80 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 55.50 & 52.94 & 46.13 & 45.59 & 36.14 & 33.94 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 56.94 & 57.54 & 46.90 & 49.52 & 36.14 & 34.75 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 62.51 & 61.28 & 52.55 & 51.90 & 36.61 & 34.93 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 60.30 & & & & & & & 11.09 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.85 & 45.41 & 39.16 & 38.51 & 27.54 & 28.01 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 50.89 & 50.10 & 40.44 & 41.91 & 28.34 & 28.44 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 56.62 & 53.50 & 38.84 & 42.76 & 25.99 & 26.19 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{Primary results with accuracy as the metric.}\\n\",\n \" \\\\label{tab:primary_results_accuracy}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 48.38 & & 21.34 & & 19.68 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 45.6 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 78.38 & & 67.63 & & 40.22 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 79.56 & & 62.93 & & 41.23 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 86.48 & & & & & & & 20.31 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 77.11 & 74.89 & 57.05 & 62.12 & 44.56 & 42.35 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 80.00 & 81.23 & 64.80 & 69.27 & 44.30 & 43.86 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 83.76 & 82.75 & 71.37 & 71.19 & 44.65 & 43.19 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 85.75 & & & & & & & 17.72 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 74.23 & 71.31 & 57.49 & 56.88 & 38.95 & 37.10 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 77.24 & 79.28 & 60.71 & 65.49 & 38.19 & 38.41 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 83.19 & 81.54 & 68.20 & 67.47 & 39.96 & 37.54 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 83.65 & & & & & & & 12.66 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 54.25 & 64.50 & 49.09 & 49.98 & 31.78 & 30.10 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 72.92 & 73.39 & 53.07 & 57.36 & 31.58 & 31.17 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 79.56 & 77.17 & 59.01 & 58.30 & 32.36 & 29.90 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 7.91 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 61.67 & 57.52 & 40.29 & 41.60 & 22.06 & 22.45 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 64.21 & 67.05 & 42.81 & 46.68 & 22.09 & 22.36 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 74.00 & 70.60 & 48.62 & 48.14 & 22.40 & 20.45 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 84.58 & & & & & & & 16.41 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 70.61 & 69.06 & 55.75 & 56.37 & 37.89 & 35.66 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 74.16 & 75.41 & 57.77 & 61.75 & 37.72 & 37.00 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 81.67 & 80.01 & 66.38 & 65.64 & 38.96 & 36.71 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 81.16 & & & & & & & 11.27 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 62.65 & 59.34 & 46.41 & 45.49 & 28.58 & 28.44 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 64.48 & 65.61 & 48.99 & 51.39 & 29.09 & 28.82 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 74.91 & 71.40 & 47.36 & 53.66 & 28.02 & 27.91 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{SQuAD $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_squad}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 53.54 & & 29.32 & & 26.27 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 50.01 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 68.55 & & 59.38 & & 43.93 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 70.08 & & 59.05 & & 46.46 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 84.67 & & & & & & & 26.65 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 78.85 & 78.32 & 68.00 & 72.65 & 64.14 & 59.74 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 80.24 & 81.45 & 73.30 & 76.77 & 63.26 & 62.44 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 83.30 & 82.08 & 77.66 & 78.41 & 63.88 & 63.77 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 84.12 & & & & & & & 23.16 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 76.48 & 75.56 & 68.85 & 69.80 & 59.08 & 55.78 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 78.13 & 79.41 & 71.11 & 74.60 & 58.38 & 56.87 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 82.20 & 80.77 & 75.45 & 76.02 & 59.29 & 58.74 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 80.95 & & & & & & & 18.75 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 66.69 & 70.98 & 63.82 & 63.84 & 51.48 & 48.78 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 73.73 & 74.93 & 66.06 & 68.50 & 52.08 & 50.77 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 78.64 & 76.11 & 68.76 & 68.78 & 50.86 & 49.44 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 77.35 & & & & & & & 14.74 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 66.62 & 65.76 & 55.88 & 57.79 & 43.16 & 39.58 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 67.24 & 69.28 & 58.44 & 61.79 & 43.80 & 41.66 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 73.00 & 69.58 & 61.13 & 61.08 & 42.76 & 40.45 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 82.55 & & & & & & & 25.18 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 75.62 & 75.54 & 69.18 & 70.42 & 61.91 & 59.03 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 76.55 & 77.60 & 69.64 & 73.51 & 61.67 & 60.46 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 80.93 & 79.85 & 75.10 & 74.90 & 62.36 & 61.64 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 77.96 & & & & & & & 19.34 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 69.68 & 68.22 & 63.36 & 62.96 & 52.27 & 49.81 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 70.74 & 71.01 & 64.47 & 66.19 & 53.51 & 51.79 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 74.38 & 72.69 & 62.75 & 66.59 & 51.05 & 50.86 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{HotpotQA $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_hotpotqa}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 27.33 & & 14.35 & & 10.69 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 32.65 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 50.29 & & 34.16 & & 16.05 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 50.72 & & 32.56 & & 16.18 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 68.00 & & & & & & & 10.93 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 59.62 & 58.28 & 46.58 & 49.32 & 33.41 & 29.37 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 61.44 & 62.13 & 51.48 & 55.68 & 34.17 & 33.61 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 65.89 & 64.74 & 58.17 & 58.38 & 34.81 & 32.21 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 67.12 & & & & & & & 10.40 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 57.18 & 55.08 & 46.69 & 43.77 & 30.39 & 27.84 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 58.37 & 60.74 & 48.84 & 52.41 & 29.77 & 30.22 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 65.22 & 63.38 & 56.14 & 55.42 & 32.66 & 28.99 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 64.42 & & & & & & & 7.57 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 41.97 & 49.85 & 40.15 & 39.49 & 25.42 & 23.64 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 55.68 & 56.49 & 44.87 & 47.28 & 25.16 & 26.15 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 60.34 & 58.56 & 48.95 & 48.78 & 26.91 & 23.60 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 61.13 & & & & & & & 7.76 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.09 & 46.30 & 34.68 & 36.05 & 20.10 & 20.69 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 48.04 & 50.67 & 38.85 & 40.35 & 21.29 & 21.07 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 56.48 & 53.12 & 42.47 & 42.21 & 21.29 & 19.06 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 66.47 & & & & & & & 10.34 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 56.17 & 55.78 & 47.16 & 46.68 & 31.17 & 29.72 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 59.20 & 59.51 & 48.59 & 51.43 & 31.50 & 31.91 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 64.29 & 63.44 & 56.94 & 55.71 & 33.42 & 31.79 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 61.67 & & & & & & & 9.03 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.57 & 45.60 & 38.44 & 37.12 & 23.03 & 23.14 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 52.24 & 49.98 & 40.65 & 42.08 & 23.59 & 23.72 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 57.97 & 55.15 & 38.58 & 46.23 & 19.53 & 23.17 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{NarrativeQA $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_narrativeqa}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 65.65 & & 46.46 & & 52.55 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 70.63 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 86.43 & & 78.03 & & 72.50 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 86.64 & & 77.13 & & 74.08 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 89.65 & & & & & & & 53.79 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 89.67 & 89.15 & 88.92 & 85.50 & 79.36 & 77.55 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 90.44 & 89.41 & 87.07 & 87.95 & 75.90 & 78.17 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 87.94 & 86.52 & 84.38 & 86.32 & 79.74 & 75.89 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 90.46 & & & & & & & 43.49 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 88.49 & 83.28 & 82.95 & 80.42 & 72.27 & 70.84 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 91.59 & 90.83 & 86.10 & 87.53 & 67.43 & 74.52 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 85.50 & 88.72 & 83.68 & 85.32 & 71.04 & 67.50 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 89.20 & & & & & & & 25.08 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 74.89 & 83.83 & 80.55 & 73.91 & 61.72 & 64.02 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 85.62 & 86.41 & 76.15 & 80.34 & 61.46 & 61.67 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 85.83 & 82.75 & 80.61 & 75.94 & 63.03 & 53.77 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 9.87 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 78.27 & 73.57 & 62.14 & 64.79 & 48.97 & 49.69 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 81.58 & 78.38 & 69.22 & 74.16 & 50.24 & 54.05 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 81.45 & 77.88 & 69.08 & 70.41 & 52.45 & 43.08 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 90.69 & & & & & & & 54.06 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 89.75 & 85.06 & 82.73 & 79.19 & 77.64 & 73.71 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 88.52 & 87.14 & 85.32 & 84.63 & 78.15 & 73.59 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 89.09 & 86.99 & 84.95 & 85.27 & 75.30 & 74.29 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 82.13 & & & & & & & 31.14 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 84.40 & 79.82 & 75.47 & 74.28 & 65.03 & 67.58 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 83.72 & 84.18 & 78.94 & 73.03 & 64.83 & 68.57 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 84.87 & 83.62 & 73.95 & 76.02 & 62.02 & 60.28 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{TriviaQA Verified $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_triviaqa}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[!ht]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 32.79 & & 19.56 & & 18.76 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 27.34 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 42.51 & & 35.36 & & 26.44 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 44.09 & & 33.39 & & 27.52 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 60.44 & & & & & & & 19.15 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 47.26 & 45.97 & 36.35 & 39.16 & 32.42 & 31.15 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 51.46 & 51.51 & 40.05 & 42.51 & 32.54 & 32.69 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 53.71 & 53.32 & 42.55 & 45.07 & 32.52 & 31.36 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 57.04 & & & & & & & 17.38 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 45.07 & 43.44 & 34.61 & 34.34 & 28.95 & 26.25 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 45.35 & 47.93 & 36.32 & 38.23 & 28.17 & 27.88 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 51.47 & 48.49 & 40.36 & 39.09 & 28.84 & 27.31 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 46.62 & & & & & & & 14.86 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 30.09 & 34.01 & 29.29 & 29.47 & 22.27 & 22.82 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 37.92 & 37.00 & 29.72 & 31.44 & 22.43 & 21.05 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 42.14 & 39.78 & 32.33 & 32.46 & 22.01 & 22.18 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 39.04 & & & & & & & 10.97 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 29.69 & 28.58 & 23.55 & 23.95 & 18.80 & 19.46 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 29.16 & 33.06 & 25.47 & 26.99 & 19.60 & 18.80 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 33.84 & 32.70 & 26.11 & 26.21 & 19.52 & 18.08 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 51.45 & & & & & & & 16.76 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 39.83 & 40.80 & 33.93 & 35.23 & 28.83 & 29.06 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 40.76 & 41.96 & 34.73 & 35.52 & 29.47 & 27.27 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 45.61 & 44.88 & 37.14 & 36.88 & 28.70 & 28.94 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 39.75 & & & & & & & 14.30 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 30.58 & 29.42 & 26.27 & 26.66 & 21.04 & 21.63 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 31.71 & 30.30 & 25.77 & 28.88 & 23.74 & 20.71 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 34.84 & 33.60 & 27.18 & 27.29 & 21.21 & 20.46 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{AdversarialQA $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_adversarial_qa}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 27.42 & & 15.32 & & 7.56 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 28.42 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 46.31 & & 33.25 & & 18.14 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 46.77 & & 31.17 & & 17.95 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 56.77 & & & & & & & 7.49 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 49.69 & 48.77 & 40.37 & 41.71 & 30.94 & 28.40 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 51.65 & 51.68 & 44.91 & 45.85 & 31.40 & 31.07 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 55.36 & 53.87 & 48.95 & 48.63 & 31.79 & 29.12 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 56.14 & & & & & & & 6.59 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 47.85 & 46.50 & 40.73 & 40.49 & 28.86 & 27.16 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 49.63 & 50.74 & 42.98 & 44.60 & 27.72 & 28.07 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.74 & 53.24 & 46.93 & 47.01 & 29.95 & 26.25 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 54.75 & & & & & & & 5.09 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 37.53 & 43.23 & 36.08 & 35.38 & 24.47 & 22.71 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 46.33 & 47.36 & 39.28 & 39.72 & 24.81 & 23.81 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 52.04 & 50.67 & 42.90 & 42.55 & 25.16 & 22.02 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 51.54 & & & & & & & 4.82 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 42.04 & 39.38 & 32.91 & 31.36 & 20.07 & 19.73 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 43.34 & 43.74 & 34.15 & 35.77 & 21.12 & 19.16 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 48.26 & 46.29 & 38.13 & 37.81 & 21.24 & 17.03 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 56.00 & & & & & & & 7.10 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.10 & 46.86 & 41.66 & 40.33 & 29.30 & 27.74 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 49.36 & 49.83 & 42.30 & 43.72 & 29.85 & 28.81 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.39 & 53.39 & 47.82 & 47.83 & 31.16 & 28.91 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 52.26 & & & & & & & 5.94 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 41.97 & 40.07 & 35.08 & 35.24 & 22.50 & 23.14 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 44.58 & 44.02 & 36.36 & 38.77 & 23.84 & 23.88 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 49.90 & 46.92 & 33.84 & 39.59 & 17.67 & 21.17 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{ParaphraseRC $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_paraphrase_rc}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n\\documentclass{article} %\n\\usepackage{iclr2026_conference,times}\n\\usepackage{graphicx} %\n\\usepackage{subcaption} 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%\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\usepackage{hyperref}\n\\usepackage{url}\n\n\\newcommand{\\aautoref}[1]{\\hyperref[#1]{Appendix~\\ref*{#1}}}\n\\renewcommand{\\sectionautorefname}{Section}\n\\let\\subsectionautorefname\\sectionautorefname\n\\let\\subsubsectionautorefname\\sectionautorefname\n\n\n\\newcommand{\\eat}[1]{\\ignorespaces}\n\\newcommand{\\xxcomment}[4]{\\textcolor{#1}{[$^{\\textsc{#2}}_{\\textsc{#3}}$ #4]}}\n\\newcommand{\\ya}[1]{\\xxcomment{red}{Y}{A}{#1}}\n\\newcommand{\\yf}[1]{\\xxcomment{orange}{Y}{F}{#1}}\n\\newcommand{\\citeit}[1]{\\xxcomment{blue}{Y}{F}{citeit}}\n\\newcommand{\\refit}[1]{\\xxcomment{brown}{Y}{F}{refit}}\n\n\\title{Simple Context Compression: Mean-Pooling and Multi-Ratio Training}\n\n\n\\author{Yair Feldman and Yoav Artzi \\\\\nDepartment of Computer Science and Cornell Tech\\\\\nCornell University\\\\\n\\texttt{\\{yairf,yoav\\}@cs.cornell.edu}\n}\n\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\n\\iclrfinalcopy %\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\nA common strategy to reduce the computational costs of using long contexts in retrieval-augmented generation (RAG) with large language models (LLMs) is \\emph{soft context compression}, where the input sequence is transformed into a shorter continuous representation. \nWe develop a lightweight and simple mean-pooling approach that consistently outperforms the widely used compression-tokens architecture, and study training the same compressor to output multiple compression ratios. \nWe conduct extensive experiments across in-domain and out-of-domain QA datasets, as well as across model families, scales, and compression ratios. \nOverall, our simple mean-pooling approach achieves the strongest performance, with a relatively small drop when training for multiple compression ratios. \nMore broadly though, across architectures and training regimes the trade-offs are more nuanced, illustrating the complex landscape of compression methods. \n\n\n\n\n\n\n\n\\end{abstract}\n\n\\section{Introduction}\n\n\n\nReasoning over long documents is common in scenarios of retrieval-augmented generation (RAG). This is a computationally costly process, both as far as time and memory. \nTime is impacted by processing the document itself and self-attending over its computed representations in later parts of the generation process. \nMemory costs spike due to the key-value (KV) cache of the processed document. \nThe common way to reduce these costs is \\emph{soft context compression}, where a sequence of continuous representations is pre-computed. This representation is compressed in the sense that its length is significantly lower than the document length, thereby reducing both time and memory costs of reasoning over the document. \nThis compressed representation is computed once, and then retrieved as needed. \nThis important problem is receiving significant attention~\\citep[e.g.,][]{ge2024incontext, xrag, dai-etal-2025-pretraining}. \n\n\n\nWe study both compressor model design and the compression training process, with simplicity in mind. \nThe compression encoder we design is composed of an encoding LLM, and straightforward mean-pooling operations to collapse together representations to achieve a target compression ratio. \nThis approach adds no parameters beyond the encoder LLM, and the computation beyond the encoding of the document is minimal. It also naturally allows for compression ratio flexibility, raising the question of the benefits or downsides of training the same compressor to support multiple compression ratios. \nWe design a simple training objective and process to achieve this. \nThis is motivated foremost by the benefit of training a single model to serve different compute budgets, rather than maintaining and training a separate model for each compression ratio. \nIt also allows to examine if and when training to compress at multiple ratios can perform better than training for a single ratio. \n\n\n\n\nWe construct a rigorous evaluation suite using multiple question-answering (QA) datasets. We distinguish between datasets that are part of our training set, and these that are completely held-out, allowing us to better gauge generalization. \nWe conduct a battery of experiments, across three model families, model scales, and variations of both compressor architecture and multi-ratio training. \n\nWe find that our approach consistently outperforms the conventional compression-tokens approach, while being more efficient. In addition, we also show that by simply altering the attention pattern in the conventional compression tokens method, one can mitigate the gap between the approaches significantly, albeit not entirely. \nOur multi-ratio training experiments reveal that it is possible to train and deploy only a single model for a wide range of compression ratios with only minor performance drops. Interestingly, our proposed enhancement for the compression-tokens approach even benefits from multi-ratio training. \nA comparison of compression performances for scales between 0.6B to 8B shows that compression quality increases with scale, amplifying the benefits of applying such compression methods to larger models.\nOur code is available at \\url{https://github.com/lil-lab/simple-context-compression}.\n\n\n\\section{Task Definition}\n\nSoft context compression is an approach where a document of length $L$ is mapped to a sequence of vectors of length $C$, where $L \\gg C$. \nWhile the original document can be described as a sequence of tokens, the compression is made of dense continuous vectors, hence \\emph{soft}.\nThis process allows an LLM that uses the compressed version of the document to invest significantly less computation, both in time and key-value (KV) cache space, both reduced from dependence on $L$ to dependence on $C$. \nThis benefit increases with repeated use of the document, as is likely in RAG scenarios. \n\nFormally, we define soft context compression to support multiple compression ratios. \nLet $\\mathcal{M}$ be a language model and $\\mathcal{R} \\subseteq \\mathbb{N_+}$ the admissible set of compression ratios. \nLet $\\mathcal{V}$ denote the vocabulary and $d$ the embedding dimension of $\\mathcal{M}$. \nThe goal of learning is to construct a compression function\n\\begin{equation}\nf_c : \\mathcal{V}^{L} \\times \\mathcal{R} \\to \\mathbb{R}^{C \\times d}\\;\\;,\n\\end{equation}\nwhich maps a token sequence $T = (t_{1}, \\ldots, t_{L})$, $t_i \\in \\mathcal{V}$ of length $L$ and a ratio $r \\in \\mathcal{R}$ to a compressed representation of $C$ vectors of dimension $d$. The length $C$ is determined by the specified ratio $C = \\left\\lceil L / r \\right\\rceil$.\n\n\nAn ideal compressor $f_c$ preserves the conditional distribution of the model using the compressed version for any prompt $P$:\n\\begin{equation}\np_{\\mathcal{M}}(\\cdot \\mid T, P) \\;\\approx\\; p_{\\tilde{\\mathcal{M}}}(\\cdot \\mid f_c(T; r), P)\\;\\;,\n\\end{equation}\nwhere $\\tilde{\\mathcal{M}}$ is an adapted version of $\\mathcal{M}$, for example augmented with lightweight parameters such as LoRA~\\citep{hu2022lora} modules that can be fused into the base model without altering its capacity.\n\n\n\\section{Background and Related Work}\n\n\\paragraph{Soft Context Compression}\nA dominant line of research on context compression adopts the use of artificial \\emph{compression tokens}. \nAs shown in \\autoref{fig:arch:tokens}, a sequence of length $L$ with a target compression ratio $r$ is augmented with $C = \\lceil L/r \\rceil$ additional identical tokens. \\footnote{Although some works utilize a fixed number of compression tokens and then learn a distinct embedding for each position.}\nThe embedding of the compression token is learned. \nThe final hidden state at the time steps of the compression tokens is taken as the compressed representation. \nA decoder, conditioned on this representation and a downstream prompt (e.g., a question), produces the output. \nTraining typically combines a language modeling objective on the decoder with a distillation loss that encourages the compressor–decoder to approximate the behavior of a target LLM with access to the full uncompressed context (\\autoref{fig:arch:regular_llm}). \nThe decoder parameters are either tuned during learning or are frozen. \n\nThis paradigm has been explored extensively in recent work. \nAutoCompressors~\\citep{chevalier2023adapting} introduce recursive compression by appending a fixed set of compression tokens and extracting their hidden states. They tie the encoder and decoder weights. \nThe ICAE framework~\\citep{ge2024incontext} adopts an encoder–decoder setup where the decoder is frozen and only the encoder is trained, with a two-stage process of autoencoding pretraining and task-specific finetuning. \nCOCOM~\\citep{cocom} extends this approach to retrieval-augmented QA, experimenting with lighter encoders and with training decoders to jointly process multiple compressed contexts. \nOther work has sought more aggressive reduction: xRAG~\\citep{xrag} maps document retrieval embeddings directly into the decoder’s input space, achieving single-token compression but with severe constraints on sequence length and generality. \nPISCO~\\citep{louis-etal-2025-pisco} demonstrates that training compressors on LLM-generated answers improves downstream RAG performance, while PCC~\\citep{dai-etal-2025-pretraining} decouples the compressor from the target LLM by learning a converter to project compressed representations into another model’s hidden space. \nMost recently, GMSA~\\citep{tang2025gmsaenhancingcontextcompression} proposed grouping hidden representations and learning a layer semantic alignment module that bridges the gap between the encoder's final hidden states and the decoder's first attention layers. \nTheir approach is related to our study of pooling, but differs in the complexity of multi-stage reconstruction training and the use of compression-decoder adapters.\\footnote{While we consider this approach an important point of comparison, we were unable to include it in our evaluation because their code and models were not publicly available at the time of writing.}\n\nIn this work, we revisit some of these design choices and provide a systematic comparison with token-based architectures under both single- and multi-ratio training regimes. \n\n\\paragraph{KV Cache Compression}\nIn contrast to representing contexts as input embeddings, another line of work compresses the entire set of key–value (KV) states. \nSome approaches remove or compress less informative entries in the KV cache without additional training~\\citep{xiao2024efficient_streamingllm, oren-etal-2024-transformers_TOVA,li2024snapkv}, while others train the model to perform the compression explicitly~\\citep{qin-etal-2024-dodo,DynamicMemoryCompression}. \nA different variant introduces compression tokens, but instead of retaining only the final hidden representation, all KV states are propagated to the decoder~\\citep[e.g.,][]{zhang2025long_activationbeacon,li-etal-2025-500xcompressor}. \nAlthough these methods provide higher-capacity compressed representations that are well suited for efficient long-context comprehension, their increased size makes it impractical to store them for reuse in retrieval-augmented generation frameworks, where caching compressed representations could otherwise avoid recomputation. \n\n\\paragraph{Hard Prompt Compression}\nAn alternative approach is to compress contexts directly in the token space. \nThis has been done by removing unimportant tokens or lexical units~\\citep[e.g.,][]{li-etal-2023-selectivecontext,jiang-etal-2023-llmlingua, pan-etal-2024-llmlingua2} or generating concise summaries that preserve salient details~\\citep{chuang-etal-2024-learning_NanoCapsulator}. \nWhile these methods can be more interpretable and storage-efficient, they are inherently constrained by their reliance on explicit tokens. \n\n\\section{Methodology}\\label{sec:method}\n\n\\newcommand{\\context}{T}\n\\newcommand{\\prompt}{P}\n\\newcommand{\\numpoolops}{b}\n\\newcommand{\\lencompression}{C}\n\\newcommand{\\lencontext}{L}\n\\newcommand{\\comprate}{r}\n\\newcommand{\\allcomprates}{\\mathcal{R}}\n\\newcommand{\\embdim}{d}\n\\newcommand{\\encodingseq}{h}\n\\newcommand{\\encoding}{h}\n\n\n\n\n\nWe propose a compression model design where representations of adjacent tokens are pooled together to reduce the document representation length. We train via knowledge distillation to replicate the functionality of a teacher receiving the original (uncompressed) input. \n\n\\begin{figure}[t]\n \\centering\n \n \\def\\uniformscale{0.23} %\n \n \\newlength{\\fixedheight}\n \\setlength{\\fixedheight}{5.3cm}\n \n \\begin{subfigure}[t]{0.31\\textwidth}\n \\centering\n \\vbox to \\fixedheight{%\n \\includegraphics[page=1, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n \\vfill\n }\n \\caption{Processing with a regular language model (no compression).}\n \\label{fig:arch:regular_llm}\n \\end{subfigure}\n \\hfill\n \\begin{minipage}[t]{0.02\\textwidth}\n \\centering\n \\rule[0pt]{0pt}{\\fixedheight}%\n \\begin{tikzpicture}\n \\draw[dashed, gray, very thin] (0,0) -- (0,\\fixedheight);\n \\end{tikzpicture}\n \\end{minipage}%\n \\hfill\n \\begin{subfigure}[t]{0.31\\textwidth}\n \\centering\n \\vbox to \\fixedheight{%\n \\includegraphics[page=2, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n \\vfill\n }\n \\caption{Compression tokens approach for context compression.}\n \\label{fig:arch:tokens}\n \\end{subfigure}\n \\hfill\n \\begin{minipage}[t]{0.02\\textwidth}\n \\centering\n \\rule[0pt]{0pt}{\\fixedheight}%\n \\begin{tikzpicture}\n \\draw[dashed, gray, very thin] (0,0) -- (0,\\fixedheight);\n \\end{tikzpicture}\n \\end{minipage}%\n \\hfill\n \\begin{subfigure}[t]{0.31\\textwidth}\n \\centering\n \\vbox to \\fixedheight{%\n \\includegraphics[page=3, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n \\vfill\n }\n \\caption{Our proposed method: no extra tokens; mean pooling of final hidden states.}\n \\label{fig:arch:pool}\n \\end{subfigure}\n \n \\caption{Comparison of context processing methods: regular LM, compression tokens, and our proposed approach --- mean pooling. The figure illustrates a compression ratio of $4\\times$.}\n \\label{fig:arch}\n\\end{figure}\n\n\n\\subsection{Compression via Mean Pooling}\\label{sec:method:pool}\n\nWe propose a simple compression architecture that relies only on mean pooling of encoded representations. \n\\autoref{fig:arch:pool} illustrates our approach. \nGiven a document, we compute its representation with an encoder, and \napply a non-overlapping mean pooling operator with window size $\\comprate$, the same size as the compression ratio, and stride $\\comprate$ to generate continuous vectors as the output compression.\n\nFormally, let $\\encodingseq = (\\encoding_1,\\ldots,\\encoding_\\lencontext) \\in \\mathbb{R}^{\\lencontext \\times \\embdim}$ denote the sequence of hidden states produced by the encoder.\nFor a compression ratio $\\comprate \\in \\allcomprates$, we partition the sequence into $k$ consecutive, non-overlapping blocks:\n\\begin{equation}\nS_k = \\{(k-1)\\comprate+1,\\ldots,\\min(k\\comprate, \\lencontext)\\}\\;\\;, \\qquad k=1,\\ldots,\\lceil \\lencontext/\\comprate \\rceil\\;\\;. \n\\end{equation}\nThe compressed representation of length $\\lceil \\lencontext/\\comprate \\rceil$ is obtained by averaging within each block:\n\\begin{equation}\nf_c(T,\\comprate) = (z_1,\\ldots,z_{\\lceil \\lencontext/\\comprate \\rceil}) \\in \\mathbb{R}^{\\lceil \\lencontext/\\comprate \\rceil \\times d} \\hspace{1em}\\text{s.t.}\\hspace{1em}z_k = \\frac{1}{|S_k|} \\sum_{i \\in S_k} h_i\\;\\;. \n\\end{equation}\n\n\nThe encoder we use is Transformer-based. \nCritically, we use a full self-attention mask during encoding, allowing each encoded vector to include information from the entire context, and thereby each compressed segment to aggregate information across the entire context. \nIn practice, we initialize with an autoregressive LLM, and remove the self-attention mask before learning. \n\nOur pooling design introduces no additional parameters beyond those of the encoder backbone and the decoder (i.e., target LLM) using the compressed representation, and has low computational overhead. The compression-tokens method is slightly more expensive. It requires an encoder input of size $\\lencontext + \\lencontext/\\comprate$, while our approach only processes the original $\\lencontext$ tokens, with negligible overhead for the pooling operator.\n\n\\subsection{Training Objective}\\label{sec:method:train}\n\n\\newcommand{\\answertoken}{a}\n\\newcommand{\\answerseq}{A}\n\nOur objective is to approximate the behavior of the target LLM before any fine-tuning when provided with the full uncompressed context (\\autoref{fig:arch:regular_llm}). \nWe consider this LLM as the teacher model within a knowledge distillation framework. \nEach training instance consists of a context $\\context$, a prompt $\\prompt$, and a ground-truth answer $\\answerseq = (\\answertoken_1,\\ldots,\\answertoken_m)$. For each answer position $i = 1,\\dots,m$, the teacher defines the distribution $q(\\cdot \\mid \\context, \\prompt, \\answerseq_{<i})$, where $\\answerseq_{<i} = (\\answertoken_1,\\ldots,\\answertoken_{i-1})$ denotes the gold prefix of the answer. \nThe compressor produces a compressed representation $f_c(T,r)$, which is passed to the fine-tuned decoder together with $(P, A_{<i})$, yielding the student distribution $p_\\theta(\\cdot \\mid f_c(T,r), P, A_{<i})$.\nThis combined encoder-decoder model is the student. \n\nFor a single compression ratio $\\comprate$, the distillation loss is the token-level KL divergence between the teacher and student distributions:\n\\begin{equation}\n\\mathcal{\\lencontext}_{\\text{KD}}(\\context,\\prompt,\\answerseq; \\comprate) \\;=\\;\n\\sum_{i=1}^m\n\\mathrm{KL}\\!\\left(\nq(\\cdot \\mid \\context,\\prompt,\\answerseq_{<i})\n\\;\\|\\;\np_\\theta(\\cdot \\mid f_c(\\context,\\comprate),\\prompt,\\answerseq_{<i})\n\\right)\\;\\;.\n\\end{equation}\n\nWe propose a unified training strategy in which a single compressor is trained to handle multiple ratios simultaneously. \nThis is in contrast to most previous work, where a separate model is trained for each compression ratio. \nWe generate compressed representations for all ratios $r \\in \\mathcal{R}$ for each training instance. Each compressed representation is passed independently to the decoder, and the corresponding losses are computed. The final objective for one training instance is obtained by summing across the ratios:\n\\begin{equation}\n\\mathcal{L}_{\\text{multi}}(\\context,\\prompt,\\answerseq) \\;=\\;\n\\sum_{\\comprate \\in \\allcomprates} \n\\mathcal{L}_{\\text{KD}}(\\context,\\prompt,\\answerseq; \\comprate)\\;\\;.\n\\end{equation}\n\nThe iteration over ratios is performed within each batch, and a single parameter update is applied after aggregating the losses. Since the encoder computation is shared across all ratios, this procedure is substantially more efficient than training separate models. By relying exclusively on knowledge distillation, rather than combining it with a language modeling objective, we enable a direct and fair comparison between the original model and the compressor.\n\n\\section{Experiments and Results}\\label{sec:exp}\n\nOur central objective is to isolate the contribution of context compression itself, without entanglement with retrieval noise or incomplete supervision. \nWhile compression methods are often demonstrated in retrieval-augmented generation (RAG) settings, these introduce extraneous challenges, such as when retrieved passages may not contain sufficient evidence, making performance conflate retrieval quality with compression quality. \nTo avoid this confounder, we focus exclusively on reading comprehension, where given contexts are guaranteed to contain the necessary evidence to answer the question. \nThis setup allows for a controlled, head-to-head comparison of different compression strategies, across a range of datasets that stress both single-hop and multi-hop reasoning. \n\n\\subsection{Experimental Setup}\\label{sec:exp:setup}\n\n\\paragraph{Data} \nWe curated our training set by mixing multiple context-based datasets, in tasks spanning reading comprehension (RC) and summarization. \nA detailed list of the datasets we incorporated in our training mixture can be found in \\autoref{tab:training_datasets}.\nWe evaluate with six reading comprehension benchmarks: SQuAD~\\citep{rajpurkar-etal-2016-squad}, NarrativeQA~\\citep{kocisky-etal-2018-narrativeqa}, HotpotQA~\\citep{yang-etal-2018-hotpotqa}, AdversarialQA~\\citep{bartolo2020beat_adversarialqa}, TriviaQA~\\citep{joshi-etal-2017-triviaqa}, and ParaphraseRC~\\citep{saha-etal-2018-duorc}.\nThis selection covers a broad spectrum of reasoning styles, from factual extraction to adversarial paraphrasing, thereby testing the generality of compression. \nFor TriviaQA, we restrict the evaluation to the verified subset, ensuring that every question has sufficient supporting evidence. \nThe training mixture includes the train splits of SQuAD, NarrativeQA, and HotpotQA, which thus serve as in-domain testbeds. \nAdversarialQA, TriviaQA, and ParaphraseRC are excluded from the training mixture and instead used purely for out-of-domain evaluation. \n\n\n\\paragraph{Model Training} For each target language model, we first finetune it on the training mixture using LoRA~\\citep{hu2022lora}. \nThis finetuned model is then fixed and used as the teacher in the distillation process. This ensures that performance differences stem solely from the compressor rather than mismatched finetuning (e.g., to the question domain). \nBoth the compressor’s encoder and decoder are initialized from the same target LLM but are trained with separate LoRA weights. We always use the instruction-tuned model weights as our backbone. For multi-ratio training, we always train on the ratios $\\{4\\times, 8\\times, 16\\times, 32\\times, 64\\times, 128\\times\\}$, unless stated otherwise. In addition, we found that applying a single linear layer slightly improves performance for both our method and the compression-tokens method, so for all experiments in this paper a learned matrix $W\\in\\mathbb{R}^{d\\times d}$ is applied to $f_c(T,\\comprate)$ before the compressed representation is given as input to the decoder LLM, unless stated otherwise. Detailed training configuration and hyperparameter choices are provided in \\autoref{app:exp}. \n\n\\paragraph{Implementation of the Compression-Tokens Approach} \nThe main approach we compare ours against is using compression tokens. \nA central design consideration in our experiments is the attention pattern applied to compression tokens. \nUnder the compression-tokens paradigm, the causal attention mask typically employed by transformer-based LLMs imposes a strong Matryoshka-style~\\citep{kusupati2022matryoshka} constraint: compressed representations at smaller lengths must correspond to strict prefixes of those at larger lengths. \nWe relax this restriction by allowing compression tokens to attend bidirectionally among themselves, while retaining causal attention over the original context. \nThis simple, albeit not explored in prior work, modification makes the model aware of how many compression tokens are available (i.e., its compression budget), and therefore to allocate information differently for each ratio while still benefiting from shared computation and KV caching.\nWe experiment with both the conventional causal attention mask and our bidirectional modification. \nEmpirically, we observe that this modification significantly improves the approach's performance. \nIn addition, in our implementation of the compression-tokens models, we utilize only a single compression token that is appended $\\lceil \\lencontext/\\comprate \\rceil$ times to the context, rather than having several compression tokens. This enables us to compress any context to any arbitrary ratio we choose, while retaining an equal number of parameters in the model. \n\n\n\\paragraph{Metrics}\nWe evaluate our models using the standard \\emph{exact match} (EM) and $F_1$ metrics.\\footnote{We show only $F_1$ scores in the main text but full EM results with similar trends are reported in \\autoref{tab:primary_results_EM}.} Several recent works reported QA performance using a substring accuracy metric, which assigns a score of 1 if the exact match is a substring of the output and 0 otherwise. We opt against the adoption of this metric as it is easily exploitable.\\footnote{Consider a question where the answer is a US state, and the model lists all 50 states as an answer.} This forces us to exclude some baselines from our primary results. \n\nIn addition, for each metric, we also define its \\emph{teacher-normalized} version. Given a metric $M$, a target language model $\\mathcal{M}$ and a compressor $f_c$, we calculate the following: $M_T$, the teacher's score, by passing the original uncompressed contexts to the decoder model; $M^{\\varnothing}_T$, the no-context score, by passing only the question without any context; and $M_{f_c}$, by using the compressed context. Then, the teacher-normalized score is given by $\\frac{M_{f_c}-M^\\varnothing_T}{M_T -M^\\varnothing_T}$. This score does two things. \nFirst, it scales the compressor's score with respect to the teacher's, allowing for a direct assessment of the amount of retained performance under compression. \nSecond, it accounts for how easy it is for the model to answer the input question without any context. This latter consideration comes to account for cases where a question does not really require the context, potentially inflating the score of the compression model, while actually simply ignoring the compressed input. \n\n\\paragraph{Systems}\n\nOur main comparison point is our implementations of the compression tokens method, with causal or bidirectional attention. \nWe compare against these two systems throughout our experiments. \nWe also include comparisons to other soft context compression methods: ICAE~\\citep{ge2024incontext} and PCC~\\citep{dai-etal-2025-pretraining}. \nWe also evaluate LLMLingua2 \\citep{pan-etal-2024-llmlingua2}, a hard prompting compression approach, by passing LLMLingua's compressed prompts to our finetuned Qwen3-8B teacher model. \n\nComparison between compression methods is challenging in general, due to inconsistencies in the training procedures. \nOur main goal is to build a systematic understanding of the architecture landscape, and we compare ourselves to other methods mainly to showcase the validity of our experiments.\nShowing the strength of performance compared to the prior state of the art is secondary, and not even necessarily feasible because many approaches do not release code or models, or adopt training methods that complicate the evaluation. \nThis challenge is demonstrated well by the PISCO~\\citep{louis-etal-2025-pisco} method. Their training method is not well suited for the traditional EM/$F_1$ metrics and performs poorly on these metrics, and indeed the authors evaluated their method only using a more forgiving substring accuracy score. We therefore omit this method from our primary comparisons, but include it and report substring accuracy in \\aautoref{app:results:metrics} (\\autoref{tab:primary_results_accuracy}). \n\nAll experiments are conducted with context lengths up to 1{,}024 tokens, a practical limitation imposed by our computational budget. \n\n\n\\subsection{Results}\\label{sec:exp:results} \n\n\n\n\n\n\n\n\n\n\\begin{table*}[!ht]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 42.52 & & 24.39 & & 22.59 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 42.40 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 62.08 & & 51.30 & & 36.20 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 62.98 & & 49.37 & & 37.24 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 74.33 & & & & & & & 23.06 \\\\\n & Compression-Tokens (Causal) & & 67.03 & 65.90 & 56.21 & 58.41 & 47.47 & 44.76 & \\\\\n & Compression-Tokens (Bidirectional) & & 69.20 & 69.57 & 60.27 & 63.01 & 46.93 & \\textbf{46.97} & \\\\\n & Mean-Pooling & & \\textbf{71.66} & \\textbf{70.55} & \\textbf{63.85} & \\textbf{64.67} & \\textbf{47.90} & 45.92 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 73.44 & & & & & & & 19.79 \\\\\n & Compression-Tokens (Causal) & & 64.88 & 62.53 & 55.22 & 54.28 & 43.08 & 40.83 & \\\\\n & Compression-Tokens (Bidirectional) & & 66.72 & 68.15 & 57.68 & 60.48 & 41.61 & \\textbf{42.66} & \\\\\n & Mean-Pooling & & \\textbf{70.39} & \\textbf{69.36} & \\textbf{61.79} & \\textbf{61.72} & \\textbf{43.62} & 41.05 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 69.93 & & & & & & & 14.00 \\\\\n & Compression-Tokens (Causal) & & 50.90 & 57.73 & 49.83 & 48.68 & 36.19 & 35.34 & \\\\\n & Compression-Tokens (Bidirectional) & & 62.04 & 62.60 & 51.53 & 54.11 & 36.25 & \\textbf{35.77} & \\\\\n & Mean-Pooling & & \\textbf{66.43} & \\textbf{64.17} & \\textbf{55.43} & \\textbf{54.47} & \\textbf{36.72} & 33.48 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 65.36 & & & & & & & 9.34 \\\\\n & Compression-Tokens (Causal) & & 54.40 & 51.85 & 41.57 & 42.59 & 28.86 & 28.60 & \\\\\n & Compression-Tokens (Bidirectional) & & 55.59 & 57.03 & 44.82 & 47.62 & 29.69 & \\textbf{29.51} & \\\\\n & Mean-Pooling & & \\textbf{61.17} & \\textbf{58.36} & \\textbf{47.59} & \\textbf{47.64} & \\textbf{29.94} & 26.36 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 71.96 & & & & & & & 21.64 \\\\\n & Compression-Tokens (Causal) & & 63.35 & 62.18 & 55.07 & 54.70 & 44.46 & 42.49 & \\\\\n & Compression-Tokens (Bidirectional) & & 64.76 & 65.24 & 56.39 & 58.43 & 44.73 & 43.17 & \\\\\n & Mean-Pooling & & \\textbf{69.33} & \\textbf{68.09} & \\textbf{61.39} & \\textbf{61.04} & \\textbf{44.98} & \\textbf{43.71} & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 65.82 & & & & & & & 15.17 \\\\\n & Compression-Tokens (Causal) & & 56.31 & 53.74 & 47.51 & 46.96 & 35.41 & 35.62 & \\\\\n & Compression-Tokens (Bidirectional) & & 57.91 & 57.52 & \\textbf{49.20} & 50.06 & \\textbf{36.43} & \\textbf{36.25} & \\\\\n & Mean-Pooling & & \\textbf{62.81} & \\textbf{60.56} & 47.28 & \\textbf{51.56} & 33.25 & 33.98 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}}\n\\medskip\n\\includegraphics[width=\\textwidth]{figures/methods_ratios_comparison.pdf}\n\\caption{\nPrimary results. Values in the table are $F_1$ scores macro-averaged across all datasets in our evaluation suite. \n\\textbf{Original} stands for the teacher model's score when given the full context. \\textbf{No Ctx} stands for the teacher model's score when not given any context at all. For each ratio, we display both single- and multi-ratio versions. For the baseline systems (top section), we include results for the compression ratios supported by these methods, unsupported ratios are left blank. The best method for each (model, ratio, single/multi-ratio training) setting is \\textbf{bolded}.\nBottom figures present aggregated views of the results in the table, but instead of $F_1$ show the teacher-normalized $F_1$ metric (Relative F1). Scores are obtained by averaging over all models listed in the table. \n}\\label{tab:primary_results_hybrid_transpose}\n\\end{table*}\n\n\\autoref{tab:primary_results_hybrid_transpose} shows our main results. We demonstrate the robustness and generality of our findings by comparing six different models, spanning three model families and four model scales: Llama3.2-1B~\\citep{grattafiori2024llama}, Gemma2-2b~\\citep{team2024gemma}, and Qwen3-0.6/1.7/4/8B~\\citep{yang2025qwen3}. \nWe show the average $F_1$ scores over all six evaluation datasets. \nBelow the results table, we provide bar charts that summarize the results along specific dimensions that emphasize trends. \nThe bar charts show the teacher-normalized $F_1$ metric averaged across all models and datasets to get a single aggregated result per method. \nWe provide the teacher model's performance with the original context (\"Original\") and without context at all (\"No Ctx\"). In between we report the results for different compression ratios and for both the single- and multi-ratio training schemes. \n\nOur mean-pooling method is consistently better than both the standard (causal) compression tokens architecture and the bidirectional variation. \nSimply adding bidirectional attention between the compression tokens dramatically improves performance. \nComparing the single-ratio models to the multi-ratio models, we see that the bidirectional compression tokens approach significantly benefits from multi-ratio training, while for the mean-pooling approach a trade-off clearly exists. \nThis is potentially because the bidirectional approach has a clear signal about the target compression ratio -- the forward attention allows each time step to be aware of the total length of the compressed output. \nWithout this, the model must produce a one-size-fits-all representation in each time step. \nLastly, while we do see a performance drop in the multi-ratio setting at $128\\times$ for all methods, it must be taken in the context of the already relatively low performance retention at that ratio.\n\n\\paragraph{Compression Scaling}\n\\begin{figure}[htb]\n \\centering\n \\includegraphics[width=0.6\\linewidth]{figures/scaling_law_qwen3.pdf}\n \\caption{Compression Scaling. We show the teacher-normalized $F_1$ scores (Relative F1) across four Qwen3 model scales. The scores are averages of the scores of all datasets. We can clearly observe the benefits of scaling for LLM compressors.}\n \\label{fig:scaling_law}\n\\end{figure}\nIt is well known that LLM performance increases with scale, if scaled appropriately~\\citep{cheng2024training_chinchilla}. But does compression quality scale as well? In \\autoref{tab:primary_results_hybrid_transpose} we can see that the teacher's performance improves as the model size grows. Having a compressor increase in performance at the same rate as the teacher would actually tell us that the compressor does not scale well, since that would mean that the teacher-normalized scores stay constant throughout the scales. \n\\autoref{fig:scaling_law} shows the compression performances of the four Qwen3 model scales we use. \nWe train the models under the multi-ratio setting to efficiently evaluate multiple ratios. \nWe evaluate using the teacher-normalized $F_1$ score, and present the average scores across all datasets. The results are exciting\\textemdash the compressors clearly have desirable scaling properties. \nCritically, the efficiency gains of context compression are much larger as the model size increases. \nTherefore, observing that larger models retain higher levels of performance (higher relative F1) justifies this line of research. \nSimilar trends are observed for the other methods (\\autoref{tab:primary_results_hybrid_transpose}), demonstrating the generality of this finding. \n\n\\paragraph{In-Domain vs. Out-of-Domain}\n\\begin{figure}[t]\n \\centering\n \\begin{subfigure}[t]{0.95\\linewidth}\n \\centering\n \\includegraphics[width=\\linewidth]{figures/in_vs_out_fig.pdf}\n \\caption{In-domain vs.\\ out-of-domain performance across compression ratios.}\n \\label{fig:in-vs-out}\n \\end{subfigure}\n\n \\vspace{0.8em} %\n\n \\begin{subfigure}[t]{0.95\\linewidth}\n \\centering\n \\includegraphics[width=\\linewidth]{figures/in_out_gap_fig.pdf}\n \\caption{Performance drop (in–out gap) per method across compression ratios (in teacher-normalized Relative $F_1$ units). Higher values mean a larger domain performance gap. Negative values mean that the out-of-domain performance is better than in-domain performance.}\n \\label{fig:in-out-gap}\n \\end{subfigure}\n\n \\caption{In-domain and out-of-domain comparison. (a) Line plots show performance on in-domain vs.\\ out-of-domain datasets. (b) Bar plots show the in–out performance gap per method, which is the difference between in-domain and out-of-domain teacher-normalized $F_1$ scores.}\n \\label{fig:in-out-combined}\n\\end{figure}\n\nWe construct our evaluation suite with both in-domain QA datasets and out-of-domain QA datasets (\\autoref{sec:exp:setup}). The training splits of the in-domain datasets are included in the training data mixture, while the out-of-domains datasets are not. \nIt is expected that downstream performance will drop for out-of-domain datasets. \nCritical for our study, though, is the performance drop of the compressor itself. \n\\autoref{fig:in-vs-out} plots the in-domain and out-of-domain performance using the teacher-normalized $F_1$ score for the Qwen3-8B model, averaged over the datasets in each category. \nWe first observe that while the mean-pooling approach is superior for ratios up to $16\\times$ in all settings, its performance deteriorates as the compression ratio increases. \nTo better understand the performance change due to the domain gap, we plot the differences between the in-domain and out-of-domain performance in \\autoref{fig:in-out-gap}. \nThe performance gap is higher for low ratios, and lower for higher ratios. \nOne possible explanation is that at low compression ratios the compressed representations still retain much of the original contextual signal, so the model is more sensitive to domain-specific distributional shifts; differences between in-domain and out-of-domain language patterns thus manifest as a larger performance gap. By contrast, at higher compression ratios much of the fine-grained contextual detail is already lost to compression noise, which dominates over the domain gap. In this regime, both in-domain and out-of-domain datasets suffer similarly from the limited representational capacity, resulting in a smaller relative difference. \n \n\\paragraph{Model Ablations}\n\\begin{table}[t]\n\\centering\n\\resizebox{0.92\\linewidth}{!}{%\n\\begin{tabular}{l r r r r r r c}\n\\toprule\n\\textbf{Ablation} (\\textsc{Gemma2-2B}) & 4$\\times$ & 8$\\times$ & 16$\\times$ & 32$\\times$ & 64$\\times$ & 128$\\times$ & $\\Delta$ \\\\\n\\midrule\nDefault & \\textbf{68.1} & \\textbf{65.4} & \\textbf{61.0} & \\textbf{54.9} & \\textbf{48.8} & \\textbf{43.7} & \\,($+0.0$) \\\\\nFixed Decoder & 64.9 & 61.9 & 57.0 & 51.5 & 45.0 & 39.8 & \\,($-3.6$) \\\\\nFixed Encoder & 57.4 & 49.9 & 44.1 & 39.8 & 36.2 & 34.8 & \\,($-13.3$) \\\\\nNo Encoder & 58.7 & 51.9 & 44.9 & 40.2 & 36.2 & 34.1 & \\,($-12.6$) \\\\\nw/o Linear Layer & 67.7 & 64.5 & 60.0 & 54.1 & 48.1 & 43.2 & \\,($-0.7$) \\\\\nRatio Sampling & 67.1 & 64.0 & 59.3 & 53.5 & 47.5 & 42.2 & \\,($-1.4$) \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Ablation study for mean pooling using \\textsc{Gemma2-2B} as the teacher LLM. Numbers are macro-averaged $F_1$ scores. \\emph{$\\Delta$}: mean change vs. Default across ratios; \\textbf{bold} = best per column.}\n\\label{tab:abl_gemma2_mean}\n\\end{table}\n\nWe run all our ablations using the Gemma2-2B model, since it demonstrates strong performance while being relatively compute-efficient. \\autoref{tab:abl_gemma2_mean} presents the ablation results. \nWe conduct several ablations: (1) Fixed Decoder: the decoder is kept frozen and only the encoder is trained; (2) Fixed Encoder: the encoder is kept frozen and only the decoder is trained; (3) No Encoder: we remove the encoder entirely, and obtain the initial context representation using only the token embeddings of the decoder model; (4) w/o Linear Layer: we remove the linear layer that is applied after the pooling operation; (5) Ratio Sampling: instead of training on all ratios for each sample, a single ratio is randomly chosen for each sample during training. \n\nFreezing the decoder results in considerable performance reduction, although not catastrophic. This is in line with findings of previous works (\\citep{louis-etal-2025-pisco}). Freezing or removing the encoder is more detrimental, lowering performance by more than 12\\%. The effect of the linear layer is not very significant, its removal results in a reduction of only 0.7\\%. \nFinally, while randomly sampling a single ratio per sample would speed up training significantly, it does so at the cost of a small drop in performance (1.4\\%), likely because each ratio gets less updates during training. \n\n\\section{Discussion}\\label{sec:discussion}\n\nWe provide a systematic study of soft context compression, showing that a simple mean-pooling approach consistently outperforms compression-tokens architectures while requiring no additional parameters. We further demonstrate that multi-ratio training is both feasible and effective, enabling a single compressor to support a wide range of compression budgets with only minor performance degradation.\nInterestingly, we observe that the bidirectional compression-tokens method consistently benefits from multi-ratio training. A plausible explanation is that, unlike mean-pooling or causal compression-tokens, this method has explicit access to the number of compression tokens available, allowing it to adapt to the target budget. Exploring how to incorporate similar signals into other architectures is an important direction for future work.\n\nFinally, our study highlights a broader open problem: the evaluation of compression methods remains hindered by inconsistent setups, metrics, and benchmarks. By isolating compression quality from retrieval confounders and applying a uniform evaluation across models, scales, and domains, we aim to provide a rigorous basis for future research on soft context compression. We hope this work helps establish more standardized practices and clarifies the core principles that should guide the development of next-generation compressors.\n\n\\section*{Acknowledgements}\\label{sec:acknowledgements}\n\n\n\nThis research was supported by a gift to the LinkedIn–Cornell Bowers Strategic Partnership, NSF under grant No. OAC-2311521, NASA under award No. 20-OSTFL20-0053, and a gift from Open Philanthropy. \nWe thank Google for enabling experiments with Gemini through a gift.\nThis research was supported with Cloud TPUs from Google's TPU Research Cloud (TRC).\nWe thank Nathan Godey for his comments. \n\n\\bibliographystyle{iclr2026_conference}\n\\bibliography{iclr2026_conference}\n\n\\newpage\n\\appendix\n\\section{Additional Experimental Setup Details}\n\\label{app:exp}\n\\subsection{Data}\\label{app:exp:data}\n\n\\autoref{tab:training_datasets} and \\autoref{tab:evaluation_datasets} provide detailed lists of our training data mixture and evaluation suite.\nWe use the summaries as contexts for NarrativeQA, instead of the full stories. For HotpotQA, we only use the two gold paragraphs as contexts, and remove the distractors. \n\nWe increase the training data diversity by randomly sample a prompt template that fits the task, when training samples are composed of a context $C$, question $Q$ and answer $A$. For example, for the extractive QA task, an example of a prompt template is: \\textit{``\\textless C\\textgreater \\textbackslash n Extract the answer from the text above. \\textbackslash n Question: \\textless Q\\textgreater \\textbackslash n Answer: \\textless A\\textgreater''}. Similar templates are defined for other tasks as well. \nWe created approximately 100 prompt templates for each task. The full list of templates for each task is available along with our code. \n\\begin{table}[H]\n\\centering\n\\begin{tabular}{lrrr}\n\\toprule\nDataset & Avg. Context Tokens & \\#Samples & \\#Contexts \\\\\n\\midrule\n\\multicolumn{4}{l}{\\textbf{Summarization}} \\\\\nCNN/DM~\\citep{see-etal-2017-get_cnndm} & 649 & 198{,}732 & 196{,}601 \\\\\nDialogSum~\\citep{chen-etal-2021-dialogsum} & 208 & 12{,}452 & 12{,}450 \\\\\nSAMSum~\\citep{Gliwa_2019_samsum} & 145 & 14{,}730 & 14{,}254 \\\\\nXSum~\\citep{narayan-etal-2018-dont_xsum} & 408 & 185{,}760 & 185{,}566 \\\\\n\\addlinespace\n\\multicolumn{4}{l}{\\textbf{Reading Comprehension}} \\\\\nBoolQ~\\citep{clark-etal-2019-boolq} & 126 & 9{,}427 & 7{,}927 \\\\\nDROP~\\citep{dua-etal-2019-drop} & 295 & 76{,}751 & 5{,}477 \\\\\nHotpotQA~\\citep{yang-etal-2018-hotpotqa} & 247 & 90{,}327 & 84{,}705 \\\\\nNarrativeQA~\\citep{kocisky-etal-2018-narrativeqa} & 668 & 28{,}299 & 953 \\\\\nPubMedQA~\\citep{jin-etal-2019-pubmedqa} & 318 & 211{,}218 & 211{,}164 \\\\\nQuAC~\\citep{choi-etal-2018-quac} & 515 & 81{,}391 & 6{,}574 \\\\\nQuAIL~\\citep{rogers2020getting_quail} & 416 & 10{,}246 & 560 \\\\\nRACE~\\citep{lai-etal-2017-race} & 349 & 87{,}749 & 25{,}108 \\\\\nSQuAD~\\citep{rajpurkar-etal-2016-squad} & 162 & 86{,}821 & 18{,}877 \\\\\nPWC~\\citep{ge2024incontext} & 477 & 241{,}563 & 16{,}382 \\\\\n\\midrule\n\\textbf{Total} & \\textbf{410} & \\textbf{1,335,466} & \\textbf{786,598} \\\\\n\\bottomrule\n\\end{tabular}\n\\caption{Training datasets with average context length (tokens), number of samples, number of distinct contexts, and task category. The overall average context length is weighted by the number of samples.}\n\\label{tab:training_datasets}\n\\end{table}\n\\begin{table}[H]\n\\centering\n\\begin{tabular}{lrrr}\n\\toprule\nDataset & Avg. Context Tokens & \\#Samples & \\#Contexts \\\\\n\\midrule\nAdversarialQA~\\citep{bartolo2020beat_adversarialqa} & 154 & 1{,}000 & 341 \\\\\nHotpotQA~\\citep{yang-etal-2018-hotpotqa} & 254 & 7{,}394 & 7{,}352 \\\\\nNarrativeQA~\\citep{kocisky-etal-2018-narrativeqa} & 639 & 3{,}002 & 100 \\\\\nParaphraseRC~\\citep{saha-etal-2018-duorc} & 685 & 4{,}835 & 560 \\\\\nSQuAD~\\citep{rajpurkar-etal-2016-squad} & 169 & 5{,}928 & 1{,}204 \\\\\nTriviaQA (Verified)~\\citep{joshi-etal-2017-triviaqa} & 539 & 185 & 185 \\\\\n\\midrule\n\\textbf{Total} & \\textbf{375} & \\textbf{22{,}344} & \\textbf{9{,}742} \\\\\n\\bottomrule\n\\end{tabular}\n\\caption{Evaluation datasets with average context length (tokens), number of samples, and number of distinct contexts. The overall average context length is weighted by the number of samples.}\n\\label{tab:evaluation_datasets}\n\\end{table}\n\\newpage\n\\subsection{Training Hyperparameters}\\label{app:exp:hps}\n\\begin{table}[ht!]\n \\centering\n \\begin{tabular}{cc}\n \\toprule\n \\textbf{Hyperparameter} & \\textbf{Value} \\\\\n \\midrule\n LoRA $r$ & 16 \\\\\n LoRA $\\alpha$ & 16 \\\\ \n optimizer & AdamW \\\\\n $\\beta_1$ & 0.9 \\\\\n $\\beta_2$ & 0.95 \\\\\n clip norm & 1 \\\\\n peak learning rate & 2e-4 \\\\\n final learning rate & 2e-5 \\\\\n lr scheduler type & cosine \\\\\n warmup ratio & 0.05 \\\\\n weight decay & 0.0 \\\\\n steps & 48,000 \\\\\n batch size & 32 \\\\\n max context length & 1024 \\\\\n max answer tokens & 256 \\\\\n \\bottomrule\n \\end{tabular}\n \\caption{Hyperparameters for training all the models used in this work.} \n \\label{table:hyperparameters}\n\\end{table}\n\\newpage\n\\section{Additional Results}\\label{app:results}\nWe provide additional results from the same experiments conducted in the main body of the paper. \\aautoref{app:results:metrics} provides the primary results of the paper with the EM and substring accuracy metrics. \\aautoref{app:results:datasets} shows the $F_1$ performance on each individual dataset from the evaluation suite. \n\\subsection{Primary Results \\textemdash Additional Metrics}\\label{app:results:metrics}\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 30.02 & & 16.16 & & 16.06 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 24.94 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 48.81 & & 38.38 & & 25.94 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 49.34 & & 36.64 & & 27.92 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 59.82 & & & & & & & 16.19 \\\\\n & Compression-Tokens (Causal) & & 51.59 & 50.01 & 41.26 & 42.99 & 34.21 & 32.50 & \\\\\n & Compression-Tokens (Bidirectional) & & 53.44 & 53.99 & 44.92 & 47.15 & 33.60 & 34.27 & \\\\\n & Mean-Pooling & & 56.41 & 55.04 & 47.95 & 49.02 & 34.72 & 33.15 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 58.87 & & & & & & & 13.74 \\\\\n & Compression-Tokens (Causal) & & 49.66 & 46.26 & 40.05 & 39.59 & 30.07 & 28.84 & \\\\\n & Compression-Tokens (Bidirectional) & & 51.06 & 52.37 & 42.53 & 45.14 & 28.84 & 29.51 & \\\\\n & Mean-Pooling & & 55.25 & 53.77 & 45.43 & 45.86 & 30.91 & 28.38 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 55.19 & & & & & & & 9.07 \\\\\n & Compression-Tokens (Causal) & & 36.66 & 41.64 & 35.49 & 34.64 & 24.27 & 24.04 & \\\\\n & Compression-Tokens (Bidirectional) & & 46.45 & 46.72 & 36.62 & 38.93 & 24.31 & 24.33 & \\\\\n & Mean-Pooling & & 51.28 & 48.77 & 40.45 & 39.04 & 25.15 & 22.01 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 50.85 & & & & & & & 4.78 \\\\\n & Compression-Tokens (Causal) & & 39.66 & 36.76 & 27.99 & 29.00 & 18.23 & 18.20 & \\\\\n & Compression-Tokens (Bidirectional) & & 40.98 & 41.92 & 30.92 & 33.64 & 18.82 & 18.55 & \\\\\n & Mean-Pooling & & 45.82 & 43.07 & 32.50 & 33.09 & 19.05 & 16.07 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 57.63 & & & & & & & 15.00 \\\\\n & Compression-Tokens (Causal) & & 47.90 & 45.98 & 39.57 & 39.74 & 32.02 & 29.66 & \\\\\n & Compression-Tokens (Bidirectional) & & 49.43 & 49.40 & 40.89 & 42.70 & 31.79 & 30.43 & \\\\\n & Mean-Pooling & & 54.20 & 52.77 & 45.88 & 45.68 & 32.41 & 30.83 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 51.67 & & & & & & & 9.47 \\\\\n & Compression-Tokens (Causal) & & 41.84 & 39.03 & 33.73 & 33.38 & 24.11 & 24.64 & \\\\\n & Compression-Tokens (Bidirectional) & & 43.46 & 42.96 & 35.04 & 35.46 & 24.91 & 24.56 & \\\\\n & Mean-Pooling & & 47.97 & 45.45 & 33.15 & 36.93 & 22.89 & 22.70 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{Primary results with exact match (EM) as the metric.}\n \\label{tab:primary_results_EM}\n\\end{table}\n\\newpage\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 33.63 & & 18.30 & & 17.36 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 49.18 & & & & & & \\\\\n& \\emph{PISCO} (Llama3.1-8B) & & & & 53.62 & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 54.05 & & 43.67 & & 30.03 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 55.17 & & 41.79 & & 30.10 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.84 & & & & & & & 17.98 \\\\\n & Compression-Tokens (Causal) & & 59.79 & 58.58 & 47.07 & 49.99 & 39.09 & 37.05 & \\\\\n & Compression-Tokens (Bidirectional) & & 62.50 & 63.58 & 52.22 & 55.26 & 38.72 & 39.36 & \\\\\n & Mean-Pooling & & 65.91 & 65.06 & 55.68 & 56.77 & 39.95 & 37.80 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.69 & & & & & & & 15.00 \\\\\n & Compression-Tokens (Causal) & & 57.12 & 54.17 & 46.06 & 45.47 & 34.83 & 33.48 & \\\\\n & Compression-Tokens (Bidirectional) & & 59.35 & 60.99 & 48.92 & 52.23 & 33.20 & 34.33 & \\\\\n & Mean-Pooling & & 64.05 & 62.94 & 52.77 & 52.82 & 35.49 & 32.37 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.21 & & & & & & & 9.85 \\\\\n & Compression-Tokens (Causal) & & 43.01 & 49.31 & 41.31 & 40.45 & 28.45 & 27.90 & \\\\\n & Compression-Tokens (Bidirectional) & & 54.31 & 54.70 & 42.66 & 45.13 & 28.33 & 28.04 & \\\\\n & Mean-Pooling & & 60.03 & 57.28 & 46.63 & 45.07 & 28.96 & 25.82 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 59.67 & & & & & & & 5.62 \\\\\n & Compression-Tokens (Causal) & & 46.36 & 43.62 & 33.07 & 34.30 & 21.13 & 21.71 & \\\\\n & Compression-Tokens (Bidirectional) & & 48.04 & 48.84 & 36.11 & 39.50 & 22.13 & 22.00 & \\\\\n & Mean-Pooling & & 54.36 & 51.16 & 38.30 & 38.68 & 22.44 & 18.87 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.14 & & & & & & & 16.80 \\\\\n & Compression-Tokens (Causal) & & 55.50 & 52.94 & 46.13 & 45.59 & 36.14 & 33.94 & \\\\\n & Compression-Tokens (Bidirectional) & & 56.94 & 57.54 & 46.90 & 49.52 & 36.14 & 34.75 & \\\\\n & Mean-Pooling & & 62.51 & 61.28 & 52.55 & 51.90 & 36.61 & 34.93 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 60.30 & & & & & & & 11.09 \\\\\n & Compression-Tokens (Causal) & & 48.85 & 45.41 & 39.16 & 38.51 & 27.54 & 28.01 & \\\\\n & Compression-Tokens (Bidirectional) & & 50.89 & 50.10 & 40.44 & 41.91 & 28.34 & 28.44 & \\\\\n & Mean-Pooling & & 56.62 & 53.50 & 38.84 & 42.76 & 25.99 & 26.19 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{Primary results with accuracy as the metric.}\n \\label{tab:primary_results_accuracy}\n\\end{table}\n\n\\subsection{Results Per Dataset}\\label{app:results:datasets}\n\\subsubsection{In Domain Datasets Results}\\label{app:results:datasets:in}\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 48.38 & & 21.34 & & 19.68 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 45.6 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 78.38 & & 67.63 & & 40.22 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 79.56 & & 62.93 & & 41.23 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 86.48 & & & & & & & 20.31 \\\\\n & Compression-Tokens (Causal) & & 77.11 & 74.89 & 57.05 & 62.12 & 44.56 & 42.35 & \\\\\n & Compression-Tokens (Bidirectional) & & 80.00 & 81.23 & 64.80 & 69.27 & 44.30 & 43.86 & \\\\\n & Mean-Pooling & & 83.76 & 82.75 & 71.37 & 71.19 & 44.65 & 43.19 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 85.75 & & & & & & & 17.72 \\\\\n & Compression-Tokens (Causal) & & 74.23 & 71.31 & 57.49 & 56.88 & 38.95 & 37.10 & \\\\\n & Compression-Tokens (Bidirectional) & & 77.24 & 79.28 & 60.71 & 65.49 & 38.19 & 38.41 & \\\\\n & Mean-Pooling & & 83.19 & 81.54 & 68.20 & 67.47 & 39.96 & 37.54 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 83.65 & & & & & & & 12.66 \\\\\n & Compression-Tokens (Causal) & & 54.25 & 64.50 & 49.09 & 49.98 & 31.78 & 30.10 & \\\\\n & Compression-Tokens (Bidirectional) & & 72.92 & 73.39 & 53.07 & 57.36 & 31.58 & 31.17 & \\\\\n & Mean-Pooling & & 79.56 & 77.17 & 59.01 & 58.30 & 32.36 & 29.90 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 7.91 \\\\\n & Compression-Tokens (Causal) & & 61.67 & 57.52 & 40.29 & 41.60 & 22.06 & 22.45 & \\\\\n & Compression-Tokens (Bidirectional) & & 64.21 & 67.05 & 42.81 & 46.68 & 22.09 & 22.36 & \\\\\n & Mean-Pooling & & 74.00 & 70.60 & 48.62 & 48.14 & 22.40 & 20.45 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 84.58 & & & & & & & 16.41 \\\\\n & Compression-Tokens (Causal) & & 70.61 & 69.06 & 55.75 & 56.37 & 37.89 & 35.66 & \\\\\n & Compression-Tokens (Bidirectional) & & 74.16 & 75.41 & 57.77 & 61.75 & 37.72 & 37.00 & \\\\\n & Mean-Pooling & & 81.67 & 80.01 & 66.38 & 65.64 & 38.96 & 36.71 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 81.16 & & & & & & & 11.27 \\\\\n & Compression-Tokens (Causal) & & 62.65 & 59.34 & 46.41 & 45.49 & 28.58 & 28.44 & \\\\\n & Compression-Tokens (Bidirectional) & & 64.48 & 65.61 & 48.99 & 51.39 & 29.09 & 28.82 & \\\\\n & Mean-Pooling & & 74.91 & 71.40 & 47.36 & 53.66 & 28.02 & 27.91 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{SQuAD $F_1$.}\n \\label{tab:primary_results_squad}\n\\end{table}\n\\newpage\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 53.54 & & 29.32 & & 26.27 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 50.01 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 68.55 & & 59.38 & & 43.93 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 70.08 & & 59.05 & & 46.46 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 84.67 & & & & & & & 26.65 \\\\\n & Compression-Tokens (Causal) & & 78.85 & 78.32 & 68.00 & 72.65 & 64.14 & 59.74 & \\\\\n & Compression-Tokens (Bidirectional) & & 80.24 & 81.45 & 73.30 & 76.77 & 63.26 & 62.44 & \\\\\n & Mean-Pooling & & 83.30 & 82.08 & 77.66 & 78.41 & 63.88 & 63.77 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 84.12 & & & & & & & 23.16 \\\\\n & Compression-Tokens (Causal) & & 76.48 & 75.56 & 68.85 & 69.80 & 59.08 & 55.78 & \\\\\n & Compression-Tokens (Bidirectional) & & 78.13 & 79.41 & 71.11 & 74.60 & 58.38 & 56.87 & \\\\\n & Mean-Pooling & & 82.20 & 80.77 & 75.45 & 76.02 & 59.29 & 58.74 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 80.95 & & & & & & & 18.75 \\\\\n & Compression-Tokens (Causal) & & 66.69 & 70.98 & 63.82 & 63.84 & 51.48 & 48.78 & \\\\\n & Compression-Tokens (Bidirectional) & & 73.73 & 74.93 & 66.06 & 68.50 & 52.08 & 50.77 & \\\\\n & Mean-Pooling & & 78.64 & 76.11 & 68.76 & 68.78 & 50.86 & 49.44 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 77.35 & & & & & & & 14.74 \\\\\n & Compression-Tokens (Causal) & & 66.62 & 65.76 & 55.88 & 57.79 & 43.16 & 39.58 & \\\\\n & Compression-Tokens (Bidirectional) & & 67.24 & 69.28 & 58.44 & 61.79 & 43.80 & 41.66 & \\\\\n & Mean-Pooling & & 73.00 & 69.58 & 61.13 & 61.08 & 42.76 & 40.45 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 82.55 & & & & & & & 25.18 \\\\\n & Compression-Tokens (Causal) & & 75.62 & 75.54 & 69.18 & 70.42 & 61.91 & 59.03 & \\\\\n & Compression-Tokens (Bidirectional) & & 76.55 & 77.60 & 69.64 & 73.51 & 61.67 & 60.46 & \\\\\n & Mean-Pooling & & 80.93 & 79.85 & 75.10 & 74.90 & 62.36 & 61.64 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 77.96 & & & & & & & 19.34 \\\\\n & Compression-Tokens (Causal) & & 69.68 & 68.22 & 63.36 & 62.96 & 52.27 & 49.81 & \\\\\n & Compression-Tokens (Bidirectional) & & 70.74 & 71.01 & 64.47 & 66.19 & 53.51 & 51.79 & \\\\\n & Mean-Pooling & & 74.38 & 72.69 & 62.75 & 66.59 & 51.05 & 50.86 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{HotpotQA $F_1$.}\n \\label{tab:primary_results_hotpotqa}\n\\end{table}\n\\newpage\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 27.33 & & 14.35 & & 10.69 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 32.65 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 50.29 & & 34.16 & & 16.05 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 50.72 & & 32.56 & & 16.18 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.00 & & & & & & & 10.93 \\\\\n & Compression-Tokens (Causal) & & 59.62 & 58.28 & 46.58 & 49.32 & 33.41 & 29.37 & \\\\\n & Compression-Tokens (Bidirectional) & & 61.44 & 62.13 & 51.48 & 55.68 & 34.17 & 33.61 & \\\\\n & Mean-Pooling & & 65.89 & 64.74 & 58.17 & 58.38 & 34.81 & 32.21 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.12 & & & & & & & 10.40 \\\\\n & Compression-Tokens (Causal) & & 57.18 & 55.08 & 46.69 & 43.77 & 30.39 & 27.84 & \\\\\n & Compression-Tokens (Bidirectional) & & 58.37 & 60.74 & 48.84 & 52.41 & 29.77 & 30.22 & \\\\\n & Mean-Pooling & & 65.22 & 63.38 & 56.14 & 55.42 & 32.66 & 28.99 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.42 & & & & & & & 7.57 \\\\\n & Compression-Tokens (Causal) & & 41.97 & 49.85 & 40.15 & 39.49 & 25.42 & 23.64 & \\\\\n & Compression-Tokens (Bidirectional) & & 55.68 & 56.49 & 44.87 & 47.28 & 25.16 & 26.15 & \\\\\n & Mean-Pooling & & 60.34 & 58.56 & 48.95 & 48.78 & 26.91 & 23.60 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 61.13 & & & & & & & 7.76 \\\\\n & Compression-Tokens (Causal) & & 48.09 & 46.30 & 34.68 & 36.05 & 20.10 & 20.69 & \\\\\n & Compression-Tokens (Bidirectional) & & 48.04 & 50.67 & 38.85 & 40.35 & 21.29 & 21.07 & \\\\\n & Mean-Pooling & & 56.48 & 53.12 & 42.47 & 42.21 & 21.29 & 19.06 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.47 & & & & & & & 10.34 \\\\\n & Compression-Tokens (Causal) & & 56.17 & 55.78 & 47.16 & 46.68 & 31.17 & 29.72 & \\\\\n & Compression-Tokens (Bidirectional) & & 59.20 & 59.51 & 48.59 & 51.43 & 31.50 & 31.91 & \\\\\n & Mean-Pooling & & 64.29 & 63.44 & 56.94 & 55.71 & 33.42 & 31.79 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 61.67 & & & & & & & 9.03 \\\\\n & Compression-Tokens (Causal) & & 48.57 & 45.60 & 38.44 & 37.12 & 23.03 & 23.14 & \\\\\n & Compression-Tokens (Bidirectional) & & 52.24 & 49.98 & 40.65 & 42.08 & 23.59 & 23.72 & \\\\\n & Mean-Pooling & & 57.97 & 55.15 & 38.58 & 46.23 & 19.53 & 23.17 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{NarrativeQA $F_1$.}\n \\label{tab:primary_results_narrativeqa}\n\\end{table}\n\\newpage\n\\subsubsection{Out-of-Domain Datasets Results}\\label{app:results:datasets:out}\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 65.65 & & 46.46 & & 52.55 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 70.63 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 86.43 & & 78.03 & & 72.50 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 86.64 & & 77.13 & & 74.08 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 89.65 & & & & & & & 53.79 \\\\\n & Compression-Tokens (Causal) & & 89.67 & 89.15 & 88.92 & 85.50 & 79.36 & 77.55 & \\\\\n & Compression-Tokens (Bidirectional) & & 90.44 & 89.41 & 87.07 & 87.95 & 75.90 & 78.17 & \\\\\n & Mean-Pooling & & 87.94 & 86.52 & 84.38 & 86.32 & 79.74 & 75.89 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 90.46 & & & & & & & 43.49 \\\\\n & Compression-Tokens (Causal) & & 88.49 & 83.28 & 82.95 & 80.42 & 72.27 & 70.84 & \\\\\n & Compression-Tokens (Bidirectional) & & 91.59 & 90.83 & 86.10 & 87.53 & 67.43 & 74.52 & \\\\\n & Mean-Pooling & & 85.50 & 88.72 & 83.68 & 85.32 & 71.04 & 67.50 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 89.20 & & & & & & & 25.08 \\\\\n & Compression-Tokens (Causal) & & 74.89 & 83.83 & 80.55 & 73.91 & 61.72 & 64.02 & \\\\\n & Compression-Tokens (Bidirectional) & & 85.62 & 86.41 & 76.15 & 80.34 & 61.46 & 61.67 & \\\\\n & Mean-Pooling & & 85.83 & 82.75 & 80.61 & 75.94 & 63.03 & 53.77 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 9.87 \\\\\n & Compression-Tokens (Causal) & & 78.27 & 73.57 & 62.14 & 64.79 & 48.97 & 49.69 & \\\\\n & Compression-Tokens (Bidirectional) & & 81.58 & 78.38 & 69.22 & 74.16 & 50.24 & 54.05 & \\\\\n & Mean-Pooling & & 81.45 & 77.88 & 69.08 & 70.41 & 52.45 & 43.08 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 90.69 & & & & & & & 54.06 \\\\\n & Compression-Tokens (Causal) & & 89.75 & 85.06 & 82.73 & 79.19 & 77.64 & 73.71 & \\\\\n & Compression-Tokens (Bidirectional) & & 88.52 & 87.14 & 85.32 & 84.63 & 78.15 & 73.59 & \\\\\n & Mean-Pooling & & 89.09 & 86.99 & 84.95 & 85.27 & 75.30 & 74.29 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 82.13 & & & & & & & 31.14 \\\\\n & Compression-Tokens (Causal) & & 84.40 & 79.82 & 75.47 & 74.28 & 65.03 & 67.58 & \\\\\n & Compression-Tokens (Bidirectional) & & 83.72 & 84.18 & 78.94 & 73.03 & 64.83 & 68.57 & \\\\\n & Mean-Pooling & & 84.87 & 83.62 & 73.95 & 76.02 & 62.02 & 60.28 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{TriviaQA Verified $F_1$.}\n \\label{tab:primary_results_triviaqa}\n\\end{table}\n\\newpage\n\\begin{table}[!ht]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 32.79 & & 19.56 & & 18.76 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 27.34 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 42.51 & & 35.36 & & 26.44 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 44.09 & & 33.39 & & 27.52 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 60.44 & & & & & & & 19.15 \\\\\n & Compression-Tokens (Causal) & & 47.26 & 45.97 & 36.35 & 39.16 & 32.42 & 31.15 & \\\\\n & Compression-Tokens (Bidirectional) & & 51.46 & 51.51 & 40.05 & 42.51 & 32.54 & 32.69 & \\\\\n & Mean-Pooling & & 53.71 & 53.32 & 42.55 & 45.07 & 32.52 & 31.36 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 57.04 & & & & & & & 17.38 \\\\\n & Compression-Tokens (Causal) & & 45.07 & 43.44 & 34.61 & 34.34 & 28.95 & 26.25 & \\\\\n & Compression-Tokens (Bidirectional) & & 45.35 & 47.93 & 36.32 & 38.23 & 28.17 & 27.88 & \\\\\n & Mean-Pooling & & 51.47 & 48.49 & 40.36 & 39.09 & 28.84 & 27.31 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 46.62 & & & & & & & 14.86 \\\\\n & Compression-Tokens (Causal) & & 30.09 & 34.01 & 29.29 & 29.47 & 22.27 & 22.82 & \\\\\n & Compression-Tokens (Bidirectional) & & 37.92 & 37.00 & 29.72 & 31.44 & 22.43 & 21.05 & \\\\\n & Mean-Pooling & & 42.14 & 39.78 & 32.33 & 32.46 & 22.01 & 22.18 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 39.04 & & & & & & & 10.97 \\\\\n & Compression-Tokens (Causal) & & 29.69 & 28.58 & 23.55 & 23.95 & 18.80 & 19.46 & \\\\\n & Compression-Tokens (Bidirectional) & & 29.16 & 33.06 & 25.47 & 26.99 & 19.60 & 18.80 & \\\\\n & Mean-Pooling & & 33.84 & 32.70 & 26.11 & 26.21 & 19.52 & 18.08 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 51.45 & & & & & & & 16.76 \\\\\n & Compression-Tokens (Causal) & & 39.83 & 40.80 & 33.93 & 35.23 & 28.83 & 29.06 & \\\\\n & Compression-Tokens (Bidirectional) & & 40.76 & 41.96 & 34.73 & 35.52 & 29.47 & 27.27 & \\\\\n & Mean-Pooling & & 45.61 & 44.88 & 37.14 & 36.88 & 28.70 & 28.94 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 39.75 & & & & & & & 14.30 \\\\\n & Compression-Tokens (Causal) & & 30.58 & 29.42 & 26.27 & 26.66 & 21.04 & 21.63 & \\\\\n & Compression-Tokens (Bidirectional) & & 31.71 & 30.30 & 25.77 & 28.88 & 23.74 & 20.71 & \\\\\n & Mean-Pooling & & 34.84 & 33.60 & 27.18 & 27.29 & 21.21 & 20.46 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{AdversarialQA $F_1$.}\n \\label{tab:primary_results_adversarial_qa}\n\\end{table}\n\\newpage\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 27.42 & & 15.32 & & 7.56 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 28.42 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 46.31 & & 33.25 & & 18.14 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 46.77 & & 31.17 & & 17.95 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 56.77 & & & & & & & 7.49 \\\\\n & Compression-Tokens (Causal) & & 49.69 & 48.77 & 40.37 & 41.71 & 30.94 & 28.40 & \\\\\n & Compression-Tokens (Bidirectional) & & 51.65 & 51.68 & 44.91 & 45.85 & 31.40 & 31.07 & \\\\\n & Mean-Pooling & & 55.36 & 53.87 & 48.95 & 48.63 & 31.79 & 29.12 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 56.14 & & & & & & & 6.59 \\\\\n & Compression-Tokens (Causal) & & 47.85 & 46.50 & 40.73 & 40.49 & 28.86 & 27.16 & \\\\\n & Compression-Tokens (Bidirectional) & & 49.63 & 50.74 & 42.98 & 44.60 & 27.72 & 28.07 & \\\\\n & Mean-Pooling & & 54.74 & 53.24 & 46.93 & 47.01 & 29.95 & 26.25 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 54.75 & & & & & & & 5.09 \\\\\n & Compression-Tokens (Causal) & & 37.53 & 43.23 & 36.08 & 35.38 & 24.47 & 22.71 & \\\\\n & Compression-Tokens (Bidirectional) & & 46.33 & 47.36 & 39.28 & 39.72 & 24.81 & 23.81 & \\\\\n & Mean-Pooling & & 52.04 & 50.67 & 42.90 & 42.55 & 25.16 & 22.02 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 51.54 & & & & & & & 4.82 \\\\\n & Compression-Tokens (Causal) & & 42.04 & 39.38 & 32.91 & 31.36 & 20.07 & 19.73 & \\\\\n & Compression-Tokens (Bidirectional) & & 43.34 & 43.74 & 34.15 & 35.77 & 21.12 & 19.16 & \\\\\n & Mean-Pooling & & 48.26 & 46.29 & 38.13 & 37.81 & 21.24 & 17.03 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 56.00 & & & & & & & 7.10 \\\\\n & Compression-Tokens (Causal) & & 48.10 & 46.86 & 41.66 & 40.33 & 29.30 & 27.74 & \\\\\n & Compression-Tokens (Bidirectional) & & 49.36 & 49.83 & 42.30 & 43.72 & 29.85 & 28.81 & \\\\\n & Mean-Pooling & & 54.39 & 53.39 & 47.82 & 47.83 & 31.16 & 28.91 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 52.26 & & & & & & & 5.94 \\\\\n & Compression-Tokens (Causal) & & 41.97 & 40.07 & 35.08 & 35.24 & 22.50 & 23.14 & \\\\\n & Compression-Tokens (Bidirectional) & & 44.58 & 44.02 & 36.36 & 38.77 & 23.84 & 23.88 & \\\\\n & Mean-Pooling & & 49.90 & 46.92 & 33.84 & 39.59 & 17.67 & 21.17 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{ParaphraseRC $F_1$.}\n \\label{tab:primary_results_paraphrase_rc}\n\\end{table}\n\\newpage\n\\section{LLM Usage}\\label{app:llm}\nLLMs (specifically, ChatGPT) were used in the process of writing this paper for creating tables and figures, as well as proof-reading.\n\n\\end{document}\n"},"question":{"kind":"string","value":"Across the proposed methods using 4×Single training only, for each base model select the method whose score is closest to the midpoint between its Original and No Ctx scores. Among these selected methods, which (model, method) achieves the highest 16× Multi score, and what is the difference between 16×Multi and 128×Single for that same method?"},"answer":{"kind":"string","value":"Qwen3-8B, Compression-Tokens (Causal), 10.94"},"plan":{"kind":"string","value":"SELECT all base models\nLOOP for each base model\n COMPUTE midpoint = average(Original score, No Ctx score)\n SELECT all methods of this base model under 4× Single\n LOOP for each method\n COMPUTE distance_to_midpoint = absolute(4× Single score − midpoint)\n COMPUTE selected_method = argmin method over distance_to_midpoint\n\n\nSELECT all selected_methods\nCOMPUTE best_method = argmax method over 16× Multi score of selected_methods\n\n\nCOMPUTE difference = best_method 16× Multi score − best_method 128× Single score\n\n\nRETURN base_model of best_method, best_method, difference\n"}}},{"rowIdx":358,"cells":{"paper":{"kind":"string","value":"2510.20797"},"relevant_tables":{"kind":"list like","value":[["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 30.02 & & 16.16 & & 16.06 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 24.94 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 48.81 & & 38.38 & & 25.94 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 49.34 & & 36.64 & & 27.92 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 59.82 & & & & & & & 16.19 \\\\\n"," & Compression-Tokens (Causal) & & 51.59 & 50.01 & 41.26 & 42.99 & 34.21 & 32.50 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 53.44 & 53.99 & 44.92 & 47.15 & 33.60 & 34.27 & \\\\\n"," & Mean-Pooling & & 56.41 & 55.04 & 47.95 & 49.02 & 34.72 & 33.15 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 58.87 & & & & & & & 13.74 \\\\\n"," & Compression-Tokens (Causal) & & 49.66 & 46.26 & 40.05 & 39.59 & 30.07 & 28.84 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 51.06 & 52.37 & 42.53 & 45.14 & 28.84 & 29.51 & \\\\\n"," & Mean-Pooling & & 55.25 & 53.77 & 45.43 & 45.86 & 30.91 & 28.38 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 55.19 & & & & & & & 9.07 \\\\\n"," & Compression-Tokens (Causal) & & 36.66 & 41.64 & 35.49 & 34.64 & 24.27 & 24.04 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 46.45 & 46.72 & 36.62 & 38.93 & 24.31 & 24.33 & \\\\\n"," & Mean-Pooling & & 51.28 & 48.77 & 40.45 & 39.04 & 25.15 & 22.01 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 50.85 & & & & & & & 4.78 \\\\\n"," & Compression-Tokens (Causal) & & 39.66 & 36.76 & 27.99 & 29.00 & 18.23 & 18.20 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 40.98 & 41.92 & 30.92 & 33.64 & 18.82 & 18.55 & \\\\\n"," & Mean-Pooling & & 45.82 & 43.07 & 32.50 & 33.09 & 19.05 & 16.07 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 57.63 & & & & & & & 15.00 \\\\\n"," & Compression-Tokens (Causal) & & 47.90 & 45.98 & 39.57 & 39.74 & 32.02 & 29.66 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 49.43 & 49.40 & 40.89 & 42.70 & 31.79 & 30.43 & \\\\\n"," & Mean-Pooling & & 54.20 & 52.77 & 45.88 & 45.68 & 32.41 & 30.83 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 51.67 & & & & & & & 9.47 \\\\\n"," & Compression-Tokens (Causal) & & 41.84 & 39.03 & 33.73 & 33.38 & 24.11 & 24.64 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 43.46 & 42.96 & 35.04 & 35.46 & 24.91 & 24.56 & \\\\\n"," & Mean-Pooling & & 47.97 & 45.45 & 33.15 & 36.93 & 22.89 & 22.70 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{Primary results with exact match (EM) as the metric.}\n"," \\label{tab:primary_results_EM}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 33.63 & & 18.30 & & 17.36 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 49.18 & & & & & & \\\\\n","& \\emph{PISCO} (Llama3.1-8B) & & & & 53.62 & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 54.05 & & 43.67 & & 30.03 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 55.17 & & 41.79 & & 30.10 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.84 & & & & & & & 17.98 \\\\\n"," & Compression-Tokens (Causal) & & 59.79 & 58.58 & 47.07 & 49.99 & 39.09 & 37.05 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 62.50 & 63.58 & 52.22 & 55.26 & 38.72 & 39.36 & \\\\\n"," & Mean-Pooling & & 65.91 & 65.06 & 55.68 & 56.77 & 39.95 & 37.80 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.69 & & & & & & & 15.00 \\\\\n"," & Compression-Tokens (Causal) & & 57.12 & 54.17 & 46.06 & 45.47 & 34.83 & 33.48 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 59.35 & 60.99 & 48.92 & 52.23 & 33.20 & 34.33 & \\\\\n"," & Mean-Pooling & & 64.05 & 62.94 & 52.77 & 52.82 & 35.49 & 32.37 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.21 & & & & & & & 9.85 \\\\\n"," & Compression-Tokens (Causal) & & 43.01 & 49.31 & 41.31 & 40.45 & 28.45 & 27.90 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 54.31 & 54.70 & 42.66 & 45.13 & 28.33 & 28.04 & \\\\\n"," & Mean-Pooling & & 60.03 & 57.28 & 46.63 & 45.07 & 28.96 & 25.82 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 59.67 & & & & & & & 5.62 \\\\\n"," & Compression-Tokens (Causal) & & 46.36 & 43.62 & 33.07 & 34.30 & 21.13 & 21.71 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 48.04 & 48.84 & 36.11 & 39.50 & 22.13 & 22.00 & \\\\\n"," & Mean-Pooling & & 54.36 & 51.16 & 38.30 & 38.68 & 22.44 & 18.87 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.14 & & & & & & & 16.80 \\\\\n"," & Compression-Tokens (Causal) & & 55.50 & 52.94 & 46.13 & 45.59 & 36.14 & 33.94 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 56.94 & 57.54 & 46.90 & 49.52 & 36.14 & 34.75 & \\\\\n"," & Mean-Pooling & & 62.51 & 61.28 & 52.55 & 51.90 & 36.61 & 34.93 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 60.30 & & & & & & & 11.09 \\\\\n"," & Compression-Tokens (Causal) & & 48.85 & 45.41 & 39.16 & 38.51 & 27.54 & 28.01 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 50.89 & 50.10 & 40.44 & 41.91 & 28.34 & 28.44 & \\\\\n"," & Mean-Pooling & & 56.62 & 53.50 & 38.84 & 42.76 & 25.99 & 26.19 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{Primary results with accuracy as the metric.}\n"," \\label{tab:primary_results_accuracy}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 30.02 & & 16.16 & & 16.06 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 24.94 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 48.81 & & 38.38 & & 25.94 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 49.34 & & 36.64 & & 27.92 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 59.82 & & & & & & & 16.19 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 51.59 & 50.01 & 41.26 & 42.99 & 34.21 & 32.50 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 53.44 & 53.99 & 44.92 & 47.15 & 33.60 & 34.27 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 56.41 & 55.04 & 47.95 & 49.02 & 34.72 & 33.15 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 58.87 & & & & & & & 13.74 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 49.66 & 46.26 & 40.05 & 39.59 & 30.07 & 28.84 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 51.06 & 52.37 & 42.53 & 45.14 & 28.84 & 29.51 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 55.25 & 53.77 & 45.43 & 45.86 & 30.91 & 28.38 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 55.19 & & & & & & & 9.07 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 36.66 & 41.64 & 35.49 & 34.64 & 24.27 & 24.04 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 46.45 & 46.72 & 36.62 & 38.93 & 24.31 & 24.33 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 51.28 & 48.77 & 40.45 & 39.04 & 25.15 & 22.01 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 50.85 & & & & & & & 4.78 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 39.66 & 36.76 & 27.99 & 29.00 & 18.23 & 18.20 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 40.98 & 41.92 & 30.92 & 33.64 & 18.82 & 18.55 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 45.82 & 43.07 & 32.50 & 33.09 & 19.05 & 16.07 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 57.63 & & & & & & & 15.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 47.90 & 45.98 & 39.57 & 39.74 & 32.02 & 29.66 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 49.43 & 49.40 & 40.89 & 42.70 & 31.79 & 30.43 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.20 & 52.77 & 45.88 & 45.68 & 32.41 & 30.83 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 51.67 & & & & & & & 9.47 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 41.84 & 39.03 & 33.73 & 33.38 & 24.11 & 24.64 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 43.46 & 42.96 & 35.04 & 35.46 & 24.91 & 24.56 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 47.97 & 45.45 & 33.15 & 36.93 & 22.89 & 22.70 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{Primary results with exact match (EM) as the metric.}\\n\",\n \" \\\\label{tab:primary_results_EM}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 33.63 & & 18.30 & & 17.36 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 49.18 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PISCO} (Llama3.1-8B) & & & & 53.62 & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 54.05 & & 43.67 & & 30.03 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 55.17 & & 41.79 & & 30.10 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 68.84 & & & & & & & 17.98 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 59.79 & 58.58 & 47.07 & 49.99 & 39.09 & 37.05 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 62.50 & 63.58 & 52.22 & 55.26 & 38.72 & 39.36 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 65.91 & 65.06 & 55.68 & 56.77 & 39.95 & 37.80 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 67.69 & & & & & & & 15.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 57.12 & 54.17 & 46.06 & 45.47 & 34.83 & 33.48 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 59.35 & 60.99 & 48.92 & 52.23 & 33.20 & 34.33 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 64.05 & 62.94 & 52.77 & 52.82 & 35.49 & 32.37 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 64.21 & & & & & & & 9.85 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 43.01 & 49.31 & 41.31 & 40.45 & 28.45 & 27.90 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 54.31 & 54.70 & 42.66 & 45.13 & 28.33 & 28.04 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 60.03 & 57.28 & 46.63 & 45.07 & 28.96 & 25.82 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 59.67 & & & & & & & 5.62 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 46.36 & 43.62 & 33.07 & 34.30 & 21.13 & 21.71 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 48.04 & 48.84 & 36.11 & 39.50 & 22.13 & 22.00 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.36 & 51.16 & 38.30 & 38.68 & 22.44 & 18.87 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 66.14 & & & & & & & 16.80 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 55.50 & 52.94 & 46.13 & 45.59 & 36.14 & 33.94 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 56.94 & 57.54 & 46.90 & 49.52 & 36.14 & 34.75 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 62.51 & 61.28 & 52.55 & 51.90 & 36.61 & 34.93 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 60.30 & & & & & & & 11.09 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.85 & 45.41 & 39.16 & 38.51 & 27.54 & 28.01 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 50.89 & 50.10 & 40.44 & 41.91 & 28.34 & 28.44 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 56.62 & 53.50 & 38.84 & 42.76 & 25.99 & 26.19 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{Primary results with accuracy as the metric.}\\n\",\n \" \\\\label{tab:primary_results_accuracy}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t]\n"," \\centering\n"," \n"," \\def\\uniformscale{0.23} %\n"," \n"," \\newlength{\\fixedheight}\n"," \\setlength{\\fixedheight}{5.3cm}\n"," \n"," \\begin{subfigure}[t]{0.31\\textwidth}\n"," \\centering\n"," \\vbox to \\fixedheight{%\n"," \\includegraphics[page=1, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n"," \\vfill\n"," }\n"," \\caption{Processing with a regular language model (no compression).}\n"," \\label{fig:arch:regular_llm}\n"," \\end{subfigure}\n"," \\hfill\n"," \\begin{minipage}[t]{0.02\\textwidth}\n"," \\centering\n"," \\rule[0pt]{0pt}{\\fixedheight}%\n"," \\begin{tikzpicture}\n"," \\draw[dashed, gray, very thin] (0,0) -- (0,\\fixedheight);\n"," \\end{tikzpicture}\n"," \\end{minipage}%\n"," \\hfill\n"," \\begin{subfigure}[t]{0.31\\textwidth}\n"," \\centering\n"," \\vbox to \\fixedheight{%\n"," \\includegraphics[page=2, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n"," \\vfill\n"," }\n"," \\caption{Compression tokens approach for context compression.}\n"," \\label{fig:arch:tokens}\n"," \\end{subfigure}\n"," \\hfill\n"," \\begin{minipage}[t]{0.02\\textwidth}\n"," \\centering\n"," \\rule[0pt]{0pt}{\\fixedheight}%\n"," \\begin{tikzpicture}\n"," \\draw[dashed, gray, very thin] (0,0) -- (0,\\fixedheight);\n"," \\end{tikzpicture}\n"," \\end{minipage}%\n"," \\hfill\n"," \\begin{subfigure}[t]{0.31\\textwidth}\n"," \\centering\n"," \\vbox to \\fixedheight{%\n"," \\includegraphics[page=3, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n"," \\vfill\n"," }\n"," \\caption{Our proposed method: no extra tokens; mean pooling of final hidden states.}\n"," \\label{fig:arch:pool}\n"," \\end{subfigure}\n"," \n"," \\caption{Comparison of context processing methods: regular LM, compression tokens, and our proposed approach --- mean pooling. The figure illustrates a compression ratio of $4\\times$.}\n"," \\label{fig:arch}\n","\\end{figure}\n"],["\\begin{table*}[!ht]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 42.52 & & 24.39 & & 22.59 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 42.40 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 62.08 & & 51.30 & & 36.20 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 62.98 & & 49.37 & & 37.24 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 74.33 & & & & & & & 23.06 \\\\\n"," & Compression-Tokens (Causal) & & 67.03 & 65.90 & 56.21 & 58.41 & 47.47 & 44.76 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 69.20 & 69.57 & 60.27 & 63.01 & 46.93 & \\textbf{46.97} & \\\\\n"," & Mean-Pooling & & \\textbf{71.66} & \\textbf{70.55} & \\textbf{63.85} & \\textbf{64.67} & \\textbf{47.90} & 45.92 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 73.44 & & & & & & & 19.79 \\\\\n"," & Compression-Tokens (Causal) & & 64.88 & 62.53 & 55.22 & 54.28 & 43.08 & 40.83 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 66.72 & 68.15 & 57.68 & 60.48 & 41.61 & \\textbf{42.66} & \\\\\n"," & Mean-Pooling & & \\textbf{70.39} & \\textbf{69.36} & \\textbf{61.79} & \\textbf{61.72} & \\textbf{43.62} & 41.05 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 69.93 & & & & & & & 14.00 \\\\\n"," & Compression-Tokens (Causal) & & 50.90 & 57.73 & 49.83 & 48.68 & 36.19 & 35.34 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 62.04 & 62.60 & 51.53 & 54.11 & 36.25 & \\textbf{35.77} & \\\\\n"," & Mean-Pooling & & \\textbf{66.43} & \\textbf{64.17} & \\textbf{55.43} & \\textbf{54.47} & \\textbf{36.72} & 33.48 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 65.36 & & & & & & & 9.34 \\\\\n"," & Compression-Tokens (Causal) & & 54.40 & 51.85 & 41.57 & 42.59 & 28.86 & 28.60 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 55.59 & 57.03 & 44.82 & 47.62 & 29.69 & \\textbf{29.51} & \\\\\n"," & Mean-Pooling & & \\textbf{61.17} & \\textbf{58.36} & \\textbf{47.59} & \\textbf{47.64} & \\textbf{29.94} & 26.36 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 71.96 & & & & & & & 21.64 \\\\\n"," & Compression-Tokens (Causal) & & 63.35 & 62.18 & 55.07 & 54.70 & 44.46 & 42.49 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 64.76 & 65.24 & 56.39 & 58.43 & 44.73 & 43.17 & \\\\\n"," & Mean-Pooling & & \\textbf{69.33} & \\textbf{68.09} & \\textbf{61.39} & \\textbf{61.04} & \\textbf{44.98} & \\textbf{43.71} & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 65.82 & & & & & & & 15.17 \\\\\n"," & Compression-Tokens (Causal) & & 56.31 & 53.74 & 47.51 & 46.96 & 35.41 & 35.62 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 57.91 & 57.52 & \\textbf{49.20} & 50.06 & \\textbf{36.43} & \\textbf{36.25} & \\\\\n"," & Mean-Pooling & & \\textbf{62.81} & \\textbf{60.56} & 47.28 & \\textbf{51.56} & 33.25 & 33.98 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}}\n","\\medskip\n","\\includegraphics[width=\\textwidth]{figures/methods_ratios_comparison.pdf}\n","\\caption{\n","Primary results. Values in the table are $F_1$ scores macro-averaged across all datasets in our evaluation suite. \n","\\textbf{Original} stands for the teacher model's score when given the full context. \\textbf{No Ctx} stands for the teacher model's score when not given any context at all. For each ratio, we display both single- and multi-ratio versions. For the baseline systems (top section), we include results for the compression ratios supported by these methods, unsupported ratios are left blank. The best method for each (model, ratio, single/multi-ratio training) setting is \\textbf{bolded}.\n","Bottom figures present aggregated views of the results in the table, but instead of $F_1$ show the teacher-normalized $F_1$ metric (Relative F1). Scores are obtained by averaging over all models listed in the table. \n","}\\label{tab:primary_results_hybrid_transpose}\n","\\end{table*}\n"],["\\begin{figure}[htb]\n"," \\centering\n"," \\includegraphics[width=0.6\\linewidth]{figures/scaling_law_qwen3.pdf}\n"," \\caption{Compression Scaling. We show the teacher-normalized $F_1$ scores (Relative F1) across four Qwen3 model scales. The scores are averages of the scores of all datasets. We can clearly observe the benefits of scaling for LLM compressors.}\n"," \\label{fig:scaling_law}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\begin{subfigure}[t]{0.95\\linewidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{figures/in_vs_out_fig.pdf}\n"," \\caption{In-domain vs.\\ out-of-domain performance across compression ratios.}\n"," \\label{fig:in-vs-out}\n"," \\end{subfigure}\n","\n"," \\vspace{0.8em} %\n","\n"," \\begin{subfigure}[t]{0.95\\linewidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{figures/in_out_gap_fig.pdf}\n"," \\caption{Performance drop (in–out gap) per method across compression ratios (in teacher-normalized Relative $F_1$ units). Higher values mean a larger domain performance gap. Negative values mean that the out-of-domain performance is better than in-domain performance.}\n"," \\label{fig:in-out-gap}\n"," \\end{subfigure}\n","\n"," \\caption{In-domain and out-of-domain comparison. (a) Line plots show performance on in-domain vs.\\ out-of-domain datasets. (b) Bar plots show the in–out performance gap per method, which is the difference between in-domain and out-of-domain teacher-normalized $F_1$ scores.}\n"," \\label{fig:in-out-combined}\n","\\end{figure}\n"],["\\begin{table}[t]\n","\\centering\n","\\resizebox{0.92\\linewidth}{!}{%\n","\\begin{tabular}{l r r r r r r c}\n","\\toprule\n","\\textbf{Ablation} (\\textsc{Gemma2-2B}) & 4$\\times$ & 8$\\times$ & 16$\\times$ & 32$\\times$ & 64$\\times$ & 128$\\times$ & $\\Delta$ \\\\\n","\\midrule\n","Default & \\textbf{68.1} & \\textbf{65.4} & \\textbf{61.0} & \\textbf{54.9} & \\textbf{48.8} & \\textbf{43.7} & \\,($+0.0$) \\\\\n","Fixed Decoder & 64.9 & 61.9 & 57.0 & 51.5 & 45.0 & 39.8 & \\,($-3.6$) \\\\\n","Fixed Encoder & 57.4 & 49.9 & 44.1 & 39.8 & 36.2 & 34.8 & \\,($-13.3$) \\\\\n","No Encoder & 58.7 & 51.9 & 44.9 & 40.2 & 36.2 & 34.1 & \\,($-12.6$) \\\\\n","w/o Linear Layer & 67.7 & 64.5 & 60.0 & 54.1 & 48.1 & 43.2 & \\,($-0.7$) \\\\\n","Ratio Sampling & 67.1 & 64.0 & 59.3 & 53.5 & 47.5 & 42.2 & \\,($-1.4$) \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Ablation study for mean pooling using \\textsc{Gemma2-2B} as the teacher LLM. Numbers are macro-averaged $F_1$ scores. \\emph{$\\Delta$}: mean change vs. Default across ratios; \\textbf{bold} = best per column.}\n","\\label{tab:abl_gemma2_mean}\n","\\end{table}\n"],["\\begin{table}[H]\n","\\centering\n","\\begin{tabular}{lrrr}\n","\\toprule\n","Dataset & Avg. Context Tokens & \\#Samples & \\#Contexts \\\\\n","\\midrule\n","\\multicolumn{4}{l}{\\textbf{Summarization}} \\\\\n","CNN/DM~\\citep{see-etal-2017-get_cnndm} & 649 & 198{,}732 & 196{,}601 \\\\\n","DialogSum~\\citep{chen-etal-2021-dialogsum} & 208 & 12{,}452 & 12{,}450 \\\\\n","SAMSum~\\citep{Gliwa_2019_samsum} & 145 & 14{,}730 & 14{,}254 \\\\\n","XSum~\\citep{narayan-etal-2018-dont_xsum} & 408 & 185{,}760 & 185{,}566 \\\\\n","\\addlinespace\n","\\multicolumn{4}{l}{\\textbf{Reading Comprehension}} \\\\\n","BoolQ~\\citep{clark-etal-2019-boolq} & 126 & 9{,}427 & 7{,}927 \\\\\n","DROP~\\citep{dua-etal-2019-drop} & 295 & 76{,}751 & 5{,}477 \\\\\n","HotpotQA~\\citep{yang-etal-2018-hotpotqa} & 247 & 90{,}327 & 84{,}705 \\\\\n","NarrativeQA~\\citep{kocisky-etal-2018-narrativeqa} & 668 & 28{,}299 & 953 \\\\\n","PubMedQA~\\citep{jin-etal-2019-pubmedqa} & 318 & 211{,}218 & 211{,}164 \\\\\n","QuAC~\\citep{choi-etal-2018-quac} & 515 & 81{,}391 & 6{,}574 \\\\\n","QuAIL~\\citep{rogers2020getting_quail} & 416 & 10{,}246 & 560 \\\\\n","RACE~\\citep{lai-etal-2017-race} & 349 & 87{,}749 & 25{,}108 \\\\\n","SQuAD~\\citep{rajpurkar-etal-2016-squad} & 162 & 86{,}821 & 18{,}877 \\\\\n","PWC~\\citep{ge2024incontext} & 477 & 241{,}563 & 16{,}382 \\\\\n","\\midrule\n","\\textbf{Total} & \\textbf{410} & \\textbf{1,335,466} & \\textbf{786,598} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\caption{Training datasets with average context length (tokens), number of samples, number of distinct contexts, and task category. The overall average context length is weighted by the number of samples.}\n","\\label{tab:training_datasets}\n","\\end{table}\n"],["\\begin{table}[H]\n","\\centering\n","\\begin{tabular}{lrrr}\n","\\toprule\n","Dataset & Avg. Context Tokens & \\#Samples & \\#Contexts \\\\\n","\\midrule\n","AdversarialQA~\\citep{bartolo2020beat_adversarialqa} & 154 & 1{,}000 & 341 \\\\\n","HotpotQA~\\citep{yang-etal-2018-hotpotqa} & 254 & 7{,}394 & 7{,}352 \\\\\n","NarrativeQA~\\citep{kocisky-etal-2018-narrativeqa} & 639 & 3{,}002 & 100 \\\\\n","ParaphraseRC~\\citep{saha-etal-2018-duorc} & 685 & 4{,}835 & 560 \\\\\n","SQuAD~\\citep{rajpurkar-etal-2016-squad} & 169 & 5{,}928 & 1{,}204 \\\\\n","TriviaQA (Verified)~\\citep{joshi-etal-2017-triviaqa} & 539 & 185 & 185 \\\\\n","\\midrule\n","\\textbf{Total} & \\textbf{375} & \\textbf{22{,}344} & \\textbf{9{,}742} \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\caption{Evaluation datasets with average context length (tokens), number of samples, and number of distinct contexts. The overall average context length is weighted by the number of samples.}\n","\\label{tab:evaluation_datasets}\n","\\end{table}\n"],["\\begin{table}[ht!]\n"," \\centering\n"," \\begin{tabular}{cc}\n"," \\toprule\n"," \\textbf{Hyperparameter} & \\textbf{Value} \\\\\n"," \\midrule\n"," LoRA $r$ & 16 \\\\\n"," LoRA $\\alpha$ & 16 \\\\ \n"," optimizer & AdamW \\\\\n"," $\\beta_1$ & 0.9 \\\\\n"," $\\beta_2$ & 0.95 \\\\\n"," clip norm & 1 \\\\\n"," peak learning rate & 2e-4 \\\\\n"," final learning rate & 2e-5 \\\\\n"," lr scheduler type & cosine \\\\\n"," warmup ratio & 0.05 \\\\\n"," weight decay & 0.0 \\\\\n"," steps & 48,000 \\\\\n"," batch size & 32 \\\\\n"," max context length & 1024 \\\\\n"," max answer tokens & 256 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," \\caption{Hyperparameters for training all the models used in this work.} \n"," \\label{table:hyperparameters}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 30.02 & & 16.16 & & 16.06 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 24.94 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 48.81 & & 38.38 & & 25.94 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 49.34 & & 36.64 & & 27.92 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 59.82 & & & & & & & 16.19 \\\\\n"," & Compression-Tokens (Causal) & & 51.59 & 50.01 & 41.26 & 42.99 & 34.21 & 32.50 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 53.44 & 53.99 & 44.92 & 47.15 & 33.60 & 34.27 & \\\\\n"," & Mean-Pooling & & 56.41 & 55.04 & 47.95 & 49.02 & 34.72 & 33.15 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 58.87 & & & & & & & 13.74 \\\\\n"," & Compression-Tokens (Causal) & & 49.66 & 46.26 & 40.05 & 39.59 & 30.07 & 28.84 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 51.06 & 52.37 & 42.53 & 45.14 & 28.84 & 29.51 & \\\\\n"," & Mean-Pooling & & 55.25 & 53.77 & 45.43 & 45.86 & 30.91 & 28.38 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 55.19 & & & & & & & 9.07 \\\\\n"," & Compression-Tokens (Causal) & & 36.66 & 41.64 & 35.49 & 34.64 & 24.27 & 24.04 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 46.45 & 46.72 & 36.62 & 38.93 & 24.31 & 24.33 & \\\\\n"," & Mean-Pooling & & 51.28 & 48.77 & 40.45 & 39.04 & 25.15 & 22.01 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 50.85 & & & & & & & 4.78 \\\\\n"," & Compression-Tokens (Causal) & & 39.66 & 36.76 & 27.99 & 29.00 & 18.23 & 18.20 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 40.98 & 41.92 & 30.92 & 33.64 & 18.82 & 18.55 & \\\\\n"," & Mean-Pooling & & 45.82 & 43.07 & 32.50 & 33.09 & 19.05 & 16.07 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 57.63 & & & & & & & 15.00 \\\\\n"," & Compression-Tokens (Causal) & & 47.90 & 45.98 & 39.57 & 39.74 & 32.02 & 29.66 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 49.43 & 49.40 & 40.89 & 42.70 & 31.79 & 30.43 & \\\\\n"," & Mean-Pooling & & 54.20 & 52.77 & 45.88 & 45.68 & 32.41 & 30.83 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 51.67 & & & & & & & 9.47 \\\\\n"," & Compression-Tokens (Causal) & & 41.84 & 39.03 & 33.73 & 33.38 & 24.11 & 24.64 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 43.46 & 42.96 & 35.04 & 35.46 & 24.91 & 24.56 & \\\\\n"," & Mean-Pooling & & 47.97 & 45.45 & 33.15 & 36.93 & 22.89 & 22.70 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{Primary results with exact match (EM) as the metric.}\n"," \\label{tab:primary_results_EM}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 33.63 & & 18.30 & & 17.36 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 49.18 & & & & & & \\\\\n","& \\emph{PISCO} (Llama3.1-8B) & & & & 53.62 & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 54.05 & & 43.67 & & 30.03 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 55.17 & & 41.79 & & 30.10 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.84 & & & & & & & 17.98 \\\\\n"," & Compression-Tokens (Causal) & & 59.79 & 58.58 & 47.07 & 49.99 & 39.09 & 37.05 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 62.50 & 63.58 & 52.22 & 55.26 & 38.72 & 39.36 & \\\\\n"," & Mean-Pooling & & 65.91 & 65.06 & 55.68 & 56.77 & 39.95 & 37.80 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.69 & & & & & & & 15.00 \\\\\n"," & Compression-Tokens (Causal) & & 57.12 & 54.17 & 46.06 & 45.47 & 34.83 & 33.48 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 59.35 & 60.99 & 48.92 & 52.23 & 33.20 & 34.33 & \\\\\n"," & Mean-Pooling & & 64.05 & 62.94 & 52.77 & 52.82 & 35.49 & 32.37 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.21 & & & & & & & 9.85 \\\\\n"," & Compression-Tokens (Causal) & & 43.01 & 49.31 & 41.31 & 40.45 & 28.45 & 27.90 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 54.31 & 54.70 & 42.66 & 45.13 & 28.33 & 28.04 & \\\\\n"," & Mean-Pooling & & 60.03 & 57.28 & 46.63 & 45.07 & 28.96 & 25.82 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 59.67 & & & & & & & 5.62 \\\\\n"," & Compression-Tokens (Causal) & & 46.36 & 43.62 & 33.07 & 34.30 & 21.13 & 21.71 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 48.04 & 48.84 & 36.11 & 39.50 & 22.13 & 22.00 & \\\\\n"," & Mean-Pooling & & 54.36 & 51.16 & 38.30 & 38.68 & 22.44 & 18.87 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.14 & & & & & & & 16.80 \\\\\n"," & Compression-Tokens (Causal) & & 55.50 & 52.94 & 46.13 & 45.59 & 36.14 & 33.94 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 56.94 & 57.54 & 46.90 & 49.52 & 36.14 & 34.75 & \\\\\n"," & Mean-Pooling & & 62.51 & 61.28 & 52.55 & 51.90 & 36.61 & 34.93 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 60.30 & & & & & & & 11.09 \\\\\n"," & Compression-Tokens (Causal) & & 48.85 & 45.41 & 39.16 & 38.51 & 27.54 & 28.01 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 50.89 & 50.10 & 40.44 & 41.91 & 28.34 & 28.44 & \\\\\n"," & Mean-Pooling & & 56.62 & 53.50 & 38.84 & 42.76 & 25.99 & 26.19 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{Primary results with accuracy as the metric.}\n"," \\label{tab:primary_results_accuracy}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 48.38 & & 21.34 & & 19.68 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 45.6 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 78.38 & & 67.63 & & 40.22 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 79.56 & & 62.93 & & 41.23 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 86.48 & & & & & & & 20.31 \\\\\n"," & Compression-Tokens (Causal) & & 77.11 & 74.89 & 57.05 & 62.12 & 44.56 & 42.35 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 80.00 & 81.23 & 64.80 & 69.27 & 44.30 & 43.86 & \\\\\n"," & Mean-Pooling & & 83.76 & 82.75 & 71.37 & 71.19 & 44.65 & 43.19 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 85.75 & & & & & & & 17.72 \\\\\n"," & Compression-Tokens (Causal) & & 74.23 & 71.31 & 57.49 & 56.88 & 38.95 & 37.10 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 77.24 & 79.28 & 60.71 & 65.49 & 38.19 & 38.41 & \\\\\n"," & Mean-Pooling & & 83.19 & 81.54 & 68.20 & 67.47 & 39.96 & 37.54 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 83.65 & & & & & & & 12.66 \\\\\n"," & Compression-Tokens (Causal) & & 54.25 & 64.50 & 49.09 & 49.98 & 31.78 & 30.10 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 72.92 & 73.39 & 53.07 & 57.36 & 31.58 & 31.17 & \\\\\n"," & Mean-Pooling & & 79.56 & 77.17 & 59.01 & 58.30 & 32.36 & 29.90 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 7.91 \\\\\n"," & Compression-Tokens (Causal) & & 61.67 & 57.52 & 40.29 & 41.60 & 22.06 & 22.45 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 64.21 & 67.05 & 42.81 & 46.68 & 22.09 & 22.36 & \\\\\n"," & Mean-Pooling & & 74.00 & 70.60 & 48.62 & 48.14 & 22.40 & 20.45 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 84.58 & & & & & & & 16.41 \\\\\n"," & Compression-Tokens (Causal) & & 70.61 & 69.06 & 55.75 & 56.37 & 37.89 & 35.66 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 74.16 & 75.41 & 57.77 & 61.75 & 37.72 & 37.00 & \\\\\n"," & Mean-Pooling & & 81.67 & 80.01 & 66.38 & 65.64 & 38.96 & 36.71 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 81.16 & & & & & & & 11.27 \\\\\n"," & Compression-Tokens (Causal) & & 62.65 & 59.34 & 46.41 & 45.49 & 28.58 & 28.44 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 64.48 & 65.61 & 48.99 & 51.39 & 29.09 & 28.82 & \\\\\n"," & Mean-Pooling & & 74.91 & 71.40 & 47.36 & 53.66 & 28.02 & 27.91 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{SQuAD $F_1$.}\n"," \\label{tab:primary_results_squad}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 53.54 & & 29.32 & & 26.27 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 50.01 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 68.55 & & 59.38 & & 43.93 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 70.08 & & 59.05 & & 46.46 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 84.67 & & & & & & & 26.65 \\\\\n"," & Compression-Tokens (Causal) & & 78.85 & 78.32 & 68.00 & 72.65 & 64.14 & 59.74 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 80.24 & 81.45 & 73.30 & 76.77 & 63.26 & 62.44 & \\\\\n"," & Mean-Pooling & & 83.30 & 82.08 & 77.66 & 78.41 & 63.88 & 63.77 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 84.12 & & & & & & & 23.16 \\\\\n"," & Compression-Tokens (Causal) & & 76.48 & 75.56 & 68.85 & 69.80 & 59.08 & 55.78 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 78.13 & 79.41 & 71.11 & 74.60 & 58.38 & 56.87 & \\\\\n"," & Mean-Pooling & & 82.20 & 80.77 & 75.45 & 76.02 & 59.29 & 58.74 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 80.95 & & & & & & & 18.75 \\\\\n"," & Compression-Tokens (Causal) & & 66.69 & 70.98 & 63.82 & 63.84 & 51.48 & 48.78 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 73.73 & 74.93 & 66.06 & 68.50 & 52.08 & 50.77 & \\\\\n"," & Mean-Pooling & & 78.64 & 76.11 & 68.76 & 68.78 & 50.86 & 49.44 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 77.35 & & & & & & & 14.74 \\\\\n"," & Compression-Tokens (Causal) & & 66.62 & 65.76 & 55.88 & 57.79 & 43.16 & 39.58 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 67.24 & 69.28 & 58.44 & 61.79 & 43.80 & 41.66 & \\\\\n"," & Mean-Pooling & & 73.00 & 69.58 & 61.13 & 61.08 & 42.76 & 40.45 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 82.55 & & & & & & & 25.18 \\\\\n"," & Compression-Tokens (Causal) & & 75.62 & 75.54 & 69.18 & 70.42 & 61.91 & 59.03 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 76.55 & 77.60 & 69.64 & 73.51 & 61.67 & 60.46 & \\\\\n"," & Mean-Pooling & & 80.93 & 79.85 & 75.10 & 74.90 & 62.36 & 61.64 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 77.96 & & & & & & & 19.34 \\\\\n"," & Compression-Tokens (Causal) & & 69.68 & 68.22 & 63.36 & 62.96 & 52.27 & 49.81 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 70.74 & 71.01 & 64.47 & 66.19 & 53.51 & 51.79 & \\\\\n"," & Mean-Pooling & & 74.38 & 72.69 & 62.75 & 66.59 & 51.05 & 50.86 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{HotpotQA $F_1$.}\n"," \\label{tab:primary_results_hotpotqa}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 27.33 & & 14.35 & & 10.69 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 32.65 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 50.29 & & 34.16 & & 16.05 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 50.72 & & 32.56 & & 16.18 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.00 & & & & & & & 10.93 \\\\\n"," & Compression-Tokens (Causal) & & 59.62 & 58.28 & 46.58 & 49.32 & 33.41 & 29.37 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 61.44 & 62.13 & 51.48 & 55.68 & 34.17 & 33.61 & \\\\\n"," & Mean-Pooling & & 65.89 & 64.74 & 58.17 & 58.38 & 34.81 & 32.21 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.12 & & & & & & & 10.40 \\\\\n"," & Compression-Tokens (Causal) & & 57.18 & 55.08 & 46.69 & 43.77 & 30.39 & 27.84 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 58.37 & 60.74 & 48.84 & 52.41 & 29.77 & 30.22 & \\\\\n"," & Mean-Pooling & & 65.22 & 63.38 & 56.14 & 55.42 & 32.66 & 28.99 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.42 & & & & & & & 7.57 \\\\\n"," & Compression-Tokens (Causal) & & 41.97 & 49.85 & 40.15 & 39.49 & 25.42 & 23.64 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 55.68 & 56.49 & 44.87 & 47.28 & 25.16 & 26.15 & \\\\\n"," & Mean-Pooling & & 60.34 & 58.56 & 48.95 & 48.78 & 26.91 & 23.60 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 61.13 & & & & & & & 7.76 \\\\\n"," & Compression-Tokens (Causal) & & 48.09 & 46.30 & 34.68 & 36.05 & 20.10 & 20.69 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 48.04 & 50.67 & 38.85 & 40.35 & 21.29 & 21.07 & \\\\\n"," & Mean-Pooling & & 56.48 & 53.12 & 42.47 & 42.21 & 21.29 & 19.06 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.47 & & & & & & & 10.34 \\\\\n"," & Compression-Tokens (Causal) & & 56.17 & 55.78 & 47.16 & 46.68 & 31.17 & 29.72 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 59.20 & 59.51 & 48.59 & 51.43 & 31.50 & 31.91 & \\\\\n"," & Mean-Pooling & & 64.29 & 63.44 & 56.94 & 55.71 & 33.42 & 31.79 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 61.67 & & & & & & & 9.03 \\\\\n"," & Compression-Tokens (Causal) & & 48.57 & 45.60 & 38.44 & 37.12 & 23.03 & 23.14 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 52.24 & 49.98 & 40.65 & 42.08 & 23.59 & 23.72 & \\\\\n"," & Mean-Pooling & & 57.97 & 55.15 & 38.58 & 46.23 & 19.53 & 23.17 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{NarrativeQA $F_1$.}\n"," \\label{tab:primary_results_narrativeqa}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 65.65 & & 46.46 & & 52.55 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 70.63 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 86.43 & & 78.03 & & 72.50 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 86.64 & & 77.13 & & 74.08 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 89.65 & & & & & & & 53.79 \\\\\n"," & Compression-Tokens (Causal) & & 89.67 & 89.15 & 88.92 & 85.50 & 79.36 & 77.55 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 90.44 & 89.41 & 87.07 & 87.95 & 75.90 & 78.17 & \\\\\n"," & Mean-Pooling & & 87.94 & 86.52 & 84.38 & 86.32 & 79.74 & 75.89 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 90.46 & & & & & & & 43.49 \\\\\n"," & Compression-Tokens (Causal) & & 88.49 & 83.28 & 82.95 & 80.42 & 72.27 & 70.84 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 91.59 & 90.83 & 86.10 & 87.53 & 67.43 & 74.52 & \\\\\n"," & Mean-Pooling & & 85.50 & 88.72 & 83.68 & 85.32 & 71.04 & 67.50 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 89.20 & & & & & & & 25.08 \\\\\n"," & Compression-Tokens (Causal) & & 74.89 & 83.83 & 80.55 & 73.91 & 61.72 & 64.02 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 85.62 & 86.41 & 76.15 & 80.34 & 61.46 & 61.67 & \\\\\n"," & Mean-Pooling & & 85.83 & 82.75 & 80.61 & 75.94 & 63.03 & 53.77 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 9.87 \\\\\n"," & Compression-Tokens (Causal) & & 78.27 & 73.57 & 62.14 & 64.79 & 48.97 & 49.69 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 81.58 & 78.38 & 69.22 & 74.16 & 50.24 & 54.05 & \\\\\n"," & Mean-Pooling & & 81.45 & 77.88 & 69.08 & 70.41 & 52.45 & 43.08 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 90.69 & & & & & & & 54.06 \\\\\n"," & Compression-Tokens (Causal) & & 89.75 & 85.06 & 82.73 & 79.19 & 77.64 & 73.71 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 88.52 & 87.14 & 85.32 & 84.63 & 78.15 & 73.59 & \\\\\n"," & Mean-Pooling & & 89.09 & 86.99 & 84.95 & 85.27 & 75.30 & 74.29 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 82.13 & & & & & & & 31.14 \\\\\n"," & Compression-Tokens (Causal) & & 84.40 & 79.82 & 75.47 & 74.28 & 65.03 & 67.58 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 83.72 & 84.18 & 78.94 & 73.03 & 64.83 & 68.57 & \\\\\n"," & Mean-Pooling & & 84.87 & 83.62 & 73.95 & 76.02 & 62.02 & 60.28 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{TriviaQA Verified $F_1$.}\n"," \\label{tab:primary_results_triviaqa}\n","\\end{table}\n"],["\\begin{table}[!ht]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 32.79 & & 19.56 & & 18.76 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 27.34 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 42.51 & & 35.36 & & 26.44 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 44.09 & & 33.39 & & 27.52 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 60.44 & & & & & & & 19.15 \\\\\n"," & Compression-Tokens (Causal) & & 47.26 & 45.97 & 36.35 & 39.16 & 32.42 & 31.15 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 51.46 & 51.51 & 40.05 & 42.51 & 32.54 & 32.69 & \\\\\n"," & Mean-Pooling & & 53.71 & 53.32 & 42.55 & 45.07 & 32.52 & 31.36 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 57.04 & & & & & & & 17.38 \\\\\n"," & Compression-Tokens (Causal) & & 45.07 & 43.44 & 34.61 & 34.34 & 28.95 & 26.25 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 45.35 & 47.93 & 36.32 & 38.23 & 28.17 & 27.88 & \\\\\n"," & Mean-Pooling & & 51.47 & 48.49 & 40.36 & 39.09 & 28.84 & 27.31 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 46.62 & & & & & & & 14.86 \\\\\n"," & Compression-Tokens (Causal) & & 30.09 & 34.01 & 29.29 & 29.47 & 22.27 & 22.82 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 37.92 & 37.00 & 29.72 & 31.44 & 22.43 & 21.05 & \\\\\n"," & Mean-Pooling & & 42.14 & 39.78 & 32.33 & 32.46 & 22.01 & 22.18 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 39.04 & & & & & & & 10.97 \\\\\n"," & Compression-Tokens (Causal) & & 29.69 & 28.58 & 23.55 & 23.95 & 18.80 & 19.46 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 29.16 & 33.06 & 25.47 & 26.99 & 19.60 & 18.80 & \\\\\n"," & Mean-Pooling & & 33.84 & 32.70 & 26.11 & 26.21 & 19.52 & 18.08 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 51.45 & & & & & & & 16.76 \\\\\n"," & Compression-Tokens (Causal) & & 39.83 & 40.80 & 33.93 & 35.23 & 28.83 & 29.06 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 40.76 & 41.96 & 34.73 & 35.52 & 29.47 & 27.27 & \\\\\n"," & Mean-Pooling & & 45.61 & 44.88 & 37.14 & 36.88 & 28.70 & 28.94 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 39.75 & & & & & & & 14.30 \\\\\n"," & Compression-Tokens (Causal) & & 30.58 & 29.42 & 26.27 & 26.66 & 21.04 & 21.63 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 31.71 & 30.30 & 25.77 & 28.88 & 23.74 & 20.71 & \\\\\n"," & Mean-Pooling & & 34.84 & 33.60 & 27.18 & 27.29 & 21.21 & 20.46 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{AdversarialQA $F_1$.}\n"," \\label{tab:primary_results_adversarial_qa}\n","\\end{table}\n"],["\\begin{table}[H]\n"," \\small\n"," \\centering\n"," \\setlength{\\tabcolsep}{5pt}\n"," \\resizebox{\\textwidth}{!}{%\n","\\begin{tabular}{llcccccccc}\n","\\toprule\n","\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n","\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n","\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n","& \\emph{LLMLingua2} (Qwen3-8B) & & & 27.42 & & 15.32 & & 7.56 & \\\\\n","& \\emph{ICAE} (Mistral-7B) & & 28.42 & & & & & & \\\\\n","& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 46.31 & & 33.25 & & 18.14 & & \\\\\n","& \\emph{PCC Large} (Llama3.1-8B) & & 46.77 & & 31.17 & & 17.95 & & \\\\\n","\\midrule\n","\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n","\\addlinespace[2pt]\n","\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 56.77 & & & & & & & 7.49 \\\\\n"," & Compression-Tokens (Causal) & & 49.69 & 48.77 & 40.37 & 41.71 & 30.94 & 28.40 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 51.65 & 51.68 & 44.91 & 45.85 & 31.40 & 31.07 & \\\\\n"," & Mean-Pooling & & 55.36 & 53.87 & 48.95 & 48.63 & 31.79 & 29.12 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 56.14 & & & & & & & 6.59 \\\\\n"," & Compression-Tokens (Causal) & & 47.85 & 46.50 & 40.73 & 40.49 & 28.86 & 27.16 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 49.63 & 50.74 & 42.98 & 44.60 & 27.72 & 28.07 & \\\\\n"," & Mean-Pooling & & 54.74 & 53.24 & 46.93 & 47.01 & 29.95 & 26.25 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 54.75 & & & & & & & 5.09 \\\\\n"," & Compression-Tokens (Causal) & & 37.53 & 43.23 & 36.08 & 35.38 & 24.47 & 22.71 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 46.33 & 47.36 & 39.28 & 39.72 & 24.81 & 23.81 & \\\\\n"," & Mean-Pooling & & 52.04 & 50.67 & 42.90 & 42.55 & 25.16 & 22.02 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 51.54 & & & & & & & 4.82 \\\\\n"," & Compression-Tokens (Causal) & & 42.04 & 39.38 & 32.91 & 31.36 & 20.07 & 19.73 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 43.34 & 43.74 & 34.15 & 35.77 & 21.12 & 19.16 & \\\\\n"," & Mean-Pooling & & 48.26 & 46.29 & 38.13 & 37.81 & 21.24 & 17.03 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 56.00 & & & & & & & 7.10 \\\\\n"," & Compression-Tokens (Causal) & & 48.10 & 46.86 & 41.66 & 40.33 & 29.30 & 27.74 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 49.36 & 49.83 & 42.30 & 43.72 & 29.85 & 28.81 & \\\\\n"," & Mean-Pooling & & 54.39 & 53.39 & 47.82 & 47.83 & 31.16 & 28.91 & \\\\\n","\\midrule\n","\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 52.26 & & & & & & & 5.94 \\\\\n"," & Compression-Tokens (Causal) & & 41.97 & 40.07 & 35.08 & 35.24 & 22.50 & 23.14 & \\\\\n"," & Compression-Tokens (Bidirectional) & & 44.58 & 44.02 & 36.36 & 38.77 & 23.84 & 23.88 & \\\\\n"," & Mean-Pooling & & 49.90 & 46.92 & 33.84 & 39.59 & 17.67 & 21.17 & \\\\\n","\\midrule\n","\\bottomrule\n","\\end{tabular}\n"," }\n"," \\caption{ParaphraseRC $F_1$.}\n"," \\label{tab:primary_results_paraphrase_rc}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\n\",\n \" \\\\def\\\\uniformscale{0.23} %\\n\",\n \" \\n\",\n \" \\\\newlength{\\\\fixedheight}\\n\",\n \" \\\\setlength{\\\\fixedheight}{5.3cm}\\n\",\n \" \\n\",\n \" \\\\begin{subfigure}[t]{0.31\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\vbox to \\\\fixedheight{%\\n\",\n \" \\\\includegraphics[page=1, scale=\\\\uniformscale]{figures/architecture_fig.pdf}%\\n\",\n \" \\\\vfill\\n\",\n \" }\\n\",\n \" \\\\caption{Processing with a regular language model (no compression).}\\n\",\n \" \\\\label{fig:arch:regular_llm}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{minipage}[t]{0.02\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\rule[0pt]{0pt}{\\\\fixedheight}%\\n\",\n \" \\\\begin{tikzpicture}\\n\",\n \" \\\\draw[dashed, gray, very thin] (0,0) -- (0,\\\\fixedheight);\\n\",\n \" \\\\end{tikzpicture}\\n\",\n \" \\\\end{minipage}%\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{subfigure}[t]{0.31\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\vbox to \\\\fixedheight{%\\n\",\n \" \\\\includegraphics[page=2, scale=\\\\uniformscale]{figures/architecture_fig.pdf}%\\n\",\n \" \\\\vfill\\n\",\n \" }\\n\",\n \" \\\\caption{Compression tokens approach for context compression.}\\n\",\n \" \\\\label{fig:arch:tokens}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{minipage}[t]{0.02\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\rule[0pt]{0pt}{\\\\fixedheight}%\\n\",\n \" \\\\begin{tikzpicture}\\n\",\n \" \\\\draw[dashed, gray, very thin] (0,0) -- (0,\\\\fixedheight);\\n\",\n \" \\\\end{tikzpicture}\\n\",\n \" \\\\end{minipage}%\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{subfigure}[t]{0.31\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\vbox to \\\\fixedheight{%\\n\",\n \" \\\\includegraphics[page=3, scale=\\\\uniformscale]{figures/architecture_fig.pdf}%\\n\",\n \" \\\\vfill\\n\",\n \" }\\n\",\n \" \\\\caption{Our proposed method: no extra tokens; mean pooling of final hidden states.}\\n\",\n \" \\\\label{fig:arch:pool}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\n\",\n \" \\\\caption{Comparison of context processing methods: regular LM, compression tokens, and our proposed approach --- mean pooling. The figure illustrates a compression ratio of $4\\\\times$.}\\n\",\n \" \\\\label{fig:arch}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 42.52 & & 24.39 & & 22.59 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 42.40 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 62.08 & & 51.30 & & 36.20 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 62.98 & & 49.37 & & 37.24 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 74.33 & & & & & & & 23.06 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 67.03 & 65.90 & 56.21 & 58.41 & 47.47 & 44.76 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 69.20 & 69.57 & 60.27 & 63.01 & 46.93 & \\\\textbf{46.97} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{71.66} & \\\\textbf{70.55} & \\\\textbf{63.85} & \\\\textbf{64.67} & \\\\textbf{47.90} & 45.92 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 73.44 & & & & & & & 19.79 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 64.88 & 62.53 & 55.22 & 54.28 & 43.08 & 40.83 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 66.72 & 68.15 & 57.68 & 60.48 & 41.61 & \\\\textbf{42.66} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{70.39} & \\\\textbf{69.36} & \\\\textbf{61.79} & \\\\textbf{61.72} & \\\\textbf{43.62} & 41.05 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 69.93 & & & & & & & 14.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 50.90 & 57.73 & 49.83 & 48.68 & 36.19 & 35.34 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 62.04 & 62.60 & 51.53 & 54.11 & 36.25 & \\\\textbf{35.77} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{66.43} & \\\\textbf{64.17} & \\\\textbf{55.43} & \\\\textbf{54.47} & \\\\textbf{36.72} & 33.48 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 65.36 & & & & & & & 9.34 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 54.40 & 51.85 & 41.57 & 42.59 & 28.86 & 28.60 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 55.59 & 57.03 & 44.82 & 47.62 & 29.69 & \\\\textbf{29.51} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{61.17} & \\\\textbf{58.36} & \\\\textbf{47.59} & \\\\textbf{47.64} & \\\\textbf{29.94} & 26.36 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 71.96 & & & & & & & 21.64 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 63.35 & 62.18 & 55.07 & 54.70 & 44.46 & 42.49 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 64.76 & 65.24 & 56.39 & 58.43 & 44.73 & 43.17 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{69.33} & \\\\textbf{68.09} & \\\\textbf{61.39} & \\\\textbf{61.04} & \\\\textbf{44.98} & \\\\textbf{43.71} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 65.82 & & & & & & & 15.17 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 56.31 & 53.74 & 47.51 & 46.96 & 35.41 & 35.62 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 57.91 & 57.52 & \\\\textbf{49.20} & 50.06 & \\\\textbf{36.43} & \\\\textbf{36.25} & \\\\\\\\\\n\",\n \" & Mean-Pooling & & \\\\textbf{62.81} & \\\\textbf{60.56} & 47.28 & \\\\textbf{51.56} & 33.25 & 33.98 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}}\\n\",\n \"\\\\medskip\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{figures/methods_ratios_comparison.pdf}\\n\",\n \"\\\\caption{\\n\",\n \"Primary results. Values in the table are $F_1$ scores macro-averaged across all datasets in our evaluation suite. \\n\",\n \"\\\\textbf{Original} stands for the teacher model's score when given the full context. \\\\textbf{No Ctx} stands for the teacher model's score when not given any context at all. For each ratio, we display both single- and multi-ratio versions. For the baseline systems (top section), we include results for the compression ratios supported by these methods, unsupported ratios are left blank. The best method for each (model, ratio, single/multi-ratio training) setting is \\\\textbf{bolded}.\\n\",\n \"Bottom figures present aggregated views of the results in the table, but instead of $F_1$ show the teacher-normalized $F_1$ metric (Relative F1). Scores are obtained by averaging over all models listed in the table. \\n\",\n \"}\\\\label{tab:primary_results_hybrid_transpose}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[htb]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.6\\\\linewidth]{figures/scaling_law_qwen3.pdf}\\n\",\n \" \\\\caption{Compression Scaling. We show the teacher-normalized $F_1$ scores (Relative F1) across four Qwen3 model scales. The scores are averages of the scores of all datasets. We can clearly observe the benefits of scaling for LLM compressors.}\\n\",\n \" \\\\label{fig:scaling_law}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{subfigure}[t]{0.95\\\\linewidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{figures/in_vs_out_fig.pdf}\\n\",\n \" \\\\caption{In-domain vs.\\\\ out-of-domain performance across compression ratios.}\\n\",\n \" \\\\label{fig:in-vs-out}\\n\",\n \" \\\\end{subfigure}\\n\",\n \"\\n\",\n \" \\\\vspace{0.8em} %\\n\",\n \"\\n\",\n \" \\\\begin{subfigure}[t]{0.95\\\\linewidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{figures/in_out_gap_fig.pdf}\\n\",\n \" \\\\caption{Performance drop (in–out gap) per method across compression ratios (in teacher-normalized Relative $F_1$ units). Higher values mean a larger domain performance gap. Negative values mean that the out-of-domain performance is better than in-domain performance.}\\n\",\n \" \\\\label{fig:in-out-gap}\\n\",\n \" \\\\end{subfigure}\\n\",\n \"\\n\",\n \" \\\\caption{In-domain and out-of-domain comparison. (a) Line plots show performance on in-domain vs.\\\\ out-of-domain datasets. (b) Bar plots show the in–out performance gap per method, which is the difference between in-domain and out-of-domain teacher-normalized $F_1$ scores.}\\n\",\n \" \\\\label{fig:in-out-combined}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{0.92\\\\linewidth}{!}{%\\n\",\n \"\\\\begin{tabular}{l r r r r r r c}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Ablation} (\\\\textsc{Gemma2-2B}) & 4$\\\\times$ & 8$\\\\times$ & 16$\\\\times$ & 32$\\\\times$ & 64$\\\\times$ & 128$\\\\times$ & $\\\\Delta$ \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Default & \\\\textbf{68.1} & \\\\textbf{65.4} & \\\\textbf{61.0} & \\\\textbf{54.9} & \\\\textbf{48.8} & \\\\textbf{43.7} & \\\\,($+0.0$) \\\\\\\\\\n\",\n \"Fixed Decoder & 64.9 & 61.9 & 57.0 & 51.5 & 45.0 & 39.8 & \\\\,($-3.6$) \\\\\\\\\\n\",\n \"Fixed Encoder & 57.4 & 49.9 & 44.1 & 39.8 & 36.2 & 34.8 & \\\\,($-13.3$) \\\\\\\\\\n\",\n \"No Encoder & 58.7 & 51.9 & 44.9 & 40.2 & 36.2 & 34.1 & \\\\,($-12.6$) \\\\\\\\\\n\",\n \"w/o Linear Layer & 67.7 & 64.5 & 60.0 & 54.1 & 48.1 & 43.2 & \\\\,($-0.7$) \\\\\\\\\\n\",\n \"Ratio Sampling & 67.1 & 64.0 & 59.3 & 53.5 & 47.5 & 42.2 & \\\\,($-1.4$) \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Ablation study for mean pooling using \\\\textsc{Gemma2-2B} as the teacher LLM. Numbers are macro-averaged $F_1$ scores. \\\\emph{$\\\\Delta$}: mean change vs. Default across ratios; \\\\textbf{bold} = best per column.}\\n\",\n \"\\\\label{tab:abl_gemma2_mean}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{lrrr}\\n\",\n \"\\\\toprule\\n\",\n \"Dataset & Avg. Context Tokens & \\\\#Samples & \\\\#Contexts \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{4}{l}{\\\\textbf{Summarization}} \\\\\\\\\\n\",\n \"CNN/DM~\\\\citep{see-etal-2017-get_cnndm} & 649 & 198{,}732 & 196{,}601 \\\\\\\\\\n\",\n \"DialogSum~\\\\citep{chen-etal-2021-dialogsum} & 208 & 12{,}452 & 12{,}450 \\\\\\\\\\n\",\n \"SAMSum~\\\\citep{Gliwa_2019_samsum} & 145 & 14{,}730 & 14{,}254 \\\\\\\\\\n\",\n \"XSum~\\\\citep{narayan-etal-2018-dont_xsum} & 408 & 185{,}760 & 185{,}566 \\\\\\\\\\n\",\n \"\\\\addlinespace\\n\",\n \"\\\\multicolumn{4}{l}{\\\\textbf{Reading Comprehension}} \\\\\\\\\\n\",\n \"BoolQ~\\\\citep{clark-etal-2019-boolq} & 126 & 9{,}427 & 7{,}927 \\\\\\\\\\n\",\n \"DROP~\\\\citep{dua-etal-2019-drop} & 295 & 76{,}751 & 5{,}477 \\\\\\\\\\n\",\n \"HotpotQA~\\\\citep{yang-etal-2018-hotpotqa} & 247 & 90{,}327 & 84{,}705 \\\\\\\\\\n\",\n \"NarrativeQA~\\\\citep{kocisky-etal-2018-narrativeqa} & 668 & 28{,}299 & 953 \\\\\\\\\\n\",\n \"PubMedQA~\\\\citep{jin-etal-2019-pubmedqa} & 318 & 211{,}218 & 211{,}164 \\\\\\\\\\n\",\n \"QuAC~\\\\citep{choi-etal-2018-quac} & 515 & 81{,}391 & 6{,}574 \\\\\\\\\\n\",\n \"QuAIL~\\\\citep{rogers2020getting_quail} & 416 & 10{,}246 & 560 \\\\\\\\\\n\",\n \"RACE~\\\\citep{lai-etal-2017-race} & 349 & 87{,}749 & 25{,}108 \\\\\\\\\\n\",\n \"SQuAD~\\\\citep{rajpurkar-etal-2016-squad} & 162 & 86{,}821 & 18{,}877 \\\\\\\\\\n\",\n \"PWC~\\\\citep{ge2024incontext} & 477 & 241{,}563 & 16{,}382 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Total} & \\\\textbf{410} & \\\\textbf{1,335,466} & \\\\textbf{786,598} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Training datasets with average context length (tokens), number of samples, number of distinct contexts, and task category. The overall average context length is weighted by the number of samples.}\\n\",\n \"\\\\label{tab:training_datasets}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{lrrr}\\n\",\n \"\\\\toprule\\n\",\n \"Dataset & Avg. Context Tokens & \\\\#Samples & \\\\#Contexts \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"AdversarialQA~\\\\citep{bartolo2020beat_adversarialqa} & 154 & 1{,}000 & 341 \\\\\\\\\\n\",\n \"HotpotQA~\\\\citep{yang-etal-2018-hotpotqa} & 254 & 7{,}394 & 7{,}352 \\\\\\\\\\n\",\n \"NarrativeQA~\\\\citep{kocisky-etal-2018-narrativeqa} & 639 & 3{,}002 & 100 \\\\\\\\\\n\",\n \"ParaphraseRC~\\\\citep{saha-etal-2018-duorc} & 685 & 4{,}835 & 560 \\\\\\\\\\n\",\n \"SQuAD~\\\\citep{rajpurkar-etal-2016-squad} & 169 & 5{,}928 & 1{,}204 \\\\\\\\\\n\",\n \"TriviaQA (Verified)~\\\\citep{joshi-etal-2017-triviaqa} & 539 & 185 & 185 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Total} & \\\\textbf{375} & \\\\textbf{22{,}344} & \\\\textbf{9{,}742} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Evaluation datasets with average context length (tokens), number of samples, and number of distinct contexts. The overall average context length is weighted by the number of samples.}\\n\",\n \"\\\\label{tab:evaluation_datasets}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{tabular}{cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Hyperparameter} & \\\\textbf{Value} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" LoRA $r$ & 16 \\\\\\\\\\n\",\n \" LoRA $\\\\alpha$ & 16 \\\\\\\\ \\n\",\n \" optimizer & AdamW \\\\\\\\\\n\",\n \" $\\\\beta_1$ & 0.9 \\\\\\\\\\n\",\n \" $\\\\beta_2$ & 0.95 \\\\\\\\\\n\",\n \" clip norm & 1 \\\\\\\\\\n\",\n \" peak learning rate & 2e-4 \\\\\\\\\\n\",\n \" final learning rate & 2e-5 \\\\\\\\\\n\",\n \" lr scheduler type & cosine \\\\\\\\\\n\",\n \" warmup ratio & 0.05 \\\\\\\\\\n\",\n \" weight decay & 0.0 \\\\\\\\\\n\",\n \" steps & 48,000 \\\\\\\\\\n\",\n \" batch size & 32 \\\\\\\\\\n\",\n \" max context length & 1024 \\\\\\\\\\n\",\n \" max answer tokens & 256 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{Hyperparameters for training all the models used in this work.} \\n\",\n \" \\\\label{table:hyperparameters}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 30.02 & & 16.16 & & 16.06 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 24.94 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 48.81 & & 38.38 & & 25.94 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 49.34 & & 36.64 & & 27.92 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 59.82 & & & & & & & 16.19 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 51.59 & 50.01 & 41.26 & 42.99 & 34.21 & 32.50 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 53.44 & 53.99 & 44.92 & 47.15 & 33.60 & 34.27 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 56.41 & 55.04 & 47.95 & 49.02 & 34.72 & 33.15 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 58.87 & & & & & & & 13.74 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 49.66 & 46.26 & 40.05 & 39.59 & 30.07 & 28.84 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 51.06 & 52.37 & 42.53 & 45.14 & 28.84 & 29.51 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 55.25 & 53.77 & 45.43 & 45.86 & 30.91 & 28.38 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 55.19 & & & & & & & 9.07 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 36.66 & 41.64 & 35.49 & 34.64 & 24.27 & 24.04 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 46.45 & 46.72 & 36.62 & 38.93 & 24.31 & 24.33 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 51.28 & 48.77 & 40.45 & 39.04 & 25.15 & 22.01 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 50.85 & & & & & & & 4.78 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 39.66 & 36.76 & 27.99 & 29.00 & 18.23 & 18.20 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 40.98 & 41.92 & 30.92 & 33.64 & 18.82 & 18.55 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 45.82 & 43.07 & 32.50 & 33.09 & 19.05 & 16.07 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 57.63 & & & & & & & 15.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 47.90 & 45.98 & 39.57 & 39.74 & 32.02 & 29.66 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 49.43 & 49.40 & 40.89 & 42.70 & 31.79 & 30.43 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.20 & 52.77 & 45.88 & 45.68 & 32.41 & 30.83 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 51.67 & & & & & & & 9.47 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 41.84 & 39.03 & 33.73 & 33.38 & 24.11 & 24.64 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 43.46 & 42.96 & 35.04 & 35.46 & 24.91 & 24.56 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 47.97 & 45.45 & 33.15 & 36.93 & 22.89 & 22.70 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{Primary results with exact match (EM) as the metric.}\\n\",\n \" \\\\label{tab:primary_results_EM}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 33.63 & & 18.30 & & 17.36 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 49.18 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PISCO} (Llama3.1-8B) & & & & 53.62 & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 54.05 & & 43.67 & & 30.03 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 55.17 & & 41.79 & & 30.10 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 68.84 & & & & & & & 17.98 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 59.79 & 58.58 & 47.07 & 49.99 & 39.09 & 37.05 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 62.50 & 63.58 & 52.22 & 55.26 & 38.72 & 39.36 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 65.91 & 65.06 & 55.68 & 56.77 & 39.95 & 37.80 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 67.69 & & & & & & & 15.00 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 57.12 & 54.17 & 46.06 & 45.47 & 34.83 & 33.48 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 59.35 & 60.99 & 48.92 & 52.23 & 33.20 & 34.33 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 64.05 & 62.94 & 52.77 & 52.82 & 35.49 & 32.37 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 64.21 & & & & & & & 9.85 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 43.01 & 49.31 & 41.31 & 40.45 & 28.45 & 27.90 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 54.31 & 54.70 & 42.66 & 45.13 & 28.33 & 28.04 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 60.03 & 57.28 & 46.63 & 45.07 & 28.96 & 25.82 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 59.67 & & & & & & & 5.62 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 46.36 & 43.62 & 33.07 & 34.30 & 21.13 & 21.71 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 48.04 & 48.84 & 36.11 & 39.50 & 22.13 & 22.00 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.36 & 51.16 & 38.30 & 38.68 & 22.44 & 18.87 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 66.14 & & & & & & & 16.80 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 55.50 & 52.94 & 46.13 & 45.59 & 36.14 & 33.94 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 56.94 & 57.54 & 46.90 & 49.52 & 36.14 & 34.75 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 62.51 & 61.28 & 52.55 & 51.90 & 36.61 & 34.93 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 60.30 & & & & & & & 11.09 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.85 & 45.41 & 39.16 & 38.51 & 27.54 & 28.01 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 50.89 & 50.10 & 40.44 & 41.91 & 28.34 & 28.44 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 56.62 & 53.50 & 38.84 & 42.76 & 25.99 & 26.19 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{Primary results with accuracy as the metric.}\\n\",\n \" \\\\label{tab:primary_results_accuracy}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 48.38 & & 21.34 & & 19.68 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 45.6 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 78.38 & & 67.63 & & 40.22 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 79.56 & & 62.93 & & 41.23 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 86.48 & & & & & & & 20.31 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 77.11 & 74.89 & 57.05 & 62.12 & 44.56 & 42.35 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 80.00 & 81.23 & 64.80 & 69.27 & 44.30 & 43.86 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 83.76 & 82.75 & 71.37 & 71.19 & 44.65 & 43.19 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 85.75 & & & & & & & 17.72 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 74.23 & 71.31 & 57.49 & 56.88 & 38.95 & 37.10 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 77.24 & 79.28 & 60.71 & 65.49 & 38.19 & 38.41 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 83.19 & 81.54 & 68.20 & 67.47 & 39.96 & 37.54 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 83.65 & & & & & & & 12.66 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 54.25 & 64.50 & 49.09 & 49.98 & 31.78 & 30.10 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 72.92 & 73.39 & 53.07 & 57.36 & 31.58 & 31.17 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 79.56 & 77.17 & 59.01 & 58.30 & 32.36 & 29.90 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 7.91 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 61.67 & 57.52 & 40.29 & 41.60 & 22.06 & 22.45 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 64.21 & 67.05 & 42.81 & 46.68 & 22.09 & 22.36 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 74.00 & 70.60 & 48.62 & 48.14 & 22.40 & 20.45 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 84.58 & & & & & & & 16.41 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 70.61 & 69.06 & 55.75 & 56.37 & 37.89 & 35.66 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 74.16 & 75.41 & 57.77 & 61.75 & 37.72 & 37.00 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 81.67 & 80.01 & 66.38 & 65.64 & 38.96 & 36.71 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 81.16 & & & & & & & 11.27 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 62.65 & 59.34 & 46.41 & 45.49 & 28.58 & 28.44 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 64.48 & 65.61 & 48.99 & 51.39 & 29.09 & 28.82 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 74.91 & 71.40 & 47.36 & 53.66 & 28.02 & 27.91 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{SQuAD $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_squad}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 53.54 & & 29.32 & & 26.27 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 50.01 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 68.55 & & 59.38 & & 43.93 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 70.08 & & 59.05 & & 46.46 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 84.67 & & & & & & & 26.65 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 78.85 & 78.32 & 68.00 & 72.65 & 64.14 & 59.74 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 80.24 & 81.45 & 73.30 & 76.77 & 63.26 & 62.44 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 83.30 & 82.08 & 77.66 & 78.41 & 63.88 & 63.77 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 84.12 & & & & & & & 23.16 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 76.48 & 75.56 & 68.85 & 69.80 & 59.08 & 55.78 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 78.13 & 79.41 & 71.11 & 74.60 & 58.38 & 56.87 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 82.20 & 80.77 & 75.45 & 76.02 & 59.29 & 58.74 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 80.95 & & & & & & & 18.75 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 66.69 & 70.98 & 63.82 & 63.84 & 51.48 & 48.78 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 73.73 & 74.93 & 66.06 & 68.50 & 52.08 & 50.77 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 78.64 & 76.11 & 68.76 & 68.78 & 50.86 & 49.44 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 77.35 & & & & & & & 14.74 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 66.62 & 65.76 & 55.88 & 57.79 & 43.16 & 39.58 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 67.24 & 69.28 & 58.44 & 61.79 & 43.80 & 41.66 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 73.00 & 69.58 & 61.13 & 61.08 & 42.76 & 40.45 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 82.55 & & & & & & & 25.18 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 75.62 & 75.54 & 69.18 & 70.42 & 61.91 & 59.03 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 76.55 & 77.60 & 69.64 & 73.51 & 61.67 & 60.46 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 80.93 & 79.85 & 75.10 & 74.90 & 62.36 & 61.64 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 77.96 & & & & & & & 19.34 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 69.68 & 68.22 & 63.36 & 62.96 & 52.27 & 49.81 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 70.74 & 71.01 & 64.47 & 66.19 & 53.51 & 51.79 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 74.38 & 72.69 & 62.75 & 66.59 & 51.05 & 50.86 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{HotpotQA $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_hotpotqa}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 27.33 & & 14.35 & & 10.69 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 32.65 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 50.29 & & 34.16 & & 16.05 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 50.72 & & 32.56 & & 16.18 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 68.00 & & & & & & & 10.93 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 59.62 & 58.28 & 46.58 & 49.32 & 33.41 & 29.37 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 61.44 & 62.13 & 51.48 & 55.68 & 34.17 & 33.61 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 65.89 & 64.74 & 58.17 & 58.38 & 34.81 & 32.21 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 67.12 & & & & & & & 10.40 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 57.18 & 55.08 & 46.69 & 43.77 & 30.39 & 27.84 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 58.37 & 60.74 & 48.84 & 52.41 & 29.77 & 30.22 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 65.22 & 63.38 & 56.14 & 55.42 & 32.66 & 28.99 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 64.42 & & & & & & & 7.57 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 41.97 & 49.85 & 40.15 & 39.49 & 25.42 & 23.64 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 55.68 & 56.49 & 44.87 & 47.28 & 25.16 & 26.15 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 60.34 & 58.56 & 48.95 & 48.78 & 26.91 & 23.60 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 61.13 & & & & & & & 7.76 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.09 & 46.30 & 34.68 & 36.05 & 20.10 & 20.69 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 48.04 & 50.67 & 38.85 & 40.35 & 21.29 & 21.07 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 56.48 & 53.12 & 42.47 & 42.21 & 21.29 & 19.06 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 66.47 & & & & & & & 10.34 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 56.17 & 55.78 & 47.16 & 46.68 & 31.17 & 29.72 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 59.20 & 59.51 & 48.59 & 51.43 & 31.50 & 31.91 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 64.29 & 63.44 & 56.94 & 55.71 & 33.42 & 31.79 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 61.67 & & & & & & & 9.03 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.57 & 45.60 & 38.44 & 37.12 & 23.03 & 23.14 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 52.24 & 49.98 & 40.65 & 42.08 & 23.59 & 23.72 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 57.97 & 55.15 & 38.58 & 46.23 & 19.53 & 23.17 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{NarrativeQA $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_narrativeqa}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 65.65 & & 46.46 & & 52.55 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 70.63 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 86.43 & & 78.03 & & 72.50 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 86.64 & & 77.13 & & 74.08 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 89.65 & & & & & & & 53.79 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 89.67 & 89.15 & 88.92 & 85.50 & 79.36 & 77.55 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 90.44 & 89.41 & 87.07 & 87.95 & 75.90 & 78.17 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 87.94 & 86.52 & 84.38 & 86.32 & 79.74 & 75.89 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 90.46 & & & & & & & 43.49 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 88.49 & 83.28 & 82.95 & 80.42 & 72.27 & 70.84 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 91.59 & 90.83 & 86.10 & 87.53 & 67.43 & 74.52 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 85.50 & 88.72 & 83.68 & 85.32 & 71.04 & 67.50 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 89.20 & & & & & & & 25.08 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 74.89 & 83.83 & 80.55 & 73.91 & 61.72 & 64.02 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 85.62 & 86.41 & 76.15 & 80.34 & 61.46 & 61.67 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 85.83 & 82.75 & 80.61 & 75.94 & 63.03 & 53.77 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 9.87 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 78.27 & 73.57 & 62.14 & 64.79 & 48.97 & 49.69 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 81.58 & 78.38 & 69.22 & 74.16 & 50.24 & 54.05 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 81.45 & 77.88 & 69.08 & 70.41 & 52.45 & 43.08 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 90.69 & & & & & & & 54.06 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 89.75 & 85.06 & 82.73 & 79.19 & 77.64 & 73.71 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 88.52 & 87.14 & 85.32 & 84.63 & 78.15 & 73.59 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 89.09 & 86.99 & 84.95 & 85.27 & 75.30 & 74.29 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 82.13 & & & & & & & 31.14 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 84.40 & 79.82 & 75.47 & 74.28 & 65.03 & 67.58 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 83.72 & 84.18 & 78.94 & 73.03 & 64.83 & 68.57 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 84.87 & 83.62 & 73.95 & 76.02 & 62.02 & 60.28 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{TriviaQA Verified $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_triviaqa}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[!ht]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 32.79 & & 19.56 & & 18.76 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 27.34 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 42.51 & & 35.36 & & 26.44 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 44.09 & & 33.39 & & 27.52 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 60.44 & & & & & & & 19.15 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 47.26 & 45.97 & 36.35 & 39.16 & 32.42 & 31.15 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 51.46 & 51.51 & 40.05 & 42.51 & 32.54 & 32.69 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 53.71 & 53.32 & 42.55 & 45.07 & 32.52 & 31.36 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 57.04 & & & & & & & 17.38 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 45.07 & 43.44 & 34.61 & 34.34 & 28.95 & 26.25 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 45.35 & 47.93 & 36.32 & 38.23 & 28.17 & 27.88 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 51.47 & 48.49 & 40.36 & 39.09 & 28.84 & 27.31 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 46.62 & & & & & & & 14.86 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 30.09 & 34.01 & 29.29 & 29.47 & 22.27 & 22.82 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 37.92 & 37.00 & 29.72 & 31.44 & 22.43 & 21.05 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 42.14 & 39.78 & 32.33 & 32.46 & 22.01 & 22.18 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 39.04 & & & & & & & 10.97 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 29.69 & 28.58 & 23.55 & 23.95 & 18.80 & 19.46 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 29.16 & 33.06 & 25.47 & 26.99 & 19.60 & 18.80 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 33.84 & 32.70 & 26.11 & 26.21 & 19.52 & 18.08 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 51.45 & & & & & & & 16.76 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 39.83 & 40.80 & 33.93 & 35.23 & 28.83 & 29.06 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 40.76 & 41.96 & 34.73 & 35.52 & 29.47 & 27.27 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 45.61 & 44.88 & 37.14 & 36.88 & 28.70 & 28.94 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 39.75 & & & & & & & 14.30 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 30.58 & 29.42 & 26.27 & 26.66 & 21.04 & 21.63 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 31.71 & 30.30 & 25.77 & 28.88 & 23.74 & 20.71 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 34.84 & 33.60 & 27.18 & 27.29 & 21.21 & 20.46 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{AdversarialQA $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_adversarial_qa}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[H]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \"\\\\begin{tabular}{llcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multicolumn{2}{c}{} & \\\\multicolumn{1}{c}{\\\\textbf{Original}} & \\\\multicolumn2{c}{\\\\textbf{4x}} & \\\\multicolumn2{c}{\\\\textbf{16x}} & \\\\multicolumn2{c}{\\\\textbf{128x}} & \\\\multicolumn{1}{c}{\\\\textbf{No Ctx}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){3-3}\\\\cmidrule(lr){4-5}\\\\cmidrule(lr){6-7}\\\\cmidrule(lr){8-9}\\\\cmidrule(l){10-10}\\n\",\n \"\\\\multicolumn{2}{c}{} & & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\textbf{Single} & \\\\textbf{Multi} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Baseline Systems}} \\\\\\\\\\n\",\n \"& \\\\emph{LLMLingua2} (Qwen3-8B) & & & 27.42 & & 15.32 & & 7.56 & \\\\\\\\\\n\",\n \"& \\\\emph{ICAE} (Mistral-7B) & & 28.42 & & & & & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Lite} (GPT2-Large \\\\& Llama3.1-8B) & & 46.31 & & 33.25 & & 18.14 & & \\\\\\\\\\n\",\n \"& \\\\emph{PCC Large} (Llama3.1-8B) & & 46.77 & & 31.17 & & 17.95 & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{l}{\\\\textbf{Our Methods}} \\\\\\\\\\n\",\n \"\\\\addlinespace[2pt]\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-8B}} & 56.77 & & & & & & & 7.49 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 49.69 & 48.77 & 40.37 & 41.71 & 30.94 & 28.40 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 51.65 & 51.68 & 44.91 & 45.85 & 31.40 & 31.07 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 55.36 & 53.87 & 48.95 & 48.63 & 31.79 & 29.12 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-4B}} & 56.14 & & & & & & & 6.59 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 47.85 & 46.50 & 40.73 & 40.49 & 28.86 & 27.16 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 49.63 & 50.74 & 42.98 & 44.60 & 27.72 & 28.07 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.74 & 53.24 & 46.93 & 47.01 & 29.95 & 26.25 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-1.7B}} & 54.75 & & & & & & & 5.09 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 37.53 & 43.23 & 36.08 & 35.38 & 24.47 & 22.71 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 46.33 & 47.36 & 39.28 & 39.72 & 24.81 & 23.81 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 52.04 & 50.67 & 42.90 & 42.55 & 25.16 & 22.02 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Qwen3-0.6B}} & 51.54 & & & & & & & 4.82 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 42.04 & 39.38 & 32.91 & 31.36 & 20.07 & 19.73 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 43.34 & 43.74 & 34.15 & 35.77 & 21.12 & 19.16 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 48.26 & 46.29 & 38.13 & 37.81 & 21.24 & 17.03 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Gemma2-2B}} & 56.00 & & & & & & & 7.10 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 48.10 & 46.86 & 41.66 & 40.33 & 29.30 & 27.74 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 49.36 & 49.83 & 42.30 & 43.72 & 29.85 & 28.81 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 54.39 & 53.39 & 47.82 & 47.83 & 31.16 & 28.91 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{\\\\textbf{Llama3.2-1B}} & 52.26 & & & & & & & 5.94 \\\\\\\\\\n\",\n \" & Compression-Tokens (Causal) & & 41.97 & 40.07 & 35.08 & 35.24 & 22.50 & 23.14 & \\\\\\\\\\n\",\n \" & Compression-Tokens (Bidirectional) & & 44.58 & 44.02 & 36.36 & 38.77 & 23.84 & 23.88 & \\\\\\\\\\n\",\n \" & Mean-Pooling & & 49.90 & 46.92 & 33.84 & 39.59 & 17.67 & 21.17 & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{ParaphraseRC $F_1$.}\\n\",\n \" \\\\label{tab:primary_results_paraphrase_rc}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n\\documentclass{article} %\n\\usepackage{iclr2026_conference,times}\n\\usepackage{graphicx} %\n\\usepackage{subcaption} 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%\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} %\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\usepackage{hyperref}\n\\usepackage{url}\n\n\\newcommand{\\aautoref}[1]{\\hyperref[#1]{Appendix~\\ref*{#1}}}\n\\renewcommand{\\sectionautorefname}{Section}\n\\let\\subsectionautorefname\\sectionautorefname\n\\let\\subsubsectionautorefname\\sectionautorefname\n\n\n\\newcommand{\\eat}[1]{\\ignorespaces}\n\\newcommand{\\xxcomment}[4]{\\textcolor{#1}{[$^{\\textsc{#2}}_{\\textsc{#3}}$ #4]}}\n\\newcommand{\\ya}[1]{\\xxcomment{red}{Y}{A}{#1}}\n\\newcommand{\\yf}[1]{\\xxcomment{orange}{Y}{F}{#1}}\n\\newcommand{\\citeit}[1]{\\xxcomment{blue}{Y}{F}{citeit}}\n\\newcommand{\\refit}[1]{\\xxcomment{brown}{Y}{F}{refit}}\n\n\\title{Simple Context Compression: Mean-Pooling and Multi-Ratio Training}\n\n\n\\author{Yair Feldman and Yoav Artzi \\\\\nDepartment of Computer Science and Cornell Tech\\\\\nCornell University\\\\\n\\texttt{\\{yairf,yoav\\}@cs.cornell.edu}\n}\n\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\n\\iclrfinalcopy %\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\nA common strategy to reduce the computational costs of using long contexts in retrieval-augmented generation (RAG) with large language models (LLMs) is \\emph{soft context compression}, where the input sequence is transformed into a shorter continuous representation. \nWe develop a lightweight and simple mean-pooling approach that consistently outperforms the widely used compression-tokens architecture, and study training the same compressor to output multiple compression ratios. \nWe conduct extensive experiments across in-domain and out-of-domain QA datasets, as well as across model families, scales, and compression ratios. \nOverall, our simple mean-pooling approach achieves the strongest performance, with a relatively small drop when training for multiple compression ratios. \nMore broadly though, across architectures and training regimes the trade-offs are more nuanced, illustrating the complex landscape of compression methods. \n\n\n\n\n\n\n\n\\end{abstract}\n\n\\section{Introduction}\n\n\n\nReasoning over long documents is common in scenarios of retrieval-augmented generation (RAG). This is a computationally costly process, both as far as time and memory. \nTime is impacted by processing the document itself and self-attending over its computed representations in later parts of the generation process. \nMemory costs spike due to the key-value (KV) cache of the processed document. \nThe common way to reduce these costs is \\emph{soft context compression}, where a sequence of continuous representations is pre-computed. This representation is compressed in the sense that its length is significantly lower than the document length, thereby reducing both time and memory costs of reasoning over the document. \nThis compressed representation is computed once, and then retrieved as needed. \nThis important problem is receiving significant attention~\\citep[e.g.,][]{ge2024incontext, xrag, dai-etal-2025-pretraining}. \n\n\n\nWe study both compressor model design and the compression training process, with simplicity in mind. \nThe compression encoder we design is composed of an encoding LLM, and straightforward mean-pooling operations to collapse together representations to achieve a target compression ratio. \nThis approach adds no parameters beyond the encoder LLM, and the computation beyond the encoding of the document is minimal. It also naturally allows for compression ratio flexibility, raising the question of the benefits or downsides of training the same compressor to support multiple compression ratios. \nWe design a simple training objective and process to achieve this. \nThis is motivated foremost by the benefit of training a single model to serve different compute budgets, rather than maintaining and training a separate model for each compression ratio. \nIt also allows to examine if and when training to compress at multiple ratios can perform better than training for a single ratio. \n\n\n\n\nWe construct a rigorous evaluation suite using multiple question-answering (QA) datasets. We distinguish between datasets that are part of our training set, and these that are completely held-out, allowing us to better gauge generalization. \nWe conduct a battery of experiments, across three model families, model scales, and variations of both compressor architecture and multi-ratio training. \n\nWe find that our approach consistently outperforms the conventional compression-tokens approach, while being more efficient. In addition, we also show that by simply altering the attention pattern in the conventional compression tokens method, one can mitigate the gap between the approaches significantly, albeit not entirely. \nOur multi-ratio training experiments reveal that it is possible to train and deploy only a single model for a wide range of compression ratios with only minor performance drops. Interestingly, our proposed enhancement for the compression-tokens approach even benefits from multi-ratio training. \nA comparison of compression performances for scales between 0.6B to 8B shows that compression quality increases with scale, amplifying the benefits of applying such compression methods to larger models.\nOur code is available at \\url{https://github.com/lil-lab/simple-context-compression}.\n\n\n\\section{Task Definition}\n\nSoft context compression is an approach where a document of length $L$ is mapped to a sequence of vectors of length $C$, where $L \\gg C$. \nWhile the original document can be described as a sequence of tokens, the compression is made of dense continuous vectors, hence \\emph{soft}.\nThis process allows an LLM that uses the compressed version of the document to invest significantly less computation, both in time and key-value (KV) cache space, both reduced from dependence on $L$ to dependence on $C$. \nThis benefit increases with repeated use of the document, as is likely in RAG scenarios. \n\nFormally, we define soft context compression to support multiple compression ratios. \nLet $\\mathcal{M}$ be a language model and $\\mathcal{R} \\subseteq \\mathbb{N_+}$ the admissible set of compression ratios. \nLet $\\mathcal{V}$ denote the vocabulary and $d$ the embedding dimension of $\\mathcal{M}$. \nThe goal of learning is to construct a compression function\n\\begin{equation}\nf_c : \\mathcal{V}^{L} \\times \\mathcal{R} \\to \\mathbb{R}^{C \\times d}\\;\\;,\n\\end{equation}\nwhich maps a token sequence $T = (t_{1}, \\ldots, t_{L})$, $t_i \\in \\mathcal{V}$ of length $L$ and a ratio $r \\in \\mathcal{R}$ to a compressed representation of $C$ vectors of dimension $d$. The length $C$ is determined by the specified ratio $C = \\left\\lceil L / r \\right\\rceil$.\n\n\nAn ideal compressor $f_c$ preserves the conditional distribution of the model using the compressed version for any prompt $P$:\n\\begin{equation}\np_{\\mathcal{M}}(\\cdot \\mid T, P) \\;\\approx\\; p_{\\tilde{\\mathcal{M}}}(\\cdot \\mid f_c(T; r), P)\\;\\;,\n\\end{equation}\nwhere $\\tilde{\\mathcal{M}}$ is an adapted version of $\\mathcal{M}$, for example augmented with lightweight parameters such as LoRA~\\citep{hu2022lora} modules that can be fused into the base model without altering its capacity.\n\n\n\\section{Background and Related Work}\n\n\\paragraph{Soft Context Compression}\nA dominant line of research on context compression adopts the use of artificial \\emph{compression tokens}. \nAs shown in \\autoref{fig:arch:tokens}, a sequence of length $L$ with a target compression ratio $r$ is augmented with $C = \\lceil L/r \\rceil$ additional identical tokens. \\footnote{Although some works utilize a fixed number of compression tokens and then learn a distinct embedding for each position.}\nThe embedding of the compression token is learned. \nThe final hidden state at the time steps of the compression tokens is taken as the compressed representation. \nA decoder, conditioned on this representation and a downstream prompt (e.g., a question), produces the output. \nTraining typically combines a language modeling objective on the decoder with a distillation loss that encourages the compressor–decoder to approximate the behavior of a target LLM with access to the full uncompressed context (\\autoref{fig:arch:regular_llm}). \nThe decoder parameters are either tuned during learning or are frozen. \n\nThis paradigm has been explored extensively in recent work. \nAutoCompressors~\\citep{chevalier2023adapting} introduce recursive compression by appending a fixed set of compression tokens and extracting their hidden states. They tie the encoder and decoder weights. \nThe ICAE framework~\\citep{ge2024incontext} adopts an encoder–decoder setup where the decoder is frozen and only the encoder is trained, with a two-stage process of autoencoding pretraining and task-specific finetuning. \nCOCOM~\\citep{cocom} extends this approach to retrieval-augmented QA, experimenting with lighter encoders and with training decoders to jointly process multiple compressed contexts. \nOther work has sought more aggressive reduction: xRAG~\\citep{xrag} maps document retrieval embeddings directly into the decoder’s input space, achieving single-token compression but with severe constraints on sequence length and generality. \nPISCO~\\citep{louis-etal-2025-pisco} demonstrates that training compressors on LLM-generated answers improves downstream RAG performance, while PCC~\\citep{dai-etal-2025-pretraining} decouples the compressor from the target LLM by learning a converter to project compressed representations into another model’s hidden space. \nMost recently, GMSA~\\citep{tang2025gmsaenhancingcontextcompression} proposed grouping hidden representations and learning a layer semantic alignment module that bridges the gap between the encoder's final hidden states and the decoder's first attention layers. \nTheir approach is related to our study of pooling, but differs in the complexity of multi-stage reconstruction training and the use of compression-decoder adapters.\\footnote{While we consider this approach an important point of comparison, we were unable to include it in our evaluation because their code and models were not publicly available at the time of writing.}\n\nIn this work, we revisit some of these design choices and provide a systematic comparison with token-based architectures under both single- and multi-ratio training regimes. \n\n\\paragraph{KV Cache Compression}\nIn contrast to representing contexts as input embeddings, another line of work compresses the entire set of key–value (KV) states. \nSome approaches remove or compress less informative entries in the KV cache without additional training~\\citep{xiao2024efficient_streamingllm, oren-etal-2024-transformers_TOVA,li2024snapkv}, while others train the model to perform the compression explicitly~\\citep{qin-etal-2024-dodo,DynamicMemoryCompression}. \nA different variant introduces compression tokens, but instead of retaining only the final hidden representation, all KV states are propagated to the decoder~\\citep[e.g.,][]{zhang2025long_activationbeacon,li-etal-2025-500xcompressor}. \nAlthough these methods provide higher-capacity compressed representations that are well suited for efficient long-context comprehension, their increased size makes it impractical to store them for reuse in retrieval-augmented generation frameworks, where caching compressed representations could otherwise avoid recomputation. \n\n\\paragraph{Hard Prompt Compression}\nAn alternative approach is to compress contexts directly in the token space. \nThis has been done by removing unimportant tokens or lexical units~\\citep[e.g.,][]{li-etal-2023-selectivecontext,jiang-etal-2023-llmlingua, pan-etal-2024-llmlingua2} or generating concise summaries that preserve salient details~\\citep{chuang-etal-2024-learning_NanoCapsulator}. \nWhile these methods can be more interpretable and storage-efficient, they are inherently constrained by their reliance on explicit tokens. \n\n\\section{Methodology}\\label{sec:method}\n\n\\newcommand{\\context}{T}\n\\newcommand{\\prompt}{P}\n\\newcommand{\\numpoolops}{b}\n\\newcommand{\\lencompression}{C}\n\\newcommand{\\lencontext}{L}\n\\newcommand{\\comprate}{r}\n\\newcommand{\\allcomprates}{\\mathcal{R}}\n\\newcommand{\\embdim}{d}\n\\newcommand{\\encodingseq}{h}\n\\newcommand{\\encoding}{h}\n\n\n\n\n\nWe propose a compression model design where representations of adjacent tokens are pooled together to reduce the document representation length. We train via knowledge distillation to replicate the functionality of a teacher receiving the original (uncompressed) input. \n\n\\begin{figure}[t]\n \\centering\n \n \\def\\uniformscale{0.23} %\n \n \\newlength{\\fixedheight}\n \\setlength{\\fixedheight}{5.3cm}\n \n \\begin{subfigure}[t]{0.31\\textwidth}\n \\centering\n \\vbox to \\fixedheight{%\n \\includegraphics[page=1, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n \\vfill\n }\n \\caption{Processing with a regular language model (no compression).}\n \\label{fig:arch:regular_llm}\n \\end{subfigure}\n \\hfill\n \\begin{minipage}[t]{0.02\\textwidth}\n \\centering\n \\rule[0pt]{0pt}{\\fixedheight}%\n \\begin{tikzpicture}\n \\draw[dashed, gray, very thin] (0,0) -- (0,\\fixedheight);\n \\end{tikzpicture}\n \\end{minipage}%\n \\hfill\n \\begin{subfigure}[t]{0.31\\textwidth}\n \\centering\n \\vbox to \\fixedheight{%\n \\includegraphics[page=2, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n \\vfill\n }\n \\caption{Compression tokens approach for context compression.}\n \\label{fig:arch:tokens}\n \\end{subfigure}\n \\hfill\n \\begin{minipage}[t]{0.02\\textwidth}\n \\centering\n \\rule[0pt]{0pt}{\\fixedheight}%\n \\begin{tikzpicture}\n \\draw[dashed, gray, very thin] (0,0) -- (0,\\fixedheight);\n \\end{tikzpicture}\n \\end{minipage}%\n \\hfill\n \\begin{subfigure}[t]{0.31\\textwidth}\n \\centering\n \\vbox to \\fixedheight{%\n \\includegraphics[page=3, scale=\\uniformscale]{figures/architecture_fig.pdf}%\n \\vfill\n }\n \\caption{Our proposed method: no extra tokens; mean pooling of final hidden states.}\n \\label{fig:arch:pool}\n \\end{subfigure}\n \n \\caption{Comparison of context processing methods: regular LM, compression tokens, and our proposed approach --- mean pooling. The figure illustrates a compression ratio of $4\\times$.}\n \\label{fig:arch}\n\\end{figure}\n\n\n\\subsection{Compression via Mean Pooling}\\label{sec:method:pool}\n\nWe propose a simple compression architecture that relies only on mean pooling of encoded representations. \n\\autoref{fig:arch:pool} illustrates our approach. \nGiven a document, we compute its representation with an encoder, and \napply a non-overlapping mean pooling operator with window size $\\comprate$, the same size as the compression ratio, and stride $\\comprate$ to generate continuous vectors as the output compression.\n\nFormally, let $\\encodingseq = (\\encoding_1,\\ldots,\\encoding_\\lencontext) \\in \\mathbb{R}^{\\lencontext \\times \\embdim}$ denote the sequence of hidden states produced by the encoder.\nFor a compression ratio $\\comprate \\in \\allcomprates$, we partition the sequence into $k$ consecutive, non-overlapping blocks:\n\\begin{equation}\nS_k = \\{(k-1)\\comprate+1,\\ldots,\\min(k\\comprate, \\lencontext)\\}\\;\\;, \\qquad k=1,\\ldots,\\lceil \\lencontext/\\comprate \\rceil\\;\\;. \n\\end{equation}\nThe compressed representation of length $\\lceil \\lencontext/\\comprate \\rceil$ is obtained by averaging within each block:\n\\begin{equation}\nf_c(T,\\comprate) = (z_1,\\ldots,z_{\\lceil \\lencontext/\\comprate \\rceil}) \\in \\mathbb{R}^{\\lceil \\lencontext/\\comprate \\rceil \\times d} \\hspace{1em}\\text{s.t.}\\hspace{1em}z_k = \\frac{1}{|S_k|} \\sum_{i \\in S_k} h_i\\;\\;. \n\\end{equation}\n\n\nThe encoder we use is Transformer-based. \nCritically, we use a full self-attention mask during encoding, allowing each encoded vector to include information from the entire context, and thereby each compressed segment to aggregate information across the entire context. \nIn practice, we initialize with an autoregressive LLM, and remove the self-attention mask before learning. \n\nOur pooling design introduces no additional parameters beyond those of the encoder backbone and the decoder (i.e., target LLM) using the compressed representation, and has low computational overhead. The compression-tokens method is slightly more expensive. It requires an encoder input of size $\\lencontext + \\lencontext/\\comprate$, while our approach only processes the original $\\lencontext$ tokens, with negligible overhead for the pooling operator.\n\n\\subsection{Training Objective}\\label{sec:method:train}\n\n\\newcommand{\\answertoken}{a}\n\\newcommand{\\answerseq}{A}\n\nOur objective is to approximate the behavior of the target LLM before any fine-tuning when provided with the full uncompressed context (\\autoref{fig:arch:regular_llm}). \nWe consider this LLM as the teacher model within a knowledge distillation framework. \nEach training instance consists of a context $\\context$, a prompt $\\prompt$, and a ground-truth answer $\\answerseq = (\\answertoken_1,\\ldots,\\answertoken_m)$. For each answer position $i = 1,\\dots,m$, the teacher defines the distribution $q(\\cdot \\mid \\context, \\prompt, \\answerseq_{<i})$, where $\\answerseq_{<i} = (\\answertoken_1,\\ldots,\\answertoken_{i-1})$ denotes the gold prefix of the answer. \nThe compressor produces a compressed representation $f_c(T,r)$, which is passed to the fine-tuned decoder together with $(P, A_{<i})$, yielding the student distribution $p_\\theta(\\cdot \\mid f_c(T,r), P, A_{<i})$.\nThis combined encoder-decoder model is the student. \n\nFor a single compression ratio $\\comprate$, the distillation loss is the token-level KL divergence between the teacher and student distributions:\n\\begin{equation}\n\\mathcal{\\lencontext}_{\\text{KD}}(\\context,\\prompt,\\answerseq; \\comprate) \\;=\\;\n\\sum_{i=1}^m\n\\mathrm{KL}\\!\\left(\nq(\\cdot \\mid \\context,\\prompt,\\answerseq_{<i})\n\\;\\|\\;\np_\\theta(\\cdot \\mid f_c(\\context,\\comprate),\\prompt,\\answerseq_{<i})\n\\right)\\;\\;.\n\\end{equation}\n\nWe propose a unified training strategy in which a single compressor is trained to handle multiple ratios simultaneously. \nThis is in contrast to most previous work, where a separate model is trained for each compression ratio. \nWe generate compressed representations for all ratios $r \\in \\mathcal{R}$ for each training instance. Each compressed representation is passed independently to the decoder, and the corresponding losses are computed. The final objective for one training instance is obtained by summing across the ratios:\n\\begin{equation}\n\\mathcal{L}_{\\text{multi}}(\\context,\\prompt,\\answerseq) \\;=\\;\n\\sum_{\\comprate \\in \\allcomprates} \n\\mathcal{L}_{\\text{KD}}(\\context,\\prompt,\\answerseq; \\comprate)\\;\\;.\n\\end{equation}\n\nThe iteration over ratios is performed within each batch, and a single parameter update is applied after aggregating the losses. Since the encoder computation is shared across all ratios, this procedure is substantially more efficient than training separate models. By relying exclusively on knowledge distillation, rather than combining it with a language modeling objective, we enable a direct and fair comparison between the original model and the compressor.\n\n\\section{Experiments and Results}\\label{sec:exp}\n\nOur central objective is to isolate the contribution of context compression itself, without entanglement with retrieval noise or incomplete supervision. \nWhile compression methods are often demonstrated in retrieval-augmented generation (RAG) settings, these introduce extraneous challenges, such as when retrieved passages may not contain sufficient evidence, making performance conflate retrieval quality with compression quality. \nTo avoid this confounder, we focus exclusively on reading comprehension, where given contexts are guaranteed to contain the necessary evidence to answer the question. \nThis setup allows for a controlled, head-to-head comparison of different compression strategies, across a range of datasets that stress both single-hop and multi-hop reasoning. \n\n\\subsection{Experimental Setup}\\label{sec:exp:setup}\n\n\\paragraph{Data} \nWe curated our training set by mixing multiple context-based datasets, in tasks spanning reading comprehension (RC) and summarization. \nA detailed list of the datasets we incorporated in our training mixture can be found in \\autoref{tab:training_datasets}.\nWe evaluate with six reading comprehension benchmarks: SQuAD~\\citep{rajpurkar-etal-2016-squad}, NarrativeQA~\\citep{kocisky-etal-2018-narrativeqa}, HotpotQA~\\citep{yang-etal-2018-hotpotqa}, AdversarialQA~\\citep{bartolo2020beat_adversarialqa}, TriviaQA~\\citep{joshi-etal-2017-triviaqa}, and ParaphraseRC~\\citep{saha-etal-2018-duorc}.\nThis selection covers a broad spectrum of reasoning styles, from factual extraction to adversarial paraphrasing, thereby testing the generality of compression. \nFor TriviaQA, we restrict the evaluation to the verified subset, ensuring that every question has sufficient supporting evidence. \nThe training mixture includes the train splits of SQuAD, NarrativeQA, and HotpotQA, which thus serve as in-domain testbeds. \nAdversarialQA, TriviaQA, and ParaphraseRC are excluded from the training mixture and instead used purely for out-of-domain evaluation. \n\n\n\\paragraph{Model Training} For each target language model, we first finetune it on the training mixture using LoRA~\\citep{hu2022lora}. \nThis finetuned model is then fixed and used as the teacher in the distillation process. This ensures that performance differences stem solely from the compressor rather than mismatched finetuning (e.g., to the question domain). \nBoth the compressor’s encoder and decoder are initialized from the same target LLM but are trained with separate LoRA weights. We always use the instruction-tuned model weights as our backbone. For multi-ratio training, we always train on the ratios $\\{4\\times, 8\\times, 16\\times, 32\\times, 64\\times, 128\\times\\}$, unless stated otherwise. In addition, we found that applying a single linear layer slightly improves performance for both our method and the compression-tokens method, so for all experiments in this paper a learned matrix $W\\in\\mathbb{R}^{d\\times d}$ is applied to $f_c(T,\\comprate)$ before the compressed representation is given as input to the decoder LLM, unless stated otherwise. Detailed training configuration and hyperparameter choices are provided in \\autoref{app:exp}. \n\n\\paragraph{Implementation of the Compression-Tokens Approach} \nThe main approach we compare ours against is using compression tokens. \nA central design consideration in our experiments is the attention pattern applied to compression tokens. \nUnder the compression-tokens paradigm, the causal attention mask typically employed by transformer-based LLMs imposes a strong Matryoshka-style~\\citep{kusupati2022matryoshka} constraint: compressed representations at smaller lengths must correspond to strict prefixes of those at larger lengths. \nWe relax this restriction by allowing compression tokens to attend bidirectionally among themselves, while retaining causal attention over the original context. \nThis simple, albeit not explored in prior work, modification makes the model aware of how many compression tokens are available (i.e., its compression budget), and therefore to allocate information differently for each ratio while still benefiting from shared computation and KV caching.\nWe experiment with both the conventional causal attention mask and our bidirectional modification. \nEmpirically, we observe that this modification significantly improves the approach's performance. \nIn addition, in our implementation of the compression-tokens models, we utilize only a single compression token that is appended $\\lceil \\lencontext/\\comprate \\rceil$ times to the context, rather than having several compression tokens. This enables us to compress any context to any arbitrary ratio we choose, while retaining an equal number of parameters in the model. \n\n\n\\paragraph{Metrics}\nWe evaluate our models using the standard \\emph{exact match} (EM) and $F_1$ metrics.\\footnote{We show only $F_1$ scores in the main text but full EM results with similar trends are reported in \\autoref{tab:primary_results_EM}.} Several recent works reported QA performance using a substring accuracy metric, which assigns a score of 1 if the exact match is a substring of the output and 0 otherwise. We opt against the adoption of this metric as it is easily exploitable.\\footnote{Consider a question where the answer is a US state, and the model lists all 50 states as an answer.} This forces us to exclude some baselines from our primary results. \n\nIn addition, for each metric, we also define its \\emph{teacher-normalized} version. Given a metric $M$, a target language model $\\mathcal{M}$ and a compressor $f_c$, we calculate the following: $M_T$, the teacher's score, by passing the original uncompressed contexts to the decoder model; $M^{\\varnothing}_T$, the no-context score, by passing only the question without any context; and $M_{f_c}$, by using the compressed context. Then, the teacher-normalized score is given by $\\frac{M_{f_c}-M^\\varnothing_T}{M_T -M^\\varnothing_T}$. This score does two things. \nFirst, it scales the compressor's score with respect to the teacher's, allowing for a direct assessment of the amount of retained performance under compression. \nSecond, it accounts for how easy it is for the model to answer the input question without any context. This latter consideration comes to account for cases where a question does not really require the context, potentially inflating the score of the compression model, while actually simply ignoring the compressed input. \n\n\\paragraph{Systems}\n\nOur main comparison point is our implementations of the compression tokens method, with causal or bidirectional attention. \nWe compare against these two systems throughout our experiments. \nWe also include comparisons to other soft context compression methods: ICAE~\\citep{ge2024incontext} and PCC~\\citep{dai-etal-2025-pretraining}. \nWe also evaluate LLMLingua2 \\citep{pan-etal-2024-llmlingua2}, a hard prompting compression approach, by passing LLMLingua's compressed prompts to our finetuned Qwen3-8B teacher model. \n\nComparison between compression methods is challenging in general, due to inconsistencies in the training procedures. \nOur main goal is to build a systematic understanding of the architecture landscape, and we compare ourselves to other methods mainly to showcase the validity of our experiments.\nShowing the strength of performance compared to the prior state of the art is secondary, and not even necessarily feasible because many approaches do not release code or models, or adopt training methods that complicate the evaluation. \nThis challenge is demonstrated well by the PISCO~\\citep{louis-etal-2025-pisco} method. Their training method is not well suited for the traditional EM/$F_1$ metrics and performs poorly on these metrics, and indeed the authors evaluated their method only using a more forgiving substring accuracy score. We therefore omit this method from our primary comparisons, but include it and report substring accuracy in \\aautoref{app:results:metrics} (\\autoref{tab:primary_results_accuracy}). \n\nAll experiments are conducted with context lengths up to 1{,}024 tokens, a practical limitation imposed by our computational budget. \n\n\n\\subsection{Results}\\label{sec:exp:results} \n\n\n\n\n\n\n\n\n\n\\begin{table*}[!ht]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 42.52 & & 24.39 & & 22.59 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 42.40 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 62.08 & & 51.30 & & 36.20 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 62.98 & & 49.37 & & 37.24 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 74.33 & & & & & & & 23.06 \\\\\n & Compression-Tokens (Causal) & & 67.03 & 65.90 & 56.21 & 58.41 & 47.47 & 44.76 & \\\\\n & Compression-Tokens (Bidirectional) & & 69.20 & 69.57 & 60.27 & 63.01 & 46.93 & \\textbf{46.97} & \\\\\n & Mean-Pooling & & \\textbf{71.66} & \\textbf{70.55} & \\textbf{63.85} & \\textbf{64.67} & \\textbf{47.90} & 45.92 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 73.44 & & & & & & & 19.79 \\\\\n & Compression-Tokens (Causal) & & 64.88 & 62.53 & 55.22 & 54.28 & 43.08 & 40.83 & \\\\\n & Compression-Tokens (Bidirectional) & & 66.72 & 68.15 & 57.68 & 60.48 & 41.61 & \\textbf{42.66} & \\\\\n & Mean-Pooling & & \\textbf{70.39} & \\textbf{69.36} & \\textbf{61.79} & \\textbf{61.72} & \\textbf{43.62} & 41.05 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 69.93 & & & & & & & 14.00 \\\\\n & Compression-Tokens (Causal) & & 50.90 & 57.73 & 49.83 & 48.68 & 36.19 & 35.34 & \\\\\n & Compression-Tokens (Bidirectional) & & 62.04 & 62.60 & 51.53 & 54.11 & 36.25 & \\textbf{35.77} & \\\\\n & Mean-Pooling & & \\textbf{66.43} & \\textbf{64.17} & \\textbf{55.43} & \\textbf{54.47} & \\textbf{36.72} & 33.48 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 65.36 & & & & & & & 9.34 \\\\\n & Compression-Tokens (Causal) & & 54.40 & 51.85 & 41.57 & 42.59 & 28.86 & 28.60 & \\\\\n & Compression-Tokens (Bidirectional) & & 55.59 & 57.03 & 44.82 & 47.62 & 29.69 & \\textbf{29.51} & \\\\\n & Mean-Pooling & & \\textbf{61.17} & \\textbf{58.36} & \\textbf{47.59} & \\textbf{47.64} & \\textbf{29.94} & 26.36 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 71.96 & & & & & & & 21.64 \\\\\n & Compression-Tokens (Causal) & & 63.35 & 62.18 & 55.07 & 54.70 & 44.46 & 42.49 & \\\\\n & Compression-Tokens (Bidirectional) & & 64.76 & 65.24 & 56.39 & 58.43 & 44.73 & 43.17 & \\\\\n & Mean-Pooling & & \\textbf{69.33} & \\textbf{68.09} & \\textbf{61.39} & \\textbf{61.04} & \\textbf{44.98} & \\textbf{43.71} & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 65.82 & & & & & & & 15.17 \\\\\n & Compression-Tokens (Causal) & & 56.31 & 53.74 & 47.51 & 46.96 & 35.41 & 35.62 & \\\\\n & Compression-Tokens (Bidirectional) & & 57.91 & 57.52 & \\textbf{49.20} & 50.06 & \\textbf{36.43} & \\textbf{36.25} & \\\\\n & Mean-Pooling & & \\textbf{62.81} & \\textbf{60.56} & 47.28 & \\textbf{51.56} & 33.25 & 33.98 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}}\n\\medskip\n\\includegraphics[width=\\textwidth]{figures/methods_ratios_comparison.pdf}\n\\caption{\nPrimary results. Values in the table are $F_1$ scores macro-averaged across all datasets in our evaluation suite. \n\\textbf{Original} stands for the teacher model's score when given the full context. \\textbf{No Ctx} stands for the teacher model's score when not given any context at all. For each ratio, we display both single- and multi-ratio versions. For the baseline systems (top section), we include results for the compression ratios supported by these methods, unsupported ratios are left blank. The best method for each (model, ratio, single/multi-ratio training) setting is \\textbf{bolded}.\nBottom figures present aggregated views of the results in the table, but instead of $F_1$ show the teacher-normalized $F_1$ metric (Relative F1). Scores are obtained by averaging over all models listed in the table. \n}\\label{tab:primary_results_hybrid_transpose}\n\\end{table*}\n\n\\autoref{tab:primary_results_hybrid_transpose} shows our main results. We demonstrate the robustness and generality of our findings by comparing six different models, spanning three model families and four model scales: Llama3.2-1B~\\citep{grattafiori2024llama}, Gemma2-2b~\\citep{team2024gemma}, and Qwen3-0.6/1.7/4/8B~\\citep{yang2025qwen3}. \nWe show the average $F_1$ scores over all six evaluation datasets. \nBelow the results table, we provide bar charts that summarize the results along specific dimensions that emphasize trends. \nThe bar charts show the teacher-normalized $F_1$ metric averaged across all models and datasets to get a single aggregated result per method. \nWe provide the teacher model's performance with the original context (\"Original\") and without context at all (\"No Ctx\"). In between we report the results for different compression ratios and for both the single- and multi-ratio training schemes. \n\nOur mean-pooling method is consistently better than both the standard (causal) compression tokens architecture and the bidirectional variation. \nSimply adding bidirectional attention between the compression tokens dramatically improves performance. \nComparing the single-ratio models to the multi-ratio models, we see that the bidirectional compression tokens approach significantly benefits from multi-ratio training, while for the mean-pooling approach a trade-off clearly exists. \nThis is potentially because the bidirectional approach has a clear signal about the target compression ratio -- the forward attention allows each time step to be aware of the total length of the compressed output. \nWithout this, the model must produce a one-size-fits-all representation in each time step. \nLastly, while we do see a performance drop in the multi-ratio setting at $128\\times$ for all methods, it must be taken in the context of the already relatively low performance retention at that ratio.\n\n\\paragraph{Compression Scaling}\n\\begin{figure}[htb]\n \\centering\n \\includegraphics[width=0.6\\linewidth]{figures/scaling_law_qwen3.pdf}\n \\caption{Compression Scaling. We show the teacher-normalized $F_1$ scores (Relative F1) across four Qwen3 model scales. The scores are averages of the scores of all datasets. We can clearly observe the benefits of scaling for LLM compressors.}\n \\label{fig:scaling_law}\n\\end{figure}\nIt is well known that LLM performance increases with scale, if scaled appropriately~\\citep{cheng2024training_chinchilla}. But does compression quality scale as well? In \\autoref{tab:primary_results_hybrid_transpose} we can see that the teacher's performance improves as the model size grows. Having a compressor increase in performance at the same rate as the teacher would actually tell us that the compressor does not scale well, since that would mean that the teacher-normalized scores stay constant throughout the scales. \n\\autoref{fig:scaling_law} shows the compression performances of the four Qwen3 model scales we use. \nWe train the models under the multi-ratio setting to efficiently evaluate multiple ratios. \nWe evaluate using the teacher-normalized $F_1$ score, and present the average scores across all datasets. The results are exciting\\textemdash the compressors clearly have desirable scaling properties. \nCritically, the efficiency gains of context compression are much larger as the model size increases. \nTherefore, observing that larger models retain higher levels of performance (higher relative F1) justifies this line of research. \nSimilar trends are observed for the other methods (\\autoref{tab:primary_results_hybrid_transpose}), demonstrating the generality of this finding. \n\n\\paragraph{In-Domain vs. Out-of-Domain}\n\\begin{figure}[t]\n \\centering\n \\begin{subfigure}[t]{0.95\\linewidth}\n \\centering\n \\includegraphics[width=\\linewidth]{figures/in_vs_out_fig.pdf}\n \\caption{In-domain vs.\\ out-of-domain performance across compression ratios.}\n \\label{fig:in-vs-out}\n \\end{subfigure}\n\n \\vspace{0.8em} %\n\n \\begin{subfigure}[t]{0.95\\linewidth}\n \\centering\n \\includegraphics[width=\\linewidth]{figures/in_out_gap_fig.pdf}\n \\caption{Performance drop (in–out gap) per method across compression ratios (in teacher-normalized Relative $F_1$ units). Higher values mean a larger domain performance gap. Negative values mean that the out-of-domain performance is better than in-domain performance.}\n \\label{fig:in-out-gap}\n \\end{subfigure}\n\n \\caption{In-domain and out-of-domain comparison. (a) Line plots show performance on in-domain vs.\\ out-of-domain datasets. (b) Bar plots show the in–out performance gap per method, which is the difference between in-domain and out-of-domain teacher-normalized $F_1$ scores.}\n \\label{fig:in-out-combined}\n\\end{figure}\n\nWe construct our evaluation suite with both in-domain QA datasets and out-of-domain QA datasets (\\autoref{sec:exp:setup}). The training splits of the in-domain datasets are included in the training data mixture, while the out-of-domains datasets are not. \nIt is expected that downstream performance will drop for out-of-domain datasets. \nCritical for our study, though, is the performance drop of the compressor itself. \n\\autoref{fig:in-vs-out} plots the in-domain and out-of-domain performance using the teacher-normalized $F_1$ score for the Qwen3-8B model, averaged over the datasets in each category. \nWe first observe that while the mean-pooling approach is superior for ratios up to $16\\times$ in all settings, its performance deteriorates as the compression ratio increases. \nTo better understand the performance change due to the domain gap, we plot the differences between the in-domain and out-of-domain performance in \\autoref{fig:in-out-gap}. \nThe performance gap is higher for low ratios, and lower for higher ratios. \nOne possible explanation is that at low compression ratios the compressed representations still retain much of the original contextual signal, so the model is more sensitive to domain-specific distributional shifts; differences between in-domain and out-of-domain language patterns thus manifest as a larger performance gap. By contrast, at higher compression ratios much of the fine-grained contextual detail is already lost to compression noise, which dominates over the domain gap. In this regime, both in-domain and out-of-domain datasets suffer similarly from the limited representational capacity, resulting in a smaller relative difference. \n \n\\paragraph{Model Ablations}\n\\begin{table}[t]\n\\centering\n\\resizebox{0.92\\linewidth}{!}{%\n\\begin{tabular}{l r r r r r r c}\n\\toprule\n\\textbf{Ablation} (\\textsc{Gemma2-2B}) & 4$\\times$ & 8$\\times$ & 16$\\times$ & 32$\\times$ & 64$\\times$ & 128$\\times$ & $\\Delta$ \\\\\n\\midrule\nDefault & \\textbf{68.1} & \\textbf{65.4} & \\textbf{61.0} & \\textbf{54.9} & \\textbf{48.8} & \\textbf{43.7} & \\,($+0.0$) \\\\\nFixed Decoder & 64.9 & 61.9 & 57.0 & 51.5 & 45.0 & 39.8 & \\,($-3.6$) \\\\\nFixed Encoder & 57.4 & 49.9 & 44.1 & 39.8 & 36.2 & 34.8 & \\,($-13.3$) \\\\\nNo Encoder & 58.7 & 51.9 & 44.9 & 40.2 & 36.2 & 34.1 & \\,($-12.6$) \\\\\nw/o Linear Layer & 67.7 & 64.5 & 60.0 & 54.1 & 48.1 & 43.2 & \\,($-0.7$) \\\\\nRatio Sampling & 67.1 & 64.0 & 59.3 & 53.5 & 47.5 & 42.2 & \\,($-1.4$) \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Ablation study for mean pooling using \\textsc{Gemma2-2B} as the teacher LLM. Numbers are macro-averaged $F_1$ scores. \\emph{$\\Delta$}: mean change vs. Default across ratios; \\textbf{bold} = best per column.}\n\\label{tab:abl_gemma2_mean}\n\\end{table}\n\nWe run all our ablations using the Gemma2-2B model, since it demonstrates strong performance while being relatively compute-efficient. \\autoref{tab:abl_gemma2_mean} presents the ablation results. \nWe conduct several ablations: (1) Fixed Decoder: the decoder is kept frozen and only the encoder is trained; (2) Fixed Encoder: the encoder is kept frozen and only the decoder is trained; (3) No Encoder: we remove the encoder entirely, and obtain the initial context representation using only the token embeddings of the decoder model; (4) w/o Linear Layer: we remove the linear layer that is applied after the pooling operation; (5) Ratio Sampling: instead of training on all ratios for each sample, a single ratio is randomly chosen for each sample during training. \n\nFreezing the decoder results in considerable performance reduction, although not catastrophic. This is in line with findings of previous works (\\citep{louis-etal-2025-pisco}). Freezing or removing the encoder is more detrimental, lowering performance by more than 12\\%. The effect of the linear layer is not very significant, its removal results in a reduction of only 0.7\\%. \nFinally, while randomly sampling a single ratio per sample would speed up training significantly, it does so at the cost of a small drop in performance (1.4\\%), likely because each ratio gets less updates during training. \n\n\\section{Discussion}\\label{sec:discussion}\n\nWe provide a systematic study of soft context compression, showing that a simple mean-pooling approach consistently outperforms compression-tokens architectures while requiring no additional parameters. We further demonstrate that multi-ratio training is both feasible and effective, enabling a single compressor to support a wide range of compression budgets with only minor performance degradation.\nInterestingly, we observe that the bidirectional compression-tokens method consistently benefits from multi-ratio training. A plausible explanation is that, unlike mean-pooling or causal compression-tokens, this method has explicit access to the number of compression tokens available, allowing it to adapt to the target budget. Exploring how to incorporate similar signals into other architectures is an important direction for future work.\n\nFinally, our study highlights a broader open problem: the evaluation of compression methods remains hindered by inconsistent setups, metrics, and benchmarks. By isolating compression quality from retrieval confounders and applying a uniform evaluation across models, scales, and domains, we aim to provide a rigorous basis for future research on soft context compression. We hope this work helps establish more standardized practices and clarifies the core principles that should guide the development of next-generation compressors.\n\n\\section*{Acknowledgements}\\label{sec:acknowledgements}\n\n\n\nThis research was supported by a gift to the LinkedIn–Cornell Bowers Strategic Partnership, NSF under grant No. OAC-2311521, NASA under award No. 20-OSTFL20-0053, and a gift from Open Philanthropy. \nWe thank Google for enabling experiments with Gemini through a gift.\nThis research was supported with Cloud TPUs from Google's TPU Research Cloud (TRC).\nWe thank Nathan Godey for his comments. \n\n\\bibliographystyle{iclr2026_conference}\n\\bibliography{iclr2026_conference}\n\n\\newpage\n\\appendix\n\\section{Additional Experimental Setup Details}\n\\label{app:exp}\n\\subsection{Data}\\label{app:exp:data}\n\n\\autoref{tab:training_datasets} and \\autoref{tab:evaluation_datasets} provide detailed lists of our training data mixture and evaluation suite.\nWe use the summaries as contexts for NarrativeQA, instead of the full stories. For HotpotQA, we only use the two gold paragraphs as contexts, and remove the distractors. \n\nWe increase the training data diversity by randomly sample a prompt template that fits the task, when training samples are composed of a context $C$, question $Q$ and answer $A$. For example, for the extractive QA task, an example of a prompt template is: \\textit{``\\textless C\\textgreater \\textbackslash n Extract the answer from the text above. \\textbackslash n Question: \\textless Q\\textgreater \\textbackslash n Answer: \\textless A\\textgreater''}. Similar templates are defined for other tasks as well. \nWe created approximately 100 prompt templates for each task. The full list of templates for each task is available along with our code. \n\\begin{table}[H]\n\\centering\n\\begin{tabular}{lrrr}\n\\toprule\nDataset & Avg. Context Tokens & \\#Samples & \\#Contexts \\\\\n\\midrule\n\\multicolumn{4}{l}{\\textbf{Summarization}} \\\\\nCNN/DM~\\citep{see-etal-2017-get_cnndm} & 649 & 198{,}732 & 196{,}601 \\\\\nDialogSum~\\citep{chen-etal-2021-dialogsum} & 208 & 12{,}452 & 12{,}450 \\\\\nSAMSum~\\citep{Gliwa_2019_samsum} & 145 & 14{,}730 & 14{,}254 \\\\\nXSum~\\citep{narayan-etal-2018-dont_xsum} & 408 & 185{,}760 & 185{,}566 \\\\\n\\addlinespace\n\\multicolumn{4}{l}{\\textbf{Reading Comprehension}} \\\\\nBoolQ~\\citep{clark-etal-2019-boolq} & 126 & 9{,}427 & 7{,}927 \\\\\nDROP~\\citep{dua-etal-2019-drop} & 295 & 76{,}751 & 5{,}477 \\\\\nHotpotQA~\\citep{yang-etal-2018-hotpotqa} & 247 & 90{,}327 & 84{,}705 \\\\\nNarrativeQA~\\citep{kocisky-etal-2018-narrativeqa} & 668 & 28{,}299 & 953 \\\\\nPubMedQA~\\citep{jin-etal-2019-pubmedqa} & 318 & 211{,}218 & 211{,}164 \\\\\nQuAC~\\citep{choi-etal-2018-quac} & 515 & 81{,}391 & 6{,}574 \\\\\nQuAIL~\\citep{rogers2020getting_quail} & 416 & 10{,}246 & 560 \\\\\nRACE~\\citep{lai-etal-2017-race} & 349 & 87{,}749 & 25{,}108 \\\\\nSQuAD~\\citep{rajpurkar-etal-2016-squad} & 162 & 86{,}821 & 18{,}877 \\\\\nPWC~\\citep{ge2024incontext} & 477 & 241{,}563 & 16{,}382 \\\\\n\\midrule\n\\textbf{Total} & \\textbf{410} & \\textbf{1,335,466} & \\textbf{786,598} \\\\\n\\bottomrule\n\\end{tabular}\n\\caption{Training datasets with average context length (tokens), number of samples, number of distinct contexts, and task category. The overall average context length is weighted by the number of samples.}\n\\label{tab:training_datasets}\n\\end{table}\n\\begin{table}[H]\n\\centering\n\\begin{tabular}{lrrr}\n\\toprule\nDataset & Avg. Context Tokens & \\#Samples & \\#Contexts \\\\\n\\midrule\nAdversarialQA~\\citep{bartolo2020beat_adversarialqa} & 154 & 1{,}000 & 341 \\\\\nHotpotQA~\\citep{yang-etal-2018-hotpotqa} & 254 & 7{,}394 & 7{,}352 \\\\\nNarrativeQA~\\citep{kocisky-etal-2018-narrativeqa} & 639 & 3{,}002 & 100 \\\\\nParaphraseRC~\\citep{saha-etal-2018-duorc} & 685 & 4{,}835 & 560 \\\\\nSQuAD~\\citep{rajpurkar-etal-2016-squad} & 169 & 5{,}928 & 1{,}204 \\\\\nTriviaQA (Verified)~\\citep{joshi-etal-2017-triviaqa} & 539 & 185 & 185 \\\\\n\\midrule\n\\textbf{Total} & \\textbf{375} & \\textbf{22{,}344} & \\textbf{9{,}742} \\\\\n\\bottomrule\n\\end{tabular}\n\\caption{Evaluation datasets with average context length (tokens), number of samples, and number of distinct contexts. The overall average context length is weighted by the number of samples.}\n\\label{tab:evaluation_datasets}\n\\end{table}\n\\newpage\n\\subsection{Training Hyperparameters}\\label{app:exp:hps}\n\\begin{table}[ht!]\n \\centering\n \\begin{tabular}{cc}\n \\toprule\n \\textbf{Hyperparameter} & \\textbf{Value} \\\\\n \\midrule\n LoRA $r$ & 16 \\\\\n LoRA $\\alpha$ & 16 \\\\ \n optimizer & AdamW \\\\\n $\\beta_1$ & 0.9 \\\\\n $\\beta_2$ & 0.95 \\\\\n clip norm & 1 \\\\\n peak learning rate & 2e-4 \\\\\n final learning rate & 2e-5 \\\\\n lr scheduler type & cosine \\\\\n warmup ratio & 0.05 \\\\\n weight decay & 0.0 \\\\\n steps & 48,000 \\\\\n batch size & 32 \\\\\n max context length & 1024 \\\\\n max answer tokens & 256 \\\\\n \\bottomrule\n \\end{tabular}\n \\caption{Hyperparameters for training all the models used in this work.} \n \\label{table:hyperparameters}\n\\end{table}\n\\newpage\n\\section{Additional Results}\\label{app:results}\nWe provide additional results from the same experiments conducted in the main body of the paper. \\aautoref{app:results:metrics} provides the primary results of the paper with the EM and substring accuracy metrics. \\aautoref{app:results:datasets} shows the $F_1$ performance on each individual dataset from the evaluation suite. \n\\subsection{Primary Results \\textemdash Additional Metrics}\\label{app:results:metrics}\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 30.02 & & 16.16 & & 16.06 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 24.94 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 48.81 & & 38.38 & & 25.94 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 49.34 & & 36.64 & & 27.92 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 59.82 & & & & & & & 16.19 \\\\\n & Compression-Tokens (Causal) & & 51.59 & 50.01 & 41.26 & 42.99 & 34.21 & 32.50 & \\\\\n & Compression-Tokens (Bidirectional) & & 53.44 & 53.99 & 44.92 & 47.15 & 33.60 & 34.27 & \\\\\n & Mean-Pooling & & 56.41 & 55.04 & 47.95 & 49.02 & 34.72 & 33.15 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 58.87 & & & & & & & 13.74 \\\\\n & Compression-Tokens (Causal) & & 49.66 & 46.26 & 40.05 & 39.59 & 30.07 & 28.84 & \\\\\n & Compression-Tokens (Bidirectional) & & 51.06 & 52.37 & 42.53 & 45.14 & 28.84 & 29.51 & \\\\\n & Mean-Pooling & & 55.25 & 53.77 & 45.43 & 45.86 & 30.91 & 28.38 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 55.19 & & & & & & & 9.07 \\\\\n & Compression-Tokens (Causal) & & 36.66 & 41.64 & 35.49 & 34.64 & 24.27 & 24.04 & \\\\\n & Compression-Tokens (Bidirectional) & & 46.45 & 46.72 & 36.62 & 38.93 & 24.31 & 24.33 & \\\\\n & Mean-Pooling & & 51.28 & 48.77 & 40.45 & 39.04 & 25.15 & 22.01 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 50.85 & & & & & & & 4.78 \\\\\n & Compression-Tokens (Causal) & & 39.66 & 36.76 & 27.99 & 29.00 & 18.23 & 18.20 & \\\\\n & Compression-Tokens (Bidirectional) & & 40.98 & 41.92 & 30.92 & 33.64 & 18.82 & 18.55 & \\\\\n & Mean-Pooling & & 45.82 & 43.07 & 32.50 & 33.09 & 19.05 & 16.07 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 57.63 & & & & & & & 15.00 \\\\\n & Compression-Tokens (Causal) & & 47.90 & 45.98 & 39.57 & 39.74 & 32.02 & 29.66 & \\\\\n & Compression-Tokens (Bidirectional) & & 49.43 & 49.40 & 40.89 & 42.70 & 31.79 & 30.43 & \\\\\n & Mean-Pooling & & 54.20 & 52.77 & 45.88 & 45.68 & 32.41 & 30.83 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 51.67 & & & & & & & 9.47 \\\\\n & Compression-Tokens (Causal) & & 41.84 & 39.03 & 33.73 & 33.38 & 24.11 & 24.64 & \\\\\n & Compression-Tokens (Bidirectional) & & 43.46 & 42.96 & 35.04 & 35.46 & 24.91 & 24.56 & \\\\\n & Mean-Pooling & & 47.97 & 45.45 & 33.15 & 36.93 & 22.89 & 22.70 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{Primary results with exact match (EM) as the metric.}\n \\label{tab:primary_results_EM}\n\\end{table}\n\\newpage\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 33.63 & & 18.30 & & 17.36 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 49.18 & & & & & & \\\\\n& \\emph{PISCO} (Llama3.1-8B) & & & & 53.62 & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 54.05 & & 43.67 & & 30.03 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 55.17 & & 41.79 & & 30.10 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.84 & & & & & & & 17.98 \\\\\n & Compression-Tokens (Causal) & & 59.79 & 58.58 & 47.07 & 49.99 & 39.09 & 37.05 & \\\\\n & Compression-Tokens (Bidirectional) & & 62.50 & 63.58 & 52.22 & 55.26 & 38.72 & 39.36 & \\\\\n & Mean-Pooling & & 65.91 & 65.06 & 55.68 & 56.77 & 39.95 & 37.80 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.69 & & & & & & & 15.00 \\\\\n & Compression-Tokens (Causal) & & 57.12 & 54.17 & 46.06 & 45.47 & 34.83 & 33.48 & \\\\\n & Compression-Tokens (Bidirectional) & & 59.35 & 60.99 & 48.92 & 52.23 & 33.20 & 34.33 & \\\\\n & Mean-Pooling & & 64.05 & 62.94 & 52.77 & 52.82 & 35.49 & 32.37 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.21 & & & & & & & 9.85 \\\\\n & Compression-Tokens (Causal) & & 43.01 & 49.31 & 41.31 & 40.45 & 28.45 & 27.90 & \\\\\n & Compression-Tokens (Bidirectional) & & 54.31 & 54.70 & 42.66 & 45.13 & 28.33 & 28.04 & \\\\\n & Mean-Pooling & & 60.03 & 57.28 & 46.63 & 45.07 & 28.96 & 25.82 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 59.67 & & & & & & & 5.62 \\\\\n & Compression-Tokens (Causal) & & 46.36 & 43.62 & 33.07 & 34.30 & 21.13 & 21.71 & \\\\\n & Compression-Tokens (Bidirectional) & & 48.04 & 48.84 & 36.11 & 39.50 & 22.13 & 22.00 & \\\\\n & Mean-Pooling & & 54.36 & 51.16 & 38.30 & 38.68 & 22.44 & 18.87 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.14 & & & & & & & 16.80 \\\\\n & Compression-Tokens (Causal) & & 55.50 & 52.94 & 46.13 & 45.59 & 36.14 & 33.94 & \\\\\n & Compression-Tokens (Bidirectional) & & 56.94 & 57.54 & 46.90 & 49.52 & 36.14 & 34.75 & \\\\\n & Mean-Pooling & & 62.51 & 61.28 & 52.55 & 51.90 & 36.61 & 34.93 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 60.30 & & & & & & & 11.09 \\\\\n & Compression-Tokens (Causal) & & 48.85 & 45.41 & 39.16 & 38.51 & 27.54 & 28.01 & \\\\\n & Compression-Tokens (Bidirectional) & & 50.89 & 50.10 & 40.44 & 41.91 & 28.34 & 28.44 & \\\\\n & Mean-Pooling & & 56.62 & 53.50 & 38.84 & 42.76 & 25.99 & 26.19 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{Primary results with accuracy as the metric.}\n \\label{tab:primary_results_accuracy}\n\\end{table}\n\n\\subsection{Results Per Dataset}\\label{app:results:datasets}\n\\subsubsection{In Domain Datasets Results}\\label{app:results:datasets:in}\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 48.38 & & 21.34 & & 19.68 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 45.6 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 78.38 & & 67.63 & & 40.22 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 79.56 & & 62.93 & & 41.23 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 86.48 & & & & & & & 20.31 \\\\\n & Compression-Tokens (Causal) & & 77.11 & 74.89 & 57.05 & 62.12 & 44.56 & 42.35 & \\\\\n & Compression-Tokens (Bidirectional) & & 80.00 & 81.23 & 64.80 & 69.27 & 44.30 & 43.86 & \\\\\n & Mean-Pooling & & 83.76 & 82.75 & 71.37 & 71.19 & 44.65 & 43.19 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 85.75 & & & & & & & 17.72 \\\\\n & Compression-Tokens (Causal) & & 74.23 & 71.31 & 57.49 & 56.88 & 38.95 & 37.10 & \\\\\n & Compression-Tokens (Bidirectional) & & 77.24 & 79.28 & 60.71 & 65.49 & 38.19 & 38.41 & \\\\\n & Mean-Pooling & & 83.19 & 81.54 & 68.20 & 67.47 & 39.96 & 37.54 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 83.65 & & & & & & & 12.66 \\\\\n & Compression-Tokens (Causal) & & 54.25 & 64.50 & 49.09 & 49.98 & 31.78 & 30.10 & \\\\\n & Compression-Tokens (Bidirectional) & & 72.92 & 73.39 & 53.07 & 57.36 & 31.58 & 31.17 & \\\\\n & Mean-Pooling & & 79.56 & 77.17 & 59.01 & 58.30 & 32.36 & 29.90 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 7.91 \\\\\n & Compression-Tokens (Causal) & & 61.67 & 57.52 & 40.29 & 41.60 & 22.06 & 22.45 & \\\\\n & Compression-Tokens (Bidirectional) & & 64.21 & 67.05 & 42.81 & 46.68 & 22.09 & 22.36 & \\\\\n & Mean-Pooling & & 74.00 & 70.60 & 48.62 & 48.14 & 22.40 & 20.45 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 84.58 & & & & & & & 16.41 \\\\\n & Compression-Tokens (Causal) & & 70.61 & 69.06 & 55.75 & 56.37 & 37.89 & 35.66 & \\\\\n & Compression-Tokens (Bidirectional) & & 74.16 & 75.41 & 57.77 & 61.75 & 37.72 & 37.00 & \\\\\n & Mean-Pooling & & 81.67 & 80.01 & 66.38 & 65.64 & 38.96 & 36.71 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 81.16 & & & & & & & 11.27 \\\\\n & Compression-Tokens (Causal) & & 62.65 & 59.34 & 46.41 & 45.49 & 28.58 & 28.44 & \\\\\n & Compression-Tokens (Bidirectional) & & 64.48 & 65.61 & 48.99 & 51.39 & 29.09 & 28.82 & \\\\\n & Mean-Pooling & & 74.91 & 71.40 & 47.36 & 53.66 & 28.02 & 27.91 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{SQuAD $F_1$.}\n \\label{tab:primary_results_squad}\n\\end{table}\n\\newpage\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 53.54 & & 29.32 & & 26.27 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 50.01 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 68.55 & & 59.38 & & 43.93 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 70.08 & & 59.05 & & 46.46 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 84.67 & & & & & & & 26.65 \\\\\n & Compression-Tokens (Causal) & & 78.85 & 78.32 & 68.00 & 72.65 & 64.14 & 59.74 & \\\\\n & Compression-Tokens (Bidirectional) & & 80.24 & 81.45 & 73.30 & 76.77 & 63.26 & 62.44 & \\\\\n & Mean-Pooling & & 83.30 & 82.08 & 77.66 & 78.41 & 63.88 & 63.77 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 84.12 & & & & & & & 23.16 \\\\\n & Compression-Tokens (Causal) & & 76.48 & 75.56 & 68.85 & 69.80 & 59.08 & 55.78 & \\\\\n & Compression-Tokens (Bidirectional) & & 78.13 & 79.41 & 71.11 & 74.60 & 58.38 & 56.87 & \\\\\n & Mean-Pooling & & 82.20 & 80.77 & 75.45 & 76.02 & 59.29 & 58.74 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 80.95 & & & & & & & 18.75 \\\\\n & Compression-Tokens (Causal) & & 66.69 & 70.98 & 63.82 & 63.84 & 51.48 & 48.78 & \\\\\n & Compression-Tokens (Bidirectional) & & 73.73 & 74.93 & 66.06 & 68.50 & 52.08 & 50.77 & \\\\\n & Mean-Pooling & & 78.64 & 76.11 & 68.76 & 68.78 & 50.86 & 49.44 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 77.35 & & & & & & & 14.74 \\\\\n & Compression-Tokens (Causal) & & 66.62 & 65.76 & 55.88 & 57.79 & 43.16 & 39.58 & \\\\\n & Compression-Tokens (Bidirectional) & & 67.24 & 69.28 & 58.44 & 61.79 & 43.80 & 41.66 & \\\\\n & Mean-Pooling & & 73.00 & 69.58 & 61.13 & 61.08 & 42.76 & 40.45 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 82.55 & & & & & & & 25.18 \\\\\n & Compression-Tokens (Causal) & & 75.62 & 75.54 & 69.18 & 70.42 & 61.91 & 59.03 & \\\\\n & Compression-Tokens (Bidirectional) & & 76.55 & 77.60 & 69.64 & 73.51 & 61.67 & 60.46 & \\\\\n & Mean-Pooling & & 80.93 & 79.85 & 75.10 & 74.90 & 62.36 & 61.64 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 77.96 & & & & & & & 19.34 \\\\\n & Compression-Tokens (Causal) & & 69.68 & 68.22 & 63.36 & 62.96 & 52.27 & 49.81 & \\\\\n & Compression-Tokens (Bidirectional) & & 70.74 & 71.01 & 64.47 & 66.19 & 53.51 & 51.79 & \\\\\n & Mean-Pooling & & 74.38 & 72.69 & 62.75 & 66.59 & 51.05 & 50.86 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{HotpotQA $F_1$.}\n \\label{tab:primary_results_hotpotqa}\n\\end{table}\n\\newpage\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 27.33 & & 14.35 & & 10.69 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 32.65 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 50.29 & & 34.16 & & 16.05 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 50.72 & & 32.56 & & 16.18 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 68.00 & & & & & & & 10.93 \\\\\n & Compression-Tokens (Causal) & & 59.62 & 58.28 & 46.58 & 49.32 & 33.41 & 29.37 & \\\\\n & Compression-Tokens (Bidirectional) & & 61.44 & 62.13 & 51.48 & 55.68 & 34.17 & 33.61 & \\\\\n & Mean-Pooling & & 65.89 & 64.74 & 58.17 & 58.38 & 34.81 & 32.21 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 67.12 & & & & & & & 10.40 \\\\\n & Compression-Tokens (Causal) & & 57.18 & 55.08 & 46.69 & 43.77 & 30.39 & 27.84 & \\\\\n & Compression-Tokens (Bidirectional) & & 58.37 & 60.74 & 48.84 & 52.41 & 29.77 & 30.22 & \\\\\n & Mean-Pooling & & 65.22 & 63.38 & 56.14 & 55.42 & 32.66 & 28.99 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 64.42 & & & & & & & 7.57 \\\\\n & Compression-Tokens (Causal) & & 41.97 & 49.85 & 40.15 & 39.49 & 25.42 & 23.64 & \\\\\n & Compression-Tokens (Bidirectional) & & 55.68 & 56.49 & 44.87 & 47.28 & 25.16 & 26.15 & \\\\\n & Mean-Pooling & & 60.34 & 58.56 & 48.95 & 48.78 & 26.91 & 23.60 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 61.13 & & & & & & & 7.76 \\\\\n & Compression-Tokens (Causal) & & 48.09 & 46.30 & 34.68 & 36.05 & 20.10 & 20.69 & \\\\\n & Compression-Tokens (Bidirectional) & & 48.04 & 50.67 & 38.85 & 40.35 & 21.29 & 21.07 & \\\\\n & Mean-Pooling & & 56.48 & 53.12 & 42.47 & 42.21 & 21.29 & 19.06 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 66.47 & & & & & & & 10.34 \\\\\n & Compression-Tokens (Causal) & & 56.17 & 55.78 & 47.16 & 46.68 & 31.17 & 29.72 & \\\\\n & Compression-Tokens (Bidirectional) & & 59.20 & 59.51 & 48.59 & 51.43 & 31.50 & 31.91 & \\\\\n & Mean-Pooling & & 64.29 & 63.44 & 56.94 & 55.71 & 33.42 & 31.79 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 61.67 & & & & & & & 9.03 \\\\\n & Compression-Tokens (Causal) & & 48.57 & 45.60 & 38.44 & 37.12 & 23.03 & 23.14 & \\\\\n & Compression-Tokens (Bidirectional) & & 52.24 & 49.98 & 40.65 & 42.08 & 23.59 & 23.72 & \\\\\n & Mean-Pooling & & 57.97 & 55.15 & 38.58 & 46.23 & 19.53 & 23.17 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{NarrativeQA $F_1$.}\n \\label{tab:primary_results_narrativeqa}\n\\end{table}\n\\newpage\n\\subsubsection{Out-of-Domain Datasets Results}\\label{app:results:datasets:out}\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 65.65 & & 46.46 & & 52.55 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 70.63 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 86.43 & & 78.03 & & 72.50 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 86.64 & & 77.13 & & 74.08 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 89.65 & & & & & & & 53.79 \\\\\n & Compression-Tokens (Causal) & & 89.67 & 89.15 & 88.92 & 85.50 & 79.36 & 77.55 & \\\\\n & Compression-Tokens (Bidirectional) & & 90.44 & 89.41 & 87.07 & 87.95 & 75.90 & 78.17 & \\\\\n & Mean-Pooling & & 87.94 & 86.52 & 84.38 & 86.32 & 79.74 & 75.89 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 90.46 & & & & & & & 43.49 \\\\\n & Compression-Tokens (Causal) & & 88.49 & 83.28 & 82.95 & 80.42 & 72.27 & 70.84 & \\\\\n & Compression-Tokens (Bidirectional) & & 91.59 & 90.83 & 86.10 & 87.53 & 67.43 & 74.52 & \\\\\n & Mean-Pooling & & 85.50 & 88.72 & 83.68 & 85.32 & 71.04 & 67.50 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 89.20 & & & & & & & 25.08 \\\\\n & Compression-Tokens (Causal) & & 74.89 & 83.83 & 80.55 & 73.91 & 61.72 & 64.02 & \\\\\n & Compression-Tokens (Bidirectional) & & 85.62 & 86.41 & 76.15 & 80.34 & 61.46 & 61.67 & \\\\\n & Mean-Pooling & & 85.83 & 82.75 & 80.61 & 75.94 & 63.03 & 53.77 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 81.55 & & & & & & & 9.87 \\\\\n & Compression-Tokens (Causal) & & 78.27 & 73.57 & 62.14 & 64.79 & 48.97 & 49.69 & \\\\\n & Compression-Tokens (Bidirectional) & & 81.58 & 78.38 & 69.22 & 74.16 & 50.24 & 54.05 & \\\\\n & Mean-Pooling & & 81.45 & 77.88 & 69.08 & 70.41 & 52.45 & 43.08 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 90.69 & & & & & & & 54.06 \\\\\n & Compression-Tokens (Causal) & & 89.75 & 85.06 & 82.73 & 79.19 & 77.64 & 73.71 & \\\\\n & Compression-Tokens (Bidirectional) & & 88.52 & 87.14 & 85.32 & 84.63 & 78.15 & 73.59 & \\\\\n & Mean-Pooling & & 89.09 & 86.99 & 84.95 & 85.27 & 75.30 & 74.29 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 82.13 & & & & & & & 31.14 \\\\\n & Compression-Tokens (Causal) & & 84.40 & 79.82 & 75.47 & 74.28 & 65.03 & 67.58 & \\\\\n & Compression-Tokens (Bidirectional) & & 83.72 & 84.18 & 78.94 & 73.03 & 64.83 & 68.57 & \\\\\n & Mean-Pooling & & 84.87 & 83.62 & 73.95 & 76.02 & 62.02 & 60.28 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{TriviaQA Verified $F_1$.}\n \\label{tab:primary_results_triviaqa}\n\\end{table}\n\\newpage\n\\begin{table}[!ht]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 32.79 & & 19.56 & & 18.76 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 27.34 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 42.51 & & 35.36 & & 26.44 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 44.09 & & 33.39 & & 27.52 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 60.44 & & & & & & & 19.15 \\\\\n & Compression-Tokens (Causal) & & 47.26 & 45.97 & 36.35 & 39.16 & 32.42 & 31.15 & \\\\\n & Compression-Tokens (Bidirectional) & & 51.46 & 51.51 & 40.05 & 42.51 & 32.54 & 32.69 & \\\\\n & Mean-Pooling & & 53.71 & 53.32 & 42.55 & 45.07 & 32.52 & 31.36 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 57.04 & & & & & & & 17.38 \\\\\n & Compression-Tokens (Causal) & & 45.07 & 43.44 & 34.61 & 34.34 & 28.95 & 26.25 & \\\\\n & Compression-Tokens (Bidirectional) & & 45.35 & 47.93 & 36.32 & 38.23 & 28.17 & 27.88 & \\\\\n & Mean-Pooling & & 51.47 & 48.49 & 40.36 & 39.09 & 28.84 & 27.31 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 46.62 & & & & & & & 14.86 \\\\\n & Compression-Tokens (Causal) & & 30.09 & 34.01 & 29.29 & 29.47 & 22.27 & 22.82 & \\\\\n & Compression-Tokens (Bidirectional) & & 37.92 & 37.00 & 29.72 & 31.44 & 22.43 & 21.05 & \\\\\n & Mean-Pooling & & 42.14 & 39.78 & 32.33 & 32.46 & 22.01 & 22.18 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 39.04 & & & & & & & 10.97 \\\\\n & Compression-Tokens (Causal) & & 29.69 & 28.58 & 23.55 & 23.95 & 18.80 & 19.46 & \\\\\n & Compression-Tokens (Bidirectional) & & 29.16 & 33.06 & 25.47 & 26.99 & 19.60 & 18.80 & \\\\\n & Mean-Pooling & & 33.84 & 32.70 & 26.11 & 26.21 & 19.52 & 18.08 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 51.45 & & & & & & & 16.76 \\\\\n & Compression-Tokens (Causal) & & 39.83 & 40.80 & 33.93 & 35.23 & 28.83 & 29.06 & \\\\\n & Compression-Tokens (Bidirectional) & & 40.76 & 41.96 & 34.73 & 35.52 & 29.47 & 27.27 & \\\\\n & Mean-Pooling & & 45.61 & 44.88 & 37.14 & 36.88 & 28.70 & 28.94 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 39.75 & & & & & & & 14.30 \\\\\n & Compression-Tokens (Causal) & & 30.58 & 29.42 & 26.27 & 26.66 & 21.04 & 21.63 & \\\\\n & Compression-Tokens (Bidirectional) & & 31.71 & 30.30 & 25.77 & 28.88 & 23.74 & 20.71 & \\\\\n & Mean-Pooling & & 34.84 & 33.60 & 27.18 & 27.29 & 21.21 & 20.46 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{AdversarialQA $F_1$.}\n \\label{tab:primary_results_adversarial_qa}\n\\end{table}\n\\newpage\n\\begin{table}[H]\n \\small\n \\centering\n \\setlength{\\tabcolsep}{5pt}\n \\resizebox{\\textwidth}{!}{%\n\\begin{tabular}{llcccccccc}\n\\toprule\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{4x}} & \\multicolumn2{c}{\\textbf{16x}} & \\multicolumn2{c}{\\textbf{128x}} & \\multicolumn{1}{c}{\\textbf{No Ctx}} \\\\\n\\cmidrule(lr){3-3}\\cmidrule(lr){4-5}\\cmidrule(lr){6-7}\\cmidrule(lr){8-9}\\cmidrule(l){10-10}\n\\multicolumn{2}{c}{} & & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\textbf{Single} & \\textbf{Multi} & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Baseline Systems}} \\\\\n& \\emph{LLMLingua2} (Qwen3-8B) & & & 27.42 & & 15.32 & & 7.56 & \\\\\n& \\emph{ICAE} (Mistral-7B) & & 28.42 & & & & & & \\\\\n& \\emph{PCC Lite} (GPT2-Large \\& Llama3.1-8B) & & 46.31 & & 33.25 & & 18.14 & & \\\\\n& \\emph{PCC Large} (Llama3.1-8B) & & 46.77 & & 31.17 & & 17.95 & & \\\\\n\\midrule\n\\multicolumn{10}{l}{\\textbf{Our Methods}} \\\\\n\\addlinespace[2pt]\n\\multicolumn{2}{l}{\\textbf{Qwen3-8B}} & 56.77 & & & & & & & 7.49 \\\\\n & Compression-Tokens (Causal) & & 49.69 & 48.77 & 40.37 & 41.71 & 30.94 & 28.40 & \\\\\n & Compression-Tokens (Bidirectional) & & 51.65 & 51.68 & 44.91 & 45.85 & 31.40 & 31.07 & \\\\\n & Mean-Pooling & & 55.36 & 53.87 & 48.95 & 48.63 & 31.79 & 29.12 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-4B}} & 56.14 & & & & & & & 6.59 \\\\\n & Compression-Tokens (Causal) & & 47.85 & 46.50 & 40.73 & 40.49 & 28.86 & 27.16 & \\\\\n & Compression-Tokens (Bidirectional) & & 49.63 & 50.74 & 42.98 & 44.60 & 27.72 & 28.07 & \\\\\n & Mean-Pooling & & 54.74 & 53.24 & 46.93 & 47.01 & 29.95 & 26.25 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-1.7B}} & 54.75 & & & & & & & 5.09 \\\\\n & Compression-Tokens (Causal) & & 37.53 & 43.23 & 36.08 & 35.38 & 24.47 & 22.71 & \\\\\n & Compression-Tokens (Bidirectional) & & 46.33 & 47.36 & 39.28 & 39.72 & 24.81 & 23.81 & \\\\\n & Mean-Pooling & & 52.04 & 50.67 & 42.90 & 42.55 & 25.16 & 22.02 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Qwen3-0.6B}} & 51.54 & & & & & & & 4.82 \\\\\n & Compression-Tokens (Causal) & & 42.04 & 39.38 & 32.91 & 31.36 & 20.07 & 19.73 & \\\\\n & Compression-Tokens (Bidirectional) & & 43.34 & 43.74 & 34.15 & 35.77 & 21.12 & 19.16 & \\\\\n & Mean-Pooling & & 48.26 & 46.29 & 38.13 & 37.81 & 21.24 & 17.03 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Gemma2-2B}} & 56.00 & & & & & & & 7.10 \\\\\n & Compression-Tokens (Causal) & & 48.10 & 46.86 & 41.66 & 40.33 & 29.30 & 27.74 & \\\\\n & Compression-Tokens (Bidirectional) & & 49.36 & 49.83 & 42.30 & 43.72 & 29.85 & 28.81 & \\\\\n & Mean-Pooling & & 54.39 & 53.39 & 47.82 & 47.83 & 31.16 & 28.91 & \\\\\n\\midrule\n\\multicolumn{2}{l}{\\textbf{Llama3.2-1B}} & 52.26 & & & & & & & 5.94 \\\\\n & Compression-Tokens (Causal) & & 41.97 & 40.07 & 35.08 & 35.24 & 22.50 & 23.14 & \\\\\n & Compression-Tokens (Bidirectional) & & 44.58 & 44.02 & 36.36 & 38.77 & 23.84 & 23.88 & \\\\\n & Mean-Pooling & & 49.90 & 46.92 & 33.84 & 39.59 & 17.67 & 21.17 & \\\\\n\\midrule\n\\bottomrule\n\\end{tabular}\n }\n \\caption{ParaphraseRC $F_1$.}\n \\label{tab:primary_results_paraphrase_rc}\n\\end{table}\n\\newpage\n\\section{LLM Usage}\\label{app:llm}\nLLMs (specifically, ChatGPT) were used in the process of writing this paper for creating tables and figures, as well as proof-reading.\n\n\\end{document}\n"},"question":{"kind":"string","value":"Within the proposed methods, keep only those (model, method) pairs whose change from 4×Multi to 4×Single change has opposite signs when measured by exact match and accuracy. Among those pairs, find the one that maximizes the mean of the absolute difference between 16×Multi and 16×Single computed with both metrics. Report its model and method, and that mean 16× gap."},"answer":{"kind":"string","value":"Gemma2-2B, Compression-Tokens (Bidirectional), 2.215"},"plan":{"kind":"string","value":"SELECT all model names under Our Methods\nLOOP for each model\n SELECT all methods under this model\n LOOP for each method\n COMPUTE diff_em_4 = 4× Multi exact match score − 4× Single exact match score\n COMPUTE diff_acc_4 = 4x Multi accuracy score - 4x Single accuracy score\n IF diff_em_4 and diff_acc_4 have opposite signs\n COMPUTE gap_em_16 = absolute(16x Multi exact match score - 16x Single exact match score)\n COMPUTE gap_acc_16 = absolute(16x Multi accuracy score - 16x Single accuracy score)\n COMPUTE mean_gap_16 = average of gap_em_16 and gap_acc_16\nCOMPUTE best_pair = argmax model and method pair over mean_gap_16\nRETURN model of best_pair, method of best_pair, mean_gap_16 of best_pair \n"}}},{"rowIdx":359,"cells":{"paper":{"kind":"string","value":"2509.03962"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n"," & 26.00 & 16.92 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n"," & 35.05 & 23.17 \\\\\n"," & FSL-GPT-4o \n"," & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n"," & 30.08 & 20.42 \\\\\n"," & FT-Llama 3.1 8B \n"," & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n"," & 36.60 & 30.98 \\\\\n"," & FT-Llama 3.1 70B \n"," & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n"," & 35.87 & 23.99 \\\\\n"," & Mbart-large-50 \n"," & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n"," & 38.66 & 35.23 \\\\\n"," & NLLB 1.3 B \n"," & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n"," & \\underline{45.98} & \\underline{41.58} \\\\\n"," & Benchmark (LLM) \n"," & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n"," & 28.98 & 18.60 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n"," & 46.28 & \\textbf{42.15} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_ladin}\n"," Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \\n\",\n \" & 26.00 & 16.92 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \\n\",\n \" & 35.05 & 23.17 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \\n\",\n \" & 30.08 & 20.42 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \\n\",\n \" & 36.60 & 30.98 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \\n\",\n \" & 35.87 & 23.99 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \\n\",\n \" & 38.66 & 35.23 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & \\\\underline{18.54} & \\\\underline{16.85} & \\\\underline{17.88} & \\\\textbf{51.59} & \\\\underline{51.55} & \\\\underline{55.29} & \\\\textbf{46.24}\\n\",\n \" & \\\\underline{45.98} & \\\\underline{41.58} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \\n\",\n \" & 28.98 & 18.60 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & 18.30 & 17.69 & \\\\textbf{18.29} & 51.40 & \\\\textbf{52.92} & \\\\textbf{56.65} & 45.44 \\n\",\n \" & 46.28 & \\\\textbf{42.15} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{20.93} & \\\\textbf{19.32} & 16.65 & - & - & - & \\\\textbf{47.65} & \\\\textbf{46.58} & 38.16 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_ladin}\\n\",\n \" Translation performance of various models for Italian → Ladin across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[!t]\n"," \\centering\n"," \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n"," \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n"," \\label{fig:LadinArea}\n","\\end{figure}\n"],["\\begin{figure*}[t]\n"," \\centering\n"," \\includegraphics[width=5.3in]{latex/Figure_2.png}\n"," \\caption{Synthetic data generation process. Initially, we translate the Italian data \\( D\\textsubscript{\\textit{Ita}}\\) of SA and MCQA into Ladin. The Ladin translation \\(D\\textsubscript{\\textit{Lad}}\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\(D\\textsubscript{\\textit{Lad}}\\) is back-translated into Italian \\( D^{\\prime}\\textsubscript{\\textit{Ita}}\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\n"," \\label{fig:experiments}\n","\\end{figure*}\n"],["\\begin{table*}\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llcccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{2}{c}{\\textbf{BLEU}} \n"," & \\multicolumn{2}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{2}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-8}\n"," &\n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\n"," & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\n"," & FSL-GPT-4o & 4.27 & \\underline{22.84} & 25.86 & \\underline{52.28} & 27.47 & 48.23 \\\\\n"," & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\n"," & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\n"," & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\n"," & FT-NLLB 1.3 B & \\underline{17.76} & 21.41 & \\underline{52.81} & 49.91 & \\underline{44.60 } & \\underline{48.40} \\\\\n"," & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\n"," \n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B & 18.30 & \\textbf{24.50} & \\textbf{53.66} & \\textbf{52.64} & \\textbf{44.62} & \\textbf{50.76} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{translation-performance}\n"," Comparison of different models based on average translation performance metrics on the test set \\( T \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.}\n","\n","\\end{table*}\n"],["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n"," & 26.00 & 16.92 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n"," & 35.05 & 23.17 \\\\\n"," & FSL-GPT-4o \n"," & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n"," & 30.08 & 20.42 \\\\\n"," & FT-Llama 3.1 8B \n"," & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n"," & 36.60 & 30.98 \\\\\n"," & FT-Llama 3.1 70B \n"," & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n"," & 35.87 & 23.99 \\\\\n"," & Mbart-large-50 \n"," & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n"," & 38.66 & 35.23 \\\\\n"," & NLLB 1.3 B \n"," & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n"," & \\underline{45.98} & \\underline{41.58} \\\\\n"," & Benchmark (LLM) \n"," & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n"," & 28.98 & 18.60 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n"," & 46.28 & \\textbf{42.15} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_ladin}\n"," Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"],["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \n"," & 38.89 & 23.41 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \n"," & 48.66 & 36.91 \\\\\n"," & FSL-GPT-4o \n"," & 29.23 & 23.38 & 15.90 & 61.39 & \\textbf{53.37} & 42.07 & 55.73 \n"," & 50.33 & 38.64 \\\\\n"," & FT-Llama 3.1 8B \n"," & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \n"," & 44.11 & 33.66 \\\\\n"," & FT-Llama 3.1 70B \n"," & \\textbf{30.78} & \\textbf{23.65} & 13.02 & \\textbf{61.91} & 52.10 & 38.29 & \\textbf{57.23} \n"," & \\underline{50.53} & 36.12 \\\\\n"," & Mbart-large-50 \n"," & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \n"," & 42.15 & 36.81 \\\\\n"," & NLLB 1.3 B \n"," & 27.15 & 19.77 & \\underline{17.31} & 55.54 & 48.27 & \\underline{46.03} & 54.45\n"," & 49.66 & \\underline{41.09} \\\\\n"," & Benchmark (LLM) \n"," & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \n"," & 48.52 & 32.36 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & \\underline{30.46} & \\underline{22.71} & \\textbf{20.33} & 58.11 & 50.71 & \\textbf{49.11} & \\underline{56.95} \n"," & \\textbf{51.49} & \\textbf{43.83} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \n"," & 49.08 & 40.76 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_italian}\n"," Translation performance of various models for Ladin → Italian across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"],["\\begin{table}[t]\n"," \\small\n"," \\centering\n"," \\makebox[3.1in][r]{\n"," \\begin{tabular}{lcc}\n"," \\hline\n"," \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n"," & \\textbf{Italian} & \\textbf{Ladin} \\\\\n"," \\hline\n"," Average number of words per entry & 65 & 70 \\\\\n"," Average number of characters per entry & 144 & 348 \\\\\n"," Positive label count & 9,842 & 9,842 \\\\\n"," Negative label count & 2,669 & 2,669 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SD-SA}\n"," Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\n"," }\n","\\end{table}\n"],["\\begin{table}[t]\n"," \\centering\n"," \\small\n"," \\makebox[3.2in][r]{\n"," \\begin{tabular}{lcc}\n"," \\hline\n"," \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n"," & \\textbf{Italian} & \\textbf{Ladin} \\\\\n"," \\hline\n"," Average number of words per question & 18 & 19 \\\\\n"," Average number of characters per question & 108 & 97 \\\\\n"," Average number of words per choices & 28 & 30 \\\\\n"," Average number of characters per choices & 187 & 174 \\\\\n"," Frequency of entries with 3 choices & 304 & 304 \\\\\n"," Frequency of entries with 4 choices & 196 & 196 \\\\\n"," Frequency of entries with 5 choices & 264 & 264 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SD-MCQA}\n"," Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\n"," }\n","\\end{table}\n"],["\\begin{table*}[t]\n"," \\centering\n"," \\small\n"," \\makebox[\\textwidth]{\n"," \\begin{tabular}{lcccc@{\\hspace{2em}}cccc}\n"," \\hline\n"," \\textbf{Model} &\n"," \\multicolumn{4}{c}{\\textbf{Ladin}} &\n"," \\multicolumn{4}{c}{\\textbf{Italian}} \\\\\n"," \\cline{2-9}\n"," & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}}\n"," & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}} \\\\\n"," \n"," & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1}\n"," & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1} \\\\\n"," \\hline\n"," FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\n"," & 97.92 & 98.18 & 54.79 & 54.18 \\\\\n"," m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \n"," & 94.78 & 96.41 & 30.73 & 30.29 \\\\\n"," XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \n"," & 97.14 & 98.08 & 26.14 & 26.14 \\\\\n"," mT5 & 50.09 & 69.37 & 23.50 & 23.16 \n"," & 49.98 & 69.25 & 22.62 & 21.92 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SA-MCQA} \n"," Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\n"," } \n","\\end{table*}\n"],["\\begin{figure*}[tp]\n"," \\centering\n"," \\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\n"," \\caption{chrF++ scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n"," \\label{fig:chrf_AD}\n","\\end{figure*}\n"],["\\begin{figure*}[tp]\n"," \\centering\n"," \\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\n"," \\caption{BLEU scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n"," \\label{fig:bleu_AD}\n","\\end{figure*}\n"]],"string":"[\n [\n \"\\\\begin{figure}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\\n\",\n \" \\\\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\\n\",\n \" \\\\label{fig:LadinArea}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=5.3in]{latex/Figure_2.png}\\n\",\n \" \\\\caption{Synthetic data generation process. Initially, we translate the Italian data \\\\( D\\\\textsubscript{\\\\textit{Ita}}\\\\) of SA and MCQA into Ladin. The Ladin translation \\\\(D\\\\textsubscript{\\\\textit{Lad}}\\\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\\\(D\\\\textsubscript{\\\\textit{Lad}}\\\\) is back-translated into Italian \\\\( D^{\\\\prime}\\\\textsubscript{\\\\textit{Ita}}\\\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\\n\",\n \" \\\\label{fig:experiments}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llcccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{BLEU}} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-8}\\n\",\n \" &\\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\\\\\\n\",\n \" & FSL-GPT-4o & 4.27 & \\\\underline{22.84} & 25.86 & \\\\underline{52.28} & 27.47 & 48.23 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\\\\\\n\",\n \" & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\\\\\\n\",\n \" & FT-NLLB 1.3 B & \\\\underline{17.76} & 21.41 & \\\\underline{52.81} & 49.91 & \\\\underline{44.60 } & \\\\underline{48.40} \\\\\\\\\\n\",\n \" & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B & 18.30 & \\\\textbf{24.50} & \\\\textbf{53.66} & \\\\textbf{52.64} & \\\\textbf{44.62} & \\\\textbf{50.76} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{translation-performance}\\n\",\n \" Comparison of different models based on average translation performance metrics on the test set \\\\( T \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.}\\n\",\n \"\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \\n\",\n \" & 26.00 & 16.92 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \\n\",\n \" & 35.05 & 23.17 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \\n\",\n \" & 30.08 & 20.42 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \\n\",\n \" & 36.60 & 30.98 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \\n\",\n \" & 35.87 & 23.99 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \\n\",\n \" & 38.66 & 35.23 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & \\\\underline{18.54} & \\\\underline{16.85} & \\\\underline{17.88} & \\\\textbf{51.59} & \\\\underline{51.55} & \\\\underline{55.29} & \\\\textbf{46.24}\\n\",\n \" & \\\\underline{45.98} & \\\\underline{41.58} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \\n\",\n \" & 28.98 & 18.60 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & 18.30 & 17.69 & \\\\textbf{18.29} & 51.40 & \\\\textbf{52.92} & \\\\textbf{56.65} & 45.44 \\n\",\n \" & 46.28 & \\\\textbf{42.15} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{20.93} & \\\\textbf{19.32} & 16.65 & - & - & - & \\\\textbf{47.65} & \\\\textbf{46.58} & 38.16 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_ladin}\\n\",\n \" Translation performance of various models for Italian → Ladin across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \\n\",\n \" & 38.89 & 23.41 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \\n\",\n \" & 48.66 & 36.91 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 29.23 & 23.38 & 15.90 & 61.39 & \\\\textbf{53.37} & 42.07 & 55.73 \\n\",\n \" & 50.33 & 38.64 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \\n\",\n \" & 44.11 & 33.66 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & \\\\textbf{30.78} & \\\\textbf{23.65} & 13.02 & \\\\textbf{61.91} & 52.10 & 38.29 & \\\\textbf{57.23} \\n\",\n \" & \\\\underline{50.53} & 36.12 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \\n\",\n \" & 42.15 & 36.81 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & 27.15 & 19.77 & \\\\underline{17.31} & 55.54 & 48.27 & \\\\underline{46.03} & 54.45\\n\",\n \" & 49.66 & \\\\underline{41.09} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \\n\",\n \" & 48.52 & 32.36 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & \\\\underline{30.46} & \\\\underline{22.71} & \\\\textbf{20.33} & 58.11 & 50.71 & \\\\textbf{49.11} & \\\\underline{56.95} \\n\",\n \" & \\\\textbf{51.49} & \\\\textbf{43.83} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \\n\",\n \" & 49.08 & 40.76 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_italian}\\n\",\n \" Translation performance of various models for Ladin → Italian across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\makebox[3.1in][r]{\\n\",\n \" \\\\begin{tabular}{lcc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Feature} & \\\\multicolumn{2}{c}{\\\\textbf{Language}} \\\\\\\\\\n\",\n \" & \\\\textbf{Italian} & \\\\textbf{Ladin} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" Average number of words per entry & 65 & 70 \\\\\\\\\\n\",\n \" Average number of characters per entry & 144 & 348 \\\\\\\\\\n\",\n \" Positive label count & 9,842 & 9,842 \\\\\\\\\\n\",\n \" Negative label count & 2,669 & 2,669 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SD-SA}\\n\",\n \" Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\\n\",\n \" }\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\makebox[3.2in][r]{\\n\",\n \" \\\\begin{tabular}{lcc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Feature} & \\\\multicolumn{2}{c}{\\\\textbf{Language}} \\\\\\\\\\n\",\n \" & \\\\textbf{Italian} & \\\\textbf{Ladin} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" Average number of words per question & 18 & 19 \\\\\\\\\\n\",\n \" Average number of characters per question & 108 & 97 \\\\\\\\\\n\",\n \" Average number of words per choices & 28 & 30 \\\\\\\\\\n\",\n \" Average number of characters per choices & 187 & 174 \\\\\\\\\\n\",\n \" Frequency of entries with 3 choices & 304 & 304 \\\\\\\\\\n\",\n \" Frequency of entries with 4 choices & 196 & 196 \\\\\\\\\\n\",\n \" Frequency of entries with 5 choices & 264 & 264 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SD-MCQA}\\n\",\n \" Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\\n\",\n \" }\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\makebox[\\\\textwidth]{\\n\",\n \" \\\\begin{tabular}{lcccc@{\\\\hspace{2em}}cccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Model} &\\n\",\n \" \\\\multicolumn{4}{c}{\\\\textbf{Ladin}} &\\n\",\n \" \\\\multicolumn{4}{c}{\\\\textbf{Italian}} \\\\\\\\\\n\",\n \" \\\\cline{2-9}\\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{SA}} & \\\\multicolumn{2}{c}{\\\\textbf{MCQA}}\\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{SA}} & \\\\multicolumn{2}{c}{\\\\textbf{MCQA}} \\\\\\\\\\n\",\n \" \\n\",\n \" & \\\\textbf{Acc} & \\\\textbf{F1} & \\\\textbf{Acc} & \\\\textbf{F1}\\n\",\n \" & \\\\textbf{Acc} & \\\\textbf{F1} & \\\\textbf{Acc} & \\\\textbf{F1} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\\n\",\n \" & 97.92 & 98.18 & 54.79 & 54.18 \\\\\\\\\\n\",\n \" m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \\n\",\n \" & 94.78 & 96.41 & 30.73 & 30.29 \\\\\\\\\\n\",\n \" XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \\n\",\n \" & 97.14 & 98.08 & 26.14 & 26.14 \\\\\\\\\\n\",\n \" mT5 & 50.09 & 69.37 & 23.50 & 23.16 \\n\",\n \" & 49.98 & 69.25 & 22.62 & 21.92 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SA-MCQA} \\n\",\n \" Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\\n\",\n \" } \\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[tp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\\n\",\n \" \\\\caption{chrF++ scores of the models using \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} as the training data}\\n\",\n \" \\\\label{fig:chrf_AD}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[tp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\\n\",\n \" \\\\caption{BLEU scores of the models using \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} as the training data}\\n\",\n \" \\\\label{fig:bleu_AD}\\n\",\n \"\\\\end{figure*}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"% This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.\n\\pdfoutput=1\n% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.\n\n\\documentclass[11pt]{article}\n\n% Change \"review\" to \"final\" to generate the final (sometimes called camera-ready) version.\n% Change to \"preprint\" to generate a non-anonymous version with page numbers.\n\\usepackage[preprint]{acl}\n\n% Standard package includes\n\\usepackage{times}\n\\usepackage{latexsym}\n\n% For proper rendering and hyphenation of words containing Latin characters (including in bib files)\n\\usepackage[T1]{fontenc}\n% For Vietnamese characters\n% \\usepackage[T5]{fontenc}\n% See https://www.latex-project.org/help/documentation/encguide.pdf for other character sets\n\n% This assumes your files are encoded as UTF8\n\\usepackage[utf8]{inputenc}\n\n% This is not strictly necessary, and may be commented out,\n% but it will improve the layout of the manuscript,\n% and will typically save some space.\n\\usepackage{microtype}\n\n% This is also not strictly necessary, and may be commented out.\n% However, it will improve the aesthetics of text in\n% the typewriter font.\n\\usepackage{inconsolata}\n\n%Including images in your LaTeX document requires adding\n%additional package(s)\n\\usepackage{graphicx}\n\n% If the title and author information does not fit in the area allocated, uncomment the following\n%\n%\\setlength\\titlebox{<dim>}\n%\n% and set <dim> to something 5cm or larger.\n\n\\title{ \nExploring NLP Benchmarks in an Extremely Low-Resource Setting\n%Synthetic Data for Ladin NLP: Toward Democratized Language Models for Indigenous Languages\n}\n\n% Author information can be set in various styles:\n% For several authors from the same institution:\n% \\author{Author 1 \\and ... \\and Author n \\\\\n% Address line \\\\ ... \\\\ Address line}\n% if the names do not fit well on one line use\n% Author 1 \\\\ {\\bf Author 2} \\\\ ... \\\\ {\\bf Author n} \\\\\n% For authors from different institutions:\n% \\author{Author 1 \\\\ Address line \\\\ ... \\\\ Address line\n% \\And ... \\And\n% Author n \\\\ Address line \\\\ ... \\\\ Address line}\n% To start a separate ``row'' of authors use \\AND, as in\n% \\author{Author 1 \\\\ Address line \\\\ ... \\\\ Address line\n% \\AND\n% Author 2 \\\\ Address line \\\\ ... \\\\ Address line \\And\n% Author 3 \\\\ Address line \\\\ ... \\\\ Address line}\n\n\\author{\n Ulin Nuha\\thanks{Work done while the author was a PhD student at NKUST.} \\\\\n National Kaohsiung University \\\\\n of Science and Technology \\\\\n \\texttt{ulinnuha.id@icloud.com}\n \\And\n Adam Jatowt \\\\\n University of Innsbruck \\\\\n \\texttt{adam.jatowt@uibk.ac.at}\n}\n%\\author{\n% \\textbf{First Author\\textsuperscript{1}},\n% \\textbf{Second Author\\textsuperscript{1,2}},\n% \\textbf{Third T. Author\\textsuperscript{1}},\n% \\textbf{Fourth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Fifth Author\\textsuperscript{1,2}},\n% \\textbf{Sixth Author\\textsuperscript{1}},\n% \\textbf{Seventh Author\\textsuperscript{1}},\n% \\textbf{Eighth Author \\textsuperscript{1,2,3,4}},\n%\\\\\n% \\textbf{Ninth Author\\textsuperscript{1}},\n% \\textbf{Tenth Author\\textsuperscript{1}},\n% \\textbf{Eleventh E. Author\\textsuperscript{1,2,3,4,5}},\n% \\textbf{Twelfth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Thirteenth Author\\textsuperscript{3}},\n% \\textbf{Fourteenth F. Author\\textsuperscript{2,4}},\n% \\textbf{Fifteenth Author\\textsuperscript{1}},\n% \\textbf{Sixteenth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Seventeenth S. Author\\textsuperscript{4,5}},\n% \\textbf{Eighteenth Author\\textsuperscript{3,4}},\n% \\textbf{Nineteenth N. Author\\textsuperscript{2,5}},\n% \\textbf{Twentieth Author\\textsuperscript{1}}\n%\\\\\n%\\\\\n% \\textsuperscript{1}Affiliation 1,\n% \\textsuperscript{2}Affiliation 2,\n% \\textsuperscript{3}Affiliation 3,\n% \\textsuperscript{4}Affiliation 4,\n% \\textsuperscript{5}Affiliation 5\n%\\\\\n% \\small{\n% \\textbf{Correspondence:} \\href{mailto:email@domain}{email@domain}\n% }\n%}\n\n\\begin{document}\n\\maketitle\n\\begin{abstract}\n%Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of natural language processing (NLP) tasks. However, \nThe effectiveness of Large Language Models (LLMs) diminishes for extremely low-resource languages, such as indigenous languages, primarily due to the lack of labeled data. Despite growing interest, the availability of high-quality natural language processing (NLP) datasets for these languages remains limited, making it difficult to develop robust language technologies. This paper addresses such gap by focusing on Ladin, an endangered Romance language, specifically targeting the Val Badia variant. Leveraging a small set of parallel Ladin–Italian sentence pairs, we create synthetic datasets for sentiment analysis and multiple-choice question answering (MCQA) by translating monolingual Italian data. To ensure linguistic quality and reliability, we apply rigorous filtering and back-translation procedures in our method. We further demonstrate that incorporating these synthetic datasets into machine translation training leads to substantial improvements over existing Italian–Ladin translation baselines. Our contributions include the first publicly available sentiment analysis and MCQA datasets for Ladin, establishing foundational resources that can support broader NLP research and downstream applications for this underrepresented language.\n\\end{abstract}\n\n\\section{Introduction}\n\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n \\label{fig:LadinArea}\n\\end{figure}\n\n\nLarge language models (LLMs) have garnered significant attention in diverse audiences \\citep{Yuxia:2024, Gambardella:2024} due to their ability to effectively perform natural language tasks with only a few input-output examples \\citep{Cheng:24}, while also eliminating the need for gradient updates of the model \\citep{Nguyen:2024}. \nLLMs achieve remarkable performance through pre-training on large corpora, but their reliance on high-resource languages (HRLs) limits their effectiveness for low-resource languages (LRLs) \\citep{Pham:2024}, especially extreme ones \\citep{purason2024llms}. Efforts to address this limitation include various techniques such as in-context learning \\citep{Cahyawijaya:2024} and fine-tuning \\citep{Alabi:2022, Su2024Unlocking} to transfer LLM capabilities to LRLs. Additionally, some studies \\citep{yong2024lexc, morim2024, tran24irish} have focused on developing translation systems between LRLs and HRLs to address the lack of language technology resources. The limited advancement of natural language processing (NLP) in LRLs stems largely from the disproportionate focus of research on improving language models for HRLs, often at the expense of developing tools and resources for low-resource counterparts \\citep{zhang24llm}. Moreover, the scarcity of NLP datasets for extremely low-resource languages (ELRLs) constitutes a major barrier to progress in this area, highlighting the need for more inclusive AI technologies to support marginalized languages.\n\nThis paper advances NLP research for Ladin language, an Indigenous and extremely low-resource language of Northern Italy (see Fig.~\\ref{fig:LadinArea}). %Sharing roots with Italian, Ladin is a Romance (Neo-Latin) language.\nDespite progress in NLP for LRLs, Ladin’s dialectal diversity and limited digitized corpora pose unique challenges. Building on the prior work \\citep{frontull24}, which established a machine translation (MT) benchmark between Italian and Ladin (Val Badia variant), we further improve the translation performance for Ladin.\n\nLadin is a Rhaeto-Romance language spoken by about 30,000 people in South Tyrol, Northern Italy. It comprises five dialects (Val Badia, Fascia, Anpezo, Fodom, and Gherdëina) which vary significantly in morpho-syntactic and orthographic conventions. Although standardized efforts such as Ladin Dolomitan exist, it is not officially recognized and is used only to a limited extent, while speakers report minimal familiarity with Ladin varieties beyond their own \\citep{connor2023ladin}. Linguistic conventions have also changed over time within dialects. This linguistic diversity presents major challenges for machine translation and resource creation. Publicly available resources are extremely limited, with only a few lexicons, dictionaries, and minor corpora. There is a major source of monolingual Ladin data in \\textit{La Usc di Ladins}\\footnote{https://www.lausc.it/}, a newspaper published in five variants and digitally archived since 2012, but this resource remains underutilized due to the lack of alignment and limited annotation. Our work focuses on the Val Badia variant of Ladin%\\footnote{Ladin originally comprises five variants: Val Badia, Gherdëina, Fascia, Fodom, and Anpezo.}\n, due to the availability of the largest accessible dataset. Previous work on MT for Ladin's Fascia variant exists \\citep{FasciaLadin}; however, the parallel dataset used in that work consists of only 1,135 sentences. \n\nUnlike prior studies, our work also extends beyond MT for Ladin to include sentiment analysis (SA) and multiple-choice question answering (MCQA), establishing the first datasets for these tasks in Ladin. First, we compare MT approaches, including few-shot learning and fine-tuning, using available Ladin–Italian sentence pairs. Subsequently, we construct high-quality synthetic Ladin datasets for SA and MCQA through the translation from monolingual Italian data, applying rigorous filtering to ensure high quality. These datasets not only contribute to SA and MCQA but also enhance MT. To assess this, we incorporate our synthetic dataset into existing Italian–Ladin translation benchmarks and evaluate its impact.\n\nIn summary, the primary contributions of our work can be outlined as follows:\n\\begin{itemize}\n \\item We conduct a comparative study on translation between Italian and Ladin, focusing on the Val Badia variant. Our model significantly outperforms the current benchmark, demonstrating the effectiveness of our approach for this extremely low-resource language (LRL).\n \n \\item We construct a high-quality synthetic dataset of Ladin–Italian sentence pairs, referred to as \\textit{SD\\textsubscript{Lad--Ita}}, derived from monolingual Italian data using a language model and rigorous filtering techniques.\n \n \\item We showcase the utility of the synthetic dataset beyond MT by applying it to additional downstream NLP tasks, including SA (text classification) and MCQA, establishing the first such datasets in Ladin.\n\\end{itemize}\n\n%By highlighting the severe scarcity of NLP datasets for extremely LRLs compared to those for LRLs, and by \nBy fostering NLP research on Ladin, we aim to support the preservation and accessibility of this critically underrepresented language—benefiting education, digital communication, and cultural documentation for Indigenous communities.\n\n\\section{Background and Related Work}\n\nNLP for ELRLs has garnered increasing attention from researchers, largely due to the enduring challenges associated with data scarcity. These languages typically possess fewer than 0.1 million available parallel sentence pairs \\citep{Ranathunga23}, which are often insufficient for effectively training neural machine translation (NMT) models \\citep{rudra:19}. For instance, Ladin has fewer than 100 thousand parallel sentences available for MT \\citep{frontull24}, while resources for other NLP tasks, such as text classification and question answering, remain non-existent. \n\nLadin and Italian are both Romance languages with shared Latin roots, resulting in potential similarities in lexical and syntactic aspects. This linguistic proximity facilitates cross-lingual transfer, allowing multilingual models fine-tuned on Italian to generalize moderately well to Ladin. However, key divergences remain due to Ladin’s unique phonological and morphological traits \\citep{LucaM}. These differences are further shaped by historical geographic isolation and varying degrees of contact with dominant surrounding languages, particularly regional varieties of German and Italian. Most Ladin speakers in Italy are bi- or tri-lingual, using Ladin in private domains and Italian, German, or both in public settings, as neighboring communities typically lack comprehension of Ladin \\citep{SilviaLadin}. This contact has led to regional variation. For instance, Gherdëina and Val Badia exhibit stronger German influence, while southern valleys show more Italian features. Val Badia is often perceived as having the “purest” Ladin, though this reflects relative rather than absolute isolation from external influence. These dynamics pose several challenges for translation. The lack of a commonly adopted standard variety necessitates dialect-specific translation strategies, complicating mutual intelligibility and the development of shared resources. Furthermore, long-standing language contact has introduced borrowings and calques, making it difficult to isolate core Ladin structures.\n\n\nTo address the scarcity of resources in ELRLs, recent efforts have focused on leveraging transfer learning techniques, particularly through the use of large language models (LLMs) \\citep{Pham:2024, lim:24}. However, success remains limited in such settings \\citep{tran24irish}, where extreme data sparsity poses challenges for effective domain adaptation and language alignment. In addition, a key aspect of transfer learning with LLMs involves leveraging token similarity and cross-region similarity to better capture shared cultural and linguistic features \\citep{SinaBN}. \\citet{RAG-LLM} proposed a MT framework that integrates Retrieval-Augmented Generation (RAG) with LLMs to address these challenges, whereas \\citet{DPO-LLM} explored the use of LLMs in combination with Direct Preference Optimization (DPO) to enhance translation quality. \n\nDespite promising results, the above-mentioned methods incur high computational costs. Multimodal approaches, which incorporate additional modalities such as visual context to enhance translation \\citep{rajpoot:24, sami:dcu, hatami:24}, require supplementary datasets that are often unavailable for these languages and face considerable computational and complexity challenges. Then, Rule-based machine translation (RBMT), exemplified by Apertium \\citep{garcia:24, sanchez:24}, offers a less resource-intensive alternative, with lower computational requirements compared to NMT systems. However, RBMT systems are labor-intensive, requiring extensive manual effort to create and maintain linguistic rules, with scalability further hindered by the challenge of ensuring rule self-consistency \\citep{liu-multil:24}. \n\nAnother approach to supporting technologies for LRLs is the development of benchmarks. For example, \\citet{urbizu} introduced BasqueGLUE, a benchmark covering multiple NLP tasks for the Basque language.\nSimilarly, \\citet{FarsInstruct} presented FarsInstruct, a large-scale dataset developed to strengthen LLMs’ capacity to follow instructions in Persian, a globally low-represented language. However, recent work in language revitalization and human-centered NLP shows the importance of going beyond performance metrics in developing technologies for endangered languages \\citep{StevenBird}. Effective systems should align with long-term community goals, such as intergenerational transmission and cultural continuity.\n\nIn line with this perspective, our work presents a comparative study of MT approaches, including instruction learning and fine-tuning \\citep{zhang:mt23}, using several language models such as NLLB and GPT-4. %Given Ladin’s underrepresentation, we adapt sequence modeling techniques for this new linguistic setting \\citep{Degenaro:24}. \nTo evaluate translation quality, we use both statistical and semantical metrics, particularly for synthetic data. While prior research has made progress in NLP for LRLs, substantial gaps remain for ELRLs such as Ladin. This study addresses these gaps by leveraging data augmentation techniques and introducing benchmark datasets for MT, text classification, and question answering tasks.\n\n\\section{Experiments}\n\n\\begin{figure*}[t]\n \\centering\n \\includegraphics[width=5.3in]{latex/Figure_2.png}\n \\caption{Synthetic data generation process. Initially, we translate the Italian data \\( D\\textsubscript{\\textit{Ita}}\\) of SA and MCQA into Ladin. The Ladin translation \\(D\\textsubscript{\\textit{Lad}}\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\(D\\textsubscript{\\textit{Lad}}\\) is back-translated into Italian \\( D^{\\prime}\\textsubscript{\\textit{Ita}}\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\n \\label{fig:experiments}\n\\end{figure*}\n\n%Our study focuses on translating the Ladin language in its Val Badia variant. Among the five Ladin variants, parallel data availability is limited to the Val Badia variant paired with Italian. \n%In addition, our experiments explore translation tasks using various sequence-to-sequence modeling and LLMs across multiple settings.\n\n\\subsection{Data sources}\nIn this section, we provide an overview of the data sources used in our study. We prepared datasets for three tasks: MT, SA, and MCQA. These resources were collected from publicly available datasets. Figure~\\ref{fig:experiments} illustrates the synthetic paired Ladin-Italian data generation process. As the creation of the SA and MCQA datasets depends on the availability of a translation model, we first constructed the MT dataset. Once the translation model was established, we proceeded with the generation of the SA and MCQA datasets accordingly.\n\\noindent\\textbf{Machine translation.} The parallel Italian–Ladin dataset used for both training and testing in our MT experiments was initially derived from prior work \\citep{frontull24}. The authentic Italian-Ladin training dataset \\textit{AD\\textsubscript{Ita\\_Lad}} comprises 18,139 sentence pairs, carefully crafted as basic and concise examples to illustrate the use of specific words and phrases. \nThe average sentence length in \\textit{AD\\textsubscript{Ita\\_Lad}} is 23.43 characters for Ladin and 25.69 characters for Italian, while the average number of words per sentence is 5.02 for Ladin and 4.36 for Italian. Following that work, the testing dataset, \\textit{\\( T = \\{t\\textsubscript{1}, t\\textsubscript{2}, t\\textsubscript{3}\\} \\)}, consists of three subsets: \\( t_1 \\) (424 sentences) focuses on formal and legal terminology; \\( t_2 \\) (833 sentences) blends stylistic and lexical elements, reflecting regional cultural and historical contexts; \\( t_3 \\) (1,563 sentences) includes narrative prose, dialogue, and idiomatic expressions, offering diverse challenges. For Italian in the testing dataset, the average word counts for \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\) are 21.25, 26.65, and 15.61, respectively. In comparison, the corresponding averages for \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\) in Ladin are 23.58, 24.52, and 13.05, respectively.\n\n\\noindent\\textbf{Sentiment analysis.} We construct datasets for NLP tasks in Ladin by leveraging labeled monolingual Italian resources, including SA and MCQA datasets. We use the monolingual Italian SA dataset \\textit{D\\textsubscript{Ita\\_SA}} from \\citet{desole2025} for the SA task. \\textit{D\\textsubscript{Ita\\_SA}} comprises abundant Tripadvisor reviews labeled as positive or negative. The initial dataset contains 41,077 entries. To mitigate the impact of excessively long reviews, we filter the dataset to retain only those entries with word counts up to the third quartile (Q3), resulting in a maximum review length of 138 words. This screening results in a reduced dataset size of 30,712 entries. Given that the raw dataset, collected via web scraping, contains grammatical errors, we employ GPT-4 to correct these while preserving the original semantic content. Following grammar correction, the average number of words per sentence in \\textit{D\\textsubscript{Ita\\_SA}} is 70.44.\n\n\\noindent\\textbf{MCQA.} Finally, for the MCQA task, we use the monolingual Italian MCQA dataset \\textit{D\\textsubscript{Ita\\_MCQA}} from \\citet{multi_it24}. \\textit{D\\textsubscript{Ita\\_MCQA}} comprises over 5,000 manually crafted questions covering a wide range of topics. This MCQA dataset contains questions with 2, 3, 4, 5, or 6 answer choices. However, we exclude questions with 2 and 6 options due to their very limited number.\n\n\\subsection{Language model settings for machine translation}\nWe now discuss the process of building a MT model using existing Italian–Ladin parallel data, which serves as a prerequisite for the subsequent synthetic data generation process. To facilitate translation between Italian and Ladin, we employ both LLMs and sequence-to-sequence (seq2seq) models. For LLM-based approaches, we utilize LLaMA 3.1 (8B and 70B variants) and GPT-4o. The LLaMA models are evaluated in two configurations: few-shot learning (FSL) and supervised fine-tuning (FT). Appendix ~\\ref{sec:fsl} provides an example prompt used for the FSL approach. To perform the FSL approach, we utilize the \\textit{LLaMA-v3.1-8b-instruct} and \\textit{LLaMA-v3.1-70b-instruct} models via the DeepInfra API. Similarly, the FSL approach with GPT-4o is conducted using the OpenAI\\footnote{https://deepinfra.com/} API. For the FT approach using LLaMA, we leverage the Together AI\\footnote{https://www.together.ai/} fine-tuning API with the LoRA adapter configuration (\\textit{r} = 32), employing a batch size of 8 and 3 epochs.\n\nFor the seq2seq models, we employ MBART-large-50 and NLLB-200-1.3B, both of which are encoder-decoder architectures specifically designed for multilingual MT. The fine-tuning models of NLLB-1.3B and MBART-large-50 are conducted on an NVIDIA RTX A6000 GPU with a batch size of 8 and over 7 epochs. To accommodate Ladin, an unseen language for both seq2seq models, we introduce a Ladin-specific language tag in the tokenizer. This modification aids in the identification and processing of Ladin texts during translation tasks, facilitating better handling of the language.\n\nSubsequently, we evaluate translation performance using standard metrics: Sacre BLEU, ROUGE, and chrF++, providing a comprehensive assessment of translation quality.\n\n\\subsection{Synthetic data creation}\n\n\\begin{table*}\n \\centering\n \\small\n \\begin{tabular}{llcccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{2}{c}{\\textbf{BLEU}} \n & \\multicolumn{2}{c}{\\textbf{Rouge}} \n & \\multicolumn{2}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-8}\n &\n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\n & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\n & FSL-GPT-4o & 4.27 & \\underline{22.84} & 25.86 & \\underline{52.28} & 27.47 & 48.23 \\\\\n & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\n & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\n & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\n & FT-NLLB 1.3 B & \\underline{17.76} & 21.41 & \\underline{52.81} & 49.91 & \\underline{44.60 } & \\underline{48.40} \\\\\n & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\n \n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B & 18.30 & \\textbf{24.50} & \\textbf{53.66} & \\textbf{52.64} & \\textbf{44.62} & \\textbf{50.76} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & \\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\n \\hline\n \\end{tabular}\n \\caption{\\label{translation-performance}\n Comparison of different models based on average translation performance metrics on the test set \\( T \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.}\n\n\\end{table*}\n\nWe aim to create datasets for NLP tasks in the Ladin language by translating \\textit{D\\textsubscript{Ita\\_SA}} and \\textit{D\\textsubscript{Ita\\_MCQA}} from Italian data \\textit{D\\textsubscript{Ita}} to Ladin data \\textit{D\\textsubscript{Lad}}. These translated datasets serve multiple purposes, including translation (Italian–Ladin pairs), text classification, and question answering tasks. To ensure high-quality translation, we first select the best-performing MT model—identified in the previous section based on its performance on a held-out testing data \\( T \\), and use this model to translate \\textit{D\\textsubscript{Ita}} into \\textit{D\\textsubscript{Lad}}. The creation of this synthetic dataset shown in Figure~\\ref{fig:experiments} involves several key steps, as described below.\n\n\\noindent\\textbf{Italian-to-Ladin translation.} We begin by translating the labeled monolingual Italian datasets \\textit{D\\textsubscript{Ita}} of SA and MCQA tasks into Ladin, resulting in \\textit{D\\textsubscript{Lad}}. This translation process is carried out using the best-performing MT model identified in our evaluation, ensuring the highest possible quality of the synthetic Ladin data.\n\n\\noindent\\textbf{Filtering I.} To ensure the semantic quality of the Italian → Ladin translations, we apply a filtering step using similarity scores computed by the Language-Agnostic BERT Sentence Embedding (LaBSE) model \\citep{labse:22}. This step evaluates the alignment between each translated Ladin sentence and its original Italian counterpart. Specifically, we retain only those sentence pairs with a cosine similarity score \\( c \\geq 0.68 \\), which corresponds to the average similarity observed in the aligned dataset \\textit{AD\\textsubscript{Ita\\_Lad}}. This threshold helps eliminate semantically inconsistent translations while preserving high-quality aligned pairs for downstream tasks.\n\n\\noindent\\textbf{Back-translation.} We employ back-translation to further refine the synthetic dataset prior to conducting a second round of filtering. Specifically, the Ladin translations \\( D\\textsubscript{\\textit{Lad}} \\) are retranslated into Italian, yielding \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\), which are then compared against the original Italian datasets \\( D\\textsubscript{Ita} \\). This step helps identify and discard translations that deviate significantly from the original semantics, thereby improving data quality.\n\n\\noindent\\textbf{Filtering II.} To finalize the synthetic dataset, we apply a second filtering step based on automatic evaluation metrics. Specifically, we compute the Sacre BLEU and METEOR scores between the original Italian data (\\( D\\textsubscript{\\textit{Ita}} \\) and the back-translated Italian data \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)). A translation instance is retained if \n\\( BLEU \\)(\\( D\\textsubscript{\\textit{Ita}} \\), \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)) \\(\\geq \\mu{BLEU} \\) \nand \n\\( METEOR \\)(\\( D\\textsubscript{\\textit{Ita}} \\), \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)) \\(\\geq \\mu{METEOR} \\).\nwhere \\( \\mu{BLEU} \\) and \\( \\mu{METEOR} \\) represent the average scores computed across all translation pairs. These threshold values ensure semantic fidelity and fluency by eliminating noise and inaccuracy, thus improving the quality of the synthetic dataset.\n\n\\subsection{Synthetic data evaluation}\n\nTo evaluate the quality and impact of the Italian–Ladin synthetic parallel dataset \\textit{SD\\textsubscript{Ita\\_Lad}} = {(\\textit{D\\textsubscript{Ita\\_SA}}, \\textit{D\\textsubscript{Lad\\_SA}}), (\\textit{D\\textsubscript{Ita\\_MCQA}}, \\textit{D\\textsubscript{Lad\\_MCQA}})}, we combine it with the authentic dataset \\textit{AD\\textsubscript{Ita\\_Lad}} and assess performance on the testing data \\( T \\). This setup allows us to measure the effect of synthetic data augmentation on translation quality. To assess lexical and syntactic adequacy of the synthetic translations, we construct a manually translated gold dataset \\( GD \\)%\\footnote{Datasets will be released upon publication under an open license (CC BY-NC 4.0).}\n, containing 50 examples each from \\textit{D\\textsubscript{Ita\\_SA}} and \\textit{D\\textsubscript{Ita\\_MCQA}}, translated into Ladin by a native speaker of Italian and Ladin. We compute cosine similarity between the synthetic and gold translations using sentence embeddings, providing a measure of semantic alignment.% Additionally, we adopt the error typology from the Multidimensional Quality Metrics (MQM) framework as qualitative analysis \\cite{MQM}, selecting a subset of high-level error dimensions to examine the strengths and limitations of the translation outputs. Specifically, we focus on three dimensions, accuracy, linguistic conventions, and terminology, drawn from the full set defined in the MQM core typology\\cite{MQM24}, based on their relevance to our task and the constraints of our annotation process.\n\n\\section{Results and Discussion}\nIn this section, we report the results of MT using the existing Italian–Ladin parallel data. We then present the evaluation of the synthetic Ladin datasets for SA and MCQA, including both quantitative metrics and qualitative analysis.\n\n\\begin{table*}[!t]\n \\centering\n \\small\n \\begin{tabular}{llccccccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-11} &\n & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n & 26.00 & 16.92 \\\\\n & FSL-Llama 3.1 70B \n & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n & 35.05 & 23.17 \\\\\n & FSL-GPT-4o \n & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n & 30.08 & 20.42 \\\\\n & FT-Llama 3.1 8B \n & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n & 36.60 & 30.98 \\\\\n & FT-Llama 3.1 70B \n & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n & 35.87 & 23.99 \\\\\n & Mbart-large-50 \n & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n & 38.66 & 35.23 \\\\\n & NLLB 1.3 B \n & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n & \\underline{45.98} & \\underline{41.58} \\\\\n & Benchmark (LLM) \n & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n & 28.98 & 18.60 \\\\\n\\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B \n & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n & 46.28 & \\textbf{42.15} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n \\hline\n \\end{tabular}\n \\caption{\\label{add-trans_to_ladin}\n Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n }\n\\end{table*}\n\n\\begin{table*}[!t]\n \\centering\n \\small\n \\begin{tabular}{llccccccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-11} &\n & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \n & 38.89 & 23.41 \\\\\n & FSL-Llama 3.1 70B \n & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \n & 48.66 & 36.91 \\\\\n & FSL-GPT-4o \n & 29.23 & 23.38 & 15.90 & 61.39 & \\textbf{53.37} & 42.07 & 55.73 \n & 50.33 & 38.64 \\\\\n & FT-Llama 3.1 8B \n & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \n & 44.11 & 33.66 \\\\\n & FT-Llama 3.1 70B \n & \\textbf{30.78} & \\textbf{23.65} & 13.02 & \\textbf{61.91} & 52.10 & 38.29 & \\textbf{57.23} \n & \\underline{50.53} & 36.12 \\\\\n & Mbart-large-50 \n & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \n & 42.15 & 36.81 \\\\\n & NLLB 1.3 B \n & 27.15 & 19.77 & \\underline{17.31} & 55.54 & 48.27 & \\underline{46.03} & 54.45\n & 49.66 & \\underline{41.09} \\\\\n & Benchmark (LLM) \n & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \n & 48.52 & 32.36 \\\\\n\\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B \n & \\underline{30.46} & \\underline{22.71} & \\textbf{20.33} & 58.11 & 50.71 & \\textbf{49.11} & \\underline{56.95} \n & \\textbf{51.49} & \\textbf{43.83} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \n & 49.08 & 40.76 \\\\\\\\ \n \\hline\n \\end{tabular}\n \\caption{\\label{add-trans_to_italian}\n Translation performance of various models for Ladin → Italian across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n }\n\\end{table*}\n\n\\subsection{Machine translation of Italian and Ladin}\nTable~\\ref{translation-performance} presents the translation performance results for both Italian → Ladin and Ladin → Italian across diverse language model configurations. For experiments using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data, we report results from the benchmark approach proposed by \\citet{frontull24}, which employs the LLM \\verb|GPT-3.5-turbo-0125|, for comparison purposes. %This detailed evaluation not only highlights the effectiveness of different model settings but also underscores the challenges and opportunities in machine translation for LRL pairs.We also present the detailed results of the experimental results across various scenarios.\nWhile Table~\\ref{translation-performance} presents the overall average performance metrics of each translation model evaluated on the testing data \\( T \\), Tables~\\ref{add-trans_to_ladin} and~\\ref{add-trans_to_italian} offer a more fine-grained analysis. They report detailed metric scores for the individual test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\), allowing for a closer examination of model behavior across different data segments.\n\nIn both translation directions in Table~\\ref{translation-performance}, the fine-tuned NLLB (FT-NLLB) model achieves significant performance across evaluation metrics. Specifically, the model performs best on the translation from Italian → Ladin, with a BLEU score approaching 18, indicating relatively good translation accuracy for extremely low-resource settings. Although the Ladin → Italian translation performance of the FT-NLLB model slightly lags behind that of the FT-LLaMA 3.1 70B model, the FT-NLLB model achieves the highest chrF++ scores in both translation directions, indicating superior overall translation quality. These findings underscore a persistent challenge in extremely low-resource NLP. Despite the impressive capabilities of LLMs, their performance often suffers in extremely low-resource scenarios due to training biases toward HRLs with abundant data. Consequently, the Ladin → Italian translation achieves higher BLEU scores, reflecting the model’s stronger proficiency in HRLs. \n\nAlthough Ladin and Italian both belong to the Romance language family, translation into Ladin remains challenging due to its status as the extremely low-resource language, including unique vocabulary, dialectal variations, and a lack of direct equivalence to Italian. In contrast, the NLLB model demonstrates relatively robust performance, likely benefiting from its multilingual training across 200+ languages, including over 150 LRLs \\citep{nllb2022}. Notably, the NLLB model was trained on Friulian, a closely related Raeto-Romance language \\citep{UNESCO}, which may contribute to its improved generalization on Ladin.\n\nAdditionally, we evaluate the suitability and effectiveness of the NLLB tokenizer for processing Ladin text. Our analysis reveals an average tokens-per-word ratio of 1.50 for Ladin, compared to 1.39 for Italian. This modest overhead indicates that the NLLB tokenizer segments Ladin reasonably well, despite the language's extremely low-resource status, suggesting its viability for downstream translation tasks.\n\n\\subsection{Qualitative error analysis}\n\n\\begin{table}[t]\n \\small\n \\centering\n \\makebox[3.1in][r]{\n \\begin{tabular}{lcc}\n \\hline\n \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n & \\textbf{Italian} & \\textbf{Ladin} \\\\\n \\hline\n Average number of words per entry & 65 & 70 \\\\\n Average number of characters per entry & 144 & 348 \\\\\n Positive label count & 9,842 & 9,842 \\\\\n Negative label count & 2,669 & 2,669 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SD-SA}\n Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\n }\n\\end{table}\n\nTo assess the qualitative aspects of translation performance using the FT-NLLB model, we analyze specific examples of translation errors from Italian to Ladin. This analysis helps identify common error types—such as lexical inaccuracies, syntactic issues, and morphological mismatches—and provides insight into the strengths and limitations of the machine-generated translations. For instance, consider the following sentence pair, where the Ladin translation is largely faithful to the Italian source, successfully preserving both structure and meaning.\n\n\\textbf{Italian}: \\textit{Sono stata a un congresso a Torino e ho passato due notti al Best Western Crystal Palace, un hotel 4 stelle di fianco alla stazione di Porta Nuova. Ho apprezzato molto la vasca idromassaggio e il giornale ogni giorno: La Stampa, con un foglio di sintesi degli argomenti principali.}\n\n\\textbf{Ladin}: \\textit{I sun stada a n congres a Torin y i à sté döes nöts tl Best Western Crystal Palace, n hotel da 4 stëres dlungia la staziun de Porta Nuova. I á dër aprijé la vasca da iade y le foliet da vigni de: La Stampa, cun na plata de ressumé di argomënc prinzipai.}\n\nUpon closer inspection above, the Ladin translation only exhibits minor grammatical and lexical inaccuracies. The phrase “\\textit{I á sté döes nöts}” should be corrected to “\\textit{I sun stada döes nöts}” to ensure grammatical correctness. Additionally, “\\textit{la vasca da iade}” ought to be revised to “\\textit{la vasca idromassaje}” to more accurately reflect the original Italian phrase “\\textit{la vasca idromassaggio}.” These examples illustrate the model’s general ability to produce semantically faithful translations, while also highlighting areas where linguistic precision can be improved. Overall, the model demonstrates strong potential for handling Ladin.\n\n\\subsection{Ladin synthetic datasets}\n\n\\begin{table}[t]\n \\centering\n \\small\n \\makebox[3.2in][r]{\n \\begin{tabular}{lcc}\n \\hline\n \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n & \\textbf{Italian} & \\textbf{Ladin} \\\\\n \\hline\n Average number of words per question & 18 & 19 \\\\\n Average number of characters per question & 108 & 97 \\\\\n Average number of words per choices & 28 & 30 \\\\\n Average number of characters per choices & 187 & 174 \\\\\n Frequency of entries with 3 choices & 304 & 304 \\\\\n Frequency of entries with 4 choices & 196 & 196 \\\\\n Frequency of entries with 5 choices & 264 & 264 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SD-MCQA}\n Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\n }\n\\end{table}\n\n\\begin{table*}[t]\n \\centering\n \\small\n \\makebox[\\textwidth]{\n \\begin{tabular}{lcccc@{\\hspace{2em}}cccc}\n \\hline\n \\textbf{Model} &\n \\multicolumn{4}{c}{\\textbf{Ladin}} &\n \\multicolumn{4}{c}{\\textbf{Italian}} \\\\\n \\cline{2-9}\n & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}}\n & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}} \\\\\n \n & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1}\n & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1} \\\\\n \\hline\n FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\n & 97.92 & 98.18 & 54.79 & 54.18 \\\\\n m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \n & 94.78 & 96.41 & 30.73 & 30.29 \\\\\n XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \n & 97.14 & 98.08 & 26.14 & 26.14 \\\\\n mT5 & 50.09 & 69.37 & 23.50 & 23.16 \n & 49.98 & 69.25 & 22.62 & 21.92 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SA-MCQA} \n Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\n } \n\\end{table*}\n\nSince the FT-NLLB model demonstrates the best performance for translation in our experiments using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data, we utilize this model to translate \\textit{D\\textsubscript{Ita}} into \\textit{D\\textsubscript{Lad}} through the framework shown in Figure~\\ref{fig:experiments}.\nInitially, we obtained 30,477 paired entries for (\\textit{D\\textsubscript{Ita\\_SA}}, \\textit{D\\textsubscript{Lad\\_SA}}) as the SA dataset after applying the first filtering step based on cosine similarity between Italian and Ladin with the threshold of 0.68. This value is derived from the cosine similarity between both languages in \\textit{AD\\textsubscript{Ita\\_Lad}}. Subsequently, we perform back-translation from \\textit{D\\textsubscript{Lad\\_SA}} to \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_SA}}\\). The threshold for the second filtering step is determined based on the average (\\(\\mu\\)) BLEU and METEOR scores calculated for each entry by comparing \\textit{D\\textsubscript{Ita\\_SA}} with \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_SA}}\\). These scores were found to be 33.63 and 0.58, respectively. The final filtered synthetic SA dataset, consisting of 12,511 entries, statistically is detailed in Table~\\ref{SD-SA}. This SA dataset contains an average of 65 and 70 words per entry for Italian and Ladin, respectively. Additionally, the majority of entries in the final dataset—over 9,000 instances—are labeled with positive sentiment.\n\nConcurrently, we obtained 4,651 paired entries of (\\textit{D\\textsubscript{Ita\\_MCQA}}, \\textit{D\\textsubscript{Lad\\_MCQA}}) as the MCQA dataset, following an initial filtering step based on cosine similarity, similar to the procedure used for the synthetic SA dataset. The thresholds for the second filtering step are also determined using the average BLEU and METEOR scores calculated between \\textit{D\\textsubscript{Ita\\_MCQA}} and \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_MCQA}}\\), which are 36.58 and 0.62, respectively. The final filtered synthetic MCQA dataset, comprising 764 entries, is presented in Table~\\ref{SD-MCQA}, with the majority of questions featuring three answer choices. Notably, both Italian-Ladin paired datasets of SA and MCQA tasks exhibit a higher average number of words and characters per entry compared to the authentic parallel dataset \\textit{AD\\textsubscript{Ita\\_Lad}}. \n\n\\subsection{Synthetic data assessment for NLP tasks}\n\nAfter obtaining the new synthetic datasets \\textit{SD\\textsubscript{Ita\\_Lad}}%\\footnote{Datasets and codes will be released after paper publication under an open license (CC BY-NC 4.0).}\n, we compare them against the manually translated golden dataset \n\\( GD \\) to evaluate translation quality. Specifically, we use cosine similarity metrics to evaluate the semantic alignment between the synthetic and manually created data. The cosine similarity scores of \\textit{SD\\textsubscript{Ita\\_Lad}} and \\( GD \\), with respect to \\textit{AD\\textsubscript{Ita\\_Lad}}, are 86.61 and 85.75, respectively. These results indicate a high degree of semantic consistency and minimal disparity between the synthetic and human-translated datasets.\n\nSubsequently, we combine \\textit{SD\\textsubscript{Ita\\_Lad}} with \\textit{AD\\textsubscript{Ita\\_Lad}} to construct the training data for fine-tuning the FT-NLLB model as the MT model. The testing data \\( T \\) is then used to evaluate the performance of the resulting translation model on these combined datasets, as shown in the lower section of Table ~\\ref{translation-performance}. Detailed results for the three subsets (\\( t_1 \\), \\( t_2 \\), and \\( t_3 \\)) of \\( T \\) are also presented in the lower section of Tables~\\ref{add-trans_to_ladin} and~\\ref{add-trans_to_italian}. We compare our results with the augmented synthetic translations generated by the RBMT system proposed by \\citet{frontull24}, which incorporates additional monolingual data in both Ladin and Italian. As summarized in Table~\\ref{translation-performance}, experimental results demonstrate that incorporating our synthetic data consistently improves performance across all evaluation metrics, surpassing the previous benchmark. In both translation directions, the FT-NLLB model performs well compared to its counterpart model.\n\nGiven that \\textit{SD\\textsubscript{Ita\\_Lad}} encompasses SA and MCQA tasks in Ladin, we establish a benchmark to evaluate model performance on these tasks. We adopt the few-shot learning (FSL) using LLaMA 3.1 70B as our LLM's approach. Appendices~\\ref{sec:fsl-sa} and~\\ref{sec:fsl-mcqa} provide example prompts used in the FSL approach. In parallel, we assess the performance of several transformer-based models, including the Distilbert-base-multilingual-cased (m-DistilBERT)\nmodel, the XLM-RoBERTa base model, and the mT5-small model. Table~\\ref{SA-MCQA} summarizes the results for SA and MCQA tasks in Ladin, with Italian results included for comparison. The LLM-based approach achieves the highest scores in both tasks in terms of balanced accuracy (Acc) and F1-score (F1), although the improvements over other models are marginal. m-DistilBERT also performs well across both tasks. Specifically, the results indicate that the SA dataset in Ladin is generally well-handled by the evaluated models, with the exception of mT5. This indicates that our created Ladin SA dataset is sufficiently informative and well-aligned with the task objectives to support effective model training. In contrast, performance on the MCQA task remains low across all models, even when evaluated on Italian data. This suggests that the MCQA task is inherently more challenging than the SA task. The difficulty may be attributed to the limited size of the MCQA dataset and the broad topical coverage of the questions, both of which may hinder model generalization.\n\n\\section{Conclusions and Future Work}\nIn this work, we explore various strategies for translating Ladin—an extremely low-resource language—and demonstrate that our NLLB-based model consistently outperforms counterpart models. Beyond translation, we introduce the first comprehensive Ladin benchmark dataset covering machine translation, sentiment analysis, and multiple-choice question answering, all derived through synthetic augmentation from monolingual Italian resources. \n\nOur evaluation shows that while synthetic data enables competitive performance across tasks further progress is needed to enhance knowledge transfer from high-resource to low-resource languages. This study lays foundational work for future NLP research on Ladin and similarly underrepresented languages. \n\nFuture work will investigate knowledge distillation techniques to more effectively transfer knowledge from high-resource languages to low-resource ones, as well as explore advanced methods to better exploit available monolingual Ladin data for improved model performance. We are also committed to further foster developments of Ladin resources and to engaging community in actively researching this language by establishing leaderboards based on the created datasets.\n\n\\section*{Limitations}\n\nThe Ladin-Italian dataset used in this study primarily consists of short sentences, which may limit the generalizability of the models to longer and more complex sentence structures. Moreover, the limited availability of manually crafted monolingual Italian MCQA datasets restricts the number of usable samples, which may impact the robustness and reliability of the experimental results. \n\n%\\section*{Acknowledgments}\n\n%This document has been adapted\n\n\n% Bibliography entries for the entire Anthology, followed by custom entries\n%\\bibliography{anthology,custom}\n% Custom bibliography entries only\n\\bibliography{custom}\n\n\\appendix\n\\section{Additional Experimental Results}\n\\label{sec:add-results}\nThis section presents detailed experimental results for machine translation performance using \\textit{AD\\textsubscript{Ita\\_Lad}} as the sole training data, as reported in the upper section of Table~\\ref{translation-performance}. Figure~\\ref{fig:chrf_AD} illustrates the chrF++ scores achieved by various models, while Figure~\\ref{fig:bleu_AD} presents the corresponding BLEU score comparisons. \n\n\\section{Back-translation Results}\nAs illustrated in Figure~\\ref{fig:experiments}, we perform a second round of filtering by back-translating Ladin data into Italian and evaluating the results using BLEU and METEOR scores. For the SA dataset, which contains 30,477 samples, the average BLEU and METEOR scores are 33.63 and 0.58, respectively. In the case of the MCQA dataset (4,651 samples), the corresponding averages are 36.58 and 0.62. Below, we present examples comparing back-translated Italian samples with their original counterparts to facilitate a more detailed analysis.\n\n\\section{A Few-shot Learning Prompt Template in the MT task}\n\\label{sec:fsl}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Here are examples of translations in a JSON \nformat between Italian and Ladin with the \nVal Badia variant:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n{\n \"translations\": [\n {\n \"Italian\": \"è venuta la mia ora\",\n \"Ladin\": \"al é gnü mia ora\"\n },\n {\n \"Italian\": \"vado dalle cugine!\",\n \"Ladin\": \"i vá dales jormanes\"\n },\n {\n \"Italian\": \"staccare la luce\",\n \"Ladin\": \"destodé la löm\"\n },\n ...\n {\n \"Italian\": \"a ottobre inoltrato\",\n \"Ladin\": \"d'otober fora\"\n }\n ]\n }\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}Please provide the translation of the fol-\nlowing 15 entries in the JSON format, fill-\ning the empty 'Ladin' fields for each entry.\nDo not include any additional explanations \nor text:\n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n{\n \"translations\": [\n {\n \"Italian\": \"imprimere nella mente\",\n \"Ladin\": \"\"\n },\n {\n \"Italian\": \"temperare la matita\",\n \"Ladin\": \"\"\n },\n {\n \"Italian\": \"mettere paura a qcn.\",\n \"Ladin\": \"\"\n },\n ...\n {\n \"Italian\": \"un animale scattante\",\n \"Ladin\": \"\"\n }\n ]\n }\n\\end{verbatim}\n\n\\section{A Few-shot Learning Prompt Template in the SA task}\n\\label{sec:fsl-sa}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Below are Tripadvisor reviews in Ladin (Val\nBadia variant) along with their sentiment \nlabels:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n {\n[review: \"I sun stá chiló por 7 nes. Le gost\né é bun. Porimpó é i chelins cherdá indormed\ní pormal. ...\", label: 1], [review: \"Lalber\nch é bunorté te na zona chîta dlungia na plaz\na. Gní zoruch vigni sëra ê sciöche ciafé nao\nasa. ...\" label: 0], \n...\n[review: \"I un passé chiló n bel fin dledema\nhotel nët, personal da orëi bun, bun ince le\ngosté y na posiziun ezelënta, impormó do lab\nela plaza San Marco. ...\", label: 0]\n }\n\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}\nPlease classify the sentiment for the follo\nwing 10 Tripadvisor reviews in Ladin (Val \nBadia variant) as either 0 (Positive) or 1\n(Negative). Fill in the empty 'label' field\ns with only 0 or 1. Respond with the sentime\nnt labels in list format like this: [x, x, \n...]. Do not include any additional explana\ntions or text.\n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n {\n[review: \"Por na vistada y na fuga a Milan \n(na mostra, na cörta vijita, na spazirada)\nél perfet. ...\", label: ], [review: \"Le bru\nnch ne joav nia le prisc. Lhotel é n pü' dal\nunc dal Duomo. ...\", label: ], \n...\n[review: \"Rezeziun ezelënta, dantadöt le \nconcierje cun sües racomanaziuns. ...\", \nlabel: ]\n } \n\\end{verbatim}\n\n\\section{A Few-shot Learning Prompt Template in the MCQA task}\n\\label{sec:fsl-mcqa}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Below are multiple-choice questions in Lad\nin (Val Badia variant) with 3, 4, or 5 answer \nchoices. The correct answer is explicitly pr\novided as an id number corresponding to the \norder of the choices:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n {\n[question: aladô dla lege 241/1990, olá é pa \nmetüda sö la comisciun por l'azes ai documën\nc aministratifs?, choices: ['pro la Presidën\nza dl Consei di Minisć', 'Por vigni Entité pu\nblica dl post', 'pro vigni Entité publica eco\nnomica de competënza regionala'], answer: 0]\n, [question: aladô dla DGR 514/2009, por PAI \ny PEI se intendi rispetivamënter:, choices: \n[\"Plan d'Assistënza Indicisé y Program Etich \nIndividualisé\", 'Program de Asistënza Indivi\nduala y Program Educatif Individualisé', \"Pl\nan d' Assistënza Individualisé y Plan d'Educ\naziun Individualisé\"], answer: 2],\n...\n[question: aladô de REICAT l'intestaziun uni\nforme por na porsona:, choices: ['al corespo\ngn tresala forma dl inom che vëgn dant tla pr\nöma ediziundles operes dl autur.', 'al se ba\nsa söl inom cun chël che la porsona medema é\ngeneralmente identifiada.', 'ara ne pó mai e\nster metüda adöm da npseudonom.'], answer: 1]\n }\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}Please answer the questions based on the ava\nilable choices, by filling in the empty 'answ\ner' fields with the id number corresponding to\nthe order of the choices. Provide the answers \nin a list format like this: [x, x, x, ..., x].\nDo not include any additional explanations or\ntext. \n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n {\n[question: na coleziun de figurines é metüda\nadöm da 84 toc, 14 por vigni contignidú. 7 fi\ngurines de vigni contignidú é lamincards, i \nrestanc fotocartes. Tan de figurines de fo to\ncartes ál pa la coleziun?, choices: ['42', '43'\n, '44'], answer:], \n...\n, [question: ci frasa, danter chëses listi\ngades, á pa n complemënt de gauja?, choices:\n['Laura é piada demez por n iade de plajëi',\n'i ápormó cumpré na scincunda por le compliann\nde Marco', \"por na taiada de strom s'á ascensur\nbloché\"], answer: ]\n }\n\\end{verbatim}\n\n\\clearpage % Force the figure to go on its own page\n\\begin{figure*}[tp]\n \\centering\n \\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\n \\caption{chrF++ scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n \\label{fig:chrf_AD}\n\\end{figure*}\n\n\\begin{figure*}[tp]\n \\centering\n \\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\n \\caption{BLEU scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n \\label{fig:bleu_AD}\n\\end{figure*}\n\n\\end{document}\n"},"question":{"kind":"string","value":"If we take the ratio of t1 subset to t2 subset for all the models and multiply that value with t3 subset along which metric is the net value highest? For which model? Also, for that model across the table, formulate a polynomial regression function f, what is f(2)?"},"answer":{"kind":"string","value":"55.33,Rouge NLLB 1.3 B,23992.3"},"plan":{"kind":"string","value":"SELECT all metrics\nLOOP for each metric\n SELECT all models\n LOOP for each model\n COMPUTE net_value = t1 / t2 × t3\nCOMPUTE best_pair = argmax model and metric pair over net_value\n\n\nSELECT all numeric values for best_model across the table in left-to-right order as coeff_list\n\n\nCOMPUTE degree = count of coeff_list − 1\n\n\nLOOP for each coeff in coeff_list with its index i in order\n COMPUTE f2 = f2 + coeff * (2 ^ (degree − i))\n\n\nRETURN metric of best_pair, model of best_pair, f2\n"}}},{"rowIdx":360,"cells":{"paper":{"kind":"string","value":"2509.03962"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n"," & 26.00 & 16.92 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n"," & 35.05 & 23.17 \\\\\n"," & FSL-GPT-4o \n"," & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n"," & 30.08 & 20.42 \\\\\n"," & FT-Llama 3.1 8B \n"," & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n"," & 36.60 & 30.98 \\\\\n"," & FT-Llama 3.1 70B \n"," & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n"," & 35.87 & 23.99 \\\\\n"," & Mbart-large-50 \n"," & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n"," & 38.66 & 35.23 \\\\\n"," & NLLB 1.3 B \n"," & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n"," & \\underline{45.98} & \\underline{41.58} \\\\\n"," & Benchmark (LLM) \n"," & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n"," & 28.98 & 18.60 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n"," & 46.28 & \\textbf{42.15} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_ladin}\n"," Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \\n\",\n \" & 26.00 & 16.92 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \\n\",\n \" & 35.05 & 23.17 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \\n\",\n \" & 30.08 & 20.42 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \\n\",\n \" & 36.60 & 30.98 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \\n\",\n \" & 35.87 & 23.99 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \\n\",\n \" & 38.66 & 35.23 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & \\\\underline{18.54} & \\\\underline{16.85} & \\\\underline{17.88} & \\\\textbf{51.59} & \\\\underline{51.55} & \\\\underline{55.29} & \\\\textbf{46.24}\\n\",\n \" & \\\\underline{45.98} & \\\\underline{41.58} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \\n\",\n \" & 28.98 & 18.60 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & 18.30 & 17.69 & \\\\textbf{18.29} & 51.40 & \\\\textbf{52.92} & \\\\textbf{56.65} & 45.44 \\n\",\n \" & 46.28 & \\\\textbf{42.15} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{20.93} & \\\\textbf{19.32} & 16.65 & - & - & - & \\\\textbf{47.65} & \\\\textbf{46.58} & 38.16 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_ladin}\\n\",\n \" Translation performance of various models for Italian → Ladin across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[!t]\n"," \\centering\n"," \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n"," \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n"," \\label{fig:LadinArea}\n","\\end{figure}\n"],["\\begin{figure*}[t]\n"," \\centering\n"," \\includegraphics[width=5.3in]{latex/Figure_2.png}\n"," \\caption{Synthetic data generation process. Initially, we translate the Italian data \\( D\\textsubscript{\\textit{Ita}}\\) of SA and MCQA into Ladin. The Ladin translation \\(D\\textsubscript{\\textit{Lad}}\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\(D\\textsubscript{\\textit{Lad}}\\) is back-translated into Italian \\( D^{\\prime}\\textsubscript{\\textit{Ita}}\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\n"," \\label{fig:experiments}\n","\\end{figure*}\n"],["\\begin{table*}\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llcccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{2}{c}{\\textbf{BLEU}} \n"," & \\multicolumn{2}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{2}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-8}\n"," &\n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\n"," & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\n"," & FSL-GPT-4o & 4.27 & \\underline{22.84} & 25.86 & \\underline{52.28} & 27.47 & 48.23 \\\\\n"," & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\n"," & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\n"," & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\n"," & FT-NLLB 1.3 B & \\underline{17.76} & 21.41 & \\underline{52.81} & 49.91 & \\underline{44.60 } & \\underline{48.40} \\\\\n"," & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\n"," \n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B & 18.30 & \\textbf{24.50} & \\textbf{53.66} & \\textbf{52.64} & \\textbf{44.62} & \\textbf{50.76} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{translation-performance}\n"," Comparison of different models based on average translation performance metrics on the test set \\( T \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.}\n","\n","\\end{table*}\n"],["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n"," & 26.00 & 16.92 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n"," & 35.05 & 23.17 \\\\\n"," & FSL-GPT-4o \n"," & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n"," & 30.08 & 20.42 \\\\\n"," & FT-Llama 3.1 8B \n"," & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n"," & 36.60 & 30.98 \\\\\n"," & FT-Llama 3.1 70B \n"," & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n"," & 35.87 & 23.99 \\\\\n"," & Mbart-large-50 \n"," & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n"," & 38.66 & 35.23 \\\\\n"," & NLLB 1.3 B \n"," & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n"," & \\underline{45.98} & \\underline{41.58} \\\\\n"," & Benchmark (LLM) \n"," & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n"," & 28.98 & 18.60 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n"," & 46.28 & \\textbf{42.15} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_ladin}\n"," Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"],["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \n"," & 38.89 & 23.41 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \n"," & 48.66 & 36.91 \\\\\n"," & FSL-GPT-4o \n"," & 29.23 & 23.38 & 15.90 & 61.39 & \\textbf{53.37} & 42.07 & 55.73 \n"," & 50.33 & 38.64 \\\\\n"," & FT-Llama 3.1 8B \n"," & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \n"," & 44.11 & 33.66 \\\\\n"," & FT-Llama 3.1 70B \n"," & \\textbf{30.78} & \\textbf{23.65} & 13.02 & \\textbf{61.91} & 52.10 & 38.29 & \\textbf{57.23} \n"," & \\underline{50.53} & 36.12 \\\\\n"," & Mbart-large-50 \n"," & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \n"," & 42.15 & 36.81 \\\\\n"," & NLLB 1.3 B \n"," & 27.15 & 19.77 & \\underline{17.31} & 55.54 & 48.27 & \\underline{46.03} & 54.45\n"," & 49.66 & \\underline{41.09} \\\\\n"," & Benchmark (LLM) \n"," & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \n"," & 48.52 & 32.36 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & \\underline{30.46} & \\underline{22.71} & \\textbf{20.33} & 58.11 & 50.71 & \\textbf{49.11} & \\underline{56.95} \n"," & \\textbf{51.49} & \\textbf{43.83} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \n"," & 49.08 & 40.76 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_italian}\n"," Translation performance of various models for Ladin → Italian across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"],["\\begin{table}[t]\n"," \\small\n"," \\centering\n"," \\makebox[3.1in][r]{\n"," \\begin{tabular}{lcc}\n"," \\hline\n"," \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n"," & \\textbf{Italian} & \\textbf{Ladin} \\\\\n"," \\hline\n"," Average number of words per entry & 65 & 70 \\\\\n"," Average number of characters per entry & 144 & 348 \\\\\n"," Positive label count & 9,842 & 9,842 \\\\\n"," Negative label count & 2,669 & 2,669 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SD-SA}\n"," Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\n"," }\n","\\end{table}\n"],["\\begin{table}[t]\n"," \\centering\n"," \\small\n"," \\makebox[3.2in][r]{\n"," \\begin{tabular}{lcc}\n"," \\hline\n"," \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n"," & \\textbf{Italian} & \\textbf{Ladin} \\\\\n"," \\hline\n"," Average number of words per question & 18 & 19 \\\\\n"," Average number of characters per question & 108 & 97 \\\\\n"," Average number of words per choices & 28 & 30 \\\\\n"," Average number of characters per choices & 187 & 174 \\\\\n"," Frequency of entries with 3 choices & 304 & 304 \\\\\n"," Frequency of entries with 4 choices & 196 & 196 \\\\\n"," Frequency of entries with 5 choices & 264 & 264 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SD-MCQA}\n"," Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\n"," }\n","\\end{table}\n"],["\\begin{table*}[t]\n"," \\centering\n"," \\small\n"," \\makebox[\\textwidth]{\n"," \\begin{tabular}{lcccc@{\\hspace{2em}}cccc}\n"," \\hline\n"," \\textbf{Model} &\n"," \\multicolumn{4}{c}{\\textbf{Ladin}} &\n"," \\multicolumn{4}{c}{\\textbf{Italian}} \\\\\n"," \\cline{2-9}\n"," & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}}\n"," & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}} \\\\\n"," \n"," & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1}\n"," & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1} \\\\\n"," \\hline\n"," FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\n"," & 97.92 & 98.18 & 54.79 & 54.18 \\\\\n"," m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \n"," & 94.78 & 96.41 & 30.73 & 30.29 \\\\\n"," XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \n"," & 97.14 & 98.08 & 26.14 & 26.14 \\\\\n"," mT5 & 50.09 & 69.37 & 23.50 & 23.16 \n"," & 49.98 & 69.25 & 22.62 & 21.92 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SA-MCQA} \n"," Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\n"," } \n","\\end{table*}\n"],["\\begin{figure*}[tp]\n"," \\centering\n"," \\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\n"," \\caption{chrF++ scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n"," \\label{fig:chrf_AD}\n","\\end{figure*}\n"],["\\begin{figure*}[tp]\n"," \\centering\n"," \\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\n"," \\caption{BLEU scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n"," \\label{fig:bleu_AD}\n","\\end{figure*}\n"]],"string":"[\n [\n \"\\\\begin{figure}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\\n\",\n \" \\\\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\\n\",\n \" \\\\label{fig:LadinArea}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=5.3in]{latex/Figure_2.png}\\n\",\n \" \\\\caption{Synthetic data generation process. Initially, we translate the Italian data \\\\( D\\\\textsubscript{\\\\textit{Ita}}\\\\) of SA and MCQA into Ladin. The Ladin translation \\\\(D\\\\textsubscript{\\\\textit{Lad}}\\\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\\\(D\\\\textsubscript{\\\\textit{Lad}}\\\\) is back-translated into Italian \\\\( D^{\\\\prime}\\\\textsubscript{\\\\textit{Ita}}\\\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\\n\",\n \" \\\\label{fig:experiments}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llcccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{BLEU}} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-8}\\n\",\n \" &\\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\\\\\\n\",\n \" & FSL-GPT-4o & 4.27 & \\\\underline{22.84} & 25.86 & \\\\underline{52.28} & 27.47 & 48.23 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\\\\\\n\",\n \" & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\\\\\\n\",\n \" & FT-NLLB 1.3 B & \\\\underline{17.76} & 21.41 & \\\\underline{52.81} & 49.91 & \\\\underline{44.60 } & \\\\underline{48.40} \\\\\\\\\\n\",\n \" & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B & 18.30 & \\\\textbf{24.50} & \\\\textbf{53.66} & \\\\textbf{52.64} & \\\\textbf{44.62} & \\\\textbf{50.76} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{translation-performance}\\n\",\n \" Comparison of different models based on average translation performance metrics on the test set \\\\( T \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.}\\n\",\n \"\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \\n\",\n \" & 26.00 & 16.92 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \\n\",\n \" & 35.05 & 23.17 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \\n\",\n \" & 30.08 & 20.42 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \\n\",\n \" & 36.60 & 30.98 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \\n\",\n \" & 35.87 & 23.99 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \\n\",\n \" & 38.66 & 35.23 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & \\\\underline{18.54} & \\\\underline{16.85} & \\\\underline{17.88} & \\\\textbf{51.59} & \\\\underline{51.55} & \\\\underline{55.29} & \\\\textbf{46.24}\\n\",\n \" & \\\\underline{45.98} & \\\\underline{41.58} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \\n\",\n \" & 28.98 & 18.60 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & 18.30 & 17.69 & \\\\textbf{18.29} & 51.40 & \\\\textbf{52.92} & \\\\textbf{56.65} & 45.44 \\n\",\n \" & 46.28 & \\\\textbf{42.15} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{20.93} & \\\\textbf{19.32} & 16.65 & - & - & - & \\\\textbf{47.65} & \\\\textbf{46.58} & 38.16 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_ladin}\\n\",\n \" Translation performance of various models for Italian → Ladin across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \\n\",\n \" & 38.89 & 23.41 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \\n\",\n \" & 48.66 & 36.91 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 29.23 & 23.38 & 15.90 & 61.39 & \\\\textbf{53.37} & 42.07 & 55.73 \\n\",\n \" & 50.33 & 38.64 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \\n\",\n \" & 44.11 & 33.66 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & \\\\textbf{30.78} & \\\\textbf{23.65} & 13.02 & \\\\textbf{61.91} & 52.10 & 38.29 & \\\\textbf{57.23} \\n\",\n \" & \\\\underline{50.53} & 36.12 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \\n\",\n \" & 42.15 & 36.81 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & 27.15 & 19.77 & \\\\underline{17.31} & 55.54 & 48.27 & \\\\underline{46.03} & 54.45\\n\",\n \" & 49.66 & \\\\underline{41.09} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \\n\",\n \" & 48.52 & 32.36 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & \\\\underline{30.46} & \\\\underline{22.71} & \\\\textbf{20.33} & 58.11 & 50.71 & \\\\textbf{49.11} & \\\\underline{56.95} \\n\",\n \" & \\\\textbf{51.49} & \\\\textbf{43.83} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \\n\",\n \" & 49.08 & 40.76 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_italian}\\n\",\n \" Translation performance of various models for Ladin → Italian across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\makebox[3.1in][r]{\\n\",\n \" \\\\begin{tabular}{lcc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Feature} & \\\\multicolumn{2}{c}{\\\\textbf{Language}} \\\\\\\\\\n\",\n \" & \\\\textbf{Italian} & \\\\textbf{Ladin} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" Average number of words per entry & 65 & 70 \\\\\\\\\\n\",\n \" Average number of characters per entry & 144 & 348 \\\\\\\\\\n\",\n \" Positive label count & 9,842 & 9,842 \\\\\\\\\\n\",\n \" Negative label count & 2,669 & 2,669 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SD-SA}\\n\",\n \" Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\\n\",\n \" }\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\makebox[3.2in][r]{\\n\",\n \" \\\\begin{tabular}{lcc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Feature} & \\\\multicolumn{2}{c}{\\\\textbf{Language}} \\\\\\\\\\n\",\n \" & \\\\textbf{Italian} & \\\\textbf{Ladin} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" Average number of words per question & 18 & 19 \\\\\\\\\\n\",\n \" Average number of characters per question & 108 & 97 \\\\\\\\\\n\",\n \" Average number of words per choices & 28 & 30 \\\\\\\\\\n\",\n \" Average number of characters per choices & 187 & 174 \\\\\\\\\\n\",\n \" Frequency of entries with 3 choices & 304 & 304 \\\\\\\\\\n\",\n \" Frequency of entries with 4 choices & 196 & 196 \\\\\\\\\\n\",\n \" Frequency of entries with 5 choices & 264 & 264 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SD-MCQA}\\n\",\n \" Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\\n\",\n \" }\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\makebox[\\\\textwidth]{\\n\",\n \" \\\\begin{tabular}{lcccc@{\\\\hspace{2em}}cccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Model} &\\n\",\n \" \\\\multicolumn{4}{c}{\\\\textbf{Ladin}} &\\n\",\n \" \\\\multicolumn{4}{c}{\\\\textbf{Italian}} \\\\\\\\\\n\",\n \" \\\\cline{2-9}\\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{SA}} & \\\\multicolumn{2}{c}{\\\\textbf{MCQA}}\\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{SA}} & \\\\multicolumn{2}{c}{\\\\textbf{MCQA}} \\\\\\\\\\n\",\n \" \\n\",\n \" & \\\\textbf{Acc} & \\\\textbf{F1} & \\\\textbf{Acc} & \\\\textbf{F1}\\n\",\n \" & \\\\textbf{Acc} & \\\\textbf{F1} & \\\\textbf{Acc} & \\\\textbf{F1} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\\n\",\n \" & 97.92 & 98.18 & 54.79 & 54.18 \\\\\\\\\\n\",\n \" m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \\n\",\n \" & 94.78 & 96.41 & 30.73 & 30.29 \\\\\\\\\\n\",\n \" XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \\n\",\n \" & 97.14 & 98.08 & 26.14 & 26.14 \\\\\\\\\\n\",\n \" mT5 & 50.09 & 69.37 & 23.50 & 23.16 \\n\",\n \" & 49.98 & 69.25 & 22.62 & 21.92 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SA-MCQA} \\n\",\n \" Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\\n\",\n \" } \\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[tp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\\n\",\n \" \\\\caption{chrF++ scores of the models using \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} as the training data}\\n\",\n \" \\\\label{fig:chrf_AD}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[tp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\\n\",\n \" \\\\caption{BLEU scores of the models using \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} as the training data}\\n\",\n \" \\\\label{fig:bleu_AD}\\n\",\n \"\\\\end{figure*}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"% This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.\n\\pdfoutput=1\n% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.\n\n\\documentclass[11pt]{article}\n\n% Change \"review\" to \"final\" to generate the final (sometimes called camera-ready) version.\n% Change to \"preprint\" to generate a non-anonymous version with page numbers.\n\\usepackage[preprint]{acl}\n\n% Standard package includes\n\\usepackage{times}\n\\usepackage{latexsym}\n\n% For proper rendering and hyphenation of words containing Latin characters (including in bib files)\n\\usepackage[T1]{fontenc}\n% For Vietnamese characters\n% \\usepackage[T5]{fontenc}\n% See https://www.latex-project.org/help/documentation/encguide.pdf for other character sets\n\n% This assumes your files are encoded as UTF8\n\\usepackage[utf8]{inputenc}\n\n% This is not strictly necessary, and may be commented out,\n% but it will improve the layout of the manuscript,\n% and will typically save some space.\n\\usepackage{microtype}\n\n% This is also not strictly necessary, and may be commented out.\n% However, it will improve the aesthetics of text in\n% the typewriter font.\n\\usepackage{inconsolata}\n\n%Including images in your LaTeX document requires adding\n%additional package(s)\n\\usepackage{graphicx}\n\n% If the title and author information does not fit in the area allocated, uncomment the following\n%\n%\\setlength\\titlebox{<dim>}\n%\n% and set <dim> to something 5cm or larger.\n\n\\title{ \nExploring NLP Benchmarks in an Extremely Low-Resource Setting\n%Synthetic Data for Ladin NLP: Toward Democratized Language Models for Indigenous Languages\n}\n\n% Author information can be set in various styles:\n% For several authors from the same institution:\n% \\author{Author 1 \\and ... \\and Author n \\\\\n% Address line \\\\ ... \\\\ Address line}\n% if the names do not fit well on one line use\n% Author 1 \\\\ {\\bf Author 2} \\\\ ... \\\\ {\\bf Author n} \\\\\n% For authors from different institutions:\n% \\author{Author 1 \\\\ Address line \\\\ ... \\\\ Address line\n% \\And ... \\And\n% Author n \\\\ Address line \\\\ ... \\\\ Address line}\n% To start a separate ``row'' of authors use \\AND, as in\n% \\author{Author 1 \\\\ Address line \\\\ ... \\\\ Address line\n% \\AND\n% Author 2 \\\\ Address line \\\\ ... \\\\ Address line \\And\n% Author 3 \\\\ Address line \\\\ ... \\\\ Address line}\n\n\\author{\n Ulin Nuha\\thanks{Work done while the author was a PhD student at NKUST.} \\\\\n National Kaohsiung University \\\\\n of Science and Technology \\\\\n \\texttt{ulinnuha.id@icloud.com}\n \\And\n Adam Jatowt \\\\\n University of Innsbruck \\\\\n \\texttt{adam.jatowt@uibk.ac.at}\n}\n%\\author{\n% \\textbf{First Author\\textsuperscript{1}},\n% \\textbf{Second Author\\textsuperscript{1,2}},\n% \\textbf{Third T. Author\\textsuperscript{1}},\n% \\textbf{Fourth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Fifth Author\\textsuperscript{1,2}},\n% \\textbf{Sixth Author\\textsuperscript{1}},\n% \\textbf{Seventh Author\\textsuperscript{1}},\n% \\textbf{Eighth Author \\textsuperscript{1,2,3,4}},\n%\\\\\n% \\textbf{Ninth Author\\textsuperscript{1}},\n% \\textbf{Tenth Author\\textsuperscript{1}},\n% \\textbf{Eleventh E. Author\\textsuperscript{1,2,3,4,5}},\n% \\textbf{Twelfth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Thirteenth Author\\textsuperscript{3}},\n% \\textbf{Fourteenth F. Author\\textsuperscript{2,4}},\n% \\textbf{Fifteenth Author\\textsuperscript{1}},\n% \\textbf{Sixteenth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Seventeenth S. Author\\textsuperscript{4,5}},\n% \\textbf{Eighteenth Author\\textsuperscript{3,4}},\n% \\textbf{Nineteenth N. Author\\textsuperscript{2,5}},\n% \\textbf{Twentieth Author\\textsuperscript{1}}\n%\\\\\n%\\\\\n% \\textsuperscript{1}Affiliation 1,\n% \\textsuperscript{2}Affiliation 2,\n% \\textsuperscript{3}Affiliation 3,\n% \\textsuperscript{4}Affiliation 4,\n% \\textsuperscript{5}Affiliation 5\n%\\\\\n% \\small{\n% \\textbf{Correspondence:} \\href{mailto:email@domain}{email@domain}\n% }\n%}\n\n\\begin{document}\n\\maketitle\n\\begin{abstract}\n%Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of natural language processing (NLP) tasks. However, \nThe effectiveness of Large Language Models (LLMs) diminishes for extremely low-resource languages, such as indigenous languages, primarily due to the lack of labeled data. Despite growing interest, the availability of high-quality natural language processing (NLP) datasets for these languages remains limited, making it difficult to develop robust language technologies. This paper addresses such gap by focusing on Ladin, an endangered Romance language, specifically targeting the Val Badia variant. Leveraging a small set of parallel Ladin–Italian sentence pairs, we create synthetic datasets for sentiment analysis and multiple-choice question answering (MCQA) by translating monolingual Italian data. To ensure linguistic quality and reliability, we apply rigorous filtering and back-translation procedures in our method. We further demonstrate that incorporating these synthetic datasets into machine translation training leads to substantial improvements over existing Italian–Ladin translation baselines. Our contributions include the first publicly available sentiment analysis and MCQA datasets for Ladin, establishing foundational resources that can support broader NLP research and downstream applications for this underrepresented language.\n\\end{abstract}\n\n\\section{Introduction}\n\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n \\label{fig:LadinArea}\n\\end{figure}\n\n\nLarge language models (LLMs) have garnered significant attention in diverse audiences \\citep{Yuxia:2024, Gambardella:2024} due to their ability to effectively perform natural language tasks with only a few input-output examples \\citep{Cheng:24}, while also eliminating the need for gradient updates of the model \\citep{Nguyen:2024}. \nLLMs achieve remarkable performance through pre-training on large corpora, but their reliance on high-resource languages (HRLs) limits their effectiveness for low-resource languages (LRLs) \\citep{Pham:2024}, especially extreme ones \\citep{purason2024llms}. Efforts to address this limitation include various techniques such as in-context learning \\citep{Cahyawijaya:2024} and fine-tuning \\citep{Alabi:2022, Su2024Unlocking} to transfer LLM capabilities to LRLs. Additionally, some studies \\citep{yong2024lexc, morim2024, tran24irish} have focused on developing translation systems between LRLs and HRLs to address the lack of language technology resources. The limited advancement of natural language processing (NLP) in LRLs stems largely from the disproportionate focus of research on improving language models for HRLs, often at the expense of developing tools and resources for low-resource counterparts \\citep{zhang24llm}. Moreover, the scarcity of NLP datasets for extremely low-resource languages (ELRLs) constitutes a major barrier to progress in this area, highlighting the need for more inclusive AI technologies to support marginalized languages.\n\nThis paper advances NLP research for Ladin language, an Indigenous and extremely low-resource language of Northern Italy (see Fig.~\\ref{fig:LadinArea}). %Sharing roots with Italian, Ladin is a Romance (Neo-Latin) language.\nDespite progress in NLP for LRLs, Ladin’s dialectal diversity and limited digitized corpora pose unique challenges. Building on the prior work \\citep{frontull24}, which established a machine translation (MT) benchmark between Italian and Ladin (Val Badia variant), we further improve the translation performance for Ladin.\n\nLadin is a Rhaeto-Romance language spoken by about 30,000 people in South Tyrol, Northern Italy. It comprises five dialects (Val Badia, Fascia, Anpezo, Fodom, and Gherdëina) which vary significantly in morpho-syntactic and orthographic conventions. Although standardized efforts such as Ladin Dolomitan exist, it is not officially recognized and is used only to a limited extent, while speakers report minimal familiarity with Ladin varieties beyond their own \\citep{connor2023ladin}. Linguistic conventions have also changed over time within dialects. This linguistic diversity presents major challenges for machine translation and resource creation. Publicly available resources are extremely limited, with only a few lexicons, dictionaries, and minor corpora. There is a major source of monolingual Ladin data in \\textit{La Usc di Ladins}\\footnote{https://www.lausc.it/}, a newspaper published in five variants and digitally archived since 2012, but this resource remains underutilized due to the lack of alignment and limited annotation. Our work focuses on the Val Badia variant of Ladin%\\footnote{Ladin originally comprises five variants: Val Badia, Gherdëina, Fascia, Fodom, and Anpezo.}\n, due to the availability of the largest accessible dataset. Previous work on MT for Ladin's Fascia variant exists \\citep{FasciaLadin}; however, the parallel dataset used in that work consists of only 1,135 sentences. \n\nUnlike prior studies, our work also extends beyond MT for Ladin to include sentiment analysis (SA) and multiple-choice question answering (MCQA), establishing the first datasets for these tasks in Ladin. First, we compare MT approaches, including few-shot learning and fine-tuning, using available Ladin–Italian sentence pairs. Subsequently, we construct high-quality synthetic Ladin datasets for SA and MCQA through the translation from monolingual Italian data, applying rigorous filtering to ensure high quality. These datasets not only contribute to SA and MCQA but also enhance MT. To assess this, we incorporate our synthetic dataset into existing Italian–Ladin translation benchmarks and evaluate its impact.\n\nIn summary, the primary contributions of our work can be outlined as follows:\n\\begin{itemize}\n \\item We conduct a comparative study on translation between Italian and Ladin, focusing on the Val Badia variant. Our model significantly outperforms the current benchmark, demonstrating the effectiveness of our approach for this extremely low-resource language (LRL).\n \n \\item We construct a high-quality synthetic dataset of Ladin–Italian sentence pairs, referred to as \\textit{SD\\textsubscript{Lad--Ita}}, derived from monolingual Italian data using a language model and rigorous filtering techniques.\n \n \\item We showcase the utility of the synthetic dataset beyond MT by applying it to additional downstream NLP tasks, including SA (text classification) and MCQA, establishing the first such datasets in Ladin.\n\\end{itemize}\n\n%By highlighting the severe scarcity of NLP datasets for extremely LRLs compared to those for LRLs, and by \nBy fostering NLP research on Ladin, we aim to support the preservation and accessibility of this critically underrepresented language—benefiting education, digital communication, and cultural documentation for Indigenous communities.\n\n\\section{Background and Related Work}\n\nNLP for ELRLs has garnered increasing attention from researchers, largely due to the enduring challenges associated with data scarcity. These languages typically possess fewer than 0.1 million available parallel sentence pairs \\citep{Ranathunga23}, which are often insufficient for effectively training neural machine translation (NMT) models \\citep{rudra:19}. For instance, Ladin has fewer than 100 thousand parallel sentences available for MT \\citep{frontull24}, while resources for other NLP tasks, such as text classification and question answering, remain non-existent. \n\nLadin and Italian are both Romance languages with shared Latin roots, resulting in potential similarities in lexical and syntactic aspects. This linguistic proximity facilitates cross-lingual transfer, allowing multilingual models fine-tuned on Italian to generalize moderately well to Ladin. However, key divergences remain due to Ladin’s unique phonological and morphological traits \\citep{LucaM}. These differences are further shaped by historical geographic isolation and varying degrees of contact with dominant surrounding languages, particularly regional varieties of German and Italian. Most Ladin speakers in Italy are bi- or tri-lingual, using Ladin in private domains and Italian, German, or both in public settings, as neighboring communities typically lack comprehension of Ladin \\citep{SilviaLadin}. This contact has led to regional variation. For instance, Gherdëina and Val Badia exhibit stronger German influence, while southern valleys show more Italian features. Val Badia is often perceived as having the “purest” Ladin, though this reflects relative rather than absolute isolation from external influence. These dynamics pose several challenges for translation. The lack of a commonly adopted standard variety necessitates dialect-specific translation strategies, complicating mutual intelligibility and the development of shared resources. Furthermore, long-standing language contact has introduced borrowings and calques, making it difficult to isolate core Ladin structures.\n\n\nTo address the scarcity of resources in ELRLs, recent efforts have focused on leveraging transfer learning techniques, particularly through the use of large language models (LLMs) \\citep{Pham:2024, lim:24}. However, success remains limited in such settings \\citep{tran24irish}, where extreme data sparsity poses challenges for effective domain adaptation and language alignment. In addition, a key aspect of transfer learning with LLMs involves leveraging token similarity and cross-region similarity to better capture shared cultural and linguistic features \\citep{SinaBN}. \\citet{RAG-LLM} proposed a MT framework that integrates Retrieval-Augmented Generation (RAG) with LLMs to address these challenges, whereas \\citet{DPO-LLM} explored the use of LLMs in combination with Direct Preference Optimization (DPO) to enhance translation quality. \n\nDespite promising results, the above-mentioned methods incur high computational costs. Multimodal approaches, which incorporate additional modalities such as visual context to enhance translation \\citep{rajpoot:24, sami:dcu, hatami:24}, require supplementary datasets that are often unavailable for these languages and face considerable computational and complexity challenges. Then, Rule-based machine translation (RBMT), exemplified by Apertium \\citep{garcia:24, sanchez:24}, offers a less resource-intensive alternative, with lower computational requirements compared to NMT systems. However, RBMT systems are labor-intensive, requiring extensive manual effort to create and maintain linguistic rules, with scalability further hindered by the challenge of ensuring rule self-consistency \\citep{liu-multil:24}. \n\nAnother approach to supporting technologies for LRLs is the development of benchmarks. For example, \\citet{urbizu} introduced BasqueGLUE, a benchmark covering multiple NLP tasks for the Basque language.\nSimilarly, \\citet{FarsInstruct} presented FarsInstruct, a large-scale dataset developed to strengthen LLMs’ capacity to follow instructions in Persian, a globally low-represented language. However, recent work in language revitalization and human-centered NLP shows the importance of going beyond performance metrics in developing technologies for endangered languages \\citep{StevenBird}. Effective systems should align with long-term community goals, such as intergenerational transmission and cultural continuity.\n\nIn line with this perspective, our work presents a comparative study of MT approaches, including instruction learning and fine-tuning \\citep{zhang:mt23}, using several language models such as NLLB and GPT-4. %Given Ladin’s underrepresentation, we adapt sequence modeling techniques for this new linguistic setting \\citep{Degenaro:24}. \nTo evaluate translation quality, we use both statistical and semantical metrics, particularly for synthetic data. While prior research has made progress in NLP for LRLs, substantial gaps remain for ELRLs such as Ladin. This study addresses these gaps by leveraging data augmentation techniques and introducing benchmark datasets for MT, text classification, and question answering tasks.\n\n\\section{Experiments}\n\n\\begin{figure*}[t]\n \\centering\n \\includegraphics[width=5.3in]{latex/Figure_2.png}\n \\caption{Synthetic data generation process. Initially, we translate the Italian data \\( D\\textsubscript{\\textit{Ita}}\\) of SA and MCQA into Ladin. The Ladin translation \\(D\\textsubscript{\\textit{Lad}}\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\(D\\textsubscript{\\textit{Lad}}\\) is back-translated into Italian \\( D^{\\prime}\\textsubscript{\\textit{Ita}}\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\n \\label{fig:experiments}\n\\end{figure*}\n\n%Our study focuses on translating the Ladin language in its Val Badia variant. Among the five Ladin variants, parallel data availability is limited to the Val Badia variant paired with Italian. \n%In addition, our experiments explore translation tasks using various sequence-to-sequence modeling and LLMs across multiple settings.\n\n\\subsection{Data sources}\nIn this section, we provide an overview of the data sources used in our study. We prepared datasets for three tasks: MT, SA, and MCQA. These resources were collected from publicly available datasets. Figure~\\ref{fig:experiments} illustrates the synthetic paired Ladin-Italian data generation process. As the creation of the SA and MCQA datasets depends on the availability of a translation model, we first constructed the MT dataset. Once the translation model was established, we proceeded with the generation of the SA and MCQA datasets accordingly.\n\\noindent\\textbf{Machine translation.} The parallel Italian–Ladin dataset used for both training and testing in our MT experiments was initially derived from prior work \\citep{frontull24}. The authentic Italian-Ladin training dataset \\textit{AD\\textsubscript{Ita\\_Lad}} comprises 18,139 sentence pairs, carefully crafted as basic and concise examples to illustrate the use of specific words and phrases. \nThe average sentence length in \\textit{AD\\textsubscript{Ita\\_Lad}} is 23.43 characters for Ladin and 25.69 characters for Italian, while the average number of words per sentence is 5.02 for Ladin and 4.36 for Italian. Following that work, the testing dataset, \\textit{\\( T = \\{t\\textsubscript{1}, t\\textsubscript{2}, t\\textsubscript{3}\\} \\)}, consists of three subsets: \\( t_1 \\) (424 sentences) focuses on formal and legal terminology; \\( t_2 \\) (833 sentences) blends stylistic and lexical elements, reflecting regional cultural and historical contexts; \\( t_3 \\) (1,563 sentences) includes narrative prose, dialogue, and idiomatic expressions, offering diverse challenges. For Italian in the testing dataset, the average word counts for \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\) are 21.25, 26.65, and 15.61, respectively. In comparison, the corresponding averages for \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\) in Ladin are 23.58, 24.52, and 13.05, respectively.\n\n\\noindent\\textbf{Sentiment analysis.} We construct datasets for NLP tasks in Ladin by leveraging labeled monolingual Italian resources, including SA and MCQA datasets. We use the monolingual Italian SA dataset \\textit{D\\textsubscript{Ita\\_SA}} from \\citet{desole2025} for the SA task. \\textit{D\\textsubscript{Ita\\_SA}} comprises abundant Tripadvisor reviews labeled as positive or negative. The initial dataset contains 41,077 entries. To mitigate the impact of excessively long reviews, we filter the dataset to retain only those entries with word counts up to the third quartile (Q3), resulting in a maximum review length of 138 words. This screening results in a reduced dataset size of 30,712 entries. Given that the raw dataset, collected via web scraping, contains grammatical errors, we employ GPT-4 to correct these while preserving the original semantic content. Following grammar correction, the average number of words per sentence in \\textit{D\\textsubscript{Ita\\_SA}} is 70.44.\n\n\\noindent\\textbf{MCQA.} Finally, for the MCQA task, we use the monolingual Italian MCQA dataset \\textit{D\\textsubscript{Ita\\_MCQA}} from \\citet{multi_it24}. \\textit{D\\textsubscript{Ita\\_MCQA}} comprises over 5,000 manually crafted questions covering a wide range of topics. This MCQA dataset contains questions with 2, 3, 4, 5, or 6 answer choices. However, we exclude questions with 2 and 6 options due to their very limited number.\n\n\\subsection{Language model settings for machine translation}\nWe now discuss the process of building a MT model using existing Italian–Ladin parallel data, which serves as a prerequisite for the subsequent synthetic data generation process. To facilitate translation between Italian and Ladin, we employ both LLMs and sequence-to-sequence (seq2seq) models. For LLM-based approaches, we utilize LLaMA 3.1 (8B and 70B variants) and GPT-4o. The LLaMA models are evaluated in two configurations: few-shot learning (FSL) and supervised fine-tuning (FT). Appendix ~\\ref{sec:fsl} provides an example prompt used for the FSL approach. To perform the FSL approach, we utilize the \\textit{LLaMA-v3.1-8b-instruct} and \\textit{LLaMA-v3.1-70b-instruct} models via the DeepInfra API. Similarly, the FSL approach with GPT-4o is conducted using the OpenAI\\footnote{https://deepinfra.com/} API. For the FT approach using LLaMA, we leverage the Together AI\\footnote{https://www.together.ai/} fine-tuning API with the LoRA adapter configuration (\\textit{r} = 32), employing a batch size of 8 and 3 epochs.\n\nFor the seq2seq models, we employ MBART-large-50 and NLLB-200-1.3B, both of which are encoder-decoder architectures specifically designed for multilingual MT. The fine-tuning models of NLLB-1.3B and MBART-large-50 are conducted on an NVIDIA RTX A6000 GPU with a batch size of 8 and over 7 epochs. To accommodate Ladin, an unseen language for both seq2seq models, we introduce a Ladin-specific language tag in the tokenizer. This modification aids in the identification and processing of Ladin texts during translation tasks, facilitating better handling of the language.\n\nSubsequently, we evaluate translation performance using standard metrics: Sacre BLEU, ROUGE, and chrF++, providing a comprehensive assessment of translation quality.\n\n\\subsection{Synthetic data creation}\n\n\\begin{table*}\n \\centering\n \\small\n \\begin{tabular}{llcccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{2}{c}{\\textbf{BLEU}} \n & \\multicolumn{2}{c}{\\textbf{Rouge}} \n & \\multicolumn{2}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-8}\n &\n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\n & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\n & FSL-GPT-4o & 4.27 & \\underline{22.84} & 25.86 & \\underline{52.28} & 27.47 & 48.23 \\\\\n & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\n & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\n & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\n & FT-NLLB 1.3 B & \\underline{17.76} & 21.41 & \\underline{52.81} & 49.91 & \\underline{44.60 } & \\underline{48.40} \\\\\n & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\n \n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B & 18.30 & \\textbf{24.50} & \\textbf{53.66} & \\textbf{52.64} & \\textbf{44.62} & \\textbf{50.76} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & \\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\n \\hline\n \\end{tabular}\n \\caption{\\label{translation-performance}\n Comparison of different models based on average translation performance metrics on the test set \\( T \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.}\n\n\\end{table*}\n\nWe aim to create datasets for NLP tasks in the Ladin language by translating \\textit{D\\textsubscript{Ita\\_SA}} and \\textit{D\\textsubscript{Ita\\_MCQA}} from Italian data \\textit{D\\textsubscript{Ita}} to Ladin data \\textit{D\\textsubscript{Lad}}. These translated datasets serve multiple purposes, including translation (Italian–Ladin pairs), text classification, and question answering tasks. To ensure high-quality translation, we first select the best-performing MT model—identified in the previous section based on its performance on a held-out testing data \\( T \\), and use this model to translate \\textit{D\\textsubscript{Ita}} into \\textit{D\\textsubscript{Lad}}. The creation of this synthetic dataset shown in Figure~\\ref{fig:experiments} involves several key steps, as described below.\n\n\\noindent\\textbf{Italian-to-Ladin translation.} We begin by translating the labeled monolingual Italian datasets \\textit{D\\textsubscript{Ita}} of SA and MCQA tasks into Ladin, resulting in \\textit{D\\textsubscript{Lad}}. This translation process is carried out using the best-performing MT model identified in our evaluation, ensuring the highest possible quality of the synthetic Ladin data.\n\n\\noindent\\textbf{Filtering I.} To ensure the semantic quality of the Italian → Ladin translations, we apply a filtering step using similarity scores computed by the Language-Agnostic BERT Sentence Embedding (LaBSE) model \\citep{labse:22}. This step evaluates the alignment between each translated Ladin sentence and its original Italian counterpart. Specifically, we retain only those sentence pairs with a cosine similarity score \\( c \\geq 0.68 \\), which corresponds to the average similarity observed in the aligned dataset \\textit{AD\\textsubscript{Ita\\_Lad}}. This threshold helps eliminate semantically inconsistent translations while preserving high-quality aligned pairs for downstream tasks.\n\n\\noindent\\textbf{Back-translation.} We employ back-translation to further refine the synthetic dataset prior to conducting a second round of filtering. Specifically, the Ladin translations \\( D\\textsubscript{\\textit{Lad}} \\) are retranslated into Italian, yielding \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\), which are then compared against the original Italian datasets \\( D\\textsubscript{Ita} \\). This step helps identify and discard translations that deviate significantly from the original semantics, thereby improving data quality.\n\n\\noindent\\textbf{Filtering II.} To finalize the synthetic dataset, we apply a second filtering step based on automatic evaluation metrics. Specifically, we compute the Sacre BLEU and METEOR scores between the original Italian data (\\( D\\textsubscript{\\textit{Ita}} \\) and the back-translated Italian data \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)). A translation instance is retained if \n\\( BLEU \\)(\\( D\\textsubscript{\\textit{Ita}} \\), \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)) \\(\\geq \\mu{BLEU} \\) \nand \n\\( METEOR \\)(\\( D\\textsubscript{\\textit{Ita}} \\), \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)) \\(\\geq \\mu{METEOR} \\).\nwhere \\( \\mu{BLEU} \\) and \\( \\mu{METEOR} \\) represent the average scores computed across all translation pairs. These threshold values ensure semantic fidelity and fluency by eliminating noise and inaccuracy, thus improving the quality of the synthetic dataset.\n\n\\subsection{Synthetic data evaluation}\n\nTo evaluate the quality and impact of the Italian–Ladin synthetic parallel dataset \\textit{SD\\textsubscript{Ita\\_Lad}} = {(\\textit{D\\textsubscript{Ita\\_SA}}, \\textit{D\\textsubscript{Lad\\_SA}}), (\\textit{D\\textsubscript{Ita\\_MCQA}}, \\textit{D\\textsubscript{Lad\\_MCQA}})}, we combine it with the authentic dataset \\textit{AD\\textsubscript{Ita\\_Lad}} and assess performance on the testing data \\( T \\). This setup allows us to measure the effect of synthetic data augmentation on translation quality. To assess lexical and syntactic adequacy of the synthetic translations, we construct a manually translated gold dataset \\( GD \\)%\\footnote{Datasets will be released upon publication under an open license (CC BY-NC 4.0).}\n, containing 50 examples each from \\textit{D\\textsubscript{Ita\\_SA}} and \\textit{D\\textsubscript{Ita\\_MCQA}}, translated into Ladin by a native speaker of Italian and Ladin. We compute cosine similarity between the synthetic and gold translations using sentence embeddings, providing a measure of semantic alignment.% Additionally, we adopt the error typology from the Multidimensional Quality Metrics (MQM) framework as qualitative analysis \\cite{MQM}, selecting a subset of high-level error dimensions to examine the strengths and limitations of the translation outputs. Specifically, we focus on three dimensions, accuracy, linguistic conventions, and terminology, drawn from the full set defined in the MQM core typology\\cite{MQM24}, based on their relevance to our task and the constraints of our annotation process.\n\n\\section{Results and Discussion}\nIn this section, we report the results of MT using the existing Italian–Ladin parallel data. We then present the evaluation of the synthetic Ladin datasets for SA and MCQA, including both quantitative metrics and qualitative analysis.\n\n\\begin{table*}[!t]\n \\centering\n \\small\n \\begin{tabular}{llccccccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-11} &\n & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n & 26.00 & 16.92 \\\\\n & FSL-Llama 3.1 70B \n & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n & 35.05 & 23.17 \\\\\n & FSL-GPT-4o \n & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n & 30.08 & 20.42 \\\\\n & FT-Llama 3.1 8B \n & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n & 36.60 & 30.98 \\\\\n & FT-Llama 3.1 70B \n & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n & 35.87 & 23.99 \\\\\n & Mbart-large-50 \n & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n & 38.66 & 35.23 \\\\\n & NLLB 1.3 B \n & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n & \\underline{45.98} & \\underline{41.58} \\\\\n & Benchmark (LLM) \n & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n & 28.98 & 18.60 \\\\\n\\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B \n & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n & 46.28 & \\textbf{42.15} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n \\hline\n \\end{tabular}\n \\caption{\\label{add-trans_to_ladin}\n Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n }\n\\end{table*}\n\n\\begin{table*}[!t]\n \\centering\n \\small\n \\begin{tabular}{llccccccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-11} &\n & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \n & 38.89 & 23.41 \\\\\n & FSL-Llama 3.1 70B \n & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \n & 48.66 & 36.91 \\\\\n & FSL-GPT-4o \n & 29.23 & 23.38 & 15.90 & 61.39 & \\textbf{53.37} & 42.07 & 55.73 \n & 50.33 & 38.64 \\\\\n & FT-Llama 3.1 8B \n & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \n & 44.11 & 33.66 \\\\\n & FT-Llama 3.1 70B \n & \\textbf{30.78} & \\textbf{23.65} & 13.02 & \\textbf{61.91} & 52.10 & 38.29 & \\textbf{57.23} \n & \\underline{50.53} & 36.12 \\\\\n & Mbart-large-50 \n & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \n & 42.15 & 36.81 \\\\\n & NLLB 1.3 B \n & 27.15 & 19.77 & \\underline{17.31} & 55.54 & 48.27 & \\underline{46.03} & 54.45\n & 49.66 & \\underline{41.09} \\\\\n & Benchmark (LLM) \n & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \n & 48.52 & 32.36 \\\\\n\\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B \n & \\underline{30.46} & \\underline{22.71} & \\textbf{20.33} & 58.11 & 50.71 & \\textbf{49.11} & \\underline{56.95} \n & \\textbf{51.49} & \\textbf{43.83} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \n & 49.08 & 40.76 \\\\\\\\ \n \\hline\n \\end{tabular}\n \\caption{\\label{add-trans_to_italian}\n Translation performance of various models for Ladin → Italian across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n }\n\\end{table*}\n\n\\subsection{Machine translation of Italian and Ladin}\nTable~\\ref{translation-performance} presents the translation performance results for both Italian → Ladin and Ladin → Italian across diverse language model configurations. For experiments using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data, we report results from the benchmark approach proposed by \\citet{frontull24}, which employs the LLM \\verb|GPT-3.5-turbo-0125|, for comparison purposes. %This detailed evaluation not only highlights the effectiveness of different model settings but also underscores the challenges and opportunities in machine translation for LRL pairs.We also present the detailed results of the experimental results across various scenarios.\nWhile Table~\\ref{translation-performance} presents the overall average performance metrics of each translation model evaluated on the testing data \\( T \\), Tables~\\ref{add-trans_to_ladin} and~\\ref{add-trans_to_italian} offer a more fine-grained analysis. They report detailed metric scores for the individual test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\), allowing for a closer examination of model behavior across different data segments.\n\nIn both translation directions in Table~\\ref{translation-performance}, the fine-tuned NLLB (FT-NLLB) model achieves significant performance across evaluation metrics. Specifically, the model performs best on the translation from Italian → Ladin, with a BLEU score approaching 18, indicating relatively good translation accuracy for extremely low-resource settings. Although the Ladin → Italian translation performance of the FT-NLLB model slightly lags behind that of the FT-LLaMA 3.1 70B model, the FT-NLLB model achieves the highest chrF++ scores in both translation directions, indicating superior overall translation quality. These findings underscore a persistent challenge in extremely low-resource NLP. Despite the impressive capabilities of LLMs, their performance often suffers in extremely low-resource scenarios due to training biases toward HRLs with abundant data. Consequently, the Ladin → Italian translation achieves higher BLEU scores, reflecting the model’s stronger proficiency in HRLs. \n\nAlthough Ladin and Italian both belong to the Romance language family, translation into Ladin remains challenging due to its status as the extremely low-resource language, including unique vocabulary, dialectal variations, and a lack of direct equivalence to Italian. In contrast, the NLLB model demonstrates relatively robust performance, likely benefiting from its multilingual training across 200+ languages, including over 150 LRLs \\citep{nllb2022}. Notably, the NLLB model was trained on Friulian, a closely related Raeto-Romance language \\citep{UNESCO}, which may contribute to its improved generalization on Ladin.\n\nAdditionally, we evaluate the suitability and effectiveness of the NLLB tokenizer for processing Ladin text. Our analysis reveals an average tokens-per-word ratio of 1.50 for Ladin, compared to 1.39 for Italian. This modest overhead indicates that the NLLB tokenizer segments Ladin reasonably well, despite the language's extremely low-resource status, suggesting its viability for downstream translation tasks.\n\n\\subsection{Qualitative error analysis}\n\n\\begin{table}[t]\n \\small\n \\centering\n \\makebox[3.1in][r]{\n \\begin{tabular}{lcc}\n \\hline\n \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n & \\textbf{Italian} & \\textbf{Ladin} \\\\\n \\hline\n Average number of words per entry & 65 & 70 \\\\\n Average number of characters per entry & 144 & 348 \\\\\n Positive label count & 9,842 & 9,842 \\\\\n Negative label count & 2,669 & 2,669 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SD-SA}\n Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\n }\n\\end{table}\n\nTo assess the qualitative aspects of translation performance using the FT-NLLB model, we analyze specific examples of translation errors from Italian to Ladin. This analysis helps identify common error types—such as lexical inaccuracies, syntactic issues, and morphological mismatches—and provides insight into the strengths and limitations of the machine-generated translations. For instance, consider the following sentence pair, where the Ladin translation is largely faithful to the Italian source, successfully preserving both structure and meaning.\n\n\\textbf{Italian}: \\textit{Sono stata a un congresso a Torino e ho passato due notti al Best Western Crystal Palace, un hotel 4 stelle di fianco alla stazione di Porta Nuova. Ho apprezzato molto la vasca idromassaggio e il giornale ogni giorno: La Stampa, con un foglio di sintesi degli argomenti principali.}\n\n\\textbf{Ladin}: \\textit{I sun stada a n congres a Torin y i à sté döes nöts tl Best Western Crystal Palace, n hotel da 4 stëres dlungia la staziun de Porta Nuova. I á dër aprijé la vasca da iade y le foliet da vigni de: La Stampa, cun na plata de ressumé di argomënc prinzipai.}\n\nUpon closer inspection above, the Ladin translation only exhibits minor grammatical and lexical inaccuracies. The phrase “\\textit{I á sté döes nöts}” should be corrected to “\\textit{I sun stada döes nöts}” to ensure grammatical correctness. Additionally, “\\textit{la vasca da iade}” ought to be revised to “\\textit{la vasca idromassaje}” to more accurately reflect the original Italian phrase “\\textit{la vasca idromassaggio}.” These examples illustrate the model’s general ability to produce semantically faithful translations, while also highlighting areas where linguistic precision can be improved. Overall, the model demonstrates strong potential for handling Ladin.\n\n\\subsection{Ladin synthetic datasets}\n\n\\begin{table}[t]\n \\centering\n \\small\n \\makebox[3.2in][r]{\n \\begin{tabular}{lcc}\n \\hline\n \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n & \\textbf{Italian} & \\textbf{Ladin} \\\\\n \\hline\n Average number of words per question & 18 & 19 \\\\\n Average number of characters per question & 108 & 97 \\\\\n Average number of words per choices & 28 & 30 \\\\\n Average number of characters per choices & 187 & 174 \\\\\n Frequency of entries with 3 choices & 304 & 304 \\\\\n Frequency of entries with 4 choices & 196 & 196 \\\\\n Frequency of entries with 5 choices & 264 & 264 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SD-MCQA}\n Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\n }\n\\end{table}\n\n\\begin{table*}[t]\n \\centering\n \\small\n \\makebox[\\textwidth]{\n \\begin{tabular}{lcccc@{\\hspace{2em}}cccc}\n \\hline\n \\textbf{Model} &\n \\multicolumn{4}{c}{\\textbf{Ladin}} &\n \\multicolumn{4}{c}{\\textbf{Italian}} \\\\\n \\cline{2-9}\n & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}}\n & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}} \\\\\n \n & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1}\n & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1} \\\\\n \\hline\n FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\n & 97.92 & 98.18 & 54.79 & 54.18 \\\\\n m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \n & 94.78 & 96.41 & 30.73 & 30.29 \\\\\n XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \n & 97.14 & 98.08 & 26.14 & 26.14 \\\\\n mT5 & 50.09 & 69.37 & 23.50 & 23.16 \n & 49.98 & 69.25 & 22.62 & 21.92 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SA-MCQA} \n Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\n } \n\\end{table*}\n\nSince the FT-NLLB model demonstrates the best performance for translation in our experiments using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data, we utilize this model to translate \\textit{D\\textsubscript{Ita}} into \\textit{D\\textsubscript{Lad}} through the framework shown in Figure~\\ref{fig:experiments}.\nInitially, we obtained 30,477 paired entries for (\\textit{D\\textsubscript{Ita\\_SA}}, \\textit{D\\textsubscript{Lad\\_SA}}) as the SA dataset after applying the first filtering step based on cosine similarity between Italian and Ladin with the threshold of 0.68. This value is derived from the cosine similarity between both languages in \\textit{AD\\textsubscript{Ita\\_Lad}}. Subsequently, we perform back-translation from \\textit{D\\textsubscript{Lad\\_SA}} to \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_SA}}\\). The threshold for the second filtering step is determined based on the average (\\(\\mu\\)) BLEU and METEOR scores calculated for each entry by comparing \\textit{D\\textsubscript{Ita\\_SA}} with \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_SA}}\\). These scores were found to be 33.63 and 0.58, respectively. The final filtered synthetic SA dataset, consisting of 12,511 entries, statistically is detailed in Table~\\ref{SD-SA}. This SA dataset contains an average of 65 and 70 words per entry for Italian and Ladin, respectively. Additionally, the majority of entries in the final dataset—over 9,000 instances—are labeled with positive sentiment.\n\nConcurrently, we obtained 4,651 paired entries of (\\textit{D\\textsubscript{Ita\\_MCQA}}, \\textit{D\\textsubscript{Lad\\_MCQA}}) as the MCQA dataset, following an initial filtering step based on cosine similarity, similar to the procedure used for the synthetic SA dataset. The thresholds for the second filtering step are also determined using the average BLEU and METEOR scores calculated between \\textit{D\\textsubscript{Ita\\_MCQA}} and \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_MCQA}}\\), which are 36.58 and 0.62, respectively. The final filtered synthetic MCQA dataset, comprising 764 entries, is presented in Table~\\ref{SD-MCQA}, with the majority of questions featuring three answer choices. Notably, both Italian-Ladin paired datasets of SA and MCQA tasks exhibit a higher average number of words and characters per entry compared to the authentic parallel dataset \\textit{AD\\textsubscript{Ita\\_Lad}}. \n\n\\subsection{Synthetic data assessment for NLP tasks}\n\nAfter obtaining the new synthetic datasets \\textit{SD\\textsubscript{Ita\\_Lad}}%\\footnote{Datasets and codes will be released after paper publication under an open license (CC BY-NC 4.0).}\n, we compare them against the manually translated golden dataset \n\\( GD \\) to evaluate translation quality. Specifically, we use cosine similarity metrics to evaluate the semantic alignment between the synthetic and manually created data. The cosine similarity scores of \\textit{SD\\textsubscript{Ita\\_Lad}} and \\( GD \\), with respect to \\textit{AD\\textsubscript{Ita\\_Lad}}, are 86.61 and 85.75, respectively. These results indicate a high degree of semantic consistency and minimal disparity between the synthetic and human-translated datasets.\n\nSubsequently, we combine \\textit{SD\\textsubscript{Ita\\_Lad}} with \\textit{AD\\textsubscript{Ita\\_Lad}} to construct the training data for fine-tuning the FT-NLLB model as the MT model. The testing data \\( T \\) is then used to evaluate the performance of the resulting translation model on these combined datasets, as shown in the lower section of Table ~\\ref{translation-performance}. Detailed results for the three subsets (\\( t_1 \\), \\( t_2 \\), and \\( t_3 \\)) of \\( T \\) are also presented in the lower section of Tables~\\ref{add-trans_to_ladin} and~\\ref{add-trans_to_italian}. We compare our results with the augmented synthetic translations generated by the RBMT system proposed by \\citet{frontull24}, which incorporates additional monolingual data in both Ladin and Italian. As summarized in Table~\\ref{translation-performance}, experimental results demonstrate that incorporating our synthetic data consistently improves performance across all evaluation metrics, surpassing the previous benchmark. In both translation directions, the FT-NLLB model performs well compared to its counterpart model.\n\nGiven that \\textit{SD\\textsubscript{Ita\\_Lad}} encompasses SA and MCQA tasks in Ladin, we establish a benchmark to evaluate model performance on these tasks. We adopt the few-shot learning (FSL) using LLaMA 3.1 70B as our LLM's approach. Appendices~\\ref{sec:fsl-sa} and~\\ref{sec:fsl-mcqa} provide example prompts used in the FSL approach. In parallel, we assess the performance of several transformer-based models, including the Distilbert-base-multilingual-cased (m-DistilBERT)\nmodel, the XLM-RoBERTa base model, and the mT5-small model. Table~\\ref{SA-MCQA} summarizes the results for SA and MCQA tasks in Ladin, with Italian results included for comparison. The LLM-based approach achieves the highest scores in both tasks in terms of balanced accuracy (Acc) and F1-score (F1), although the improvements over other models are marginal. m-DistilBERT also performs well across both tasks. Specifically, the results indicate that the SA dataset in Ladin is generally well-handled by the evaluated models, with the exception of mT5. This indicates that our created Ladin SA dataset is sufficiently informative and well-aligned with the task objectives to support effective model training. In contrast, performance on the MCQA task remains low across all models, even when evaluated on Italian data. This suggests that the MCQA task is inherently more challenging than the SA task. The difficulty may be attributed to the limited size of the MCQA dataset and the broad topical coverage of the questions, both of which may hinder model generalization.\n\n\\section{Conclusions and Future Work}\nIn this work, we explore various strategies for translating Ladin—an extremely low-resource language—and demonstrate that our NLLB-based model consistently outperforms counterpart models. Beyond translation, we introduce the first comprehensive Ladin benchmark dataset covering machine translation, sentiment analysis, and multiple-choice question answering, all derived through synthetic augmentation from monolingual Italian resources. \n\nOur evaluation shows that while synthetic data enables competitive performance across tasks further progress is needed to enhance knowledge transfer from high-resource to low-resource languages. This study lays foundational work for future NLP research on Ladin and similarly underrepresented languages. \n\nFuture work will investigate knowledge distillation techniques to more effectively transfer knowledge from high-resource languages to low-resource ones, as well as explore advanced methods to better exploit available monolingual Ladin data for improved model performance. We are also committed to further foster developments of Ladin resources and to engaging community in actively researching this language by establishing leaderboards based on the created datasets.\n\n\\section*{Limitations}\n\nThe Ladin-Italian dataset used in this study primarily consists of short sentences, which may limit the generalizability of the models to longer and more complex sentence structures. Moreover, the limited availability of manually crafted monolingual Italian MCQA datasets restricts the number of usable samples, which may impact the robustness and reliability of the experimental results. \n\n%\\section*{Acknowledgments}\n\n%This document has been adapted\n\n\n% Bibliography entries for the entire Anthology, followed by custom entries\n%\\bibliography{anthology,custom}\n% Custom bibliography entries only\n\\bibliography{custom}\n\n\\appendix\n\\section{Additional Experimental Results}\n\\label{sec:add-results}\nThis section presents detailed experimental results for machine translation performance using \\textit{AD\\textsubscript{Ita\\_Lad}} as the sole training data, as reported in the upper section of Table~\\ref{translation-performance}. Figure~\\ref{fig:chrf_AD} illustrates the chrF++ scores achieved by various models, while Figure~\\ref{fig:bleu_AD} presents the corresponding BLEU score comparisons. \n\n\\section{Back-translation Results}\nAs illustrated in Figure~\\ref{fig:experiments}, we perform a second round of filtering by back-translating Ladin data into Italian and evaluating the results using BLEU and METEOR scores. For the SA dataset, which contains 30,477 samples, the average BLEU and METEOR scores are 33.63 and 0.58, respectively. In the case of the MCQA dataset (4,651 samples), the corresponding averages are 36.58 and 0.62. Below, we present examples comparing back-translated Italian samples with their original counterparts to facilitate a more detailed analysis.\n\n\\section{A Few-shot Learning Prompt Template in the MT task}\n\\label{sec:fsl}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Here are examples of translations in a JSON \nformat between Italian and Ladin with the \nVal Badia variant:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n{\n \"translations\": [\n {\n \"Italian\": \"è venuta la mia ora\",\n \"Ladin\": \"al é gnü mia ora\"\n },\n {\n \"Italian\": \"vado dalle cugine!\",\n \"Ladin\": \"i vá dales jormanes\"\n },\n {\n \"Italian\": \"staccare la luce\",\n \"Ladin\": \"destodé la löm\"\n },\n ...\n {\n \"Italian\": \"a ottobre inoltrato\",\n \"Ladin\": \"d'otober fora\"\n }\n ]\n }\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}Please provide the translation of the fol-\nlowing 15 entries in the JSON format, fill-\ning the empty 'Ladin' fields for each entry.\nDo not include any additional explanations \nor text:\n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n{\n \"translations\": [\n {\n \"Italian\": \"imprimere nella mente\",\n \"Ladin\": \"\"\n },\n {\n \"Italian\": \"temperare la matita\",\n \"Ladin\": \"\"\n },\n {\n \"Italian\": \"mettere paura a qcn.\",\n \"Ladin\": \"\"\n },\n ...\n {\n \"Italian\": \"un animale scattante\",\n \"Ladin\": \"\"\n }\n ]\n }\n\\end{verbatim}\n\n\\section{A Few-shot Learning Prompt Template in the SA task}\n\\label{sec:fsl-sa}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Below are Tripadvisor reviews in Ladin (Val\nBadia variant) along with their sentiment \nlabels:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n {\n[review: \"I sun stá chiló por 7 nes. Le gost\né é bun. Porimpó é i chelins cherdá indormed\ní pormal. ...\", label: 1], [review: \"Lalber\nch é bunorté te na zona chîta dlungia na plaz\na. Gní zoruch vigni sëra ê sciöche ciafé nao\nasa. ...\" label: 0], \n...\n[review: \"I un passé chiló n bel fin dledema\nhotel nët, personal da orëi bun, bun ince le\ngosté y na posiziun ezelënta, impormó do lab\nela plaza San Marco. ...\", label: 0]\n }\n\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}\nPlease classify the sentiment for the follo\nwing 10 Tripadvisor reviews in Ladin (Val \nBadia variant) as either 0 (Positive) or 1\n(Negative). Fill in the empty 'label' field\ns with only 0 or 1. Respond with the sentime\nnt labels in list format like this: [x, x, \n...]. Do not include any additional explana\ntions or text.\n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n {\n[review: \"Por na vistada y na fuga a Milan \n(na mostra, na cörta vijita, na spazirada)\nél perfet. ...\", label: ], [review: \"Le bru\nnch ne joav nia le prisc. Lhotel é n pü' dal\nunc dal Duomo. ...\", label: ], \n...\n[review: \"Rezeziun ezelënta, dantadöt le \nconcierje cun sües racomanaziuns. ...\", \nlabel: ]\n } \n\\end{verbatim}\n\n\\section{A Few-shot Learning Prompt Template in the MCQA task}\n\\label{sec:fsl-mcqa}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Below are multiple-choice questions in Lad\nin (Val Badia variant) with 3, 4, or 5 answer \nchoices. The correct answer is explicitly pr\novided as an id number corresponding to the \norder of the choices:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n {\n[question: aladô dla lege 241/1990, olá é pa \nmetüda sö la comisciun por l'azes ai documën\nc aministratifs?, choices: ['pro la Presidën\nza dl Consei di Minisć', 'Por vigni Entité pu\nblica dl post', 'pro vigni Entité publica eco\nnomica de competënza regionala'], answer: 0]\n, [question: aladô dla DGR 514/2009, por PAI \ny PEI se intendi rispetivamënter:, choices: \n[\"Plan d'Assistënza Indicisé y Program Etich \nIndividualisé\", 'Program de Asistënza Indivi\nduala y Program Educatif Individualisé', \"Pl\nan d' Assistënza Individualisé y Plan d'Educ\naziun Individualisé\"], answer: 2],\n...\n[question: aladô de REICAT l'intestaziun uni\nforme por na porsona:, choices: ['al corespo\ngn tresala forma dl inom che vëgn dant tla pr\nöma ediziundles operes dl autur.', 'al se ba\nsa söl inom cun chël che la porsona medema é\ngeneralmente identifiada.', 'ara ne pó mai e\nster metüda adöm da npseudonom.'], answer: 1]\n }\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}Please answer the questions based on the ava\nilable choices, by filling in the empty 'answ\ner' fields with the id number corresponding to\nthe order of the choices. Provide the answers \nin a list format like this: [x, x, x, ..., x].\nDo not include any additional explanations or\ntext. \n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n {\n[question: na coleziun de figurines é metüda\nadöm da 84 toc, 14 por vigni contignidú. 7 fi\ngurines de vigni contignidú é lamincards, i \nrestanc fotocartes. Tan de figurines de fo to\ncartes ál pa la coleziun?, choices: ['42', '43'\n, '44'], answer:], \n...\n, [question: ci frasa, danter chëses listi\ngades, á pa n complemënt de gauja?, choices:\n['Laura é piada demez por n iade de plajëi',\n'i ápormó cumpré na scincunda por le compliann\nde Marco', \"por na taiada de strom s'á ascensur\nbloché\"], answer: ]\n }\n\\end{verbatim}\n\n\\clearpage % Force the figure to go on its own page\n\\begin{figure*}[tp]\n \\centering\n \\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\n \\caption{chrF++ scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n \\label{fig:chrf_AD}\n\\end{figure*}\n\n\\begin{figure*}[tp]\n \\centering\n \\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\n \\caption{BLEU scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n \\label{fig:bleu_AD}\n\\end{figure*}\n\n\\end{document}\n"},"question":{"kind":"string","value":"If we take all the values across the table for NLLB 1.3B and formulate an polynomial regression function with the last term being the constant, will f(5) be greater than 10000?"},"answer":{"kind":"string","value":"Yes"},"plan":{"kind":"string","value":"SELECT all numeric values in the NLLB 1.3 B row in left-to-right order as coeff_list\n\n\nCOMPUTE degree = count of coeff_list − 1\n\n\nLOOP for each coeff in coeff_list with its index i in order\n COMPUTE f5 += coeff * (5 ^ (degree − i))\n\n\nIF f5 > 10000\n RETURN yes\nRETURN no\n"}}},{"rowIdx":361,"cells":{"paper":{"kind":"string","value":"2509.03962"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n"," & 26.00 & 16.92 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n"," & 35.05 & 23.17 \\\\\n"," & FSL-GPT-4o \n"," & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n"," & 30.08 & 20.42 \\\\\n"," & FT-Llama 3.1 8B \n"," & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n"," & 36.60 & 30.98 \\\\\n"," & FT-Llama 3.1 70B \n"," & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n"," & 35.87 & 23.99 \\\\\n"," & Mbart-large-50 \n"," & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n"," & 38.66 & 35.23 \\\\\n"," & NLLB 1.3 B \n"," & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n"," & \\underline{45.98} & \\underline{41.58} \\\\\n"," & Benchmark (LLM) \n"," & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n"," & 28.98 & 18.60 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n"," & 46.28 & \\textbf{42.15} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_ladin}\n"," Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \\n\",\n \" & 26.00 & 16.92 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \\n\",\n \" & 35.05 & 23.17 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \\n\",\n \" & 30.08 & 20.42 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \\n\",\n \" & 36.60 & 30.98 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \\n\",\n \" & 35.87 & 23.99 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \\n\",\n \" & 38.66 & 35.23 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & \\\\underline{18.54} & \\\\underline{16.85} & \\\\underline{17.88} & \\\\textbf{51.59} & \\\\underline{51.55} & \\\\underline{55.29} & \\\\textbf{46.24}\\n\",\n \" & \\\\underline{45.98} & \\\\underline{41.58} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \\n\",\n \" & 28.98 & 18.60 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & 18.30 & 17.69 & \\\\textbf{18.29} & 51.40 & \\\\textbf{52.92} & \\\\textbf{56.65} & 45.44 \\n\",\n \" & 46.28 & \\\\textbf{42.15} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{20.93} & \\\\textbf{19.32} & 16.65 & - & - & - & \\\\textbf{47.65} & \\\\textbf{46.58} & 38.16 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_ladin}\\n\",\n \" Translation performance of various models for Italian → Ladin across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[!t]\n"," \\centering\n"," \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n"," \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n"," \\label{fig:LadinArea}\n","\\end{figure}\n"],["\\begin{figure*}[t]\n"," \\centering\n"," \\includegraphics[width=5.3in]{latex/Figure_2.png}\n"," \\caption{Synthetic data generation process. Initially, we translate the Italian data \\( D\\textsubscript{\\textit{Ita}}\\) of SA and MCQA into Ladin. The Ladin translation \\(D\\textsubscript{\\textit{Lad}}\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\(D\\textsubscript{\\textit{Lad}}\\) is back-translated into Italian \\( D^{\\prime}\\textsubscript{\\textit{Ita}}\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\n"," \\label{fig:experiments}\n","\\end{figure*}\n"],["\\begin{table*}\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llcccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{2}{c}{\\textbf{BLEU}} \n"," & \\multicolumn{2}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{2}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-8}\n"," &\n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n"," & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\n"," & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\n"," & FSL-GPT-4o & 4.27 & \\underline{22.84} & 25.86 & \\underline{52.28} & 27.47 & 48.23 \\\\\n"," & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\n"," & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\n"," & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\n"," & FT-NLLB 1.3 B & \\underline{17.76} & 21.41 & \\underline{52.81} & 49.91 & \\underline{44.60 } & \\underline{48.40} \\\\\n"," & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\n"," \n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B & 18.30 & \\textbf{24.50} & \\textbf{53.66} & \\textbf{52.64} & \\textbf{44.62} & \\textbf{50.76} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{translation-performance}\n"," Comparison of different models based on average translation performance metrics on the test set \\( T \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.}\n","\n","\\end{table*}\n"],["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n"," & 26.00 & 16.92 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n"," & 35.05 & 23.17 \\\\\n"," & FSL-GPT-4o \n"," & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n"," & 30.08 & 20.42 \\\\\n"," & FT-Llama 3.1 8B \n"," & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n"," & 36.60 & 30.98 \\\\\n"," & FT-Llama 3.1 70B \n"," & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n"," & 35.87 & 23.99 \\\\\n"," & Mbart-large-50 \n"," & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n"," & 38.66 & 35.23 \\\\\n"," & NLLB 1.3 B \n"," & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n"," & \\underline{45.98} & \\underline{41.58} \\\\\n"," & Benchmark (LLM) \n"," & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n"," & 28.98 & 18.60 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n"," & 46.28 & \\textbf{42.15} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_ladin}\n"," Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"],["\\begin{table*}[!t]\n"," \\centering\n"," \\small\n"," \\begin{tabular}{llccccccccc}\n"," \\hline\n"," \\textbf{Training Data} & \\textbf{Model} \n"," & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n"," & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n"," \\cline{3-11} &\n"," & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n"," \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n"," \\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n"," & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \n"," & 38.89 & 23.41 \\\\\n"," & FSL-Llama 3.1 70B \n"," & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \n"," & 48.66 & 36.91 \\\\\n"," & FSL-GPT-4o \n"," & 29.23 & 23.38 & 15.90 & 61.39 & \\textbf{53.37} & 42.07 & 55.73 \n"," & 50.33 & 38.64 \\\\\n"," & FT-Llama 3.1 8B \n"," & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \n"," & 44.11 & 33.66 \\\\\n"," & FT-Llama 3.1 70B \n"," & \\textbf{30.78} & \\textbf{23.65} & 13.02 & \\textbf{61.91} & 52.10 & 38.29 & \\textbf{57.23} \n"," & \\underline{50.53} & 36.12 \\\\\n"," & Mbart-large-50 \n"," & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \n"," & 42.15 & 36.81 \\\\\n"," & NLLB 1.3 B \n"," & 27.15 & 19.77 & \\underline{17.31} & 55.54 & 48.27 & \\underline{46.03} & 54.45\n"," & 49.66 & \\underline{41.09} \\\\\n"," & Benchmark (LLM) \n"," & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \n"," & 48.52 & 32.36 \\\\\n","\\hline\n"," \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n"," & FT-NLLB 1.3 B \n"," & \\underline{30.46} & \\underline{22.71} & \\textbf{20.33} & 58.11 & 50.71 & \\textbf{49.11} & \\underline{56.95} \n"," & \\textbf{51.49} & \\textbf{43.83} \n"," \\\\\n"," \\rule{0pt}{5.2ex} \n"," \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n"," & \\shortstack[l]{Benchmark\\\\(RBMT)} \n"," & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \n"," & 49.08 & 40.76 \\\\\\\\ \n"," \\hline\n"," \\end{tabular}\n"," \\caption{\\label{add-trans_to_italian}\n"," Translation performance of various models for Ladin → Italian across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n"," }\n","\\end{table*}\n"],["\\begin{table}[t]\n"," \\small\n"," \\centering\n"," \\makebox[3.1in][r]{\n"," \\begin{tabular}{lcc}\n"," \\hline\n"," \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n"," & \\textbf{Italian} & \\textbf{Ladin} \\\\\n"," \\hline\n"," Average number of words per entry & 65 & 70 \\\\\n"," Average number of characters per entry & 144 & 348 \\\\\n"," Positive label count & 9,842 & 9,842 \\\\\n"," Negative label count & 2,669 & 2,669 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SD-SA}\n"," Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\n"," }\n","\\end{table}\n"],["\\begin{table}[t]\n"," \\centering\n"," \\small\n"," \\makebox[3.2in][r]{\n"," \\begin{tabular}{lcc}\n"," \\hline\n"," \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n"," & \\textbf{Italian} & \\textbf{Ladin} \\\\\n"," \\hline\n"," Average number of words per question & 18 & 19 \\\\\n"," Average number of characters per question & 108 & 97 \\\\\n"," Average number of words per choices & 28 & 30 \\\\\n"," Average number of characters per choices & 187 & 174 \\\\\n"," Frequency of entries with 3 choices & 304 & 304 \\\\\n"," Frequency of entries with 4 choices & 196 & 196 \\\\\n"," Frequency of entries with 5 choices & 264 & 264 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SD-MCQA}\n"," Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\n"," }\n","\\end{table}\n"],["\\begin{table*}[t]\n"," \\centering\n"," \\small\n"," \\makebox[\\textwidth]{\n"," \\begin{tabular}{lcccc@{\\hspace{2em}}cccc}\n"," \\hline\n"," \\textbf{Model} &\n"," \\multicolumn{4}{c}{\\textbf{Ladin}} &\n"," \\multicolumn{4}{c}{\\textbf{Italian}} \\\\\n"," \\cline{2-9}\n"," & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}}\n"," & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}} \\\\\n"," \n"," & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1}\n"," & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1} \\\\\n"," \\hline\n"," FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\n"," & 97.92 & 98.18 & 54.79 & 54.18 \\\\\n"," m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \n"," & 94.78 & 96.41 & 30.73 & 30.29 \\\\\n"," XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \n"," & 97.14 & 98.08 & 26.14 & 26.14 \\\\\n"," mT5 & 50.09 & 69.37 & 23.50 & 23.16 \n"," & 49.98 & 69.25 & 22.62 & 21.92 \\\\\n"," \\hline\n"," \\end{tabular}\n"," }\n"," \\caption{\\label{SA-MCQA} \n"," Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\n"," } \n","\\end{table*}\n"],["\\begin{figure*}[tp]\n"," \\centering\n"," \\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\n"," \\caption{chrF++ scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n"," \\label{fig:chrf_AD}\n","\\end{figure*}\n"],["\\begin{figure*}[tp]\n"," \\centering\n"," \\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\n"," \\caption{BLEU scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n"," \\label{fig:bleu_AD}\n","\\end{figure*}\n"]],"string":"[\n [\n \"\\\\begin{figure}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\\n\",\n \" \\\\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\\n\",\n \" \\\\label{fig:LadinArea}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=5.3in]{latex/Figure_2.png}\\n\",\n \" \\\\caption{Synthetic data generation process. Initially, we translate the Italian data \\\\( D\\\\textsubscript{\\\\textit{Ita}}\\\\) of SA and MCQA into Ladin. The Ladin translation \\\\(D\\\\textsubscript{\\\\textit{Lad}}\\\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\\\(D\\\\textsubscript{\\\\textit{Lad}}\\\\) is back-translated into Italian \\\\( D^{\\\\prime}\\\\textsubscript{\\\\textit{Ita}}\\\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\\n\",\n \" \\\\label{fig:experiments}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llcccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{BLEU}} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-8}\\n\",\n \" &\\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\n\",\n \" & \\\\textbf{Ita→Lad} & \\\\textbf{Lad→Ita} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\\\\\\n\",\n \" & FSL-GPT-4o & 4.27 & \\\\underline{22.84} & 25.86 & \\\\underline{52.28} & 27.47 & 48.23 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\\\\\\n\",\n \" & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\\\\\\n\",\n \" & FT-NLLB 1.3 B & \\\\underline{17.76} & 21.41 & \\\\underline{52.81} & 49.91 & \\\\underline{44.60 } & \\\\underline{48.40} \\\\\\\\\\n\",\n \" & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B & 18.30 & \\\\textbf{24.50} & \\\\textbf{53.66} & \\\\textbf{52.64} & \\\\textbf{44.62} & \\\\textbf{50.76} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{translation-performance}\\n\",\n \" Comparison of different models based on average translation performance metrics on the test set \\\\( T \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.}\\n\",\n \"\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \\n\",\n \" & 26.00 & 16.92 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \\n\",\n \" & 35.05 & 23.17 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \\n\",\n \" & 30.08 & 20.42 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \\n\",\n \" & 36.60 & 30.98 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \\n\",\n \" & 35.87 & 23.99 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \\n\",\n \" & 38.66 & 35.23 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & \\\\underline{18.54} & \\\\underline{16.85} & \\\\underline{17.88} & \\\\textbf{51.59} & \\\\underline{51.55} & \\\\underline{55.29} & \\\\textbf{46.24}\\n\",\n \" & \\\\underline{45.98} & \\\\underline{41.58} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \\n\",\n \" & 28.98 & 18.60 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & 18.30 & 17.69 & \\\\textbf{18.29} & 51.40 & \\\\textbf{52.92} & \\\\textbf{56.65} & 45.44 \\n\",\n \" & 46.28 & \\\\textbf{42.15} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & \\\\textbf{20.93} & \\\\textbf{19.32} & 16.65 & - & - & - & \\\\textbf{47.65} & \\\\textbf{46.58} & 38.16 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_ladin}\\n\",\n \" Translation performance of various models for Italian → Ladin across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\begin{tabular}{llccccccccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Training Data} & \\\\textbf{Model} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{BLEU}} & \\\\multicolumn{3}{c}{\\\\textbf{Rouge}} \\n\",\n \" & \\\\multicolumn{3}{c}{\\\\textbf{chrF++}} \\\\\\\\\\n\",\n \" \\\\cline{3-11} &\\n\",\n \" & \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} &\\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} & \\n\",\n \" \\\\textbf{\\\\boldmath\\\\( t_1 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_2 \\\\)} & \\\\textbf{\\\\boldmath\\\\( t_3 \\\\)} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} & FSL-Llama 3.1 8B \\n\",\n \" & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \\n\",\n \" & 38.89 & 23.41 \\\\\\\\\\n\",\n \" & FSL-Llama 3.1 70B \\n\",\n \" & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \\n\",\n \" & 48.66 & 36.91 \\\\\\\\\\n\",\n \" & FSL-GPT-4o \\n\",\n \" & 29.23 & 23.38 & 15.90 & 61.39 & \\\\textbf{53.37} & 42.07 & 55.73 \\n\",\n \" & 50.33 & 38.64 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 8B \\n\",\n \" & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \\n\",\n \" & 44.11 & 33.66 \\\\\\\\\\n\",\n \" & FT-Llama 3.1 70B \\n\",\n \" & \\\\textbf{30.78} & \\\\textbf{23.65} & 13.02 & \\\\textbf{61.91} & 52.10 & 38.29 & \\\\textbf{57.23} \\n\",\n \" & \\\\underline{50.53} & 36.12 \\\\\\\\\\n\",\n \" & Mbart-large-50 \\n\",\n \" & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \\n\",\n \" & 42.15 & 36.81 \\\\\\\\\\n\",\n \" & NLLB 1.3 B \\n\",\n \" & 27.15 & 19.77 & \\\\underline{17.31} & 55.54 & 48.27 & \\\\underline{46.03} & 54.45\\n\",\n \" & 49.66 & \\\\underline{41.09} \\\\\\\\\\n\",\n \" & Benchmark (LLM) \\n\",\n \" & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \\n\",\n \" & 48.52 & 32.36 \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \" \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} + \\\\textit{SD\\\\textsubscript{Ita\\\\_Lad}} \\n\",\n \" & FT-NLLB 1.3 B \\n\",\n \" & \\\\underline{30.46} & \\\\underline{22.71} & \\\\textbf{20.33} & 58.11 & 50.71 & \\\\textbf{49.11} & \\\\underline{56.95} \\n\",\n \" & \\\\textbf{51.49} & \\\\textbf{43.83} \\n\",\n \" \\\\\\\\\\n\",\n \" \\\\rule{0pt}{5.2ex} \\n\",\n \" \\\\shortstack[l]{\\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} +\\\\\\\\monolingual data} \\n\",\n \" & \\\\shortstack[l]{Benchmark\\\\\\\\(RBMT)} \\n\",\n \" & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \\n\",\n \" & 49.08 & 40.76 \\\\\\\\\\\\\\\\ \\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\\\caption{\\\\label{add-trans_to_italian}\\n\",\n \" Translation performance of various models for Ladin → Italian across three test subsets \\\\( t_1 \\\\), \\\\( t_2 \\\\), and \\\\( t_3 \\\\). The table is divided into two sections: the upper section reports results using only authentic training data \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}}, while the lower section presents results with additional synthetic data.\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \" \\\\makebox[3.1in][r]{\\n\",\n \" \\\\begin{tabular}{lcc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Feature} & \\\\multicolumn{2}{c}{\\\\textbf{Language}} \\\\\\\\\\n\",\n \" & \\\\textbf{Italian} & \\\\textbf{Ladin} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" Average number of words per entry & 65 & 70 \\\\\\\\\\n\",\n \" Average number of characters per entry & 144 & 348 \\\\\\\\\\n\",\n \" Positive label count & 9,842 & 9,842 \\\\\\\\\\n\",\n \" Negative label count & 2,669 & 2,669 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SD-SA}\\n\",\n \" Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\\n\",\n \" }\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\makebox[3.2in][r]{\\n\",\n \" \\\\begin{tabular}{lcc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Feature} & \\\\multicolumn{2}{c}{\\\\textbf{Language}} \\\\\\\\\\n\",\n \" & \\\\textbf{Italian} & \\\\textbf{Ladin} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" Average number of words per question & 18 & 19 \\\\\\\\\\n\",\n \" Average number of characters per question & 108 & 97 \\\\\\\\\\n\",\n \" Average number of words per choices & 28 & 30 \\\\\\\\\\n\",\n \" Average number of characters per choices & 187 & 174 \\\\\\\\\\n\",\n \" Frequency of entries with 3 choices & 304 & 304 \\\\\\\\\\n\",\n \" Frequency of entries with 4 choices & 196 & 196 \\\\\\\\\\n\",\n \" Frequency of entries with 5 choices & 264 & 264 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SD-MCQA}\\n\",\n \" Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\\n\",\n \" }\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\small\\n\",\n \" \\\\makebox[\\\\textwidth]{\\n\",\n \" \\\\begin{tabular}{lcccc@{\\\\hspace{2em}}cccc}\\n\",\n \" \\\\hline\\n\",\n \" \\\\textbf{Model} &\\n\",\n \" \\\\multicolumn{4}{c}{\\\\textbf{Ladin}} &\\n\",\n \" \\\\multicolumn{4}{c}{\\\\textbf{Italian}} \\\\\\\\\\n\",\n \" \\\\cline{2-9}\\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{SA}} & \\\\multicolumn{2}{c}{\\\\textbf{MCQA}}\\n\",\n \" & \\\\multicolumn{2}{c}{\\\\textbf{SA}} & \\\\multicolumn{2}{c}{\\\\textbf{MCQA}} \\\\\\\\\\n\",\n \" \\n\",\n \" & \\\\textbf{Acc} & \\\\textbf{F1} & \\\\textbf{Acc} & \\\\textbf{F1}\\n\",\n \" & \\\\textbf{Acc} & \\\\textbf{F1} & \\\\textbf{Acc} & \\\\textbf{F1} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\\n\",\n \" & 97.92 & 98.18 & 54.79 & 54.18 \\\\\\\\\\n\",\n \" m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \\n\",\n \" & 94.78 & 96.41 & 30.73 & 30.29 \\\\\\\\\\n\",\n \" XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \\n\",\n \" & 97.14 & 98.08 & 26.14 & 26.14 \\\\\\\\\\n\",\n \" mT5 & 50.09 & 69.37 & 23.50 & 23.16 \\n\",\n \" & 49.98 & 69.25 & 22.62 & 21.92 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\caption{\\\\label{SA-MCQA} \\n\",\n \" Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\\n\",\n \" } \\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[tp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\\n\",\n \" \\\\caption{chrF++ scores of the models using \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} as the training data}\\n\",\n \" \\\\label{fig:chrf_AD}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[tp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\\n\",\n \" \\\\caption{BLEU scores of the models using \\\\textit{AD\\\\textsubscript{Ita\\\\_Lad}} as the training data}\\n\",\n \" \\\\label{fig:bleu_AD}\\n\",\n \"\\\\end{figure*}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"% This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.\n\\pdfoutput=1\n% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.\n\n\\documentclass[11pt]{article}\n\n% Change \"review\" to \"final\" to generate the final (sometimes called camera-ready) version.\n% Change to \"preprint\" to generate a non-anonymous version with page numbers.\n\\usepackage[preprint]{acl}\n\n% Standard package includes\n\\usepackage{times}\n\\usepackage{latexsym}\n\n% For proper rendering and hyphenation of words containing Latin characters (including in bib files)\n\\usepackage[T1]{fontenc}\n% For Vietnamese characters\n% \\usepackage[T5]{fontenc}\n% See https://www.latex-project.org/help/documentation/encguide.pdf for other character sets\n\n% This assumes your files are encoded as UTF8\n\\usepackage[utf8]{inputenc}\n\n% This is not strictly necessary, and may be commented out,\n% but it will improve the layout of the manuscript,\n% and will typically save some space.\n\\usepackage{microtype}\n\n% This is also not strictly necessary, and may be commented out.\n% However, it will improve the aesthetics of text in\n% the typewriter font.\n\\usepackage{inconsolata}\n\n%Including images in your LaTeX document requires adding\n%additional package(s)\n\\usepackage{graphicx}\n\n% If the title and author information does not fit in the area allocated, uncomment the following\n%\n%\\setlength\\titlebox{<dim>}\n%\n% and set <dim> to something 5cm or larger.\n\n\\title{ \nExploring NLP Benchmarks in an Extremely Low-Resource Setting\n%Synthetic Data for Ladin NLP: Toward Democratized Language Models for Indigenous Languages\n}\n\n% Author information can be set in various styles:\n% For several authors from the same institution:\n% \\author{Author 1 \\and ... \\and Author n \\\\\n% Address line \\\\ ... \\\\ Address line}\n% if the names do not fit well on one line use\n% Author 1 \\\\ {\\bf Author 2} \\\\ ... \\\\ {\\bf Author n} \\\\\n% For authors from different institutions:\n% \\author{Author 1 \\\\ Address line \\\\ ... \\\\ Address line\n% \\And ... \\And\n% Author n \\\\ Address line \\\\ ... \\\\ Address line}\n% To start a separate ``row'' of authors use \\AND, as in\n% \\author{Author 1 \\\\ Address line \\\\ ... \\\\ Address line\n% \\AND\n% Author 2 \\\\ Address line \\\\ ... \\\\ Address line \\And\n% Author 3 \\\\ Address line \\\\ ... \\\\ Address line}\n\n\\author{\n Ulin Nuha\\thanks{Work done while the author was a PhD student at NKUST.} \\\\\n National Kaohsiung University \\\\\n of Science and Technology \\\\\n \\texttt{ulinnuha.id@icloud.com}\n \\And\n Adam Jatowt \\\\\n University of Innsbruck \\\\\n \\texttt{adam.jatowt@uibk.ac.at}\n}\n%\\author{\n% \\textbf{First Author\\textsuperscript{1}},\n% \\textbf{Second Author\\textsuperscript{1,2}},\n% \\textbf{Third T. Author\\textsuperscript{1}},\n% \\textbf{Fourth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Fifth Author\\textsuperscript{1,2}},\n% \\textbf{Sixth Author\\textsuperscript{1}},\n% \\textbf{Seventh Author\\textsuperscript{1}},\n% \\textbf{Eighth Author \\textsuperscript{1,2,3,4}},\n%\\\\\n% \\textbf{Ninth Author\\textsuperscript{1}},\n% \\textbf{Tenth Author\\textsuperscript{1}},\n% \\textbf{Eleventh E. Author\\textsuperscript{1,2,3,4,5}},\n% \\textbf{Twelfth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Thirteenth Author\\textsuperscript{3}},\n% \\textbf{Fourteenth F. Author\\textsuperscript{2,4}},\n% \\textbf{Fifteenth Author\\textsuperscript{1}},\n% \\textbf{Sixteenth Author\\textsuperscript{1}},\n%\\\\\n% \\textbf{Seventeenth S. Author\\textsuperscript{4,5}},\n% \\textbf{Eighteenth Author\\textsuperscript{3,4}},\n% \\textbf{Nineteenth N. Author\\textsuperscript{2,5}},\n% \\textbf{Twentieth Author\\textsuperscript{1}}\n%\\\\\n%\\\\\n% \\textsuperscript{1}Affiliation 1,\n% \\textsuperscript{2}Affiliation 2,\n% \\textsuperscript{3}Affiliation 3,\n% \\textsuperscript{4}Affiliation 4,\n% \\textsuperscript{5}Affiliation 5\n%\\\\\n% \\small{\n% \\textbf{Correspondence:} \\href{mailto:email@domain}{email@domain}\n% }\n%}\n\n\\begin{document}\n\\maketitle\n\\begin{abstract}\n%Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of natural language processing (NLP) tasks. However, \nThe effectiveness of Large Language Models (LLMs) diminishes for extremely low-resource languages, such as indigenous languages, primarily due to the lack of labeled data. Despite growing interest, the availability of high-quality natural language processing (NLP) datasets for these languages remains limited, making it difficult to develop robust language technologies. This paper addresses such gap by focusing on Ladin, an endangered Romance language, specifically targeting the Val Badia variant. Leveraging a small set of parallel Ladin–Italian sentence pairs, we create synthetic datasets for sentiment analysis and multiple-choice question answering (MCQA) by translating monolingual Italian data. To ensure linguistic quality and reliability, we apply rigorous filtering and back-translation procedures in our method. We further demonstrate that incorporating these synthetic datasets into machine translation training leads to substantial improvements over existing Italian–Ladin translation baselines. Our contributions include the first publicly available sentiment analysis and MCQA datasets for Ladin, establishing foundational resources that can support broader NLP research and downstream applications for this underrepresented language.\n\\end{abstract}\n\n\\section{Introduction}\n\\begin{figure}[!t]\n \\centering\n \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n \\label{fig:LadinArea}\n\\end{figure}\n\n\nLarge language models (LLMs) have garnered significant attention in diverse audiences \\citep{Yuxia:2024, Gambardella:2024} due to their ability to effectively perform natural language tasks with only a few input-output examples \\citep{Cheng:24}, while also eliminating the need for gradient updates of the model \\citep{Nguyen:2024}. \nLLMs achieve remarkable performance through pre-training on large corpora, but their reliance on high-resource languages (HRLs) limits their effectiveness for low-resource languages (LRLs) \\citep{Pham:2024}, especially extreme ones \\citep{purason2024llms}. Efforts to address this limitation include various techniques such as in-context learning \\citep{Cahyawijaya:2024} and fine-tuning \\citep{Alabi:2022, Su2024Unlocking} to transfer LLM capabilities to LRLs. Additionally, some studies \\citep{yong2024lexc, morim2024, tran24irish} have focused on developing translation systems between LRLs and HRLs to address the lack of language technology resources. The limited advancement of natural language processing (NLP) in LRLs stems largely from the disproportionate focus of research on improving language models for HRLs, often at the expense of developing tools and resources for low-resource counterparts \\citep{zhang24llm}. Moreover, the scarcity of NLP datasets for extremely low-resource languages (ELRLs) constitutes a major barrier to progress in this area, highlighting the need for more inclusive AI technologies to support marginalized languages.\n\nThis paper advances NLP research for Ladin language, an Indigenous and extremely low-resource language of Northern Italy (see Fig.~\\ref{fig:LadinArea}). %Sharing roots with Italian, Ladin is a Romance (Neo-Latin) language.\nDespite progress in NLP for LRLs, Ladin’s dialectal diversity and limited digitized corpora pose unique challenges. Building on the prior work \\citep{frontull24}, which established a machine translation (MT) benchmark between Italian and Ladin (Val Badia variant), we further improve the translation performance for Ladin.\n\nLadin is a Rhaeto-Romance language spoken by about 30,000 people in South Tyrol, Northern Italy. It comprises five dialects (Val Badia, Fascia, Anpezo, Fodom, and Gherdëina) which vary significantly in morpho-syntactic and orthographic conventions. Although standardized efforts such as Ladin Dolomitan exist, it is not officially recognized and is used only to a limited extent, while speakers report minimal familiarity with Ladin varieties beyond their own \\citep{connor2023ladin}. Linguistic conventions have also changed over time within dialects. This linguistic diversity presents major challenges for machine translation and resource creation. Publicly available resources are extremely limited, with only a few lexicons, dictionaries, and minor corpora. There is a major source of monolingual Ladin data in \\textit{La Usc di Ladins}\\footnote{https://www.lausc.it/}, a newspaper published in five variants and digitally archived since 2012, but this resource remains underutilized due to the lack of alignment and limited annotation. Our work focuses on the Val Badia variant of Ladin%\\footnote{Ladin originally comprises five variants: Val Badia, Gherdëina, Fascia, Fodom, and Anpezo.}\n, due to the availability of the largest accessible dataset. Previous work on MT for Ladin's Fascia variant exists \\citep{FasciaLadin}; however, the parallel dataset used in that work consists of only 1,135 sentences. \n\nUnlike prior studies, our work also extends beyond MT for Ladin to include sentiment analysis (SA) and multiple-choice question answering (MCQA), establishing the first datasets for these tasks in Ladin. First, we compare MT approaches, including few-shot learning and fine-tuning, using available Ladin–Italian sentence pairs. Subsequently, we construct high-quality synthetic Ladin datasets for SA and MCQA through the translation from monolingual Italian data, applying rigorous filtering to ensure high quality. These datasets not only contribute to SA and MCQA but also enhance MT. To assess this, we incorporate our synthetic dataset into existing Italian–Ladin translation benchmarks and evaluate its impact.\n\nIn summary, the primary contributions of our work can be outlined as follows:\n\\begin{itemize}\n \\item We conduct a comparative study on translation between Italian and Ladin, focusing on the Val Badia variant. Our model significantly outperforms the current benchmark, demonstrating the effectiveness of our approach for this extremely low-resource language (LRL).\n \n \\item We construct a high-quality synthetic dataset of Ladin–Italian sentence pairs, referred to as \\textit{SD\\textsubscript{Lad--Ita}}, derived from monolingual Italian data using a language model and rigorous filtering techniques.\n \n \\item We showcase the utility of the synthetic dataset beyond MT by applying it to additional downstream NLP tasks, including SA (text classification) and MCQA, establishing the first such datasets in Ladin.\n\\end{itemize}\n\n%By highlighting the severe scarcity of NLP datasets for extremely LRLs compared to those for LRLs, and by \nBy fostering NLP research on Ladin, we aim to support the preservation and accessibility of this critically underrepresented language—benefiting education, digital communication, and cultural documentation for Indigenous communities.\n\n\\section{Background and Related Work}\n\nNLP for ELRLs has garnered increasing attention from researchers, largely due to the enduring challenges associated with data scarcity. These languages typically possess fewer than 0.1 million available parallel sentence pairs \\citep{Ranathunga23}, which are often insufficient for effectively training neural machine translation (NMT) models \\citep{rudra:19}. For instance, Ladin has fewer than 100 thousand parallel sentences available for MT \\citep{frontull24}, while resources for other NLP tasks, such as text classification and question answering, remain non-existent. \n\nLadin and Italian are both Romance languages with shared Latin roots, resulting in potential similarities in lexical and syntactic aspects. This linguistic proximity facilitates cross-lingual transfer, allowing multilingual models fine-tuned on Italian to generalize moderately well to Ladin. However, key divergences remain due to Ladin’s unique phonological and morphological traits \\citep{LucaM}. These differences are further shaped by historical geographic isolation and varying degrees of contact with dominant surrounding languages, particularly regional varieties of German and Italian. Most Ladin speakers in Italy are bi- or tri-lingual, using Ladin in private domains and Italian, German, or both in public settings, as neighboring communities typically lack comprehension of Ladin \\citep{SilviaLadin}. This contact has led to regional variation. For instance, Gherdëina and Val Badia exhibit stronger German influence, while southern valleys show more Italian features. Val Badia is often perceived as having the “purest” Ladin, though this reflects relative rather than absolute isolation from external influence. These dynamics pose several challenges for translation. The lack of a commonly adopted standard variety necessitates dialect-specific translation strategies, complicating mutual intelligibility and the development of shared resources. Furthermore, long-standing language contact has introduced borrowings and calques, making it difficult to isolate core Ladin structures.\n\n\nTo address the scarcity of resources in ELRLs, recent efforts have focused on leveraging transfer learning techniques, particularly through the use of large language models (LLMs) \\citep{Pham:2024, lim:24}. However, success remains limited in such settings \\citep{tran24irish}, where extreme data sparsity poses challenges for effective domain adaptation and language alignment. In addition, a key aspect of transfer learning with LLMs involves leveraging token similarity and cross-region similarity to better capture shared cultural and linguistic features \\citep{SinaBN}. \\citet{RAG-LLM} proposed a MT framework that integrates Retrieval-Augmented Generation (RAG) with LLMs to address these challenges, whereas \\citet{DPO-LLM} explored the use of LLMs in combination with Direct Preference Optimization (DPO) to enhance translation quality. \n\nDespite promising results, the above-mentioned methods incur high computational costs. Multimodal approaches, which incorporate additional modalities such as visual context to enhance translation \\citep{rajpoot:24, sami:dcu, hatami:24}, require supplementary datasets that are often unavailable for these languages and face considerable computational and complexity challenges. Then, Rule-based machine translation (RBMT), exemplified by Apertium \\citep{garcia:24, sanchez:24}, offers a less resource-intensive alternative, with lower computational requirements compared to NMT systems. However, RBMT systems are labor-intensive, requiring extensive manual effort to create and maintain linguistic rules, with scalability further hindered by the challenge of ensuring rule self-consistency \\citep{liu-multil:24}. \n\nAnother approach to supporting technologies for LRLs is the development of benchmarks. For example, \\citet{urbizu} introduced BasqueGLUE, a benchmark covering multiple NLP tasks for the Basque language.\nSimilarly, \\citet{FarsInstruct} presented FarsInstruct, a large-scale dataset developed to strengthen LLMs’ capacity to follow instructions in Persian, a globally low-represented language. However, recent work in language revitalization and human-centered NLP shows the importance of going beyond performance metrics in developing technologies for endangered languages \\citep{StevenBird}. Effective systems should align with long-term community goals, such as intergenerational transmission and cultural continuity.\n\nIn line with this perspective, our work presents a comparative study of MT approaches, including instruction learning and fine-tuning \\citep{zhang:mt23}, using several language models such as NLLB and GPT-4. %Given Ladin’s underrepresentation, we adapt sequence modeling techniques for this new linguistic setting \\citep{Degenaro:24}. \nTo evaluate translation quality, we use both statistical and semantical metrics, particularly for synthetic data. While prior research has made progress in NLP for LRLs, substantial gaps remain for ELRLs such as Ladin. This study addresses these gaps by leveraging data augmentation techniques and introducing benchmark datasets for MT, text classification, and question answering tasks.\n\n\\section{Experiments}\n\n\\begin{figure*}[t]\n \\centering\n \\includegraphics[width=5.3in]{latex/Figure_2.png}\n \\caption{Synthetic data generation process. Initially, we translate the Italian data \\( D\\textsubscript{\\textit{Ita}}\\) of SA and MCQA into Ladin. The Ladin translation \\(D\\textsubscript{\\textit{Lad}}\\) of SA and MCQA is then filtered using Filtering I. Next, the filtered \\(D\\textsubscript{\\textit{Lad}}\\) is back-translated into Italian \\( D^{\\prime}\\textsubscript{\\textit{Ita}}\\), followed by Filtering II to obtain the high-quality parallel paired datasets of SA and MCQA in Ladin and Italian.}\n \\label{fig:experiments}\n\\end{figure*}\n\n%Our study focuses on translating the Ladin language in its Val Badia variant. Among the five Ladin variants, parallel data availability is limited to the Val Badia variant paired with Italian. \n%In addition, our experiments explore translation tasks using various sequence-to-sequence modeling and LLMs across multiple settings.\n\n\\subsection{Data sources}\nIn this section, we provide an overview of the data sources used in our study. We prepared datasets for three tasks: MT, SA, and MCQA. These resources were collected from publicly available datasets. Figure~\\ref{fig:experiments} illustrates the synthetic paired Ladin-Italian data generation process. As the creation of the SA and MCQA datasets depends on the availability of a translation model, we first constructed the MT dataset. Once the translation model was established, we proceeded with the generation of the SA and MCQA datasets accordingly.\n\\noindent\\textbf{Machine translation.} The parallel Italian–Ladin dataset used for both training and testing in our MT experiments was initially derived from prior work \\citep{frontull24}. The authentic Italian-Ladin training dataset \\textit{AD\\textsubscript{Ita\\_Lad}} comprises 18,139 sentence pairs, carefully crafted as basic and concise examples to illustrate the use of specific words and phrases. \nThe average sentence length in \\textit{AD\\textsubscript{Ita\\_Lad}} is 23.43 characters for Ladin and 25.69 characters for Italian, while the average number of words per sentence is 5.02 for Ladin and 4.36 for Italian. Following that work, the testing dataset, \\textit{\\( T = \\{t\\textsubscript{1}, t\\textsubscript{2}, t\\textsubscript{3}\\} \\)}, consists of three subsets: \\( t_1 \\) (424 sentences) focuses on formal and legal terminology; \\( t_2 \\) (833 sentences) blends stylistic and lexical elements, reflecting regional cultural and historical contexts; \\( t_3 \\) (1,563 sentences) includes narrative prose, dialogue, and idiomatic expressions, offering diverse challenges. For Italian in the testing dataset, the average word counts for \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\) are 21.25, 26.65, and 15.61, respectively. In comparison, the corresponding averages for \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\) in Ladin are 23.58, 24.52, and 13.05, respectively.\n\n\\noindent\\textbf{Sentiment analysis.} We construct datasets for NLP tasks in Ladin by leveraging labeled monolingual Italian resources, including SA and MCQA datasets. We use the monolingual Italian SA dataset \\textit{D\\textsubscript{Ita\\_SA}} from \\citet{desole2025} for the SA task. \\textit{D\\textsubscript{Ita\\_SA}} comprises abundant Tripadvisor reviews labeled as positive or negative. The initial dataset contains 41,077 entries. To mitigate the impact of excessively long reviews, we filter the dataset to retain only those entries with word counts up to the third quartile (Q3), resulting in a maximum review length of 138 words. This screening results in a reduced dataset size of 30,712 entries. Given that the raw dataset, collected via web scraping, contains grammatical errors, we employ GPT-4 to correct these while preserving the original semantic content. Following grammar correction, the average number of words per sentence in \\textit{D\\textsubscript{Ita\\_SA}} is 70.44.\n\n\\noindent\\textbf{MCQA.} Finally, for the MCQA task, we use the monolingual Italian MCQA dataset \\textit{D\\textsubscript{Ita\\_MCQA}} from \\citet{multi_it24}. \\textit{D\\textsubscript{Ita\\_MCQA}} comprises over 5,000 manually crafted questions covering a wide range of topics. This MCQA dataset contains questions with 2, 3, 4, 5, or 6 answer choices. However, we exclude questions with 2 and 6 options due to their very limited number.\n\n\\subsection{Language model settings for machine translation}\nWe now discuss the process of building a MT model using existing Italian–Ladin parallel data, which serves as a prerequisite for the subsequent synthetic data generation process. To facilitate translation between Italian and Ladin, we employ both LLMs and sequence-to-sequence (seq2seq) models. For LLM-based approaches, we utilize LLaMA 3.1 (8B and 70B variants) and GPT-4o. The LLaMA models are evaluated in two configurations: few-shot learning (FSL) and supervised fine-tuning (FT). Appendix ~\\ref{sec:fsl} provides an example prompt used for the FSL approach. To perform the FSL approach, we utilize the \\textit{LLaMA-v3.1-8b-instruct} and \\textit{LLaMA-v3.1-70b-instruct} models via the DeepInfra API. Similarly, the FSL approach with GPT-4o is conducted using the OpenAI\\footnote{https://deepinfra.com/} API. For the FT approach using LLaMA, we leverage the Together AI\\footnote{https://www.together.ai/} fine-tuning API with the LoRA adapter configuration (\\textit{r} = 32), employing a batch size of 8 and 3 epochs.\n\nFor the seq2seq models, we employ MBART-large-50 and NLLB-200-1.3B, both of which are encoder-decoder architectures specifically designed for multilingual MT. The fine-tuning models of NLLB-1.3B and MBART-large-50 are conducted on an NVIDIA RTX A6000 GPU with a batch size of 8 and over 7 epochs. To accommodate Ladin, an unseen language for both seq2seq models, we introduce a Ladin-specific language tag in the tokenizer. This modification aids in the identification and processing of Ladin texts during translation tasks, facilitating better handling of the language.\n\nSubsequently, we evaluate translation performance using standard metrics: Sacre BLEU, ROUGE, and chrF++, providing a comprehensive assessment of translation quality.\n\n\\subsection{Synthetic data creation}\n\n\\begin{table*}\n \\centering\n \\small\n \\begin{tabular}{llcccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{2}{c}{\\textbf{BLEU}} \n & \\multicolumn{2}{c}{\\textbf{Rouge}} \n & \\multicolumn{2}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-8}\n &\n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \n & \\textbf{Ita→Lad} & \\textbf{Lad→Ita} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B & 2.87 & 12.09 & 18.48 & 36.79 & 23.43 & 36.20 \\\\\n & FSL-Llama 3.1 70B & 6.35 & 21.97 & 31.81 & 51.09 & 31.09 & 47.26 \\\\\n & FSL-GPT-4o & 4.27 & \\underline{22.84} & 25.86 & \\underline{52.28} & 27.47 & 48.23 \\\\\n & FT-Llama 3.1 8B & 10.71 & 15.28 & 41.56 & 43.78 & 35.23 & 42.04 \\\\\n & FT-Llama 3.1 70B & 6.95 & 22.48 & 32.97 & 50.77 & 31.96 & 47.96 \\\\\n & Mbart-large-50 & 10.37 & 10.91 & 44.14 & 41.41 & 41.73 & 43.92 \\\\\n & FT-NLLB 1.3 B & \\underline{17.76} & 21.41 & \\underline{52.81} & 49.91 & \\underline{44.60 } & \\underline{48.40} \\\\\n & Benchmark (LLM) & 3.51 & 19.44 & - & - & 25.54 & 44.69 \\\\\n \n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B & 18.30 & \\textbf{24.50} & \\textbf{53.66} & \\textbf{52.64} & \\textbf{44.62} & \\textbf{50.76} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & \\textbf{18.97} & 19.32 & - & - & 44.13 & 46.69 \\\\\n \\hline\n \\end{tabular}\n \\caption{\\label{translation-performance}\n Comparison of different models based on average translation performance metrics on the test set \\( T \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.}\n\n\\end{table*}\n\nWe aim to create datasets for NLP tasks in the Ladin language by translating \\textit{D\\textsubscript{Ita\\_SA}} and \\textit{D\\textsubscript{Ita\\_MCQA}} from Italian data \\textit{D\\textsubscript{Ita}} to Ladin data \\textit{D\\textsubscript{Lad}}. These translated datasets serve multiple purposes, including translation (Italian–Ladin pairs), text classification, and question answering tasks. To ensure high-quality translation, we first select the best-performing MT model—identified in the previous section based on its performance on a held-out testing data \\( T \\), and use this model to translate \\textit{D\\textsubscript{Ita}} into \\textit{D\\textsubscript{Lad}}. The creation of this synthetic dataset shown in Figure~\\ref{fig:experiments} involves several key steps, as described below.\n\n\\noindent\\textbf{Italian-to-Ladin translation.} We begin by translating the labeled monolingual Italian datasets \\textit{D\\textsubscript{Ita}} of SA and MCQA tasks into Ladin, resulting in \\textit{D\\textsubscript{Lad}}. This translation process is carried out using the best-performing MT model identified in our evaluation, ensuring the highest possible quality of the synthetic Ladin data.\n\n\\noindent\\textbf{Filtering I.} To ensure the semantic quality of the Italian → Ladin translations, we apply a filtering step using similarity scores computed by the Language-Agnostic BERT Sentence Embedding (LaBSE) model \\citep{labse:22}. This step evaluates the alignment between each translated Ladin sentence and its original Italian counterpart. Specifically, we retain only those sentence pairs with a cosine similarity score \\( c \\geq 0.68 \\), which corresponds to the average similarity observed in the aligned dataset \\textit{AD\\textsubscript{Ita\\_Lad}}. This threshold helps eliminate semantically inconsistent translations while preserving high-quality aligned pairs for downstream tasks.\n\n\\noindent\\textbf{Back-translation.} We employ back-translation to further refine the synthetic dataset prior to conducting a second round of filtering. Specifically, the Ladin translations \\( D\\textsubscript{\\textit{Lad}} \\) are retranslated into Italian, yielding \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\), which are then compared against the original Italian datasets \\( D\\textsubscript{Ita} \\). This step helps identify and discard translations that deviate significantly from the original semantics, thereby improving data quality.\n\n\\noindent\\textbf{Filtering II.} To finalize the synthetic dataset, we apply a second filtering step based on automatic evaluation metrics. Specifically, we compute the Sacre BLEU and METEOR scores between the original Italian data (\\( D\\textsubscript{\\textit{Ita}} \\) and the back-translated Italian data \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)). A translation instance is retained if \n\\( BLEU \\)(\\( D\\textsubscript{\\textit{Ita}} \\), \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)) \\(\\geq \\mu{BLEU} \\) \nand \n\\( METEOR \\)(\\( D\\textsubscript{\\textit{Ita}} \\), \\( D^{\\prime}\\textsubscript{\\textit{Ita}} \\)) \\(\\geq \\mu{METEOR} \\).\nwhere \\( \\mu{BLEU} \\) and \\( \\mu{METEOR} \\) represent the average scores computed across all translation pairs. These threshold values ensure semantic fidelity and fluency by eliminating noise and inaccuracy, thus improving the quality of the synthetic dataset.\n\n\\subsection{Synthetic data evaluation}\n\nTo evaluate the quality and impact of the Italian–Ladin synthetic parallel dataset \\textit{SD\\textsubscript{Ita\\_Lad}} = {(\\textit{D\\textsubscript{Ita\\_SA}}, \\textit{D\\textsubscript{Lad\\_SA}}), (\\textit{D\\textsubscript{Ita\\_MCQA}}, \\textit{D\\textsubscript{Lad\\_MCQA}})}, we combine it with the authentic dataset \\textit{AD\\textsubscript{Ita\\_Lad}} and assess performance on the testing data \\( T \\). This setup allows us to measure the effect of synthetic data augmentation on translation quality. To assess lexical and syntactic adequacy of the synthetic translations, we construct a manually translated gold dataset \\( GD \\)%\\footnote{Datasets will be released upon publication under an open license (CC BY-NC 4.0).}\n, containing 50 examples each from \\textit{D\\textsubscript{Ita\\_SA}} and \\textit{D\\textsubscript{Ita\\_MCQA}}, translated into Ladin by a native speaker of Italian and Ladin. We compute cosine similarity between the synthetic and gold translations using sentence embeddings, providing a measure of semantic alignment.% Additionally, we adopt the error typology from the Multidimensional Quality Metrics (MQM) framework as qualitative analysis \\cite{MQM}, selecting a subset of high-level error dimensions to examine the strengths and limitations of the translation outputs. Specifically, we focus on three dimensions, accuracy, linguistic conventions, and terminology, drawn from the full set defined in the MQM core typology\\cite{MQM24}, based on their relevance to our task and the constraints of our annotation process.\n\n\\section{Results and Discussion}\nIn this section, we report the results of MT using the existing Italian–Ladin parallel data. We then present the evaluation of the synthetic Ladin datasets for SA and MCQA, including both quantitative metrics and qualitative analysis.\n\n\\begin{table*}[!t]\n \\centering\n \\small\n \\begin{tabular}{llccccccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-11} &\n & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n & 5.12 & 2.45 & 1.03 & 22.87 & 19.00 & 13.56 & 27.36 \n & 26.00 & 16.92 \\\\\n & FSL-Llama 3.1 70B \n & 8.43 & 7.66 & 2.96 & 35.49 & 33.85 & 26.09 & 35.05 \n & 35.05 & 23.17 \\\\\n & FSL-GPT-4o \n & 6.62 & 4.15 & 2.03 & 30.18 & 26.04 & 21.36 & 31.90 \n & 30.08 & 20.42 \\\\\n & FT-Llama 3.1 8B \n & 12.70 & 9.79 & 9.64 & 43.20 & 40.03 & 41.44 & 38.11 \n & 36.60 & 30.98 \\\\\n & FT-Llama 3.1 70B \n & 9.41 & 7.75 & 3.70 & 36.83 & 34.60 & 27.47 & 36.03 \n & 35.87 & 23.99 \\\\\n & Mbart-large-50 \n & 11.28 & 11.34 & 11.93 & 43.56 & 42.75 & 46.12 & 39.8 \n & 38.66 & 35.23 \\\\\n & NLLB 1.3 B \n & \\underline{18.54} & \\underline{16.85} & \\underline{17.88} & \\textbf{51.59} & \\underline{51.55} & \\underline{55.29} & \\textbf{46.24}\n & \\underline{45.98} & \\underline{41.58} \\\\\n & Benchmark (LLM) \n & 5.54 & 3.84 & 1.16 & - & - & - & 29.03 \n & 28.98 & 18.60 \\\\\n\\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B \n & 18.30 & 17.69 & \\textbf{18.29} & 51.40 & \\textbf{52.92} & \\textbf{56.65} & 45.44 \n & 46.28 & \\textbf{42.15} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & \\textbf{20.93} & \\textbf{19.32} & 16.65 & - & - & - & \\textbf{47.65} & \\textbf{46.58} & 38.16 \\\\\\\\ \n \\hline\n \\end{tabular}\n \\caption{\\label{add-trans_to_ladin}\n Translation performance of various models for Italian → Ladin across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n }\n\\end{table*}\n\n\\begin{table*}[!t]\n \\centering\n \\small\n \\begin{tabular}{llccccccccc}\n \\hline\n \\textbf{Training Data} & \\textbf{Model} \n & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n & \\multicolumn{3}{c}{\\textbf{chrF++}} \\\\\n \\cline{3-11} &\n & \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} &\n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} & \n \\textbf{\\boldmath\\( t_1 \\)} & \\textbf{\\boldmath\\( t_2 \\)} & \\textbf{\\boldmath\\( t_3 \\)} \\\\\n \\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} & FSL-Llama 3.1 8B \n & 19.25 & 12.74 & 4.27 & 50.09 & 38.71 & 21.56 & 46.30 \n & 38.89 & 23.41 \\\\\n & FSL-Llama 3.1 70B \n & 30.07 & 21.55 & 14.29 & 62.16 & 51.60 & 39.51 & 56.22 \n & 48.66 & 36.91 \\\\\n & FSL-GPT-4o \n & 29.23 & 23.38 & 15.90 & 61.39 & \\textbf{53.37} & 42.07 & 55.73 \n & 50.33 & 38.64 \\\\\n & FT-Llama 3.1 8B \n & 20.53 & 17.25 & 8.05 & 51.86 & 44.85 & 34.62 & 48.36 \n & 44.11 & 33.66 \\\\\n & FT-Llama 3.1 70B \n & \\textbf{30.78} & \\textbf{23.65} & 13.02 & \\textbf{61.91} & 52.10 & 38.29 & \\textbf{57.23} \n & \\underline{50.53} & 36.12 \\\\\n & Mbart-large-50 \n & 11.95 & 12.81 & 11.84 & 40.15 & 42.97 & 41.12 & 41.11 \n & 42.15 & 36.81 \\\\\n & NLLB 1.3 B \n & 27.15 & 19.77 & \\underline{17.31} & 55.54 & 48.27 & \\underline{46.03} & 54.45\n & 49.66 & \\underline{41.09} \\\\\n & Benchmark (LLM) \n & 26.77 & 21.17 & 10.37 & - & - & - & 53.20 \n & 48.52 & 32.36 \\\\\n\\hline\n \\textit{AD\\textsubscript{Ita\\_Lad}} + \\textit{SD\\textsubscript{Ita\\_Lad}} \n & FT-NLLB 1.3 B \n & \\underline{30.46} & \\underline{22.71} & \\textbf{20.33} & 58.11 & 50.71 & \\textbf{49.11} & \\underline{56.95} \n & \\textbf{51.49} & \\textbf{43.83} \n \\\\\n \\rule{0pt}{5.2ex} \n \\shortstack[l]{\\textit{AD\\textsubscript{Ita\\_Lad}} +\\\\monolingual data} \n & \\shortstack[l]{Benchmark\\\\(RBMT)} \n & 21.36 & 20.27 & 16.34 & - & - & - & 50.24 \n & 49.08 & 40.76 \\\\\\\\ \n \\hline\n \\end{tabular}\n \\caption{\\label{add-trans_to_italian}\n Translation performance of various models for Ladin → Italian across three test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\). The table is divided into two sections: the upper section reports results using only authentic training data \\textit{AD\\textsubscript{Ita\\_Lad}}, while the lower section presents results with additional synthetic data.\n }\n\\end{table*}\n\n\\subsection{Machine translation of Italian and Ladin}\nTable~\\ref{translation-performance} presents the translation performance results for both Italian → Ladin and Ladin → Italian across diverse language model configurations. For experiments using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data, we report results from the benchmark approach proposed by \\citet{frontull24}, which employs the LLM \\verb|GPT-3.5-turbo-0125|, for comparison purposes. %This detailed evaluation not only highlights the effectiveness of different model settings but also underscores the challenges and opportunities in machine translation for LRL pairs.We also present the detailed results of the experimental results across various scenarios.\nWhile Table~\\ref{translation-performance} presents the overall average performance metrics of each translation model evaluated on the testing data \\( T \\), Tables~\\ref{add-trans_to_ladin} and~\\ref{add-trans_to_italian} offer a more fine-grained analysis. They report detailed metric scores for the individual test subsets \\( t_1 \\), \\( t_2 \\), and \\( t_3 \\), allowing for a closer examination of model behavior across different data segments.\n\nIn both translation directions in Table~\\ref{translation-performance}, the fine-tuned NLLB (FT-NLLB) model achieves significant performance across evaluation metrics. Specifically, the model performs best on the translation from Italian → Ladin, with a BLEU score approaching 18, indicating relatively good translation accuracy for extremely low-resource settings. Although the Ladin → Italian translation performance of the FT-NLLB model slightly lags behind that of the FT-LLaMA 3.1 70B model, the FT-NLLB model achieves the highest chrF++ scores in both translation directions, indicating superior overall translation quality. These findings underscore a persistent challenge in extremely low-resource NLP. Despite the impressive capabilities of LLMs, their performance often suffers in extremely low-resource scenarios due to training biases toward HRLs with abundant data. Consequently, the Ladin → Italian translation achieves higher BLEU scores, reflecting the model’s stronger proficiency in HRLs. \n\nAlthough Ladin and Italian both belong to the Romance language family, translation into Ladin remains challenging due to its status as the extremely low-resource language, including unique vocabulary, dialectal variations, and a lack of direct equivalence to Italian. In contrast, the NLLB model demonstrates relatively robust performance, likely benefiting from its multilingual training across 200+ languages, including over 150 LRLs \\citep{nllb2022}. Notably, the NLLB model was trained on Friulian, a closely related Raeto-Romance language \\citep{UNESCO}, which may contribute to its improved generalization on Ladin.\n\nAdditionally, we evaluate the suitability and effectiveness of the NLLB tokenizer for processing Ladin text. Our analysis reveals an average tokens-per-word ratio of 1.50 for Ladin, compared to 1.39 for Italian. This modest overhead indicates that the NLLB tokenizer segments Ladin reasonably well, despite the language's extremely low-resource status, suggesting its viability for downstream translation tasks.\n\n\\subsection{Qualitative error analysis}\n\n\\begin{table}[t]\n \\small\n \\centering\n \\makebox[3.1in][r]{\n \\begin{tabular}{lcc}\n \\hline\n \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n & \\textbf{Italian} & \\textbf{Ladin} \\\\\n \\hline\n Average number of words per entry & 65 & 70 \\\\\n Average number of characters per entry & 144 & 348 \\\\\n Positive label count & 9,842 & 9,842 \\\\\n Negative label count & 2,669 & 2,669 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SD-SA}\n Summary statistics of the synthetic paired sentiment analysis dataset in Italian and Ladin.\n }\n\\end{table}\n\nTo assess the qualitative aspects of translation performance using the FT-NLLB model, we analyze specific examples of translation errors from Italian to Ladin. This analysis helps identify common error types—such as lexical inaccuracies, syntactic issues, and morphological mismatches—and provides insight into the strengths and limitations of the machine-generated translations. For instance, consider the following sentence pair, where the Ladin translation is largely faithful to the Italian source, successfully preserving both structure and meaning.\n\n\\textbf{Italian}: \\textit{Sono stata a un congresso a Torino e ho passato due notti al Best Western Crystal Palace, un hotel 4 stelle di fianco alla stazione di Porta Nuova. Ho apprezzato molto la vasca idromassaggio e il giornale ogni giorno: La Stampa, con un foglio di sintesi degli argomenti principali.}\n\n\\textbf{Ladin}: \\textit{I sun stada a n congres a Torin y i à sté döes nöts tl Best Western Crystal Palace, n hotel da 4 stëres dlungia la staziun de Porta Nuova. I á dër aprijé la vasca da iade y le foliet da vigni de: La Stampa, cun na plata de ressumé di argomënc prinzipai.}\n\nUpon closer inspection above, the Ladin translation only exhibits minor grammatical and lexical inaccuracies. The phrase “\\textit{I á sté döes nöts}” should be corrected to “\\textit{I sun stada döes nöts}” to ensure grammatical correctness. Additionally, “\\textit{la vasca da iade}” ought to be revised to “\\textit{la vasca idromassaje}” to more accurately reflect the original Italian phrase “\\textit{la vasca idromassaggio}.” These examples illustrate the model’s general ability to produce semantically faithful translations, while also highlighting areas where linguistic precision can be improved. Overall, the model demonstrates strong potential for handling Ladin.\n\n\\subsection{Ladin synthetic datasets}\n\n\\begin{table}[t]\n \\centering\n \\small\n \\makebox[3.2in][r]{\n \\begin{tabular}{lcc}\n \\hline\n \\textbf{Feature} & \\multicolumn{2}{c}{\\textbf{Language}} \\\\\n & \\textbf{Italian} & \\textbf{Ladin} \\\\\n \\hline\n Average number of words per question & 18 & 19 \\\\\n Average number of characters per question & 108 & 97 \\\\\n Average number of words per choices & 28 & 30 \\\\\n Average number of characters per choices & 187 & 174 \\\\\n Frequency of entries with 3 choices & 304 & 304 \\\\\n Frequency of entries with 4 choices & 196 & 196 \\\\\n Frequency of entries with 5 choices & 264 & 264 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SD-MCQA}\n Statistics of the synthetic paired MCQA dataset in Italian and Ladin.\n }\n\\end{table}\n\n\\begin{table*}[t]\n \\centering\n \\small\n \\makebox[\\textwidth]{\n \\begin{tabular}{lcccc@{\\hspace{2em}}cccc}\n \\hline\n \\textbf{Model} &\n \\multicolumn{4}{c}{\\textbf{Ladin}} &\n \\multicolumn{4}{c}{\\textbf{Italian}} \\\\\n \\cline{2-9}\n & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}}\n & \\multicolumn{2}{c}{\\textbf{SA}} & \\multicolumn{2}{c}{\\textbf{MCQA}} \\\\\n \n & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1}\n & \\textbf{Acc} & \\textbf{F1} & \\textbf{Acc} & \\textbf{F1} \\\\\n \\hline\n FSL-LLaMA & 93.99 & 96.07 & 44.20 & 44.46\n & 97.92 & 98.18 & 54.79 & 54.18 \\\\\n m-DistilBERT & 92.28 & 95.03 & 36.66 & 36.69 \n & 94.78 & 96.41 & 30.73 & 30.29 \\\\\n XLM-RoBERTa & 80.15 & 84.81 & 25.21 & 25.80 \n & 97.14 & 98.08 & 26.14 & 26.14 \\\\\n mT5 & 50.09 & 69.37 & 23.50 & 23.16 \n & 49.98 & 69.25 & 22.62 & 21.92 \\\\\n \\hline\n \\end{tabular}\n }\n \\caption{\\label{SA-MCQA} \n Results for SA and MCQA tasks in Ladin, with Italian included for comparison.\n } \n\\end{table*}\n\nSince the FT-NLLB model demonstrates the best performance for translation in our experiments using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data, we utilize this model to translate \\textit{D\\textsubscript{Ita}} into \\textit{D\\textsubscript{Lad}} through the framework shown in Figure~\\ref{fig:experiments}.\nInitially, we obtained 30,477 paired entries for (\\textit{D\\textsubscript{Ita\\_SA}}, \\textit{D\\textsubscript{Lad\\_SA}}) as the SA dataset after applying the first filtering step based on cosine similarity between Italian and Ladin with the threshold of 0.68. This value is derived from the cosine similarity between both languages in \\textit{AD\\textsubscript{Ita\\_Lad}}. Subsequently, we perform back-translation from \\textit{D\\textsubscript{Lad\\_SA}} to \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_SA}}\\). The threshold for the second filtering step is determined based on the average (\\(\\mu\\)) BLEU and METEOR scores calculated for each entry by comparing \\textit{D\\textsubscript{Ita\\_SA}} with \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_SA}}\\). These scores were found to be 33.63 and 0.58, respectively. The final filtered synthetic SA dataset, consisting of 12,511 entries, statistically is detailed in Table~\\ref{SD-SA}. This SA dataset contains an average of 65 and 70 words per entry for Italian and Ladin, respectively. Additionally, the majority of entries in the final dataset—over 9,000 instances—are labeled with positive sentiment.\n\nConcurrently, we obtained 4,651 paired entries of (\\textit{D\\textsubscript{Ita\\_MCQA}}, \\textit{D\\textsubscript{Lad\\_MCQA}}) as the MCQA dataset, following an initial filtering step based on cosine similarity, similar to the procedure used for the synthetic SA dataset. The thresholds for the second filtering step are also determined using the average BLEU and METEOR scores calculated between \\textit{D\\textsubscript{Ita\\_MCQA}} and \\( D^{\\prime}\\textsubscript{\\textit{Ita\\_MCQA}}\\), which are 36.58 and 0.62, respectively. The final filtered synthetic MCQA dataset, comprising 764 entries, is presented in Table~\\ref{SD-MCQA}, with the majority of questions featuring three answer choices. Notably, both Italian-Ladin paired datasets of SA and MCQA tasks exhibit a higher average number of words and characters per entry compared to the authentic parallel dataset \\textit{AD\\textsubscript{Ita\\_Lad}}. \n\n\\subsection{Synthetic data assessment for NLP tasks}\n\nAfter obtaining the new synthetic datasets \\textit{SD\\textsubscript{Ita\\_Lad}}%\\footnote{Datasets and codes will be released after paper publication under an open license (CC BY-NC 4.0).}\n, we compare them against the manually translated golden dataset \n\\( GD \\) to evaluate translation quality. Specifically, we use cosine similarity metrics to evaluate the semantic alignment between the synthetic and manually created data. The cosine similarity scores of \\textit{SD\\textsubscript{Ita\\_Lad}} and \\( GD \\), with respect to \\textit{AD\\textsubscript{Ita\\_Lad}}, are 86.61 and 85.75, respectively. These results indicate a high degree of semantic consistency and minimal disparity between the synthetic and human-translated datasets.\n\nSubsequently, we combine \\textit{SD\\textsubscript{Ita\\_Lad}} with \\textit{AD\\textsubscript{Ita\\_Lad}} to construct the training data for fine-tuning the FT-NLLB model as the MT model. The testing data \\( T \\) is then used to evaluate the performance of the resulting translation model on these combined datasets, as shown in the lower section of Table ~\\ref{translation-performance}. Detailed results for the three subsets (\\( t_1 \\), \\( t_2 \\), and \\( t_3 \\)) of \\( T \\) are also presented in the lower section of Tables~\\ref{add-trans_to_ladin} and~\\ref{add-trans_to_italian}. We compare our results with the augmented synthetic translations generated by the RBMT system proposed by \\citet{frontull24}, which incorporates additional monolingual data in both Ladin and Italian. As summarized in Table~\\ref{translation-performance}, experimental results demonstrate that incorporating our synthetic data consistently improves performance across all evaluation metrics, surpassing the previous benchmark. In both translation directions, the FT-NLLB model performs well compared to its counterpart model.\n\nGiven that \\textit{SD\\textsubscript{Ita\\_Lad}} encompasses SA and MCQA tasks in Ladin, we establish a benchmark to evaluate model performance on these tasks. We adopt the few-shot learning (FSL) using LLaMA 3.1 70B as our LLM's approach. Appendices~\\ref{sec:fsl-sa} and~\\ref{sec:fsl-mcqa} provide example prompts used in the FSL approach. In parallel, we assess the performance of several transformer-based models, including the Distilbert-base-multilingual-cased (m-DistilBERT)\nmodel, the XLM-RoBERTa base model, and the mT5-small model. Table~\\ref{SA-MCQA} summarizes the results for SA and MCQA tasks in Ladin, with Italian results included for comparison. The LLM-based approach achieves the highest scores in both tasks in terms of balanced accuracy (Acc) and F1-score (F1), although the improvements over other models are marginal. m-DistilBERT also performs well across both tasks. Specifically, the results indicate that the SA dataset in Ladin is generally well-handled by the evaluated models, with the exception of mT5. This indicates that our created Ladin SA dataset is sufficiently informative and well-aligned with the task objectives to support effective model training. In contrast, performance on the MCQA task remains low across all models, even when evaluated on Italian data. This suggests that the MCQA task is inherently more challenging than the SA task. The difficulty may be attributed to the limited size of the MCQA dataset and the broad topical coverage of the questions, both of which may hinder model generalization.\n\n\\section{Conclusions and Future Work}\nIn this work, we explore various strategies for translating Ladin—an extremely low-resource language—and demonstrate that our NLLB-based model consistently outperforms counterpart models. Beyond translation, we introduce the first comprehensive Ladin benchmark dataset covering machine translation, sentiment analysis, and multiple-choice question answering, all derived through synthetic augmentation from monolingual Italian resources. \n\nOur evaluation shows that while synthetic data enables competitive performance across tasks further progress is needed to enhance knowledge transfer from high-resource to low-resource languages. This study lays foundational work for future NLP research on Ladin and similarly underrepresented languages. \n\nFuture work will investigate knowledge distillation techniques to more effectively transfer knowledge from high-resource languages to low-resource ones, as well as explore advanced methods to better exploit available monolingual Ladin data for improved model performance. We are also committed to further foster developments of Ladin resources and to engaging community in actively researching this language by establishing leaderboards based on the created datasets.\n\n\\section*{Limitations}\n\nThe Ladin-Italian dataset used in this study primarily consists of short sentences, which may limit the generalizability of the models to longer and more complex sentence structures. Moreover, the limited availability of manually crafted monolingual Italian MCQA datasets restricts the number of usable samples, which may impact the robustness and reliability of the experimental results. \n\n%\\section*{Acknowledgments}\n\n%This document has been adapted\n\n\n% Bibliography entries for the entire Anthology, followed by custom entries\n%\\bibliography{anthology,custom}\n% Custom bibliography entries only\n\\bibliography{custom}\n\n\\appendix\n\\section{Additional Experimental Results}\n\\label{sec:add-results}\nThis section presents detailed experimental results for machine translation performance using \\textit{AD\\textsubscript{Ita\\_Lad}} as the sole training data, as reported in the upper section of Table~\\ref{translation-performance}. Figure~\\ref{fig:chrf_AD} illustrates the chrF++ scores achieved by various models, while Figure~\\ref{fig:bleu_AD} presents the corresponding BLEU score comparisons. \n\n\\section{Back-translation Results}\nAs illustrated in Figure~\\ref{fig:experiments}, we perform a second round of filtering by back-translating Ladin data into Italian and evaluating the results using BLEU and METEOR scores. For the SA dataset, which contains 30,477 samples, the average BLEU and METEOR scores are 33.63 and 0.58, respectively. In the case of the MCQA dataset (4,651 samples), the corresponding averages are 36.58 and 0.62. Below, we present examples comparing back-translated Italian samples with their original counterparts to facilitate a more detailed analysis.\n\n\\section{A Few-shot Learning Prompt Template in the MT task}\n\\label{sec:fsl}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Here are examples of translations in a JSON \nformat between Italian and Ladin with the \nVal Badia variant:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n{\n \"translations\": [\n {\n \"Italian\": \"è venuta la mia ora\",\n \"Ladin\": \"al é gnü mia ora\"\n },\n {\n \"Italian\": \"vado dalle cugine!\",\n \"Ladin\": \"i vá dales jormanes\"\n },\n {\n \"Italian\": \"staccare la luce\",\n \"Ladin\": \"destodé la löm\"\n },\n ...\n {\n \"Italian\": \"a ottobre inoltrato\",\n \"Ladin\": \"d'otober fora\"\n }\n ]\n }\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}Please provide the translation of the fol-\nlowing 15 entries in the JSON format, fill-\ning the empty 'Ladin' fields for each entry.\nDo not include any additional explanations \nor text:\n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n{\n \"translations\": [\n {\n \"Italian\": \"imprimere nella mente\",\n \"Ladin\": \"\"\n },\n {\n \"Italian\": \"temperare la matita\",\n \"Ladin\": \"\"\n },\n {\n \"Italian\": \"mettere paura a qcn.\",\n \"Ladin\": \"\"\n },\n ...\n {\n \"Italian\": \"un animale scattante\",\n \"Ladin\": \"\"\n }\n ]\n }\n\\end{verbatim}\n\n\\section{A Few-shot Learning Prompt Template in the SA task}\n\\label{sec:fsl-sa}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Below are Tripadvisor reviews in Ladin (Val\nBadia variant) along with their sentiment \nlabels:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n {\n[review: \"I sun stá chiló por 7 nes. Le gost\né é bun. Porimpó é i chelins cherdá indormed\ní pormal. ...\", label: 1], [review: \"Lalber\nch é bunorté te na zona chîta dlungia na plaz\na. Gní zoruch vigni sëra ê sciöche ciafé nao\nasa. ...\" label: 0], \n...\n[review: \"I un passé chiló n bel fin dledema\nhotel nët, personal da orëi bun, bun ince le\ngosté y na posiziun ezelënta, impormó do lab\nela plaza San Marco. ...\", label: 0]\n }\n\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}\nPlease classify the sentiment for the follo\nwing 10 Tripadvisor reviews in Ladin (Val \nBadia variant) as either 0 (Positive) or 1\n(Negative). Fill in the empty 'label' field\ns with only 0 or 1. Respond with the sentime\nnt labels in list format like this: [x, x, \n...]. Do not include any additional explana\ntions or text.\n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n {\n[review: \"Por na vistada y na fuga a Milan \n(na mostra, na cörta vijita, na spazirada)\nél perfet. ...\", label: ], [review: \"Le bru\nnch ne joav nia le prisc. Lhotel é n pü' dal\nunc dal Duomo. ...\", label: ], \n...\n[review: \"Rezeziun ezelënta, dantadöt le \nconcierje cun sües racomanaziuns. ...\", \nlabel: ]\n } \n\\end{verbatim}\n\n\\section{A Few-shot Learning Prompt Template in the MCQA task}\n\\label{sec:fsl-mcqa}\n% Switching to one-column for JSON content\n\\noindent\\begin{verbatim}Below are multiple-choice questions in Lad\nin (Val Badia variant) with 3, 4, or 5 answer \nchoices. The correct answer is explicitly pr\novided as an id number corresponding to the \norder of the choices:\n\\end{verbatim}\n\n% JSON content (formatted in monospaced font with verbatim)\n\\noindent\\begin{verbatim}\n {\n[question: aladô dla lege 241/1990, olá é pa \nmetüda sö la comisciun por l'azes ai documën\nc aministratifs?, choices: ['pro la Presidën\nza dl Consei di Minisć', 'Por vigni Entité pu\nblica dl post', 'pro vigni Entité publica eco\nnomica de competënza regionala'], answer: 0]\n, [question: aladô dla DGR 514/2009, por PAI \ny PEI se intendi rispetivamënter:, choices: \n[\"Plan d'Assistënza Indicisé y Program Etich \nIndividualisé\", 'Program de Asistënza Indivi\nduala y Program Educatif Individualisé', \"Pl\nan d' Assistënza Individualisé y Plan d'Educ\naziun Individualisé\"], answer: 2],\n...\n[question: aladô de REICAT l'intestaziun uni\nforme por na porsona:, choices: ['al corespo\ngn tresala forma dl inom che vëgn dant tla pr\nöma ediziundles operes dl autur.', 'al se ba\nsa söl inom cun chël che la porsona medema é\ngeneralmente identifiada.', 'ara ne pó mai e\nster metüda adöm da npseudonom.'], answer: 1]\n }\n\\end{verbatim}\n\n\\noindent\\begin{verbatim}Please answer the questions based on the ava\nilable choices, by filling in the empty 'answ\ner' fields with the id number corresponding to\nthe order of the choices. Provide the answers \nin a list format like this: [x, x, x, ..., x].\nDo not include any additional explanations or\ntext. \n\\end{verbatim}\n\n\n% JSON template for user input\n\n\\noindent\\begin{verbatim}\n {\n[question: na coleziun de figurines é metüda\nadöm da 84 toc, 14 por vigni contignidú. 7 fi\ngurines de vigni contignidú é lamincards, i \nrestanc fotocartes. Tan de figurines de fo to\ncartes ál pa la coleziun?, choices: ['42', '43'\n, '44'], answer:], \n...\n, [question: ci frasa, danter chëses listi\ngades, á pa n complemënt de gauja?, choices:\n['Laura é piada demez por n iade de plajëi',\n'i ápormó cumpré na scincunda por le compliann\nde Marco', \"por na taiada de strom s'á ascensur\nbloché\"], answer: ]\n }\n\\end{verbatim}\n\n\\clearpage % Force the figure to go on its own page\n\\begin{figure*}[tp]\n \\centering\n \\includegraphics[width=6.5in]{latex/chrf_scores_acl.pdf}\n \\caption{chrF++ scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n \\label{fig:chrf_AD}\n\\end{figure*}\n\n\\begin{figure*}[tp]\n \\centering\n \\includegraphics[width=6.5in]{latex/bleu_scores_acl.pdf}\n \\caption{BLEU scores of the models using \\textit{AD\\textsubscript{Ita\\_Lad}} as the training data}\n \\label{fig:bleu_AD}\n\\end{figure*}\n\n\\end{document}\n"},"question":{"kind":"string","value":"If we take all the values across the table for NLLB 1.3B and formulate an polynomial regression function with the last term being the constant, what is the degree of the polynomial function?"},"answer":{"kind":"string","value":"8"},"plan":{"kind":"string","value":"SELECT all numeric values for model NLLB 1.3 B\nCOMPUTE term_count = number of selected values\nCOMPUTE degree = term_count - 1\nRETURN degree\n"}}},{"rowIdx":362,"cells":{"paper":{"kind":"string","value":"2510.21604"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[h]\n"," \\centering\n"," \\caption{Performance Comparison of LLMs on BizFinBench~\\citep{lu2025bizfinbench0}. The colors represent the top three performers for each task: \\colorbox{golden}{golden} indicates the top-performing model, \\colorbox{lightblue}{silver} represents the second-best result, and \\colorbox{lightgreen}{bronze} denotes the third-best performance.}\n"," \\resizebox{\\textwidth}{!}{%\n"," \\begin{threeparttable}\n"," \\begin{tabular}{lrrrrrrrrrr}\n"," \\toprule\n"," \\multicolumn{1}{c}{Model~\\tnote{$\\dagger$}} & \\multicolumn{1}{c}{AEA} & \\multicolumn{1}{c}{FNC} & \\multicolumn{1}{c}{FTR} & \\multicolumn{1}{c}{FTU} & \\multicolumn{1}{c}{FQA} & \\multicolumn{1}{c}{FDD} & \\multicolumn{1}{c}{ER} & \\multicolumn{1}{c}{SP} & \\multicolumn{1}{c}{FNER} & \\multicolumn{1}{c}{Average}\\\\\n"," \\midrule\n"," \\multicolumn{11}{c}{Closed-Source LLMs} \\\\\n"," ChatGPT-o3 & \\cellcolor{lightblue}86.23 & 61.30 & \\cellcolor{lightblue}75.36 & \\cellcolor{golden}89.15 & \\cellcolor{golden}91.25 & \\cellcolor{lightgreen}98.55 & 44.48 & 53.27 & 65.13 & \\cellcolor{golden}73.86 \\\\\n"," ChatGPT-o4-mini & \\cellcolor{lightgreen}85.62 & 60.10 & 71.23 & 74.40 & \\cellcolor{lightgreen}90.27 & 95.73 & \\cellcolor{golden}47.67 & 52.32 & 64.24 & \\cellcolor{lightgreen}71.29 \\\\\n"," GPT-4o & 79.42 & 56.51 & \\cellcolor{golden}76.20 & 82.37 & 87.79 & \\cellcolor{golden}98.84 & 45.33 & 54.33 & \\cellcolor{lightgreen}65.37 & \\cellcolor{lightblue}71.80 \\\\\n"," Gemini-2.0-Flash & \\cellcolor{golden}86.94 & 62.67 & \\cellcolor{lightgreen}73.97 & 82.55 & \\cellcolor{lightblue}90.29 & \\cellcolor{lightblue}98.62 & 22.17 & \\cellcolor{golden}56.14 & 54.43 & 69.75 \\\\\n"," Claude-3.5-Sonnet & 84.68 & \\cellcolor{lightgreen}63.18 & 42.81 & \\cellcolor{lightblue}88.05 & 87.35 & 96.85 & 16.67 & 47.60 & 63.09 & 65.59 \\\\\n"," \\midrule\n"," \\multicolumn{11}{c}{Open-Weight LLMs} \\\\\n"," Qwen3-14B & 84.20 & 58.20 & 65.80 & 82.19 & 84.12 & 92.91 & 33.00 & 52.31 & 50.70 & 67.05 \\\\\n"," Qwen3-32B & 83.80 & 59.60 & 64.60 & 85.12 & 85.43 & 95.37 & 39.00 & 52.26 & 49.19 & 68.26 \\\\\n"," DeepSeek\\_R1\\_14B\\_Instruct~\\tnote{1} & 71.33 & 44.35 & 50.45 & 81.96 & 85.52 & 92.81 & 39.50 & 50.20 & 52.76 & 59.49 \\\\\n"," DeepSeek\\_R1\\_32B\\_Instruct~\\tnote{1} & 73.68 & 51.20 & 50.86 & 83.27 & 87.54 & 97.81 & 41.50 & 53.92 & 56.80 & 66.29 \\\\\n"," \\midrule\n"," \\multicolumn{11}{c}{Our LLMs} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT~\\tnote{2} & \\cellcolor{Background1}80.63 & \\cellcolor{Background1}51.67 & \\cellcolor{Background1}52.61 & \\cellcolor{Background1}83.53 & \\cellcolor{Background1}89.05 & \\cellcolor{Background1}96.72 & \\cellcolor{Background1}36.68 & \\cellcolor{Background1}50.43 & \\cellcolor{Background1}50.85 & \\cellcolor{Background1}65.36 \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+9.25} & \\textcolor{GREEN}{+7.28} & \\textcolor{GREEN}{+2.19} & \\textcolor{GREEN}{+1.53} & \\textcolor{GREEN}{+3.42} & \\textcolor{GREEN}{+3.85} & \\textcolor{RED}{-2.93} & \\textcolor{GREEN}{+0.24} & \\textcolor{RED}{-1.92} & \\textcolor{GREEN}{+5.83} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT\\_GRPO~\\tnote{2} & \\cellcolor{Background1}81.46 & \\cellcolor{Background1}52.41 & \\cellcolor{Background1}53.47 & \\cellcolor{Background1}83.57 & \\cellcolor{Background1}89.02 & \\cellcolor{Background1}95.58 & \\cellcolor{Background1}36.83 & \\cellcolor{Background1}54.06 & \\cellcolor{Background1}51.24 & \\cellcolor{Background1}66.92 \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+10.03} & \\textcolor{GREEN}{+8.09} & \\textcolor{GREEN}{+2.91} & \\textcolor{GREEN}{+1.64} & \\textcolor{GREEN}{+3.45} & \\textcolor{GREEN}{+2.63} & \\textcolor{RED}{-2.74} & \\textcolor{GREEN}{+3.82} & \\textcolor{RED}{-1.53} & \\textcolor{GREEN}{+7.46} \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.82} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+0.81} & \\textcolor{GREEN}{+0.06} & 0.00 & \\textcolor{RED}{-1.23} & \\textcolor{GREEN}{+0.25} & \\textcolor{GREEN}{+3.63} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.53} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT & \\cellcolor{Background1}80.45 & \\cellcolor{lightblue}66.42 & \\cellcolor{Background1}63.28 & \\cellcolor{lightgreen}86.88 & \\cellcolor{Background1}88.43 & \\cellcolor{Background1}93.76 & \\cellcolor{lightblue}46.05 & \\cellcolor{lightblue}55.27 & \\cellcolor{golden}68.41 & \\cellcolor{Background1}70.08 \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+6.75} & \\textcolor{GREEN}{+15.23} & \\textcolor{GREEN}{+12.37} & \\textcolor{GREEN}{+3.64} & \\textcolor{GREEN}{+0.83} & \\textcolor{RED}{-4.14} & \\textcolor{GREEN}{+4.52} & \\textcolor{GREEN}{+1.25} & \\textcolor{GREEN}{+11.63} & \\textcolor{GREEN}{+3.75} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT\\_GRPO & \\cellcolor{Background1}80.67 & \\cellcolor{golden}66.83 & \\cellcolor{Background1}64.45 & \\cellcolor{Background1}86.79 & \\cellcolor{Background1}88.52 & \\cellcolor{Background1}91.26 & \\cellcolor{lightgreen}45.68 & \\cellcolor{lightgreen}54.83 & \\cellcolor{lightblue}67.75 & \\cellcolor{Background1}70.44 \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+6.95} & \\textcolor{GREEN}{+15.62} & \\textcolor{GREEN}{+13.57} & \\textcolor{GREEN}{+3.55} & \\textcolor{GREEN}{+0.93} & \\textcolor{RED}{-6.64} & \\textcolor{GREEN}{+4.13} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+10.93} & \\textcolor{GREEN}{+4.12} \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.23} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.23} & \\textcolor{RED}{-0.06} & \\textcolor{GREEN}{+0.13} & \\textcolor{RED}{-2.53} & \\textcolor{RED}{-0.42} & \\textcolor{RED}{-0.43} & \\textcolor{RED}{-0.72} & \\textcolor{GREEN}{+0.33} \\\\\n"," \\bottomrule\n"," \\end{tabular}%\n"," \\item[$\\dagger$] Closed-source LLMs results are sourced from \\cite{lu2025bizfinbench0}. Open-weight LLMs results are reproduced using temperature $0.6$.\n"," \\item[1] DeepSeek\\_R1\\_14B\\_Instruct (32B) here is the short of DeepSeek-R1-Distill-Qwen-14B (32B) in the original paper~\\citep{deepseek-r1}.\n"," \\item[2] DeepSeek\\_R1\\_14B\\_SFT and DeepSeek\\_R1\\_14B\\_SFT\\_GRPO are DeepSeek\\_R1\\_14B\\_Instruct model after RETuning SFT stage and after RETuning SFT + GRPO stages, respectively.\n"," \\end{tablenotes}\n"]],"string":"[\n [\n \"\\\\begin{table*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Performance Comparison of LLMs on BizFinBench~\\\\citep{lu2025bizfinbench0}. The colors represent the top three performers for each task: \\\\colorbox{golden}{golden} indicates the top-performing model, \\\\colorbox{lightblue}{silver} represents the second-best result, and \\\\colorbox{lightgreen}{bronze} denotes the third-best performance.}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\begin{threeparttable}\\n\",\n \" \\\\begin{tabular}{lrrrrrrrrrr}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multicolumn{1}{c}{Model~\\\\tnote{$\\\\dagger$}} & \\\\multicolumn{1}{c}{AEA} & \\\\multicolumn{1}{c}{FNC} & \\\\multicolumn{1}{c}{FTR} & \\\\multicolumn{1}{c}{FTU} & \\\\multicolumn{1}{c}{FQA} & \\\\multicolumn{1}{c}{FDD} & \\\\multicolumn{1}{c}{ER} & \\\\multicolumn{1}{c}{SP} & \\\\multicolumn{1}{c}{FNER} & \\\\multicolumn{1}{c}{Average}\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{11}{c}{Closed-Source LLMs} \\\\\\\\\\n\",\n \" ChatGPT-o3 & \\\\cellcolor{lightblue}86.23 & 61.30 & \\\\cellcolor{lightblue}75.36 & \\\\cellcolor{golden}89.15 & \\\\cellcolor{golden}91.25 & \\\\cellcolor{lightgreen}98.55 & 44.48 & 53.27 & 65.13 & \\\\cellcolor{golden}73.86 \\\\\\\\\\n\",\n \" ChatGPT-o4-mini & \\\\cellcolor{lightgreen}85.62 & 60.10 & 71.23 & 74.40 & \\\\cellcolor{lightgreen}90.27 & 95.73 & \\\\cellcolor{golden}47.67 & 52.32 & 64.24 & \\\\cellcolor{lightgreen}71.29 \\\\\\\\\\n\",\n \" GPT-4o & 79.42 & 56.51 & \\\\cellcolor{golden}76.20 & 82.37 & 87.79 & \\\\cellcolor{golden}98.84 & 45.33 & 54.33 & \\\\cellcolor{lightgreen}65.37 & \\\\cellcolor{lightblue}71.80 \\\\\\\\\\n\",\n \" Gemini-2.0-Flash & \\\\cellcolor{golden}86.94 & 62.67 & \\\\cellcolor{lightgreen}73.97 & 82.55 & \\\\cellcolor{lightblue}90.29 & \\\\cellcolor{lightblue}98.62 & 22.17 & \\\\cellcolor{golden}56.14 & 54.43 & 69.75 \\\\\\\\\\n\",\n \" Claude-3.5-Sonnet & 84.68 & \\\\cellcolor{lightgreen}63.18 & 42.81 & \\\\cellcolor{lightblue}88.05 & 87.35 & 96.85 & 16.67 & 47.60 & 63.09 & 65.59 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{11}{c}{Open-Weight LLMs} \\\\\\\\\\n\",\n \" Qwen3-14B & 84.20 & 58.20 & 65.80 & 82.19 & 84.12 & 92.91 & 33.00 & 52.31 & 50.70 & 67.05 \\\\\\\\\\n\",\n \" Qwen3-32B & 83.80 & 59.60 & 64.60 & 85.12 & 85.43 & 95.37 & 39.00 & 52.26 & 49.19 & 68.26 \\\\\\\\\\n\",\n \" DeepSeek\\\\_R1\\\\_14B\\\\_Instruct~\\\\tnote{1} & 71.33 & 44.35 & 50.45 & 81.96 & 85.52 & 92.81 & 39.50 & 50.20 & 52.76 & 59.49 \\\\\\\\\\n\",\n \" DeepSeek\\\\_R1\\\\_32B\\\\_Instruct~\\\\tnote{1} & 73.68 & 51.20 & 50.86 & 83.27 & 87.54 & 97.81 & 41.50 & 53.92 & 56.80 & 66.29 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{11}{c}{Our LLMs} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_14B\\\\_SFT~\\\\tnote{2} & \\\\cellcolor{Background1}80.63 & \\\\cellcolor{Background1}51.67 & \\\\cellcolor{Background1}52.61 & \\\\cellcolor{Background1}83.53 & \\\\cellcolor{Background1}89.05 & \\\\cellcolor{Background1}96.72 & \\\\cellcolor{Background1}36.68 & \\\\cellcolor{Background1}50.43 & \\\\cellcolor{Background1}50.85 & \\\\cellcolor{Background1}65.36 \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT})$ & \\\\textcolor{GREEN}{+9.25} & \\\\textcolor{GREEN}{+7.28} & \\\\textcolor{GREEN}{+2.19} & \\\\textcolor{GREEN}{+1.53} & \\\\textcolor{GREEN}{+3.42} & \\\\textcolor{GREEN}{+3.85} & \\\\textcolor{RED}{-2.93} & \\\\textcolor{GREEN}{+0.24} & \\\\textcolor{RED}{-1.92} & \\\\textcolor{GREEN}{+5.83} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_14B\\\\_SFT\\\\_GRPO~\\\\tnote{2} & \\\\cellcolor{Background1}81.46 & \\\\cellcolor{Background1}52.41 & \\\\cellcolor{Background1}53.47 & \\\\cellcolor{Background1}83.57 & \\\\cellcolor{Background1}89.02 & \\\\cellcolor{Background1}95.58 & \\\\cellcolor{Background1}36.83 & \\\\cellcolor{Background1}54.06 & \\\\cellcolor{Background1}51.24 & \\\\cellcolor{Background1}66.92 \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+10.03} & \\\\textcolor{GREEN}{+8.09} & \\\\textcolor{GREEN}{+2.91} & \\\\textcolor{GREEN}{+1.64} & \\\\textcolor{GREEN}{+3.45} & \\\\textcolor{GREEN}{+2.63} & \\\\textcolor{RED}{-2.74} & \\\\textcolor{GREEN}{+3.82} & \\\\textcolor{RED}{-1.53} & \\\\textcolor{GREEN}{+7.46} \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{SFT}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+0.82} & \\\\textcolor{GREEN}{+0.85} & \\\\textcolor{GREEN}{+0.81} & \\\\textcolor{GREEN}{+0.06} & 0.00 & \\\\textcolor{RED}{-1.23} & \\\\textcolor{GREEN}{+0.25} & \\\\textcolor{GREEN}{+3.63} & \\\\textcolor{GREEN}{+0.42} & \\\\textcolor{GREEN}{+1.53} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_32B\\\\_SFT & \\\\cellcolor{Background1}80.45 & \\\\cellcolor{lightblue}66.42 & \\\\cellcolor{Background1}63.28 & \\\\cellcolor{lightgreen}86.88 & \\\\cellcolor{Background1}88.43 & \\\\cellcolor{Background1}93.76 & \\\\cellcolor{lightblue}46.05 & \\\\cellcolor{lightblue}55.27 & \\\\cellcolor{golden}68.41 & \\\\cellcolor{Background1}70.08 \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT})$ & \\\\textcolor{GREEN}{+6.75} & \\\\textcolor{GREEN}{+15.23} & \\\\textcolor{GREEN}{+12.37} & \\\\textcolor{GREEN}{+3.64} & \\\\textcolor{GREEN}{+0.83} & \\\\textcolor{RED}{-4.14} & \\\\textcolor{GREEN}{+4.52} & \\\\textcolor{GREEN}{+1.25} & \\\\textcolor{GREEN}{+11.63} & \\\\textcolor{GREEN}{+3.75} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_32B\\\\_SFT\\\\_GRPO & \\\\cellcolor{Background1}80.67 & \\\\cellcolor{golden}66.83 & \\\\cellcolor{Background1}64.45 & \\\\cellcolor{Background1}86.79 & \\\\cellcolor{Background1}88.52 & \\\\cellcolor{Background1}91.26 & \\\\cellcolor{lightgreen}45.68 & \\\\cellcolor{lightgreen}54.83 & \\\\cellcolor{lightblue}67.75 & \\\\cellcolor{Background1}70.44 \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+6.95} & \\\\textcolor{GREEN}{+15.62} & \\\\textcolor{GREEN}{+13.57} & \\\\textcolor{GREEN}{+3.55} & \\\\textcolor{GREEN}{+0.93} & \\\\textcolor{RED}{-6.64} & \\\\textcolor{GREEN}{+4.13} & \\\\textcolor{GREEN}{+0.85} & \\\\textcolor{GREEN}{+10.93} & \\\\textcolor{GREEN}{+4.12} \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{SFT}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+0.23} & \\\\textcolor{GREEN}{+0.42} & \\\\textcolor{GREEN}{+1.23} & \\\\textcolor{RED}{-0.06} & \\\\textcolor{GREEN}{+0.13} & \\\\textcolor{RED}{-2.53} & \\\\textcolor{RED}{-0.42} & \\\\textcolor{RED}{-0.43} & \\\\textcolor{RED}{-0.72} & \\\\textcolor{GREEN}{+0.33} \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}%\\n\",\n \" \\\\item[$\\\\dagger$] Closed-source LLMs results are sourced from \\\\cite{lu2025bizfinbench0}. Open-weight LLMs results are reproduced using temperature $0.6$.\\n\",\n \" \\\\item[1] DeepSeek\\\\_R1\\\\_14B\\\\_Instruct (32B) here is the short of DeepSeek-R1-Distill-Qwen-14B (32B) in the original paper~\\\\citep{deepseek-r1}.\\n\",\n \" \\\\item[2] DeepSeek\\\\_R1\\\\_14B\\\\_SFT and DeepSeek\\\\_R1\\\\_14B\\\\_SFT\\\\_GRPO are DeepSeek\\\\_R1\\\\_14B\\\\_Instruct model after RETuning SFT stage and after RETuning SFT + GRPO stages, respectively.\\n\",\n \" \\\\end{tablenotes}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}\n"," \\centering\n"," \\includegraphics[width=0.95\\textwidth]{dataset.pdf}\n"," \\caption{Overview of data sample for one stock at trading day t.}\n"," \\label{fig:dataset}\n","\\end{figure*}\n"],["\\begin{figure*}\n","\t\\centering\n","\t\\includegraphics[width=0.95\\textwidth]{method.pdf}\n","\t\\caption{Two-stage stock movement prediction model training framework: \\textbf{Stage 1} (Cold Start) uses multi-source data with human labeling and synthesis pipeline for \\textcolor{Primary1}{R}eflective \\textcolor{Primary1}{E}vidence \\textcolor{Primary1}{Tuning}; \\textbf{Stage 2} applies \\textcolor{Primary1}{Re}inforcement Fine-\\textcolor{Primary1}{Tuning} with curriculum learning, reward shaping, and inference-time scaling for final label determination.}\n","\t\\label{fig:method}\n","\\end{figure*}\n"],["\\begin{table*}[h]\n"," \\centering\n"," \\caption{Performance Comparison of LLMs on BizFinBench~\\citep{lu2025bizfinbench0}. The colors represent the top three performers for each task: \\colorbox{golden}{golden} indicates the top-performing model, \\colorbox{lightblue}{silver} represents the second-best result, and \\colorbox{lightgreen}{bronze} denotes the third-best performance.}\n"," \\resizebox{\\textwidth}{!}{%\n"," \\begin{threeparttable}\n"," \\begin{tabular}{lrrrrrrrrrr}\n"," \\toprule\n"," \\multicolumn{1}{c}{Model~\\tnote{$\\dagger$}} & \\multicolumn{1}{c}{AEA} & \\multicolumn{1}{c}{FNC} & \\multicolumn{1}{c}{FTR} & \\multicolumn{1}{c}{FTU} & \\multicolumn{1}{c}{FQA} & \\multicolumn{1}{c}{FDD} & \\multicolumn{1}{c}{ER} & \\multicolumn{1}{c}{SP} & \\multicolumn{1}{c}{FNER} & \\multicolumn{1}{c}{Average}\\\\\n"," \\midrule\n"," \\multicolumn{11}{c}{Closed-Source LLMs} \\\\\n"," ChatGPT-o3 & \\cellcolor{lightblue}86.23 & 61.30 & \\cellcolor{lightblue}75.36 & \\cellcolor{golden}89.15 & \\cellcolor{golden}91.25 & \\cellcolor{lightgreen}98.55 & 44.48 & 53.27 & 65.13 & \\cellcolor{golden}73.86 \\\\\n"," ChatGPT-o4-mini & \\cellcolor{lightgreen}85.62 & 60.10 & 71.23 & 74.40 & \\cellcolor{lightgreen}90.27 & 95.73 & \\cellcolor{golden}47.67 & 52.32 & 64.24 & \\cellcolor{lightgreen}71.29 \\\\\n"," GPT-4o & 79.42 & 56.51 & \\cellcolor{golden}76.20 & 82.37 & 87.79 & \\cellcolor{golden}98.84 & 45.33 & 54.33 & \\cellcolor{lightgreen}65.37 & \\cellcolor{lightblue}71.80 \\\\\n"," Gemini-2.0-Flash & \\cellcolor{golden}86.94 & 62.67 & \\cellcolor{lightgreen}73.97 & 82.55 & \\cellcolor{lightblue}90.29 & \\cellcolor{lightblue}98.62 & 22.17 & \\cellcolor{golden}56.14 & 54.43 & 69.75 \\\\\n"," Claude-3.5-Sonnet & 84.68 & \\cellcolor{lightgreen}63.18 & 42.81 & \\cellcolor{lightblue}88.05 & 87.35 & 96.85 & 16.67 & 47.60 & 63.09 & 65.59 \\\\\n"," \\midrule\n"," \\multicolumn{11}{c}{Open-Weight LLMs} \\\\\n"," Qwen3-14B & 84.20 & 58.20 & 65.80 & 82.19 & 84.12 & 92.91 & 33.00 & 52.31 & 50.70 & 67.05 \\\\\n"," Qwen3-32B & 83.80 & 59.60 & 64.60 & 85.12 & 85.43 & 95.37 & 39.00 & 52.26 & 49.19 & 68.26 \\\\\n"," DeepSeek\\_R1\\_14B\\_Instruct~\\tnote{1} & 71.33 & 44.35 & 50.45 & 81.96 & 85.52 & 92.81 & 39.50 & 50.20 & 52.76 & 59.49 \\\\\n"," DeepSeek\\_R1\\_32B\\_Instruct~\\tnote{1} & 73.68 & 51.20 & 50.86 & 83.27 & 87.54 & 97.81 & 41.50 & 53.92 & 56.80 & 66.29 \\\\\n"," \\midrule\n"," \\multicolumn{11}{c}{Our LLMs} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT~\\tnote{2} & \\cellcolor{Background1}80.63 & \\cellcolor{Background1}51.67 & \\cellcolor{Background1}52.61 & \\cellcolor{Background1}83.53 & \\cellcolor{Background1}89.05 & \\cellcolor{Background1}96.72 & \\cellcolor{Background1}36.68 & \\cellcolor{Background1}50.43 & \\cellcolor{Background1}50.85 & \\cellcolor{Background1}65.36 \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+9.25} & \\textcolor{GREEN}{+7.28} & \\textcolor{GREEN}{+2.19} & \\textcolor{GREEN}{+1.53} & \\textcolor{GREEN}{+3.42} & \\textcolor{GREEN}{+3.85} & \\textcolor{RED}{-2.93} & \\textcolor{GREEN}{+0.24} & \\textcolor{RED}{-1.92} & \\textcolor{GREEN}{+5.83} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT\\_GRPO~\\tnote{2} & \\cellcolor{Background1}81.46 & \\cellcolor{Background1}52.41 & \\cellcolor{Background1}53.47 & \\cellcolor{Background1}83.57 & \\cellcolor{Background1}89.02 & \\cellcolor{Background1}95.58 & \\cellcolor{Background1}36.83 & \\cellcolor{Background1}54.06 & \\cellcolor{Background1}51.24 & \\cellcolor{Background1}66.92 \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+10.03} & \\textcolor{GREEN}{+8.09} & \\textcolor{GREEN}{+2.91} & \\textcolor{GREEN}{+1.64} & \\textcolor{GREEN}{+3.45} & \\textcolor{GREEN}{+2.63} & \\textcolor{RED}{-2.74} & \\textcolor{GREEN}{+3.82} & \\textcolor{RED}{-1.53} & \\textcolor{GREEN}{+7.46} \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.82} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+0.81} & \\textcolor{GREEN}{+0.06} & 0.00 & \\textcolor{RED}{-1.23} & \\textcolor{GREEN}{+0.25} & \\textcolor{GREEN}{+3.63} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.53} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT & \\cellcolor{Background1}80.45 & \\cellcolor{lightblue}66.42 & \\cellcolor{Background1}63.28 & \\cellcolor{lightgreen}86.88 & \\cellcolor{Background1}88.43 & \\cellcolor{Background1}93.76 & \\cellcolor{lightblue}46.05 & \\cellcolor{lightblue}55.27 & \\cellcolor{golden}68.41 & \\cellcolor{Background1}70.08 \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+6.75} & \\textcolor{GREEN}{+15.23} & \\textcolor{GREEN}{+12.37} & \\textcolor{GREEN}{+3.64} & \\textcolor{GREEN}{+0.83} & \\textcolor{RED}{-4.14} & \\textcolor{GREEN}{+4.52} & \\textcolor{GREEN}{+1.25} & \\textcolor{GREEN}{+11.63} & \\textcolor{GREEN}{+3.75} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT\\_GRPO & \\cellcolor{Background1}80.67 & \\cellcolor{golden}66.83 & \\cellcolor{Background1}64.45 & \\cellcolor{Background1}86.79 & \\cellcolor{Background1}88.52 & \\cellcolor{Background1}91.26 & \\cellcolor{lightgreen}45.68 & \\cellcolor{lightgreen}54.83 & \\cellcolor{lightblue}67.75 & \\cellcolor{Background1}70.44 \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+6.95} & \\textcolor{GREEN}{+15.62} & \\textcolor{GREEN}{+13.57} & \\textcolor{GREEN}{+3.55} & \\textcolor{GREEN}{+0.93} & \\textcolor{RED}{-6.64} & \\textcolor{GREEN}{+4.13} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+10.93} & \\textcolor{GREEN}{+4.12} \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.23} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.23} & \\textcolor{RED}{-0.06} & \\textcolor{GREEN}{+0.13} & \\textcolor{RED}{-2.53} & \\textcolor{RED}{-0.42} & \\textcolor{RED}{-0.43} & \\textcolor{RED}{-0.72} & \\textcolor{GREEN}{+0.33} \\\\\n"," \\bottomrule\n"," \\end{tabular}%\n"," \\item[$\\dagger$] Closed-source LLMs results are sourced from \\cite{lu2025bizfinbench0}. Open-weight LLMs results are reproduced using temperature $0.6$.\n"," \\item[1] DeepSeek\\_R1\\_14B\\_Instruct (32B) here is the short of DeepSeek-R1-Distill-Qwen-14B (32B) in the original paper~\\citep{deepseek-r1}.\n"," \\item[2] DeepSeek\\_R1\\_14B\\_SFT and DeepSeek\\_R1\\_14B\\_SFT\\_GRPO are DeepSeek\\_R1\\_14B\\_Instruct model after RETuning SFT stage and after RETuning SFT + GRPO stages, respectively.\n"," \\end{tablenotes}\n"],["\\begin{table*}[htbp]\n"," \\centering\n"," \\caption{The training hyperparameters for Supervised Fine-Tuning (SFT). 32B, 14B, and 7B denote models based on DeepSeek-R1-Distill-Qwen with 32B, 14B, and 7B parameters respectively.}\n"," \\begin{tabularx}{\\linewidth}{l XXX} % X columns for automatic width allocation\n"," \\toprule\n"," \\cellcolor{Background1}\\textbf{Hyperparameter Category} & \\cellcolor{Background1}\\textbf{32B} & \\cellcolor{Background1}\\textbf{14B} & \\cellcolor{Background1}\\textbf{7B} \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{1. Data Configuration}}} \\\\\n"," Train Micro-Batch Size per GPU & 1 & 1 & 1 \\\\\n"," Gradient Accumulation Steps & 128 & 128 & 128 \\\\\n"," Total Effective Batch Size & 1024 & 1024 & 1024 \\\\\n"," & ($1\\times128\\times8$) & ($1\\times128\\times8$) & ($1\\times128\\times8$) \\\\\n"," Pack Sequences to Max Length & False & False & False \\\\\n"," Data Shuffling Before Packing & True & True & True \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{2. Model \\& LoRA Configuration}}} \\\\\n"," LLM Torch Dtype & torch.float16 & torch.float16 & torch.float16 \\\\\n"," LoRA Rank ($r$) & 32 & 32 & 32 \\\\\n"," LoRA Alpha ($\\alpha$) & 64 & 64 & 64 \\\\\n"," LoRA Dropout & 0.1 & 0.1 & 0.1 \\\\\n"," LoRA Bias Type & none & none & none \\\\\n"," LoRA Task Type & CAUSAL\\_LM & CAUSAL\\_LM & CAUSAL\\_LM \\\\\n"," Variable-Length Attention & False & False & False \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{3. Optimizer \\& LR Scheduler}}} \\\\\n"," Optimizer Type & \\multicolumn{3}{c}{torch.optim.AdamW} \\\\\n"," Learning Rate (LR) & $2\\times 10^{-4}$ & $2\\times 10^{-4}$ & $2\\times 10^{-4}$ \\\\\n"," AdamW Betas ($\\beta_1$, $\\beta_2$) & (0.9, 0.999) & (0.9, 0.999) & (0.9, 0.999) \\\\\n"," Weight Decay & 0 & 0 & 0 \\\\\n"," Gradient Clipping Max Norm & 1 & 1 & 1 \\\\\n"," LR Scheduler Type & \\multicolumn{3}{c}{Linear Warmup + Cosine Annealing} \\\\\n"," Warmup Ratio (Warmup Epochs / Total Epochs) & 0.03 (0.09/3) & 0.03 (0.09/3) & 0.03 (0.09/3) \\\\\n"," Warmup Start Factor & $1\\times 10^{-5}$ & $1\\times 10^{-5}$ & $1\\times 10^{-5}$ \\\\\n"," Cosine Annealing Final LR ($\\eta_{min}$) & 0.0 & 0.0 & 0.0 \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{4. Training Strategy \\& Distributed Config}}} \\\\\n"," Training Strategy Type & \\multicolumn{3}{c}{DeepSpeedStrategy} \\\\\n"," DeepSpeed Zero Optimization Stage & 3 & 3 & 3 \\\\\n"," BF16 Precision Enabled & True & True & True \\\\\n"," FP16 Precision Enabled & False & False & False \\\\\n"," Sequence Parallel Size & 8 & 8 & 8 \\\\\n"," Sampler Shuffling & True & True & True \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{6. Environment \\& Misc Config}}} \\\\\n"," Launcher Type & \\multicolumn{3}{c}{pytorch} \\\\\n"," Distributed Backend & nccl & nccl & nccl \\\\\n"," Multiprocessing Start Method & fork & fork & fork \\\\\n"," Deterministic Training & False & False & False \\\\\n"," \\bottomrule\n"," \\end{tabularx}\n"," \\label{table:hyperparameters:sft}\n","\\end{table*}\n"],["\\begin{table*}[htbp]\n"," \\centering\n"," \\caption{The training hyperparameters for GRPO. 32B SFT, 14B SFT, and 7B SFT denote models based on DeepSeek R1 with 32B, 14B, and 7B parameters after SFT stage respectively.}\n"," \\begin{tabularx}{\\linewidth}{l XXX} % X列自动分配宽度，占满\\linewidth\n"," \\toprule\n"," \\cellcolor{Background1}\\textbf{Base Model} & \\cellcolor{Background1}\\textbf{32B SFT} & \\cellcolor{Background1}\\textbf{14B SFT} & \\cellcolor{Background1}\\textbf{7B SFT} \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{1. Data Configuration}}} \\\\\n"," Training Batch Size & 256 & 256 & 256 \\\\\n"," Validation Batch Size & 256 & 256 & 256 \\\\\n"," Max Prompt Length & 32768 & 32768 & 32768 \\\\\n"," Max Response Length & 4096 & 4096 & 4096 \\\\\n"," Data Shuffling & True & True & True \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{2. Algorithm Configuration}}} \\\\\n"," Advantage Estimator & GRPO & GRPO & GRPO \\\\\n"," Gamma ($\\gamma$, Discount Factor) & 1.0 & 1.0 & 1.0 \\\\\n"," Lambda ($\\lambda$, Advantage Smoothing) & 1.0 & 1.0 & 1.0 \\\\\n"," KL Coefficient & 0.001 & 0.001 & 0.001 \\\\\n"," Target KL Divergence & 0.1 & 0.1 & 0.1 \\\\\n"," Normalize Advantage by Std & True & True & True \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{3. Actor \\& Ref Configuration}}} \\\\\n"," Learning Rate & $3 \\times 10^{-7}$ & $3 \\times 10^{-7}$ & $3 \\times 10^{-7}$ \\\\\n"," Weight Decay & 0.01 & 0.01 & 0.01 \\\\\n"," Clip Ratio & 0.2 & 0.2 & 0.2 \\\\\n"," Entropy Coefficient & 0.0 & 0.0 & 0.0 \\\\\n"," PPO Epochs & 1 & 1 & 1 \\\\\n"," Log Prob Micro Batch Size & 8 & 4 & 4 \\\\\n"," Tensor Parallel Size & 4 & 4 & 4 \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{4. Rollout Configuration}}} \\\\\n"," Rollout Count (n) & 8 & 8 & 8 \\\\\n"," Rollout Mode & sync & sync & sync \\\\\n"," Engine Name & vllm & vllm & vllm \\\\\n"," Data Type (dtype) & bfloat16 & bfloat16 & bfloat16 \\\\\n"," Temperature & 0.6 & 0.6 & 0.6 \\\\\n"," Max Num Batched Tokens & 36864 & 36864 & 36864 \\\\\n"," Tensor Parallel Size & 4 & 4 & 4 \\\\\n"," Enable Chunked Prefill & True & True & True \\\\\n"," \\hline\n"," \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{5. Trainer Configuration}}} \\\\\n"," Number of Nodes & 4 & 2 & 1 \\\\\n"," GPUs per Node & 8 & 8 & 8 \\\\\n"," Total Epochs & 1 & 1 & 1 \\\\\n"," Checkpoint Save Frequency (steps) & 10 & 10 & 10 \\\\\n"," Validation Frequency (steps) & 10 & 10 & 10 \\\\\n"," Validate Before Training & True & True & True \\\\\n"," \\bottomrule\n"," \\end{tabularx}\n"," \\label{table:hyperparameters:grpo}\n","\\end{table*}\n"],["\\begin{figure*}[htbp]\n","\t\\centering\n","\t\\includegraphics[width=1.\\textwidth]{dataset_pipeline.pdf}\n","\t\\caption{Data processing pipeline showing total 209063 points split into train/test, filtered via multiple steps (lack info, label balance, curriculum learning), and categorized for SFT, RL, OOD evaluations.}\n","\t\\label{fig:dataset_pipeline}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n","\t\\centering\n","\t\\includegraphics[width=0.9\\textwidth]{prompt_length_distribution.png}\n","\t\\caption{Prompt length distribution across the dataset, illustrating the varying lengths of input prompts used for training and evaluation.}\n","\t\\label{fig:prompt_length_distribution}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{figures/prompt.pdf}\n"," \\caption{The prompt template for stock movement prediction.}\n"," \\label{fig:appendix:prompt_template}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{figures/prompt_part_news.pdf}\n"," \\caption{Example. Part 1.1: Stock News.}\n"," \\label{fig:appendix:example_prompt_part_news}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{figures/prompt_part_news2.pdf}\n"," \\caption{Example. Part 1.2: Stock News.}\n"," \\label{fig:appendix:example_prompt_part_news2}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=0.75\\textwidth]{figures/prompt_part_price.pdf}\n"," \\caption{Example. Part 2: Stock Price Info of Current Stock and Top-3 Similar Stocks.}\n"," \\label{fig:appendix:example_prompt_part_price}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{figures/prompt_part_marco.pdf}\n"," \\caption{Example. Part 3: Macroeconomic Indicators Report.}\n"," \\label{fig:appendix:example_prompt_part_marco}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{figures/prompt_part_fundamentals.pdf}\n"," \\caption{Example. Part 4.1: Stock Fundamentals Report.}\n"," \\label{fig:appendix:example_prompt_part_fundamentals}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=0.99\\textwidth]{figures/prompt_part_fundamentals2.pdf}\n"," \\caption{Example. Part 4.2: Stock Fundamentals Report.}\n"," \\label{fig:appendix:example_prompt_part_fundamentals2}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{figures/prompt_part_baseinfo.pdf}\n"," \\caption{Example. Part 5: Stock Basic Information.}\n"," \\label{fig:appendix:example_prompt_part_baseinfo}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=0.85\\textwidth]{figures/prompt_part_quantitative_reports.pdf}\n"," \\caption{Example. Part 6: Stock Quantitative Reports.}\n"," \\label{fig:appendix:example_prompt_part_quantitative_reports}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{figures/response.pdf}\n"," \\caption{Example. Part 7: Model Response.}\n"," \\label{fig:appendix:example_response}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{response_grading.pdf}\n"," \\caption{Example. Part 8: Model Response Grading.}\n"," \\label{fig:appendix:example_response_grading}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{polish_prompt.pdf}\n"," \\caption{The polish prompt allows the backbone model to generate refined responses that follow the proposed thinking schema in Section~\\ref{sec:method:1}.}\n"," \\label{fig:appendix:polish_prompt}\n","\\end{figure*}\n"],["\\begin{table}[h]\n"," \\centering\n"," \\caption{Overview of BizFinBench~\\citep{lu2025bizfinbench0} Datasets}\n"," \\resizebox{\\textwidth}{!}{%\n"," \\begin{tabular}{cp{17.8em}p{14.445em}p{5.39em}ll}\n"," \\toprule\n"," Category & \\multicolumn{1}{l}{Data} & \\multicolumn{1}{l}{Evaluation Dimensions} & \\multicolumn{1}{l}{Metrics} & Numbers & Avg Len. \\\\\n"," \\midrule\n"," Reasoning & Anomalous Event Attribution (AEA) & Causal consistency\\newline{}Information relevance\\newline{}Noise resistance & Accuracy & 1064 & 939 \\\\\n"," & Financial Time Reasoning (FTR) & Temporal reasoning correctness & Accuracy & 514 & 1162 \\\\\n"," & Financial Tool Usage (FTU) & Tool selection appropriateness\\newline{}Parameter input accuracy\\newline{}Multi-tool coordination & Judge Score & 641 & 4556 \\\\\n"," \\midrule\n"," Numerical calculation & Financial Numerical Computation (FNC) & Computational accuracy\\newline{}Unit consistency & Accuracy & 581 & 651 \\\\\n"," \\midrule\n"," Q\\&A & Financial Knowledge QA (FQA) & Question comprehension\\newline{}Knowledge coverage\\newline{}Answer accuracy & Judge Score & 990 & 22 \\\\\n"," & Financial Data Description (FDD) & Trend accuracy\\newline{}Data consistency & Judge Score & 1461 & 311 \\\\\n"," \\midrule\n"," Prediction recognition & Emotion Recognition (ER) & Emotion classification accuracy\\newline{}Implicit information extraction & Accuracy & 600 & 2179 \\\\\n"," & Stock Price Prediction (SP) & Trend judgment, Causal reasoning & Accuracy & 497 & 4498 \\\\\n"," \\midrule\n"," Information extraction & Financial Named Entity Recognition (FNER) & Recognition accuracy\\newline{}Entity classification correctness & Accuracy & 435 & 533 \\\\\n"," \\bottomrule\n"," \\end{tabular}%\n"," }\n"," \\label{datasetall}%\n","\\end{table}%\n"],["\\begin{table}[htbp]\n"," \\centering\n"," \\caption{Token Length Statistics of BizFinBench~\\citep{lu2025bizfinbench0}.}\n"," \\label{query_token_stats}\n"," \\begin{tabular}{lrrrr}\n"," \\toprule\n"," \\textbf{Dataset} & \\textbf{Min} & \\textbf{Max} & \\textbf{Avg} & \\textbf{Count} \\\\\n"," \\midrule\n"," NER & 415 & 1,194 & 533.1 & 433 \\\\\n"," FTU & 4,169 & 6,289 & 4,555.5 & 641 \\\\\n"," AEA & 680 & 1,396 & 938.7 & 1,064 \\\\\n"," ER & 1,919 & 2,569 & 2,178.5 & 600 \\\\\n"," FNC & 287 & 2,698 & 650.5 & 581 \\\\\n"," FDD & 26 & 645 & 310.9 & 1,461 \\\\\n"," FTR & 203 & 8,265 & 1,162.0 & 514 \\\\\n"," FQA & 5 & 45 & 21.7 & 990 \\\\\n"," SP & 1,254 & 5,532 & 4,498.1 & 497 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","\\end{table}\n"],["\\begin{figure*}[htbp]\n","\t\\centering\n","\t\\includegraphics[width=0.85\\textwidth]{ablation_on_CoT_4.pdf}\n","\t\\caption{Detailed results on \\textbf{Fin-2024[December]} for different baselines.}\n","\t\\label{fig:detailed_results:fin2024december}\n","\\end{figure*}\n"],["\\begin{table*}[htbp]\n"," \\centering\n"," \\caption{Performance Comparison of Large Language Models on BizFinBench~\\citep{lu2025bizfinbench0}. The models are evaluated across multiple tasks, with results color-coded to represent the top three performers for each task: \\colorbox{golden}{golden} indicates the top-performing model, \\colorbox{lightblue}{silver} represents the second-best result, and \\colorbox{lightgreen}{bronze} denotes the third-best performance.}\n"," \\resizebox{\\textwidth}{!}{%\n"," \\begin{tabular}{lrrrrrrrrrr}\n"," \\toprule\n"," \\multicolumn{1}{c}{Model} & \\multicolumn{1}{c}{AEA} & \\multicolumn{1}{c}{FNC} & \\multicolumn{1}{c}{FTR} & \\multicolumn{1}{c}{FTU} & \\multicolumn{1}{c}{FQA} & \\multicolumn{1}{c}{FDD} & \\multicolumn{1}{c}{ER} & \\multicolumn{1}{c}{SP} & \\multicolumn{1}{c}{FNER} & \\multicolumn{1}{c}{Average}\\\\\n"," \\midrule\n"," \\multicolumn{10}{c}{Close-Source LLMs} \\\\\n"," ChatGPT-o3 & \\cellcolor{lightblue}86.23 & 61.30 & \\cellcolor{lightblue}75.36 & \\cellcolor{golden}89.15 & \\cellcolor{lightblue}91.25 & \\cellcolor{lightgreen}98.55 & 44.48 & 53.27 & 65.13 & \\cellcolor{golden}73.86 \\\\\n"," ChatGPT-o4-mini & \\cellcolor{lightgreen}85.62 & 60.10 & 71.23 & 74.40 & 90.27 & 95.73 & \\cellcolor{golden}47.67 & 52.32 & 64.24 & 71.29 \\\\\n"," GPT-4o & 79.42 & 56.51 & \\cellcolor{golden}76.20 & 82.37 & 87.79 & \\cellcolor{golden}98.84 & 45.33 & 54.33 & 65.37 & \\cellcolor{lightgreen}71.80 \\\\\n"," Gemini-2.0-Flash & \\cellcolor{golden}86.94 & 62.67 & 73.97 & 82.55 & 90.29 & \\cellcolor{lightblue}98.62 & 22.17 & \\cellcolor{lightgreen}56.14 & 54.43 & 69.75 \\\\\n"," Claude-3.5-Sonnet & 84.68 & 63.18 & 42.81 & \\cellcolor{lightblue}88.05 & 87.35 & 96.85 & 16.67 & 47.60 & 63.09 & 65.59 \\\\\n"," \\midrule\n"," \\multicolumn{10}{c}{Open-Weight LLMs} \\\\\n"," Qwen2.5-7B-Instruct & 73.87 & 32.88 & 39.38 & 79.03 & 83.34 & 78.93 & 37.50 & 51.91 & 30.31 & 56.35 \\\\\n"," Qwen2.5-72B-Instruct & 69.27 & 54.28 & 70.72 & 85.29 & 87.79 & 97.43 & 35.33 & 55.13 & 54.02 & 67.70 \\\\\n"," Qwen2.5-VL-3B & 53.85 & 15.92 & 17.29 & 8.95 & 81.60 & 59.44 & 39.50 & 52.49 & 21.57 & 38.96 \\\\\n"," Qwen2.5-VL-7B & 73.87 & 32.71 & 40.24 & 77.85 & 83.94 & 77.41 & 38.83 & 51.91 & 33.40 & 56.68 \\\\\n"," Qwen2.5-VL-14B & 37.12 & 41.44 & 53.08 & 82.07 & 84.23 & 7.97 & 37.33 & 54.93 & 47.47 & 49.52 \\\\\n"," Qwen2.5-VL-32B & 76.79 & 50.00 & 62.16 & 83.57 & 85.30 & 95.95 & 40.50 & 54.93 & 68.36 & 68.62 \\\\\n"," Qwen2.5-VL-72B & 69.55 & 54.11 & 69.86 & 85.18 & 87.37 & 97.34 & 35.00 & 54.94 & 54.41 & 67.53 \\\\\n"," Qwen3-1.7B & 77.40 & 35.80 & 33.40 & 75.82 & 73.81 & 78.62 & 22.40 & 48.53 & 11.23 & 50.78 \\\\\n"," Qwen3-4B & 83.60 & 47.40 & 50.00 & 78.19 & 82.24 & 80.16 & 42.20 & 50.51 & 25.19 & 59.94 \\\\\n"," Qwen3-14B & 84.20 & 58.20 & 65.80 & 82.19 & 84.12 & 92.91 & 33.00 & 52.31 & 50.70 & 67.05 \\\\\n"," Qwen3-32B & 83.80 & 59.60 & 64.60 & 85.12 & 85.43 & 95.37 & 39.00 & 52.26 & 49.19 & 68.26 \\\\\n"," QwQ-32B & 84.02 & 52.91 & 64.90 & 84.81 & 89.60 & 94.20 & 34.50 & \\cellcolor{lightblue}56.68 & 30.27 & 65.77 \\\\\n"," Xuanyuan3-70B & 12.14 & 19.69 & 15.41 & 80.89 & 86.51 & 83.90 & 29.83 & 52.62 & 37.33 & 46.48 \\\\\n"," Llama-3.1-8B-Instruct & 73.12 & 22.09 & 2.91 & 77.42 & 76.18 & 69.09 & 29.00 & 54.21 & 36.56 & 48.95 \\\\\n"," Llama-3.1-70B-Instruct & 16.26 & 34.25 & 56.34 & 80.64 & 79.97 & 86.90 & 33.33 & \\cellcolor{golden}62.16 & 45.95 & 55.09 \\\\\n"," Llama 4 Scout & 73.60 & 45.80 & 44.20 & 85.02 & 85.21 & 92.32 & 25.60 & 55.76 & 43.00 & 61.17 \\\\\n"," DeepSeek-V3 (671B) & 74.34 & 61.82 & 72.60 & 86.54 & \\cellcolor{lightgreen}91.07 & 98.11 & 32.67 & 55.73 & \\cellcolor{lightblue}71.24 & 71.57 \\\\\n"," DeepSeek-R1 (671B) & 80.36 & \\cellcolor{lightgreen}64.04 & \\cellcolor{lightgreen}75.00 & 81.96 & \\cellcolor{golden}91.44 & 98.41 & 39.67 & 55.13 & \\cellcolor{golden}71.46 & \\cellcolor{lightblue}73.05 \\\\\n"," DeepSeek\\_R1\\_14B\\_Instruct & 71.33 & 44.35 & 50.45 & 81.96 & 85.52 & 92.81 & 39.50 & 50.20 & 52.76 & 59.49 \\\\\n"," DeepSeek\\_R1\\_32B\\_Instruct & 73.68 & 51.20 & 50.86 & 83.27 & 87.54 & 97.81 & 41.50 & 53.92 & 56.80 & 66.29 \\\\\n"," \\midrule\n"," \\multicolumn{11}{c}{Our LLMs} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT~\\tnote{2} & \\cellcolor{Background1}80.63 & \\cellcolor{Background1}51.67 & \\cellcolor{Background1}52.61 & \\cellcolor{Background1}83.53 & \\cellcolor{Background1}89.05 & \\cellcolor{Background1}96.72 & \\cellcolor{Background1}36.68 & \\cellcolor{Background1}50.43 & \\cellcolor{Background1}50.85 & \\cellcolor{Background1}65.36 \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+9.25} & \\textcolor{GREEN}{+7.28} & \\textcolor{GREEN}{+2.19} & \\textcolor{GREEN}{+1.53} & \\textcolor{GREEN}{+3.42} & \\textcolor{GREEN}{+3.85} & \\textcolor{RED}{-2.93} & \\textcolor{GREEN}{+0.24} & \\textcolor{RED}{-1.92} & \\textcolor{GREEN}{+5.83} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT\\_GRPO~\\tnote{2} & \\cellcolor{Background1}81.46 & \\cellcolor{Background1}52.41 & \\cellcolor{Background1}53.47 & \\cellcolor{Background1}83.57 & \\cellcolor{Background1}89.02 & \\cellcolor{Background1}95.58 & \\cellcolor{Background1}36.83 & \\cellcolor{Background1}54.06 & \\cellcolor{Background1}51.24 & \\cellcolor{Background1}66.92 \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+10.03} & \\textcolor{GREEN}{+8.09} & \\textcolor{GREEN}{+2.91} & \\textcolor{GREEN}{+1.64} & \\textcolor{GREEN}{+3.45} & \\textcolor{GREEN}{+2.63} & \\textcolor{RED}{-2.74} & \\textcolor{GREEN}{+3.82} & \\textcolor{RED}{-1.53} & \\textcolor{GREEN}{+7.46} \\\\\n"," $\\quad$ 14B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.82} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+0.81} & \\textcolor{GREEN}{+0.06} & 0.00 & \\textcolor{RED}{-1.23} & \\textcolor{GREEN}{+0.25} & \\textcolor{GREEN}{+3.63} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.53} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT & \\cellcolor{Background1}80.45 & \\cellcolor{lightblue}66.42 & \\cellcolor{Background1}63.28 & \\cellcolor{lightgreen}86.88 & \\cellcolor{Background1}88.43 & \\cellcolor{Background1}93.76 & \\cellcolor{lightblue}46.05 & \\cellcolor{Background1}55.27 & \\cellcolor{lightgreen}68.41 & \\cellcolor{Background1}70.08 \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+6.75} & \\textcolor{GREEN}{+15.23} & \\textcolor{GREEN}{+12.37} & \\textcolor{GREEN}{+3.64} & \\textcolor{GREEN}{+0.83} & \\textcolor{RED}{-4.14} & \\textcolor{GREEN}{+4.52} & \\textcolor{GREEN}{+1.25} & \\textcolor{GREEN}{+11.63} & \\textcolor{GREEN}{+3.75} \\\\\n"," \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT\\_GRPO & \\cellcolor{Background1}80.67 & \\cellcolor{golden}66.83 & \\cellcolor{Background1}64.45 & \\cellcolor{Background1}86.79 & \\cellcolor{Background1}88.52 & \\cellcolor{Background1}91.26 & \\cellcolor{lightgreen}45.68 & \\cellcolor{Background1}54.83 & \\cellcolor{Background1}67.75 & \\cellcolor{Background1}70.44 \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+6.95} & \\textcolor{GREEN}{+15.62} & \\textcolor{GREEN}{+13.57} & \\textcolor{GREEN}{+3.55} & \\textcolor{GREEN}{+0.93} & \\textcolor{RED}{-6.64} & \\textcolor{GREEN}{+4.13} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+10.93} & \\textcolor{GREEN}{+4.12} \\\\\n"," $\\quad$ 32B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.23} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.23} & \\textcolor{RED}{-0.06} & \\textcolor{GREEN}{+0.13} & \\textcolor{RED}{-2.53} & \\textcolor{RED}{-0.42} & \\textcolor{RED}{-0.43} & \\textcolor{RED}{-0.72} & \\textcolor{GREEN}{+0.33} \\\\\n"," \\bottomrule\n"," \\end{tabular}%\n"," }\n"," \\label{table:bizfinbench_detailed_results}%\n","\\end{table*}%\n"],["\\begin{figure*}[htbp]\n","\t\\centering\n","\t\\includegraphics[width=1\\textwidth]{response_no_CoT.pdf}\n","\t\\caption{Zero-shot responses. The model struggles to provide accurate and relevant answers without the step-by-step reasoning process enabled by CoT prompting.}\n","\t\\label{fig:appendix:case_study:response_no_cot}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n","\t\\centering\n","\t\\includegraphics[width=1\\textwidth]{response_with_CoT.pdf}\n","\t\\caption{CoT Prompting responses. The model demonstrates improved reasoning and accuracy when guided through a step-by-step thought process.}\n","\t\\label{fig:appendix:case_study:response_with_cot}\n","\\end{figure*}\n"],["\\begin{figure*}[htbp]\n","\t\\centering\n","\t\\includegraphics[width=1\\textwidth]{response_cold_started.pdf}\n","\t\\caption{Case study on cold-started responses. Left is the original response, and right is the cold-started response. The cold-started response is more concise and to the point, avoiding unnecessary elaboration.}\n","\t\\label{fig:appendix:case_study:response_cold_started}\n","\\end{figure*}\n"]],"string":"[\n [\n \"\\\\begin{figure*}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.95\\\\textwidth]{dataset.pdf}\\n\",\n \" \\\\caption{Overview of data sample for one stock at trading day t.}\\n\",\n \" \\\\label{fig:dataset}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}\\n\",\n \"\\t\\\\centering\\n\",\n \"\\t\\\\includegraphics[width=0.95\\\\textwidth]{method.pdf}\\n\",\n \"\\t\\\\caption{Two-stage stock movement prediction model training framework: \\\\textbf{Stage 1} (Cold Start) uses multi-source data with human labeling and synthesis pipeline for \\\\textcolor{Primary1}{R}eflective \\\\textcolor{Primary1}{E}vidence \\\\textcolor{Primary1}{Tuning}; \\\\textbf{Stage 2} applies \\\\textcolor{Primary1}{Re}inforcement Fine-\\\\textcolor{Primary1}{Tuning} with curriculum learning, reward shaping, and inference-time scaling for final label determination.}\\n\",\n \"\\t\\\\label{fig:method}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Performance Comparison of LLMs on BizFinBench~\\\\citep{lu2025bizfinbench0}. The colors represent the top three performers for each task: \\\\colorbox{golden}{golden} indicates the top-performing model, \\\\colorbox{lightblue}{silver} represents the second-best result, and \\\\colorbox{lightgreen}{bronze} denotes the third-best performance.}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\begin{threeparttable}\\n\",\n \" \\\\begin{tabular}{lrrrrrrrrrr}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multicolumn{1}{c}{Model~\\\\tnote{$\\\\dagger$}} & \\\\multicolumn{1}{c}{AEA} & \\\\multicolumn{1}{c}{FNC} & \\\\multicolumn{1}{c}{FTR} & \\\\multicolumn{1}{c}{FTU} & \\\\multicolumn{1}{c}{FQA} & \\\\multicolumn{1}{c}{FDD} & \\\\multicolumn{1}{c}{ER} & \\\\multicolumn{1}{c}{SP} & \\\\multicolumn{1}{c}{FNER} & \\\\multicolumn{1}{c}{Average}\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{11}{c}{Closed-Source LLMs} \\\\\\\\\\n\",\n \" ChatGPT-o3 & \\\\cellcolor{lightblue}86.23 & 61.30 & \\\\cellcolor{lightblue}75.36 & \\\\cellcolor{golden}89.15 & \\\\cellcolor{golden}91.25 & \\\\cellcolor{lightgreen}98.55 & 44.48 & 53.27 & 65.13 & \\\\cellcolor{golden}73.86 \\\\\\\\\\n\",\n \" ChatGPT-o4-mini & \\\\cellcolor{lightgreen}85.62 & 60.10 & 71.23 & 74.40 & \\\\cellcolor{lightgreen}90.27 & 95.73 & \\\\cellcolor{golden}47.67 & 52.32 & 64.24 & \\\\cellcolor{lightgreen}71.29 \\\\\\\\\\n\",\n \" GPT-4o & 79.42 & 56.51 & \\\\cellcolor{golden}76.20 & 82.37 & 87.79 & \\\\cellcolor{golden}98.84 & 45.33 & 54.33 & \\\\cellcolor{lightgreen}65.37 & \\\\cellcolor{lightblue}71.80 \\\\\\\\\\n\",\n \" Gemini-2.0-Flash & \\\\cellcolor{golden}86.94 & 62.67 & \\\\cellcolor{lightgreen}73.97 & 82.55 & \\\\cellcolor{lightblue}90.29 & \\\\cellcolor{lightblue}98.62 & 22.17 & \\\\cellcolor{golden}56.14 & 54.43 & 69.75 \\\\\\\\\\n\",\n \" Claude-3.5-Sonnet & 84.68 & \\\\cellcolor{lightgreen}63.18 & 42.81 & \\\\cellcolor{lightblue}88.05 & 87.35 & 96.85 & 16.67 & 47.60 & 63.09 & 65.59 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{11}{c}{Open-Weight LLMs} \\\\\\\\\\n\",\n \" Qwen3-14B & 84.20 & 58.20 & 65.80 & 82.19 & 84.12 & 92.91 & 33.00 & 52.31 & 50.70 & 67.05 \\\\\\\\\\n\",\n \" Qwen3-32B & 83.80 & 59.60 & 64.60 & 85.12 & 85.43 & 95.37 & 39.00 & 52.26 & 49.19 & 68.26 \\\\\\\\\\n\",\n \" DeepSeek\\\\_R1\\\\_14B\\\\_Instruct~\\\\tnote{1} & 71.33 & 44.35 & 50.45 & 81.96 & 85.52 & 92.81 & 39.50 & 50.20 & 52.76 & 59.49 \\\\\\\\\\n\",\n \" DeepSeek\\\\_R1\\\\_32B\\\\_Instruct~\\\\tnote{1} & 73.68 & 51.20 & 50.86 & 83.27 & 87.54 & 97.81 & 41.50 & 53.92 & 56.80 & 66.29 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{11}{c}{Our LLMs} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_14B\\\\_SFT~\\\\tnote{2} & \\\\cellcolor{Background1}80.63 & \\\\cellcolor{Background1}51.67 & \\\\cellcolor{Background1}52.61 & \\\\cellcolor{Background1}83.53 & \\\\cellcolor{Background1}89.05 & \\\\cellcolor{Background1}96.72 & \\\\cellcolor{Background1}36.68 & \\\\cellcolor{Background1}50.43 & \\\\cellcolor{Background1}50.85 & \\\\cellcolor{Background1}65.36 \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT})$ & \\\\textcolor{GREEN}{+9.25} & \\\\textcolor{GREEN}{+7.28} & \\\\textcolor{GREEN}{+2.19} & \\\\textcolor{GREEN}{+1.53} & \\\\textcolor{GREEN}{+3.42} & \\\\textcolor{GREEN}{+3.85} & \\\\textcolor{RED}{-2.93} & \\\\textcolor{GREEN}{+0.24} & \\\\textcolor{RED}{-1.92} & \\\\textcolor{GREEN}{+5.83} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_14B\\\\_SFT\\\\_GRPO~\\\\tnote{2} & \\\\cellcolor{Background1}81.46 & \\\\cellcolor{Background1}52.41 & \\\\cellcolor{Background1}53.47 & \\\\cellcolor{Background1}83.57 & \\\\cellcolor{Background1}89.02 & \\\\cellcolor{Background1}95.58 & \\\\cellcolor{Background1}36.83 & \\\\cellcolor{Background1}54.06 & \\\\cellcolor{Background1}51.24 & \\\\cellcolor{Background1}66.92 \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+10.03} & \\\\textcolor{GREEN}{+8.09} & \\\\textcolor{GREEN}{+2.91} & \\\\textcolor{GREEN}{+1.64} & \\\\textcolor{GREEN}{+3.45} & \\\\textcolor{GREEN}{+2.63} & \\\\textcolor{RED}{-2.74} & \\\\textcolor{GREEN}{+3.82} & \\\\textcolor{RED}{-1.53} & \\\\textcolor{GREEN}{+7.46} \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{SFT}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+0.82} & \\\\textcolor{GREEN}{+0.85} & \\\\textcolor{GREEN}{+0.81} & \\\\textcolor{GREEN}{+0.06} & 0.00 & \\\\textcolor{RED}{-1.23} & \\\\textcolor{GREEN}{+0.25} & \\\\textcolor{GREEN}{+3.63} & \\\\textcolor{GREEN}{+0.42} & \\\\textcolor{GREEN}{+1.53} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_32B\\\\_SFT & \\\\cellcolor{Background1}80.45 & \\\\cellcolor{lightblue}66.42 & \\\\cellcolor{Background1}63.28 & \\\\cellcolor{lightgreen}86.88 & \\\\cellcolor{Background1}88.43 & \\\\cellcolor{Background1}93.76 & \\\\cellcolor{lightblue}46.05 & \\\\cellcolor{lightblue}55.27 & \\\\cellcolor{golden}68.41 & \\\\cellcolor{Background1}70.08 \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT})$ & \\\\textcolor{GREEN}{+6.75} & \\\\textcolor{GREEN}{+15.23} & \\\\textcolor{GREEN}{+12.37} & \\\\textcolor{GREEN}{+3.64} & \\\\textcolor{GREEN}{+0.83} & \\\\textcolor{RED}{-4.14} & \\\\textcolor{GREEN}{+4.52} & \\\\textcolor{GREEN}{+1.25} & \\\\textcolor{GREEN}{+11.63} & \\\\textcolor{GREEN}{+3.75} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_32B\\\\_SFT\\\\_GRPO & \\\\cellcolor{Background1}80.67 & \\\\cellcolor{golden}66.83 & \\\\cellcolor{Background1}64.45 & \\\\cellcolor{Background1}86.79 & \\\\cellcolor{Background1}88.52 & \\\\cellcolor{Background1}91.26 & \\\\cellcolor{lightgreen}45.68 & \\\\cellcolor{lightgreen}54.83 & \\\\cellcolor{lightblue}67.75 & \\\\cellcolor{Background1}70.44 \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+6.95} & \\\\textcolor{GREEN}{+15.62} & \\\\textcolor{GREEN}{+13.57} & \\\\textcolor{GREEN}{+3.55} & \\\\textcolor{GREEN}{+0.93} & \\\\textcolor{RED}{-6.64} & \\\\textcolor{GREEN}{+4.13} & \\\\textcolor{GREEN}{+0.85} & \\\\textcolor{GREEN}{+10.93} & \\\\textcolor{GREEN}{+4.12} \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{SFT}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+0.23} & \\\\textcolor{GREEN}{+0.42} & \\\\textcolor{GREEN}{+1.23} & \\\\textcolor{RED}{-0.06} & \\\\textcolor{GREEN}{+0.13} & \\\\textcolor{RED}{-2.53} & \\\\textcolor{RED}{-0.42} & \\\\textcolor{RED}{-0.43} & \\\\textcolor{RED}{-0.72} & \\\\textcolor{GREEN}{+0.33} \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}%\\n\",\n \" \\\\item[$\\\\dagger$] Closed-source LLMs results are sourced from \\\\cite{lu2025bizfinbench0}. Open-weight LLMs results are reproduced using temperature $0.6$.\\n\",\n \" \\\\item[1] DeepSeek\\\\_R1\\\\_14B\\\\_Instruct (32B) here is the short of DeepSeek-R1-Distill-Qwen-14B (32B) in the original paper~\\\\citep{deepseek-r1}.\\n\",\n \" \\\\item[2] DeepSeek\\\\_R1\\\\_14B\\\\_SFT and DeepSeek\\\\_R1\\\\_14B\\\\_SFT\\\\_GRPO are DeepSeek\\\\_R1\\\\_14B\\\\_Instruct model after RETuning SFT stage and after RETuning SFT + GRPO stages, respectively.\\n\",\n \" \\\\end{tablenotes}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{The training hyperparameters for Supervised Fine-Tuning (SFT). 32B, 14B, and 7B denote models based on DeepSeek-R1-Distill-Qwen with 32B, 14B, and 7B parameters respectively.}\\n\",\n \" \\\\begin{tabularx}{\\\\linewidth}{l XXX} % X columns for automatic width allocation\\n\",\n \" \\\\toprule\\n\",\n \" \\\\cellcolor{Background1}\\\\textbf{Hyperparameter Category} & \\\\cellcolor{Background1}\\\\textbf{32B} & \\\\cellcolor{Background1}\\\\textbf{14B} & \\\\cellcolor{Background1}\\\\textbf{7B} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{1. Data Configuration}}} \\\\\\\\\\n\",\n \" Train Micro-Batch Size per GPU & 1 & 1 & 1 \\\\\\\\\\n\",\n \" Gradient Accumulation Steps & 128 & 128 & 128 \\\\\\\\\\n\",\n \" Total Effective Batch Size & 1024 & 1024 & 1024 \\\\\\\\\\n\",\n \" & ($1\\\\times128\\\\times8$) & ($1\\\\times128\\\\times8$) & ($1\\\\times128\\\\times8$) \\\\\\\\\\n\",\n \" Pack Sequences to Max Length & False & False & False \\\\\\\\\\n\",\n \" Data Shuffling Before Packing & True & True & True \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{2. Model \\\\& LoRA Configuration}}} \\\\\\\\\\n\",\n \" LLM Torch Dtype & torch.float16 & torch.float16 & torch.float16 \\\\\\\\\\n\",\n \" LoRA Rank ($r$) & 32 & 32 & 32 \\\\\\\\\\n\",\n \" LoRA Alpha ($\\\\alpha$) & 64 & 64 & 64 \\\\\\\\\\n\",\n \" LoRA Dropout & 0.1 & 0.1 & 0.1 \\\\\\\\\\n\",\n \" LoRA Bias Type & none & none & none \\\\\\\\\\n\",\n \" LoRA Task Type & CAUSAL\\\\_LM & CAUSAL\\\\_LM & CAUSAL\\\\_LM \\\\\\\\\\n\",\n \" Variable-Length Attention & False & False & False \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{3. Optimizer \\\\& LR Scheduler}}} \\\\\\\\\\n\",\n \" Optimizer Type & \\\\multicolumn{3}{c}{torch.optim.AdamW} \\\\\\\\\\n\",\n \" Learning Rate (LR) & $2\\\\times 10^{-4}$ & $2\\\\times 10^{-4}$ & $2\\\\times 10^{-4}$ \\\\\\\\\\n\",\n \" AdamW Betas ($\\\\beta_1$, $\\\\beta_2$) & (0.9, 0.999) & (0.9, 0.999) & (0.9, 0.999) \\\\\\\\\\n\",\n \" Weight Decay & 0 & 0 & 0 \\\\\\\\\\n\",\n \" Gradient Clipping Max Norm & 1 & 1 & 1 \\\\\\\\\\n\",\n \" LR Scheduler Type & \\\\multicolumn{3}{c}{Linear Warmup + Cosine Annealing} \\\\\\\\\\n\",\n \" Warmup Ratio (Warmup Epochs / Total Epochs) & 0.03 (0.09/3) & 0.03 (0.09/3) & 0.03 (0.09/3) \\\\\\\\\\n\",\n \" Warmup Start Factor & $1\\\\times 10^{-5}$ & $1\\\\times 10^{-5}$ & $1\\\\times 10^{-5}$ \\\\\\\\\\n\",\n \" Cosine Annealing Final LR ($\\\\eta_{min}$) & 0.0 & 0.0 & 0.0 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{4. Training Strategy \\\\& Distributed Config}}} \\\\\\\\\\n\",\n \" Training Strategy Type & \\\\multicolumn{3}{c}{DeepSpeedStrategy} \\\\\\\\\\n\",\n \" DeepSpeed Zero Optimization Stage & 3 & 3 & 3 \\\\\\\\\\n\",\n \" BF16 Precision Enabled & True & True & True \\\\\\\\\\n\",\n \" FP16 Precision Enabled & False & False & False \\\\\\\\\\n\",\n \" Sequence Parallel Size & 8 & 8 & 8 \\\\\\\\\\n\",\n \" Sampler Shuffling & True & True & True \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{6. Environment \\\\& Misc Config}}} \\\\\\\\\\n\",\n \" Launcher Type & \\\\multicolumn{3}{c}{pytorch} \\\\\\\\\\n\",\n \" Distributed Backend & nccl & nccl & nccl \\\\\\\\\\n\",\n \" Multiprocessing Start Method & fork & fork & fork \\\\\\\\\\n\",\n \" Deterministic Training & False & False & False \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabularx}\\n\",\n \" \\\\label{table:hyperparameters:sft}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{The training hyperparameters for GRPO. 32B SFT, 14B SFT, and 7B SFT denote models based on DeepSeek R1 with 32B, 14B, and 7B parameters after SFT stage respectively.}\\n\",\n \" \\\\begin{tabularx}{\\\\linewidth}{l XXX} % X列自动分配宽度，占满\\\\linewidth\\n\",\n \" \\\\toprule\\n\",\n \" \\\\cellcolor{Background1}\\\\textbf{Base Model} & \\\\cellcolor{Background1}\\\\textbf{32B SFT} & \\\\cellcolor{Background1}\\\\textbf{14B SFT} & \\\\cellcolor{Background1}\\\\textbf{7B SFT} \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{1. Data Configuration}}} \\\\\\\\\\n\",\n \" Training Batch Size & 256 & 256 & 256 \\\\\\\\\\n\",\n \" Validation Batch Size & 256 & 256 & 256 \\\\\\\\\\n\",\n \" Max Prompt Length & 32768 & 32768 & 32768 \\\\\\\\\\n\",\n \" Max Response Length & 4096 & 4096 & 4096 \\\\\\\\\\n\",\n \" Data Shuffling & True & True & True \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{2. Algorithm Configuration}}} \\\\\\\\\\n\",\n \" Advantage Estimator & GRPO & GRPO & GRPO \\\\\\\\\\n\",\n \" Gamma ($\\\\gamma$, Discount Factor) & 1.0 & 1.0 & 1.0 \\\\\\\\\\n\",\n \" Lambda ($\\\\lambda$, Advantage Smoothing) & 1.0 & 1.0 & 1.0 \\\\\\\\\\n\",\n \" KL Coefficient & 0.001 & 0.001 & 0.001 \\\\\\\\\\n\",\n \" Target KL Divergence & 0.1 & 0.1 & 0.1 \\\\\\\\\\n\",\n \" Normalize Advantage by Std & True & True & True \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{3. Actor \\\\& Ref Configuration}}} \\\\\\\\\\n\",\n \" Learning Rate & $3 \\\\times 10^{-7}$ & $3 \\\\times 10^{-7}$ & $3 \\\\times 10^{-7}$ \\\\\\\\\\n\",\n \" Weight Decay & 0.01 & 0.01 & 0.01 \\\\\\\\\\n\",\n \" Clip Ratio & 0.2 & 0.2 & 0.2 \\\\\\\\\\n\",\n \" Entropy Coefficient & 0.0 & 0.0 & 0.0 \\\\\\\\\\n\",\n \" PPO Epochs & 1 & 1 & 1 \\\\\\\\\\n\",\n \" Log Prob Micro Batch Size & 8 & 4 & 4 \\\\\\\\\\n\",\n \" Tensor Parallel Size & 4 & 4 & 4 \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{4. Rollout Configuration}}} \\\\\\\\\\n\",\n \" Rollout Count (n) & 8 & 8 & 8 \\\\\\\\\\n\",\n \" Rollout Mode & sync & sync & sync \\\\\\\\\\n\",\n \" Engine Name & vllm & vllm & vllm \\\\\\\\\\n\",\n \" Data Type (dtype) & bfloat16 & bfloat16 & bfloat16 \\\\\\\\\\n\",\n \" Temperature & 0.6 & 0.6 & 0.6 \\\\\\\\\\n\",\n \" Max Num Batched Tokens & 36864 & 36864 & 36864 \\\\\\\\\\n\",\n \" Tensor Parallel Size & 4 & 4 & 4 \\\\\\\\\\n\",\n \" Enable Chunked Prefill & True & True & True \\\\\\\\\\n\",\n \" \\\\hline\\n\",\n \" \\\\multicolumn{4}{c}{\\\\cellcolor{Background1}\\\\textcolor{Font1}{\\\\textbf{5. Trainer Configuration}}} \\\\\\\\\\n\",\n \" Number of Nodes & 4 & 2 & 1 \\\\\\\\\\n\",\n \" GPUs per Node & 8 & 8 & 8 \\\\\\\\\\n\",\n \" Total Epochs & 1 & 1 & 1 \\\\\\\\\\n\",\n \" Checkpoint Save Frequency (steps) & 10 & 10 & 10 \\\\\\\\\\n\",\n \" Validation Frequency (steps) & 10 & 10 & 10 \\\\\\\\\\n\",\n \" Validate Before Training & True & True & True \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabularx}\\n\",\n \" \\\\label{table:hyperparameters:grpo}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \"\\t\\\\centering\\n\",\n \"\\t\\\\includegraphics[width=1.\\\\textwidth]{dataset_pipeline.pdf}\\n\",\n \"\\t\\\\caption{Data processing pipeline showing total 209063 points split into train/test, filtered via multiple steps (lack info, label balance, curriculum learning), and categorized for SFT, RL, OOD evaluations.}\\n\",\n \"\\t\\\\label{fig:dataset_pipeline}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \"\\t\\\\centering\\n\",\n \"\\t\\\\includegraphics[width=0.9\\\\textwidth]{prompt_length_distribution.png}\\n\",\n \"\\t\\\\caption{Prompt length distribution across the dataset, illustrating the varying lengths of input prompts used for training and evaluation.}\\n\",\n \"\\t\\\\label{fig:prompt_length_distribution}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{figures/prompt.pdf}\\n\",\n \" \\\\caption{The prompt template for stock movement prediction.}\\n\",\n \" \\\\label{fig:appendix:prompt_template}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{figures/prompt_part_news.pdf}\\n\",\n \" \\\\caption{Example. Part 1.1: Stock News.}\\n\",\n \" \\\\label{fig:appendix:example_prompt_part_news}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{figures/prompt_part_news2.pdf}\\n\",\n \" \\\\caption{Example. Part 1.2: Stock News.}\\n\",\n \" \\\\label{fig:appendix:example_prompt_part_news2}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.75\\\\textwidth]{figures/prompt_part_price.pdf}\\n\",\n \" \\\\caption{Example. Part 2: Stock Price Info of Current Stock and Top-3 Similar Stocks.}\\n\",\n \" \\\\label{fig:appendix:example_prompt_part_price}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{figures/prompt_part_marco.pdf}\\n\",\n \" \\\\caption{Example. Part 3: Macroeconomic Indicators Report.}\\n\",\n \" \\\\label{fig:appendix:example_prompt_part_marco}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{figures/prompt_part_fundamentals.pdf}\\n\",\n \" \\\\caption{Example. Part 4.1: Stock Fundamentals Report.}\\n\",\n \" \\\\label{fig:appendix:example_prompt_part_fundamentals}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.99\\\\textwidth]{figures/prompt_part_fundamentals2.pdf}\\n\",\n \" \\\\caption{Example. Part 4.2: Stock Fundamentals Report.}\\n\",\n \" \\\\label{fig:appendix:example_prompt_part_fundamentals2}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{figures/prompt_part_baseinfo.pdf}\\n\",\n \" \\\\caption{Example. Part 5: Stock Basic Information.}\\n\",\n \" \\\\label{fig:appendix:example_prompt_part_baseinfo}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.85\\\\textwidth]{figures/prompt_part_quantitative_reports.pdf}\\n\",\n \" \\\\caption{Example. Part 6: Stock Quantitative Reports.}\\n\",\n \" \\\\label{fig:appendix:example_prompt_part_quantitative_reports}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{figures/response.pdf}\\n\",\n \" \\\\caption{Example. Part 7: Model Response.}\\n\",\n \" \\\\label{fig:appendix:example_response}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{response_grading.pdf}\\n\",\n \" \\\\caption{Example. Part 8: Model Response Grading.}\\n\",\n \" \\\\label{fig:appendix:example_response_grading}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{polish_prompt.pdf}\\n\",\n \" \\\\caption{The polish prompt allows the backbone model to generate refined responses that follow the proposed thinking schema in Section~\\\\ref{sec:method:1}.}\\n\",\n \" \\\\label{fig:appendix:polish_prompt}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Overview of BizFinBench~\\\\citep{lu2025bizfinbench0} Datasets}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\begin{tabular}{cp{17.8em}p{14.445em}p{5.39em}ll}\\n\",\n \" \\\\toprule\\n\",\n \" Category & \\\\multicolumn{1}{l}{Data} & \\\\multicolumn{1}{l}{Evaluation Dimensions} & \\\\multicolumn{1}{l}{Metrics} & Numbers & Avg Len. \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Reasoning & Anomalous Event Attribution (AEA) & Causal consistency\\\\newline{}Information relevance\\\\newline{}Noise resistance & Accuracy & 1064 & 939 \\\\\\\\\\n\",\n \" & Financial Time Reasoning (FTR) & Temporal reasoning correctness & Accuracy & 514 & 1162 \\\\\\\\\\n\",\n \" & Financial Tool Usage (FTU) & Tool selection appropriateness\\\\newline{}Parameter input accuracy\\\\newline{}Multi-tool coordination & Judge Score & 641 & 4556 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Numerical calculation & Financial Numerical Computation (FNC) & Computational accuracy\\\\newline{}Unit consistency & Accuracy & 581 & 651 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Q\\\\&A & Financial Knowledge QA (FQA) & Question comprehension\\\\newline{}Knowledge coverage\\\\newline{}Answer accuracy & Judge Score & 990 & 22 \\\\\\\\\\n\",\n \" & Financial Data Description (FDD) & Trend accuracy\\\\newline{}Data consistency & Judge Score & 1461 & 311 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Prediction recognition & Emotion Recognition (ER) & Emotion classification accuracy\\\\newline{}Implicit information extraction & Accuracy & 600 & 2179 \\\\\\\\\\n\",\n \" & Stock Price Prediction (SP) & Trend judgment, Causal reasoning & Accuracy & 497 & 4498 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Information extraction & Financial Named Entity Recognition (FNER) & Recognition accuracy\\\\newline{}Entity classification correctness & Accuracy & 435 & 533 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}%\\n\",\n \" }\\n\",\n \" \\\\label{datasetall}%\\n\",\n \"\\\\end{table}%\\n\"\n ],\n [\n \"\\\\begin{table}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Token Length Statistics of BizFinBench~\\\\citep{lu2025bizfinbench0}.}\\n\",\n \" \\\\label{query_token_stats}\\n\",\n \" \\\\begin{tabular}{lrrrr}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Dataset} & \\\\textbf{Min} & \\\\textbf{Max} & \\\\textbf{Avg} & \\\\textbf{Count} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" NER & 415 & 1,194 & 533.1 & 433 \\\\\\\\\\n\",\n \" FTU & 4,169 & 6,289 & 4,555.5 & 641 \\\\\\\\\\n\",\n \" AEA & 680 & 1,396 & 938.7 & 1,064 \\\\\\\\\\n\",\n \" ER & 1,919 & 2,569 & 2,178.5 & 600 \\\\\\\\\\n\",\n \" FNC & 287 & 2,698 & 650.5 & 581 \\\\\\\\\\n\",\n \" FDD & 26 & 645 & 310.9 & 1,461 \\\\\\\\\\n\",\n \" FTR & 203 & 8,265 & 1,162.0 & 514 \\\\\\\\\\n\",\n \" FQA & 5 & 45 & 21.7 & 990 \\\\\\\\\\n\",\n \" SP & 1,254 & 5,532 & 4,498.1 & 497 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \"\\t\\\\centering\\n\",\n \"\\t\\\\includegraphics[width=0.85\\\\textwidth]{ablation_on_CoT_4.pdf}\\n\",\n \"\\t\\\\caption{Detailed results on \\\\textbf{Fin-2024[December]} for different baselines.}\\n\",\n \"\\t\\\\label{fig:detailed_results:fin2024december}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\caption{Performance Comparison of Large Language Models on BizFinBench~\\\\citep{lu2025bizfinbench0}. The models are evaluated across multiple tasks, with results color-coded to represent the top three performers for each task: \\\\colorbox{golden}{golden} indicates the top-performing model, \\\\colorbox{lightblue}{silver} represents the second-best result, and \\\\colorbox{lightgreen}{bronze} denotes the third-best performance.}\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\begin{tabular}{lrrrrrrrrrr}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multicolumn{1}{c}{Model} & \\\\multicolumn{1}{c}{AEA} & \\\\multicolumn{1}{c}{FNC} & \\\\multicolumn{1}{c}{FTR} & \\\\multicolumn{1}{c}{FTU} & \\\\multicolumn{1}{c}{FQA} & \\\\multicolumn{1}{c}{FDD} & \\\\multicolumn{1}{c}{ER} & \\\\multicolumn{1}{c}{SP} & \\\\multicolumn{1}{c}{FNER} & \\\\multicolumn{1}{c}{Average}\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{10}{c}{Close-Source LLMs} \\\\\\\\\\n\",\n \" ChatGPT-o3 & \\\\cellcolor{lightblue}86.23 & 61.30 & \\\\cellcolor{lightblue}75.36 & \\\\cellcolor{golden}89.15 & \\\\cellcolor{lightblue}91.25 & \\\\cellcolor{lightgreen}98.55 & 44.48 & 53.27 & 65.13 & \\\\cellcolor{golden}73.86 \\\\\\\\\\n\",\n \" ChatGPT-o4-mini & \\\\cellcolor{lightgreen}85.62 & 60.10 & 71.23 & 74.40 & 90.27 & 95.73 & \\\\cellcolor{golden}47.67 & 52.32 & 64.24 & 71.29 \\\\\\\\\\n\",\n \" GPT-4o & 79.42 & 56.51 & \\\\cellcolor{golden}76.20 & 82.37 & 87.79 & \\\\cellcolor{golden}98.84 & 45.33 & 54.33 & 65.37 & \\\\cellcolor{lightgreen}71.80 \\\\\\\\\\n\",\n \" Gemini-2.0-Flash & \\\\cellcolor{golden}86.94 & 62.67 & 73.97 & 82.55 & 90.29 & \\\\cellcolor{lightblue}98.62 & 22.17 & \\\\cellcolor{lightgreen}56.14 & 54.43 & 69.75 \\\\\\\\\\n\",\n \" Claude-3.5-Sonnet & 84.68 & 63.18 & 42.81 & \\\\cellcolor{lightblue}88.05 & 87.35 & 96.85 & 16.67 & 47.60 & 63.09 & 65.59 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{10}{c}{Open-Weight LLMs} \\\\\\\\\\n\",\n \" Qwen2.5-7B-Instruct & 73.87 & 32.88 & 39.38 & 79.03 & 83.34 & 78.93 & 37.50 & 51.91 & 30.31 & 56.35 \\\\\\\\\\n\",\n \" Qwen2.5-72B-Instruct & 69.27 & 54.28 & 70.72 & 85.29 & 87.79 & 97.43 & 35.33 & 55.13 & 54.02 & 67.70 \\\\\\\\\\n\",\n \" Qwen2.5-VL-3B & 53.85 & 15.92 & 17.29 & 8.95 & 81.60 & 59.44 & 39.50 & 52.49 & 21.57 & 38.96 \\\\\\\\\\n\",\n \" Qwen2.5-VL-7B & 73.87 & 32.71 & 40.24 & 77.85 & 83.94 & 77.41 & 38.83 & 51.91 & 33.40 & 56.68 \\\\\\\\\\n\",\n \" Qwen2.5-VL-14B & 37.12 & 41.44 & 53.08 & 82.07 & 84.23 & 7.97 & 37.33 & 54.93 & 47.47 & 49.52 \\\\\\\\\\n\",\n \" Qwen2.5-VL-32B & 76.79 & 50.00 & 62.16 & 83.57 & 85.30 & 95.95 & 40.50 & 54.93 & 68.36 & 68.62 \\\\\\\\\\n\",\n \" Qwen2.5-VL-72B & 69.55 & 54.11 & 69.86 & 85.18 & 87.37 & 97.34 & 35.00 & 54.94 & 54.41 & 67.53 \\\\\\\\\\n\",\n \" Qwen3-1.7B & 77.40 & 35.80 & 33.40 & 75.82 & 73.81 & 78.62 & 22.40 & 48.53 & 11.23 & 50.78 \\\\\\\\\\n\",\n \" Qwen3-4B & 83.60 & 47.40 & 50.00 & 78.19 & 82.24 & 80.16 & 42.20 & 50.51 & 25.19 & 59.94 \\\\\\\\\\n\",\n \" Qwen3-14B & 84.20 & 58.20 & 65.80 & 82.19 & 84.12 & 92.91 & 33.00 & 52.31 & 50.70 & 67.05 \\\\\\\\\\n\",\n \" Qwen3-32B & 83.80 & 59.60 & 64.60 & 85.12 & 85.43 & 95.37 & 39.00 & 52.26 & 49.19 & 68.26 \\\\\\\\\\n\",\n \" QwQ-32B & 84.02 & 52.91 & 64.90 & 84.81 & 89.60 & 94.20 & 34.50 & \\\\cellcolor{lightblue}56.68 & 30.27 & 65.77 \\\\\\\\\\n\",\n \" Xuanyuan3-70B & 12.14 & 19.69 & 15.41 & 80.89 & 86.51 & 83.90 & 29.83 & 52.62 & 37.33 & 46.48 \\\\\\\\\\n\",\n \" Llama-3.1-8B-Instruct & 73.12 & 22.09 & 2.91 & 77.42 & 76.18 & 69.09 & 29.00 & 54.21 & 36.56 & 48.95 \\\\\\\\\\n\",\n \" Llama-3.1-70B-Instruct & 16.26 & 34.25 & 56.34 & 80.64 & 79.97 & 86.90 & 33.33 & \\\\cellcolor{golden}62.16 & 45.95 & 55.09 \\\\\\\\\\n\",\n \" Llama 4 Scout & 73.60 & 45.80 & 44.20 & 85.02 & 85.21 & 92.32 & 25.60 & 55.76 & 43.00 & 61.17 \\\\\\\\\\n\",\n \" DeepSeek-V3 (671B) & 74.34 & 61.82 & 72.60 & 86.54 & \\\\cellcolor{lightgreen}91.07 & 98.11 & 32.67 & 55.73 & \\\\cellcolor{lightblue}71.24 & 71.57 \\\\\\\\\\n\",\n \" DeepSeek-R1 (671B) & 80.36 & \\\\cellcolor{lightgreen}64.04 & \\\\cellcolor{lightgreen}75.00 & 81.96 & \\\\cellcolor{golden}91.44 & 98.41 & 39.67 & 55.13 & \\\\cellcolor{golden}71.46 & \\\\cellcolor{lightblue}73.05 \\\\\\\\\\n\",\n \" DeepSeek\\\\_R1\\\\_14B\\\\_Instruct & 71.33 & 44.35 & 50.45 & 81.96 & 85.52 & 92.81 & 39.50 & 50.20 & 52.76 & 59.49 \\\\\\\\\\n\",\n \" DeepSeek\\\\_R1\\\\_32B\\\\_Instruct & 73.68 & 51.20 & 50.86 & 83.27 & 87.54 & 97.81 & 41.50 & 53.92 & 56.80 & 66.29 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{11}{c}{Our LLMs} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_14B\\\\_SFT~\\\\tnote{2} & \\\\cellcolor{Background1}80.63 & \\\\cellcolor{Background1}51.67 & \\\\cellcolor{Background1}52.61 & \\\\cellcolor{Background1}83.53 & \\\\cellcolor{Background1}89.05 & \\\\cellcolor{Background1}96.72 & \\\\cellcolor{Background1}36.68 & \\\\cellcolor{Background1}50.43 & \\\\cellcolor{Background1}50.85 & \\\\cellcolor{Background1}65.36 \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT})$ & \\\\textcolor{GREEN}{+9.25} & \\\\textcolor{GREEN}{+7.28} & \\\\textcolor{GREEN}{+2.19} & \\\\textcolor{GREEN}{+1.53} & \\\\textcolor{GREEN}{+3.42} & \\\\textcolor{GREEN}{+3.85} & \\\\textcolor{RED}{-2.93} & \\\\textcolor{GREEN}{+0.24} & \\\\textcolor{RED}{-1.92} & \\\\textcolor{GREEN}{+5.83} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_14B\\\\_SFT\\\\_GRPO~\\\\tnote{2} & \\\\cellcolor{Background1}81.46 & \\\\cellcolor{Background1}52.41 & \\\\cellcolor{Background1}53.47 & \\\\cellcolor{Background1}83.57 & \\\\cellcolor{Background1}89.02 & \\\\cellcolor{Background1}95.58 & \\\\cellcolor{Background1}36.83 & \\\\cellcolor{Background1}54.06 & \\\\cellcolor{Background1}51.24 & \\\\cellcolor{Background1}66.92 \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+10.03} & \\\\textcolor{GREEN}{+8.09} & \\\\textcolor{GREEN}{+2.91} & \\\\textcolor{GREEN}{+1.64} & \\\\textcolor{GREEN}{+3.45} & \\\\textcolor{GREEN}{+2.63} & \\\\textcolor{RED}{-2.74} & \\\\textcolor{GREEN}{+3.82} & \\\\textcolor{RED}{-1.53} & \\\\textcolor{GREEN}{+7.46} \\\\\\\\\\n\",\n \" $\\\\quad$ 14B $\\\\Delta_{\\\\text{SFT}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+0.82} & \\\\textcolor{GREEN}{+0.85} & \\\\textcolor{GREEN}{+0.81} & \\\\textcolor{GREEN}{+0.06} & 0.00 & \\\\textcolor{RED}{-1.23} & \\\\textcolor{GREEN}{+0.25} & \\\\textcolor{GREEN}{+3.63} & \\\\textcolor{GREEN}{+0.42} & \\\\textcolor{GREEN}{+1.53} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_32B\\\\_SFT & \\\\cellcolor{Background1}80.45 & \\\\cellcolor{lightblue}66.42 & \\\\cellcolor{Background1}63.28 & \\\\cellcolor{lightgreen}86.88 & \\\\cellcolor{Background1}88.43 & \\\\cellcolor{Background1}93.76 & \\\\cellcolor{lightblue}46.05 & \\\\cellcolor{Background1}55.27 & \\\\cellcolor{lightgreen}68.41 & \\\\cellcolor{Background1}70.08 \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT})$ & \\\\textcolor{GREEN}{+6.75} & \\\\textcolor{GREEN}{+15.23} & \\\\textcolor{GREEN}{+12.37} & \\\\textcolor{GREEN}{+3.64} & \\\\textcolor{GREEN}{+0.83} & \\\\textcolor{RED}{-4.14} & \\\\textcolor{GREEN}{+4.52} & \\\\textcolor{GREEN}{+1.25} & \\\\textcolor{GREEN}{+11.63} & \\\\textcolor{GREEN}{+3.75} \\\\\\\\\\n\",\n \" \\\\cellcolor{Background1}DeepSeek\\\\_R1\\\\_32B\\\\_SFT\\\\_GRPO & \\\\cellcolor{Background1}80.67 & \\\\cellcolor{golden}66.83 & \\\\cellcolor{Background1}64.45 & \\\\cellcolor{Background1}86.79 & \\\\cellcolor{Background1}88.52 & \\\\cellcolor{Background1}91.26 & \\\\cellcolor{lightgreen}45.68 & \\\\cellcolor{Background1}54.83 & \\\\cellcolor{Background1}67.75 & \\\\cellcolor{Background1}70.44 \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{Instruct}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+6.95} & \\\\textcolor{GREEN}{+15.62} & \\\\textcolor{GREEN}{+13.57} & \\\\textcolor{GREEN}{+3.55} & \\\\textcolor{GREEN}{+0.93} & \\\\textcolor{RED}{-6.64} & \\\\textcolor{GREEN}{+4.13} & \\\\textcolor{GREEN}{+0.85} & \\\\textcolor{GREEN}{+10.93} & \\\\textcolor{GREEN}{+4.12} \\\\\\\\\\n\",\n \" $\\\\quad$ 32B $\\\\Delta_{\\\\text{SFT}}(\\\\text{SFT\\\\_GRPO})$ & \\\\textcolor{GREEN}{+0.23} & \\\\textcolor{GREEN}{+0.42} & \\\\textcolor{GREEN}{+1.23} & \\\\textcolor{RED}{-0.06} & \\\\textcolor{GREEN}{+0.13} & \\\\textcolor{RED}{-2.53} & \\\\textcolor{RED}{-0.42} & \\\\textcolor{RED}{-0.43} & \\\\textcolor{RED}{-0.72} & \\\\textcolor{GREEN}{+0.33} \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}%\\n\",\n \" }\\n\",\n \" \\\\label{table:bizfinbench_detailed_results}%\\n\",\n \"\\\\end{table*}%\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \"\\t\\\\centering\\n\",\n \"\\t\\\\includegraphics[width=1\\\\textwidth]{response_no_CoT.pdf}\\n\",\n \"\\t\\\\caption{Zero-shot responses. The model struggles to provide accurate and relevant answers without the step-by-step reasoning process enabled by CoT prompting.}\\n\",\n \"\\t\\\\label{fig:appendix:case_study:response_no_cot}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \"\\t\\\\centering\\n\",\n \"\\t\\\\includegraphics[width=1\\\\textwidth]{response_with_CoT.pdf}\\n\",\n \"\\t\\\\caption{CoT Prompting responses. The model demonstrates improved reasoning and accuracy when guided through a step-by-step thought process.}\\n\",\n \"\\t\\\\label{fig:appendix:case_study:response_with_cot}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[htbp]\\n\",\n \"\\t\\\\centering\\n\",\n \"\\t\\\\includegraphics[width=1\\\\textwidth]{response_cold_started.pdf}\\n\",\n \"\\t\\\\caption{Case study on cold-started responses. Left is the original response, and right is the cold-started response. The cold-started response is more concise and to the point, avoiding unnecessary elaboration.}\\n\",\n \"\\t\\\\label{fig:appendix:case_study:response_cold_started}\\n\",\n \"\\\\end{figure*}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\documentclass{article}\n% if you need to pass options to natbib, use, e.g.:\n % \\PassOptionsToPackage{numbers, compress}{natbib}\n% before loading neurips_2022\n\n\\PassOptionsToPackage{table}{xcolor}\n% ready for submission\n% \\usepackage{neurips_2025}\n% \\usepackage{iclr2026_conference,times}\n% \\usepackage[preprint]{iclr2026_conference}\n\n\n% to compile a preprint version, e.g., for submission to arXiv, add add the\n% [preprint] option:\n\\usepackage[preprint]{neurips_2025}\n\n% to compile a camera-ready version, add the [final] option, e.g.:\n% \\usepackage[final]{neurips_2023}\n\n\n% to avoid loading the natbib package, add option nonatbib:\n% \\usepackage[nonatbib]{neurips_2023}\n\n\n\\usepackage[utf8]{inputenc} % allow utf-8 input\n\\usepackage[T1]{fontenc} % use 8-bit T1 fonts\n\\usepackage[colorlinks,linkcolor=blue,urlcolor=blue,citecolor=blue]{hyperref}% hyperlinks\n\\usepackage{url} % simple URL typesetting\n\\usepackage{booktabs} % professional-quality tables\n\\usepackage{amsfonts} % blackboard math symbols\n\\usepackage{nicefrac} % compact symbols for 1/2, etc.\n\\usepackage{microtype} % microtypography\n\n\\usepackage{xspace}\n% \\usepackage[table]{xcolor}\n\\usepackage{stmaryrd}\n\\usepackage{amsthm}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{mathtools}\n\\usepackage{times}\n% \\usepackage{latexsym}\n\\usepackage[pdftex]{graphicx}\n\\graphicspath{{figures/}}\n% \\usepackage{subfigure}\n\\usepackage{wrapfig}\n\\usepackage{subcaption}\n% \\captionsetup[subfigure]{justification=centering}\n\\usepackage{multirow}\n\\usepackage{multicol}\n\\usepackage{makecell}\n% \\usepackage{tcolorbox}\n\n\\usepackage{tabularx} % 用于灵活控制列宽\n\n\\usepackage{ragged2e} % 优化文本对齐\n% \\usepackage{listings}\n\\usepackage{algorithm}\n\\usepackage{algorithmic}\n% \\usepackage{algpseudocodex}\n\\usepackage{arydshln}\n\\usepackage{threeparttable}\n% \\usepackage[table,xcdraw]{xcolor}\n\\usepackage[most]{tcolorbox}\n% \\usepackage[table]{xcolor}\n% \\usepackage{minted}\n% \\usepackage{fontawesome5}\n\n% region command\n\n\\newcommand{\\repourl}{\\url{https://github.com/LinXueyuanStdio/RETuning}}\n% \\renewcommand{\\repourl}{\\url{https://anonymous.4open.science/r/RETuning}}\n\n\\newcommand{\\huggingfaceurl}{\\url{https://huggingface.co/collections/linxy/retuning-68c999be4d9ac2834c64fd00}}\n% \\renewcommand{\\huggingfaceurl}{\\url{https://anonymous.4open.science/r/RETuning}}\n\n\\newcommand{\\dataseturl}{\\url{https://huggingface.co/datasets/linxy/Fin-2024}}\n% \\renewcommand{\\dataseturl}{\\url{https://anonymous.4open.science/r/RETuning}}%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure reference, capital. For start of sentence\n\\def\\Figref#1{Figure~\\ref{#1}}\n% Figure reference, lower-case.\n\\def\\figref#1{figure~\\ref{#1}}\n\\def\\twofigref#1#2{figures \\ref{#1} and \\ref{#2}}\n\\def\\trifigref#1#2#3{figures \\ref{#1}, \\ref{#2} and \\ref{#3}}\n\\def\\quadfigref#1#2#3#4{figures \\ref{#1}, \\ref{#2}, \\ref{#3} and \\ref{#4}}\n\n% Section reference, capital.\n\\def\\Secref#1{Section~\\ref{#1}}\n% Section reference, lower-case.\n\\def\\secref#1{section~\\ref{#1}}\n% Reference to two sections.\n\\def\\twosecrefs#1#2{sections \\ref{#1} and \\ref{#2}}\n% Reference to three sections.\n\\def\\secrefs#1#2#3{sections \\ref{#1}, \\ref{#2} and \\ref{#3}}\n\n% Reference to an equation, upper case\n\\def\\Eqref#1{Equation~\\ref{#1}}\n% Reference to an equation, lower-case.\n\\def\\eqref#1{equation~\\ref{#1}}\n% A raw reference to an equation---avoid using if possible\n\\def\\plaineqref#1{\\ref{#1}}\n\n% Reference to an equation, upper case.\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n% Reference to a chapter, lower-case.\n\\def\\chapref#1{chapter~\\ref{#1}}\n% Reference to a range of chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n\\newtheorem{theorem}{Theorem}\n\\newtheorem{definition}{Definition}\n\\newtheorem{corollary}{Corollary}\n\\newtheorem{proposition}{Proposition}\n\\newtheorem{observation}{Observation}\n\\newtheorem{lemma}{Lemma}\n\\newtheorem{rem}{Remark}% 主色 (Primary Colors)\n\\definecolor{Primary1}{RGB}{106,62,171} % Keqing Purple – #6A3EAB：刻晴深紫色主裙，适合作为节点背景或主要强调色\n\\definecolor{Primary2}{RGB}{244,244,249} % Ivory White – #F4F4F9：刻晴衣饰中的柔和白色，用于浅色背景或图形填充\n\n% 辅色 (Secondary Colors)\n\\definecolor{Secondary1}{RGB}{179,167,225} % Silver Lilac – #B3A7E1：刻晴头发的淡紫色，与主紫相衬\n\\definecolor{Secondary2}{RGB}{199,179,230} % Lavender Mist – #C7B3E6：衣裙中浅紫的渐变色，用于增加层次感\n\\definecolor{Secondary3}{RGB}{50,43,68} % Charcoal Night – #322B44：刻晴暗紫色袜子/阴影，用作深色文字或线条\n\n% 强调色/高光 (Accent/Highlight Colors)\n\\definecolor{Highlight1}{RGB}{232,183,76} % Electro Gold – #E8B74C：金色装饰和雷电光芒，用于节点边框和小图标\n\\definecolor{Highlight2}{RGB}{176,143,243} % Lightning Violet – #B08FF3：电元素光辉的淡紫色，用于连线或边框高光\n\\definecolor{Highlight3}{RGB}{126,162,255} % Cloud Blue – #7EA2FF：裙摆边缘的浅蓝色，与紫色形成清新对比\n\n% 背景色 (Background Colors)\n\\definecolor{Background1}{RGB}{241,230,247} % Ivory Mist (Light) – #f1e6f7ff：柔和的象牙白，适合浅色背景\n\\definecolor{Background2}{RGB}{44,28,53} % Night Amethyst (Dark) – #2C1C35：深夜紫色，适合深色背景\n\n% 字体与边框色 (Font/Border Colors)\n\\definecolor{Font1}{RGB}{44,28,53} % Midnight Purple – #2C1C35：深紫灰色，用于浅色背景上的字体和边框\n\\definecolor{Font2}{RGB}{244,236,232} % Off-White – #F4ECE8：近白的浅灰色，用于深色背景上的字体和边框\n\n% #C64a11\n\\definecolor{Best1}{RGB}{198,70,17} % first best results\n% #E4A304\n\\definecolor{Best2}{RGB}{228,163,4} % second best results\n% #548235\n\\definecolor{Best3}{RGB}{84,130,53} % third best results\n\n\n\\definecolor{RED}{RGB}{198,70,17}\n\\definecolor{GREEN}{RGB}{84,130,53}\n\\definecolor{GREY}{RGB}{128,128,128}\n\n\\definecolor{golden}{RGB}{255, 215, 0} % Golden rgb(255, 215, 0)\n\\definecolor{lightblue}{RGB}{147, 170, 177} % Silver rgba(147, 170, 177, 1)\n\\definecolor{lightgreen}{RGB}{182, 124, 98} % Bronze rgba(182, 124, 98, 1)\n% Usage:\n% \\textcolor{Best1}{your\\_text\\_here}\n% \\tcbox[colback=yellow]{your\\_text\\_here}\n% \\begin{tcolorbox}[colback=blue, colframe=blue, boxrule=1pt]\n% your\\_text\\_here\n% \\end{tcolorbox}\n\n\\hypersetup{\n colorlinks=False,\n linkcolor=blue,\n citecolor=blue,\n urlcolor=blue}\n\n\\definecolor{Green}{rgb}{0.0, 0.2, 1.0}\n\\definecolor{Red}{rgb}{0.8, 0.0, 0.0}\n\\newtcolorbox{takeaway}{\n colback=white,\n colframe=green!75!black,\n fonttitle=\\bfseries,\n title=,\n boxrule=1pt,\n arc=4pt,\n auto outer arc,\n width=\\linewidth,\n breakable,\n}% correct bad hyphenation here\n\\hyphenation{op-tical net-works semi-conduc-tor}\n\n% shortcuts\n\\newcommand{\\methodname}{{\\sc Tradeformer}\\xspace}\n\\newcommand{\\ie}{\\textit{i.e.}}\n\\newcommand{\\eg}{\\textit{e.g.}}\n\\newcommand{\\hidecomments}[1]{}\n\n% \\usepackage{xcolor} % 需要加载这个宏包来支持颜色设置\n\\providecommand{\\hr}[1]{{\\color{blue} [HR: #1]}}\n\\providecommand{\\rok}[1]{{\\color{magenta} [Rok: #1]}}\n% >>> \\hr{Hello} \\rok{world}\n% [HR: Hello] [Rok: world]\n\n% endregion\n\n\n% \\title{Can Stock Movement Prediction Benefit from LLMs Inference-Time Scaling?}\n% \\title{Scaling Stock Movement Prediction for LLMs via \\textcolor{Primary1}{R}eflective \\textcolor{Primary1}{E}vidence \\textcolor{Primary1}{Tuning}}\n\\title{\\textcolor{Primary1}{RETuning}: Upgrading Inference-Time Scaling for Stock Movement Prediction with Large Language Models}\n% Enhance Stock Movement Prediction for LLMs via Reflective Evidence Tuning\n\\author{\n Xueyuan Lin$^{1,2,3}*$ \\quad Cehao Yang$^{1,2}*$ \\quad Ye Ma$^{3}$ \\quad Ming Li$^{3}$ \\quad Rongjunchen Zhang$^{3}$ \\\\\n \\textbf{Yang Ni$^{1}$ \\quad Xiaojun Wu$^{1,2}$ \\quad Chengjin Xu$^{2,4}$ \\quad Jian Guo$^{2}\\dagger$ \\quad Hui Xiong$^{1}\\dagger$} \\\\\n $^1$ The Hong Kong University of Science and Technology (Guangzhou)\\\\\n $^2$ IDEA Research \\quad $^3$ Hithink RoyalFlush Information Network Co., Ltd \\quad $^4$ DataArc Tech Ltd\\\\\n % \\small\\texttt{LinXueyuanStdio@gmail.com} \\\\\n % \\faEnvelope~\\small\\texttt{linxy59@mail2.sysu.edu.cn, \\{xlin058, yni002\\}@connect.hkust-gz.edu.cn}\\\\\n \\small\\texttt{\\{xlin058,cyang289,yni002\\}@connect.hkust-gz.edu.cn, xionghui@ust.hk} \\\\\n \\small\\texttt{\\{maye,zhangrongjunchen\\}@myhexin.com, lm92@mail.ustc.edu.cn}\\\\\n \\small\\texttt{\\{xuchengjin,wuxiaojun,guojian\\}@idea.edu.cn}\n}\n\\renewcommand{\\thefootnote}{\\large\\fnsymbol{footnote}}\n\\begin{document}\n\n\\maketitle\n\\footnotetext[1]{Equal contribution.}\n\\footnotetext[2]{Corresponding Authors.}\n\n\\begin{abstract}\nRecently, large language models (LLMs) have demonstrated outstanding reasoning capabilities and inference-time scaling on mathematical and coding tasks. However, their application to financial tasks—especially the most fundamental task of stock movement prediction—remains underexplored. We study a three-class classification problem (up, hold, down) and, by analyzing existing reasoning responses, observe that:\n(1) LLMs are easily swayed by contextual viewpoints, tending to follow analysts' opinions rather than exhibit a systematic, independent analytical logic in their chain-of-thoughts (CoTs).\n(2) LLMs often list summaries from different sources without weighing adversarial evidence, yet such counterevidence is crucial for reliable prediction.\nIt shows that the model does not make good use of its reasoning ability to complete the task.\nTo address this, we propose \\textbf{R}eflective \\textbf{E}vidence \\textbf{}uning (\\textbf{RETuning}), a cold-start method prior to reinforcement learning, to enhance prediction ability. While generating CoT, \\textbf{RETuning} encourages dynamically constructing an analytical framework from diverse information sources, organizing and scoring evidence for price up or down based on that framework—rather than on contextual viewpoints—and finally reflecting to derive the prediction. This approach maximally aligns the model with its learned analytical framework, ensuring independent logical reasoning and reducing undue influence from context.\nWe also build a large-scale dataset spanning all of 2024 for 5,123 A-share stocks, with long contexts (32K tokens) and over 200K samples. In addition to price and news, it incorporates analysts' opinions, quantitative reports, fundamental data, macroeconomic indicators, and similar stocks.\nExperiments on this new dataset show that, as a cold-start method, \\textbf{RETuning} successfully unlocks the model's reasoning ability in the financial domain. During reinforcement learning, response length steadily increases under the designed curriculum setting. Furthermore, inference-time scaling still works even after 6 months or on out-of-distribution stocks, since the models gain valuable insights about stock movement prediction.\n\\end{abstract}\n\n\\section{Introduction}\\label{sec:introduction}\n\\textbf{Stock Movement Prediction (SMP)} is one of the most fundamental and consequential tasks in finance. It not only directly affects the interests of individual investors but also plays a central role in algorithmic trading~\\citep{Mahfooz2022ImprovingST,Ta2018PredictionAP}, financial risk control~\\citep{Adyatma2022TheIS,Vui2013ARO}, and intelligent research platforms~\\citep{Shi2020StockMP}. In recent years, Large Language Models (LLMs)~\\citep{brown2020language,Achiam2023GPT4TR,Qwen,LLaMA} have demonstrated remarkable reasoning capabilities in domains such as code generation and mathematical problem-solving~\\citep{deepseek-r1,o1,uesato2022solving}. This has sparked growing interest in exploring whether such models can also excel in financial tasks. However, it remains an open question whether LLMs' strength in \\textit{reasoning} and \\textit{inference-time scaling} can be effectively harnessed for stock price prediction.\n\nIn the traditional planning phase of a financial agent, the model has access to a wide range of information sources—news articles, analyst opinions, research reports, quantitative factor analyzes, and more. Despite this richness, making reliable and interpretable predictions remains a major challenge. On one hand, \\textcolor{Primary1}{LLMs often exhibit strong prior biases due to the optimistic slant of their training data}, which is skewed toward long positions and excludes contrarian views for political or regulatory reasons. On the other hand, these models tend to \\textcolor{Primary1}{lack the ability to construct independent reasoning frameworks, reconcile conflicting information, and perform reflective analysis}—capabilities that are essential for robust financial decision-making.\n\nTo address these challenges, we propose a novel modeling paradigm that treats stock movement prediction as a \\textit{generative reasoning task}. By processing all textual information sources end-to-end, this approach aims to simulate the thought process of a human trader, ultimately generating structured and interpretable predictions. Two key innovations underpin this paradigm.\n\nFirst, we introduce \\textbf{Reflective Evidence Tuning (RETuning)}, which instills LLMs to dynamically construct reasoning frameworks based on diverse information sources, collect and evaluate evidence for potential price directions (up, down, or hold), and reflect on the evidence before making a final prediction. This structured approach is a cold-start training mechanism prior to reinforcement learning (RL). It enables models to avoid merely summarizing or echoing external viewpoints and instead follow an internally consistent logic, improving both interpretability and accuracy.\n\nSecond, we explore the role of \\textbf{inference-time scalability}, a technique that has shown promise in mathematical and programming tasks~\\citep{s1,S*}. Specifically, we investigate whether \\textit{majority voting} can significantly improve predictive accuracy in financial domain. Although widely successful elsewhere, its efficacy in stock movement prediction has not yet been systematically examined.\n\nTo support this research, we construct a large-scale, high-quality dataset that reflects the complexity and information density of real-world financial environments. Covering the full year of 2024 across over 4,000 A-share stocks, this dataset integrates six heterogeneous information sources: news, fundamentals, analyst opinions, quantitative factor reports, macroeconomic context, and stocks of similar trends. With over 200,000 samples and an average input length of up to 32K tokens, it overcomes the limitations of prior datasets that were outdated and lacked information diversity~\\citep{StockNet,CMIN,EDT}. The details of the dataset construction are discussed in Appendix~\\ref{sec:appendix:dataset_details}.\n\nEmpirical results show that \\textbf{RETuning} effectively enhances reasoning structure and improves predictive performance over strong baselines. It also generalizes beyond stock movement prediction, yielding significant improvements in other financial tasks, and demonstrates strong performance under inference-time scaling and out-of-distribution settings.\n\nOur contribution can be summarized as follows:\n(1) We build a large-scale, long-context financial dataset with diverse evidence sources beyond price and news, which fill the gap that existing datasets are outdated and lack information diversity.\n(2) We introduce \\textbf{RETuning}, synthesizing cold-start responses that guide LLMs to construct and reflect on an analytical framework for stock movement prediction. It allows significant inference-time scalability of LLMs in the prediction task.\n% 强调方法的唯一性\n% 数据集和任务更合理\n(3) We empirically show that \\textbf{RETuning} unlocks prediction ability and generalizes beyond stock movement prediction. We believe this research lays the groundwork for deploying trustworthy, reasoning-driven LLMs in real-world financial applications.\n\n\\section{Related Work}\\label{sec:relatedwork}\n\n\\paragraph{Stock Movement Prediction with LLMs.}\nRecent work has focused on exploring various types of information sources for stock movement prediction with LLMs. Several studies emphasize the importance of stock-related news in revealing fundamental market insights~\\citep{vargas2018deep,li2021modeling}. Meanwhile, other research highlights the significance of understanding the relationships between companies and industries~\\citep{feng2019temporal, hsu2021fingat}. Recent studies have also provided empirical evidence of the impact of public sentiment on market trends, with researchers working to extract sentiment and keyphrases from news and social media data~\\citep{nguyen2015sentiment, hao2021predicting}. However, these works often focus on a single type of information source, such as news or sentiment, and do not fully leverage the potential of LLMs to integrate multiple heterogeneous sources. In contrast, our work aims to construct a comprehensive dataset that incorporates diverse information sources, including news, fundamentals, analyst opinions, quantitative reports, macroeconomic indicators, and similar stocks, to enhance the predictive capabilities of LLMs in stock movement prediction.\n\n% \\paragraph{Inference-Time Scaling for LLMs.}\n% Inference-time scaling methods~\\cite{snell2024scaling} enhance LLM performance by leveraging additional computation during generation, broadly categorized into three strategies. \\textbf{Repeated sampling} improves diversity and accuracy via parallel candidate generation, utilizing verification strategies like majority voting~\\citep{li2024agentsneed,lin-etal-2024-just,wang2023selfconsistency,toh2024votescountprogramsverifiers} or best-of-N (BoN) selection with verifiers~\\citep{stiennon2020learning,cobbe2021trainingverifierssolvemath,nakano2022webgptbrowserassistedquestionansweringhuman,li-etal-2023-making,liu2025pairwise}, while efficiency optimizations prune low-scoring paths early~\\citep{zhang2024accelerating,qiu2024treebonenhancinginferencetimealignment,sun2024fast,manvi2024adaptiveinferencetimecomputellms,ye-ng-2024-preference}. \\textbf{Self-correction} iteratively refines outputs using feedback from tools, external models, or self-critique~\\cite{shinn2023reflexionlanguageagentsverbal,gou2024critic,chen2024teaching,gao-etal-2023-rarr,Yasunaga20DrRepair,paul-etal-2024-refiner,du2023improvingfactualityreasoninglanguage,xiong-etal-2023-examining,liang2024encouragingdivergentthinkinglarge,chen-etal-2024-reconcile,wang2024mixtureofagentsenhanceslargelanguage,kim2024llmsproducefaithfulexplanations,khan2024debating,chan2024chateval,cheng-etal-2024-chainlm,laban2024surechallengingllmsleads,amayuelas2024multiagentcollaborationattackinvestigating,stengeleskin2024teachingmodelsbalanceresisting,liu2024groupdebateenhancingefficiencymultiagent,li2024improvingmultiagentdebatesparse,yuan2024selfrewardinglanguagemodels,bai2022constitutionalaiharmlessnessai,madaan2023selfrefine,kim2023languagemodelssolvecomputer,li2024confidencemattersrevisitingintrinsic,song2025progcoprogramhelpsselfcorrection}, though its efficacy depends on feedback reliability~\\cite{olausson2024is,huang2024large,wang2024reasoningtokeneconomiesbudgetaware,valmeekam2023largelanguagemodelsreally,stechly2023gpt4doesntknowits,kamoi2024llmsactuallycorrectmistakes,zhang2024understandingdarkllmsintrinsic,tyen-etal-2024-llms,yang2024confidencevscritiquedecomposition}. \\textbf{Tree searching} combines parallel and sequential scaling via algorithms like MCTS or A*~\\cite{NEURIPS2023_271db992,xie2023selfevaluation,wang2024qimprovingmultistepreasoning,hao-etal-2023-reasoning,bi2024forestofthoughtscalingtesttimecompute,park2024ensembling,hu-etal-2024-serts,jiang2024ragstarenhancingdeliberativereasoning,li2024thinkciteimprovingattributedtext,feng2025airragactivatingintrinsicreasoning,luo2025kbqao1agenticknowledgebase,gan2025mastermultiagentllmspecialized,cheng2025thinkmorehallucinateless,yuan2025mctssqleffectiveframeworktexttosql,long2023largelanguagemodelguided,chari2025pheromonebasedlearningoptimalreasoning} guided by value functions~\\citep{xu2023traingainunleashmathematical,hao-etal-2023-reasoning,chen2024alphamathzeroprocesssupervision,feng2024alphazeroliketreesearchguidelarge,qi2024verifierqenhancingllmtest,qi2024mutualreasoningmakessmaller,gao2024interpretablecontrastivemontecarlo,zhang2024accessinggpt4levelmathematical,zhang2024llamaberrypairwiseoptimizationo1like}. Training techniques distill these scaling benefits into more efficient models~\\citep{gao2023scaling,hou2024doesrlhfscaleexploring,gulcehre2023reinforcedselftrainingrestlanguage,amini2024variationalbestofnalignment,gui2024bonbon,sessa2024bondaligningllmsbestofn,chow2024inferenceawarefinetuningbestofnsampling,saunders2022selfcritiquingmodelsassistinghuman,zelikman2022star,yuan2025agentrtraininglanguagemodel,subramaniam2025multiagent,an2023learning,qu2024recursiveintrospectionteachinglanguage,gao2024embeddingselfcorrectioninherentability,zhang2024learnanswertraininglanguage,xi2024enhancingllmreasoningcritique,havrilla2024glorewhenwhereimprove,welleck2023generating,kumar2024traininglanguagemodelsselfcorrect,hou2025advancinglanguagemodelreasoning,ahmadian-etal-2024-back,guo2025deepseek,shao2024deepseekmathpushinglimitsmathematical,zhai2024enhancingdecisionmakingllmagents,xu2024sramctsselfdrivenreasoningaugmentation,guan2025rstarmathsmallllmsmaster,zhang2024restmctsllmselftrainingprocess,xie2024montecarlotreesearch,wang2024selfimprovementllmsmctsleveraging,qin2024o1replicationjourneystrategic,zhao2024marcoo1openreasoningmodels,zhang2024o1codero1replicationcoding}.\n% However, these methods have not been systematically applied to financial tasks, particularly stock movement prediction. Our work aims to fill this gap by exploring how inference-time scaling can be effectively utilized in this domain.\n\\paragraph{Inference-Time Scaling for LLMs.}\nInference-time scaling methods~\\citep{snell2024scaling} enhance LLM performance by leveraging additional computation during generation, broadly categorized into three strategies. \\textbf{Repeated sampling} improves diversity and accuracy via parallel candidate generation, utilizing verification strategies like majority voting~\\citep{li2024agentsneed,lin-etal-2024-just,wang2023selfconsistency,toh2024votescountprogramsverifiers} or best-of-N (BoN) selection with verifiers~\\citep{stiennon2020learning,cobbe2021trainingverifierssolvemath,nakano2022webgptbrowserassistedquestionansweringhuman,li-etal-2023-making,liu2025pairwise}, while efficiency optimizations prune low-scoring paths early~\\citep{zhang2024accelerating,qiu2024treebonenhancinginferencetimealignment,sun2024fast,manvi2024adaptiveinferencetimecomputellms,ye-ng-2024-preference}. \\textbf{Self-correction} iteratively refines outputs using feedback from tools, external models, or self-critique~\\citep{shinn2023reflexionlanguageagentsverbal,gou2024critic,li2024confidencemattersrevisitingintrinsic,song2025progcoprogramhelpsselfcorrection}, though its efficacy depends on feedback reliability~\\citep{olausson2024is,huang2024large,wang2024reasoningtokeneconomiesbudgetaware,yang2024confidencevscritiquedecomposition}. \\textbf{Tree searching} combines parallel and sequential scaling via algorithms like MCTS or A*~\\citep{NEURIPS2023_271db992,xie2023selfevaluation,long2023largelanguagemodelguided,chari2025pheromonebasedlearningoptimalreasoning} guided by value functions~\\citep{xu2023traingainunleashmathematical,hao-etal-2023-reasoning,chen2024alphamathzeroprocesssupervision,zhang2024llamaberrypairwiseoptimizationo1like}. Training techniques distill these scaling benefits into more efficient models~\\citep{gao2023scaling,hou2024doesrlhfscaleexploring,gulcehre2023reinforcedselftrainingrestlanguage,zhang2024o1codero1replicationcoding}.\nHowever, these methods have not been systematically applied to financial tasks, particularly stock movement prediction. Our work aims to fill this gap by exploring how inference-time scaling can be effectively utilized in this domain.\n\n\\section{Preliminaries}\\label{sec:preliminary}\n\n\\subsection{Strict Controlled Dataset for Stock Movement Prediction}\\label{sec:preliminary:1}\n\nWe aim to evaluate the ability of LLMs to predict stock movements based on diverse information sources. To this end, we construct a strict controlled dataset named \\textbf{Fin-2024}, which covers the entire year of 2024, including 5,123 A-share stocks and 209,063 samples. Each sample is designed with a long context window of 32K tokens. Figure~\\ref{fig:dataset} illustrates the data sample for one stock at trading day $t$. LLMs will be trained from January to November, and then evaluated on December. In addition, we also collect data \\textbf{Fin-2025[June]} on June 2025 for long-horizon prediction evaluation. The dataset construction process is detailed in Appendix~\\ref{sec:appendix:dataset_details}.\n\n\n% 构建数据\n% 1. large-scale: over 200,000 samples\n% 2. long-context: 32K tokens\n% 3. diverse information sources: news, fundamentals, analyst opinions, quantitative reports, macroeconomic indicators, similar stocks 这些信息已经在基于机器学习的量化交易研究中被证明有用，图片显示了这些信息源的分布。\n% 4. 预测目标为下一个交易日的开盘价相对于前一个交易日的收盘价的涨跌幅。相当于预测开盘的涨跌。和基于收盘价的涨跌幅相比，这个设置在预训练数据中不常见，可以避免模型通过记忆作弊。\n% 5. 预测目标为三分类问题：上涨、持平、下跌。和只有上涨和下跌的二分类相比，三分类问题要求更显著的上涨和下跌信号。这为模型提供了一个安全区间：当模型缺乏足够信心时，便可以保持 “观望” 状态，避免做出虚假预测。\n% 6. 实际评估时，我们要求模型同时预测涨跌幅和涨跌方向，用于评估模型的指令跟随能力和预测结果一致性。\n\n% We formulate the stock movement prediction (SMP) task as a three-class classification problem, where the model predicts whether the stock price will go up, hold steady, or go down.\n% In order to\n% The input to the model consists of a long context that includes various information sources such as news articles, analyst opinions, quantitative reports, and macroeconomic indicators. The output is a prediction of the stock movement class.\n% To ensure a fair evaluation, we construct a strict controlled dataset that covers the entire year of 2024, including 4,000 A-share stocks and over 200,000 samples. The dataset is designed to be long-context (32K tokens) and includes diverse information sources beyond just price and news. This allows us to evaluate the model's ability to integrate multiple heterogeneous sources of information for stock movement prediction.\n\n\\begin{figure*}\n \\centering\n \\includegraphics[width=0.95\\textwidth]{dataset.pdf}\n \\caption{Overview of data sample for one stock at trading day t.}\n \\label{fig:dataset}\n\\end{figure*}\n\n\n\\paragraph{Information Sources}\nThe dataset consists of diverse information sources that have been proven valuable in machine learning-based quantitative trading research. These include: (1) \\textcolor{Primary1}{\\textbf{News articles}} providing real-time market updates and company-specific \\& sector-specific information, (2) \\textcolor{Primary1}{\\textbf{Fundamental reports}} reflecting company financial health and performance, (3) \\textcolor{Primary1}{\\textbf{Analyst opinions}} offering professional market insights, (4) \\textcolor{Primary1}{\\textbf{Quantitative reports}} containing technical analysis and market indicators, (5) \\textcolor{Primary1}{\\textbf{Macroeconomic indicators}} showing broader economic trends, and (6) \\textcolor{Primary1}{\\textbf{Similar stocks information}} for comparative analysis. The information are primarily textual, friendly for LLMs.\n\n\\paragraph{Prediction Target}\nWe define the prediction target as the price movement between the current trading day's opening price and the previous trading-day's closing price. This setting is less common in pre-training data compared to closing price-based movements, which helps prevent the model from exploiting memorization.\n% decision-making games\nThe setting also avoids the model from decision-making games in trading periods, which is hard to capture in the given context.\nBased on price change, we classify the stock movement into three classes: \\textbf{up} for change > 3\\%, \\textbf{down} for < -3\\%, and \\textbf{hold} for else.\nThe three-class classification scheme requires more significant signals for price movements than binary classification.\n% 诱饵\nThe \\textbf{hold} class serves as a \\textcolor{Primary1}{decoy}.\nIf the model never learns to distinguish between \\textbf{up} and \\textbf{down}, it would indicate a shortage on the model's ability to make price movement predictions.\n\n\\paragraph{Evaluation Protocol}\nDuring evaluation, we require the model to simultaneously predict both the price change percentage and direction to assess its instruction-following capability and verify the consistency between the two predictions, as the direction should align with the predicted change percentage.\n\n\\subsection{Observation on Existing Models}\\label{sec:preliminary:2}\n% 现有模型预测的问题\n% 1. 从统计上看，模型本身预测和随机猜测无异：几乎没有任何预测能力，模型的推理能力在预测任务上的贡献是 0\n% 2. 从样例分析看，模型预测和分析师观点一致、经常有泛泛而谈的转折：缺乏内在的分析框架，即原则\n% 3. cot 无法激活扩展，必须微调训练后激活扩展能力\n\n% Figure: 现有模型的性能没有超出随机猜测的区域（包括开源和闭源），且无法测试时扩展\n% Figure: case study of responses\n\n\\begin{minipage}[t]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{baselines_wo_CoT.pdf}\n \\captionof{figure}{Existing LLMs without RETuning CoT perform no better than random guessing in stock movement prediction, and most (except Qwen3 32B) fail to scale at inference time.}\n \\label{fig:baselines}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{baseline_comparison.pdf}\n \\captionof{figure}{Abaltion on CoT prompting. The proposed CoT in Section~\\ref{sec:method:1} can help improve the prediction performance on Qwen3 32B, but not smaller models. Others lose to random guessing.}\n \\label{fig:ablation_on_CoT}\n\\end{minipage}\n\nTo understand the limitations of existing models in stock movement prediction, we analyze their performance on \\textbf{Fin-2024[December]} in Section~\\ref{sec:preliminary:1}. We use 32 different random seeds to uniformly sample the prediction (hold, up, and down) to construct the random bound (grey area in the figure). Any results that are covered by the random bound will be regarded failing to make trust-worthy prediction. The results reveal two key issues:\n% 我们在这个严格的数据集上对当下先进的开源和闭源模型进行了评估，评估设置和 Experiment~\\ref{sec:exp} 中的设置一致。我们发现：\n% 1. 当前开源或闭源模型的预测能力都不受益于测试时扩展，比不过随机猜测\n% 我们进一步采样了多个样本的 response 进行 case study，发现模型的 response 具有以下问题：\n% 2. 从样例分析看，模型预测和分析师观点一致、经常有泛泛而谈的转折：缺乏内在的分析框架，即原则\n% 这促使我们思考，模型的预测能力之所以无法在测试时扩展，是因为 response 缺乏和 prediction 相关的 piror knowledge 和 insight，\n% 需要通过改变模型的 response 范式来激活预测能力，特别是将在量化交易研究中被证明有效的归纳分析框架注入到 response 中。幸运的是，在探索了多个 response 范式合成方案后，我们发现了一种有效的策略，如下一章详细所述。\n\nFirstly, by investigating existing LLMs' performance in Figure~\\ref{fig:baselines}, we observe that current LLMs are almost randomly guessing the prediction result. And the most models cannot scale their ability of prediction at inference time.\nSecondly, we prompt the model with fine-grained CoT (Section~\\ref{sec:method:1}) to inject knowledge of financial analysis into the reasoning process. We further analyze the responses of the models, as shown in Figure~\\ref{fig:ablation_on_CoT}. We find that CoT can help improve the model's prediction performance on Qwen3 32B, but not other models.\n\nTo understand why these models fail, we further sample multiple responses for case study (Appendix~\\ref{sec:appendix:case_study:cot_prompting}) and find that:\nthe outputs of these LLMs tend to be vague, detached from the prediction target, and biased toward the \\texttt{hold} class on label-balanced datasets.\nThus, we propose to utilize \\textcolor{Primary1}{supervised fine-tuning} to induce coherent, task-specific reasoning to change the output distribution of these models, as discussed in the following section.\n\n\\section{Reflective Evidence Tuning (RETuning)}\\label{sec:method}\n\nThis section introduces \\textbf{Reflective Evidence Tuning (RETuning)}, a two-stage framework designed to unlock the latent reasoning ability of LLMs in stock movement prediction tasks. As illustrated in Figure~\\ref{fig:method}, RETuning comprises: (1) an SFT stage to \\textit{cold-start generative reasoning modeling}, and (2) \\textit{rule-based reinforcement learning} for performance refinement and alignment.\n\n\\begin{figure*}\n\t\\centering\n\t\\includegraphics[width=0.95\\textwidth]{method.pdf}\n\t\\caption{Two-stage stock movement prediction model training framework: \\textbf{Stage 1} (Cold Start) uses multi-source data with human labeling and synthesis pipeline for \\textcolor{Primary1}{R}eflective \\textcolor{Primary1}{E}vidence \\textcolor{Primary1}{Tuning}; \\textbf{Stage 2} applies \\textcolor{Primary1}{Re}inforcement Fine-\\textcolor{Primary1}{Tuning} with curriculum learning, reward shaping, and inference-time scaling for final label determination.}\n\t\\label{fig:method}\n\\end{figure*}\n\n\\subsection{Stock Movement Prediction via Generative Reasoning Modeling}\\label{sec:method:1}\n% 描述冷启动数据如何构建。我们将SMP任务视为一个生成推理任务，模型需要从多种信息源中提取证据，构建分析框架，并生成预测结果。\n% ### 为什么要微调\n\n% 1. zero方法无法涌现出稳定的预测结果分布，7b模型在zero设置下response length 暴跌，1epoch后全部集中到hold。平衡数据的标签使得up：down：hold=1:1：1也没有用，模型会转而全部预测hold。\n% 2. zero方法的cot泛泛而谈，无法涌现对多个数据源的对结果有正向作用的分析。只是每个要点进行一句话总结，不关心和涨跌预测任务的关联，也不关心多个数据源信息之间的相互作用和冲突，就基于这些宽泛的总结得出答案。这是因为模型偷懒，在长上下文中 lost in the middle，无法提取长上下文的中的关联。但是这种关联是很重要的，也需要利用模型本身的推理能力去解决不同信息的冲突，消除噪声，得到可信的结果。所以\n\n% ### 反思性证据微调\n\n% 1. 理解任务，为任务建立一个认知框架：理解任务设定，比如时间区间是下一个交易日的开盘价相对于上一个交易日涨跌幅；以3%作为阈值划分涨跌幅类别。这有助于提高一致性，减少幻觉。\n% 2. 对于预测任务，整理已有信息源，基于信息源建立分析框架：有助于agent基于当前环境进行应对，适配到多种信息源\n% 3. 基于分析框架进行分析，得到若干证据：模型将基于动态框架而不是材料中的观点进行独立分析，保持理性\n% 4. 将证据按上涨和下跌分组并评分：为以上证据打上软标签，方便后续的对抗性权衡\n% 5. 获得分组平均分，进入反思：仔细检验分析\n% 6. 确定最后的涨跌幅和方向：得出结论\n% 7. 出结果：跟随格式\n% \\textcolor{Primary1}\n% Supervised Fine-Tuning\n\n\\begin{wrapfigure}{r}{0.38\\textwidth}\n \\vspace{-15pt}\n \\centering\n \\begin{subfigure}[t]{0.37\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{data_synthesis.pdf}\n \\caption{\\textbf{RETuning} guides the model to generate a principle, collect evidence, and reflect before making a prediction.}\n \\label{fig:data_synthesis}\n \\end{subfigure}\n\n % \\vspace{2pt}\n\n \\begin{subfigure}[t]{0.37\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{scaling_from_RETuning.pdf}\n \\caption{DeepSeek\\_R1\\_14B\\_SFT scales prediction performance via repeated sampling.}\n \\label{fig:scaling_on_prediction_performance}\n \\end{subfigure}\n \\vspace{-25pt}\n\\end{wrapfigure}\n\nWe frame the SMP task as a \\textcolor{Primary1}{\\textit{generative reasoning problem}}, in which the LLM leverage its reasoning ability to make predictions. It must construct an analytical framework, extract and score evidence from heterogeneous sources, and reflect before reaching a conclusion. As is shown in Figure~\\ref{fig:data_synthesis}, this contrasts with zero-shot settings, where models superficially summarize and avoid making grounded predictions.\n\nThen we employ supervised fine-tuning (SFT) to instill this reasoning structure into the model. The SFT dataset is constructed through a semi-automated pipeline (Appendix~\\ref{sec:appendix:sft_data_synthesis}) that uses DeepSeek-R1 (671B) as the backbone model to rejected sampling to synthesize 118 golden cold-start items.\n% Each training sample includes: (1) a clear understanding of the task and its parameters, (2) an analytical framework derived from the provided information sources, (3) extracted evidence supporting both upward and downward price movements, each scored for relevance and strength, (4) a reflective analysis weighing the evidence before concluding, and (5) a final prediction of price change percentage and direction in a structured format.\n\nBy grounding each prediction in a dynamically built framework, \\textbf{RETuning} promotes robust and context-aware reasoning. This reduces susceptibility to dominant context bias and improves the model’s ability to rationally weigh adversarial evidence—crucial for reliable financial forecasting.\nBy fine-tuning on this structured reasoning process, we find that the model \\textcolor{Primary1}{DeepSeek\\_R1\\_14b\\_SFT can scale its prediction performance via repeated sampling far beyond random guessing}, as shown in Figure~\\ref{fig:scaling_on_prediction_performance}. It indicates that the model already possesses a certain level of predictive capability. We can further leverage this weak predictive power to assess the difficulty of predicting samples, thereby enhancing the overall predictive performance of the model more efficiently.\n\n\n\\subsection{Rule-based Reinforcement Learning}\\label{sec:method:2}\nTo further align model outputs with desired reasoning behavior, we introduce a rule-based reinforcement learning (RL) stage. Rather than relying on simple correctness-based rewards—which are noisy and statistically uninformative in financial prediction—we design more principled signals through \\textbf{reward shaping} and \\textbf{curriculum learning}.\n% \\begin{tcolorbox}[colback=Primary2, colframe=Primary1, boxrule=1pt]\n% your\\_text\\_here\n% \\end{tcolorbox}\n\n% 奖励塑造\n\\paragraph{Reward Shaping}\n% 通过奖励塑造来引导模型的行为，使其更好地适应任务需求。\n% 预测任务是一个很难的任务，简单的基于标签的奖励不是一个可信的信号。大数定律下，涨跌幅近似正态分布，即简单奖励也是正态分布，这几乎无法提供有效的强化信号，因为即使模型探索出高质量的response，也会因为被判定为低奖励而损害模型性能。\n\n% 所以我们引入预测难度，来过滤可用的\n\n% 我们提出了基于规则的奖励，\n\n% 1. format score\n% 2. pct_change score\n% 3. answer score\n% 4. consistent score：pct_change aligned with answer\n\nWe design a \\textbf{multi-faceted reward function} to capture both the \\textcolor{Primary1}{structural} and \\textcolor{Primary1}{semantic} correctness of model outputs.\nFirst, a \\textbf{\\underline{Format Score}} ensures that the response adheres to the expected structured format, maintaining clarity and consistency.\n% The \\textbf{\\underline{Change Score}} evaluates how accurately the model estimates the magnitude of price change.\nThe \\textbf{\\underline{Accuracy Score}} focuses on whether the model correctly predicts the directional movement—\\texttt{up}, \\texttt{down}, or \\texttt{hold}.\nLastly, the \\textbf{\\underline{Consistency Score}} encourages logical alignment between the predicted percentage change and the stated directional label. Final score is given by $ R = \\alpha \\cdot \\text{Format} + \\beta \\cdot \\text{Accuracy} + \\gamma \\cdot \\text{Consistency} $, where $\\alpha, \\beta, \\gamma$ are hyperparameters.\nThis design mitigates the issue of misleading signals from noisy.\n\n% 课程学习\n\\paragraph{Curriculum Learning}\n% 课程学习：由于数据构建的缺陷，输入的信息维度是固定的，而输出的预测难度不同。\n\n% 用cold start的模型将训练集过一遍，8路采样，计算每条样本的难度为错误个数，即\n\n% $$\n% difficulty(x)=n-\\sum_{i=1}^{n} \\mathbf{1}_{y_i\\text{ is correct}}\n% $$\n\n% 其中 $y_i$ 是 prompt x 的第 i 条 response。\n\n% 得到每个样本的难度后，将所有难度分成 9 个等级，每3个难度进行聚合，得到低、中、高难度。\n\n% 我们统计每个等级内样本的分布，发现\n\n% 1. 高难度数据几乎都是up 和 down数据\n% 2. 中难度较为均匀，和数据整体分布较为匹配\n% 3. 低难度几乎都是hold数据。\n\n% 因此，我们丢弃低难度和高难度数据，并对中难度的数据按难度递增的顺序进行训练。\n\n\\begin{wrapfigure}{r}{0.45\\textwidth}\n \\vspace{-10pt}\n \\centering\n \\includegraphics[width=0.43\\textwidth]{difficulty_distribution.pdf}\n \\caption{Difficulty distribution given by the cold-started model (DeepSeek\\_R1\\_14B\\_SFT).}\n \\label{fig:difficulty_distribution}\n \\vspace{-20pt}\n\\end{wrapfigure}\n\n% Figure: difficulty distribution across different levels\nNot all samples are equally difficult: \\textbf{hold} predictions are often trivial, while confident \\textbf{up/down} predictions require strong signal integration. To make training more efficient and targeted, we propose a curriculum learning strategy:\n\nWe use \\textcolor{Primary1}{the cold-started model} to generate $N$ (=8 in practice) predictions for each training sample. The difficulty of a sample is measured by counting how many of these predictions are incorrect. Based on this difficulty score, we categorize examples into three groups: \\textbf{easy} (correct $\\in [\\frac{2}{3}N, N)$ ), \\textbf{medium} (correct $\\in [\\frac{1}{3}N, \\frac{2}{3}N)$ ), and \\textbf{hard} (correct $\\in [0, \\frac{1}{3}N)$ ).\n\n% 难度级别与标签之间存在明显的相关性。低难度级别下hold占主导，而高难度级别下down和up更为频繁。\n% 在难度级别5时，三种操作类型的分布趋于平衡，这可能表示该难度级别具有最佳的挑战性和操作多样性。\nIn Figure~\\ref{fig:difficulty_distribution}, we observe that a clear correlation between difficulty levels and labels.\nLow-difficulty samples are mostly dominated by \\textbf{hold} predictions, which tend to be either spurious or too simple to be informative. High-difficulty samples, on the other hand, often involve \\textbf{up} or \\textbf{down} predictions but with weak or noisy signals. In contrast, medium-difficulty samples tend to reflect realistic market complexities and require non-trivial reasoning.\nTo ensure the model focuses on meaningful learning signals, we discard both low and high-difficulty examples and train only on medium-difficulty ones, progressing in order of increasing difficulty.\n\n% 推理时扩展\n\\paragraph{Inference-Time Scaling}\n% majority voting\nWe apply \\textcolor{Primary1}{majority voting} on predicted labels over $n$ repeated generations with temperature 0.6. The final decision is given by: $ \\hat{y} = \\arg\\max_{y \\in \\{\\texttt{up}, \\texttt{down}, \\texttt{hold}\\}} \\sum_{i=1}^{n} \\mathbf{1}[y_i = y] $\n\n\\section{Experiment and Results}\\label{sec:exp}\n% 然后，我们展示我们发现了什么和解决了什么，现况：关于现有large reasoning model 在预测任务上的观察，并归纳问题。\n% ## 主要结果\n\n% ## 消融实验\n% 1. channel independence v.s. channel dependence\n% 2. transformer v.s. mlp\n% 3. anchor 选取策略：random v.s. clustering\n\n% ## 敏感性分析\n\n% 1. 锚序列个数，锚容量大小，window len大小，embedding dim\n% 2. 嵌入维度 [200, 400, 600, 800, 1000]\n% 3. 随机种子分别为[1,10,100,1000,10000] 的5次实验得到 error bars\n\n% ## 优势讨论\n% 1. 运行速度对比\n% 2. anchor 可视化：相似序列example\n% 3. 最小MAE、中间MAE、最大MAE分别3个example，分析序列长什么样模型会预测得更好（可能和序列形状无关）\n\nWe conduct several experiments to ascertain the effectiveness of \\textbf{RETuning}, with the aim to gain insights into the following:\n(1) Basically, can we improve the stock movement prediction performance of LLMs? How does \\textbf{RETuning} compare with existing methods? What insights does the model learn from the data?\n(2) Can we scale the prediction performance of LLMs at inference time?\n(3) What are the key factors that contribute to the success of \\textbf{RETuning}?\n(4) Does the enhanced prediction ability contribute to other financial tasks?\n\n\\subsection{Experiment Setup}\\label{sec:exp:1}\n\\paragraph{Datasets.}\nWe use the data from January to November in \\textbf{Fin-2024} for training, and the December data \\textbf{Fin-2024[December]} for testing. We also use the \\textbf{Fin-2025[June]} dataset to evaluate whether the model persists its scaling ability on prediction performance after 6 months. Besides, we evaluate the generalization ability on \\textbf{BizFinBench}~\\citep{lu2025bizfinbench0}, a comprehensive financial benchmark covering 10 tasks, including Anomalous Event Attribution (AEA), Financial Time Reasoning (FTR), Financial Tool Usage (FTU), Financial Numerical Computation (FNC), Financial Knowledge QA (FQA), Financial Data Description (FDD), Emotion Recognition (ER), Stock Price Prediction (SP), Financial Named Entity Recognition (FNER). The details of the datasets are shown in Appendix~\\ref{sec:appendix:dataset_details}.\n\n\\paragraph{Evaluation and Metrics.}\nWe care about the generalization ability and consider three types of out-of-distribution (OOD) settings: \\textbf{OOD\\_Stock}, \\textbf{OOD\\_Date}, and \\textbf{OOD\\_Stock\\&Date}. We choose 50 stocks in random as the OOD stocks and the last month of 2024 as the OOD dates. The 50 stocks are also OOD stocks in \\textbf{Fin-2025[June]}.\nWe adopt the standard metrics \\textcolor{Primary1}{F1-score} because it balances precision and recall, making it suitable for our multi-class classification task.\n\n\\paragraph{Implementation and Baselines.}\nThe models are trained on up to 4*8 H100 GPUs. Rollout $n$ is set to $8$.\nDefault results are obtained by greedy decoding.\nFor inference-time scaling, we use $k\\in\\{1,2,4,8,16,32\\}$ and temperature=$0.6$.\nMore implementation details are shown in Appendix~\\ref{sec:appendix:implementation_details}.\nBased on DeepSeek\\_R1\\_14B\\_Instruct (originally DeepSeek-R1-Distill-Qwen-14B~\\citep{deepseek-r1}), we apply \\textbf{RETuning} and get DeepSeek\\_R1\\_14B\\_SFT and DeepSeek\\_R1\\_14B\\_SFT\\_GRPO, which are after SFT stage and after SFT + GRPO stages, respectively. We also implement DeepSeek\\_R1\\_32B\\_SFT and DeepSeek\\_R1\\_32B\\_SFT\\_GRPO based on DeepSeek\\_R1\\_32B\\_Instruct.\nWe compare to several strong baselines, including:\nLLMFactor~\\citep{wang-etal-2024-llmfactor}, Fino1~\\citep{Fino1}, Fin-R1~\\citep{Fin-R1}, CMIN~\\citep{CMIN} and StockNet~\\citep{StockNet}.\nWe also report results of several state-of-the-art open-weight LLMs:\nDeepSeek~\\citep{deepseek-r1} (R1-7B, R1-14B, R1-32B, R1-671B, V3-671B), Qwen3~\\citep{yang2025qwen3technicalreport} (8B, 14B, 32B), GPT-OSS~\\citep{openai2025gpt0oss0120b} (20B, 120B).\n\n\\subsection{Results and Analysis}\\label{sec:exp:2}\n\n\n\\begin{minipage}[b]{0.49\\textwidth}\n \\centering\n \\captionof{table}{Results of different methods on \\textbf{Fin-2024[December]} benchmarks. w/ CoT means using the CoT prompting in Section~\\ref{sec:preliminary:2}. The relative improvements (\\%) over the baselines are shown in parentheses. The best results are in \\textbf{bold}.}\n \\resizebox{\\linewidth}{!}{\n \\begin{tabular}{ll}\n \\toprule\n \\textbf{Model} & \\textbf{F1 Score} \\\\\n \\midrule\\midrule\n \\multicolumn{2}{c}{\\textit{Results of Public Models}} \\\\\n Random Guessing & 0.3333 \\\\\n LLMFactor~\\citep{wang-etal-2024-llmfactor} & 0.3345 \\\\\n Fino1~\\citep{Fino1} & 0.0622 \\\\\n Fin-R1~\\citep{Fin-R1} & 0.2543 \\\\\n CMIN~\\citep{CMIN} & 0.3275 \\\\\n StockNet~\\citep{StockNet} & 0.3081 \\\\\n \\midrule\n \\multicolumn{2}{c}{\\textit{Results with CoT Ablation}} \\\\\n Qwen3\\_8B~\\citep{yang2025qwen3technicalreport} & 0.3348 \\\\\n $\\quad$ w/ CoT & 0.3319 (\\textcolor{RED}{-0.87\\%}) \\\\\n Qwen3\\_14B~\\citep{yang2025qwen3technicalreport} & 0.3406 \\\\\n $\\quad$ w/ CoT & 0.3392 (\\textcolor{RED}{-0.41\\%}) \\\\\n Qwen3\\_32B~\\citep{yang2025qwen3technicalreport} & 0.2826 \\\\\n $\\quad$ w/ CoT & 0.3037 (\\textcolor{GREEN}{+7.47\\%}) \\\\\n GPT\\_OSS\\_20B~\\citep{openai2025gpt0oss0120b} & 0.3156 \\\\\n $\\quad$ w/ CoT & 0.3249 (\\textcolor{GREEN}{+2.95\\%}) \\\\\n GPT\\_OSS\\_120B~\\citep{openai2025gpt0oss0120b} & 0.2997 \\\\\n $\\quad$ w/ CoT & 0.3436 (\\textcolor{GREEN}{+14.65\\%}) \\\\\n DeepSeek\\_R1\\_671B\\_0528 & 0.3333 \\\\\n $\\quad$ w/ CoT & 0.3494 (\\textcolor{GREEN}{+4.83\\%}) \\\\\n DeepSeek\\_V3\\_671B\\_0324 & 0.3336 \\\\\n $\\quad$ w/ CoT & 0.3456 (\\textcolor{GREEN}{+3.60\\%}) \\\\\n \\midrule\n \\multicolumn{2}{c}{\\textit{Results of Our Models}} \\\\\n DeepSeek\\_R1\\_14B\\_Instruct & 0.3475 (\\textcolor{GREY}{baseline}) \\\\\n $\\quad$ w/ CoT & 0.3604 (\\textcolor{GREEN}{+3.71\\%}) \\\\\n $\\quad$ DeepSeek\\_R1\\_14B\\_GRPO (\\textbf{Ours}) & 0.3377 (\\textcolor{RED}{-2.25\\%}) \\\\\n $\\quad$ DeepSeek\\_R1\\_14B\\_SFT (\\textbf{Ours}) & 0.3715 (\\textcolor{GREEN}{+6.91\\%}) \\\\\n $\\quad$ DeepSeek\\_R1\\_14B\\_SFT\\_GRPO (\\textbf{Ours}) & \\textbf{0.4196} (\\textcolor{GREEN}{+20.75\\%}) \\\\\n DeepSeek\\_R1\\_32B\\_Instruct & 0.3567 (\\textcolor{GREY}{baseline}) \\\\\n $\\quad$ w/ CoT & 0.3589 (\\textcolor{GREEN}{+0.62\\%}) \\\\\n $\\quad$ DeepSeek\\_R1\\_32B\\_GRPO (\\textbf{Ours}) & 0.3683 (\\textcolor{GREEN}{+3.22\\%}) \\\\\n $\\quad$ DeepSeek\\_R1\\_32B\\_SFT (\\textbf{Ours}) & 0.3639 (\\textcolor{GREEN}{+2.02\\%}) \\\\\n $\\quad$ DeepSeek\\_R1\\_32B\\_SFT\\_GRPO (\\textbf{Ours}) & 0.4071 (\\textcolor{GREEN}{+14.13\\%}) \\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{fig:compare_results}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[b]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{submain_results.pdf}\n \\captionof{figure}{Inference-time scalability results on \\textbf{Fin-2024[December]}. SFT model already has prediction ability, and GRPO further refines it.}\n \\label{fig:main_results}\n \\centering\n \\includegraphics[width=\\textwidth]{June_results.pdf}\n \\captionof{figure}{Inference-time scalability results on \\textbf{Fin-2025[June]}. Finetuned models continue to scale via repeated sampling even after 6 months.}\n \\label{fig:June_results}\n\\end{minipage}\n\n% \\begin{minipage}[b]{0.49\\textwidth}\n% \\centering\n% \\includegraphics[width=\\textwidth]{submain_results.pdf}\n% \\captionof{figure}{Inference-time scalability results on \\textbf{Fin-2024[December]}. SFT model already has prediction ability, and GRPO further refines it.}\n% \\label{fig:main_results}\n% \\end{minipage}\n% \\hfill\n% \\begin{minipage}[b]{0.49\\textwidth}\n% \\centering\n% \\includegraphics[width=\\textwidth]{June_results.pdf}\n% \\captionof{figure}{Inference-time scalability results on \\textbf{Fin-2025[June]}. Finetuned models continue to scale via repeated sampling even after 6 months.}\n% \\label{fig:June_results}\n% \\end{minipage}\n\n\n\n% \\subsubsection{Main Results}\\label{sec:exp:2:1}\n\n\\paragraph{RETuning vs baselines.}\nThe results of different methods on \\textbf{Fin-2024[December]} benchmarks are shown in Table~\\ref{fig:compare_results}.\nWe observe that RETuning (SFT + GRPO) significantly outperforms all baselines, including state-of-the-art open-weight LLMs (DeepSeek, Qwen3, GPT-OSS) and public models specifically designed for stock movement prediction (LLMFactor, Fino1, Fin-R1, CMIN, StockNet). For instance, DeepSeek\\_R1\\_14B\\_SFT\\_GRPO achieves an F1 score of 0.4196, which is a 20.75\\% relative improvement over its instruct baseline (0.3475) and surpasses the best public model (GPT-OSS-120B w/ CoT at 0.3436) by 22.15\\%. Similarly, DeepSeek\\_R1\\_32B\\_SFT\\_GRPO attains an F1 score of 0.4071, marking a 14.13\\% relative improvement over its instruct baseline (0.3567) and outperforming the best public model by 18.55\\%.\n\n\\paragraph{Can stock movement prediction benefit from inference-time scaling?}\n% RETuning后的模型开始具有推理时扩展能力，但天花板并不高，且很快就扩展到天花板，不能持续扩展。过多的采样数反而降低性能。多个证据的联合推理对提高预测性能有用，但预测任务可能更依赖于关键证据，比如内幕消息。\n% RL提高了模型的采样效率，让模型1次就可以达到未训练前8次投票扩展的性能。但是RL并没有提高模型能力边界，最高准确率没有发生明显变化。RL训练后模型的测试时扩展失去作用，在误差允许的范围内曲线是平的。\n% As shown in Table~\\ref{tab:baselines}, we observe that inference-time scaling can improve the performance of LLMs on stock movement prediction tasks, but the improvement is not as significant as in other tasks like question answering or summarization. This suggests that while LLMs can benefit from inference-time scaling, the nature of stock movement prediction may limit the extent to which this technique can be applied.\nYes, but the gains from inference-time scaling are limited. Figure~\\ref{fig:main_results} and Figure~\\ref{fig:June_results} present the inference-time scalability results on \\textbf{Fin-2024[December]} and \\textbf{Fin-2025[June]}, respectively.\nWe observe monotonic or near-monotonic improvements up to $n{\\approx}8$--$16$, after which returns plateau and can even regress for some settings. RL (GRPO) makes test-time scaling less necessary by improving one-sample quality, yet does not increase the peak accuracy.\n\n\\paragraph{Can predictive ability generalize to unseen stocks, future dates, or both?}\nYes.\nWe evaluate out-of-distribution (OOD) robustness along two axes: unseen stocks and forward-in-time generalization.\nThe dataset \\textbf{Fin-2024[December]} consists of \\textbf{OOD\\_Stock}, \\textbf{OOD\\_Date}, and \\textbf{OOD\\_Stock\\&Date} cases, where RETuning maintains or increases F1 score as the number of inference-time samples $n$ grows (Figure~\\ref{fig:main_results}).\nOn \\textbf{Fin-2025[June]} (future dates only), RETuning preserves its advantage and continues to benefit from moderate repeated sampling (Figure~\\ref{fig:June_results}), indicating strong temporal and cross-ticker generalization.\n\nTo further determine how the model scales on different OOD cases, we group the results by OOD split and present in Figure~\\ref{fig:ood_stock_f1_score}\\ref{fig:ood_date_f1_score}\\ref{fig:ood_stock_date_f1_score}. The scaling is significant in \\textbf{OOD\\_Stock}, then is \\textbf{OOD\\_Date}. \\textbf{OOD\\_Stock\\&Date} is the hardest cases to scale up, but it still outperforms baselines. We leave detailed analysis in Appendix~\\ref{sec:appendix:detailed_results:group_by_ood}.\n\n\\begin{minipage}[b]{0.32\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{OOD_stock_main_results.pdf}\n \\captionof{figure}{\\textbf{OOD\\_Stock} results on \\textbf{Fin-2024[December]}}\n \\label{fig:ood_stock_f1_score}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[b]{0.32\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{OOD_date_main_results.pdf}\n \\captionof{figure}{\\textbf{OOD\\_Date} results on \\textbf{Fin-2024[December]}}\n \\label{fig:ood_date_f1_score}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[b]{0.32\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{OOD_date_stock_main_results.pdf}\n \\captionof{figure}{\\textbf{OOD\\_Stock\\&Date} results on \\textbf{Fin-2024[December]}}\n \\label{fig:ood_stock_date_f1_score}\n\\end{minipage}\n\n\n% \\paragraph{Group by label}\nWe also explore how the model scales on different ground truth labels. The results are grouped by ground truth label and presented in Figure~\\ref{fig:label_up_f1_score}\\ref{fig:label_hold_f1_score}\\ref{fig:label_down_f1_score}. The scaling is significant in \\textbf{hold} cases, and the model performance exceeds the baseline on \\textbf{up} and \\textbf{down} cases. We claim that \\textbf{up} and \\textbf{down} cases are more challenging, and \\textbf{RETuning} enhances the model's performance in these scenarios by enabling it to better leverage its reasoning capabilities, thus to identify factors influencing stock movements more effectively, thereby allowing the model to make more accurate predictions.\n% We leave detailed analysis in Appendix~\\ref{sec:appendix:detailed_results:group_by_label}.\n\n\\begin{minipage}[b]{0.32\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{label_up_main_results.pdf}\n \\captionof{figure}{Ground truth \\textbf{up} results on \\textbf{Fin-2024[December]}}\n \\label{fig:label_up_f1_score}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[b]{0.32\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{label_hold_main_results.pdf}\n \\captionof{figure}{Ground truth \\textbf{hold} results on \\textbf{Fin-2024[December]}}\n \\label{fig:label_hold_f1_score}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[b]{0.32\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{label_down_main_results.pdf}\n \\captionof{figure}{Ground truth \\textbf{down} results on \\textbf{Fin-2024[December]}}\n \\label{fig:label_down_f1_score}\n\\end{minipage}\n\n\n\\paragraph{Ablation on CoT prompting.}\nWe further examine the effect of Chain-of-Thought (CoT) prompting (Table~\\ref{fig:compare_results}).\n% For most models, CoT improves the performance.\nIt causes slightly negative effects on smaller models (Qwen3-8B, Qwen3-14B), but significantly benefits larger models (Qwen3-32B, GPT-OSS-120B, DeepSeek-R1-671B, DeepSeek-V3-671B). This suggests that larger models have a greater capacity to leverage CoT prompting effectively.\nFor the 14B model, CoT improves the baseline by \\textcolor{GREEN}{+3.71\\%}, while the 32B model only gains a marginal \\textcolor{GREEN}{+0.62\\%}. This indicates that CoT alone yields limited benefits. In contrast, our SFT and SFT+GRPO variants consistently outperform CoT, suggesting that structured fine-tuning and reinforcement optimization are more effective than relying on prompting strategies alone.\n\n\n\\paragraph{Ablation on SFT stage.}\nWe compare the effect of applying GRPO directly versus combining it with an SFT stage (*\\_SFT\\_GRPO). For the 14B model, GRPO alone underperforms the baseline (0.3377 vs. 0.3475), while SFT followed by GRPO achieves a substantial gain (0.4196, \\textcolor{GREEN}{+20.75\\%}). A similar trend is observed in the 32B model: GRPO alone yields modest improvement (0.3683, \\textcolor{GREEN}{+3.22\\%}), whereas SFT+GRPO achieves the best performance (0.4071, \\textcolor{GREEN}{+14.13\\%}). These results highlight that the SFT stage provides essential initialization, enabling GRPO to realize its full benefit.\n\n\n\\begin{table*}[h]\n % \\vspace{-20pt}\n \\centering\n \\caption{Performance Comparison of LLMs on BizFinBench~\\citep{lu2025bizfinbench0}. The colors represent the top three performers for each task: \\colorbox{golden}{golden} indicates the top-performing model, \\colorbox{lightblue}{silver} represents the second-best result, and \\colorbox{lightgreen}{bronze} denotes the third-best performance.}\n \\resizebox{\\textwidth}{!}{%\n \\begin{threeparttable}\n \\begin{tabular}{lrrrrrrrrrr}\n \\toprule\n \\multicolumn{1}{c}{Model~\\tnote{$\\dagger$}} & \\multicolumn{1}{c}{AEA} & \\multicolumn{1}{c}{FNC} & \\multicolumn{1}{c}{FTR} & \\multicolumn{1}{c}{FTU} & \\multicolumn{1}{c}{FQA} & \\multicolumn{1}{c}{FDD} & \\multicolumn{1}{c}{ER} & \\multicolumn{1}{c}{SP} & \\multicolumn{1}{c}{FNER} & \\multicolumn{1}{c}{Average}\\\\\n \\midrule\n \\multicolumn{11}{c}{Closed-Source LLMs} \\\\\n ChatGPT-o3 & \\cellcolor{lightblue}86.23 & 61.30 & \\cellcolor{lightblue}75.36 & \\cellcolor{golden}89.15 & \\cellcolor{golden}91.25 & \\cellcolor{lightgreen}98.55 & 44.48 & 53.27 & 65.13 & \\cellcolor{golden}73.86 \\\\\n ChatGPT-o4-mini & \\cellcolor{lightgreen}85.62 & 60.10 & 71.23 & 74.40 & \\cellcolor{lightgreen}90.27 & 95.73 & \\cellcolor{golden}47.67 & 52.32 & 64.24 & \\cellcolor{lightgreen}71.29 \\\\\n GPT-4o & 79.42 & 56.51 & \\cellcolor{golden}76.20 & 82.37 & 87.79 & \\cellcolor{golden}98.84 & 45.33 & 54.33 & \\cellcolor{lightgreen}65.37 & \\cellcolor{lightblue}71.80 \\\\\n Gemini-2.0-Flash & \\cellcolor{golden}86.94 & 62.67 & \\cellcolor{lightgreen}73.97 & 82.55 & \\cellcolor{lightblue}90.29 & \\cellcolor{lightblue}98.62 & 22.17 & \\cellcolor{golden}56.14 & 54.43 & 69.75 \\\\\n Claude-3.5-Sonnet & 84.68 & \\cellcolor{lightgreen}63.18 & 42.81 & \\cellcolor{lightblue}88.05 & 87.35 & 96.85 & 16.67 & 47.60 & 63.09 & 65.59 \\\\\n \\midrule\n \\multicolumn{11}{c}{Open-Weight LLMs} \\\\\n Qwen3-14B & 84.20 & 58.20 & 65.80 & 82.19 & 84.12 & 92.91 & 33.00 & 52.31 & 50.70 & 67.05 \\\\\n Qwen3-32B & 83.80 & 59.60 & 64.60 & 85.12 & 85.43 & 95.37 & 39.00 & 52.26 & 49.19 & 68.26 \\\\\n DeepSeek\\_R1\\_14B\\_Instruct~\\tnote{1} & 71.33 & 44.35 & 50.45 & 81.96 & 85.52 & 92.81 & 39.50 & 50.20 & 52.76 & 59.49 \\\\\n DeepSeek\\_R1\\_32B\\_Instruct~\\tnote{1} & 73.68 & 51.20 & 50.86 & 83.27 & 87.54 & 97.81 & 41.50 & 53.92 & 56.80 & 66.29 \\\\\n \\midrule\n \\multicolumn{11}{c}{Our LLMs} \\\\\n \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT~\\tnote{2} & \\cellcolor{Background1}80.63 & \\cellcolor{Background1}51.67 & \\cellcolor{Background1}52.61 & \\cellcolor{Background1}83.53 & \\cellcolor{Background1}89.05 & \\cellcolor{Background1}96.72 & \\cellcolor{Background1}36.68 & \\cellcolor{Background1}50.43 & \\cellcolor{Background1}50.85 & \\cellcolor{Background1}65.36 \\\\\n $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+9.25} & \\textcolor{GREEN}{+7.28} & \\textcolor{GREEN}{+2.19} & \\textcolor{GREEN}{+1.53} & \\textcolor{GREEN}{+3.42} & \\textcolor{GREEN}{+3.85} & \\textcolor{RED}{-2.93} & \\textcolor{GREEN}{+0.24} & \\textcolor{RED}{-1.92} & \\textcolor{GREEN}{+5.83} \\\\\n \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT\\_GRPO~\\tnote{2} & \\cellcolor{Background1}81.46 & \\cellcolor{Background1}52.41 & \\cellcolor{Background1}53.47 & \\cellcolor{Background1}83.57 & \\cellcolor{Background1}89.02 & \\cellcolor{Background1}95.58 & \\cellcolor{Background1}36.83 & \\cellcolor{Background1}54.06 & \\cellcolor{Background1}51.24 & \\cellcolor{Background1}66.92 \\\\\n $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+10.03} & \\textcolor{GREEN}{+8.09} & \\textcolor{GREEN}{+2.91} & \\textcolor{GREEN}{+1.64} & \\textcolor{GREEN}{+3.45} & \\textcolor{GREEN}{+2.63} & \\textcolor{RED}{-2.74} & \\textcolor{GREEN}{+3.82} & \\textcolor{RED}{-1.53} & \\textcolor{GREEN}{+7.46} \\\\\n $\\quad$ 14B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.82} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+0.81} & \\textcolor{GREEN}{+0.06} & 0.00 & \\textcolor{RED}{-1.23} & \\textcolor{GREEN}{+0.25} & \\textcolor{GREEN}{+3.63} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.53} \\\\\n \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT & \\cellcolor{Background1}80.45 & \\cellcolor{lightblue}66.42 & \\cellcolor{Background1}63.28 & \\cellcolor{lightgreen}86.88 & \\cellcolor{Background1}88.43 & \\cellcolor{Background1}93.76 & \\cellcolor{lightblue}46.05 & \\cellcolor{lightblue}55.27 & \\cellcolor{golden}68.41 & \\cellcolor{Background1}70.08 \\\\\n $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+6.75} & \\textcolor{GREEN}{+15.23} & \\textcolor{GREEN}{+12.37} & \\textcolor{GREEN}{+3.64} & \\textcolor{GREEN}{+0.83} & \\textcolor{RED}{-4.14} & \\textcolor{GREEN}{+4.52} & \\textcolor{GREEN}{+1.25} & \\textcolor{GREEN}{+11.63} & \\textcolor{GREEN}{+3.75} \\\\\n \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT\\_GRPO & \\cellcolor{Background1}80.67 & \\cellcolor{golden}66.83 & \\cellcolor{Background1}64.45 & \\cellcolor{Background1}86.79 & \\cellcolor{Background1}88.52 & \\cellcolor{Background1}91.26 & \\cellcolor{lightgreen}45.68 & \\cellcolor{lightgreen}54.83 & \\cellcolor{lightblue}67.75 & \\cellcolor{Background1}70.44 \\\\\n $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+6.95} & \\textcolor{GREEN}{+15.62} & \\textcolor{GREEN}{+13.57} & \\textcolor{GREEN}{+3.55} & \\textcolor{GREEN}{+0.93} & \\textcolor{RED}{-6.64} & \\textcolor{GREEN}{+4.13} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+10.93} & \\textcolor{GREEN}{+4.12} \\\\\n $\\quad$ 32B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.23} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.23} & \\textcolor{RED}{-0.06} & \\textcolor{GREEN}{+0.13} & \\textcolor{RED}{-2.53} & \\textcolor{RED}{-0.42} & \\textcolor{RED}{-0.43} & \\textcolor{RED}{-0.72} & \\textcolor{GREEN}{+0.33} \\\\\n \\bottomrule\n \\end{tabular}%\n % 脚注内容\n \\begin{tablenotes}\n \\item[$\\dagger$] Closed-source LLMs results are sourced from \\cite{lu2025bizfinbench0}. Open-weight LLMs results are reproduced using temperature $0.6$.\n \\item[1] DeepSeek\\_R1\\_14B\\_Instruct (32B) here is the short of DeepSeek-R1-Distill-Qwen-14B (32B) in the original paper~\\citep{deepseek-r1}.\n \\item[2] DeepSeek\\_R1\\_14B\\_SFT and DeepSeek\\_R1\\_14B\\_SFT\\_GRPO are DeepSeek\\_R1\\_14B\\_Instruct model after RETuning SFT stage and after RETuning SFT + GRPO stages, respectively.\n \\end{tablenotes}\n \\end{threeparttable}\n }\n \\label{tab:contribution_to_other_fin_tasks}%\n\\end{table*}\n\n% DeepSeek\\_R1\\_14B\\_sft & 81.4 & 51.2 & 54.0 & - & - & - & 36.6 & 50.4 & 43.8 & 65.3 \\\\\n% DeepSeek\\_R1\\_14b\\_sft\\_grpo & 81.8 & 51.4 & 54.6 & - & - & - & 36.8 & 54.0 & 40.2 & 64.9 \\\\\n% DeepSeek\\_R1\\_32b\\_sft & 76.2 & 61.0 & 67.5 & - & - & - & 46.0 & 55.2 & 67.0 & 66.1 \\\\\n% DeepSeek\\_R1\\_32b\\_sft\\_grpo & 75.8 & 66.4 & 59.6 & - & - & - & 45.6 & 54.8 & 66.9 & 65.7 \\\\\n\n% DeepSeek\\_R1\\_14B\\_SFT & 80.6 & 51.6 & 52.6 & 89.53 & 89.0 & 96.7 & 17.0 & 52.9 & 38.5 & 63.16 \\\\\n% \\;\\;\\;\\;14B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & + & 51.6 & 52.6 & 89.53 & 89.0 & 96.7 & 17.0 & 52.9 & 38.5 & 63.16 \\\\\n% DeepSeek\\_R1\\_14b\\_SFT\\_GRPO & 81.4 & 52.4 & 53.4 & \\cellcolor{lightgreen}89.57 & 89.0 & 95.5 & 18.2 & 50.5 & 40.1 & 63.34 \\\\\n% DeepSeek\\_R1\\_32b\\_SFT & 80.4 & \\cellcolor{lightblue}66.4 & 63.2 & \\cellcolor{golden}92.88 & 88.4 & 93.7 & 34.0 & 52.3 & \\cellcolor{golden}68.4 & 71.08 \\\\\n% DeepSeek\\_R1\\_32b\\_SFT\\_GRPO & 80.6 & \\cellcolor{golden}66.8 & 64.4 & \\cellcolor{lightblue}92.79 & 88.5 & 91.2 & 31.8 & 52.7 & \\cellcolor{lightblue}67.7 & 70.72 \\\\\n\n\\paragraph{Does the enhanced predictive ability contribute to other financial tasks?}\nYes. On the financial benchmark BizFinBench~\\citep{lu2025bizfinbench0} (Table~\\ref{tab:contribution_to_other_fin_tasks}), \\textbf{RETuning} generalizes beyond SMP: for 14B, the average score improves from 59.49 (Instruct) to 65.36 (SFT, $+5.83$) and 66.92 (SFT+GRPO, $+7.46$); for 32B, it improves from 66.29 to 70.08 ($+3.75$) and 70.44 ($+4.12$). The 32B models reach top-3 results on several tasks (e.g., FNC, FTU, ER, SP, FNER), while minor regressions appear on highly saturated dimensions (e.g., FDD after RL: $-1.23$ for 14B, $-2.53$ for 32B). Overall, \\textbf{RETuning} yields broad, transferable gains with small trade-offs on a few tasks.\n% 金融任务评估，看 avg，(DSR1_24B, DSR1_32B, Qwen3_14B, Qwen3_32B) x (base, sft, sft_grpo) 的性能对比\n\n% \\subsubsection{Ablation Studies}\\label{sec:exp:2:2}\n\n% \\paragraph{Inference-time scaling is more effective than scaling model sizes.}\n% We also investigate the performance on\n\n\n% \\paragraph{Ablation on RL stage}\n% % 2. 对比有 sft 和无 sft 时候的 RL 的性能\n% SFT stage enhances reinforcement learning by providing a more effective way to fine-tune the model on specific tasks. This targeted fine-tuning allows the model to better understand the nuances of the task at hand, leading to improved performance and more efficient learning. By incorporating SFT into the reinforcement learning process, we can achieve better results with fewer training iterations.\n% \\textbf{Can reinforcement learning expand the boundaries of a model's ability to predict stock movement?} No. RL can improve the efficiency of the model's sampling process, allowing it to achieve performance levels comparable to multiple rounds of voting with just a single pass. However, it does not enhance the model's overall capability or accuracy ceiling.\n% TODO grpo 和 base_grpo 比，sft_grpo 和 sft 比, (DSR1_24B, DSR1_32B, Qwen3_14B, Qwen3_32B) x (base, base_grpo, sft, sft_grpo) 的性能对比\n\n% \\paragraph{Ablation on curriculum learning}\n% 对比有 curriculum learning 和无 curriculum learning 时候的性能\n\n% To evaluate the impact of curriculum learning, we conduct an ablation study by removing the curriculum learning component from our RETuning framework. The results show that without curriculum learning, the model's performance significantly declines, indicating that this strategy is essential for effectively training the model on stock movement prediction tasks.\n\n% TODO (DSR1\\_24B, DSR1\\_32B, Qwen3\\_14B, Qwen3\\_32B) x (sft, sft\\_grpo\\_w/ curriculum, sft\\_grpo\\_w/o curriculum)\n\n% TODO Observation: 难度上升，response length 显著上升。\n% TODO 两个设置：先训 medium 后训 hard；均匀训 medium 和 hard，统计步骤数 vs response length\n% \\paragraph{What affects response length most?}\n% performance, and prediction difficulty\n% 预测难度能显著影响响应长度，正相关。模型 performance 的提升不带来响应长度的提升，固定难度的训练下反而会导致响应长度的下降。这暗示推理能力，或者通过延长 cot 进行测试时计算的能力对预测性能没有明显增益\n% TODO the impact of prediction difficulty on response length\n\n% \\subsection{Observations and Case Studies}\\label{sec:exp:3}\n\n\\paragraph{What insights does model learn to predict stock movement?}\nThrough analyzing the model's responses detailed in Appendix~\\ref{sec:appendix:case_study:response}, we find that the model learns to:\n1. Identifying key evidences that influence daily fluctuations in stock prices from multiple information sources.\n2. Trending to correctly evaluate the short-term impact of gathered evidences, which benefits from the trade-off ability induced by adversarial scoring.\n3. Gradually improving the consistency between the predicted fluctuation and the movement label during reinforcement learning, which we named \"vibe prediction\".\n\n% Generative Analytic Framework 的演化\n% TODO 样例\n\n% TODO the evolution of generative analytic framework\n\n% TODO the evolution of reflective reasoning\n\n% \\paragraph{Reward Hacking}\n% TODO 样例\n\n% TODO\n\n% \\paragraph{Junk and Repetition}\n% % TODO 样例\n% TODO\n\n\n\n\\section{Conclusion}\\label{sec:conclusion}\n% We investigated stock movement prediction with LLMs and identified their tendency to follow contextual viewpoints rather than reason independently. To mitigate this, we proposed \\textbf{RETuning}, which enhances evidence-based reasoning and prediction. Experiments on our large-scale financial dataset show that RETuning consistently outperforms baselines, generalizes to broader financial tasks, and maintains robustness under inference-time scaling and out-of-distribution evaluation.\n\n% \\section{Conclusion}\nIn this work, we explored the underexamined problem of applying large language models (LLMs) to stock movement prediction. Our analysis revealed that vanilla LLMs tend to rely on contextual viewpoints rather than developing independent analytical reasoning, which limits their predictive reliability. To address this challenge, we introduced \\textbf{RETuning}, a reflective evidence-based tuning method that encourages models to construct analytical frameworks, weigh adversarial evidence, and refine predictions through reflection. Experiments on our newly constructed large-scale financial dataset demonstrate that RETuning substantially improves predictive performance over strong baselines, enabling more systematic reasoning in the financial domain. Moreover, RETuning generalizes beyond stock movement prediction, yielding gains across diverse financial tasks, and exhibits robustness under inference-time scaling and out-of-distribution settings. Overall, this study highlights the importance of evidence-oriented reasoning in financial LLMs and establishes RETuning as a promising direction for enhancing their reliability and applicability in real-world financial decision-making.\n\n\n\\newpage\n% \\begin{ack}\n% \\end{ack}\n\n\\section*{Ethics Statement} \\label{sec:ethics_statement}\nTo address potential ethical considerations related to our research on large language models (LLMs) for stock movement prediction, we provide the following statement:\n\nFirst, regarding data ethics: Our large-scale dataset (spanning 2024 for 5,123 A-share stocks) is constructed exclusively from \\textcolor{Primary1}{publicly available sources}, including market price data, publicly disclosed news, analysts’ public opinions, company fundamental reports, official macroeconomic indicators, and publicly accessible information on peer stocks. We strictly comply with China’s Data Security Law, Securities Law, and relevant financial regulatory requirements, ensuring no collection or use of private, sensitive personal data, or non-public material information that could violate market fairness.\n\nSecond, on potential harm and application boundaries: This research is conducted for \\textcolor{Primary1}{academic purposes only} to advance LLM reasoning capabilities in financial tasks. We explicitly emphasize that our model (RETuning) and findings do not constitute financial advice, nor do they endorse or promote real-world investment decisions. Stock market prediction inherently carries high uncertainty, and any practical application of such models for trading could lead to financial risks; we disclaim responsibility for any losses arising from non-academic use of our work.\n\nThird, on bias and fairness: While we designed RETuning to enhance independent logical reasoning (reducing undue reliance on contextual viewpoints) and constructed a diverse dataset to cover a broad range of A-share stocks, we acknowledge potential residual biases (e.g., sector-specific skews in training data or sensitivity to market cycles). Future work will further validate and mitigate such biases to improve the model’s fairness across different market scenarios.\n\nFinally, regarding research integrity: Our study involves no human subjects, so institutional review board (IRB) approval is not applicable. We commit to transparency in dataset construction details and methodology implementation (as detailed in the full paper) to enable reproducibility. We adhere to rigorous academic standards to avoid misrepresentation of results or misuse of technical insights.\n\n\\section*{Reproducibility Statement} \\label{sec:reproducibility_statement}\n\nWe make every effort to ensure that the experiments in this paper are reproducible. Specifically, anonymized source code (training and evaluation scripts), model checkpoints, and processed dataset splits will be released as supplementary material and at the repositories indicated in the Appendix.\\footnote{\\repourl, \\huggingfaceurl, \\dataseturl} The Appendix contains detailed descriptions of data collection and preprocessing (Appendix~\\ref{sec:appendix:dataset_details}), the prompt templates and example inputs/outputs (Figures~\\ref{fig:appendix:prompt_template}--\\ref{fig:appendix:example_response_grading}), and the exact training and evaluation settings including compute and hardware details (Appendix~\\ref{sec:appendix:implementation_details}, Tables~\\ref{table:hyperparameters:sft} and~\\ref{table:hyperparameters:grpo}). Evaluation splits used for OOD and long-horizon tests (e.g., \\textbf{Fin-2024[December]}, \\textbf{Fin-2025[June]}) and the scripts to compute all reported metrics will also be provided. Where full raw data cannot be released due to third-party licensing or privacy constraints, we describe the access procedure and provide processed, reproducible derivatives in the supplementary materials.\n\n\n\\section*{Broader Impact} \\label{sec:broader_impact}\nThis work investigates the use of large language models (LLMs) for stock movement prediction, a domain with potentially high economic and societal implications. Our proposed method, RETuning, demonstrates how reflective evidence organization can enhance independent reasoning in financial tasks. On the positive side, this research contributes to the broader effort of making LLMs more reliable in high-stakes applications by encouraging systematic analysis rather than context-driven imitation. Such improvements may benefit both academic research in reasoning and practical applications in financial decision-support systems.\n\nAt the same time, we emphasize that financial forecasting is inherently uncertain and subject to market volatility, regulatory constraints, and ethical considerations. Automated prediction systems, if misused, could amplify risks, encourage speculative behavior, or contribute to unfair advantages for certain market participants. Our dataset and methods are designed for research purposes only, and we strongly discourage their direct use for live trading or investment without rigorous safeguards, human oversight, and compliance with financial regulations.\n\nMore broadly, this work highlights both the opportunities and limitations of applying LLMs in sensitive domains. We hope that our findings spur further research into building transparent, evidence-based reasoning frameworks that improve model reliability while also ensuring responsible deployment in practice.\n\n\n\\section*{Limitations} \\label{sec:limitation}\n\n\\paragraph{Domain specificity.}\nOur study focuses on the Chinese A-share market in 2024, which provides a rich testbed but may limit the generalizability of findings to other markets, such as U.S. equities or emerging markets with different structures, liquidity, and regulatory conditions.\n\n\\paragraph{Data coverage.}\nAlthough our dataset integrates multiple information sources (prices, news, analyst opinions, fundamentals, and macroeconomic indicators), it remains incomplete. Certain high-frequency signals (e.g., intraday order flow, alternative data, or global macro shocks) are not incorporated, potentially constraining predictive accuracy.\n\n\\paragraph{Model assumptions.}\nRETuning assumes that LLMs can benefit from explicitly structuring and reflecting on evidence. While this holds in our experiments, the approach may be less effective in domains like healthcare or cryptocurrency, where reliable evidence is scarce, noisy, or difficult to formalize.\n\n\\paragraph{Evaluation scope.}\nOur evaluation mainly relies on F1 scores for three-class stock movement prediction and selected benchmarks (e.g., BizFinBench~\\citep{lu2025bizfinbench0}). Broader metrics, such as profitability in trading simulations or risk-adjusted returns, are not considered. It takes time to validate real-world trading performance, which is beyond the scope of this paper.\n\n\\paragraph{Computation and scalability.}\nBoth training (SFT + GRPO) and inference-time scaling are computationally expensive. This may limit accessibility for smaller institutions or researchers without large-scale compute resources, raising questions about cost-efficiency in real-world deployment.\n\n\n\\section*{Future Work} \\label{sec:future_work}\n\n% In the future, we would like to explore the following research directions:\n\n\\paragraph{Extending to other markets.}\nFuture research could examine the effectiveness of RETuning across diverse markets such as U.S. equities, European exchanges, and emerging markets. This would validate whether the approach generalizes under different regulatory regimes, liquidity conditions, and investor behaviors.\n\n\\paragraph{Incorporating richer data sources.}\nEnhancing the dataset with high-frequency trading signals, alternative data (e.g., satellite imagery, ESG reports), and global macroeconomic factors could provide a more comprehensive information environment and further strengthen predictive power.\n\n\\paragraph{Advancing reasoning frameworks.}\nWhile RETuning encourages evidence-based reasoning, future work may integrate causal inference, probabilistic reasoning, or game-theoretic perspectives to capture deeper structures behind stock movements and reduce susceptibility to spurious correlations.\n\n\\paragraph{Evaluation beyond prediction accuracy.}\nA natural next step is to link model predictions with financial outcomes, such as profitability, portfolio optimization, and risk-adjusted returns. This would bridge the gap between benchmark metrics and real-world decision-making.\n\n\\paragraph{Efficiency and accessibility.}\nResearch on lightweight RETuning variants, parameter-efficient fine-tuning, and inference-time acceleration could reduce computational costs, making the method more accessible to practitioners and researchers with limited resources.\n\n% {\n% \\small\n% % \\bibliographystyle{neurips_2025}\n% % \\bibliographystyle{plainnat}\n% % \\bibliography{iclr2026_conference}\n% }\n\\bibliographystyle{iclr2026_conference}\n\\bibliography{references/_paper, references/timeseries}\n\n\n% \\input{checklist}\n\\newpage\n\\appendix\n\n\\begin{center}\n\\begin{huge}\n\\textbf{Appendix}\n\\end{huge}\n\\end{center}\n\n\\section{The Usage of Large Language Models (LLMs)} \\label{sec:llm_usage}\n\nThis section details the specific role of Large Language Models (LLMs) in this paper.\n\nWe employ LLMs \\textit{GPT-5} (developed by OpenAI) and \\textit{Doubao} (developed by ByteDance) to enhance the clarity, coherence, and overall quality of our manuscript.\nThe LLM assistance primarily focus on language polishing (refining structure, terminology consistency, grammar) and formatting adjustments, ensuring that the paper meets high standards of academic writing.\nNo other LLMs were used for research ideation or image generation.\n\nAll reviewed/approved by authors.\nAll authors bear \\textit{full responsibility} for the final paper. All content (including LLM-generated/polished text) was verified: factual claims cross-checked against datasets/literature, and the manuscript screened to avoid unintended plagiarism.\n\n\\section{Implementation Details} \\label{sec:appendix:implementation_details}\n\n\\subsection{Open Source, Open Weights, and Open Data}\nThe source code is available at GitHub\\footnote{\\repourl}.\nThe model weights are available at HuggingFace\\footnote{\\huggingfaceurl}. The training and evaluation datasets are available at HuggingFace\\footnote{\\dataseturl}.\n\n\\subsection{Model Training}\nThe models are trained on up to 4*8 H100 GPUs. Rollout $n$ is set to $8$.\nThe training epochs are set to $3$ for SFT and $1$ for RL.\nThe details of the data synthesis workflow for building SFT dataset are shown in Appendix~\\ref{sec:appendix:sft_data_synthesis}. With the help of the SFT model to determine the prediction difficulty, we further apply GRPO~\\citep{deepseek-math} with curriculum learning and reward shaping. The objective is\n\\begin{equation}\n \\footnotesize\n \\begin{split}\n & \\mathcal{J}_{GRPO}(\\theta) = \\mathbb{E}{[q \\sim P(Q), \\{o_i\\}_{i=1}^G \\sim \\pi_{\\theta_{old}}(O|q)]} \\frac{1}{G}\\sum_{i=1}^G\\frac{1}{|o_i|} \\sum_{t=1}^{|o_i|} \\\\\n & \\left\\{ \\min \\left[ \\frac{\\pi_\\theta(o_{i,t} | q, o_{i,<t})}{\\pi_{\\theta_{old}}(o_{i,t} | q, o_{i,<t})} \\hat{A}_{i,t}, \\text{clip} \\left( \\frac{\\pi_\\theta(o_{i,t} | q, o_{i,<t})}{\\pi_{\\theta_{old}}(o_{i,t} | q, o_{i,<t})}, 1 - \\epsilon, 1 + \\epsilon \\right) \\hat{A}_{i,t} \\right] - \\beta \\mathbb{D}_{KL}\\left[\\pi_{\\theta} || \\pi_{ref}\\right]\\right\\} ,\n \\end{split}\n \\label{eq:GRPO-obj}\n\\end{equation}\nwhere advantage $\\hat{A}_{i, t} = \\frac{r_i- {\\rm mean}(\\mathbf{r})}{{\\rm std}(\\mathbf{r})}$, $G$ is the group size, $\\beta$ is the coefficient of KL penalty, and $q = (x, \\{y_i\\}_{i=1}^n)$ with prompt $x$ and $n$ generations $y$.\n\n% \\subsection{Baseline Implementation}\n\n\n\\subsection{Hyperparameters}\nWe report the detailed hyperparameters for Supervised Fine-Tuning (SFT) in Table~\\ref{table:hyperparameters:sft} and for GRPO in Table~\\ref{table:hyperparameters:grpo}. We use up to 4*8 H100 80GB GPUs for experiments.\n\n\\subsection{Training Frameworks}\nWe use Xtuner~\\citep{2023xtuner} to SFT with DeepSpeed~\\citep{deepspeed} to accelerate training and ZeRO-3 to reduce memory usage, and verl~\\citep{verl} to implement GRPO.\n\n\\begin{table*}[htbp]\n \\centering\n \\caption{The training hyperparameters for Supervised Fine-Tuning (SFT). 32B, 14B, and 7B denote models based on DeepSeek-R1-Distill-Qwen with 32B, 14B, and 7B parameters respectively.}\n \\begin{tabularx}{\\linewidth}{l XXX} % X columns for automatic width allocation\n \\toprule\n \\cellcolor{Background1}\\textbf{Hyperparameter Category} & \\cellcolor{Background1}\\textbf{32B} & \\cellcolor{Background1}\\textbf{14B} & \\cellcolor{Background1}\\textbf{7B} \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{1. Data Configuration}}} \\\\\n Train Micro-Batch Size per GPU & 1 & 1 & 1 \\\\\n Gradient Accumulation Steps & 128 & 128 & 128 \\\\\n Total Effective Batch Size & 1024 & 1024 & 1024 \\\\\n & ($1\\times128\\times8$) & ($1\\times128\\times8$) & ($1\\times128\\times8$) \\\\\n Pack Sequences to Max Length & False & False & False \\\\\n Data Shuffling Before Packing & True & True & True \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{2. Model \\& LoRA Configuration}}} \\\\\n LLM Torch Dtype & torch.float16 & torch.float16 & torch.float16 \\\\\n LoRA Rank ($r$) & 32 & 32 & 32 \\\\\n LoRA Alpha ($\\alpha$) & 64 & 64 & 64 \\\\\n LoRA Dropout & 0.1 & 0.1 & 0.1 \\\\\n LoRA Bias Type & none & none & none \\\\\n LoRA Task Type & CAUSAL\\_LM & CAUSAL\\_LM & CAUSAL\\_LM \\\\\n Variable-Length Attention & False & False & False \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{3. Optimizer \\& LR Scheduler}}} \\\\\n Optimizer Type & \\multicolumn{3}{c}{torch.optim.AdamW} \\\\\n Learning Rate (LR) & $2\\times 10^{-4}$ & $2\\times 10^{-4}$ & $2\\times 10^{-4}$ \\\\\n AdamW Betas ($\\beta_1$, $\\beta_2$) & (0.9, 0.999) & (0.9, 0.999) & (0.9, 0.999) \\\\\n Weight Decay & 0 & 0 & 0 \\\\\n Gradient Clipping Max Norm & 1 & 1 & 1 \\\\\n LR Scheduler Type & \\multicolumn{3}{c}{Linear Warmup + Cosine Annealing} \\\\\n Warmup Ratio (Warmup Epochs / Total Epochs) & 0.03 (0.09/3) & 0.03 (0.09/3) & 0.03 (0.09/3) \\\\\n Warmup Start Factor & $1\\times 10^{-5}$ & $1\\times 10^{-5}$ & $1\\times 10^{-5}$ \\\\\n Cosine Annealing Final LR ($\\eta_{min}$) & 0.0 & 0.0 & 0.0 \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{4. Training Strategy \\& Distributed Config}}} \\\\\n Training Strategy Type & \\multicolumn{3}{c}{DeepSpeedStrategy} \\\\\n DeepSpeed Zero Optimization Stage & 3 & 3 & 3 \\\\\n BF16 Precision Enabled & True & True & True \\\\\n FP16 Precision Enabled & False & False & False \\\\\n Sequence Parallel Size & 8 & 8 & 8 \\\\\n Sampler Shuffling & True & True & True \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{6. Environment \\& Misc Config}}} \\\\\n Launcher Type & \\multicolumn{3}{c}{pytorch} \\\\\n Distributed Backend & nccl & nccl & nccl \\\\\n Multiprocessing Start Method & fork & fork & fork \\\\\n Deterministic Training & False & False & False \\\\\n \\bottomrule\n \\end{tabularx}\n \\label{table:hyperparameters:sft}\n\\end{table*}\n\n\\begin{table*}[htbp]\n \\centering\n \\caption{The training hyperparameters for GRPO. 32B SFT, 14B SFT, and 7B SFT denote models based on DeepSeek R1 with 32B, 14B, and 7B parameters after SFT stage respectively.}\n \\begin{tabularx}{\\linewidth}{l XXX} % X列自动分配宽度，占满\\linewidth\n \\toprule\n \\cellcolor{Background1}\\textbf{Base Model} & \\cellcolor{Background1}\\textbf{32B SFT} & \\cellcolor{Background1}\\textbf{14B SFT} & \\cellcolor{Background1}\\textbf{7B SFT} \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{1. Data Configuration}}} \\\\\n Training Batch Size & 256 & 256 & 256 \\\\\n Validation Batch Size & 256 & 256 & 256 \\\\\n Max Prompt Length & 32768 & 32768 & 32768 \\\\\n Max Response Length & 4096 & 4096 & 4096 \\\\\n Data Shuffling & True & True & True \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{2. Algorithm Configuration}}} \\\\\n Advantage Estimator & GRPO & GRPO & GRPO \\\\\n Gamma ($\\gamma$, Discount Factor) & 1.0 & 1.0 & 1.0 \\\\\n Lambda ($\\lambda$, Advantage Smoothing) & 1.0 & 1.0 & 1.0 \\\\\n KL Coefficient & 0.001 & 0.001 & 0.001 \\\\\n Target KL Divergence & 0.1 & 0.1 & 0.1 \\\\\n Normalize Advantage by Std & True & True & True \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{3. Actor \\& Ref Configuration}}} \\\\\n Learning Rate & $3 \\times 10^{-7}$ & $3 \\times 10^{-7}$ & $3 \\times 10^{-7}$ \\\\\n Weight Decay & 0.01 & 0.01 & 0.01 \\\\\n Clip Ratio & 0.2 & 0.2 & 0.2 \\\\\n Entropy Coefficient & 0.0 & 0.0 & 0.0 \\\\\n PPO Epochs & 1 & 1 & 1 \\\\\n Log Prob Micro Batch Size & 8 & 4 & 4 \\\\\n Tensor Parallel Size & 4 & 4 & 4 \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{4. Rollout Configuration}}} \\\\\n Rollout Count (n) & 8 & 8 & 8 \\\\\n Rollout Mode & sync & sync & sync \\\\\n Engine Name & vllm & vllm & vllm \\\\\n Data Type (dtype) & bfloat16 & bfloat16 & bfloat16 \\\\\n Temperature & 0.6 & 0.6 & 0.6 \\\\\n Max Num Batched Tokens & 36864 & 36864 & 36864 \\\\\n Tensor Parallel Size & 4 & 4 & 4 \\\\\n Enable Chunked Prefill & True & True & True \\\\\n \\hline\n \\multicolumn{4}{c}{\\cellcolor{Background1}\\textcolor{Font1}{\\textbf{5. Trainer Configuration}}} \\\\\n Number of Nodes & 4 & 2 & 1 \\\\\n GPUs per Node & 8 & 8 & 8 \\\\\n Total Epochs & 1 & 1 & 1 \\\\\n Checkpoint Save Frequency (steps) & 10 & 10 & 10 \\\\\n Validation Frequency (steps) & 10 & 10 & 10 \\\\\n Validate Before Training & True & True & True \\\\\n \\bottomrule\n \\end{tabularx}\n \\label{table:hyperparameters:grpo}\n\\end{table*}\n\n\n\\section{Dataset Details} \\label{sec:appendix:dataset_details}\n\n\n\\subsection{Fin-2024 and Fin-2025}\nWe consider studying the stock movement prediction task based on data from the Chinese A-share market. Naturally, the collected data are in Chinese, and consequently, the associated prompts and synthetic data are also in Chinese. This consistency within a single language allows LLMs to achieve better understanding and more coherent reasoning over the data. Thus, the language model can fully leverage its pre-trained knowledge in Chinese to analyze the stock market. Therefore, in this paper, we choose Qwen~\\citep{Qwen} and DeepSeek~\\citep{deepseek-r1} as the backbone models, both of which are strong Chinese LLMs. We apologize for any inconvenience the language gap may cause to readers who are not native Chinese speakers, and we hope that this gap will not hinder the understanding of our work.\n\nThe reason why we decide to construct a new dataset to study the stock movement prediction task is twofold. First, existing datasets (StockNet~\\citep{StockNet}, CMIN-US~\\citep{CMIN}, CMIN-CN~\\citep{CMIN}, EDT~\\citep{EDT}) are outdated and do not reflect the current market conditions. Financial markets are dynamic and constantly evolving, with new trends, regulations, and events shaping the landscape. Using outdated datasets may lead to models that are not well-suited for current market scenarios. Second, existing datasets lack diversity in data sources. Relying solely on price and news data may not capture the full complexity of stock movements. Incorporating additional data sources such as analyst reports, macroeconomic indicators, and quantitative reports can provide a more comprehensive view of the market and improve prediction accuracy. Rich enough data sources are crucial for reliable forecasting in the high–signal-noise ratio of financial markets.\n\nThen, we build a new dataset \\textbf{Fin-2024} covering January to December 2024, with a test split set \\textbf{Fin-2024[December]} and an additional long-horizon evaluation set \\textbf{Fin-2025[June]}. We collect data from multiple sources, including stock prices, financial news, analyst reports, macroeconomic indicators, and quantitative reports. We process the raw data into a structured format suitable for LLMs, including entity recognition, sentiment analysis, event extraction, and traditional time-series analysis (for generating quantitative reports). The dataset contains 209,063 data points across 5,123 A-share stocks from various sectors. Each data point includes a timestamp, stock identifier, historical prices (open, close, high, low, volume), relevant news articles, analyst reports, macroeconomic indicators, quantitative reports, and the corresponding stock movement label (up/down/hold), which is based on the change\\_pct between the open price of the next trading day and the close price of the current trading day.\n\nIn order to ensure data quality, we apply several filtering steps. We remove data points with missing or incomplete information, filter out stocks with low trading volume or insufficient historical data, and balance the label distribution in the dataset to avoid bias towards any particular class. The data processing pipeline is shown in Figure~\\ref{fig:dataset_pipeline}, and the prompt length distribution is shown in Figure~\\ref{fig:prompt_length_distribution}.\n\nThe final dataset is split into training (90\\%) and out-of-distribution (OOD) (10\\%) sets. The training set is used for model fine-tuning and reinforcement learning, and the OOD set for final evaluation. The long-horizon evaluation set \\textbf{Fin-2025[June]} contains data from June 2025 to assess model performance in a future market scenario.\nPlease refer to Figure~\\ref{fig:dataset_pipeline} for detailed numbers and splits.\n\nWe present an example of the prompt template in Figure~\\ref{fig:appendix:prompt_template}, which consists of multiple parts: stock news (Figure~\\ref{fig:appendix:example_prompt_part_news} and Figure~\\ref{fig:appendix:example_prompt_part_news2}), stock price information of the current stock and top-3 similar stocks (Figure~\\ref{fig:appendix:example_prompt_part_price}), macroeconomic indicators report (Figure~\\ref{fig:appendix:example_prompt_part_marco}), stock fundamentals report (Figure~\\ref{fig:appendix:example_prompt_part_fundamentals} and Figure~\\ref{fig:appendix:example_prompt_part_fundamentals2}), stock basic information (Figure~\\ref{fig:appendix:example_prompt_part_baseinfo}), stock quantitative reports (Figure~\\ref{fig:appendix:example_prompt_part_quantitative_reports}), model response (Figure~\\ref{fig:appendix:example_response}), and model response grading (Figure~\\ref{fig:appendix:example_response_grading}).\n\n\\begin{figure*}[htbp]\n\t\\centering\n\t\\includegraphics[width=1.\\textwidth]{dataset_pipeline.pdf}\n\t\\caption{Data processing pipeline showing total 209063 points split into train/test, filtered via multiple steps (lack info, label balance, curriculum learning), and categorized for SFT, RL, OOD evaluations.}\n\t\\label{fig:dataset_pipeline}\n\\end{figure*}\n\n\\begin{figure*}[htbp]\n\t\\centering\n\t\\includegraphics[width=0.9\\textwidth]{prompt_length_distribution.png}\n\t\\caption{Prompt length distribution across the dataset, illustrating the varying lengths of input prompts used for training and evaluation.}\n\t\\label{fig:prompt_length_distribution}\n\\end{figure*}\n\n% \\inputminted{jinja}{prompt.jinja}\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{figures/prompt.pdf}\n \\caption{The prompt template for stock movement prediction.}\n \\label{fig:appendix:prompt_template}\n\\end{figure*}\n\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{figures/prompt_part_news.pdf}\n \\caption{Example. Part 1.1: Stock News.}\n \\label{fig:appendix:example_prompt_part_news}\n\\end{figure*}\n\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{figures/prompt_part_news2.pdf}\n \\caption{Example. Part 1.2: Stock News.}\n \\label{fig:appendix:example_prompt_part_news2}\n\\end{figure*}\n\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=0.75\\textwidth]{figures/prompt_part_price.pdf}\n \\caption{Example. Part 2: Stock Price Info of Current Stock and Top-3 Similar Stocks.}\n \\label{fig:appendix:example_prompt_part_price}\n\\end{figure*}\n\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{figures/prompt_part_marco.pdf}\n \\caption{Example. Part 3: Macroeconomic Indicators Report.}\n \\label{fig:appendix:example_prompt_part_marco}\n\\end{figure*}\n\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{figures/prompt_part_fundamentals.pdf}\n \\caption{Example. Part 4.1: Stock Fundamentals Report.}\n \\label{fig:appendix:example_prompt_part_fundamentals}\n\\end{figure*}\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=0.99\\textwidth]{figures/prompt_part_fundamentals2.pdf}\n \\caption{Example. Part 4.2: Stock Fundamentals Report.}\n \\label{fig:appendix:example_prompt_part_fundamentals2}\n\\end{figure*}\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{figures/prompt_part_baseinfo.pdf}\n \\caption{Example. Part 5: Stock Basic Information.}\n \\label{fig:appendix:example_prompt_part_baseinfo}\n\\end{figure*}\n\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=0.85\\textwidth]{figures/prompt_part_quantitative_reports.pdf}\n \\caption{Example. Part 6: Stock Quantitative Reports.}\n \\label{fig:appendix:example_prompt_part_quantitative_reports}\n\\end{figure*}\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{figures/response.pdf}\n \\caption{Example. Part 7: Model Response.}\n \\label{fig:appendix:example_response}\n\\end{figure*}\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{response_grading.pdf}\n \\caption{Example. Part 8: Model Response Grading.}\n \\label{fig:appendix:example_response_grading}\n\\end{figure*}\n\n\\subsection{Fin-2024-SFT}\\label{sec:appendix:sft_data_synthesis}\n\nThe dataset \\textbf{Fin-2024-SFT} contains 188 cold-start items and 10K general reasoning samples. Firstly, we selected 10K items from \\url{https://huggingface.co/datasets/GeneralReasoning/GeneralThought-323K}, which aims to avoid catastrophic forgetting~\\citep{catastrophic_forgetting} and even strengthen reasoning ability when fine-tuning the model. These data points are related to math, code, common sense, chatting, role play, writing, etc. However, they are not allowed to be related to finance to avoid bias, so that we can determine the model's performance in a more controlled setting.\n\nThen, the samples for cold-starting are constructed using a workflow with DeepSeek-R1 (671B) as the backbone model and the polish prompt (Figure~\\ref{fig:appendix:polish_prompt}) to generate high-quality, diverse training samples that follow the proposed thinking schema presented in Section~\\ref{sec:method:1}. These synthesized samples are further filtered by a reward function, which checks format, validates prediction (\\texttt{<score>}, \\texttt{<change\\_pct>}, \\texttt{<answer>}) against the ground truth, and ensures adherence to the desired output style. At this stage, 300 samples passed the validation. From these, we cherry-picked 188 samples in total, which required approximately six hours of expert annotation (around 100 USD) for final curation.\n\nNotably, the financial data we collected spans the entire year of 2024 and June 2025. Among these, the data from January to November 2024 were used for training. From this subset of training, we extracted 300 instances (100 labeled as \\emph{up}, 100 as \\emph{hold}, and 100 as \\emph{down}) to construct the cold-start dataset for synthesis.\n\n\\textbf{RETuning} guides the model through a multistep process:\n\n\\begin{enumerate}\n \\item \\textbf{\\underline{Understand the Task.}} The model first internalizes the task—predicting the direction of price movement from the previous close to the next open, with a $\\pm3\\%$ threshold—improving alignment and reducing hallucination.\n \\item \\textbf{\\underline{Establish Analytical Principles.}} It constructs a dynamic analytical framework (e.g., fundamentals, news trends, macro signals), independent of analyst commentary.\n \\item \\textbf{\\underline{Extract Evidence.}} The model collects multiple context-based signals and assesses their support for each directional hypothesis.\n \\item \\textbf{\\underline{Group and Score.}} Extracted evidence is grouped and scored by directional leaning, forming a soft-evidence pool.\n \\item \\textbf{\\underline{Reflect and Reconcile.}} Averaging directional scores, the model enters a reflection phase to resolve conflicting evidence.\n \\item \\textbf{\\underline{Produce Structured Output.}} The model generates a final decision in a consistent, interpretable format, specifying both direction and percentage change.\n\\end{enumerate}\n\nIn detail, we employed the following workflow:\n\n\\begin{itemize}\n \\item \\textbf{Step 1: Multi-Source Data Aggregation.} We systematically collected a diverse range of financial data covering the period from January 2024 to June 2025. This included quantitative data, such as historical stock prices (open, high, low, close) and trading volumes, alongside qualitative data from relevant financial news articles. For training purposes, we focused on the January--November 2024 subset, from which 300 balanced instances (up, hold, down) were selected for cold-start data synthesis. To ensure the dataset's breadth and representativeness, we selected a varied portfolio of stocks from multiple market sectors.\n\n \\item \\textbf{Step 2: Structured Prompt Formulation.} We engineered a series of structured prompts designed to elicit detailed, context-aware analytical reasoning from the language model. These prompts incorporated explicit instructions, illustrative examples (few-shot learning), and comprehensive contextual information (e.g., market conditions, company background) to precisely guide the model's generation process according to our proposed thinking schema.\n\n \\item \\textbf{Step 3: Controlled Response Generation.} Leveraging the 671B-parameter DeepSeek-R1 model, we executed inference on the engineered prompts. To foster response diversity and prevent deterministic outputs, we employed stochastic sampling techniques, specifically temperature sampling and top-k sampling. This allowed the model to explore a wider range of analytical paths and linguistic styles.\n\n \\item \\textbf{Step 4: Hybrid Quality Assurance.} The generated responses underwent a rigorous two-stage filtering process. Initially, automated metrics were used to assess fundamental quality attributes such as textual coherence, logical consistency, and relevance to the prompt. Subsequently, all machine-vetted samples were subjected to manual review by a financial expert to discard any outputs that were factually incorrect, nonsensical, or failed to meet the required analytical depth.\n\n \\item \\textbf{Step 5: Semantic Data Augmentation.} To enrich the dataset and enhance model robustness, we applied several data augmentation techniques to the high-quality samples. Methods such as paraphrasing, synonym replacement, and back-translation were utilized to create semantically equivalent but syntactically diverse training instances, thereby reducing the risk of overfitting to specific phrasings.\n\n \\item \\textbf{Step 6: Final Dataset Curation.} The fully processed and augmented data was compiled into the final training set. During this stage, we ensured a balanced class distribution among the target labels (up, down, hold) and a representative allocation of stocks across different sectors and market conditions to form a well-rounded and unbiased dataset for fine-tuning.\n\\end{itemize}\n\n\n\\begin{figure*}[htbp]\n \\centering\n \\includegraphics[width=\\textwidth]{polish_prompt.pdf}\n \\caption{The polish prompt allows the backbone model to generate refined responses that follow the proposed thinking schema in Section~\\ref{sec:method:1}.}\n \\label{fig:appendix:polish_prompt}\n\\end{figure*}\n\n\\subsection{BizFinBench}\n\nBizFinBench~\\citep{lu2025bizfinbench0} is a comprehensive financial benchmark covering 10 tasks, including financial analysis, financial news classification, financial text summarization, financial question answering, and financial named entity recognition. We evaluate the generalization ability of \\textbf{RETuning} on BizFinBench. The details of each dataset type are as follows.\n\n\\begin{itemize}\n \\item \\textbf{Anomalous Event Attribution (AEA):} This dataset evaluates the model's ability to trace financial anomalies based on given information such as timestamps, news articles, financial reports, and stock movements. The model must identify the cause-and-effect relationships behind sudden market fluctuations and distinguish relevant factors from noise.\n \\item \\textbf{Financial Numerical Computation (FNC):} This dataset assesses the model's ability to perform accurate numerical calculations in financial scenarios, including interest rate calculations, return on investment (ROI), and financial ratios.\n \\item \\textbf{Financial Time Reasoning (FTR):} This dataset tests the model’s ability to understand and reason about time-based financial events, such as predicting interest accruals, identifying the impact of quarterly reports, and assessing financial trends over different periods.\n \\item \\textbf{Financial Tool Usage (FTU):} This dataset evaluates the model's ability to comprehend user queries and effectively use financial tools to solve real-world problems. It covers scenarios like investment analysis, market research, and information retrieval, requiring the model to select appropriate tools, input parameters accurately, and coordinate multiple tools when needed.\n \\item \\textbf{Financial Knowledge QA (FQA):} This dataset evaluates the model's understanding and response capabilities regarding core knowledge in the financial domain. It spans a wide range of financial topics, encompassing key areas such as fundamental financial concepts, financial markets, investment theory, macroeconomics, and finance.\n \\item \\textbf{Financial Data Description (FDD):} This dataset measures the model's ability to analyze and describe structured and unstructured financial data, such as balance sheets, stock reports, and financial statements.\n \\item \\textbf{Emotion Recognition (ER):} This dataset evaluates the model's capability to recognize nuanced user emotions in complex financial market environments. The input data encompasses multiple dimensions, including market conditions, news articles, research reports, user portfolio information, and queries. The dataset covers six distinct emotional categories: optimism, anxiety, negativity, excitement, calmness, and regret.\n \\item \\textbf{Stock Price Prediction (SP):} This dataset evaluates the model’s ability to predict future stock prices based on historical trends, financial indicators, and market news.\n \\item \\textbf{Financial Named Entity Recognition (FNER):} This dataset focuses on evaluating the model’s ability to identify and classify financial entities such as company names, stock symbols, financial instruments, regulatory agencies, and economic indicators.\n % \\item Portfolio optimization (PO): This dataset evaluates the model's ability to construct short-term investment portfolios in complex financial markets based on multi-dimensional information. Input data includes various technical indicators and recent one-week news related to each stock. The model needs to integrate technical analysis with news sentiment analysis to generate an optimized short-term investment portfolio strategy, aiming to maximize returns while controlling risks.\n\\end{itemize}\n\nTable~\\ref{datasetall} presents a detailed breakdown of the dataset, covering the evaluation dimensions, corresponding metrics, the number of instances per task, and the average token length per entry. Notably, the dataset shows considerable variability in input length, spanning from a minimum of 22 tokens to a maximum of 4,556 tokens. This wide range not only mirrors the complexity and heterogeneity of real-world financial scenarios but also poses a meaningful challenge for models—specifically, in demonstrating their capability to process both short and long financial texts effectively.\nTable~\\ref{query_token_stats} presents their maximum token length, minimum token length, and average length.\n\n\\begin{table}[h]\n \\centering\n \\caption{Overview of BizFinBench~\\citep{lu2025bizfinbench0} Datasets}\n \\resizebox{\\textwidth}{!}{%\n \\begin{tabular}{cp{17.8em}p{14.445em}p{5.39em}ll}\n \\toprule\n Category & \\multicolumn{1}{l}{Data} & \\multicolumn{1}{l}{Evaluation Dimensions} & \\multicolumn{1}{l}{Metrics} & Numbers & Avg Len. \\\\\n \\midrule\n Reasoning & Anomalous Event Attribution (AEA) & Causal consistency\\newline{}Information relevance\\newline{}Noise resistance & Accuracy & 1064 & 939 \\\\\n & Financial Time Reasoning (FTR) & Temporal reasoning correctness & Accuracy & 514 & 1162 \\\\\n & Financial Tool Usage (FTU) & Tool selection appropriateness\\newline{}Parameter input accuracy\\newline{}Multi-tool coordination & Judge Score & 641 & 4556 \\\\\n \\midrule\n Numerical calculation & Financial Numerical Computation (FNC) & Computational accuracy\\newline{}Unit consistency & Accuracy & 581 & 651 \\\\\n \\midrule\n Q\\&A & Financial Knowledge QA (FQA) & Question comprehension\\newline{}Knowledge coverage\\newline{}Answer accuracy & Judge Score & 990 & 22 \\\\\n & Financial Data Description (FDD) & Trend accuracy\\newline{}Data consistency & Judge Score & 1461 & 311 \\\\\n \\midrule\n Prediction recognition & Emotion Recognition (ER) & Emotion classification accuracy\\newline{}Implicit information extraction & Accuracy & 600 & 2179 \\\\\n & Stock Price Prediction (SP) & Trend judgment, Causal reasoning & Accuracy & 497 & 4498 \\\\\n \\midrule\n Information extraction & Financial Named Entity Recognition (FNER) & Recognition accuracy\\newline{}Entity classification correctness & Accuracy & 435 & 533 \\\\\n \\bottomrule\n \\end{tabular}%\n }\n \\label{datasetall}%\n\\end{table}%\n\n\\begin{table}[htbp]\n \\centering\n \\caption{Token Length Statistics of BizFinBench~\\citep{lu2025bizfinbench0}.}\n \\label{query_token_stats}\n \\begin{tabular}{lrrrr}\n \\toprule\n \\textbf{Dataset} & \\textbf{Min} & \\textbf{Max} & \\textbf{Avg} & \\textbf{Count} \\\\\n \\midrule\n NER & 415 & 1,194 & 533.1 & 433 \\\\\n FTU & 4,169 & 6,289 & 4,555.5 & 641 \\\\\n AEA & 680 & 1,396 & 938.7 & 1,064 \\\\\n ER & 1,919 & 2,569 & 2,178.5 & 600 \\\\\n FNC & 287 & 2,698 & 650.5 & 581 \\\\\n FDD & 26 & 645 & 310.9 & 1,461 \\\\\n FTR & 203 & 8,265 & 1,162.0 & 514 \\\\\n FQA & 5 & 45 & 21.7 & 990 \\\\\n SP & 1,254 & 5,532 & 4,498.1 & 497 \\\\\n \\bottomrule\n \\end{tabular}\n\\end{table}\n\n\\section{Evaluation Details} \\label{sec:appendix:evaluation_details}\nWe evaluate our model using several metrics, including accuracy, precision, recall, and F1-score. These metrics provide a comprehensive view of the model's performance across different aspects.\n\n\\subsection{Detailed Results on Fin-2024[December]} \\label{sec:appendix:detailed_results:fin2024december}\n\nWe present detailed results on \\textbf{Fin-2024[December]} for different baselines in Figure~\\ref{fig:detailed_results:fin2024december}. The results are grouped by the number of repeated sampling counts \\( n \\) (log\\(_2\\) scale: 1, 2, 4, 8, 16, 32). Performance is measured using the stock movement prediction (SMP) F1 score. It can be observed that current LLMs struggle to achieve satisfactory performance on this challenging task. Most of them are not able to scale up their performance with increasing \\( n \\). In contrast, our proposed \\textbf{RETuning} method demonstrates significant improvements, especially when combined with larger models and reinforcement learning techniques. Notably, the \\textbf{DeepSeek\\_R1\\_32B\\_SFT\\_GRPO} model achieves the highest F1 score of approximately 0.44 at \\( n=32 \\), showcasing the effectiveness of our approach in enhancing model capabilities for stock movement prediction.\n\n\\begin{figure*}[htbp]\n\t\\centering\n\t\\includegraphics[width=0.85\\textwidth]{ablation_on_CoT_4.pdf}\n\t\\caption{Detailed results on \\textbf{Fin-2024[December]} for different baselines.}\n\t\\label{fig:detailed_results:fin2024december}\n\\end{figure*}\n\n\\subsection{Results Grouped by OOD split on Fin-2024[December] and Fin-2025[June]} \\label{sec:appendix:detailed_results:group_by_ood}\n\nThis section analyzes the performance of different models on the \\textbf{stock movement prediction (SMP) task}, a 3-category classification problem based on price changes, under four out-of-distribution (OOD) scenarios. The evaluation focuses on the models’ ability to \\emph{scale up} by increasing the repeated sampling count \\( n \\) (log\\(_2\\) scale: 1, 2, 4, 8, 16, 32). Performance is measured using the SMP F1 score, and the comparison includes a baseline (Random Bound), the 14B/32B variants of DeepSeek-R1, and their optimized versions (SFT, SFT+GRPO).\n\n\\begin{minipage}[b]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{submain_results.pdf}\n \\captionof{figure}{\\textbf{Overall} f1 score results on \\textbf{Fin-2024[December]}.}\n \\label{fig:appendix:overall_f1_score}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[b]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{OOD_stock_main_results.pdf}\n \\captionof{figure}{\\textbf{OOD\\_Stock} f1 score results on \\textbf{Fin-2024[December]}.}\n \\label{fig:appendix:ood_stock_f1_score}\n\\end{minipage}\n\n\\begin{minipage}[b]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{OOD_date_main_results.pdf}\n \\captionof{figure}{\\textbf{OOD\\_Date} f1 score results on \\textbf{Fin-2024[December]}.}\n \\label{fig:appendix:ood_date_f1_score}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[b]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{OOD_date_stock_main_results.pdf}\n \\captionof{figure}{\\textbf{OOD\\_Stock\\&Date} f1 score results on \\textbf{Fin-2024[December]}.}\n \\label{fig:appendix:ood_stock_date_f1_score}\n\\end{minipage}\n\n\\begin{minipage}[b]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{OOD_date_June_results.pdf}\n \\captionof{figure}{\\textbf{OOD\\_Date} f1 score results on \\textbf{Fin-2025[June]}.}\n \\label{fig:appendix:ood_date_f1_score_June}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[b]{0.49\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{OOD_date_stock_June_results.pdf}\n \\captionof{figure}{\\textbf{OOD\\_Stock\\&Date} f1 score results on \\textbf{Fin-20254[June]}.}\n \\label{fig:appendix:ood_stock_date_f1_score_June}\n\\end{minipage}\n\n\\subsubsection{Overall OOD Performance}\nAs shown in Figure~\\ref{fig:appendix:overall_f1_score}, which aggregates results from the \\textbf{OOD\\_Stock}, \\textbf{OOD\\_Date}, and \\textbf{OOD\\_Stock\\&Date} scenarios, two consistent trends emerge. First, a clear performance hierarchy is observed: 32B models consistently outperform their 14B counterparts, and optimization further improves results (SFT $>$ Base; SFT+GRPO $>$ SFT). Among all configurations, the \\textbf{DeepSeek\\_R1\\_32B\\_SFT\\_GRPO} model achieves the highest F1 score of approximately 0.44 at \\( n=32 \\), followed by the 32B SFT and Base models. Importantly, all variants surpass the Random Bound baseline (F1 $<$ 0.30), demonstrating the benefits of both scaling and optimization. Second, all models exhibit \\emph{monotonic gains} as \\( n \\) increases. For instance, DeepSeek\\_R1\\_32B\\_SFT\\_GRPO improves from about 0.36 at \\( n=1 \\) to 0.44 at \\( n=32 \\), corresponding to a relative gain of roughly 22\\%. In contrast, the 14B baseline improves only from 0.28 to 0.34 over the same range. These results confirm that repeated sampling consistently enhances performance, with larger and optimized models benefiting the most.\n\n\\subsubsection{OOD\\_Stock Scenario (Unseen Stocks)}\nFigure~\\ref{fig:appendix:ood_stock_f1_score} evaluates performance when predicting trends for \\textbf{stocks unseen during training}. This setting achieves the second-highest peak performance across all scenarios, with DeepSeek\\_R1\\_32B\\_SFT\\_GRPO reaching about 0.45 at \\( n=32 \\). The performance gap between 32B and 14B optimized models widens to roughly 0.07 at this sampling level, underscoring the importance of parameter scale for generalizing to new stocks. Moreover, F1 scores rise sharply as \\( n \\) increases. For example, the 32B SFT model improves from 0.37 at \\( n=1 \\) to 0.43 at \\( n=32 \\), a gain of around 16\\%. These findings suggest that repeated sampling effectively reduces noise in trend estimation for unfamiliar stocks, thereby mitigating the distribution shift.\n\n\\subsubsection{OOD\\_Date Scenario (Unseen Time Periods)}\nIn the \\textbf{OOD\\_Date} setting (Figure~\\ref{fig:appendix:ood_date_f1_score}), where models are tested on unseen time periods such as December 2024, performance is notably weaker. This scenario yields the lowest peak among all four settings, with the best-performing model (32B SFT+GRPO) reaching only about 0.42 at \\( n=32 \\). Even with maximum scaling, the gains are modest: DeepSeek\\_R1\\_32B\\_SFT\\_GRPO improves by only 0.08 (from 0.34 to 0.42) as \\( n \\) increases from 1 to 32, which is smaller than the gains observed in stock-based shifts. These results indicate that temporal distribution shifts, likely caused by market regime changes, are more difficult to address with repeated sampling alone.\n\n\\subsubsection{OOD\\_Stock\\&Date Scenario (Dual Distribution Shifts)}\nThe most challenging case, involving \\textbf{both unseen stocks and unseen time periods}, is shown in Figure~\\ref{fig:appendix:ood_stock_date_f1_score}. Surprisingly, this dual-shift setting achieves the \\emph{highest overall peak performance}. DeepSeek\\_R1\\_32B\\_SFT\\_GRPO reaches approximately 0.50 at \\( n=32 \\), surpassing even the OOD\\_Stock scenario. The scaling effect is particularly strong: the model improves by about 0.12 (from 0.38 to 0.50) when \\( n \\) increases from 1 to 32. Moreover, the performance gap between the 32B optimized model and the 14B baseline widens substantially with larger \\( n \\). These results highlight a synergy between model scale and repeated sampling, suggesting that larger models are especially capable of leveraging additional samples to disentangle stock-specific volatility from time-dependent shifts.\n\n\\subsubsection{Summary of Scaling-Up Ability Across OOD Scenarios}\nTaken together, the results provide several key insights. First, repeated sampling proves to be a universally valid strategy, as all models improve with increasing \\( n \\) across every OOD setting. Second, the magnitude of gains is scenario-dependent: the largest improvements occur in the dual OOD\\_Stock\\&Date scenario (12--22\\% increase), while the OOD\\_Date scenario yields the smallest gains (8--15\\%), reflecting the particular difficulty of temporal shifts. Third, the optimal configuration for scaling-up ability is the \\textbf{DeepSeek\\_R1\\_32B\\_SFT\\_GRPO} model at \\( n=32 \\), which achieves F1 scores of roughly 0.50 (OOD\\_Stock\\&Date), 0.45 (OOD\\_Stock), 0.44 (Overall OOD), and 0.42 (OOD\\_Date), consistently outperforming all other settings by 5--15\\%. Finally, the results underscore the \\textbf{synergy between model scale, optimization, and repeated sampling}: larger models not only benefit more from optimization but also extract greater value from additional samples, with the effect most pronounced in dual-shift scenarios.\n\n% \\subsection{Results Grouped by Label on Fin-2024[December] and Fin-2025[June]} \\label{sec:appendix:detailed_results:group_by_label}\n\n\n\\subsection{Detailed Results on BizFinBench} \\label{sec:appendix:detailed_results:bizfinbench}\n\nWe present the detailed results of various large language models on the BizFinBench benchmark~\\citep{lu2025bizfinbench0}, as summarized in Table~\\ref{table:bizfinbench_detailed_results}. The evaluation encompasses a range of tasks, including financial entity recognition, financial question answering, financial text classification, and more. The results are color-coded to highlight the top three performers for each task: \\colorbox{golden}{golden} indicates the top-performing model, \\colorbox{lightblue}{silver} represents the second-best result, and \\colorbox{lightgreen}{bronze} denotes the third-best performance.\n\n\n\\begin{table*}[htbp]\n \\centering\n \\caption{Performance Comparison of Large Language Models on BizFinBench~\\citep{lu2025bizfinbench0}. The models are evaluated across multiple tasks, with results color-coded to represent the top three performers for each task: \\colorbox{golden}{golden} indicates the top-performing model, \\colorbox{lightblue}{silver} represents the second-best result, and \\colorbox{lightgreen}{bronze} denotes the third-best performance.}\n \\resizebox{\\textwidth}{!}{%\n \\begin{tabular}{lrrrrrrrrrr}\n \\toprule\n \\multicolumn{1}{c}{Model} & \\multicolumn{1}{c}{AEA} & \\multicolumn{1}{c}{FNC} & \\multicolumn{1}{c}{FTR} & \\multicolumn{1}{c}{FTU} & \\multicolumn{1}{c}{FQA} & \\multicolumn{1}{c}{FDD} & \\multicolumn{1}{c}{ER} & \\multicolumn{1}{c}{SP} & \\multicolumn{1}{c}{FNER} & \\multicolumn{1}{c}{Average}\\\\\n \\midrule\n \\multicolumn{10}{c}{Close-Source LLMs} \\\\\n ChatGPT-o3 & \\cellcolor{lightblue}86.23 & 61.30 & \\cellcolor{lightblue}75.36 & \\cellcolor{golden}89.15 & \\cellcolor{lightblue}91.25 & \\cellcolor{lightgreen}98.55 & 44.48 & 53.27 & 65.13 & \\cellcolor{golden}73.86 \\\\\n ChatGPT-o4-mini & \\cellcolor{lightgreen}85.62 & 60.10 & 71.23 & 74.40 & 90.27 & 95.73 & \\cellcolor{golden}47.67 & 52.32 & 64.24 & 71.29 \\\\\n GPT-4o & 79.42 & 56.51 & \\cellcolor{golden}76.20 & 82.37 & 87.79 & \\cellcolor{golden}98.84 & 45.33 & 54.33 & 65.37 & \\cellcolor{lightgreen}71.80 \\\\\n Gemini-2.0-Flash & \\cellcolor{golden}86.94 & 62.67 & 73.97 & 82.55 & 90.29 & \\cellcolor{lightblue}98.62 & 22.17 & \\cellcolor{lightgreen}56.14 & 54.43 & 69.75 \\\\\n Claude-3.5-Sonnet & 84.68 & 63.18 & 42.81 & \\cellcolor{lightblue}88.05 & 87.35 & 96.85 & 16.67 & 47.60 & 63.09 & 65.59 \\\\\n \\midrule\n \\multicolumn{10}{c}{Open-Weight LLMs} \\\\\n Qwen2.5-7B-Instruct & 73.87 & 32.88 & 39.38 & 79.03 & 83.34 & 78.93 & 37.50 & 51.91 & 30.31 & 56.35 \\\\\n Qwen2.5-72B-Instruct & 69.27 & 54.28 & 70.72 & 85.29 & 87.79 & 97.43 & 35.33 & 55.13 & 54.02 & 67.70 \\\\\n Qwen2.5-VL-3B & 53.85 & 15.92 & 17.29 & 8.95 & 81.60 & 59.44 & 39.50 & 52.49 & 21.57 & 38.96 \\\\\n Qwen2.5-VL-7B & 73.87 & 32.71 & 40.24 & 77.85 & 83.94 & 77.41 & 38.83 & 51.91 & 33.40 & 56.68 \\\\\n Qwen2.5-VL-14B & 37.12 & 41.44 & 53.08 & 82.07 & 84.23 & 7.97 & 37.33 & 54.93 & 47.47 & 49.52 \\\\\n Qwen2.5-VL-32B & 76.79 & 50.00 & 62.16 & 83.57 & 85.30 & 95.95 & 40.50 & 54.93 & 68.36 & 68.62 \\\\\n Qwen2.5-VL-72B & 69.55 & 54.11 & 69.86 & 85.18 & 87.37 & 97.34 & 35.00 & 54.94 & 54.41 & 67.53 \\\\\n Qwen3-1.7B & 77.40 & 35.80 & 33.40 & 75.82 & 73.81 & 78.62 & 22.40 & 48.53 & 11.23 & 50.78 \\\\\n Qwen3-4B & 83.60 & 47.40 & 50.00 & 78.19 & 82.24 & 80.16 & 42.20 & 50.51 & 25.19 & 59.94 \\\\\n Qwen3-14B & 84.20 & 58.20 & 65.80 & 82.19 & 84.12 & 92.91 & 33.00 & 52.31 & 50.70 & 67.05 \\\\\n Qwen3-32B & 83.80 & 59.60 & 64.60 & 85.12 & 85.43 & 95.37 & 39.00 & 52.26 & 49.19 & 68.26 \\\\\n QwQ-32B & 84.02 & 52.91 & 64.90 & 84.81 & 89.60 & 94.20 & 34.50 & \\cellcolor{lightblue}56.68 & 30.27 & 65.77 \\\\\n Xuanyuan3-70B & 12.14 & 19.69 & 15.41 & 80.89 & 86.51 & 83.90 & 29.83 & 52.62 & 37.33 & 46.48 \\\\\n Llama-3.1-8B-Instruct & 73.12 & 22.09 & 2.91 & 77.42 & 76.18 & 69.09 & 29.00 & 54.21 & 36.56 & 48.95 \\\\\n Llama-3.1-70B-Instruct & 16.26 & 34.25 & 56.34 & 80.64 & 79.97 & 86.90 & 33.33 & \\cellcolor{golden}62.16 & 45.95 & 55.09 \\\\\n Llama 4 Scout & 73.60 & 45.80 & 44.20 & 85.02 & 85.21 & 92.32 & 25.60 & 55.76 & 43.00 & 61.17 \\\\\n DeepSeek-V3 (671B) & 74.34 & 61.82 & 72.60 & 86.54 & \\cellcolor{lightgreen}91.07 & 98.11 & 32.67 & 55.73 & \\cellcolor{lightblue}71.24 & 71.57 \\\\\n DeepSeek-R1 (671B) & 80.36 & \\cellcolor{lightgreen}64.04 & \\cellcolor{lightgreen}75.00 & 81.96 & \\cellcolor{golden}91.44 & 98.41 & 39.67 & 55.13 & \\cellcolor{golden}71.46 & \\cellcolor{lightblue}73.05 \\\\\n DeepSeek\\_R1\\_14B\\_Instruct & 71.33 & 44.35 & 50.45 & 81.96 & 85.52 & 92.81 & 39.50 & 50.20 & 52.76 & 59.49 \\\\\n DeepSeek\\_R1\\_32B\\_Instruct & 73.68 & 51.20 & 50.86 & 83.27 & 87.54 & 97.81 & 41.50 & 53.92 & 56.80 & 66.29 \\\\\n \\midrule\n \\multicolumn{11}{c}{Our LLMs} \\\\\n \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT~\\tnote{2} & \\cellcolor{Background1}80.63 & \\cellcolor{Background1}51.67 & \\cellcolor{Background1}52.61 & \\cellcolor{Background1}83.53 & \\cellcolor{Background1}89.05 & \\cellcolor{Background1}96.72 & \\cellcolor{Background1}36.68 & \\cellcolor{Background1}50.43 & \\cellcolor{Background1}50.85 & \\cellcolor{Background1}65.36 \\\\\n $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+9.25} & \\textcolor{GREEN}{+7.28} & \\textcolor{GREEN}{+2.19} & \\textcolor{GREEN}{+1.53} & \\textcolor{GREEN}{+3.42} & \\textcolor{GREEN}{+3.85} & \\textcolor{RED}{-2.93} & \\textcolor{GREEN}{+0.24} & \\textcolor{RED}{-1.92} & \\textcolor{GREEN}{+5.83} \\\\\n \\cellcolor{Background1}DeepSeek\\_R1\\_14B\\_SFT\\_GRPO~\\tnote{2} & \\cellcolor{Background1}81.46 & \\cellcolor{Background1}52.41 & \\cellcolor{Background1}53.47 & \\cellcolor{Background1}83.57 & \\cellcolor{Background1}89.02 & \\cellcolor{Background1}95.58 & \\cellcolor{Background1}36.83 & \\cellcolor{Background1}54.06 & \\cellcolor{Background1}51.24 & \\cellcolor{Background1}66.92 \\\\\n $\\quad$ 14B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+10.03} & \\textcolor{GREEN}{+8.09} & \\textcolor{GREEN}{+2.91} & \\textcolor{GREEN}{+1.64} & \\textcolor{GREEN}{+3.45} & \\textcolor{GREEN}{+2.63} & \\textcolor{RED}{-2.74} & \\textcolor{GREEN}{+3.82} & \\textcolor{RED}{-1.53} & \\textcolor{GREEN}{+7.46} \\\\\n $\\quad$ 14B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.82} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+0.81} & \\textcolor{GREEN}{+0.06} & 0.00 & \\textcolor{RED}{-1.23} & \\textcolor{GREEN}{+0.25} & \\textcolor{GREEN}{+3.63} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.53} \\\\\n \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT & \\cellcolor{Background1}80.45 & \\cellcolor{lightblue}66.42 & \\cellcolor{Background1}63.28 & \\cellcolor{lightgreen}86.88 & \\cellcolor{Background1}88.43 & \\cellcolor{Background1}93.76 & \\cellcolor{lightblue}46.05 & \\cellcolor{Background1}55.27 & \\cellcolor{lightgreen}68.41 & \\cellcolor{Background1}70.08 \\\\\n $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT})$ & \\textcolor{GREEN}{+6.75} & \\textcolor{GREEN}{+15.23} & \\textcolor{GREEN}{+12.37} & \\textcolor{GREEN}{+3.64} & \\textcolor{GREEN}{+0.83} & \\textcolor{RED}{-4.14} & \\textcolor{GREEN}{+4.52} & \\textcolor{GREEN}{+1.25} & \\textcolor{GREEN}{+11.63} & \\textcolor{GREEN}{+3.75} \\\\\n \\cellcolor{Background1}DeepSeek\\_R1\\_32B\\_SFT\\_GRPO & \\cellcolor{Background1}80.67 & \\cellcolor{golden}66.83 & \\cellcolor{Background1}64.45 & \\cellcolor{Background1}86.79 & \\cellcolor{Background1}88.52 & \\cellcolor{Background1}91.26 & \\cellcolor{lightgreen}45.68 & \\cellcolor{Background1}54.83 & \\cellcolor{Background1}67.75 & \\cellcolor{Background1}70.44 \\\\\n $\\quad$ 32B $\\Delta_{\\text{Instruct}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+6.95} & \\textcolor{GREEN}{+15.62} & \\textcolor{GREEN}{+13.57} & \\textcolor{GREEN}{+3.55} & \\textcolor{GREEN}{+0.93} & \\textcolor{RED}{-6.64} & \\textcolor{GREEN}{+4.13} & \\textcolor{GREEN}{+0.85} & \\textcolor{GREEN}{+10.93} & \\textcolor{GREEN}{+4.12} \\\\\n $\\quad$ 32B $\\Delta_{\\text{SFT}}(\\text{SFT\\_GRPO})$ & \\textcolor{GREEN}{+0.23} & \\textcolor{GREEN}{+0.42} & \\textcolor{GREEN}{+1.23} & \\textcolor{RED}{-0.06} & \\textcolor{GREEN}{+0.13} & \\textcolor{RED}{-2.53} & \\textcolor{RED}{-0.42} & \\textcolor{RED}{-0.43} & \\textcolor{RED}{-0.72} & \\textcolor{GREEN}{+0.33} \\\\\n \\bottomrule\n \\end{tabular}%\n }\n \\label{table:bizfinbench_detailed_results}%\n\\end{table*}%\n\n\n\\section{Case Study} \\label{sec:appendix:case_study}\n\n\n\\subsection{Case study on zero-shot CoT prompting} \\label{sec:appendix:case_study:cot_prompting}\n\nWe present a case study comparing the responses of GPT4o, DeepSeek-R1 and Qwen3 under two different prompting strategies: zero-shot prompting without Chain-of-Thought (CoT) and zero-shot prompting with CoT. The results are illustrated in Figures~\\ref{fig:appendix:case_study:response_no_cot} and~\\ref{fig:appendix:case_study:response_with_cot}.\n\nWe observe that without CoT prompting (Figure~\\ref{fig:appendix:case_study:response_no_cot}), the models struggle to provide accurate and relevant answers. Their responses often lack depth and fail to address the nuances of the questions. In contrast, with CoT prompting (Figure~\\ref{fig:appendix:case_study:response_with_cot}), the models demonstrate improved reasoning and accuracy. The step-by-step thought process enabled by CoT helps the models to break down complex questions and arrive at more precise answers.\n\n\\begin{figure*}[htbp]\n\t\\centering\n\t\\includegraphics[width=1\\textwidth]{response_no_CoT.pdf}\n\t\\caption{Zero-shot responses. The model struggles to provide accurate and relevant answers without the step-by-step reasoning process enabled by CoT prompting.}\n\t\\label{fig:appendix:case_study:response_no_cot}\n\\end{figure*}\n\n\n\\begin{figure*}[htbp]\n\t\\centering\n\t\\includegraphics[width=1\\textwidth]{response_with_CoT.pdf}\n\t\\caption{CoT Prompting responses. The model demonstrates improved reasoning and accuracy when guided through a step-by-step thought process.}\n\t\\label{fig:appendix:case_study:response_with_cot}\n\\end{figure*}\n\n\\subsection{Case study on cold-started responses} \\label{sec:appendix:case_study:response}\n\nWe present a case study comparing the original response and the cold-started response generated by DeepSeek\\_R1\\_14B\\_Instruct and DeepSeek\\_R1\\_14B\\_SFT. The results are illustrated in Figure~\\ref{fig:appendix:case_study:response_cold_started}.\nBefore applying cold-starting techniques, the original response tends to be verbose and includes unnecessary elaboration. After cold-starting, the response becomes more concise and is much longer, which indicates the cold-started model is leveraging its reasoning capabilities to provide a more comprehensive answer.\nThis demonstrates the effectiveness of cold-starting in enhancing the clarity and relevance of model-generated responses.\n\n\\begin{figure*}[htbp]\n\t\\centering\n\t\\includegraphics[width=1\\textwidth]{response_cold_started.pdf}\n\t\\caption{Case study on cold-started responses. Left is the original response, and right is the cold-started response. The cold-started response is more concise and to the point, avoiding unnecessary elaboration.}\n\t\\label{fig:appendix:case_study:response_cold_started}\n\\end{figure*}\n\n\\end{document}\n"},"question":{"kind":"string","value":"Among the proposed LLMs, keep only model families whose Average increases monotonically from Instruct --> SFT --> SFT GRPO, which family has the larger gain from Instruct to SFT GRPO? For that family's SFT GRPO model, on how many metrics does it outperform GPT-4o?"},"answer":{"kind":"string","value":"14B, 3"},"plan":{"kind":"string","value":"SELECT all model families in Our LLMs\nLOOP for each family\n IF Instruct Average < SFT Average AND SFT Average < SFT GRPO Average\n COMPUTE gain = SFT GRPO Average − Instruct Average\nCOMPUTE target_family = argmax family over gain\n\n\nCOMPUTE outperform_count = 0\nSELECT all task metrics excluding average\nLOOP for each metric\n IF target_family SFT GRPO metric score > GPT-4o metric score\n COMPUTE increase outperform_count\n\n\nRETURN target_family, outperform_count\n"}}},{"rowIdx":363,"cells":{"paper":{"kind":"string","value":"2406.02069"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\n","H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\n","SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\n","Ours & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n","\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\n","SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\n","H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\n","Ours & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\n","SLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\n","H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\n","Ours & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\n","SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\n","H2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\n","Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\n","SLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\n","H2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\n","Ours & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \n","SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \n","H2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \n","Ours & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\n","\\label{table:longbench}\n","\\vspace{-3mm}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 19.86 & 9.09 & 27.89 & \\\\textbf{37.34} & 28.35 & \\\\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\\\\\\n\",\n \"H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\\\textbf{37.76} & \\\\textbf{5.63} & 69.33 & \\\\textbf{53.44} & \\\\textbf{50.15} & 33.89 \\\\\\\\\\n\",\n \"SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\\\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\\\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.13} & \\\\textbf{14.18} & \\\\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\\\textbf{18.33} & \\\\textbf{21.65} & \\\\textbf{19.23} & \\\\textbf{58.00} & \\\\textbf{88.31} & 37.07 & 5.23 & \\\\textbf{69.50} & 52.61 & 45.74 & \\\\textbf{34.76} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & \\\\textbf{25.86} & 29.55 & \\\\textbf{41.10} & \\\\textbf{44.99} & \\\\textbf{35.80} & 21.81 & 25.98 & \\\\textbf{23.40} & 26.46 & \\\\textbf{73.50} & \\\\textbf{90.56} & 41.66 & 5.17 & \\\\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\\\\\\n\",\n \"SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\\\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\\\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\\\\\\n\",\n \"H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\\\textbf{90.56} & 41.84 & 4.91 & \\\\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\\\\\\n\",\n \"Ours & 25.40 & \\\\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\\\textbf{21.98} & \\\\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\\\textbf{90.56} & \\\\textbf{42.14} & 5.22 & \\\\textbf{69.25} & \\\\textbf{58.76} & \\\\textbf{51.18} & \\\\textbf{41.49} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 16.94&17.17&39.51&\\\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\\\\\\n\",\n \"SLM & 15.01&13.84&28.74&30.97&\\\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\\\\\\n\",\n \"H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\\\textbf{21.52}&\\\\textbf{21.98}&37.00&81.02&\\\\textbf{38.62}&\\\\textbf{5.00}&\\\\textbf{66.03}&43.54&\\\\textbf{40.46}&30.88\\\\\\\\\\n\",\n \"Ours & \\\\textbf{20.91}&\\\\textbf{20.21}&\\\\textbf{39.94}&33.57&22.87&\\\\textbf{15.70}&\\\\textbf{17.31}&21.23&21.41&\\\\textbf{54.00}&81.98&36.96&3.58&60.83&\\\\textbf{44.52}&37.99&\\\\textbf{32.19}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV &\\\\textbf{25.89} & \\\\textbf{32.93} & 48.56 & \\\\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\\\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\\\textbf{5.50} & \\\\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\\\\\\n\",\n \"SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\\\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\\\\\\n\",\n \"H2O & 25.76 & 31.10 & \\\\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\\\textbf{86.35} & 42.48 & \\\\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\\\\\\n\",\n \"Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\\\textbf{27.50} & \\\\textbf{19.36} & 26.60 & 23.97 & \\\\textbf{26.73} & \\\\textbf{71.00} & 86.25 & \\\\textbf{42.94} & 4.50 & 87.90 & \\\\textbf{53.12} & \\\\textbf{47.21} & \\\\textbf{41.63} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\\\textbf{91.06}&40.26&12.00&\\\\textbf{72.50}&43.33&57.62&39.45\\\\\\\\\\n\",\n \"SLM & 22.07&23.53&27.31&43.21&\\\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\\\textbf{72.50}&40.23&50.20&35.47\\\\\\\\\\n\",\n \"H2O & 25.45&34.64&33.23&\\\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\\\textbf{41.58}&12.00&71.50&43.83&\\\\textbf{58.16}&39.94\\\\\\\\\\n\",\n \"Ours & \\\\textbf{25.47}&\\\\textbf{36.71}&\\\\textbf{42.29}&47.08&46.21&\\\\textbf{28.30}&\\\\textbf{20.60}&\\\\textbf{21.62}&\\\\textbf{21.62}&\\\\textbf{64.50}&89.61&41.28&\\\\textbf{12.50}&\\\\textbf{72.50}&\\\\textbf{45.34}&56.50&\\\\textbf{42.01}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 26.73&45.18&47.91&\\\\textbf{52.00}&\\\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\\\textbf{72.50}&\\\\textbf{41.52}&\\\\textbf{69.27}&46.36\\\\\\\\ \\n\",\n \"SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\\\\\ \\n\",\n \"H2O & \\\\textbf{27.67}&\\\\textbf{46.51}&\\\\textbf{49.54}&51.49&53.85&29.97&28.57&\\\\textbf{22.79}&\\\\textbf{27.53}&59.00&\\\\textbf{92.63}&\\\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\\\\\ \\n\",\n \"Ours & 27.22&46.19&48.72&51.62&54.56&\\\\textbf{31.11}&\\\\textbf{29.76}&22.50&27.27&\\\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\\\textbf{46.55}\\\\\\\\ \\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\\n\",\n \"\\\\label{table:longbench}\\n\",\n \"\\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/dynamickv4.pdf}\n"," \\caption{\n"," Illustration of~\\method compared with existing KV cache compression methods.\n"," (a) Full KV has all tokens stored in the KV cache in each layer; cache size increases as the input length increases.\n"," (b) StreamingLLM~\\citep{xiao2023efficient} only keeps few initial tokens with a fixed cache size in each layer.\n"," (c) SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} keep a fixed cache size across Transformer layers, and their selection is based on the attention score.\n"," (d)~\\method maintains pyramid-like cache sizes, allocating more cache budget to lower layers and less to higher layers. This approach to KV cache selection better aligns with the increasing attention sparsity observed in multi-layer Transformers (\\Scref{section:observation}).\n"," }\n"," \\label{figure:comparison}\n","\\end{figure}\n"],["\\begin{figure}[ht]\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/obs.pdf}\n"," \\caption{\n"," Attention patterns of retrieval-augmented generation across layers in LlaMa~\\citep{touvron2023llama, touvron2023llama2} reveal that in the lower layers, the model exhibits a broad-spectrum mode of attention, distributing attention scores uniformly across all content. In the middle layers, attention becomes more localized within each document, indicating refined information aggregation (dotted red triangular shapes in layers 6 and 10). This culminates in the upper layers, where ``massive attention'' focuses on a few key tokens (concentrated attention bars after layer 18), efficiently extracting essential information for answers.\n"," }\n"," \\label{figure:rag_flow}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/method2.pdf}\n"," \\caption{\n"," Illustration of~\\method. At the lower level of the transformer, the \\method selects more keys and values based on the exhibited average attention pattern. Fewer keys and values at the higher level are selected based on the massive activation pattern, where we observe that attention scores are concentrated over local regions.}\n"," \\label{figure:method}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\begin{minipage}{0.33\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/result1.pdf}\n"," \\end{minipage}%\n"," \\hfill\n"," \\begin{minipage}{0.33\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/result2.pdf}\n"," \\end{minipage}%\n"," \\hfill\n"," \\begin{minipage}{0.33\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/result3.pdf}\n"," \\end{minipage}\n"," \\vspace{-3mm}\n"," \\caption{The evaluation results from LongBench~\\citep{bai2023longbench} across 64, 96, 128 and 256 cache sizes at LLaMa-3-8B-Instruct (Left), Mistral-7B-Instruct (Middle) and LLaMa-3-70B-Instruct (Right).\n"," The evaluation metrics are the average score of LongBench across datasets.\n"," ~\\method outperforms H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv} and StreamingLLM~\\citep{xiao2023efficient}, especially in small KV cache sizes.}\n"," \\label{figure:results}\n","\\end{figure}\n"],["\\begin{table*}[t]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\n","H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\n","SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\n","Ours & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n","\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\n","SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\n","H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\n","Ours & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\n","SLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\n","H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\n","Ours & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\n","SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\n","H2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\n","Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\n","SLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\n","H2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\n","Ours & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \n","SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \n","H2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \n","Ours & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\n","\\label{table:longbench}\n","\\vspace{-3mm}\n","\\end{table*}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_main.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} and \\textbf{LlaMa-3-70B-Instruct} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length.\n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," \\textbf{PyramidKV with 128 KV cache size achieves the same 100.0 Acc. performance compared with FullKV with 8k context size for LLaMA-3-70B-Instruct.}\n"," }\n"," \\label{figure:needle_llama}\n","\\end{figure}\n"],["\\begin{table*}[h]\n","\\small\n","\\centering\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{ccc|cccccc}\n","\\toprule\n"," cache size & Memory & Compression Ratio & QMSum & TREC & TriviaQA & PCount & PRe & Lcc \\\\\n","\n","\\midrule\n","64 & 53M & 0.8\\% & 21.65 & 58.00 & 88.31 & 5.23 & 69.50 & 52.61 \\\\ \n","128 & 107M & 1.6\\% & 22.48 & 66.50 & 89.35 & 5.92 & 69.00 & 56.49 \\\\ \n","256 & 214M & 3.1\\% & 22.69 & 71.00 & 90.48 & 5.83 & 69.25 & 56.94 \\\\\n","512 & 428M & 6.3\\% & 22.80 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\n","1024 & 856M & 12.5\\% & 22.55 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\n","2048 & 1712M & 25.0\\% & 22.55 & 72.00 & 90.56 & 5.58 & 69.25 & 56.79 \\\\\n","Full & 6848M & 100.0\\% & 23.30 & 73.00 & 90.56 & 5.22 & 69.25 & 58.76 \\\\\n","\n","\n","\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Memory reduction effect and benchmark result by using \\method. We conducted a comparison of memory consumption between the Llama-3-8B-Instruct model utilizing the Full KV cache and the Llama-3-8B-Instruct model compressed with the \\method.\n","}\n","\n","\n","\n","\\label{tab:memory_reduction}\n","\\vspace{-3mm}\n","\\end{table*}\n"],["\\begin{table}[htbp]\n","\\centering \n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{llrccc}\n","\\toprule\n","Dataset & Source & Avg len & Metric & Language & \\#data \\\\\n","\\midrule\n","\\emph{Single-Document QA} \\\\\n","NarrativeQA & Literature, Film & 18,409 & F1 & English & 200 \\\\\n","Qasper & Science & 3,619 & F1 & English & 200 \\\\\n","MultiFieldQA-en & Multi-field & 4,559 & F1 & English & 150 \\\\\n","\\midrule\n","\\emph{Multi-Document QA} \\\\\n","HotpotQA & Wikipedia & 9,151 & F1 & English & 200 \\\\\n","2WikiMultihopQA & Wikipedia & 4,887 & F1 & English & 200 \\\\\n","MuSiQue & Wikipedia & 11,214 & F1 & English & 200 \\\\\n","\\midrule\n","\\emph{Summarization} \\\\\n","GovReport & Government report & 8,734 & Rouge-L & English & 200 \\\\\n","QMSum & Meeting & 10,614 & Rouge-L & English & 200 \\\\\n","MultiNews & News & 2,113 & Rouge-L & English & 200 \\\\\n","\\midrule\n","\\emph{Few-shot Learning} \\\\\n","TREC & Web question & 5,177 & Accuracy (CLS) & English & 200 \\\\\n","TriviaQA & Wikipedia, Web & 8,209 & F1 & English & 200 \\\\\n","SAMSum & Dialogue & 6,258 & Rouge-L & English & 200 \\\\\n","\\midrule\n","\\emph{Synthetic Task} \\\\\n","PassageCount & Wikipedia & 11,141 & Accuracy (EM) & English & 200 \\\\\n","PassageRetrieval-en & Wikipedia & 9,289 & Accuracy (EM) & English & 200 \\\\\n","\\midrule\n","\\emph{Code Completion} \\\\\n","LCC & Github & 1,235 & Edit Sim & Python/C\\#/Java & 500 \\\\\n","RepoBench-P & Github repository & 4,206 & Edit Sim & Python/Java & 500 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{An overview of the dataset statistics in LongBench~\\citep{bai2023longbench}. `Source' denotes the origin of the context. `Accuracy (CLS)' refers to classification accuracy, while `Accuracy (EM)' refers to exact match accuracy.}\n","\\label{table:stat}\n","\\end{table}\n"],["\\begin{table*}[htbp]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{4}{*}{$\\alpha$} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & Avg. \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\midrule\n","\n","8 & 21.40 & 16.92 & 31.62 & 38.45 & 28.72 & 18.59 & 19.96 & 22.49 & 20.96 & 66.50 & 89.35 & 38.43 & 5.92 & 69.00 & 57.86 & 51.80 & 37.37 \\\\ \n","16 & 23.37 & 16.21 & 33.93 & 38.24 & 27.28 & 20.57 & 19.71 & 21.93 & 20.86 & 60.00 & 88.75 & 38.34 & 5.48 & 69.12 & 57.84 & 53.42 & 37.19 \\\\ \n","24 & 22.85 & 14.51 & 32.26 & 38.38 & 28.36 & 20.33 & 19.55 & 21.72 & 20.72 & 54.50 & 88.71 & 38.46 & 5.48 & 69.50 & 56.83 & 53.65 & 36.61 \\\\ \n","32 & 23.01 & 14.54 & 31.68 & 38.86 & 29.90 & 19.16 & 19.20 & 21.83 & 20.52 & 49.50 & 87.01 & 38.01 & 5.75 & 69.50 & 57.02 & 54.54 & 36.25 \\\\ \n","40 & 21.70 & 13.06 & 30.14 & 36.78 & 27.34 & 18.88 & 18.72 & 21.37 & 19.79 & 44.00 & 87.74 & 38.43 & 6.08 & 69.25 & 56.11 & 53.89 & 35.21 \\\\ \n","48 & 21.51 & 12.30 & 29.77 & 39.04 & 26.76 & 17.97 & 18.65 & 21.20 & 20.29 & 44.50 & 87.73 & 38.44 & 5.51 & 69.25 & 56.73 & 53.88 & 35.22 \\\\ \n","\n","\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Ablation on $\\alpha$.}\n","\\label{table:ablation_step_a}\n","\\end{table*}\n"],["\\begin{table*}[htbp]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{4}{*}{$\\beta$} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & Avg. \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\midrule\n","20 & 21.40 & 16.92 & 33.79 & 39.73 & 28.72 & 18.59 & 19.86 & 22.48 & 20.95 & 66.50 & 89.35 & 38.39 & 5.92 & 69.00 & 56.49 & 47.95 & 37.25 \\\\\n","18 & 21.71 & 16.24 & 33.59 & 39.89 & 27.94 & 18.38 & 19.76 & 22.32 & 21.20 & 66.50 & 88.98 & 38.93 & 5.46 & 69.50 & 56.47 & 49.23 & 37.25 \\\\\n","16 & 21.74 & 14.86 & 33.64 & 39.18 & 28.17 & 18.77 & 19.57 & 22.25 & 21.48 & 66.50 & 89.69 & 38.87 & 5.82 & 69.50 & 57.02 & 50.11 & 37.32 \\\\\n","14 & 22.53 & 16.31 & 33.50 & 40.50 & 28.15 & 19.26 & 19.66 & 22.39 & 21.38 & 65.50 & 90.02 & 38.56 & 5.75 & 69.50 & 57.51 & 49.71 & 37.51 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Ablation on $\\beta$.}\n","\\label{table:ablation_step_b}\n","\\end{table*}\n"],["\\begin{table}[h!]\n","\\centering\n","\\small\n","\\begin{tabular}{ccccccccc}\n","\\toprule\n","\\textbf{Prompt Length} & \\textbf{Generation Length} & \\textbf{Inference Time} & \\textbf{Allocation Time} & \\textbf{Selection Time} \\\\\n","\\midrule\n","512&512 & 18.26 & 0.0000003 & 0.0194 \\\\\n","512&1024 & 34.69 & 0.000002 & 0.0133 \\\\\n","512&2048 & 70.69 & 0.000003 & 0.013 \\\\\n","512&4096 & 138.62 & 0.000005 & 0.013 \\\\\n","1024&512 & 17.32 & 0.000002 & 0.0131 \\\\\n","1024&1024 & 34.67 & 0.000002 & 0.01288 \\\\\n","1024&2048 & 70.21 & 0.000005 & 0.01296 \\\\\n","1024&4096 & 138.61 & 0.000003 & 0.01297 \\\\\n","2048&512 & 17.48 & 0.000004 & 0.0128 \\\\\n","2048&1024 & 34.78 & 0.000006 & 0.0129 \\\\\n","2048&2048 & 69.50 & 0.000003 & 0.01297 \\\\\n","2048&4096 & 138.59 & 0.000003 & 0.013 \\\\\n","4096&512 & 17.58 & 0.000002 & 0.013 \\\\\n","4096&1024 & 34.93 & 0.000004 & 0.0129 \\\\\n","4096&2048 & 69.65 & 0.000002 & 0.013 \\\\\n","4096&4096 & 138.87 & 0.000002 & 0.013 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\caption{Extra inference overhead of~\\method }\n","\\label{table:inference_overhead}\n","\\end{table}\n"],["\\begin{table}[h!]\n","\\centering\n","\\small\n","\\begin{tabular}{ccccccc}\n","\\toprule\n","\\textbf{Prompt Length} & \\textbf{Generation Length} & \\textbf{H2O} & \\textbf{SnapKV} & \\textbf{StreamingLLM} & \\textbf{PyramidKV} \\\\ \n","\\midrule\n","512&512 & 18.47 & 18.25 & 18.96 & 18.26 \\\\\n","512&1024 & 35.10 & 34.76 & 36.20 & 34.69 \\\\\n","512&2048 & 70.21 & 69.60 & 72.35 & 70.69 \\\\ \n","512&4096 & 140.80 & 139.42 & 146.37 & 138.62 \\\\\n","1024&512 & 17.63 & 17.34 & 18.12 & 17.32 \\\\\n","1024&1024 & 35.16 & 34.61 & 36.17 & 34.67 \\\\\n","1024&2048 & 71.02 & 69.17 & 72.37 & 70.21 \\\\\n","1024&4096 & 140.51 & 138.83 & 146.09 & 138.61 \\\\ \n","2048&512 & 17.64 & 19.54 & 18.22 & 17.48 \\\\ \n","2048&1024 & 35.09 & 34.76 & 36.29 & 34.78 \\\\ \n","2048&2048 & 70.84 & 69.56 & 72.46 & 69.50 \\\\ \n","2048&4096 & 140.16 & 139.55 & 145.22 & 138.59 \\\\ \n","4096&512 & 17.75 & 17.67 & 18.40 & 17.58 \\\\ \n","4096&1024 & 35.20 & 35.08 & 36.46 & 34.93 \\\\ \n","4096&2048 & 70.02 & 69.26 & 72.58 & 69.65 \\\\ \n","4096&4096 & 139.87 & 138.57 & 144.98 & 138.87 \\\\ \n","\\bottomrule\n","\\end{tabular}\n","\\caption{Performance comparison across different configurations and methods.}\n","\\label{table:inference_speed_comparison}\n","\\end{table}\n"],["\\begin{table*}\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 04.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\n","H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\n","SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\n","Ours & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 96} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 20.45 & 10.34 & 31.84 & 37.85 & 28.65 & \\textbf{18.52} & 17.90 & 21.26 & 19.07 & 41.50 & 86.95 & 37.82 & 5.08 & 69.12 & 54.69 & \\textbf{51.31} & 34.51 \\\\\n","H2O & 21.55 & 11.21 & 28.73 & 37.66 & 30.12 & 18.47 & 19.57 & 21.57 & 20.44 & 38.50 & \\textbf{87.63} & \\textbf{38.47} & 5.60 & 69.00 & 54.51 & 50.16 & 34.57 \\\\\n","SLM & 18.67 & 8.43 & 24.98 & 38.35 & \\textbf{30.59} & 16.37 & 17.33 & 19.84 & 18.41 & 41.00 & 73.92 & 29.38 & 5.80 & \\textbf{69.50} & 47.15 & 45.61 & 31.58 \\\\\n","Ours & \\textbf{21.67} & \\textbf{15.10} & \\textbf{33.50} & \\textbf{39.73} & 26.48 & 17.47 & \\textbf{19.64} & \\textbf{22.28} & \\textbf{20.49} & \\textbf{61.50} & 87.38 & 38.18 & \\textbf{6.00} & 69.25 & \\textbf{55.30} & 46.78 & \\textbf{36.29} \\\\\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 128} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\textbf{51.82} & 35.50 \\\\\n","H2O & \\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\textbf{32.71} & 18.45 & \\textbf{20.32} & 22.02 & \\textbf{21.10} & 38.50 & 87.75 & \\textbf{39.14} & 5.83 & \\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\n","SLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\n","Ours & 21.40 & \\textbf{16.92} & \\textbf{33.79} & \\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\textbf{22.48} & 20.95 & \\textbf{66.50} & \\textbf{89.35} & 38.39 & \\textbf{5.92} & 69.00 & \\textbf{56.49} & 47.95 & \\textbf{37.25} \\\\\n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\n","SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\n","H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\n","Ours & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n","}\n","\\label{table:longbench_appendix_llama3_8b}\n","\\end{table*}\n"],["\\begin{table*}\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\n","SLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\n","H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\n","Ours & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 96} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & 19.92&18.80&\\textbf{43.29}&\\textbf{39.66}&23.08&\\textbf{15.94}&16.65&21.26&21.47&43.50&83.48&39.74&4.00&60.10&45.53&41.12&32.47\\\\\n","SLM & 15.15&15.48&31.44&30.03&\\textbf{23.93}&12.73&16.76&19.15&19.19&41.50&75.31&28.71&5.00&28.48&38.92&36.05&26.37\\\\\n","H2O & 19.44&20.81&38.78&32.39&21.51&14.43&17.68&\\textbf{22.40}&\\textbf{21.99}&38.00&82.51&\\textbf{39.94}&\\textbf{6.06}&\\textbf{77.48}&45.18&\\textbf{42.43}&32.67\\\\\n","Ours & \\textbf{20.35}&\\textbf{21.87}&41.15&34.94&21.85&15.81&\\textbf{18.21}&21.66&21.43&\\textbf{65.00}&\\textbf{83.60}&39.60&4.50&67.80&\\textbf{45.83}&39.38&\\textbf{34.08}\\\\\n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 128} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","\n","SKV & 19.16 & 21.46 & 43.52 & \\textbf{38.60} & \\textbf{23.35} & \\textbf{16.09} & 17.66 & 21.84 & 21.47 & 47.50 & \\textbf{84.15} & 40.24 & 5.00 & 69.31 & \\textbf{46.98} & \\textbf{42.97} & 34.96 \\\\\n","SLM & 16.57 & 14.68 & 32.40 & 30.19 & 22.64 & 12.34 & 18.08 & 18.96 & 19.19 & 43.50 & 74.22 & 29.02 & 4.50 & 29.48 & 39.23 & 36.16 & 27.57 \\\\\n","H2O & 21.20 & 21.90 & 41.55 & 33.56 & 21.28 & 12.93 & \\textbf{18.59} & \\textbf{22.61} & \\textbf{21.99} & 39.00 & 82.37 & \\textbf{40.44} & \\textbf{6.00} & \\textbf{83.19} & 46.41 & 42.66 & 34.73 \\\\\n","Ours & \\textbf{21.75} & \\textbf{22.03} & \\textbf{44.32} & 34.06 & 22.79 & 15.77 & 18.58 & 21.89 & 21.43 & \\textbf{66.00} & 83.46 & 39.75 & 4.50 & 66.90 & 46.96 & 41.28 & \\textbf{35.72} \\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","\n","SKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\n","SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\n","H2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\n","Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for Mistral-7B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n","}\n","\\label{table:longbench_appendix_mistral}\n","\\end{table*}\n"],["\\begin{table*}[!t]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 27.75& \t46.48& \t49.45\t& 52.04& \t54.9& \t30.42& \t32.37& \t22.27\t& 27.58\t& 73.5& \t92.46& \t45.73\t& 12.5\t& 72.5\t& 40.96\t& 63.91\t& 46.55 \\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\n","SLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\n","H2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\n","Ours & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 96} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","\n","SKV & \\textbf{25.78}&35.71&42.13&\\textbf{50.38}&\\textbf{51.46}&26.68&19.61&21.40&21.98&48.50&\\textbf{92.11}&41.21&12.00&72.00&44.85&59.05&41.55\\\\\n","SLM & 23.31&29.46&29.21&41.85&45.92&23.00&18.42&19.71&18.57&45.00&76.79&33.54&12.00&\\textbf{72.50}&40.49&50.73&36.28\\\\\n","H2O & 25.30&35.13&35.54&47.39&50.61&26.20&20.87&\\textbf{21.80}&\\textbf{22.93}&41.00&90.47&\\textbf{43.42}&12.00&72.00&43.84&\\textbf{59.86}&40.52\\\\\n","Ours & 25.47&\\textbf{37.61}&\\textbf{44.00}&47.33&45.36&\\textbf{27.91}&\\textbf{21.05}&21.60&22.31&\\textbf{66.00}&91.45&42.36&12.00&\\textbf{72.50}&\\textbf{45.12}&56.88&\\textbf{42.43}\\\\\n","\n","\n","\n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 128} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & \\textbf{26.22}&37.49&\\textbf{45.70}&\\textbf{50.86}&\\textbf{52.82}&28.50&20.38&21.72&22.56&53.00&91.61&41.43&12.00&71.50&45.06&\\textbf{60.50}&42.58 \\\\\n","SLM & 24.25&29.12&29.24&40.20&46.28&21.80&19.55&19.42&20.61&48.00&76.60&33.21&12.00&\\textbf{72.50}&40.65&51.03&36.53 \\\\\n","H2O & 25.61&35.02&37.74&47.77&51.16&26.87&20.57&20.78&23.33&42.00&91.65&43.85&12.00&\\textbf{72.50}&43.50&59.67&40.88 \\\\\n","Ours & 26.06&\\textbf{40.35}&45.67&50.20&52.78&\\textbf{29.36}&\\textbf{22.31}&\\textbf{22.02}&\\textbf{23.69}&\\textbf{71.00}&\\textbf{92.27}&\\textbf{44.33}&12.00&\\textbf{72.50}&\\textbf{45.90}&59.55&\\textbf{44.37} \\\\\n","\n","\n","\n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \n","SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \n","H2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \n","Ours & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n","\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n","}\n","\\label{table:longbench_appendix_llama3_70b}\n","\\end{table*}\n"],["\\begin{table*}[h]\n","\\small\n","\\centering\n","\\begin{tabular}{lcccccc}\n","\\toprule\n"," Model & Length & KV Cache & Full KV Acc. & PyramidKV Acc. & SnapKV Acc. & H2O Acc. \\\\\n","\\midrule\n"," Mistral-7B & 32k & 64 & 100.00 & 80.50 & 43.90 & 48.40 \\\\\n"," Mistral-7B & 32k & 96 & 100.00 & 90.50 & 72.20 & 59.10 \\\\\n"," Mistral-7B & 32k & 128 & 100.00 & 91.60 & 80.10 & 64.90 \\\\\n"," \\midrule\n"," LLaMa-3-8B & 8k & 64 & 100.00 & 92.90 & 62.00 & 31.90 \\\\\n"," LLaMa-3-8B & 8k & 96 & 100.00 & 95.80 & 80.70 & 44.20 \\\\\n"," LLaMa-3-8B & 8k & 128 & 100.00 & 97.40 & 87.40 & 49.10 \\\\\n"," \\midrule\n","LLaMa-3-70B & 8k & 64 & 100.00 & 99.60 & 76.20 & 47.30 \\\\\n","LLaMa-3-70B & 8k & 96 & 100.00 & 98.60 & 94.40 & 69.90 \\\\\n","LLaMa-3-70B & 8k & 128 & 100.00 & 100.00 & 98.60 & 82.30 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{figure:needle}\n","\\caption{Recall Accuracy performance from Fact Retrieval Across Context Lengths (``Needle In A HayStack'')\n","}\n","\\vspace{-3mm}\n","\\end{table*}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_64.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{64} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_mistral_64}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_96.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{96} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_mistral_96}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_128.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{128} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_mistral_128}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama_64.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{64} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama_64}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama_96.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{96} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama_96}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama_128.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama_128}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_64.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{64} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama70_64}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_96.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{96} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama70_96}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_128.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama70_128}\n","\\end{figure}\n"]],"string":"[\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/dynamickv4.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Illustration of~\\\\method compared with existing KV cache compression methods.\\n\",\n \" (a) Full KV has all tokens stored in the KV cache in each layer; cache size increases as the input length increases.\\n\",\n \" (b) StreamingLLM~\\\\citep{xiao2023efficient} only keeps few initial tokens with a fixed cache size in each layer.\\n\",\n \" (c) SnapKV~\\\\citep{li2024snapkv} and H2O~\\\\citep{zhang2024h2o} keep a fixed cache size across Transformer layers, and their selection is based on the attention score.\\n\",\n \" (d)~\\\\method maintains pyramid-like cache sizes, allocating more cache budget to lower layers and less to higher layers. This approach to KV cache selection better aligns with the increasing attention sparsity observed in multi-layer Transformers (\\\\Scref{section:observation}).\\n\",\n \" }\\n\",\n \" \\\\label{figure:comparison}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/obs.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Attention patterns of retrieval-augmented generation across layers in LlaMa~\\\\citep{touvron2023llama, touvron2023llama2} reveal that in the lower layers, the model exhibits a broad-spectrum mode of attention, distributing attention scores uniformly across all content. In the middle layers, attention becomes more localized within each document, indicating refined information aggregation (dotted red triangular shapes in layers 6 and 10). This culminates in the upper layers, where ``massive attention'' focuses on a few key tokens (concentrated attention bars after layer 18), efficiently extracting essential information for answers.\\n\",\n \" }\\n\",\n \" \\\\label{figure:rag_flow}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/method2.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Illustration of~\\\\method. At the lower level of the transformer, the \\\\method selects more keys and values based on the exhibited average attention pattern. Fewer keys and values at the higher level are selected based on the massive activation pattern, where we observe that attention scores are concentrated over local regions.}\\n\",\n \" \\\\label{figure:method}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{minipage}{0.33\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/result1.pdf}\\n\",\n \" \\\\end{minipage}%\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{minipage}{0.33\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/result2.pdf}\\n\",\n \" \\\\end{minipage}%\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{minipage}{0.33\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/result3.pdf}\\n\",\n \" \\\\end{minipage}\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \" \\\\caption{The evaluation results from LongBench~\\\\citep{bai2023longbench} across 64, 96, 128 and 256 cache sizes at LLaMa-3-8B-Instruct (Left), Mistral-7B-Instruct (Middle) and LLaMa-3-70B-Instruct (Right).\\n\",\n \" The evaluation metrics are the average score of LongBench across datasets.\\n\",\n \" ~\\\\method outperforms H2O~\\\\citep{zhang2024h2o}, SnapKV~\\\\citep{li2024snapkv} and StreamingLLM~\\\\citep{xiao2023efficient}, especially in small KV cache sizes.}\\n\",\n \" \\\\label{figure:results}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 19.86 & 9.09 & 27.89 & \\\\textbf{37.34} & 28.35 & \\\\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\\\\\\n\",\n \"H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\\\textbf{37.76} & \\\\textbf{5.63} & 69.33 & \\\\textbf{53.44} & \\\\textbf{50.15} & 33.89 \\\\\\\\\\n\",\n \"SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\\\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\\\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.13} & \\\\textbf{14.18} & \\\\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\\\textbf{18.33} & \\\\textbf{21.65} & \\\\textbf{19.23} & \\\\textbf{58.00} & \\\\textbf{88.31} & 37.07 & 5.23 & \\\\textbf{69.50} & 52.61 & 45.74 & \\\\textbf{34.76} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & \\\\textbf{25.86} & 29.55 & \\\\textbf{41.10} & \\\\textbf{44.99} & \\\\textbf{35.80} & 21.81 & 25.98 & \\\\textbf{23.40} & 26.46 & \\\\textbf{73.50} & \\\\textbf{90.56} & 41.66 & 5.17 & \\\\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\\\\\\n\",\n \"SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\\\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\\\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\\\\\\n\",\n \"H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\\\textbf{90.56} & 41.84 & 4.91 & \\\\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\\\\\\n\",\n \"Ours & 25.40 & \\\\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\\\textbf{21.98} & \\\\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\\\textbf{90.56} & \\\\textbf{42.14} & 5.22 & \\\\textbf{69.25} & \\\\textbf{58.76} & \\\\textbf{51.18} & \\\\textbf{41.49} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 16.94&17.17&39.51&\\\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\\\\\\n\",\n \"SLM & 15.01&13.84&28.74&30.97&\\\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\\\\\\n\",\n \"H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\\\textbf{21.52}&\\\\textbf{21.98}&37.00&81.02&\\\\textbf{38.62}&\\\\textbf{5.00}&\\\\textbf{66.03}&43.54&\\\\textbf{40.46}&30.88\\\\\\\\\\n\",\n \"Ours & \\\\textbf{20.91}&\\\\textbf{20.21}&\\\\textbf{39.94}&33.57&22.87&\\\\textbf{15.70}&\\\\textbf{17.31}&21.23&21.41&\\\\textbf{54.00}&81.98&36.96&3.58&60.83&\\\\textbf{44.52}&37.99&\\\\textbf{32.19}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV &\\\\textbf{25.89} & \\\\textbf{32.93} & 48.56 & \\\\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\\\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\\\textbf{5.50} & \\\\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\\\\\\n\",\n \"SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\\\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\\\\\\n\",\n \"H2O & 25.76 & 31.10 & \\\\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\\\textbf{86.35} & 42.48 & \\\\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\\\\\\n\",\n \"Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\\\textbf{27.50} & \\\\textbf{19.36} & 26.60 & 23.97 & \\\\textbf{26.73} & \\\\textbf{71.00} & 86.25 & \\\\textbf{42.94} & 4.50 & 87.90 & \\\\textbf{53.12} & \\\\textbf{47.21} & \\\\textbf{41.63} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\\\textbf{91.06}&40.26&12.00&\\\\textbf{72.50}&43.33&57.62&39.45\\\\\\\\\\n\",\n \"SLM & 22.07&23.53&27.31&43.21&\\\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\\\textbf{72.50}&40.23&50.20&35.47\\\\\\\\\\n\",\n \"H2O & 25.45&34.64&33.23&\\\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\\\textbf{41.58}&12.00&71.50&43.83&\\\\textbf{58.16}&39.94\\\\\\\\\\n\",\n \"Ours & \\\\textbf{25.47}&\\\\textbf{36.71}&\\\\textbf{42.29}&47.08&46.21&\\\\textbf{28.30}&\\\\textbf{20.60}&\\\\textbf{21.62}&\\\\textbf{21.62}&\\\\textbf{64.50}&89.61&41.28&\\\\textbf{12.50}&\\\\textbf{72.50}&\\\\textbf{45.34}&56.50&\\\\textbf{42.01}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 26.73&45.18&47.91&\\\\textbf{52.00}&\\\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\\\textbf{72.50}&\\\\textbf{41.52}&\\\\textbf{69.27}&46.36\\\\\\\\ \\n\",\n \"SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\\\\\ \\n\",\n \"H2O & \\\\textbf{27.67}&\\\\textbf{46.51}&\\\\textbf{49.54}&51.49&53.85&29.97&28.57&\\\\textbf{22.79}&\\\\textbf{27.53}&59.00&\\\\textbf{92.63}&\\\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\\\\\ \\n\",\n \"Ours & 27.22&46.19&48.72&51.62&54.56&\\\\textbf{31.11}&\\\\textbf{29.76}&22.50&27.27&\\\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\\\textbf{46.55}\\\\\\\\ \\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\\n\",\n \"\\\\label{table:longbench}\\n\",\n \"\\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_main.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-8B-Instruct} and \\\\textbf{LlaMa-3-70B-Instruct} with \\\\textbf{8k} context size in \\\\textbf{128} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length.\\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" \\\\textbf{PyramidKV with 128 KV cache size achieves the same 100.0 Acc. performance compared with FullKV with 8k context size for LLaMA-3-70B-Instruct.}\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\small\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{ccc|cccccc}\\n\",\n \"\\\\toprule\\n\",\n \" cache size & Memory & Compression Ratio & QMSum & TREC & TriviaQA & PCount & PRe & Lcc \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"64 & 53M & 0.8\\\\% & 21.65 & 58.00 & 88.31 & 5.23 & 69.50 & 52.61 \\\\\\\\ \\n\",\n \"128 & 107M & 1.6\\\\% & 22.48 & 66.50 & 89.35 & 5.92 & 69.00 & 56.49 \\\\\\\\ \\n\",\n \"256 & 214M & 3.1\\\\% & 22.69 & 71.00 & 90.48 & 5.83 & 69.25 & 56.94 \\\\\\\\\\n\",\n \"512 & 428M & 6.3\\\\% & 22.80 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\\\\\\n\",\n \"1024 & 856M & 12.5\\\\% & 22.55 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\\\\\\n\",\n \"2048 & 1712M & 25.0\\\\% & 22.55 & 72.00 & 90.56 & 5.58 & 69.25 & 56.79 \\\\\\\\\\n\",\n \"Full & 6848M & 100.0\\\\% & 23.30 & 73.00 & 90.56 & 5.22 & 69.25 & 58.76 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Memory reduction effect and benchmark result by using \\\\method. We conducted a comparison of memory consumption between the Llama-3-8B-Instruct model utilizing the Full KV cache and the Llama-3-8B-Instruct model compressed with the \\\\method.\\n\",\n \"}\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\label{tab:memory_reduction}\\n\",\n \"\\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[htbp]\\n\",\n \"\\\\centering \\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{llrccc}\\n\",\n \"\\\\toprule\\n\",\n \"Dataset & Source & Avg len & Metric & Language & \\\\#data \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Single-Document QA} \\\\\\\\\\n\",\n \"NarrativeQA & Literature, Film & 18,409 & F1 & English & 200 \\\\\\\\\\n\",\n \"Qasper & Science & 3,619 & F1 & English & 200 \\\\\\\\\\n\",\n \"MultiFieldQA-en & Multi-field & 4,559 & F1 & English & 150 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Multi-Document QA} \\\\\\\\\\n\",\n \"HotpotQA & Wikipedia & 9,151 & F1 & English & 200 \\\\\\\\\\n\",\n \"2WikiMultihopQA & Wikipedia & 4,887 & F1 & English & 200 \\\\\\\\\\n\",\n \"MuSiQue & Wikipedia & 11,214 & F1 & English & 200 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Summarization} \\\\\\\\\\n\",\n \"GovReport & Government report & 8,734 & Rouge-L & English & 200 \\\\\\\\\\n\",\n \"QMSum & Meeting & 10,614 & Rouge-L & English & 200 \\\\\\\\\\n\",\n \"MultiNews & News & 2,113 & Rouge-L & English & 200 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Few-shot Learning} \\\\\\\\\\n\",\n \"TREC & Web question & 5,177 & Accuracy (CLS) & English & 200 \\\\\\\\\\n\",\n \"TriviaQA & Wikipedia, Web & 8,209 & F1 & English & 200 \\\\\\\\\\n\",\n \"SAMSum & Dialogue & 6,258 & Rouge-L & English & 200 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Synthetic Task} \\\\\\\\\\n\",\n \"PassageCount & Wikipedia & 11,141 & Accuracy (EM) & English & 200 \\\\\\\\\\n\",\n \"PassageRetrieval-en & Wikipedia & 9,289 & Accuracy (EM) & English & 200 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Code Completion} \\\\\\\\\\n\",\n \"LCC & Github & 1,235 & Edit Sim & Python/C\\\\#/Java & 500 \\\\\\\\\\n\",\n \"RepoBench-P & Github repository & 4,206 & Edit Sim & Python/Java & 500 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{An overview of the dataset statistics in LongBench~\\\\citep{bai2023longbench}. `Source' denotes the origin of the context. `Accuracy (CLS)' refers to classification accuracy, while `Accuracy (EM)' refers to exact match accuracy.}\\n\",\n \"\\\\label{table:stat}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{4}{*}{$\\\\alpha$} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & Avg. \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\n\",\n \"8 & 21.40 & 16.92 & 31.62 & 38.45 & 28.72 & 18.59 & 19.96 & 22.49 & 20.96 & 66.50 & 89.35 & 38.43 & 5.92 & 69.00 & 57.86 & 51.80 & 37.37 \\\\\\\\ \\n\",\n \"16 & 23.37 & 16.21 & 33.93 & 38.24 & 27.28 & 20.57 & 19.71 & 21.93 & 20.86 & 60.00 & 88.75 & 38.34 & 5.48 & 69.12 & 57.84 & 53.42 & 37.19 \\\\\\\\ \\n\",\n \"24 & 22.85 & 14.51 & 32.26 & 38.38 & 28.36 & 20.33 & 19.55 & 21.72 & 20.72 & 54.50 & 88.71 & 38.46 & 5.48 & 69.50 & 56.83 & 53.65 & 36.61 \\\\\\\\ \\n\",\n \"32 & 23.01 & 14.54 & 31.68 & 38.86 & 29.90 & 19.16 & 19.20 & 21.83 & 20.52 & 49.50 & 87.01 & 38.01 & 5.75 & 69.50 & 57.02 & 54.54 & 36.25 \\\\\\\\ \\n\",\n \"40 & 21.70 & 13.06 & 30.14 & 36.78 & 27.34 & 18.88 & 18.72 & 21.37 & 19.79 & 44.00 & 87.74 & 38.43 & 6.08 & 69.25 & 56.11 & 53.89 & 35.21 \\\\\\\\ \\n\",\n \"48 & 21.51 & 12.30 & 29.77 & 39.04 & 26.76 & 17.97 & 18.65 & 21.20 & 20.29 & 44.50 & 87.73 & 38.44 & 5.51 & 69.25 & 56.73 & 53.88 & 35.22 \\\\\\\\ \\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Ablation on $\\\\alpha$.}\\n\",\n \"\\\\label{table:ablation_step_a}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{4}{*}{$\\\\beta$} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & Avg. \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"20 & 21.40 & 16.92 & 33.79 & 39.73 & 28.72 & 18.59 & 19.86 & 22.48 & 20.95 & 66.50 & 89.35 & 38.39 & 5.92 & 69.00 & 56.49 & 47.95 & 37.25 \\\\\\\\\\n\",\n \"18 & 21.71 & 16.24 & 33.59 & 39.89 & 27.94 & 18.38 & 19.76 & 22.32 & 21.20 & 66.50 & 88.98 & 38.93 & 5.46 & 69.50 & 56.47 & 49.23 & 37.25 \\\\\\\\\\n\",\n \"16 & 21.74 & 14.86 & 33.64 & 39.18 & 28.17 & 18.77 & 19.57 & 22.25 & 21.48 & 66.50 & 89.69 & 38.87 & 5.82 & 69.50 & 57.02 & 50.11 & 37.32 \\\\\\\\\\n\",\n \"14 & 22.53 & 16.31 & 33.50 & 40.50 & 28.15 & 19.26 & 19.66 & 22.39 & 21.38 & 65.50 & 90.02 & 38.56 & 5.75 & 69.50 & 57.51 & 49.71 & 37.51 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Ablation on $\\\\beta$.}\\n\",\n \"\\\\label{table:ablation_step_b}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{ccccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Prompt Length} & \\\\textbf{Generation Length} & \\\\textbf{Inference Time} & \\\\textbf{Allocation Time} & \\\\textbf{Selection Time} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"512&512 & 18.26 & 0.0000003 & 0.0194 \\\\\\\\\\n\",\n \"512&1024 & 34.69 & 0.000002 & 0.0133 \\\\\\\\\\n\",\n \"512&2048 & 70.69 & 0.000003 & 0.013 \\\\\\\\\\n\",\n \"512&4096 & 138.62 & 0.000005 & 0.013 \\\\\\\\\\n\",\n \"1024&512 & 17.32 & 0.000002 & 0.0131 \\\\\\\\\\n\",\n \"1024&1024 & 34.67 & 0.000002 & 0.01288 \\\\\\\\\\n\",\n \"1024&2048 & 70.21 & 0.000005 & 0.01296 \\\\\\\\\\n\",\n \"1024&4096 & 138.61 & 0.000003 & 0.01297 \\\\\\\\\\n\",\n \"2048&512 & 17.48 & 0.000004 & 0.0128 \\\\\\\\\\n\",\n \"2048&1024 & 34.78 & 0.000006 & 0.0129 \\\\\\\\\\n\",\n \"2048&2048 & 69.50 & 0.000003 & 0.01297 \\\\\\\\\\n\",\n \"2048&4096 & 138.59 & 0.000003 & 0.013 \\\\\\\\\\n\",\n \"4096&512 & 17.58 & 0.000002 & 0.013 \\\\\\\\\\n\",\n \"4096&1024 & 34.93 & 0.000004 & 0.0129 \\\\\\\\\\n\",\n \"4096&2048 & 69.65 & 0.000002 & 0.013 \\\\\\\\\\n\",\n \"4096&4096 & 138.87 & 0.000002 & 0.013 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Extra inference overhead of~\\\\method }\\n\",\n \"\\\\label{table:inference_overhead}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{ccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Prompt Length} & \\\\textbf{Generation Length} & \\\\textbf{H2O} & \\\\textbf{SnapKV} & \\\\textbf{StreamingLLM} & \\\\textbf{PyramidKV} \\\\\\\\ \\n\",\n \"\\\\midrule\\n\",\n \"512&512 & 18.47 & 18.25 & 18.96 & 18.26 \\\\\\\\\\n\",\n \"512&1024 & 35.10 & 34.76 & 36.20 & 34.69 \\\\\\\\\\n\",\n \"512&2048 & 70.21 & 69.60 & 72.35 & 70.69 \\\\\\\\ \\n\",\n \"512&4096 & 140.80 & 139.42 & 146.37 & 138.62 \\\\\\\\\\n\",\n \"1024&512 & 17.63 & 17.34 & 18.12 & 17.32 \\\\\\\\\\n\",\n \"1024&1024 & 35.16 & 34.61 & 36.17 & 34.67 \\\\\\\\\\n\",\n \"1024&2048 & 71.02 & 69.17 & 72.37 & 70.21 \\\\\\\\\\n\",\n \"1024&4096 & 140.51 & 138.83 & 146.09 & 138.61 \\\\\\\\ \\n\",\n \"2048&512 & 17.64 & 19.54 & 18.22 & 17.48 \\\\\\\\ \\n\",\n \"2048&1024 & 35.09 & 34.76 & 36.29 & 34.78 \\\\\\\\ \\n\",\n \"2048&2048 & 70.84 & 69.56 & 72.46 & 69.50 \\\\\\\\ \\n\",\n \"2048&4096 & 140.16 & 139.55 & 145.22 & 138.59 \\\\\\\\ \\n\",\n \"4096&512 & 17.75 & 17.67 & 18.40 & 17.58 \\\\\\\\ \\n\",\n \"4096&1024 & 35.20 & 35.08 & 36.46 & 34.93 \\\\\\\\ \\n\",\n \"4096&2048 & 70.02 & 69.26 & 72.58 & 69.65 \\\\\\\\ \\n\",\n \"4096&4096 & 139.87 & 138.57 & 144.98 & 138.87 \\\\\\\\ \\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Performance comparison across different configurations and methods.}\\n\",\n \"\\\\label{table:inference_speed_comparison}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 04.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 19.86 & 9.09 & 27.89 & \\\\textbf{37.34} & 28.35 & \\\\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\\\\\\n\",\n \"H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\\\textbf{37.76} & \\\\textbf{5.63} & 69.33 & \\\\textbf{53.44} & \\\\textbf{50.15} & 33.89 \\\\\\\\\\n\",\n \"SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\\\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\\\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.13} & \\\\textbf{14.18} & \\\\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\\\textbf{18.33} & \\\\textbf{21.65} & \\\\textbf{19.23} & \\\\textbf{58.00} & \\\\textbf{88.31} & 37.07 & 5.23 & \\\\textbf{69.50} & 52.61 & 45.74 & \\\\textbf{34.76} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 96} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 20.45 & 10.34 & 31.84 & 37.85 & 28.65 & \\\\textbf{18.52} & 17.90 & 21.26 & 19.07 & 41.50 & 86.95 & 37.82 & 5.08 & 69.12 & 54.69 & \\\\textbf{51.31} & 34.51 \\\\\\\\\\n\",\n \"H2O & 21.55 & 11.21 & 28.73 & 37.66 & 30.12 & 18.47 & 19.57 & 21.57 & 20.44 & 38.50 & \\\\textbf{87.63} & \\\\textbf{38.47} & 5.60 & 69.00 & 54.51 & 50.16 & 34.57 \\\\\\\\\\n\",\n \"SLM & 18.67 & 8.43 & 24.98 & 38.35 & \\\\textbf{30.59} & 16.37 & 17.33 & 19.84 & 18.41 & 41.00 & 73.92 & 29.38 & 5.80 & \\\\textbf{69.50} & 47.15 & 45.61 & 31.58 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.67} & \\\\textbf{15.10} & \\\\textbf{33.50} & \\\\textbf{39.73} & 26.48 & 17.47 & \\\\textbf{19.64} & \\\\textbf{22.28} & \\\\textbf{20.49} & \\\\textbf{61.50} & 87.38 & 38.18 & \\\\textbf{6.00} & 69.25 & \\\\textbf{55.30} & 46.78 & \\\\textbf{36.29} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 128} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\\\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\\\textbf{51.82} & 35.50 \\\\\\\\\\n\",\n \"H2O & \\\\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\\\textbf{32.71} & 18.45 & \\\\textbf{20.32} & 22.02 & \\\\textbf{21.10} & 38.50 & 87.75 & \\\\textbf{39.14} & 5.83 & \\\\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\\\\\\n\",\n \"SLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\\\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\\\\\\n\",\n \"Ours & 21.40 & \\\\textbf{16.92} & \\\\textbf{33.79} & \\\\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\\\textbf{22.48} & 20.95 & \\\\textbf{66.50} & \\\\textbf{89.35} & 38.39 & \\\\textbf{5.92} & 69.00 & \\\\textbf{56.49} & 47.95 & \\\\textbf{37.25} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & \\\\textbf{25.86} & 29.55 & \\\\textbf{41.10} & \\\\textbf{44.99} & \\\\textbf{35.80} & 21.81 & 25.98 & \\\\textbf{23.40} & 26.46 & \\\\textbf{73.50} & \\\\textbf{90.56} & 41.66 & 5.17 & \\\\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\\\\\\n\",\n \"SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\\\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\\\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\\\\\\n\",\n \"H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\\\textbf{90.56} & 41.84 & 4.91 & \\\\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\\\\\\n\",\n \"Ours & 25.40 & \\\\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\\\textbf{21.98} & \\\\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\\\textbf{90.56} & \\\\textbf{42.14} & 5.22 & \\\\textbf{69.25} & \\\\textbf{58.76} & \\\\textbf{51.18} & \\\\textbf{41.49} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\\n\",\n \"}\\n\",\n \"\\\\label{table:longbench_appendix_llama3_8b}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & 16.94&17.17&39.51&\\\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\\\\\\n\",\n \"SLM & 15.01&13.84&28.74&30.97&\\\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\\\\\\n\",\n \"H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\\\textbf{21.52}&\\\\textbf{21.98}&37.00&81.02&\\\\textbf{38.62}&\\\\textbf{5.00}&\\\\textbf{66.03}&43.54&\\\\textbf{40.46}&30.88\\\\\\\\\\n\",\n \"Ours & \\\\textbf{20.91}&\\\\textbf{20.21}&\\\\textbf{39.94}&33.57&22.87&\\\\textbf{15.70}&\\\\textbf{17.31}&21.23&21.41&\\\\textbf{54.00}&81.98&36.96&3.58&60.83&\\\\textbf{44.52}&37.99&\\\\textbf{32.19}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 96} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & 19.92&18.80&\\\\textbf{43.29}&\\\\textbf{39.66}&23.08&\\\\textbf{15.94}&16.65&21.26&21.47&43.50&83.48&39.74&4.00&60.10&45.53&41.12&32.47\\\\\\\\\\n\",\n \"SLM & 15.15&15.48&31.44&30.03&\\\\textbf{23.93}&12.73&16.76&19.15&19.19&41.50&75.31&28.71&5.00&28.48&38.92&36.05&26.37\\\\\\\\\\n\",\n \"H2O & 19.44&20.81&38.78&32.39&21.51&14.43&17.68&\\\\textbf{22.40}&\\\\textbf{21.99}&38.00&82.51&\\\\textbf{39.94}&\\\\textbf{6.06}&\\\\textbf{77.48}&45.18&\\\\textbf{42.43}&32.67\\\\\\\\\\n\",\n \"Ours & \\\\textbf{20.35}&\\\\textbf{21.87}&41.15&34.94&21.85&15.81&\\\\textbf{18.21}&21.66&21.43&\\\\textbf{65.00}&\\\\textbf{83.60}&39.60&4.50&67.80&\\\\textbf{45.83}&39.38&\\\\textbf{34.08}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 128} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"\\n\",\n \"SKV & 19.16 & 21.46 & 43.52 & \\\\textbf{38.60} & \\\\textbf{23.35} & \\\\textbf{16.09} & 17.66 & 21.84 & 21.47 & 47.50 & \\\\textbf{84.15} & 40.24 & 5.00 & 69.31 & \\\\textbf{46.98} & \\\\textbf{42.97} & 34.96 \\\\\\\\\\n\",\n \"SLM & 16.57 & 14.68 & 32.40 & 30.19 & 22.64 & 12.34 & 18.08 & 18.96 & 19.19 & 43.50 & 74.22 & 29.02 & 4.50 & 29.48 & 39.23 & 36.16 & 27.57 \\\\\\\\\\n\",\n \"H2O & 21.20 & 21.90 & 41.55 & 33.56 & 21.28 & 12.93 & \\\\textbf{18.59} & \\\\textbf{22.61} & \\\\textbf{21.99} & 39.00 & 82.37 & \\\\textbf{40.44} & \\\\textbf{6.00} & \\\\textbf{83.19} & 46.41 & 42.66 & 34.73 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.75} & \\\\textbf{22.03} & \\\\textbf{44.32} & 34.06 & 22.79 & 15.77 & 18.58 & 21.89 & 21.43 & \\\\textbf{66.00} & 83.46 & 39.75 & 4.50 & 66.90 & 46.96 & 41.28 & \\\\textbf{35.72} \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"\\n\",\n \"SKV &\\\\textbf{25.89} & \\\\textbf{32.93} & 48.56 & \\\\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\\\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\\\textbf{5.50} & \\\\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\\\\\\n\",\n \"SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\\\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\\\\\\n\",\n \"H2O & 25.76 & 31.10 & \\\\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\\\textbf{86.35} & 42.48 & \\\\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\\\\\\n\",\n \"Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\\\textbf{27.50} & \\\\textbf{19.36} & 26.60 & 23.97 & \\\\textbf{26.73} & \\\\textbf{71.00} & 86.25 & \\\\textbf{42.94} & 4.50 & 87.90 & \\\\textbf{53.12} & \\\\textbf{47.21} & \\\\textbf{41.63} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for Mistral-7B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\\n\",\n \"}\\n\",\n \"\\\\label{table:longbench_appendix_mistral}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 27.75& \\t46.48& \\t49.45\\t& 52.04& \\t54.9& \\t30.42& \\t32.37& \\t22.27\\t& 27.58\\t& 73.5& \\t92.46& \\t45.73\\t& 12.5\\t& 72.5\\t& 40.96\\t& 63.91\\t& 46.55 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\\\textbf{91.06}&40.26&12.00&\\\\textbf{72.50}&43.33&57.62&39.45\\\\\\\\\\n\",\n \"SLM & 22.07&23.53&27.31&43.21&\\\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\\\textbf{72.50}&40.23&50.20&35.47\\\\\\\\\\n\",\n \"H2O & 25.45&34.64&33.23&\\\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\\\textbf{41.58}&12.00&71.50&43.83&\\\\textbf{58.16}&39.94\\\\\\\\\\n\",\n \"Ours & \\\\textbf{25.47}&\\\\textbf{36.71}&\\\\textbf{42.29}&47.08&46.21&\\\\textbf{28.30}&\\\\textbf{20.60}&\\\\textbf{21.62}&\\\\textbf{21.62}&\\\\textbf{64.50}&89.61&41.28&\\\\textbf{12.50}&\\\\textbf{72.50}&\\\\textbf{45.34}&56.50&\\\\textbf{42.01}\\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 96} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"\\n\",\n \"SKV & \\\\textbf{25.78}&35.71&42.13&\\\\textbf{50.38}&\\\\textbf{51.46}&26.68&19.61&21.40&21.98&48.50&\\\\textbf{92.11}&41.21&12.00&72.00&44.85&59.05&41.55\\\\\\\\\\n\",\n \"SLM & 23.31&29.46&29.21&41.85&45.92&23.00&18.42&19.71&18.57&45.00&76.79&33.54&12.00&\\\\textbf{72.50}&40.49&50.73&36.28\\\\\\\\\\n\",\n \"H2O & 25.30&35.13&35.54&47.39&50.61&26.20&20.87&\\\\textbf{21.80}&\\\\textbf{22.93}&41.00&90.47&\\\\textbf{43.42}&12.00&72.00&43.84&\\\\textbf{59.86}&40.52\\\\\\\\\\n\",\n \"Ours & 25.47&\\\\textbf{37.61}&\\\\textbf{44.00}&47.33&45.36&\\\\textbf{27.91}&\\\\textbf{21.05}&21.60&22.31&\\\\textbf{66.00}&91.45&42.36&12.00&\\\\textbf{72.50}&\\\\textbf{45.12}&56.88&\\\\textbf{42.43}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 128} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & \\\\textbf{26.22}&37.49&\\\\textbf{45.70}&\\\\textbf{50.86}&\\\\textbf{52.82}&28.50&20.38&21.72&22.56&53.00&91.61&41.43&12.00&71.50&45.06&\\\\textbf{60.50}&42.58 \\\\\\\\\\n\",\n \"SLM & 24.25&29.12&29.24&40.20&46.28&21.80&19.55&19.42&20.61&48.00&76.60&33.21&12.00&\\\\textbf{72.50}&40.65&51.03&36.53 \\\\\\\\\\n\",\n \"H2O & 25.61&35.02&37.74&47.77&51.16&26.87&20.57&20.78&23.33&42.00&91.65&43.85&12.00&\\\\textbf{72.50}&43.50&59.67&40.88 \\\\\\\\\\n\",\n \"Ours & 26.06&\\\\textbf{40.35}&45.67&50.20&52.78&\\\\textbf{29.36}&\\\\textbf{22.31}&\\\\textbf{22.02}&\\\\textbf{23.69}&\\\\textbf{71.00}&\\\\textbf{92.27}&\\\\textbf{44.33}&12.00&\\\\textbf{72.50}&\\\\textbf{45.90}&59.55&\\\\textbf{44.37} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & 26.73&45.18&47.91&\\\\textbf{52.00}&\\\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\\\textbf{72.50}&\\\\textbf{41.52}&\\\\textbf{69.27}&46.36\\\\\\\\ \\n\",\n \"SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\\\\\ \\n\",\n \"H2O & \\\\textbf{27.67}&\\\\textbf{46.51}&\\\\textbf{49.54}&51.49&53.85&29.97&28.57&\\\\textbf{22.79}&\\\\textbf{27.53}&59.00&\\\\textbf{92.63}&\\\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\\\\\ \\n\",\n \"Ours & 27.22&46.19&48.72&51.62&54.56&\\\\textbf{31.11}&\\\\textbf{29.76}&22.50&27.27&\\\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\\\textbf{46.55}\\\\\\\\ \\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-70B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\\n\",\n \"}\\n\",\n \"\\\\label{table:longbench_appendix_llama3_70b}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\small\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{lcccccc}\\n\",\n \"\\\\toprule\\n\",\n \" Model & Length & KV Cache & Full KV Acc. & PyramidKV Acc. & SnapKV Acc. & H2O Acc. \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \" Mistral-7B & 32k & 64 & 100.00 & 80.50 & 43.90 & 48.40 \\\\\\\\\\n\",\n \" Mistral-7B & 32k & 96 & 100.00 & 90.50 & 72.20 & 59.10 \\\\\\\\\\n\",\n \" Mistral-7B & 32k & 128 & 100.00 & 91.60 & 80.10 & 64.90 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" LLaMa-3-8B & 8k & 64 & 100.00 & 92.90 & 62.00 & 31.90 \\\\\\\\\\n\",\n \" LLaMa-3-8B & 8k & 96 & 100.00 & 95.80 & 80.70 & 44.20 \\\\\\\\\\n\",\n \" LLaMa-3-8B & 8k & 128 & 100.00 & 97.40 & 87.40 & 49.10 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"LLaMa-3-70B & 8k & 64 & 100.00 & 99.60 & 76.20 & 47.30 \\\\\\\\\\n\",\n \"LLaMa-3-70B & 8k & 96 & 100.00 & 98.60 & 94.40 & 69.90 \\\\\\\\\\n\",\n \"LLaMa-3-70B & 8k & 128 & 100.00 & 100.00 & 98.60 & 82.30 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{figure:needle}\\n\",\n \"\\\\caption{Recall Accuracy performance from Fact Retrieval Across Context Lengths (``Needle In A HayStack'')\\n\",\n \"}\\n\",\n \"\\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_mistral_64.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{Mistral-7B-Instruct} with \\\\textbf{32k} context size in \\\\textbf{64} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_mistral_64}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_mistral_96.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{Mistral-7B-Instruct} with \\\\textbf{32k} context size in \\\\textbf{96} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_mistral_96}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_mistral_128.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{Mistral-7B-Instruct} with \\\\textbf{32k} context size in \\\\textbf{128} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_mistral_128}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama_64.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-8B-Instruct} with \\\\textbf{8k} context size in \\\\textbf{64} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama_64}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama_96.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-8B-Instruct} with \\\\textbf{8k} context size in \\\\textbf{96} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama_96}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama_128.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-8B-Instruct} with \\\\textbf{8k} context size in \\\\textbf{128} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama_128}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama70_64.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-70B} with \\\\textbf{8k} context size in \\\\textbf{64} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama70_64}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama70_96.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-70B} with \\\\textbf{8k} context size in \\\\textbf{96} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama70_96}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama70_128.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-70B} with \\\\textbf{8k} context size in \\\\textbf{128} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama70_128}\\n\",\n \"\\\\end{figure}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\documentclass{article}\n\n\n\n% if you need to pass options to natbib, use, e.g.:\n% 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chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n% \\newtheorem{definition}[theorem]{Definition}\n\n\\newcommand{\\tabincell}[2]{\\begin{tabular}{@{}#1@{}}#2\\end{tabular}} \n\n\\newcommand{\\draftonly}[1]{#1} \n\\newcommand{\\draftcomment}[3]{\\draftonly{{\\textcolor{#3}{[\\textbf{#1--\\textsc{#2}}]}}}}\n\\newcommand{\\jh}[1]{\\draftcomment{#1}{Junjie}{blue}}\n\\newcommand{\\wx}[1]{\\draftcomment{#1}{Wen}{olive}}\n\\newcommand{\\zc}[1]{\\draftcomment{#1}{Zefan}{red}}\n\\newcommand{\\yd}[1]{\\draftcomment{#1}{Yue}{purple}}\n\\newcommand{\\yc}[1]{\\draftcomment{#1}{Yichi}{pink}}\n\n\n\n\\usepackage{xspace}\n\\newcommand{\\pattern}[0]{RAG flow}\n\\newcommand{\\method}[0]{PyramidKV\\xspace}\n\n\\usepackage{cleveref}\n\\newcommand{\\Scref}[1]{\\S\\ref{#1}}\n\n\\title{PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling}\n\n\n% DinamicKV: Dynamic Layer-Wise Spasity-Aware KV Cache Compression\n% DinamicKV: Dynamic Spasity-based KV Cache Compression\n% RAG Flow: Understanding Retrieval-Augmented Generation in Information Flow Perspective\n% InstructKV: Instruciton-Aware KV Cache Pruning with Information Aggregation Flow\n\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to LaTeX to determine where to break the\n% lines. Using \\AND forces a line break at that point. So, if LaTeX puts 3 of 4\n% authors names on the first line, and the last on the second line, try using\n% \\AND instead of \\And before the third author name.\n\n\n\\author{%\nZefan Cai$^{1}$,\nYichi Zhang$^{2}$,\nBofei Gao$^{2}$,\nYuliang Liu$^{3}$, \nTianyu Liu$^{4}$, \n\\textbf{Keming Lu}$^4$, \\\\\n\\textbf{Wayne Xiong}$^{6}$,\n\\textbf{Yue Dong}$^{5}$,\n\\textbf{Baobao Chang}$^{2}$,\n\\textbf{Junjie Hu}$^{1}$,\n\\textbf{Wen Xiao}$^{6}$,\n\\\\\n$^1$University of Wisconsin - Madison \n$^2$Peking University \n$^3$Nanjing University \n$^4$Qwen \\\\\n$^5$University of California - Riverside \n$^6$Microsoft \\\\\n \\texttt{zefncai@gmail.com} \\\\\n % \\url{https://github.com/Zefan-Cai/PyramidKV} \\\\\n\\url{https://github.com/Zefan-Cai/PyramidKV} \\\\\n}\n\n\n\n\\begin{document}\n\n\n\\maketitle\n\\begin{abstract}\n%% \\yd{this pattern name can be changed}\\wx{I think this name makes sense, will replace the current one in the paper},\n\nIn this study, we investigate whether attention-based information flow inside large language models (LLMs) is aggregated through noticeable patterns for long context processing. Our observations reveal that LLMs aggregate information through \n\\textbf{Pyramidal} Information Funneling where attention is scattering widely in lower layers, progressively consolidating within specific contexts, and ultimately focusing on critical tokens (a.k.a massive activation or attention sink) in higher layers. Motivated by these insights, we developed \\method, a novel and effective KV cache compression method. This approach dynamically adjusts the KV cache size across different layers, allocating more cache in lower layers and less in higher ones, diverging from traditional methods that maintain a uniform KV cache size.\nOur experimental evaluations, utilizing the LongBench benchmark, show that \\method matches the performance of models with a full KV cache while retaining only 12\\% of the KV cache, thus significantly reducing memory usage. In scenarios emphasizing memory efficiency, where only 0.7\\% of the KV cache is maintained, \\method surpasses other KV cache compression techniques, achieving up to a 20.5 absolute accuracy improvement on TREC dataset. In the Needle-in-a-Haystack experiment, \\method outperforms competing methods in maintaining long-context comprehension in LLMs; notably, retaining just 128 KV cache entries enables the LLAMA-3-70B model to achieve 100.0 Acc. performance, matching that of a full KV cache.\n% \\zc{Need to mention we preserve full performance at LongBench at 2k and full performance at needle at 128}\n\n% In this study, we investigate whether attention-based information flow inside large language models (LLMs) is aggregated through noticeable patterns for long context processing. Our observations reveal that LLMs aggregate information through \n% Pyramidal Information Funneling where attention is scattering widely in lower layers, progressively consolidating within specific contexts, and ultimately focusing on critical tokens (a.k.a massive activation or attention sink) in higher layers. Motivated by these insights, we developed PyramidKV, a novel and effective KV cache compression method. This approach dynamically adjusts the KV cache size across different layers, allocating more cache in lower layers and less in higher ones, diverging from traditional methods that maintain a uniform KV cache size.\n% Our experimental evaluations, utilizing the LongBench benchmark, show that PyramidKV matches the performance of models with a full KV cache while retaining only 12\\% of the KV cache, thus significantly reducing memory usage. In scenarios emphasizing memory efficiency, where only 0.7\\% of the KV cache is maintained, PyramidKV surpasses other KV cache compression techniques, achieving up to a 20.5 absolute accuracy improvement on TREC dataset. In the Needle-in-a-Haystack experiment, PyramidKV outperforms competing methods in maintaining long-context comprehension in LLMs; notably, retaining just 128 KV cache entries enables the LLAMA-3-70B model to achieve 100\\% Acc. performance, matching that of a full KV cache.\n\n\n% In this work, we study the intrinsic attention patterns of Large Language Models (LLMs) when they answer questions based on long-context documents.\n% We discover that LLMs implicitly perform information aggregation from shallow layers to deeper ones. Specifically, in shallow layers, the information is first spread globally, and then aggregated within local context, and when it gets deeper, the information is further aggregated to few important tokens, which is so-called Massive Activation or Attention Sink in previous works. Insprired by the observation, we propose a novel and effective KV compression method called \\method. Different from the previous works in KV cache compression that retains the size of the maintained KV cache the same across different layers in LLM, we keep different numbers of KV cache for different layers, with lower layers retaining more while higher layers fewer.\n% In our experiments on LongBench, \\method shows a comparable performance with Full KV cache with only 5.8\\% KV cache kept, reducing the memory by xx\\%. In memory-efficient scenarios (when only 0.5\\% KV cache remaining), our model performs much better than other KV cache compression methods, leading up to 20\\% absolute improvement on the tasks.\n\n% The performance \n% ~\\method is xxx times faster than full KV cache technique while maintaining the same performance across LLM series (LlaMa and Mistral), sizes ($7$B, $13$B and $70$B) and architectures (Dense and MoE).\n% Our experiments also demonstrate that ~\\method is effective and efficient in streaming applications.\n\n% In shallow layers, the information flows from the context to the initial tokens for each document; in mature layers, the information flows from the initial tokens for each document to some abstract tokens. In the top layer, LLMs generate outputs almost solely rely on some global abstractive tokens with massive attention scores.\n% Based on the aforementioned study, we propose a plug-and-play method inference accelerate method ~\\method to perform KV cache compression.\n% Different from the KV cache compression that retains the size of the maintained key and value vectors the same across Transformer layers, we conduct a dynamic KV Cache compression method that \n% targeted profiling to discern the intrinsic structure of attention modules. \n% ~\\method is xxx times faster than full KV cache technique while maintaining the same performance across LLM series (LlaMa and Mistral), sizes ($7$B, $13$B and $70$B) and architectures (Dense and MoE).\n% Our experiments also demonstrate that ~\\method is effective and efficient in streaming applications.\n\\end{abstract}\n\n\n\n\\section{Introduction}\n\\label{section:introduction}\n% \\wx{I rewrite the introduction section below.}\n\nLarge language models (LLMs)~\\citep{achiam2023gpt,touvron2023llama,touvron2023llama2,jiang2023mistral} are integral to various natural language processing applications, including dialogue systems~\\citep{vicuna2023}, document summarization~\\citep{fabbri-etal-2019-multi}, and code completion~\\citep{roziere2023code}. These models have recently been scaled up to handle long contexts~\\citep{fu2024data, ding2024longrope, zhu2023pose, chen2023longlora}, with GPT-4 processing up to 128K tokens and Gemini-pro-1.5 handling 1M tokens. However, scaling LLMs to extremely long contexts naturally leads to a significant delay due to the quadratic computation of attention over long contexts. A common solution to mitigate such inference delays involves caching the key and value states (KV) of previous tokens~\\citep{waddington2013kv}, with the trade-off of requiring extensive GPU memory storage. For instance, maintaining a KV cache for 100K tokens in LLaMA-2 7B requires over 50GB of memory, while a 2K context requires less than 1GB of memory~\\citep{wu2024retrieval}.\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/dynamickv4.pdf}\n \\caption{\n Illustration of~\\method compared with existing KV cache compression methods.\n (a) Full KV has all tokens stored in the KV cache in each layer; cache size increases as the input length increases.\n (b) StreamingLLM~\\citep{xiao2023efficient} only keeps few initial tokens with a fixed cache size in each layer.\n (c) SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} keep a fixed cache size across Transformer layers, and their selection is based on the attention score.\n (d)~\\method maintains pyramid-like cache sizes, allocating more cache budget to lower layers and less to higher layers. This approach to KV cache selection better aligns with the increasing attention sparsity observed in multi-layer Transformers (\\Scref{section:observation}).\n }\n \\label{figure:comparison}\n\\end{figure}\n\nTo tackle these memory constraints, recent studies have explored the optimization of KV caching, including approaches such as low-rank decomposition of the KV cache~\\citep{dong2024get} or pruning non-essential KV cache~\\citep{zhang2024h2o, li2024snapkv, ge2023model}. Notably, it has been shown that maintaining merely 20\\% of the KV cache can preserve a substantial level of performance~\\citep{zhang2024h2o}. Moreover, extreme compression of the KV cache for tasks of longer contexts (e.g., retrieval augmented generation or RAG for short) can drastically improve efficiency and further reduce resource use. However, questions about the universal applicability of these strategies across all layers of an LLM remain open. (1) \\textit{Are these KV cache strategies applicable to all layers? }(2) \\textit{Is it computationally efficient to use the same KV cache size across layers as previous studies have done?} These considerations suggest a need for an in-depth, more nuanced understanding of KV cache optimization in LLMs. %\\jh{What is missing in the literature? we need one more sentence to motivate our research. Why do we perform this study? something like: ``However, a comprehensive understanding of the KV cache optimization is still missing.''}\\wx{Agree, added several sentences for motivation.}\n\nTo examine these questions, we aim to systematically investigate the design principles of the KV cache compression across different layers, specifically tailored to the behaviors of the attention mechanism. We first investigate how information flow is aggregated via attention mechanisms across different layers in multi-document question answering (QA), a classic task involving long contexts. Our analysis identifies a notable transition of attention distribution from a broad coverage of global contexts to a narrow focus of local tokens over layers in LLMs. This pattern suggests an aggregated information flow where information is initially gathered broadly and subsequently narrowed down to key tokens, epitomizing the massive attention phenomenon. Our findings provide unique insights beyond the previously documented ``massive activation''~\\citep{sun2024massive} that very few activations exhibit significantly larger values than others when calculating multi-head attention in LLMs and ``attention sink''~\\citep{xiao2023efficient} that keeping the KV of initial tokens will largely recover the performance of window attention.\n\nBuilding on these insights on how information flows are aggregated through a pyramid pattern, we design a novel and effective KV cache pruning approach that mirrors the geometric shape, named PyramidKV. As shown in \\autoref{figure:comparison}, unlike the fixed-and-same length KV cache pruning common in prior works~\\citep{zhang2024h2o, ge2023model, li2024snapkv}, PyramidKV allocates more KV cache to the lower layers where information is more dispersed and each KV holds less information while reducing the KV cache in higher layers where information becomes concentrated in fewer key tokens. To the best of our knowledge, PyramidKV is the first KV cache compression method with varied cache retention across layers, tailoring cache amounts to the informational needs of each layer and paving the way for future research.\n\n\nWe conducted comprehensive experiments on LongBench~\\citep{bai2023longbench} using 17 datasets across various tasks and domains with three backbone models (LLaMa-3-8B-Instruct, LLaMa-3-70B-Instruct and Mistral-7B~\\citep{jiang2023mistral}). The results show that \\method preserves performance using just 12.0\\% of the KV cache (KV Cache size = 2048) on the LongBench benchmark and significantly outperforms other methods in extreme conditions, retaining only 0.7\\% of the KV cache. Moreover, \\method outperforms baseline models (H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv}, StreamingLLM~\\citep{xiao2023efficient}) across all tested cache sizes (64, 96, 128, 256), with its advantages most pronounced at smaller cache sizes. In the Needle In A Haystack experiment, \\method effectively maintains the long-context comprehension in LLMs, outperforming than competing methods. Remarkably, with \\method, retaining only 128 KV cache entries allows the LLaMa-3-70B-Instruct model to achieve 100.0 Acc. performance, matching the performance of a full KV cache.\n% \\zc{Need to mention we preserve full performance at LongBench at 2k and full performance at needle at 128}\n\n\n\n\n\n\n\n\n% We conduct extensive experiments on LongBench~\\citep{bai2023longbench} (including 17 datasets across different tasks and domains) with two different base models (LLaMa-3-8B-Instruct and Mistral-7B~\\citep{jiang2023mistral}) in \\Scref{section:experiment}. The experiment results show that PyramidKV can preserve the performance with only 12.0\\% KV cache, and outperforms the baseline methods in extreme scenarios (with only 0.7\\% KV cache kept).\n% Our evaluation also shows that ~\\method outperforms baselines (i.e., H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv} and StreamingLLM~\\citep{xiao2023efficient}) across various cache sizes (64, 96, 128, 256, 512), and the performance strengths of PyramidKV are more evident in\n% small KV Cache sizes.\n% Our experiment on Needle In A HayStask demonstrates that~\\method preserves the long-context understanding ability of LLMs better than other compression methods, which may explain the superiority of ~\\method in LongBench.\n\n\n% \\jh{Check this link: \\url{https://cs.stanford.edu/people/widom/paper-writing.html}. Make sure you answer the five questions suggested in the blog post.}\n\n% Comment out \n% Large Language Models (LLMs)~\\citep{achiam2023gpt,touvron2023llama1,touvron2023llama} are now widely applied in many natural language processing applications, including dialog systems~\\citep{vicuna2023}, document summarization~\\citep{fabbri-etal-2019-multi}, code completion~\\citep{roziere2023code}.\n\n% Deploying and inferring with LLMs in a long context requires a significant waiting time. Caching previous tokens' Key and Value states (KV) ~\\citep{waddington2013kv} is a widely adopted technique for accelerating inference, but it will consume massive extensive memory scaling linearly with the sequence length and batch size. For example, for LLaMA 2 7B, the KV cache of 100K tokens requires more than 50GB memory,\n% while 2K context requires less than 1GB memory\\citep{} (cite retrieval head paper).\n% Existing works focus on KV cache compression to reduce memory consumption.\n% H2)~\\citep{zhang2024h2o}\n% FastGen~\\citep{ge2023model} decides separate KV cache compression strategies for each head in multi-head transformers.\n% StreamingLLM~\\citep{xiao2023efficient} keeps the very few initial tokens with extreme attention scores and the local window tokens based on the observation of Attention Sink.\n% However, StreamingLLM fails in lots of \n\n% To understand the failure of Streaming, we find an interesting phenomenon of autoregressive\n% LLMs: a surprisingly large amount of attention score is allocated to the initial tokens \\jh{Some existing works also find this pattern. Make sure we don't overclaim but also highlight the unique insight. Make a clear comparison.}\n\n% \\jh{Change ``initial tokens'' to ``first few tokens''}\n% In shallow layers (i.e., layer 0 to layer 16), LLMs implicitly perform document abstraction through multi-layer transformers.\n% For each document, the context of each document increases the attention score to the initial few tokens of the document as the information flows from shallow layers to deep layers.\n% The initial tokens inside each document serve as abstraction tokens to store the knowledge of the document.\n\n% \\paragraph{Multi-Document Abstraction}\n% In middle layers (i.e., layer 16 to layer 32), LLMs implicitly perform multi-document abstraction through multi-layer transformers.\n% Specifically, the context of each document decreases the attention score of the first few tokens and increases the attention scores of some global abstractive tokens as the information flows from shallow layers to deep layers.\n\n% \\jh{It's not very natural to see the transition from the observations above to the design of our KV cache. Need some smoothing. We need a compact sentence to summarize the key property of the KV cache method which is inspired from the observation.}\n\n% \\wx{agree, revised (replace text starting from 'To understand the failure of Streaming...'): \n% Through the investigation of attention matrices in large language models (LLMs), we observed that, in addition to the 'massive attention' noted in prior studies \\citep{}, the attention scores shift from a global to a local focus, ultimately concentrating on a few tokens as one moves from lower to higher layers. This pattern suggests an aggregated information flow within the model: information is first gathered locally from the context and then concentrated into a few tokens, leading to the massive attention phenomenon.}\n% Based on the aforementioned analysis, it is intuitive to explore the application of efficient inference methods, since the LLM generates outputs solely relying on the global abstractive tokens.\n% Based on the aforementioned patterns, we argue that KV Cache pruning should consistently compress the same tokens across layers and heads.\n\n% During the decoding stage, caching previous tokens' Key and Value states (KV) consumes extensive memory \n% ~\\citep{xiao2023efficient}\n\n\n\n% Fortunately, our preliminary obse has yielded intriguing observations about the empirical\n% properties of LLMs. These findings pave the way for the potential design of an efficient KV cache:\n\n% (1) Unlike the hypothesis of previous works that XXX\\jh{summarize the prior work}, we observe that the attention matrices of LLMs increase from less than 30\\% sparse in bottom layers to over 95\\% sparse across a wide range of LLMs and tasks.\n% This may weaken the previous conclusion that only a small percentage of the KV cache is sufficient for decoding the same output token at each generation step.\n% Therefore, the required KV cache may decrease as the layer increases.\n\n% Based on the aforementioned observations, we argue that\n% (1) the \n\n\n\\section{Related Work}\n\\label{section:related_work}\n\n% \\subsection{Attention Pattern of LLMs}\n% \\jh{my overall impression after reading this section is that it's not clear what new things we bring to the community. and in which aspects? }\\wx{added several sentences in each subsection.}\n\n% \\subsection*{Interpretation of LLMs}\n% \\wx{Done with this section}\n% Previous works have explored the attention mechanism in LLMs, and it has been found that the attention matrices are usually sparse - few tokens have been attended excessively while others receiving little attention - which is also in-line with our findings. For example, \\citet{xiao2023efficient} observes attention sink, that keeping the KV of initial tokens will largely recover the performance of window attention even if they are not semantically important. Similarly, \\citet{sun2024massive} discovers massive activations, that very few activations exhibit significantly larger values than others inside LLMs (but not necessarily the first few tokens) and the values largely stay constant regardless of the input, and they function as indispensable bias terms. In another line of work, researchers found that there are certain patterns existing across different attention heads or layers. \\citet{li2024snapkv} discovers that each attention head in the model consistently focuses on specific prompt attention features during generation. And \\citet{wang2023label} reveals that label words in the demonstration examples of In-Context Learning function as anchors - semantic information aggregates into label word representations during the shallow computation layers’ processing and then the consolidated\n% information in label words serves as a reference for LLMs’ final predictions. Beyond language models, \\citet{chen2024image} identifies the inefficient attention phenomena in Large Vision-Language Models (LVLMs), that the attention computation over visual tokens is of extreme inefficiency in the deep layers.\n\n\\paragraph{Interpretation of LLMs}\nPrior research has shown that attention matrices in LLMs are typically sparse~\\citep{chen2024image,xiao2023efficient,zhang2024h2o}, focusing disproportionately on a few tokens. For instance, \\citet{xiao2023efficient} identified an ``attention sink'' phenomenon, where maintaining the Key and Value (KV) states of the first few tokens can substantially restore the performance of windowed attention, despite these tokens not being semantically crucial. Similarly, \\citet{sun2024massive} identified a ``massive activations'' pattern, where a minority of activations show significantly larger values than others within LLMs. Interestingly, these values remain relatively constant across different inputs and act as critical bias terms in the model. %\\jh{As we have Sec 3. to analyze the attention pattern in the main paper, what are the new findings to the community compared to the literature? We should make a clear distinction and show the significance of our work}\\wx{added one sentence below.}\n\nFurther explorations in this field reveal distinct patterns across various attention heads and layers. \\citet{li2024snapkv} observed that certain attention heads consistently target specific prompt attention features during decoding. Additionally, \\citet{wang2023label} discovered that in In-Context Learning scenarios, label words in demonstration examples serve as semantic anchors. In the lower layers of an \nLLM, shallow semantic information coalesces around these label words, which subsequently guide the LLMs’ final output predictions by serving as reference points. Recently,\n\\citet{wu2024retrieval} revealed that a special type of attention head, the so-called retrieval head, is largely responsible for retrieving information. Inspired by these findings that the attention mechanism exhibits varying behaviors across different layers, we discovered that ``Massive Activation'' does not consistently manifest across all layers in long context sequences; instead, it predominantly occurs in the upper layers. Additionally, we identified a novel trend of information aggregation specific to long-context inputs, which will be further explained in \\Scref{section:observation}.\n\n% Extending beyond the realm of language models, \\citet{chen2024image} reported similar inefficiencies in Large Vision-Language Models (LVLMs), particularly noting that attention processing over visual tokens becomes markedly inefficient in deeper layers. These findings across different types of models highlight a broader pattern of specific, intense focus areas within attention mechanisms, which are pivotal for the models' processing and output generation capabilities. \\jh{This paragraph on VLM seems a bit distracting. Maybe omit if space is limited.}\\wx{agree, can be removed}\n\n\n\n\n% \\subsection{LLM Acceleration}\n% \\subsection*{KV Cache Compression}\n% As \n% FastGen~\\citep{ge2023model} constructs the KV cache in an adaptive manner: evicting long-range contexts on attention heads emphasizing local contexts, discarding non-special tokens on attention heads centered on special tokens, and only employing the standard KV cache for attention heads that broadly attend to all tokens.\n% \\wx{Need to add at least snapkv, h20 } \\zc{Done}\n% SnapKV~\\citep{li2024snapkv} automatically compresses KV caches by selecting clustered important KV positions for each attention head based on their attention scores.\n% ~\\citep{zhang2024h2o} proposes Heavy Hitter Oracle (H2O), a KV cache eviction policy that dynamically retains a balance of recent and H2 tokens.\n% StreamingLLM~\\citep{xiao2023efficient} proposes an efficient framework\n% that enables LLMs trained with a finite length attention window to generalize to infinite sequence length without any fine-tuning.\n\n\\paragraph{KV Cache Compression}\nThere has been a growing interest in addressing LLMs' memory constraints on processing long context inputs. FastGen~\\citep{ge2023model} introduces an adaptive KV cache management strategy that optimizes memory use by tailoring retention tactics to the specific nature of attention heads. This method involves evicting long-range contexts from heads that prioritize local interactions, discarding non-special tokens from heads focused on special tokens, and maintaining a standard KV cache for heads that engage broadly across tokens. SnapKV~\\citep{li2024snapkv} improves efficiency by compressing KV caches via selecting/clustering significant KV positions based on their attention scores. Heavy Hitter Oracle (H2O)~\\citep{zhang2024h2o} implements a dynamic eviction policy that effectively balances the retention of recent and historically significant tokens, optimizing memory usage while preserving essential information. StreamingLLM~\\citep{xiao2023efficient} enables LLMs trained on finite attention windows to handle infinite sequence lengths without fine-tuning, thus expanding the models' applicability to broader contexts. LM-Infinite~\\citep{han2023lm} allows LLMs pre-trained with 2K or 4K-long segments to generalize to up to 200M length inputs while retaining perplexity without parameter updates.\n\nWhile these approaches have significantly advanced the efficient management of memory for LLMs, they generally apply a fixed KV cache size across all layers. In contrast, our investigations into the attention mechanisms across different layers of LLMs reveal that the attention patterns vary from layer to layer, making a one-size-fits-all approach to KV cache management suboptimal. In response to this inefficiency, we propose a novel KV cache compression method, called \\method that allocates different KV cache budgets across different layers, tailored to the unique demands and operational logic of each layer's attention mechanism. This layer-specific strategy takes a significant step toward balancing both memory efficiency and model performance, addressing a key limitation in existing methodologies.\n\n\n\n% \\section{Aggregated Information Flow}\n\\section{Pyramidal Information Funneling}\n\\label{section:observation}\n% \\wx{I rewrite this section}\\yc{Fix the correspondence between Figure2 and text, But it seems like LLaMA3 doesn't have the \"massive activation\" pattern and \"attention sink\"} \n% \\zc{Got a solution: mention llama and cite llama-1 and llama-2 report.}\n\nTo systematically understand the attention mechanism over layers in LLMs for long-context inputs, we conduct a fine-grained study focusing on the multi-document question answering (QA) task. The model is presented with multiple interrelated documents and prompted to generate an answer for the given query. The main target is to investigate how the model aggregates dispersed information within these retrieved documents for accurate responses. \n\n\\begin{figure}[ht]\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/obs.pdf}\n \\caption{\n Attention patterns of retrieval-augmented generation across layers in LlaMa~\\citep{touvron2023llama, touvron2023llama2} reveal that in the lower layers, the model exhibits a broad-spectrum mode of attention, distributing attention scores uniformly across all content. In the middle layers, attention becomes more localized within each document, indicating refined information aggregation (dotted red triangular shapes in layers 6 and 10). This culminates in the upper layers, where ``massive attention'' focuses on a few key tokens (concentrated attention bars after layer 18), efficiently extracting essential information for answers.\n % \\footnote{The attention analysis is based on LlaMa-2-7B-chat.}\n }\n \\label{figure:rag_flow}\n\\end{figure}\n\n% \\begin{figure}[ht]\n% \\centering\n% \\includegraphics[width=\\columnwidth]{Figures/layers.pdf}\n% \\caption{\n% \\zc{To be done}\n% }\n% \\label{figure:rag_flow}\n% \\end{figure}\n\nIn particular, we focus on our analysis of the LLaMa~\\citep{touvron2023llama, touvron2023llama2} and visualize the distribution and behavior of attention scores over layers. %\\jh{How do you visualize the attention in MHA? Which attention head do you select for visualization?}\\wx{\nTo assess the distinct behaviors of each multi-head self-attention layer, we compute the average attention from all heads within each layer. \\autoref{figure:rag_flow} shows the attention patterns of one QA example over six different layers (i.e., 0, 6, 12, 18, 24, and 30).\n\nWe identify an approximately uniform distribution of attention scores from the lower layers (e.g., the 0th layer). This suggests that the model operates in a broad-spectrum mode at the lower layers, aggregating information globally from all available content without prioritizing its attention on specific input segments. Notably, a distinct transition to a more localized attention pattern within each document emerges, as the model progresses to encode information at the middle layers (6th to 18th layers). In this phase, attention is predominantly directed towards tokens within the same document, suggesting a more refined aggregation of information within individual contexts.\n\n\n\nThis trend continues and intensifies in the upper layers (from the 24th to the 30th layer), where we observed the emergence of `massive attention' phenomena. In these layers, the attention mechanism concentrates overwhelmingly on a few key tokens. This pattern of attention allocation, where extremely high attention scores are registered, signifies that the model has aggregated the essential information into these focal tokens. Such behavior underscores a sophisticated mechanism by which LLMs manage and streamline complex and voluminous information, culminating in the efficient extraction of the most pertinent data points necessary for generating accurate answers.\n\n%The primary objective was for the model to synthesize the dispersed information contained within these documents to formulate a coherent and accurate response, effectively simulating a typical real-life information retrieval scenario.\n% To delve deeper into the operational dynamics of the attention mechanism in LLMs, especially when dealing with lengthy contextual inputs, we initiated a comprehensive study centered on the task of multi-document question answering (QA). This experimental setup involved presenting the model with multiple interrelated documents alongside a specific query. The primary objective was for the model to synthesize the dispersed information contained within these documents to formulate a coherent and accurate response, effectively simulating a typical real-life information retrieval scenario.\n\n% Our analysis included a detailed investigation of the distribution and behavior of attention scores across various layers of the model. We show a real example with sampled layers - 5, 10, 15, 20, 25, and 30—as illustrated in \\autoref{figure:rag_flow}.\n\n% The findings from the lower layers (specifically, the 5th layer) indicated an approximately uniform distribution of attention scores. This suggests that at this stage, the model operates in a broad-spectrum mode, capturing and assimilating information globally from all available content without prioritizing specific sections of the input. As the model progresses to the middle layers (10th to 15th layers), there is a distinct transition to a more localized approach. In this phase, attention is predominantly directed towards tokens within the same document, suggesting a more refined aggregation of information within individual contexts.\n\n\n% \\autoref{figure:rag_flow} presents the information flow inside LLMs when they generate outputs based on external resources.\n% \\paragraph{Single-Document Aggregation}\n% In shallow layers (i.e., layer 0 to layer 16), LLMs implicitly perform document abstraction through multi-layer transformers.\n% For each document, the context of each document increases the attention score to the first few tokens of each document as the information flows from shallow layers to deep layers.\n% The first few tokens inside each document serve as abstraction tokens to store the knowledge of the document.\n% \\paragraph{Multi-Document Abstraction}\n% In middle layers (i.e., layer 16 to layer 32), LLMs implicitly perform multi-document abstraction through multi-layer transformers.\n% Specifically, the context of each document decreases the attention score of the initial few tokens and increases the attention scores of some global abstractive tokens as the information flows from shallow layers to deep layers.\\jh{How can we derive this conclusion? Are you referring to the vertical bars in the figure? We should explicitly point the reader to the pattern in the figure.}\n% \\paragraph{Generation based on Global Abstractive Tokens}\n% In upper layers, the attention score to the global abstractive tokens becomes really massive that the LLMs generate outputs even solely rely on the global abstractive tokens.\n\n\n\n% Based on the aforementioned analysis, it is intuitive to explore the application of efficient inference methods, since the LLM generates outputs solely relying on the global abstractive tokens.\n% Previous work~\\citep{li2024snapkv, ge2023model} that performs separate KV cache pruning strategies across attention heads and transformer layers.\n\n% Based on the aforementioned patterns, we propose three hypotheses for KV cache prune: \\jh{If we have experimental results to verify these hypotheses, we should mention to refer the readers to the later section.}\n\n% \\begin{enumerate}[leftmargin=15pt,topsep=1pt] \\itemsep-0.2em\n% \\item \\textbf{Consistent Prune} KV Cache pruning should consistently compress the same tokens across layers and attention heads. Otherwise, the pruning will cut off the information flow inside LLMs and decrease the performance.\n% \\item \\textbf{Deep Layer leads} Middle layers know which tokens the information is aggregated, while the attention patterns of shallow layers ignore the patterns of document abstractive tokens; the attention patterns of upper layers ignore the patterns of global abstractive tokens.\n% \\end{enumerate}\n\n\n% \\jh{TODO: need more mathematical formulation.}\n% \\zc{It is done. I believe the formulation and method part need some paraphrase to make it more clear. It is too detailed and long as for now.}\n\n\\section{PyramidKV}\n\\label{section:method} \n\\subsection{Preliminaries and Problem Formulation}\n% \\label{section:problem_formulation}\n\nIn an autoregressive transformer-based LLM, the generation of the \n$i$-th token requires that the attention module computes the query, key, and value vectors for all previous $i-1$ tokens. To speed up the inference process and avoid duplicate computations, the key and value matrices are typically stored in the GPU memory. While the KV cache enhances inference speed and reduces redundant computations, it can consume significant memory when dealing with long input contexts. To optimize memory usage, a strategy called KV cache compression is proposed~\\citep{zhang2024h2o, xiao2023efficient, li2024snapkv}, which involves retaining only a minimal amount of KV cache while preserving as much information as possible.\n\n% During the decoding stage, caching previous tokens' Key and Value states (KV) consumes extensive memory, especially when the input sequence and the generation output are long.\n% KV cache compression aims to alleviate this challenge by retaining the important key and value matrix with limited KV cache.\n\n% \\jh{The notation below is a bit complicated and unclear to me. Need a bit of simplification.}\n% \\jh{Formally, we should use $\\mK\\in \\R^{n\\times d}$ for a matrix and use $K$ for a scalar}\n\nIn a language model with $m$ transformer layers, we denote the key and value matrices in the $l$-th attention layer respectively as $\\mK^l, \\mV^l \\in \\R^{n\\times d}, \\forall l\\in [0, m-1]$ when encoding a sequence of $n$ tokens. The goal of KV cache compression is to seek two sub-matrices $\\mK^l_s, \\mV^l_s \\in \\R^{k^l \\times d}$ from the full matrices $\\mK^l$ and $\\mV^l$, given a cache budget $k^l<n$ for each layer $l\\in [0, m-1]$ while maximizing performance preservation. That is, a language model with KV cache compression only uses $\\mK^l_s$ and $\\mV^l_s$ in the GPU memory for inference on a dataset $\\gD$, and obtains a similar result to a full model according to an evaluation scoring metric, i.e., $\\text{score}(\\mK^l, \\mV^l, \\gD) \\approx \\text{score}(\\mK^l_s, \\mV^l_s, \\gD)$. \n\n% \\paragraph{KV Cache Compression for A Single-layer Transformer}\n% In the context of a single-layer transformer within one attention head, let $K$ and $V$ denote the full key and value matrices, respectively, each of dimension $\\mathbb{R}^{n \\times d}$. The objective of KV cache compression is to identify and retain smaller sub-matrices $K_s \\in \\mathbb{R}^{k \\times d}$ and $V_s \\in \\mathbb{R}^{k \\times d}$, where $k$ is less than $n$ and represents the number of key-value pairs retained. This approach aims to ensure that the outputs computed using these sub-matrices closely approximate those derived from the complete $K$ and $V$ matrices.\n% Formally, we define the generative process with KV cache size for a single layer transformer.\n\n\n% $K_{\\leq n,*}$ represents the first $n$-th row of $K \\in \\mathbb{R}^{n \\times d}$ and $V_{\\leq n, *}$ represents the first $n$ rows of $V \\in \\mathbb{R}^{n \\times d}$. Let $k$ denote the budget of space and $k < n$.\n\n% The selected rows $K_s \\in \\mathbb{R}^{k \\times d}$ denotes a sub-matrix of $K \\in \\mathbb{R}^{n \\times d}$ which selects $k$ rows from $K \\in \\mathbb{R}^{n \\times d}$, and the selected $V_s \\in \\mathbb{R}^{k \\times d}$ denotes a sub-matrix of $K \\in \\mathbb{R}^{n \\times d}$ which selects $k$ rows from $V \\in \\mathbb{R}^{n \\times d}$.\n\n% % For the non-selected rows $K_d \\in \\mathbb{R}^{k \\times d}$\n% The discarded rows $K_c \\in \\mathbb{R}^{n - k \\times d}$ denotes a sub-matrix of $K \\in \\mathbb{R}^{n - k \\times d}$ which were not selected, and the discarded rows $V_c \\in \\mathbb{R}^{n - k \\times d}$ denotes a sub-matrix of $V \\in \\mathbb{R}^{n - k \\times d}$ which were not selected, we do not keep that rows in the GPU memory.\n\n% % \\begin{definition}[KV cache compression policy, informal]\n% % \\label{definition:kv_cache_compression_policy}\n\n% Let $K$ and $V$ denote the source set. Let $K_s$ and $V_s$ denote the target set.\n% % Let $k$ denotes the budget of key and value matrix space.\n% Our goal is to find a KV cache compression method that the output $i$-th token of the generative process based on $K$ and $V$ is similar to the output of the generative process based on $K_s$ and $V_s$.\n% We defined the compression policy $p: K, V \\to K_s, V_s$.\n\n% For the generation of the $i$-th token, we have\n% \\begin{itemize}[itemsep=0.1pt,topsep=0pt,leftmargin=*]\n% \\item $|K_s| = k$ and $|V_s| = k$\n% \\item The standard multi-head attention output is $o_i = D_i^{-1} \\cdot exp(Q_i \\cdot (K_i)^T)$, where \n% \\item $| S_i \\backslash S_{i-1} | \\leq 1$ or equivalently $|S_i \\cap S_{i-1}| \\geq k-1$ (we can evict at most $1$ $\\kv$ in the $\\kv$ $\\cache$)\n% \\end{itemize}\n\n% \\end{definition}\n\n\n% \\paragraph{KV cache compression for multi-layer transformers} \\wx{I don't see any difference between these two settings, I think we can remove this paragraph.}\\jh{Agreed.}\n\n% Then we switch to define the generative process with limited KV cache size for multi-layer transformers.\n\n% The cache size limitation is defined as $K = {k^0, ..., k^m}$, where $k^l < n$ denotes the cache size limitation for layer $l$ and $m$ denotes the number of layers for transformers.\n\n% For layer $l < m$, $K^l_{\\leq n,*}$ represents the first $n$-th row of $K^l \\in \\mathbb{R}^{n \\times d}$ and $V^l_{\\leq n, *}$ represents the first $n$ rows of $V^l \\in \\mathbb{R}^{n \\times d}$.\n% The selected rows $K^l_s \\in \\mathbb{R}^{k \\times d}$ denotes a sub-matrix of $K^l \\in \\mathbb{R}^{n \\times d}$ which selects $k^l$ rows from $K^l \\in \\mathbb{R}^{n \\times d}$, and the selected $V^l_s \\in \\mathbb{R}^{k \\times d}$ denotes a sub-matrix of $K^l \\in \\mathbb{R}^{n \\times d}$ which selects $k^l$ rows from $V^l \\in \\mathbb{R}^{n \\times d}$.\n\n% For layer $l < m + 1$, the discarded rows $K^l_c \\in \\mathbb{R}^{n - k \\times d}$ denotes a sub-matrix of $K^l \\in \\mathbb{R}^{n - k \\times d}$ which were not selected, and the discarded rows $V^l_c \\in \\mathbb{R}^{n - k \\times d}$ denotes a sub-matrix of $V^l \\in \\mathbb{R}^{n - k \\times d}$ which were not selected, we do not keep that rows in the GPU memory.\n\n% For layer $l < m$, let $K^l$ and $V^l$ denote the source set. Let $K^l_s$ and $V^l_s$ denote the target set.\n% % Let $k^l$ denotes the budget of key and value matrix space.\n% Our goal is to find a KV cache compression method that the output $i$-th token of the generative process based on $K^l$ and $V^l$ is similar to the output of the generative process based on $K^l_s$ and $V^l_s$.\n\n% \\end{definition}\n\n\n% \\subsection{Ineffective Greedy Algorithm}\n\n% We empirically observe that local attention, which is calculated using local statistics at every decoding step\n% by summing up the attention scores of the previous tokens, is ineffective as taking into account\n% the attention of future tokens.\n% Formally,\n\n% Fortunately, the attention scores to the previous tokens are accessible when performing KV cache compression. Therefore, we build a layer-wise dynamic compression. Formally,\n\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/method2.pdf}\n \\caption{\n Illustration of~\\method. At the lower level of the transformer, the \\method selects more keys and values based on the exhibited average attention pattern. Fewer keys and values at the higher level are selected based on the massive activation pattern, where we observe that attention scores are concentrated over local regions.}\n \\label{figure:method}\n\\end{figure}\n\n\n\\subsection{Proposed Method}\n\\label{section:method}\n\n% \\jh{Zefan, could you follow the notation in Sec 4 to polish the method section? It seems a bit complicated. Please check this link for formal writing of math equations: \\url{http://demo.clab.cs.cmu.edu/cdyer/short-guide-typesetting.pdf}}\n% \\zc{I re-write this section based on the notation. The subsection \n% as two parts of this method should be re-named.}\n\nIn this section, we introduce our method, \\method, based on the pyramidal information funneling observed across different layers in \\Scref{section:observation}. \\method consists of two steps: (1) Dynamically allocating different KV cache sizes/budgets across different layers (\\Scref{subsection:pyramid_size_allocation}); and (2) Selecting important KV vectors in each attention head for caching (\\Scref{subsection:key_and_value_selection}).\n\n\\subsubsection{KV Cache Size/Budget Allocation}\n\\label{subsection:pyramid_size_allocation}\n% \\wx{I have rewritten this part}\nPrevious work on KV cache compression~\\citep{li2024snapkv,zhang2024h2o,xiao2023efficient} often allocates a fixed KV cache size across LLM layers. However, as our analysis in \\Scref{section:observation} demonstrates, attention patterns are not identical across different layers. Particularly dense attention is observed in the lower layers, and sparse attention in higher layers. Therefore, using a fixed KV cache size across different layers may lead to suboptimal performance. These approaches may retain many unimportant tokens in the higher layers of sparser attentions while potentially overlooking many crucial tokens in the lower layers of denser attentions.\n% SnapKV~\\citep{li2024snapkv}, H2O~\\citep{zhang2024h2o} and StreamingLLM~\\citep{xiao2023efficient} apply a fixed key and value matrix cache size $k$ across multi transformer layers.\n% Based on our observation at \\Scref{section:observation}, we find that the attention sparsity of LLMs increase from lower layers to upper layers.\n% The efficiency of aforementioned methods suffers a lot, because they retaining a large number of unimportant tokens in the sparse tiop layers while missing many important tokens in the dense bottom layers.\n\nThus, we propose to increase compression efficiency by dynamically allocating the cache budgets across layers to reflect the aggregated information flow based on attention patterns.\nSpecifically, \\method allocates more KV cache to the lower layers where information is\nmore dispersed and each KV state contains less information, while reducing the KV cache in higher layers where information becomes concentrated in a few key tokens.\n\n% (within a local window---a document for instance)\n% \\jh{Did you define what ``local window'' is? Is it a fixed-size text segment? Are you referring to a document in the multi-document QA?} \n% \\zc{local window is defined and used by h2o and snapKV, They use it to represent a fixed size Key and Value cache in the last few tokens of the input sequence.} \\wx{I still feel `local' window is a bit confusing in this context, instead we call them instruction tokens (which is referred as local window in (cite), dooes it sound good?'} \n% \\zc{instruction tokens (which is referred as local window in (cite) looks good.}\n\nFollowing the common practice in KV cache compression~\\citep{li2024snapkv, xiao2023efficient}, %\\wx{cite the work with local window} \\zc{Done}, \nwe first retain the KV cache for the last $\\alpha$ tokens of the input across all layers, as these tokens have been shown to contain the most immediate task-related information, where $\\alpha$ is a hyperparameter, controlling the number of last few tokens being included in the KV cache.\n% \\jh{It's confusing. Isn't $\\alpha$ denoting the last $\\alpha$ tokens to retain?}\n% \\zc{Yes, $\\alpha$ denoting the last $\\alpha$ tokens to retain, namely the size of local window.}\nFor simplicity, we call these tokens ``\\textit{instruction tokens}'', which is also referred to as ``\\textit{local window}'' in previous literature~\\citep{zhang2024h2o, li2024snapkv, xiao2023efficient}. \n\nSubsequently, given the remaining total cache budget $k^\\text{total} = \\sum_{l \\in [0, m-1]} k^l$ that can be used over all transformer layers (noted as $m$), we first determine the cache sizes for the top and bottom layers, and use an arithmetic sequence to compute the cache sizes for the intermediate layers to form the pyramidal shape. The key intuition is to follow the attention pattern in aggregated information flow, reflecting a monotonically decreasing pattern of important tokens for attention from lower layers to upper layers. We allocate $k^0 = (2 \\cdot k^\\text{total}) / m$ for the first bottom layer, and $k^{m-1} = k^\\text{total} / (\\beta \\cdot m) - k^0$ for the top layer, where $\\beta$ is a hyperparameter to adjust the pyramid's shape. Once the cache sizes of the bottom and top layers are determined, the cache sizes for all intermediate layers are set according to an arithmetic sequence, defined as \n\\begin{align} \\label{eq:budget}\nk^l = k^{m-1} - \\frac{k^{m-1} - k^0}{m} \\times l.\n\\end{align}\n\n% \\jh{use $\\times$ for scalar product, and $\\cdot$ for vector dot product} \n\n% Formally, given total key and value matrix limitation $\\sum_{l \\leq m}$ where $m$ denotes the number of layers,\n% the total key and value cache limitation is $\\sum_{l \\in [1, m]} k^l$.\n% Our goal is to allocate the cache limitation efficiently.\n% For bottom layer $l = 1$, we apply $k^1 = (2 \\cdot \\sum_{l \\in [1, m]} k^l) / m$, which is the maximum cache limitation across transformer layers.\n% For top layer $l = m$, we apply $k^m = \\sum_{l \\in [1, m]} k^l / (\\beta * m)$, which is the minimum cache limitation across transformer layers. $\\beta$ is a super parameter.\n% % The step size is calculated by $s = $.\n% The cache size for layer $l$ is calculated as below: $k^l = k^m - ((k^m - k^1) / m) \\cdot (l - 1)$.\n% We name this KV cache compression approach with dynamic cache size by mirroring the geometric shape, named PyramidKV. \n\n\n\n% for layer $l$ in multi-layer transformers, we have\n\n% \\begin{itemize}\n% \\item \n \n% The max limitation $k^0 = 2 \\cdot k$ is applied in the bottom layer $l = 0$;\n% \\item The minimum limitation $k^{m - 1} = k / \\beta$ is applied in the top layer $l = m - 1$, where $\\beta$ is a super parameter;\n% \\item The step size of layer $l$ is larger than that of layer $l-1$ is: $s = k^{m - 1} - k^1$;\n% \\item the cache size for layer $l$ is $k^l = k^m - s \\cdot l$.\n% \\end{itemize}\n% \\wx{This is not clear to me.. need to rewrite}\n\n\n\n\\subsubsection{KV Cache Selection}\n\\label{subsection:key_and_value_selection}\n\nOnce the KV cache budget is determined for each layer, our method needs to select specific KV states for caching within each layer in LLMs. As described in the previous section, the KV cache of the last $\\alpha$ tokens, referred to as instruction tokens, are retained across all layers. Following SnapKV~\\citep{li2024snapkv}, the selection of the remaining tokens is then guided by the attention scores derived from these instruction tokens---tokens receiving higher attention scores are deemed more relevant to the generation process and are thus their KV states are prioritized for retention in the GPU cache.\n\nIn a typical LLM, the attention mechanism in each head $h$ is calculated using the formula: \n\\begin{align} \\label{eq:Al}\n \\mA^h = \\text{softmax}(\\mQ^h \\cdot (\\mK^h)^\\top / \\sqrt{d_k}),\n\\end{align}\nwhere $d_k$ denotes the dimension of the key vectors. Following~\\citep{li2024snapkv}, we utilize a pooling layer at $\\mA^h$ to avoid the risk of being misled by some massive activation scores. %\\jh{Can you write down the pooling operation here?} \\jh{Pooling along which dimension? What is the exact pooling operation? Is it a max pooing or something else? what is the output shape after pooling?}\n\nTo quantify the importance of each token during the generation process, we measure the level of attention each token receives from the instruction tokens, and use this measurement to select important tokens for KV caching. Specifically, we compute the score of selecting $i$-th token for retention in the KV cache as $s^h_i$ in each attention head $h$ by: \n\\begin{align}\\label{eq:att_score}\n s^h_i = \\sum_{j\\in [n-\\alpha,n]} \\mA^h_{ij}\n\\end{align}\nwhere $[n-\\alpha, n]$ is the range of the instruction tokens. In each layer $l$ and for each head $h$, the top $k^l$ tokens with the highest scores are selected, and their respective KV caches are retained. All other KV caches are discarded and will not be utilized in any subsequent computations throughout the generation process.\n\n% \\jh{Why do you use this score? Need a sentence to explain your design rationale }\\wx{we have it in the paragraph above, do we need to repeat and rephrase here?}\n\n% \\zc{We also apply a pooling layer, as the same at Sec 4.2 at SnapKV. So I added this sentence to show the pooling.} \n% \\jh{$s^h_i$ is a scalar, how do you perform pooling? Do you stack the scores of all tokens together to form a vector $\\vs^h\\in\\R^{n}$ and then do pooling? This should be clearly written in the equation. }\\wx{need to be more clear here}\n% \\zc{The pooling is to the attention matrix. It was a typo.} \\jh{Pooling along which dimension? What is the exact pooling operation? Is it a max pooing or something else? what is the output shape after pooling?}\n\n\n\n% Based on the allocation method at \\Scref{subsection:pyramid_size_allocation}, the cache size limitation is $k^l = k^m - s \\cdot (l - 1)$ is for layer $l$.\n% We define a local window size $\\alpha < k^l$, where $\\alpha$ is a super parameter.\n% Given $\\mQ^l \\in \\mathbb{R}^{n - \\alpha \\times d}$, $\\mK^l \\in \\mathbb{R}^{n - \\alpha \\times d}$ and $\\mV^l \\in \\mathbb{R}^{n - \\alpha \\times d}$, we calculate the multi-head attention score:\n% \\begin{align} \\label{eq:Al}\n% \\mA^l = \\text{softmax}(\\mQ^l \\cdot (\\mK^l)^\\top / \\sqrt{d_\\text{head}}),\n% \\end{align}\n% where $d_{head}$ denotes the dimension of attention heads.\n\n% Then we sum up the attention score from each query $q$:\n% \\begin{align}\\label{eq:att_score}\n% \\mS^l = \\sum_{q \\leq n} \\mA^l\n% \\end{align}\n\n% \\jh{More importantly, you should also explain why you select the sub-matrics in this way. Highlight the key intuition.}\n% Finally we could select $\\mK_{k - \\alpha}^l \\in \\mathbb{R}^{k^l \\times d}$ and $\\mV_{k - \\alpha}^l \\in \\mathbb{R}^{k^l \\times d}$ by choosing the top $k - \\alpha$ scores and corresponding positions based on $Score^l$.\n% THen the chooses $\\mK_{k - \\alpha}^l \\in \\mathbb{R}^{k^l \\times d}$ and $\\mV_{k - \\alpha}^l \\in \\mathbb{R}^{k^l \\times d}$ would be concatenated with the local window $\\mK_\\alpha^l \\in \\mathbb{R}^{k^l \\times d}$ and $\\mV_\\alpha^l \\in \\mathbb{R}^{k^l \\times d}$ to get the selected Key Value cache $\\mK_k^l \\in \\mathbb{R}^{k^l \\times d}$ and $\\mV_k^l \\in \\mathbb{R}^{k^l \\times d}$.\n\n\n\n\n\n\\section{Experiment}\n\\label{section:experiment}\n\n% Trade-off between performance and memory reduction\n\nWe conduct comprehensive experiments to evaluate the effectiveness of \\method on performance preserving and memory reduction.\nFirst, we introduce the backbone LLMs (\\Scref{subsection:llms}), the evaluation datasets (\\Scref{subsection:datasets}), the baselines in comparison (\\Scref{subsection:baselines}), and the experiment setup (\\Scref{subsection:experiment_setup}).\nNext, we report the performance in a memory-oriented scenario and a performance-oriented scenario experiments in \\Scref{subsection:results}. We also test if the model can preserve the performance on long-context inputs on the Needle-in-the-haystack experiment (\\Scref{subsection:needle_in_the_haystack}). Finally, we discuss the trade-off between memory, time, and performance in \\Scref{subsection:memory}.\n\n% trade-off between memory reduction and performance on short-context tasks in \\Scref{subsection:short_context_results} and long-context tasks in \\Scref{subsection:long_context_results}.\n% Secondly, we perform an analysis of long-context ability of ~\\method based on a needle in a haystack.\n% Thirdly, we discuss the smallest compression ratio of ~\\method to maintain generation quality in \\Scref{subsection:memory}, the end-to-end latency improvement in \\Scref{subsection:latency} and the computation cost in \\Scref{subsection:profiling}.\n\n\\subsection{Backbone LLMs}\n\\label{subsection:llms}\n\nWe compare \\method against baselines using state-of-the-art open-sourced LLMs, namely LLaMa-3-8B-Instruct, Mistral-7B-Instruct~\\citep{jiang2023mistral} and LLaMa-3-70B-Instruct. Testing examples are evaluated in a generative format, with answers generated by greedy decoding across all tasks to ensure a fair comparison.\n\n\\subsection{Datasets}\n\\label{subsection:datasets}\n\n% \\paragraph{Factual knowledge} Factual knowledge is essential for language models to serve users’ information needs. We use the Massive Multitask Language Understanding dataset (MMLU) for measuring models’ factual knowledge. MMLU consists of a set of questions about 57 subjects ranging in difficulty from elementary levels to professional levels, and its multiple-choice format makes it suitable for probing models’ knowledge without worrying about the open-endedness of generations.\n% \\paragraph{Reasoning} Reasoning is another fundamental ability for models, especially for solving complex tasks. We use the test split of Grade School Math dataset (GSM) to evaluate models’ mathematical reasoning capabilities. We also adopt Big-Bench-Hard (BBH), which contains 23 challenging tasks from Big-Bench, to evaluate models’ general reasoning capabilities.\n% \\paragraph{Multilinguality} Multilinguality acts as an important perspective of models for serving people from different backgrounds. We use TyDiQA, a multilingual question answering benchmark covering 11 typologically diverse languages for testing how much models can process non-Engish text. We use the gold-passage setup where one passage containing the reference answer is given.\n% \\paragraph{Coding} Coding is a particular application that people have used language models for and might be important for integrating these models with external tools. We use the HumanEval dataset and MBPP dataset to evaluate the models’ capability to generate functionally correct programs from docstrings. To avoid ambiguity with our human evaluation, we call this dataset Codex-Eval in this paper.\n% \\paragraph{Open-ended instruction following} While the performance on the benchmarks above quantifies the models’ ability at specific skills, it may not reflect how well the models can handle instructions from real users, which cover highly diverse requests and are often open-ended. For example, the popular ShareGPT dataset contains instances of users asking for programming help, resume formatting tips, educational role-playing, pronunciation suggestion, fanfiction writing, and more. We evaluate such open-ended instructability of models using both model-based evaluation and human evaluation, both of which consist of multiple test sets from existing studies\n% \\paragraph{Safety} Safety is of particular concern regarding the fast-developing language models to ensure the ethical and proper use of them. Following LLaMa-2, we employ ToxiGen to measure the amount of toxic language and hate speech generation across different groups when the models are prompted to do so. We also adopt TruthfulQA to measure how well models can avoid generating known falsehoods due to misconceptions or false beliefs while providing useful information.\n% \\paragraph{Long-Context Question Answering}\n\nWe use LongBench~\\citep{bai2023longbench} to assess the performance of \\method on tasks involving long-context inputs. LongBench is a meticulously designed benchmark suite that tests the capabilities of language models in handling extended documents and complex information sequences. This benchmark was created for comprehensive multi-task evaluation of long context inputs. It includes 17 datasets covering tasks such as single-document QA~\\citep{kovcisky2018narrativeqa,dasigi2021dataset}, multi-document QA~\\citep{yang2018hotpotqa,ho2020constructing}, summarization~\\citep{huang2021efficient,zhong2021qmsum,fabbri2019multi}, few-shot learning~\\citep{li2002learning,gliwa2019samsum,joshi2017triviaqa}, synthetic, and code generation~\\citep{guo2023longcoder,liu2023repobench}. The datasets feature an average input length ranging from 1,235 to 18,409 tokens (detailed average lengths can be found in~\\autoref{table:longbench}), necessitating substantial memory for KV cache management. For all these tasks, we adhered to the standard metrics recommended by LongBench~\\citep{bai2023longbench} (i.e., F1 for QA, Rouge-L for summarization, Acc. for synthetic and Edit Sim. for code generation.) We refer readers to more details at~\\autoref{appendix:evaluation}.\n% We refer the reader to ~\\autoref{appendix:evaluation} for the evaluation details. \n% can be added in the next version, we don't have time on it.\n\n% comment version\n% We use LongBench\\citep{bai2023longbench} to assess the performance of \\method on tasks involving long-context inputs. LongBench is a meticulously designed benchmark suite that tests the capabilities of language models in handling extended documents and complex information sequences. This benchmark was created for multi-task evaluation of long context inputs. It includes 17 datasets covering tasks such as single-document QA, multi-document QA, summarization, few-shot learning\\jh{of what?} \\zc{QA and summerization}, synthetic \\jh{parsing?} \\zc{synthetic is like finding the pattern in the context, i.e. counting the passages in the input. LongBench called this task synthetic task.}, and code generation. The datasets feature an average input length ranging from 8,714 to 36,418 tokens (detailed average lengths can be found in~\\autoref{table:longbench}), necessitating substantial memory for KV cache management. For all these tasks, we adhered to the standard metrics recommended by LongBench~\\citep{bai2023longbench}.\\jh{Need a brief description of the evaluation metrics} \\zc{Each dataset has its own metrics, including F1, rouge, Acc. Can we add a table of metrics in Appendix? Then we do not describe metrics in this section.} We refer the reader to the Appendix XX\\jh{add the number}for the setup details. \n\n\n\n% We calculate F1 scores for GSM8k, NQ and TQA, and use the code execution Pass@1 rate for HumanEval.\n% while we subsample some benchmarks to a reasonable size to improve the efficiency of doing chain-of-thought reasoning.\n% For short tasks including Factuality, Reasoning, Multilinguality, Coding, Open-ended Instruction Following, Safety, we use KV Cache retained ratio as the variant.\n% For Long-Context context tasks, we use KV Cache retained size as the variant, because for long-context tasks generally have very long input length with up to $16000$ tokens. In this case, most of the tokens may be not important for generation, especially for LongBench, which is a question-answering benchmark targeted at generation the answer based on a large set of passages. We would like to show the performance of KV Cache compression methods in a extremely small retained size.\n\n\n\n\\subsection{Baselines}\n\\label{subsection:baselines}\nWe compare \\method with three baselines, all of which keep the same KV cache size across different layers, with different strategies for KV cache selection.\n% We refer readers to \\autoref{appendix:baselines} for more details.\n% \\paragraph{RandomKV (RKV)} is a naive baseline that randomly selects KV cache to retain. We use a fixed cache size across Transformer layers for this baseline. This baseline represents the bottom bound of KV cache compression methods.\n\n\\paragraph{StreamingLLM (SLM)}~\\citep{xiao2023efficient} is an efficient framework that enables LLMs trained with a finite length attention window to generalize to infinite sequence length without any fine-tuning. They propose StreamingLLM based on the attention sink phenomenon that keeping the KV of the first few tokens will largely recover the performance of window attention. StreamingLLM is a competitive method to solve long-context tasks. In our experiments, to be consistent with other methods, we simply keep the KV cache of the last $\\alpha$ tokens and the first $k-\\alpha$ tokens, as suggested in the paper.\n% \\paragraph{FastGen} constructs the KV cache in an adaptive manner: evicting long-range contexts on attention heads emphasizing local contexts, discarding non-special tokens on attention heads centered on special tokens, and only employing the standard KV cache for attention heads that broadly attend to all tokens.\n\n\\paragraph{Heavy Hitter Oracle (H2O)}~\\citep{zhang2024h2o} is a KV cache compression policy that dynamically retains a balance of recent and Heavy Hitter (H2) tokens. H2O keeps a fixed cache size of the Key and Value matrix across Transformer layers. The selection process for the KV cache is driven by attention scores, specifically utilizing the average attention scores from all queries across all tokens to guide the selection.\n\n\\paragraph{SnapKV (SKV)}~\\citep{li2024snapkv} automatically compresses KV caches by selecting clustered important tokens for each attention head. This method discerns the attention patterns of the Key and Value matrices using a localized observation window positioned at the end of the prompts. However, unlike H2O, SnapKV employs a more nuanced clustering algorithm that includes a pooling layer. Additionally, SnapKV captures attention signals using patterns from a localized window (Instruction Tokens), rather than aggregating attention across all queries, allowing for more targeted and efficient compression.\n\n% The same as H2O, SnapKV also keeps a fixed cache size of the Key and Value matrix across Transformer layers, and the selection of the Key and Value matrix is also based on the attention score.\n% \\wx{not clear, need to make it clear, as it is an important baseline}\n% \\zc{Done}\n% Different from H2O, SnapKV applies a fine-grained clustering algorithm utilizing a pooling layer, and they use the attention pattern from a local window to capture the attention signal instead of using the attention from all queries.\n\n\\paragraph{FullKV (FKV)} caches all keys and values for each input token in each layer. All methods are compared to the FullKV simultaneously.\n\n% In addition to the baseline models, we also benchmark our model against the gold standard, which utilizes the full KV cache.\n% \\paragraph{DynamicKV}\\wx{cite} is a baseline of using the attention sparsity as the exclusive signal to determine the number of Key and Value vectors to retain for each layer. Layers with greater sparsity would be allocated less tickets, while layers with weaker sparsity would be allocated more tickets.\n\n\n% All the baseline models keep the same KV cache size across different layers.\n% H2O, StreamingLLM, FastGen, SnapKV, DynamicKV and RandomKV keep a same KV Cache compression size across layers. None of them have dynamic compression size across layers, so their compression may be less efficient compared to ~\\method, because their compression on top layers be redundant as only a very small number of key and value tensors retained could could build up up to 90\\% of the Attention scores. So the redundant tickets could be alleviated to bottom layers.\n\n\\subsection{Experiment Setup}\n\\label{subsection:experiment_setup}\n\n% We compare ~\\method with baselines at this same KV cache size limitation for a fair comparison.\nWe maintain a fixed constant KV cache size for each layer for the baseline methods. In contrast, \\method employs varying KV cache sizes across different layers. To ensure a fair comparison, we adjusted the average KV cache size in \\method to match that of the baseline models, to keep the total memory consumption of all methods the same.\n% For each KV cache size limitation, we ensure that the total memory consumption of all methods are the same.\nIn our experiment, we set $\\beta=20$ and $\\alpha=8$. We use the same prompt for each dataset in all the experiments.\n\n% \\zc{We need to talk about how to ensure fair comparison.}\n\n% We compare the performance of KV Cache compression methods as below\n\n\n% \\subsection{Short Context Results}\n% \\label{subsection:short_context_results}\n\n% The evaluation results of short context tasks is presented at \\autoref{table:short}. We present the evaluation results for various KV Cache size retain ratios.\n% ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. Note that the performance strengths of ~\\method is more evident in small KV Cache sizes.\n% We also notice that ~\\method generally achieves stronger performance in larger models, showing the scaling potential of ~\\method.\n\n% \\input{Tables/short_results}\n\n\n% \\subsection{Results}\n\\subsection{\\method Excels in Memory-constrained Settings}\n\\label{subsection:results}\n\n\n% \\begin{figure}\n% \\centering\n% \\includegraphics[width=1.0\\columnwidth]{Figures/results_v2.pdf}\n% \\vspace{-3mm}\n% \\caption{\n% The evaluation results from LongBench\\citep{bai2023longbench} across 64, 96, 128, 256 and 512 cache sizes.\n% The evaluation metrics are the average score of LongBench across datasets.\n% ~\\method outperforms H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv} and StreamingLLM~\\citep{xiao2023efficient}, especially in small KV cache sizes.\n% % \\jh{What are the evaluation metrics? accuracy? this should be mentioned when introducing the LongBench in Sec 6.2}\n% }\n% \\vspace{-3mm}\n% \\label{figure:results2}\n% \\end{figure}\n\n\\begin{figure}\n \\centering\n \\begin{minipage}{0.33\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/result1.pdf}\n \\end{minipage}%\n \\hfill\n \\begin{minipage}{0.33\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/result2.pdf}\n \\end{minipage}%\n \\hfill\n \\begin{minipage}{0.33\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/result3.pdf}\n \\end{minipage}\n \\vspace{-3mm}\n \\caption{The evaluation results from LongBench~\\citep{bai2023longbench} across 64, 96, 128 and 256 cache sizes at LLaMa-3-8B-Instruct (Left), Mistral-7B-Instruct (Middle) and LLaMa-3-70B-Instruct (Right).\n The evaluation metrics are the average score of LongBench across datasets.\n ~\\method outperforms H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv} and StreamingLLM~\\citep{xiao2023efficient}, especially in small KV cache sizes.}\n \\label{figure:results}\n\\end{figure}\n\n\n\n\n\n\\begin{table*}[t]\n\n\\centering\n\n% \\wx{need to label the best in each block} \n% \\jh{the font size is too small. Suggestion: 1. write abbreviations for method names, e.g., RKV -> RKV, SLM -> SLM, SKV -> SKV, and write the full name in the caption. 2. Reduce the space between columns using ``c@{\\hspace{0.05ex}}c''}\n\n\n% credit to https://arxiv.org/abs/2401.01325\n% \\scalebox{0.48}{\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\cmidrule(lr){2-17}\n&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n\n\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n% \\midrule\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\nH2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\nSLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\nOurs & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 128} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n% % RKV & 3.22 & 6.97 & 8.87 & 22.92 & 15.53 & 7.83 & 1.75 & 6.57 & 1.36 & 32.5 & 22.13 & 6.92 & 6.0 & 60.4 & 10.13 & 10.72 & 13.98 \\\\\n% SKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\textbf{51.82} & 35.50 \\\\\n% SLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\n% H2O & \\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\textbf{32.71} & 18.45 & \\textbf{20.32} & 22.02 & \\textbf{21.10} & 38.50 & 87.75 & \\textbf{39.14} & 5.83 & \\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\n% Ours & 21.40 & \\textbf{16.92} & \\textbf{33.79} & \\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\textbf{22.48} & 20.95 & \\textbf{66.50} & \\textbf{89.35} & 38.39 & \\textbf{5.92} & 69.00 & \\textbf{56.49} & 47.95 & \\textbf{37.25} \\\\\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\nSLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\nH2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\nOurs & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nFKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\nSLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\nH2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\nOurs & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n\n\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 128} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n% % RKV & 2.04 & 2.22 & 3.23 & 5.25 & 5.18 & 0.33 & 0.8 & 1.8 & 2.42 & 32.0 & 3.24 & 1.8 & 0.62 & 1.8 & 17.41 & 15.88 & 6.00 \\\\\n% SKV & 19.16 & 21.46 & 43.52 & \\textbf{38.60} & 23.35 & \\textbf{16.09} & 17.66 & 21.84 & \\textbf{21.45} & 47.50 & \\textbf{84.15} & 40.24 & 5.00 & 69.31 & \\textbf{46.98} & \\textbf{42.97} & 34.96\\\\\n% SLM & 16.57 & 14.68 & 32.40 & 30.19 & 22.64 & 12.34 & 18.08 & 18.96 & 21.98 & 43.50 & 74.22 & 29.02 & 4.50 & 29.48 & 39.23 & 36.16 & 27.57 \\\\\n% H2O & 21.20 & 21.90 & 41.55 & 33.56 & 21.28 & 12.93 & \\textbf{18.59} & \\textbf{22.61} & 19.17 & 39.00 & 82.37 & \\textbf{40.44} & \\textbf{6.00} & \\textbf{83.19} & 46.41 & 42.66 & 34.73 \\\\\n% Ours & \\textbf{21.75} & \\textbf{22.03} & \\textbf{44.32} & 34.06 & \\textbf{22.79} & 15.77 & 18.58 & 21.89 & 21.41 & \\textbf{66.00} & 83.46 & 39.75 & 4.50 & 66.90 & 46.96 & 41.28 & \\textbf{35.72} \\\\\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\nSLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\nH2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\nOurs & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\n% \\midrule\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\nSLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\nH2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\nOurs & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 128} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n% % RKV & 3.22 & 6.97 & 8.87 & 22.92 & 15.53 & 7.83 & 1.75 & 6.57 & 1.36 & 32.5 & 22.13 & 6.92 & 6.0 & 60.4 & 10.13 & 10.72 & 13.98 \\\\\n% SKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\textbf{51.82} & 35.50 \\\\\n% SLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\n% H2O & \\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\textbf{32.71} & 18.45 & \\textbf{20.32} & 22.02 & \\textbf{21.10} & 38.50 & 87.75 & \\textbf{39.14} & 5.83 & \\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\n% Ours & 21.40 & \\textbf{16.92} & \\textbf{33.79} & \\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\textbf{22.48} & 20.95 & \\textbf{66.50} & \\textbf{89.35} & 38.39 & \\textbf{5.92} & 69.00 & \\textbf{56.49} & 47.95 & \\textbf{37.25} \\\\\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n% RKV & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\\\\nSKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \nSLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \nH2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \nOurs & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n\n\n\n\n\n\n\\arrayrulecolor{black}\\bottomrule\n\\end{tabular}\n}\n\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\n\\label{table:longbench}\n\\vspace{-3mm}\n\\end{table*}\nThe evaluation results from LongBench~\\citep{bai2023longbench} are shown in \\autoref{table:longbench} and \\autoref{figure:results}.\nIn \\autoref{figure:results}, we report the average score across datasets for 64, 96, 128, and 256 case sizes.\nIn \\autoref{table:longbench}, we report the results for two different KV cache sizes with 64 and 2048. These two sizes represent two distinct operational scenarios---the memory-efficient scenario and the performance-preserving scenario, respectively for a trade-off between memory and model performance. \nIn \\autoref{appendix:results}, we report the results of KV cache sizes with 64, 96, 128 and 2048.\n\nOverall, \\method preserves the performance with only 12\\% of the KV cache and it consistently surpasses other method across a range of KV cache sizes and different backbone models, with its performance advantages becoming particularly pronounced in memory-constrained environments where only about 0.7\\% of the KV cache from the prompt is retained. Upon examining specific tasks, \\method demonstrates a notably superior performance on the TREC task, a few-shot question answering challenge. This suggests that the model effectively aggregates information from the few-shot examples, highlighting the potential for further investigation into in-context learning tasks.\n\nNotably, we initially observe the pyramidal attention patterns from the visualization analysis on the multi-document QA task (\\autoref{figure:rag_flow}), but the pyramid heuristic has demonstrated its effectiveness on a range of other LongBench tasks (e.g., single-document QA, In-Context Learning), suggesting its promising generalizability beyond multi-document QA.\n% ~\\method preserves the performance with only 11\\% of the KV cache. \n\n\nThe performance advantage of \\method increases as the KV cache memory decreases. By focusing on optimizing budget allocation across layers, \\method accurately allocates resources in memory-constrained scenarios, ensuring that retained information is effectively preserved to maintain model performance. Moreover, as in long bench results shown in \\autoref{table:longbench}, even in the performance-preserving scenario (i.e., KV cache size = 2048), \\method still improves the performance over baseline methods and even outperforms the performance of FullKV.\n\n\n\n\n\n\n\n% Taking a win rate over 45\\% as little-to-no quality regression, ~\\method can achieve $\\sim$40\\% memory reduction in LLaMa 1-65B, $\\sim$30\\% in LLaMa 1-30B, $\\sim$20\\% in LLaMa 1-13B and LLaMa 1-7B. \n\n\n\n\\subsection{\\method Preserves the Long-Context Understanding Ability}\n\\label{subsection:needle_in_the_haystack}\n% \\jh{Key take-away message for the subsection title.}\n% \\zc{Done}\n\n% We perform Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test to see how \\method improves the long-context understanding of LLMs test in-context retrieval ability of long context LLMs\n\n\nWe conduct the \"Fact Retrieval Across Context Lengths\" (Needle In A Haystack) experiment~\\citep{liu2023lost,fu2024data}, which is a dataset designed to test whether a model can find key information in long input sequences, to evaluate the in-context retrieval capabilities of LLMs when utilizing various KV cache compression methods. For this purpose, we employ \\textbf{LlaMa-3-8B-Instruct} and \\textbf{LlaMa-3-70B-Instruct} as our base, with context lengths extending up to 8k. We compared several KV cache compression techniques (\\method, SnapKV~\\citep{li2024snapkv}, and H2O~\\citep{zhang2024h2o}) at cache sizes of \\textbf{128} and full cache. The results, presented in \\autoref{figure:needle_llama} \\footnote{Additional results with 64, 96 and 128 KV cache sizes with \\textbf{LlaMa-3-8B-Instruct} at 8k context length, \\textbf{LlaMa-3-70B-Instruct} at 8k context length, and \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} at 32k context length are available in \\autoref{appendix:needle}}. The results demonstrate that with only 128 KV cache retained, \\method effectively maintains the model's ability to understand short contexts, and shows only modest degradation for longer contexts. In contrast, other KV cache compression methods significantly hinder the performance of LLMs. Notably, for the larger model (\\textbf{LlaMa-3-70B-Instruct}), \\method achieves 100.0 Acc. performance, matching the results of FullKV, thereby demonstrating its ability to preserve long-context comprehension with a substantially reduced KV cache.\n\n\n% We perform Fact Retrieval Across Context Lengths (``Needle In A HayStack'')~\\citep{liu2023lost,fu2024data} to test the in-context retrieval ability of LLMs after leveraging different KV cache methods. \n% Specifically, we use \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} as the base model, with context length up to \\textbf{32k}. We compare KV cache compression methods (\\method, SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o}) with cache size 64 and the full cache, and the results are shown in \\autoref{figure:needle}. (More experiment results with different KV cache size can be found in \\autoref{appendix:needle})\n% The results show that \\method can preserve the model's long context understanding ability significantly more than other KV cache compression methods significantly hurt the performance of LLMs in the evaluation. \n\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_main.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} and \\textbf{LlaMa-3-70B-Instruct} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n \\textbf{PyramidKV with 128 KV cache size achieves the same 100.0 Acc. performance compared with FullKV with 8k context size for LLaMA-3-70B-Instruct.}\n }\n \\label{figure:needle_llama}\n\\end{figure}\n% final score: standard: 0.650 pyramid: 0.626 snapkv: 0.573\n\n% \\begin{figure}\n% \\centering\n% \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_64.pdf}\n% \\caption{\n% Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with \\textbf{32k} context size in \\textbf{64} KV cache size.\n% The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n% % (a) represents the results of Full KV cache size. \n% % (b) represents the results of ~\\method.\n% % (c) represents the results of SnapKV.\n% ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n% % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n% % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n% }\n% \\label{figure:needle_mistral}\n% \\end{figure}\n\n\n\n\n\n\n\\subsection{~\\method Significantly Reduces Memory with Limited Performance Drop}\n\\label{subsection:memory}\n% \\jh{Key take-away message for the subsection title.}\n% \\zc{Done}\n\nIn this section, we study how sensitive the methods are with different sizes of KV cache. \nWe report the KV cache memory reduction in Table \\ref{tab:memory_reduction}.\nWe evaluate the memory consumption of LLaMa-3-8B-Instruct.\nSpecifically, we evaluate the memory consumption of all methods with a fixed batch size of 1, a sequence length of 8192, and model weights in fp16 format.\nWe observe that \\method substantially reduces the KV cache memory across different numbers of cache sizes.\n\nWe also present that the allocation strategy and score-based selection add minimal complexity in the inference phase compared to the computation required for next-token predictions as~\\autoref{appendix:inference_overhead}.\n\n\n\\begin{table*}[h]\n\\small\n\\centering\n\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{ccc|cccccc}\n\\toprule\n cache size & Memory & Compression Ratio & QMSum & TREC & TriviaQA & PCount & PRe & Lcc \\\\\n\n\\midrule\n64 & 53M & 0.8\\% & 21.65 & 58.00 & 88.31 & 5.23 & 69.50 & 52.61 \\\\ \n128 & 107M & 1.6\\% & 22.48 & 66.50 & 89.35 & 5.92 & 69.00 & 56.49 \\\\ \n256 & 214M & 3.1\\% & 22.69 & 71.00 & 90.48 & 5.83 & 69.25 & 56.94 \\\\\n512 & 428M & 6.3\\% & 22.80 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\n1024 & 856M & 12.5\\% & 22.55 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\n2048 & 1712M & 25.0\\% & 22.55 & 72.00 & 90.56 & 5.58 & 69.25 & 56.79 \\\\\nFull & 6848M & 100.0\\% & 23.30 & 73.00 & 90.56 & 5.22 & 69.25 & 58.76 \\\\\n\n\n\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Memory reduction effect and benchmark result by using \\method. We conducted a comparison of memory consumption between the Llama-3-8B-Instruct model utilizing the Full KV cache and the Llama-3-8B-Instruct model compressed with the \\method.\n}\n\n\n\n\\label{tab:memory_reduction}\n\\vspace{-3mm}\n\\end{table*}\n\n% 64 17150\n% 128 17132\n% 256 17122\n% 512 17336\n\n\n% step 214/256\n\n\n\n\n\n\n\n\n\n\n% \\subsection{End-to-end Latency Improvement}\n% \\label{subsection:latency}\n\n% \\input{Tables/latency}\n\n% \\subsection{Profiling Cost}\n% \\label{subsection:profiling}\n\n% \\input{Tables/profiling}\n\n% We implement a sparsity kernel for KV-cache compression and present the end-to-end latency improvement in Table.\n% For the Full-cache baseline, we use the widely used Hugging Face Accelerate (HF).\n\n% In the experiment, we record the total duration in seconds, measured from the start of prompt encoding, until the end of generation as the end-to-end latency.\n\n% For ~\\method, we implemented a customized kernel to handle the KV cache pruning operation. Specifically, we adapt the kernel from Deepspeed by adding the KV cache sparsity operation. All methods are tested on the same Nvidia V100 GPUs.\n\n% As shown in Table, we can observe that ~\\method achieves significant end-to-end speed-up across all the generation settings. For the least significant case, Fastgen can have a decent 16.04\\% latency improvement over the full-cache baseline on a short generation length of 512. In the best cases, we can achieve up to 55.0\\% latency reduction with Fastgen at a generation length of 16k.\n\n% We can also observe that the relative speedup is greater with longer generation length. For example, given $batch\\_size = 1$, FastGen’s relative speed-up rises from $16.04\\%$ to $55.0\\%$, as the generation length grows from $512$ to $16k$. The tendency can also be observed in other batch settings.\n\n% This analysis confirms that FastGen can achieve major speed-up in real development, especially in long generation settings. \n\n\n\n% \\input{Files/6_Discussion}\n\\section{Conclusion}\n\\label{section:conclusion}\nIn this study, we investigate the intrinsic attention patterns of Large Language Models (LLMs) when processing long context inputs. Our empirical analysis leads us to discover the existence of Pyramidal Information Funneling in the attention across layers: it distributes information broadly in lower layers, increasingly concentrates it within specific contexts, and ultimately focuses on critical tokens in higher layers with massive activation or attention sink. Motivated by this discovery, we design a novel KV cache compression approach \\method that utilizes this information flow pattern. It varies KV cache sizes across layers, uniquely designed to complement the attention behavior observed across different layers. By leveraging the Pyramidal Information Funneling into KV cache compression design, our method excels in memory-constrained settings, preserves long-context understanding ability, and significantly reduces memory usage with minimal performance trade-offs compared to the baselines.\n\n\n\n% employs a pyramidal sizing strategy for KV cache, which is tailored to the intrinsic behavior of the attention module.\n% % Experiments show that PyramidKV\n\n % Our experimental evaluations, conducted using the LongBench benchmark, demonstrate that \\method achieves performance comparable to models with a full KV cache while only retaining 11.7\\% of the KV cache, thereby significantly reducing memory usage by 75\\%. In scenarios that prioritize memory efficiency—where only 1.6\\% of the KV cache is maintained—\\method outperforms other KV cache compression techniques, delivering up to a 32.33\\% absolute improvement on specific tasks.\n \n% Looking ahead, there is potential to refine KV Cache Compression even further by dynamically adjusting it based on real-time analysis of the attention matrices, ensuring that the compression method remains perfectly aligned with the shifting patterns of attention within LLMs.\n\n% In this work, we study the intrinsic attention patterns of Large Language Models (LLMs) when they answer questions based on long-context documents.\n% We discover that LLMs implicitly perform information aggregation through multi-layer transformers.\n% In shallow layers, the information flows from the context to the initial tokens for each document; in mature layers, the information flows from the initial tokens for each document to some abstract tokens. In the top layer, LLMs generate outputs that almost solely rely on some global abstractive tokens with massive attention scores.\n% Based on the aforementioned study, we propose a plug-and-play method inference accelerate method ~\\method to perform KV cache compression.\n% Different from the KV cache compression that retains the size of the maintained key and value vectors the same across Transformer layers, we conduct a dynamic KV Cache compression method that \n% targeted profiling to discern the intrinsic structure of attention modules. \n% ~\\method is xxx times faster than full KV cache technique while maintaining the same performance across LLM series (LlaMa and Mistral), sizes ($7$B, $13$B and $70$B) and architectures (Dense and MoE).\n% Our experiments also demonstrate that ~\\method is effective and efficient in streaming applications.\n\\bibliographystyle{plainnat}\n\\bibliography{reference}\n\n% \\maketitle\n\\appendix\n% \\section{Limitations}\n% \\label{section:limitations}\n\n% Our study on KV cache compression, despite its advances, faces several limitations.\n% Our cache size allocation does not dynamically allocate the cache size based on the attention score, so the allocation would inevitably be sub-optimal.\n% Looking ahead, there is potential to refine KV Cache Compression even further by dynamically adjusting it based on real-time analysis of the attention matrices, ensuring that the compression method remains perfectly aligned with the shifting patterns of attention within LLMs.\n\\clearpage\n\\newpage\n\n\\section{Limitations}\n\\label{section:limitations}\nOur experiments were limited to three base models: LLAMA-3-8B-Instruct, LLAMA-3-70B-Instruct and Mistral-7B-Instruct. While these models demonstrated consistent trends, the robustness of our findings could be enhanced by testing a broader array of model families, should resources permit. Additionally, our research was conducted exclusively in English, with no investigations into how these findings might be transferred to other languages. Expanding the linguistic scope of our experiments could provide a more comprehensive understanding of the applicability of our results globally.\nBased on our results at LongBench and Needle-in-a-HayStack experiment, PyramidKV generally works decently in most of the language tasks (i.e., Single-Document QA, Multi-Document QA, Summerization, Few-Shot In-Context Learning, etc.). Although we observe that PyramidKV performs better in some tasks (i.e., Few-Shot In-Context Learning) compared with some other tasks (i.e., Summerization), we have not observed cases that the decoding result collapses at some tasks. This remains a new topic for future work to explore. \n\n\\section{Future Work}\n\\label{section:future_work}\nOur investigation on PyramidKV highlights considerable opportunities for optimizing KV cache compression by adjusting the number of KV caches retained according to the distinct attention patterns of each layer (or even for each head). For instance, the retention of KV cache for each layer could be dynamically modified based on real-time analysis of the attention matrices, ensuring that the compression strategy is consistently aligned with the changing attention dynamics within LLMs. Furthermore, our experiments indicate that PyramidKV significantly surpasses other methods in few-shot learning tasks, suggesting promising applications of KV cache in in-context learning. This approach could potentially enable the use of more shots within constrained memory limits.\n% Due to the resource limits, we only conduct experiments on two base models, LLAMA-3-8B-Instruct and Mistral-7B-Instruct. Although both models show the same trend, it could be more solid to conduct experiments on more model families if there is sufficient resource. In addition, all the experiments are in English only, no explorations are conducted in other languages.\n% Our study on KV cache compression, despite its advances, faces several limitations.\n% Our cache size allocation does not dynamically allocate the cache size based on the attention score, so the allocation would inevitably be sub-optimal.\n% % Looking ahead, there is potential to refine KV Cache Compression even further by dynamically adjusting it based on real-time analysis of the attention matrices, ensuring that the compression method remains perfectly aligned with the shifting patterns of attention within LLMs.\n\n\\section{Details of Evaluation}\n\\label{appendix:evaluation}\n\n\nWe use LongBench~\\citep{bai2023longbench} to assess the performance of \\method on tasks involving long-context inputs. LongBench is a meticulously designed benchmark suite that tests the capabilities of language models in handling extended documents and complex information sequences. This benchmark was created for multi-task evaluation of long context inputs.\n\nWe present the details of metrics, language and data for LongBench at \\autoref{table:stat}. \n\nWe run all the experiments on NVIDIA A100.\n\n\n\\begin{table}[htbp]\n\\centering \n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{llrccc}\n\\toprule\nDataset & Source & Avg len & Metric & Language & \\#data \\\\\n\\midrule\n\\emph{Single-Document QA} \\\\\nNarrativeQA & Literature, Film & 18,409 & F1 & English & 200 \\\\\nQasper & Science & 3,619 & F1 & English & 200 \\\\\nMultiFieldQA-en & Multi-field & 4,559 & F1 & English & 150 \\\\\n\\midrule\n\\emph{Multi-Document QA} \\\\\nHotpotQA & Wikipedia & 9,151 & F1 & English & 200 \\\\\n2WikiMultihopQA & Wikipedia & 4,887 & F1 & English & 200 \\\\\nMuSiQue & Wikipedia & 11,214 & F1 & English & 200 \\\\\n\\midrule\n\\emph{Summarization} \\\\\nGovReport & Government report & 8,734 & Rouge-L & English & 200 \\\\\nQMSum & Meeting & 10,614 & Rouge-L & English & 200 \\\\\nMultiNews & News & 2,113 & Rouge-L & English & 200 \\\\\n\\midrule\n\\emph{Few-shot Learning} \\\\\nTREC & Web question & 5,177 & Accuracy (CLS) & English & 200 \\\\\nTriviaQA & Wikipedia, Web & 8,209 & F1 & English & 200 \\\\\nSAMSum & Dialogue & 6,258 & Rouge-L & English & 200 \\\\\n\\midrule\n\\emph{Synthetic Task} \\\\\nPassageCount & Wikipedia & 11,141 & Accuracy (EM) & English & 200 \\\\\nPassageRetrieval-en & Wikipedia & 9,289 & Accuracy (EM) & English & 200 \\\\\n\\midrule\n\\emph{Code Completion} \\\\\nLCC & Github & 1,235 & Edit Sim & Python/C\\#/Java & 500 \\\\\nRepoBench-P & Github repository & 4,206 & Edit Sim & Python/Java & 500 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\caption{An overview of the dataset statistics in LongBench~\\citep{bai2023longbench}. `Source' denotes the origin of the context. `Accuracy (CLS)' refers to classification accuracy, while `Accuracy (EM)' refers to exact match accuracy.}\n\\label{table:stat}\n\\end{table}\n\n\n% \\section{Baselines}\n% \\label{appendix:baselines}\n\n\\section{Handle Rotary Embedding after Tokens are Removed in~\\method}\n\nWe keep the rotary embedding unchanged after tokens are removed, so that LLMs can still capture the exact position information even if the tokens are removed. StreamingLLM~\\citep{xiao2023efficient} shows that rolling kv cache with the correct relative position is crucial for maintaining performance. This is because StreamingLLM is designed to mainly handle unlimited context sizes, where contexts exceed the LLM’s fixed context length. Without changing the rotary embedding after token removal, LLMs would receive rotary embedding of a non-monotonic position sequence. For example, after the first KV cache compression, LLMs might receive the input position embedding as [$0, 1, 2, 3, 3096, 3097, \\cdots, 4096$], and the position embedding of the generated sequences could be [$1005, 1006, 1007, \\cdots$]. The position sequence of [$0, 1, 2, 3, 3096, …, 4096, 1005, 1006, 1007, \\cdots$] is a non-monotonic sequence, which may negatively hurts the performance. In contrast, our targeting settings will not process unlimited context size. For example, given a input sequence of $4012$ length, after KV cache compression, the position sequence would be [$0, 4, 6, 16, \\cdots, 3927, 3987, 4012$], and the position sequence of the generated tokens would be [$4013, 4014, \\cdots$]. By keeping the rotary embedding unchanged after the tokens are removed, the LLM avoids non-monotonic position sequences, and the LLM can capture the exact position information even if the tokens are shifted. Our preliminary results show that rolling KV cache with the correct relative position will slightly decrease the performance.\n\n\n\\section{Ablation Study}\n\n\\subsection{Hyper Parameter $\\alpha$}\n\nWe present the study of $\\alpha$ for LlaMa-3-8B-Instruct in 128 KV cache size budget at~\\autoref{table:ablation_step_a}.We find that a small alpha value (i.e., 8, 16) leads to better performance than a larger alpha value (i.e., 24, 32, 40, 48).\n\n\n\n\\begin{table*}[htbp]\n\n\\centering\n\n\n\n% credit to https://arxiv.org/abs/2401.01325\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{4}{*}{$\\alpha$} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & Avg. \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\midrule\n\n8 & 21.40 & 16.92 & 31.62 & 38.45 & 28.72 & 18.59 & 19.96 & 22.49 & 20.96 & 66.50 & 89.35 & 38.43 & 5.92 & 69.00 & 57.86 & 51.80 & 37.37 \\\\ \n16 & 23.37 & 16.21 & 33.93 & 38.24 & 27.28 & 20.57 & 19.71 & 21.93 & 20.86 & 60.00 & 88.75 & 38.34 & 5.48 & 69.12 & 57.84 & 53.42 & 37.19 \\\\ \n24 & 22.85 & 14.51 & 32.26 & 38.38 & 28.36 & 20.33 & 19.55 & 21.72 & 20.72 & 54.50 & 88.71 & 38.46 & 5.48 & 69.50 & 56.83 & 53.65 & 36.61 \\\\ \n32 & 23.01 & 14.54 & 31.68 & 38.86 & 29.90 & 19.16 & 19.20 & 21.83 & 20.52 & 49.50 & 87.01 & 38.01 & 5.75 & 69.50 & 57.02 & 54.54 & 36.25 \\\\ \n40 & 21.70 & 13.06 & 30.14 & 36.78 & 27.34 & 18.88 & 18.72 & 21.37 & 19.79 & 44.00 & 87.74 & 38.43 & 6.08 & 69.25 & 56.11 & 53.89 & 35.21 \\\\ \n48 & 21.51 & 12.30 & 29.77 & 39.04 & 26.76 & 17.97 & 18.65 & 21.20 & 20.29 & 44.50 & 87.73 & 38.44 & 5.51 & 69.25 & 56.73 & 53.88 & 35.22 \\\\ \n\n\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Ablation on $\\alpha$.}\n\\label{table:ablation_step_a}\n\\end{table*}\n\\subsection{Hyper Parameter $\\beta$}\n\nOne topic we want to analyze for our ablation study is the selection of $\\beta$, which can determine the staircase. The smaller $\\beta$ is, the gentler the staircase is; the larger $\\beta$ is, the steeper the staircase is. We want to investigate the effect of $\\beta$ step size on the final result. Results on 128 KV cache size and LlaMa-3-8B-Instruct are shown in \\autoref{table:ablation_step_b}. The results at \\autoref{table:ablation_step_b} show that using a relatively small value of $\\beta$ yields better outcomes, and~\\method is generally robust to the selection of $\\beta$.\n\n\n\n\\begin{table*}[htbp]\n\n\\centering\n\n\n\n% credit to https://arxiv.org/abs/2401.01325\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{4}{*}{$\\beta$} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & Avg. \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\midrule\n20 & 21.40 & 16.92 & 33.79 & 39.73 & 28.72 & 18.59 & 19.86 & 22.48 & 20.95 & 66.50 & 89.35 & 38.39 & 5.92 & 69.00 & 56.49 & 47.95 & 37.25 \\\\\n18 & 21.71 & 16.24 & 33.59 & 39.89 & 27.94 & 18.38 & 19.76 & 22.32 & 21.20 & 66.50 & 88.98 & 38.93 & 5.46 & 69.50 & 56.47 & 49.23 & 37.25 \\\\\n16 & 21.74 & 14.86 & 33.64 & 39.18 & 28.17 & 18.77 & 19.57 & 22.25 & 21.48 & 66.50 & 89.69 & 38.87 & 5.82 & 69.50 & 57.02 & 50.11 & 37.32 \\\\\n14 & 22.53 & 16.31 & 33.50 & 40.50 & 28.15 & 19.26 & 19.66 & 22.39 & 21.38 & 65.50 & 90.02 & 38.56 & 5.75 & 69.50 & 57.51 & 49.71 & 37.51 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Ablation on $\\beta$.}\n\\label{table:ablation_step_b}\n\\end{table*}\n\n% \\subsection{Attention from local window or global, H2 and Local}\n\n% Another topic we are interested in is the calculation method of attention and the ablation about attention-based selection and local window selection. The selection of vectors based on attention can be done through the attention of other tokens within a local window, or through the attention of all queries to all tokens.\n% We want to explore which type of attention is a more effective signal for selection,\n% % The key and value tensors selected based on attention are heavy hitters, \n% and we hope to analyze the impact of attention-based selection and the local window on the results.\n% Results show that local window and attention-based selection are both needed for a good performance, and the attention calculation based on local window or not make minor difference.\n\n% \\input{Tables/ablation_attention}\n\n\\section{License}\n\\label{appendix:license}\nLongBench: MIT\n\n\n\n\\section{PyramidKV will cause minimal extra inference overhead.}\n\\label{appendix:inference_overhead}\n\nThe allocation strategy and score-based selection add minimal complexity in the inference phase compared to the computation required for next-token predictions as~\\autoref{table:inference_overhead}. Each row shows the setting of using a specific “[Prompt length, Generation length]” combination. We show the inference speed comparison between total inference time, time for allocation strategy and time for score-based selection on LlaMa-3-8B-Instruct. Each cell is the latency measured in seconds. Furthermore, our budget allocation can be calculated before inference, requiring only a one-time computation. Thus, PyramidKV will cause minimal extra inference overhead.\n\n\n% \\include{Tables/inference_overhead}\n\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\begin{tabular}{ccccccccc}\n\\toprule\n\\textbf{Prompt Length} & \\textbf{Generation Length} & \\textbf{Inference Time} & \\textbf{Allocation Time} & \\textbf{Selection Time} \\\\\n\\midrule\n512&512 & 18.26 & 0.0000003 & 0.0194 \\\\\n512&1024 & 34.69 & 0.000002 & 0.0133 \\\\\n512&2048 & 70.69 & 0.000003 & 0.013 \\\\\n512&4096 & 138.62 & 0.000005 & 0.013 \\\\\n1024&512 & 17.32 & 0.000002 & 0.0131 \\\\\n1024&1024 & 34.67 & 0.000002 & 0.01288 \\\\\n1024&2048 & 70.21 & 0.000005 & 0.01296 \\\\\n1024&4096 & 138.61 & 0.000003 & 0.01297 \\\\\n2048&512 & 17.48 & 0.000004 & 0.0128 \\\\\n2048&1024 & 34.78 & 0.000006 & 0.0129 \\\\\n2048&2048 & 69.50 & 0.000003 & 0.01297 \\\\\n2048&4096 & 138.59 & 0.000003 & 0.013 \\\\\n4096&512 & 17.58 & 0.000002 & 0.013 \\\\\n4096&1024 & 34.93 & 0.000004 & 0.0129 \\\\\n4096&2048 & 69.65 & 0.000002 & 0.013 \\\\\n4096&4096 & 138.87 & 0.000002 & 0.013 \\\\\n\\bottomrule\n\\end{tabular}\n\\caption{Extra inference overhead of~\\method }\n\\label{table:inference_overhead}\n\\end{table}\n\n\\section{Inference Speed Comparison}\n\\label{appendix:inference_speed_comparison}\n\n\\method does not require extra computation time for budget allocation at inference by design. We show the inference speed comparison between~\\method and baselines on LlaMa-3-8B-Instruct as~\\autoref{table:inference_speed_comparison}. Each row shows the setting of using a specific “[Prompt length, Generation length]” combination. Each cell is the latency measured in seconds.~\\method does not sacrifice the speed.~\\method provides performance improvement and memory saving while runs at a comparable speed compared with baselines (i.e. SnapKV~\\citep{li2024snapkv}, StreamingLLM~\\citep{xiao2023efficient} and H2O~\\citep{zhang2024h2o}). That’s because the allocation strategy requires very limited additional complexity in the inference/generation phase compared with computation required for generation as~\\autoref{appendix:inference_overhead}.\n\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\begin{tabular}{ccccccc}\n\\toprule\n\\textbf{Prompt Length} & \\textbf{Generation Length} & \\textbf{H2O} & \\textbf{SnapKV} & \\textbf{StreamingLLM} & \\textbf{PyramidKV} \\\\ \n\\midrule\n512&512 & 18.47 & 18.25 & 18.96 & 18.26 \\\\\n512&1024 & 35.10 & 34.76 & 36.20 & 34.69 \\\\\n512&2048 & 70.21 & 69.60 & 72.35 & 70.69 \\\\ \n512&4096 & 140.80 & 139.42 & 146.37 & 138.62 \\\\\n1024&512 & 17.63 & 17.34 & 18.12 & 17.32 \\\\\n1024&1024 & 35.16 & 34.61 & 36.17 & 34.67 \\\\\n1024&2048 & 71.02 & 69.17 & 72.37 & 70.21 \\\\\n1024&4096 & 140.51 & 138.83 & 146.09 & 138.61 \\\\ \n2048&512 & 17.64 & 19.54 & 18.22 & 17.48 \\\\ \n2048&1024 & 35.09 & 34.76 & 36.29 & 34.78 \\\\ \n2048&2048 & 70.84 & 69.56 & 72.46 & 69.50 \\\\ \n2048&4096 & 140.16 & 139.55 & 145.22 & 138.59 \\\\ \n4096&512 & 17.75 & 17.67 & 18.40 & 17.58 \\\\ \n4096&1024 & 35.20 & 35.08 & 36.46 & 34.93 \\\\ \n4096&2048 & 70.02 & 69.26 & 72.58 & 69.65 \\\\ \n4096&4096 & 139.87 & 138.57 & 144.98 & 138.87 \\\\ \n\\bottomrule\n\\end{tabular}\n\\caption{Performance comparison across different configurations and methods.}\n\\label{table:inference_speed_comparison}\n\\end{table}\n\n\n\n\\section{\\method Excels in all KV Cache Size Limitation}\n\\label{appendix:results}\n\n\n\nThe evaluation results from LongBench\\citep{bai2023longbench} are shown in \\autoref{table:longbench_appendix_llama3_8b}, \\autoref{table:longbench_appendix_mistral}, and\\autoref{table:longbench_appendix_llama3_70b}.\nWe report the results using LlaMa-3-8B-Instruct, LlaMa-3-70B-Instruct and Mistral-7B-Instruct\\citep{jiang2023mistral} for different KV cache sizes.\n\nOverall, \\method consistently surpasses other method across a range of KV cache sizes and different backbone models, with its performance advantages becoming particularly pronounced in memory-constrained environments. Upon examining specific tasks, \\method demonstrates a notably superior performance on the TREC task, a few-shot question answering challenge. This suggests that the model effectively aggregates information from the few-shot examples, highlighting the potential for further investigation into in-context learning tasks.\n\n\n\n\n\\begin{table*}\n\n\\centering\n\n% \\wx{need to label the best in each block} \n% \\jh{the font size is too small. Suggestion: 1. write abbreviations for method names, e.g., RKV -> RKV, SLM -> SLM, SKV -> SKV, and write the full name in the caption. 2. Reduce the space between columns using ``c@{\\hspace{0.05ex}}c''}\n\n\n% credit to https://arxiv.org/abs/2401.01325\n% \\scalebox{0.48}{\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\cmidrule(lr){2-17}\n&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n\n\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV & 25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 04.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\nH2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\nSLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\nOurs & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 96} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 20.45 & 10.34 & 31.84 & 37.85 & 28.65 & \\textbf{18.52} & 17.90 & 21.26 & 19.07 & 41.50 & 86.95 & 37.82 & 5.08 & 69.12 & 54.69 & \\textbf{51.31} & 34.51 \\\\\nH2O & 21.55 & 11.21 & 28.73 & 37.66 & 30.12 & 18.47 & 19.57 & 21.57 & 20.44 & 38.50 & \\textbf{87.63} & \\textbf{38.47} & 5.60 & 69.00 & 54.51 & 50.16 & 34.57 \\\\\nSLM & 18.67 & 8.43 & 24.98 & 38.35 & \\textbf{30.59} & 16.37 & 17.33 & 19.84 & 18.41 & 41.00 & 73.92 & 29.38 & 5.80 & \\textbf{69.50} & 47.15 & 45.61 & 31.58 \\\\\nOurs & \\textbf{21.67} & \\textbf{15.10} & \\textbf{33.50} & \\textbf{39.73} & 26.48 & 17.47 & \\textbf{19.64} & \\textbf{22.28} & \\textbf{20.49} & \\textbf{61.50} & 87.38 & 38.18 & \\textbf{6.00} & 69.25 & \\textbf{55.30} & 46.78 & \\textbf{36.29} \\\\\n\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 128} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\textbf{51.82} & 35.50 \\\\\nH2O & \\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\textbf{32.71} & 18.45 & \\textbf{20.32} & 22.02 & \\textbf{21.10} & 38.50 & 87.75 & \\textbf{39.14} & 5.83 & \\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\nSLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\nOurs & 21.40 & \\textbf{16.92} & \\textbf{33.79} & \\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\textbf{22.48} & 20.95 & \\textbf{66.50} & \\textbf{89.35} & 38.39 & \\textbf{5.92} & 69.00 & \\textbf{56.49} & 47.95 & \\textbf{37.25} \\\\\n\n\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 256} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n\n% SKV & 24.03&18.00&36.56&42.73&32.73&20.25&20.52&21.97&22.48&61.50&90.14&39.48&5.75&69.50&55.73&51.05&\\textbf{38.28} \\\\\n% SLM & 18.36&9.62&28.56&38.52&30.38&16.03&19.40&20.30&22.70&52.50&73.33&30.37&5.86&69.50&45.52&43.87&32.80 \\\\\n% H2O & 23.82&16.61&16.61&39.04&31.72&20.05&21.27&22.25&22.23&39.00&89.22&39.45&5.57&69.50&54.48&49.00&34.99 \\\\\n% Ours & 23.99&20.61&38.28&\\textbf{43.23}&\\textbf{31.72}&\\textbf{20.94}&\\textbf{21.27}&\\textbf{22.69}&\\textbf{22.83}&\\textbf{71.00}&\\textbf{90.48}&\\textbf{39.86}&\\textbf{5.86}&\\textbf{69.50}&\\textbf{56.94}&\\textbf{50.16}&39.31 \\\\\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\nSLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\nH2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\nOurs & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n\n\n\\arrayrulecolor{black}\\bottomrule\n\\end{tabular}\n}\n\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n}\n\\label{table:longbench_appendix_llama3_8b}\n\\end{table*}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\begin{table*}\n\n\\centering\n\n% \\wx{need to label the best in each block} \n% \\jh{the font size is too small. Suggestion: 1. write abbreviations for method names, e.g., RKV -> RKV, SLM -> SLM, SKV -> SKV, and write the full name in the caption. 2. Reduce the space between columns using ``c@{\\hspace{0.05ex}}c''}\n\n\n% credit to https://arxiv.org/abs/2401.01325\n% \\scalebox{0.48}{\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\cmidrule(lr){2-17}\n&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n\n\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\nSLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\nH2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\nOurs & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 96} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & 19.92&18.80&\\textbf{43.29}&\\textbf{39.66}&23.08&\\textbf{15.94}&16.65&21.26&21.47&43.50&83.48&39.74&4.00&60.10&45.53&41.12&32.47\\\\\nSLM & 15.15&15.48&31.44&30.03&\\textbf{23.93}&12.73&16.76&19.15&19.19&41.50&75.31&28.71&5.00&28.48&38.92&36.05&26.37\\\\\nH2O & 19.44&20.81&38.78&32.39&21.51&14.43&17.68&\\textbf{22.40}&\\textbf{21.99}&38.00&82.51&\\textbf{39.94}&\\textbf{6.06}&\\textbf{77.48}&45.18&\\textbf{42.43}&32.67\\\\\nOurs & \\textbf{20.35}&\\textbf{21.87}&41.15&34.94&21.85&15.81&\\textbf{18.21}&21.66&21.43&\\textbf{65.00}&\\textbf{83.60}&39.60&4.50&67.80&\\textbf{45.83}&39.38&\\textbf{34.08}\\\\\n\n\n\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 128} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\n\nSKV & 19.16 & 21.46 & 43.52 & \\textbf{38.60} & \\textbf{23.35} & \\textbf{16.09} & 17.66 & 21.84 & 21.47 & 47.50 & \\textbf{84.15} & 40.24 & 5.00 & 69.31 & \\textbf{46.98} & \\textbf{42.97} & 34.96 \\\\\nSLM & 16.57 & 14.68 & 32.40 & 30.19 & 22.64 & 12.34 & 18.08 & 18.96 & 19.19 & 43.50 & 74.22 & 29.02 & 4.50 & 29.48 & 39.23 & 36.16 & 27.57 \\\\\nH2O & 21.20 & 21.90 & 41.55 & 33.56 & 21.28 & 12.93 & \\textbf{18.59} & \\textbf{22.61} & \\textbf{21.99} & 39.00 & 82.37 & \\textbf{40.44} & \\textbf{6.00} & \\textbf{83.19} & 46.41 & 42.66 & 34.73 \\\\\nOurs & \\textbf{21.75} & \\textbf{22.03} & \\textbf{44.32} & 34.06 & 22.79 & 15.77 & 18.58 & 21.89 & 21.43 & \\textbf{66.00} & 83.46 & 39.75 & 4.50 & 66.90 & 46.96 & 41.28 & \\textbf{35.72} \\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\n\nSKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\nSLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\nH2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\nOurs & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n\n\n\n\\arrayrulecolor{black}\\bottomrule\n\\end{tabular}\n}\n\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for Mistral-7B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n}\n\\label{table:longbench_appendix_mistral}\n\\end{table*}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\begin{table*}[!t]\n\n\\centering\n\n% \\wx{need to label the best in each block} \n% \\jh{the font size is too small. Suggestion: 1. write abbreviations for method names, e.g., RKV -> RKV, SLM -> SLM, SKV -> SKV, and write the full name in the caption. 2. Reduce the space between columns using ``c@{\\hspace{0.05ex}}c''}\n\n\n% credit to https://arxiv.org/abs/2401.01325\n% \\scalebox{0.48}{\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\cmidrule(lr){2-17}\n&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n\n\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV & 27.75& \t46.48& \t49.45\t& 52.04& \t54.9& \t30.42& \t32.37& \t22.27\t& 27.58\t& 73.5& \t92.46& \t45.73\t& 12.5\t& 72.5\t& 40.96\t& 63.91\t& 46.55 \\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\nSLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\nH2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\nOurs & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 96} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\n\nSKV & \\textbf{25.78}&35.71&42.13&\\textbf{50.38}&\\textbf{51.46}&26.68&19.61&21.40&21.98&48.50&\\textbf{92.11}&41.21&12.00&72.00&44.85&59.05&41.55\\\\\nSLM & 23.31&29.46&29.21&41.85&45.92&23.00&18.42&19.71&18.57&45.00&76.79&33.54&12.00&\\textbf{72.50}&40.49&50.73&36.28\\\\\nH2O & 25.30&35.13&35.54&47.39&50.61&26.20&20.87&\\textbf{21.80}&\\textbf{22.93}&41.00&90.47&\\textbf{43.42}&12.00&72.00&43.84&\\textbf{59.86}&40.52\\\\\nOurs & 25.47&\\textbf{37.61}&\\textbf{44.00}&47.33&45.36&\\textbf{27.91}&\\textbf{21.05}&21.60&22.31&\\textbf{66.00}&91.45&42.36&12.00&\\textbf{72.50}&\\textbf{45.12}&56.88&\\textbf{42.43}\\\\\n\n\n\n\n\n\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 128} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & \\textbf{26.22}&37.49&\\textbf{45.70}&\\textbf{50.86}&\\textbf{52.82}&28.50&20.38&21.72&22.56&53.00&91.61&41.43&12.00&71.50&45.06&\\textbf{60.50}&42.58 \\\\\nSLM & 24.25&29.12&29.24&40.20&46.28&21.80&19.55&19.42&20.61&48.00&76.60&33.21&12.00&\\textbf{72.50}&40.65&51.03&36.53 \\\\\nH2O & 25.61&35.02&37.74&47.77&51.16&26.87&20.57&20.78&23.33&42.00&91.65&43.85&12.00&\\textbf{72.50}&43.50&59.67&40.88 \\\\\nOurs & 26.06&\\textbf{40.35}&45.67&50.20&52.78&\\textbf{29.36}&\\textbf{22.31}&\\textbf{22.02}&\\textbf{23.69}&\\textbf{71.00}&\\textbf{92.27}&\\textbf{44.33}&12.00&\\textbf{72.50}&\\textbf{45.90}&59.55&\\textbf{44.37} \\\\\n\n\n\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 256} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n\n% SKV & 26.44&40.96&45.44&51.00&54.49&29.97&23.04&22.05&24.47&66.00&91.53&43.97&12.00&72.50&45.03&62.96&\\textbf{44.49} \\\\\n% SLM & 24.75&27.99&30.01&41.40&46.55&21.51&21.78&18.99&23.88&55.00&77.49&33.67&12.00&72.50&40.82&50.66&37.44 \\\\\n% H2O & 27.95&38.12&43.33&49.41&53.58&28.23&23.60&22.20&24.60&44.00&92.73&45.08&12.00&72.50&42.74&62.73&42.68 \\\\\n% Ours & 27.14&\\textbf{42.61}&\\textbf{47.15}&\\textbf{50.60}&\\textbf{53.54}&\\textbf{30.60}&\\textbf{23.93}&\\textbf{22.19}&\\textbf{24.99}&\\textbf{73.00}&\\textbf{92.03}&\\textbf{44.82}&12.00&\\textbf{73.00}&\\textbf{44.56}&\\textbf{61.24}&45.21 \\\\\n\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \nSLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \nH2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \nOurs & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n\n\n\n\\arrayrulecolor{black}\\bottomrule\n\\end{tabular}\n}\n\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n}\n\\label{table:longbench_appendix_llama3_70b}\n\\end{table*}\n\n\n\n\n\n\n\n\n\n\n\n\\clearpage\n\\newpage\n\n\n\n\n\\section{\\method Preserves the Long-Context Understanding Ability}\n\\label{appendix:needle}\n\n\n\nWe perform Fact Retrieval Across Context Lengths (``Needle In A HayStack'')~\\citep{liu2023lost,fu2024data} to test the in-context retrieval ability of LLMs after leveraging different KV cache methods. We conducted the Needle-in-a-Haystack experiment using various LLMs (i.e., Mistral-7B-Instruct-32k, LLaMA-3-8B-Instruct-8k, and LLaMA-3-70B-Instruct-8k), various KV cache sizes (i.e., 64, 96, and 128) and various methods (i.e., FullKV, PyramidKV, H2O and StreamingLLM). \\method achieves Acc. performance closest to FullKV, while other methods show significant decreases. It is worth noting that PyramidKV with 128 KV cache size achieves the same 100.0 Acc. performance compared with FullKV with 8k context size for LLaMA-3-70B-Instruct.\n\n\\autoref{figure:needle_mistral_64}, \\autoref{figure:needle_mistral_96}, \\autoref{figure:needle_mistral_128} show the results of \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with different cache size (64, 96 and 128, respectively).\n\n\\autoref{figure:needle_llama_64}, \\autoref{figure:needle_llama_96}, \\autoref{figure:needle_llama_128} show the results of \\textbf{LlaMa-3-8B-Instruct} with different cache size (64, 96 and 128, respectively).\n\n\\autoref{figure:needle_llama70_64}, \\autoref{figure:needle_llama70_96}, \\autoref{figure:needle_llama70_128} show the results of \\textbf{LlaMa-3-70B-Instruct} with different cache size (64, 96 and 128, respectively).\n\n% \\include{Tables/needle}\n\\begin{table*}[h]\n\\small\n\\centering\n\\begin{tabular}{lcccccc}\n\\toprule\n Model & Length & KV Cache & Full KV Acc. & PyramidKV Acc. & SnapKV Acc. & H2O Acc. \\\\\n\\midrule\n Mistral-7B & 32k & 64 & 100.00 & 80.50 & 43.90 & 48.40 \\\\\n Mistral-7B & 32k & 96 & 100.00 & 90.50 & 72.20 & 59.10 \\\\\n Mistral-7B & 32k & 128 & 100.00 & 91.60 & 80.10 & 64.90 \\\\\n \\midrule\n LLaMa-3-8B & 8k & 64 & 100.00 & 92.90 & 62.00 & 31.90 \\\\\n LLaMa-3-8B & 8k & 96 & 100.00 & 95.80 & 80.70 & 44.20 \\\\\n LLaMa-3-8B & 8k & 128 & 100.00 & 97.40 & 87.40 & 49.10 \\\\\n \\midrule\nLLaMa-3-70B & 8k & 64 & 100.00 & 99.60 & 76.20 & 47.30 \\\\\nLLaMa-3-70B & 8k & 96 & 100.00 & 98.60 & 94.40 & 69.90 \\\\\nLLaMa-3-70B & 8k & 128 & 100.00 & 100.00 & 98.60 & 82.30 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{figure:needle}\n\\caption{Recall Accuracy performance from Fact Retrieval Across Context Lengths (``Needle In A HayStack'')\n}\n\\vspace{-3mm}\n\\end{table*}\n\n\n\n\n\n\n\n\n% \\autoref{figure:needle_mistral_64} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with \\textbf{32k} context size in a cache size of \\textbf{64} and a full KV cache size. \n\n% \\autoref{figure:needle_mistral_96} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with \\textbf{32k} context size in a cache size of \\textbf{96} and a full KV cache size. \n\n% \\autoref{figure:needle_mistral_128} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with \\textbf{32k} context size in a cache size of \\textbf{128} and a full KV cache size. \n\n% \\autoref{figure:needle_llama_64} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{LlaMa-3-8B} with \\textbf{8k} context size in a cache size of \\textbf{64} and a full KV cache size. \n\n% \\autoref{figure:needle_llama_96} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{LlaMa-3-8B} with \\textbf{8k} context size in a cache size of \\textbf{96} and a full KV cache size. \n\n% \\autoref{figure:needle_llama_128} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{LlaMa-3-8B} with \\textbf{8k} context size in a cache size of \\textbf{128} and a full KV cache size. \n\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_64.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{64} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_mistral_64}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_96.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{96} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_mistral_96}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_128.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{128} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_mistral_128}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama_64.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{64} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama_64}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama_96.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{96} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama_96}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama_128.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama_128}\n\\end{figure}\n\n\n\n\n\n\n\n\n\n\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_64.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{64} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama70_64}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_96.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{96} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama70_96}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_128.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama70_128}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\clearpage\n\\newpage\n\n% \\input{Files/0_Introduction}\n\n\n\n\n\n\\end{document}\n\n% \\end{document}"},"question":{"kind":"string","value":"When the proposed method is applied to Llama 8B models, is there a task where, for any of the data sets in it, the KV size of 64 outperforms both full KV cache and KV sixe of 2048. If so, name the task and the margin by which it outperforms KV size of 2048. If not, just say No "},"answer":{"kind":"string","value":"Synthetic, 0.25"},"plan":{"kind":"string","value":"SELECT all tasks where method is authors' method AND base model is llama 8b\nLOOP for each task\n SELECT all datasets in this task\n LOOP for each dataset\n IF kv size 64 score > full kv cache score AND kv size 64 score > kv size 2048 score\n COMPUTE margin = kv size 64 score - kv size 2048 score\n RETURN task, margin\nRETURN No\n"}}},{"rowIdx":364,"cells":{"paper":{"kind":"string","value":"2406.02069"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\n","H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\n","SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\n","Ours & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n","\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\n","SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\n","H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\n","Ours & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\n","SLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\n","H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\n","Ours & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\n","SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\n","H2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\n","Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\n","SLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\n","H2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\n","Ours & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \n","SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \n","H2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \n","Ours & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\n","\\label{table:longbench}\n","\\vspace{-3mm}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 19.86 & 9.09 & 27.89 & \\\\textbf{37.34} & 28.35 & \\\\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\\\\\\n\",\n \"H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\\\textbf{37.76} & \\\\textbf{5.63} & 69.33 & \\\\textbf{53.44} & \\\\textbf{50.15} & 33.89 \\\\\\\\\\n\",\n \"SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\\\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\\\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.13} & \\\\textbf{14.18} & \\\\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\\\textbf{18.33} & \\\\textbf{21.65} & \\\\textbf{19.23} & \\\\textbf{58.00} & \\\\textbf{88.31} & 37.07 & 5.23 & \\\\textbf{69.50} & 52.61 & 45.74 & \\\\textbf{34.76} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & \\\\textbf{25.86} & 29.55 & \\\\textbf{41.10} & \\\\textbf{44.99} & \\\\textbf{35.80} & 21.81 & 25.98 & \\\\textbf{23.40} & 26.46 & \\\\textbf{73.50} & \\\\textbf{90.56} & 41.66 & 5.17 & \\\\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\\\\\\n\",\n \"SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\\\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\\\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\\\\\\n\",\n \"H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\\\textbf{90.56} & 41.84 & 4.91 & \\\\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\\\\\\n\",\n \"Ours & 25.40 & \\\\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\\\textbf{21.98} & \\\\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\\\textbf{90.56} & \\\\textbf{42.14} & 5.22 & \\\\textbf{69.25} & \\\\textbf{58.76} & \\\\textbf{51.18} & \\\\textbf{41.49} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 16.94&17.17&39.51&\\\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\\\\\\n\",\n \"SLM & 15.01&13.84&28.74&30.97&\\\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\\\\\\n\",\n \"H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\\\textbf{21.52}&\\\\textbf{21.98}&37.00&81.02&\\\\textbf{38.62}&\\\\textbf{5.00}&\\\\textbf{66.03}&43.54&\\\\textbf{40.46}&30.88\\\\\\\\\\n\",\n \"Ours & \\\\textbf{20.91}&\\\\textbf{20.21}&\\\\textbf{39.94}&33.57&22.87&\\\\textbf{15.70}&\\\\textbf{17.31}&21.23&21.41&\\\\textbf{54.00}&81.98&36.96&3.58&60.83&\\\\textbf{44.52}&37.99&\\\\textbf{32.19}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV &\\\\textbf{25.89} & \\\\textbf{32.93} & 48.56 & \\\\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\\\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\\\textbf{5.50} & \\\\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\\\\\\n\",\n \"SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\\\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\\\\\\n\",\n \"H2O & 25.76 & 31.10 & \\\\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\\\textbf{86.35} & 42.48 & \\\\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\\\\\\n\",\n \"Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\\\textbf{27.50} & \\\\textbf{19.36} & 26.60 & 23.97 & \\\\textbf{26.73} & \\\\textbf{71.00} & 86.25 & \\\\textbf{42.94} & 4.50 & 87.90 & \\\\textbf{53.12} & \\\\textbf{47.21} & \\\\textbf{41.63} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\\\textbf{91.06}&40.26&12.00&\\\\textbf{72.50}&43.33&57.62&39.45\\\\\\\\\\n\",\n \"SLM & 22.07&23.53&27.31&43.21&\\\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\\\textbf{72.50}&40.23&50.20&35.47\\\\\\\\\\n\",\n \"H2O & 25.45&34.64&33.23&\\\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\\\textbf{41.58}&12.00&71.50&43.83&\\\\textbf{58.16}&39.94\\\\\\\\\\n\",\n \"Ours & \\\\textbf{25.47}&\\\\textbf{36.71}&\\\\textbf{42.29}&47.08&46.21&\\\\textbf{28.30}&\\\\textbf{20.60}&\\\\textbf{21.62}&\\\\textbf{21.62}&\\\\textbf{64.50}&89.61&41.28&\\\\textbf{12.50}&\\\\textbf{72.50}&\\\\textbf{45.34}&56.50&\\\\textbf{42.01}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 26.73&45.18&47.91&\\\\textbf{52.00}&\\\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\\\textbf{72.50}&\\\\textbf{41.52}&\\\\textbf{69.27}&46.36\\\\\\\\ \\n\",\n \"SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\\\\\ \\n\",\n \"H2O & \\\\textbf{27.67}&\\\\textbf{46.51}&\\\\textbf{49.54}&51.49&53.85&29.97&28.57&\\\\textbf{22.79}&\\\\textbf{27.53}&59.00&\\\\textbf{92.63}&\\\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\\\\\ \\n\",\n \"Ours & 27.22&46.19&48.72&51.62&54.56&\\\\textbf{31.11}&\\\\textbf{29.76}&22.50&27.27&\\\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\\\textbf{46.55}\\\\\\\\ \\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\\n\",\n \"\\\\label{table:longbench}\\n\",\n \"\\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/dynamickv4.pdf}\n"," \\caption{\n"," Illustration of~\\method compared with existing KV cache compression methods.\n"," (a) Full KV has all tokens stored in the KV cache in each layer; cache size increases as the input length increases.\n"," (b) StreamingLLM~\\citep{xiao2023efficient} only keeps few initial tokens with a fixed cache size in each layer.\n"," (c) SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} keep a fixed cache size across Transformer layers, and their selection is based on the attention score.\n"," (d)~\\method maintains pyramid-like cache sizes, allocating more cache budget to lower layers and less to higher layers. This approach to KV cache selection better aligns with the increasing attention sparsity observed in multi-layer Transformers (\\Scref{section:observation}).\n"," }\n"," \\label{figure:comparison}\n","\\end{figure}\n"],["\\begin{figure}[ht]\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/obs.pdf}\n"," \\caption{\n"," Attention patterns of retrieval-augmented generation across layers in LlaMa~\\citep{touvron2023llama, touvron2023llama2} reveal that in the lower layers, the model exhibits a broad-spectrum mode of attention, distributing attention scores uniformly across all content. In the middle layers, attention becomes more localized within each document, indicating refined information aggregation (dotted red triangular shapes in layers 6 and 10). This culminates in the upper layers, where ``massive attention'' focuses on a few key tokens (concentrated attention bars after layer 18), efficiently extracting essential information for answers.\n"," }\n"," \\label{figure:rag_flow}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/method2.pdf}\n"," \\caption{\n"," Illustration of~\\method. At the lower level of the transformer, the \\method selects more keys and values based on the exhibited average attention pattern. Fewer keys and values at the higher level are selected based on the massive activation pattern, where we observe that attention scores are concentrated over local regions.}\n"," \\label{figure:method}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\begin{minipage}{0.33\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/result1.pdf}\n"," \\end{minipage}%\n"," \\hfill\n"," \\begin{minipage}{0.33\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/result2.pdf}\n"," \\end{minipage}%\n"," \\hfill\n"," \\begin{minipage}{0.33\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figures/result3.pdf}\n"," \\end{minipage}\n"," \\vspace{-3mm}\n"," \\caption{The evaluation results from LongBench~\\citep{bai2023longbench} across 64, 96, 128 and 256 cache sizes at LLaMa-3-8B-Instruct (Left), Mistral-7B-Instruct (Middle) and LLaMa-3-70B-Instruct (Right).\n"," The evaluation metrics are the average score of LongBench across datasets.\n"," ~\\method outperforms H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv} and StreamingLLM~\\citep{xiao2023efficient}, especially in small KV cache sizes.}\n"," \\label{figure:results}\n","\\end{figure}\n"],["\\begin{table*}[t]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\n","H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\n","SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\n","Ours & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n","\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\n","SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\n","H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\n","Ours & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\n","SLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\n","H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\n","Ours & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\n","SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\n","H2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\n","Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\n","SLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\n","H2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\n","Ours & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n","\n","\n","\n","\\arrayrulecolor{black!20}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \n","SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \n","H2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \n","Ours & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\n","\\label{table:longbench}\n","\\vspace{-3mm}\n","\\end{table*}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_main.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} and \\textbf{LlaMa-3-70B-Instruct} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length.\n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," \\textbf{PyramidKV with 128 KV cache size achieves the same 100.0 Acc. performance compared with FullKV with 8k context size for LLaMA-3-70B-Instruct.}\n"," }\n"," \\label{figure:needle_llama}\n","\\end{figure}\n"],["\\begin{table*}[h]\n","\\small\n","\\centering\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{ccc|cccccc}\n","\\toprule\n"," cache size & Memory & Compression Ratio & QMSum & TREC & TriviaQA & PCount & PRe & Lcc \\\\\n","\n","\\midrule\n","64 & 53M & 0.8\\% & 21.65 & 58.00 & 88.31 & 5.23 & 69.50 & 52.61 \\\\ \n","128 & 107M & 1.6\\% & 22.48 & 66.50 & 89.35 & 5.92 & 69.00 & 56.49 \\\\ \n","256 & 214M & 3.1\\% & 22.69 & 71.00 & 90.48 & 5.83 & 69.25 & 56.94 \\\\\n","512 & 428M & 6.3\\% & 22.80 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\n","1024 & 856M & 12.5\\% & 22.55 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\n","2048 & 1712M & 25.0\\% & 22.55 & 72.00 & 90.56 & 5.58 & 69.25 & 56.79 \\\\\n","Full & 6848M & 100.0\\% & 23.30 & 73.00 & 90.56 & 5.22 & 69.25 & 58.76 \\\\\n","\n","\n","\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Memory reduction effect and benchmark result by using \\method. We conducted a comparison of memory consumption between the Llama-3-8B-Instruct model utilizing the Full KV cache and the Llama-3-8B-Instruct model compressed with the \\method.\n","}\n","\n","\n","\n","\\label{tab:memory_reduction}\n","\\vspace{-3mm}\n","\\end{table*}\n"],["\\begin{table}[htbp]\n","\\centering \n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{llrccc}\n","\\toprule\n","Dataset & Source & Avg len & Metric & Language & \\#data \\\\\n","\\midrule\n","\\emph{Single-Document QA} \\\\\n","NarrativeQA & Literature, Film & 18,409 & F1 & English & 200 \\\\\n","Qasper & Science & 3,619 & F1 & English & 200 \\\\\n","MultiFieldQA-en & Multi-field & 4,559 & F1 & English & 150 \\\\\n","\\midrule\n","\\emph{Multi-Document QA} \\\\\n","HotpotQA & Wikipedia & 9,151 & F1 & English & 200 \\\\\n","2WikiMultihopQA & Wikipedia & 4,887 & F1 & English & 200 \\\\\n","MuSiQue & Wikipedia & 11,214 & F1 & English & 200 \\\\\n","\\midrule\n","\\emph{Summarization} \\\\\n","GovReport & Government report & 8,734 & Rouge-L & English & 200 \\\\\n","QMSum & Meeting & 10,614 & Rouge-L & English & 200 \\\\\n","MultiNews & News & 2,113 & Rouge-L & English & 200 \\\\\n","\\midrule\n","\\emph{Few-shot Learning} \\\\\n","TREC & Web question & 5,177 & Accuracy (CLS) & English & 200 \\\\\n","TriviaQA & Wikipedia, Web & 8,209 & F1 & English & 200 \\\\\n","SAMSum & Dialogue & 6,258 & Rouge-L & English & 200 \\\\\n","\\midrule\n","\\emph{Synthetic Task} \\\\\n","PassageCount & Wikipedia & 11,141 & Accuracy (EM) & English & 200 \\\\\n","PassageRetrieval-en & Wikipedia & 9,289 & Accuracy (EM) & English & 200 \\\\\n","\\midrule\n","\\emph{Code Completion} \\\\\n","LCC & Github & 1,235 & Edit Sim & Python/C\\#/Java & 500 \\\\\n","RepoBench-P & Github repository & 4,206 & Edit Sim & Python/Java & 500 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{An overview of the dataset statistics in LongBench~\\citep{bai2023longbench}. `Source' denotes the origin of the context. `Accuracy (CLS)' refers to classification accuracy, while `Accuracy (EM)' refers to exact match accuracy.}\n","\\label{table:stat}\n","\\end{table}\n"],["\\begin{table*}[htbp]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{4}{*}{$\\alpha$} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & Avg. \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\midrule\n","\n","8 & 21.40 & 16.92 & 31.62 & 38.45 & 28.72 & 18.59 & 19.96 & 22.49 & 20.96 & 66.50 & 89.35 & 38.43 & 5.92 & 69.00 & 57.86 & 51.80 & 37.37 \\\\ \n","16 & 23.37 & 16.21 & 33.93 & 38.24 & 27.28 & 20.57 & 19.71 & 21.93 & 20.86 & 60.00 & 88.75 & 38.34 & 5.48 & 69.12 & 57.84 & 53.42 & 37.19 \\\\ \n","24 & 22.85 & 14.51 & 32.26 & 38.38 & 28.36 & 20.33 & 19.55 & 21.72 & 20.72 & 54.50 & 88.71 & 38.46 & 5.48 & 69.50 & 56.83 & 53.65 & 36.61 \\\\ \n","32 & 23.01 & 14.54 & 31.68 & 38.86 & 29.90 & 19.16 & 19.20 & 21.83 & 20.52 & 49.50 & 87.01 & 38.01 & 5.75 & 69.50 & 57.02 & 54.54 & 36.25 \\\\ \n","40 & 21.70 & 13.06 & 30.14 & 36.78 & 27.34 & 18.88 & 18.72 & 21.37 & 19.79 & 44.00 & 87.74 & 38.43 & 6.08 & 69.25 & 56.11 & 53.89 & 35.21 \\\\ \n","48 & 21.51 & 12.30 & 29.77 & 39.04 & 26.76 & 17.97 & 18.65 & 21.20 & 20.29 & 44.50 & 87.73 & 38.44 & 5.51 & 69.25 & 56.73 & 53.88 & 35.22 \\\\ \n","\n","\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Ablation on $\\alpha$.}\n","\\label{table:ablation_step_a}\n","\\end{table*}\n"],["\\begin{table*}[htbp]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{4}{*}{$\\beta$} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & Avg. \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\midrule\n","20 & 21.40 & 16.92 & 33.79 & 39.73 & 28.72 & 18.59 & 19.86 & 22.48 & 20.95 & 66.50 & 89.35 & 38.39 & 5.92 & 69.00 & 56.49 & 47.95 & 37.25 \\\\\n","18 & 21.71 & 16.24 & 33.59 & 39.89 & 27.94 & 18.38 & 19.76 & 22.32 & 21.20 & 66.50 & 88.98 & 38.93 & 5.46 & 69.50 & 56.47 & 49.23 & 37.25 \\\\\n","16 & 21.74 & 14.86 & 33.64 & 39.18 & 28.17 & 18.77 & 19.57 & 22.25 & 21.48 & 66.50 & 89.69 & 38.87 & 5.82 & 69.50 & 57.02 & 50.11 & 37.32 \\\\\n","14 & 22.53 & 16.31 & 33.50 & 40.50 & 28.15 & 19.26 & 19.66 & 22.39 & 21.38 & 65.50 & 90.02 & 38.56 & 5.75 & 69.50 & 57.51 & 49.71 & 37.51 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Ablation on $\\beta$.}\n","\\label{table:ablation_step_b}\n","\\end{table*}\n"],["\\begin{table}[h!]\n","\\centering\n","\\small\n","\\begin{tabular}{ccccccccc}\n","\\toprule\n","\\textbf{Prompt Length} & \\textbf{Generation Length} & \\textbf{Inference Time} & \\textbf{Allocation Time} & \\textbf{Selection Time} \\\\\n","\\midrule\n","512&512 & 18.26 & 0.0000003 & 0.0194 \\\\\n","512&1024 & 34.69 & 0.000002 & 0.0133 \\\\\n","512&2048 & 70.69 & 0.000003 & 0.013 \\\\\n","512&4096 & 138.62 & 0.000005 & 0.013 \\\\\n","1024&512 & 17.32 & 0.000002 & 0.0131 \\\\\n","1024&1024 & 34.67 & 0.000002 & 0.01288 \\\\\n","1024&2048 & 70.21 & 0.000005 & 0.01296 \\\\\n","1024&4096 & 138.61 & 0.000003 & 0.01297 \\\\\n","2048&512 & 17.48 & 0.000004 & 0.0128 \\\\\n","2048&1024 & 34.78 & 0.000006 & 0.0129 \\\\\n","2048&2048 & 69.50 & 0.000003 & 0.01297 \\\\\n","2048&4096 & 138.59 & 0.000003 & 0.013 \\\\\n","4096&512 & 17.58 & 0.000002 & 0.013 \\\\\n","4096&1024 & 34.93 & 0.000004 & 0.0129 \\\\\n","4096&2048 & 69.65 & 0.000002 & 0.013 \\\\\n","4096&4096 & 138.87 & 0.000002 & 0.013 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\caption{Extra inference overhead of~\\method }\n","\\label{table:inference_overhead}\n","\\end{table}\n"],["\\begin{table}[h!]\n","\\centering\n","\\small\n","\\begin{tabular}{ccccccc}\n","\\toprule\n","\\textbf{Prompt Length} & \\textbf{Generation Length} & \\textbf{H2O} & \\textbf{SnapKV} & \\textbf{StreamingLLM} & \\textbf{PyramidKV} \\\\ \n","\\midrule\n","512&512 & 18.47 & 18.25 & 18.96 & 18.26 \\\\\n","512&1024 & 35.10 & 34.76 & 36.20 & 34.69 \\\\\n","512&2048 & 70.21 & 69.60 & 72.35 & 70.69 \\\\ \n","512&4096 & 140.80 & 139.42 & 146.37 & 138.62 \\\\\n","1024&512 & 17.63 & 17.34 & 18.12 & 17.32 \\\\\n","1024&1024 & 35.16 & 34.61 & 36.17 & 34.67 \\\\\n","1024&2048 & 71.02 & 69.17 & 72.37 & 70.21 \\\\\n","1024&4096 & 140.51 & 138.83 & 146.09 & 138.61 \\\\ \n","2048&512 & 17.64 & 19.54 & 18.22 & 17.48 \\\\ \n","2048&1024 & 35.09 & 34.76 & 36.29 & 34.78 \\\\ \n","2048&2048 & 70.84 & 69.56 & 72.46 & 69.50 \\\\ \n","2048&4096 & 140.16 & 139.55 & 145.22 & 138.59 \\\\ \n","4096&512 & 17.75 & 17.67 & 18.40 & 17.58 \\\\ \n","4096&1024 & 35.20 & 35.08 & 36.46 & 34.93 \\\\ \n","4096&2048 & 70.02 & 69.26 & 72.58 & 69.65 \\\\ \n","4096&4096 & 139.87 & 138.57 & 144.98 & 138.87 \\\\ \n","\\bottomrule\n","\\end{tabular}\n","\\caption{Performance comparison across different configurations and methods.}\n","\\label{table:inference_speed_comparison}\n","\\end{table}\n"],["\\begin{table*}\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 04.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\n","H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\n","SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\n","Ours & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 96} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 20.45 & 10.34 & 31.84 & 37.85 & 28.65 & \\textbf{18.52} & 17.90 & 21.26 & 19.07 & 41.50 & 86.95 & 37.82 & 5.08 & 69.12 & 54.69 & \\textbf{51.31} & 34.51 \\\\\n","H2O & 21.55 & 11.21 & 28.73 & 37.66 & 30.12 & 18.47 & 19.57 & 21.57 & 20.44 & 38.50 & \\textbf{87.63} & \\textbf{38.47} & 5.60 & 69.00 & 54.51 & 50.16 & 34.57 \\\\\n","SLM & 18.67 & 8.43 & 24.98 & 38.35 & \\textbf{30.59} & 16.37 & 17.33 & 19.84 & 18.41 & 41.00 & 73.92 & 29.38 & 5.80 & \\textbf{69.50} & 47.15 & 45.61 & 31.58 \\\\\n","Ours & \\textbf{21.67} & \\textbf{15.10} & \\textbf{33.50} & \\textbf{39.73} & 26.48 & 17.47 & \\textbf{19.64} & \\textbf{22.28} & \\textbf{20.49} & \\textbf{61.50} & 87.38 & 38.18 & \\textbf{6.00} & 69.25 & \\textbf{55.30} & 46.78 & \\textbf{36.29} \\\\\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 128} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","SKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\textbf{51.82} & 35.50 \\\\\n","H2O & \\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\textbf{32.71} & 18.45 & \\textbf{20.32} & 22.02 & \\textbf{21.10} & 38.50 & 87.75 & \\textbf{39.14} & 5.83 & \\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\n","SLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\n","Ours & 21.40 & \\textbf{16.92} & \\textbf{33.79} & \\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\textbf{22.48} & 20.95 & \\textbf{66.50} & \\textbf{89.35} & 38.39 & \\textbf{5.92} & 69.00 & \\textbf{56.49} & 47.95 & \\textbf{37.25} \\\\\n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\n","SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\n","H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\n","Ours & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n","}\n","\\label{table:longbench_appendix_llama3_8b}\n","\\end{table*}\n"],["\\begin{table*}\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\n","SLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\n","H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\n","Ours & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 96} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & 19.92&18.80&\\textbf{43.29}&\\textbf{39.66}&23.08&\\textbf{15.94}&16.65&21.26&21.47&43.50&83.48&39.74&4.00&60.10&45.53&41.12&32.47\\\\\n","SLM & 15.15&15.48&31.44&30.03&\\textbf{23.93}&12.73&16.76&19.15&19.19&41.50&75.31&28.71&5.00&28.48&38.92&36.05&26.37\\\\\n","H2O & 19.44&20.81&38.78&32.39&21.51&14.43&17.68&\\textbf{22.40}&\\textbf{21.99}&38.00&82.51&\\textbf{39.94}&\\textbf{6.06}&\\textbf{77.48}&45.18&\\textbf{42.43}&32.67\\\\\n","Ours & \\textbf{20.35}&\\textbf{21.87}&41.15&34.94&21.85&15.81&\\textbf{18.21}&21.66&21.43&\\textbf{65.00}&\\textbf{83.60}&39.60&4.50&67.80&\\textbf{45.83}&39.38&\\textbf{34.08}\\\\\n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 128} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","\n","SKV & 19.16 & 21.46 & 43.52 & \\textbf{38.60} & \\textbf{23.35} & \\textbf{16.09} & 17.66 & 21.84 & 21.47 & 47.50 & \\textbf{84.15} & 40.24 & 5.00 & 69.31 & \\textbf{46.98} & \\textbf{42.97} & 34.96 \\\\\n","SLM & 16.57 & 14.68 & 32.40 & 30.19 & 22.64 & 12.34 & 18.08 & 18.96 & 19.19 & 43.50 & 74.22 & 29.02 & 4.50 & 29.48 & 39.23 & 36.16 & 27.57 \\\\\n","H2O & 21.20 & 21.90 & 41.55 & 33.56 & 21.28 & 12.93 & \\textbf{18.59} & \\textbf{22.61} & \\textbf{21.99} & 39.00 & 82.37 & \\textbf{40.44} & \\textbf{6.00} & \\textbf{83.19} & 46.41 & 42.66 & 34.73 \\\\\n","Ours & \\textbf{21.75} & \\textbf{22.03} & \\textbf{44.32} & 34.06 & 22.79 & 15.77 & 18.58 & 21.89 & 21.43 & \\textbf{66.00} & 83.46 & 39.75 & 4.50 & 66.90 & 46.96 & 41.28 & \\textbf{35.72} \\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","\n","SKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\n","SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\n","H2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\n","Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n","\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for Mistral-7B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n","}\n","\\label{table:longbench_appendix_mistral}\n","\\end{table*}\n"],["\\begin{table*}[!t]\n","\n","\\centering\n","\n","\n","\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n","\n","\\specialrule{1pt}{0pt}{2pt}\n","\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n","\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n","& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n","\\cmidrule(lr){2-17}\n","&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n","\n","\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","FKV & 27.75& \t46.48& \t49.45\t& 52.04& \t54.9& \t30.42& \t32.37& \t22.27\t& 27.58\t& 73.5& \t92.46& \t45.73\t& 12.5\t& 72.5\t& 40.96\t& 63.91\t& 46.55 \\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\n","SLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\n","H2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\n","Ours & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 96} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","\n","SKV & \\textbf{25.78}&35.71&42.13&\\textbf{50.38}&\\textbf{51.46}&26.68&19.61&21.40&21.98&48.50&\\textbf{92.11}&41.21&12.00&72.00&44.85&59.05&41.55\\\\\n","SLM & 23.31&29.46&29.21&41.85&45.92&23.00&18.42&19.71&18.57&45.00&76.79&33.54&12.00&\\textbf{72.50}&40.49&50.73&36.28\\\\\n","H2O & 25.30&35.13&35.54&47.39&50.61&26.20&20.87&\\textbf{21.80}&\\textbf{22.93}&41.00&90.47&\\textbf{43.42}&12.00&72.00&43.84&\\textbf{59.86}&40.52\\\\\n","Ours & 25.47&\\textbf{37.61}&\\textbf{44.00}&47.33&45.36&\\textbf{27.91}&\\textbf{21.05}&21.60&22.31&\\textbf{66.00}&91.45&42.36&12.00&\\textbf{72.50}&\\textbf{45.12}&56.88&\\textbf{42.43}\\\\\n","\n","\n","\n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 128} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & \\textbf{26.22}&37.49&\\textbf{45.70}&\\textbf{50.86}&\\textbf{52.82}&28.50&20.38&21.72&22.56&53.00&91.61&41.43&12.00&71.50&45.06&\\textbf{60.50}&42.58 \\\\\n","SLM & 24.25&29.12&29.24&40.20&46.28&21.80&19.55&19.42&20.61&48.00&76.60&33.21&12.00&\\textbf{72.50}&40.65&51.03&36.53 \\\\\n","H2O & 25.61&35.02&37.74&47.77&51.16&26.87&20.57&20.78&23.33&42.00&91.65&43.85&12.00&\\textbf{72.50}&43.50&59.67&40.88 \\\\\n","Ours & 26.06&\\textbf{40.35}&45.67&50.20&52.78&\\textbf{29.36}&\\textbf{22.31}&\\textbf{22.02}&\\textbf{23.69}&\\textbf{71.00}&\\textbf{92.27}&\\textbf{44.33}&12.00&\\textbf{72.50}&\\textbf{45.90}&59.55&\\textbf{44.37} \\\\\n","\n","\n","\n","\n","\n","\n","\n","\n","\n","\\arrayrulecolor{black}\\midrule\n","\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n","\\arrayrulecolor{black!20}\\midrule\n","\n","SKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \n","SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \n","H2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \n","Ours & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n","\n","\n","\n","\\arrayrulecolor{black}\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n","}\n","\\label{table:longbench_appendix_llama3_70b}\n","\\end{table*}\n"],["\\begin{table*}[h]\n","\\small\n","\\centering\n","\\begin{tabular}{lcccccc}\n","\\toprule\n"," Model & Length & KV Cache & Full KV Acc. & PyramidKV Acc. & SnapKV Acc. & H2O Acc. \\\\\n","\\midrule\n"," Mistral-7B & 32k & 64 & 100.00 & 80.50 & 43.90 & 48.40 \\\\\n"," Mistral-7B & 32k & 96 & 100.00 & 90.50 & 72.20 & 59.10 \\\\\n"," Mistral-7B & 32k & 128 & 100.00 & 91.60 & 80.10 & 64.90 \\\\\n"," \\midrule\n"," LLaMa-3-8B & 8k & 64 & 100.00 & 92.90 & 62.00 & 31.90 \\\\\n"," LLaMa-3-8B & 8k & 96 & 100.00 & 95.80 & 80.70 & 44.20 \\\\\n"," LLaMa-3-8B & 8k & 128 & 100.00 & 97.40 & 87.40 & 49.10 \\\\\n"," \\midrule\n","LLaMa-3-70B & 8k & 64 & 100.00 & 99.60 & 76.20 & 47.30 \\\\\n","LLaMa-3-70B & 8k & 96 & 100.00 & 98.60 & 94.40 & 69.90 \\\\\n","LLaMa-3-70B & 8k & 128 & 100.00 & 100.00 & 98.60 & 82.30 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\label{figure:needle}\n","\\caption{Recall Accuracy performance from Fact Retrieval Across Context Lengths (``Needle In A HayStack'')\n","}\n","\\vspace{-3mm}\n","\\end{table*}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_64.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{64} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_mistral_64}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_96.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{96} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_mistral_96}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_128.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{128} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_mistral_128}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama_64.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{64} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama_64}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama_96.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{96} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama_96}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama_128.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama_128}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_64.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{64} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama70_64}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_96.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{96} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama70_96}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_128.pdf}\n"," \\caption{\n"," Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n"," The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n"," ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n"," }\n"," \\label{figure:needle_llama70_128}\n","\\end{figure}\n"]],"string":"[\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/dynamickv4.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Illustration of~\\\\method compared with existing KV cache compression methods.\\n\",\n \" (a) Full KV has all tokens stored in the KV cache in each layer; cache size increases as the input length increases.\\n\",\n \" (b) StreamingLLM~\\\\citep{xiao2023efficient} only keeps few initial tokens with a fixed cache size in each layer.\\n\",\n \" (c) SnapKV~\\\\citep{li2024snapkv} and H2O~\\\\citep{zhang2024h2o} keep a fixed cache size across Transformer layers, and their selection is based on the attention score.\\n\",\n \" (d)~\\\\method maintains pyramid-like cache sizes, allocating more cache budget to lower layers and less to higher layers. This approach to KV cache selection better aligns with the increasing attention sparsity observed in multi-layer Transformers (\\\\Scref{section:observation}).\\n\",\n \" }\\n\",\n \" \\\\label{figure:comparison}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/obs.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Attention patterns of retrieval-augmented generation across layers in LlaMa~\\\\citep{touvron2023llama, touvron2023llama2} reveal that in the lower layers, the model exhibits a broad-spectrum mode of attention, distributing attention scores uniformly across all content. In the middle layers, attention becomes more localized within each document, indicating refined information aggregation (dotted red triangular shapes in layers 6 and 10). This culminates in the upper layers, where ``massive attention'' focuses on a few key tokens (concentrated attention bars after layer 18), efficiently extracting essential information for answers.\\n\",\n \" }\\n\",\n \" \\\\label{figure:rag_flow}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/method2.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Illustration of~\\\\method. At the lower level of the transformer, the \\\\method selects more keys and values based on the exhibited average attention pattern. Fewer keys and values at the higher level are selected based on the massive activation pattern, where we observe that attention scores are concentrated over local regions.}\\n\",\n \" \\\\label{figure:method}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{minipage}{0.33\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/result1.pdf}\\n\",\n \" \\\\end{minipage}%\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{minipage}{0.33\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/result2.pdf}\\n\",\n \" \\\\end{minipage}%\\n\",\n \" \\\\hfill\\n\",\n \" \\\\begin{minipage}{0.33\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figures/result3.pdf}\\n\",\n \" \\\\end{minipage}\\n\",\n \" \\\\vspace{-3mm}\\n\",\n \" \\\\caption{The evaluation results from LongBench~\\\\citep{bai2023longbench} across 64, 96, 128 and 256 cache sizes at LLaMa-3-8B-Instruct (Left), Mistral-7B-Instruct (Middle) and LLaMa-3-70B-Instruct (Right).\\n\",\n \" The evaluation metrics are the average score of LongBench across datasets.\\n\",\n \" ~\\\\method outperforms H2O~\\\\citep{zhang2024h2o}, SnapKV~\\\\citep{li2024snapkv} and StreamingLLM~\\\\citep{xiao2023efficient}, especially in small KV cache sizes.}\\n\",\n \" \\\\label{figure:results}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 19.86 & 9.09 & 27.89 & \\\\textbf{37.34} & 28.35 & \\\\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\\\\\\n\",\n \"H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\\\textbf{37.76} & \\\\textbf{5.63} & 69.33 & \\\\textbf{53.44} & \\\\textbf{50.15} & 33.89 \\\\\\\\\\n\",\n \"SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\\\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\\\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.13} & \\\\textbf{14.18} & \\\\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\\\textbf{18.33} & \\\\textbf{21.65} & \\\\textbf{19.23} & \\\\textbf{58.00} & \\\\textbf{88.31} & 37.07 & 5.23 & \\\\textbf{69.50} & 52.61 & 45.74 & \\\\textbf{34.76} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & \\\\textbf{25.86} & 29.55 & \\\\textbf{41.10} & \\\\textbf{44.99} & \\\\textbf{35.80} & 21.81 & 25.98 & \\\\textbf{23.40} & 26.46 & \\\\textbf{73.50} & \\\\textbf{90.56} & 41.66 & 5.17 & \\\\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\\\\\\n\",\n \"SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\\\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\\\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\\\\\\n\",\n \"H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\\\textbf{90.56} & 41.84 & 4.91 & \\\\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\\\\\\n\",\n \"Ours & 25.40 & \\\\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\\\textbf{21.98} & \\\\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\\\textbf{90.56} & \\\\textbf{42.14} & 5.22 & \\\\textbf{69.25} & \\\\textbf{58.76} & \\\\textbf{51.18} & \\\\textbf{41.49} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 16.94&17.17&39.51&\\\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\\\\\\n\",\n \"SLM & 15.01&13.84&28.74&30.97&\\\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\\\\\\n\",\n \"H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\\\textbf{21.52}&\\\\textbf{21.98}&37.00&81.02&\\\\textbf{38.62}&\\\\textbf{5.00}&\\\\textbf{66.03}&43.54&\\\\textbf{40.46}&30.88\\\\\\\\\\n\",\n \"Ours & \\\\textbf{20.91}&\\\\textbf{20.21}&\\\\textbf{39.94}&33.57&22.87&\\\\textbf{15.70}&\\\\textbf{17.31}&21.23&21.41&\\\\textbf{54.00}&81.98&36.96&3.58&60.83&\\\\textbf{44.52}&37.99&\\\\textbf{32.19}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV &\\\\textbf{25.89} & \\\\textbf{32.93} & 48.56 & \\\\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\\\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\\\textbf{5.50} & \\\\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\\\\\\n\",\n \"SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\\\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\\\\\\n\",\n \"H2O & 25.76 & 31.10 & \\\\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\\\textbf{86.35} & 42.48 & \\\\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\\\\\\n\",\n \"Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\\\textbf{27.50} & \\\\textbf{19.36} & 26.60 & 23.97 & \\\\textbf{26.73} & \\\\textbf{71.00} & 86.25 & \\\\textbf{42.94} & 4.50 & 87.90 & \\\\textbf{53.12} & \\\\textbf{47.21} & \\\\textbf{41.63} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\\\textbf{91.06}&40.26&12.00&\\\\textbf{72.50}&43.33&57.62&39.45\\\\\\\\\\n\",\n \"SLM & 22.07&23.53&27.31&43.21&\\\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\\\textbf{72.50}&40.23&50.20&35.47\\\\\\\\\\n\",\n \"H2O & 25.45&34.64&33.23&\\\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\\\textbf{41.58}&12.00&71.50&43.83&\\\\textbf{58.16}&39.94\\\\\\\\\\n\",\n \"Ours & \\\\textbf{25.47}&\\\\textbf{36.71}&\\\\textbf{42.29}&47.08&46.21&\\\\textbf{28.30}&\\\\textbf{20.60}&\\\\textbf{21.62}&\\\\textbf{21.62}&\\\\textbf{64.50}&89.61&41.28&\\\\textbf{12.50}&\\\\textbf{72.50}&\\\\textbf{45.34}&56.50&\\\\textbf{42.01}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 26.73&45.18&47.91&\\\\textbf{52.00}&\\\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\\\textbf{72.50}&\\\\textbf{41.52}&\\\\textbf{69.27}&46.36\\\\\\\\ \\n\",\n \"SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\\\\\ \\n\",\n \"H2O & \\\\textbf{27.67}&\\\\textbf{46.51}&\\\\textbf{49.54}&51.49&53.85&29.97&28.57&\\\\textbf{22.79}&\\\\textbf{27.53}&59.00&\\\\textbf{92.63}&\\\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\\\\\ \\n\",\n \"Ours & 27.22&46.19&48.72&51.62&54.56&\\\\textbf{31.11}&\\\\textbf{29.76}&22.50&27.27&\\\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\\\textbf{46.55}\\\\\\\\ \\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\\n\",\n \"\\\\label{table:longbench}\\n\",\n \"\\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_main.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-8B-Instruct} and \\\\textbf{LlaMa-3-70B-Instruct} with \\\\textbf{8k} context size in \\\\textbf{128} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length.\\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" \\\\textbf{PyramidKV with 128 KV cache size achieves the same 100.0 Acc. performance compared with FullKV with 8k context size for LLaMA-3-70B-Instruct.}\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\small\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{ccc|cccccc}\\n\",\n \"\\\\toprule\\n\",\n \" cache size & Memory & Compression Ratio & QMSum & TREC & TriviaQA & PCount & PRe & Lcc \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"64 & 53M & 0.8\\\\% & 21.65 & 58.00 & 88.31 & 5.23 & 69.50 & 52.61 \\\\\\\\ \\n\",\n \"128 & 107M & 1.6\\\\% & 22.48 & 66.50 & 89.35 & 5.92 & 69.00 & 56.49 \\\\\\\\ \\n\",\n \"256 & 214M & 3.1\\\\% & 22.69 & 71.00 & 90.48 & 5.83 & 69.25 & 56.94 \\\\\\\\\\n\",\n \"512 & 428M & 6.3\\\\% & 22.80 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\\\\\\n\",\n \"1024 & 856M & 12.5\\\\% & 22.55 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\\\\\\n\",\n \"2048 & 1712M & 25.0\\\\% & 22.55 & 72.00 & 90.56 & 5.58 & 69.25 & 56.79 \\\\\\\\\\n\",\n \"Full & 6848M & 100.0\\\\% & 23.30 & 73.00 & 90.56 & 5.22 & 69.25 & 58.76 \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Memory reduction effect and benchmark result by using \\\\method. We conducted a comparison of memory consumption between the Llama-3-8B-Instruct model utilizing the Full KV cache and the Llama-3-8B-Instruct model compressed with the \\\\method.\\n\",\n \"}\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\label{tab:memory_reduction}\\n\",\n \"\\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[htbp]\\n\",\n \"\\\\centering \\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{llrccc}\\n\",\n \"\\\\toprule\\n\",\n \"Dataset & Source & Avg len & Metric & Language & \\\\#data \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Single-Document QA} \\\\\\\\\\n\",\n \"NarrativeQA & Literature, Film & 18,409 & F1 & English & 200 \\\\\\\\\\n\",\n \"Qasper & Science & 3,619 & F1 & English & 200 \\\\\\\\\\n\",\n \"MultiFieldQA-en & Multi-field & 4,559 & F1 & English & 150 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Multi-Document QA} \\\\\\\\\\n\",\n \"HotpotQA & Wikipedia & 9,151 & F1 & English & 200 \\\\\\\\\\n\",\n \"2WikiMultihopQA & Wikipedia & 4,887 & F1 & English & 200 \\\\\\\\\\n\",\n \"MuSiQue & Wikipedia & 11,214 & F1 & English & 200 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Summarization} \\\\\\\\\\n\",\n \"GovReport & Government report & 8,734 & Rouge-L & English & 200 \\\\\\\\\\n\",\n \"QMSum & Meeting & 10,614 & Rouge-L & English & 200 \\\\\\\\\\n\",\n \"MultiNews & News & 2,113 & Rouge-L & English & 200 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Few-shot Learning} \\\\\\\\\\n\",\n \"TREC & Web question & 5,177 & Accuracy (CLS) & English & 200 \\\\\\\\\\n\",\n \"TriviaQA & Wikipedia, Web & 8,209 & F1 & English & 200 \\\\\\\\\\n\",\n \"SAMSum & Dialogue & 6,258 & Rouge-L & English & 200 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Synthetic Task} \\\\\\\\\\n\",\n \"PassageCount & Wikipedia & 11,141 & Accuracy (EM) & English & 200 \\\\\\\\\\n\",\n \"PassageRetrieval-en & Wikipedia & 9,289 & Accuracy (EM) & English & 200 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\emph{Code Completion} \\\\\\\\\\n\",\n \"LCC & Github & 1,235 & Edit Sim & Python/C\\\\#/Java & 500 \\\\\\\\\\n\",\n \"RepoBench-P & Github repository & 4,206 & Edit Sim & Python/Java & 500 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{An overview of the dataset statistics in LongBench~\\\\citep{bai2023longbench}. `Source' denotes the origin of the context. `Accuracy (CLS)' refers to classification accuracy, while `Accuracy (EM)' refers to exact match accuracy.}\\n\",\n \"\\\\label{table:stat}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{4}{*}{$\\\\alpha$} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & Avg. \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\n\",\n \"8 & 21.40 & 16.92 & 31.62 & 38.45 & 28.72 & 18.59 & 19.96 & 22.49 & 20.96 & 66.50 & 89.35 & 38.43 & 5.92 & 69.00 & 57.86 & 51.80 & 37.37 \\\\\\\\ \\n\",\n \"16 & 23.37 & 16.21 & 33.93 & 38.24 & 27.28 & 20.57 & 19.71 & 21.93 & 20.86 & 60.00 & 88.75 & 38.34 & 5.48 & 69.12 & 57.84 & 53.42 & 37.19 \\\\\\\\ \\n\",\n \"24 & 22.85 & 14.51 & 32.26 & 38.38 & 28.36 & 20.33 & 19.55 & 21.72 & 20.72 & 54.50 & 88.71 & 38.46 & 5.48 & 69.50 & 56.83 & 53.65 & 36.61 \\\\\\\\ \\n\",\n \"32 & 23.01 & 14.54 & 31.68 & 38.86 & 29.90 & 19.16 & 19.20 & 21.83 & 20.52 & 49.50 & 87.01 & 38.01 & 5.75 & 69.50 & 57.02 & 54.54 & 36.25 \\\\\\\\ \\n\",\n \"40 & 21.70 & 13.06 & 30.14 & 36.78 & 27.34 & 18.88 & 18.72 & 21.37 & 19.79 & 44.00 & 87.74 & 38.43 & 6.08 & 69.25 & 56.11 & 53.89 & 35.21 \\\\\\\\ \\n\",\n \"48 & 21.51 & 12.30 & 29.77 & 39.04 & 26.76 & 17.97 & 18.65 & 21.20 & 20.29 & 44.50 & 87.73 & 38.44 & 5.51 & 69.25 & 56.73 & 53.88 & 35.22 \\\\\\\\ \\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Ablation on $\\\\alpha$.}\\n\",\n \"\\\\label{table:ablation_step_a}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[htbp]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{4}{*}{$\\\\beta$} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & Avg. \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"20 & 21.40 & 16.92 & 33.79 & 39.73 & 28.72 & 18.59 & 19.86 & 22.48 & 20.95 & 66.50 & 89.35 & 38.39 & 5.92 & 69.00 & 56.49 & 47.95 & 37.25 \\\\\\\\\\n\",\n \"18 & 21.71 & 16.24 & 33.59 & 39.89 & 27.94 & 18.38 & 19.76 & 22.32 & 21.20 & 66.50 & 88.98 & 38.93 & 5.46 & 69.50 & 56.47 & 49.23 & 37.25 \\\\\\\\\\n\",\n \"16 & 21.74 & 14.86 & 33.64 & 39.18 & 28.17 & 18.77 & 19.57 & 22.25 & 21.48 & 66.50 & 89.69 & 38.87 & 5.82 & 69.50 & 57.02 & 50.11 & 37.32 \\\\\\\\\\n\",\n \"14 & 22.53 & 16.31 & 33.50 & 40.50 & 28.15 & 19.26 & 19.66 & 22.39 & 21.38 & 65.50 & 90.02 & 38.56 & 5.75 & 69.50 & 57.51 & 49.71 & 37.51 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Ablation on $\\\\beta$.}\\n\",\n \"\\\\label{table:ablation_step_b}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{ccccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Prompt Length} & \\\\textbf{Generation Length} & \\\\textbf{Inference Time} & \\\\textbf{Allocation Time} & \\\\textbf{Selection Time} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"512&512 & 18.26 & 0.0000003 & 0.0194 \\\\\\\\\\n\",\n \"512&1024 & 34.69 & 0.000002 & 0.0133 \\\\\\\\\\n\",\n \"512&2048 & 70.69 & 0.000003 & 0.013 \\\\\\\\\\n\",\n \"512&4096 & 138.62 & 0.000005 & 0.013 \\\\\\\\\\n\",\n \"1024&512 & 17.32 & 0.000002 & 0.0131 \\\\\\\\\\n\",\n \"1024&1024 & 34.67 & 0.000002 & 0.01288 \\\\\\\\\\n\",\n \"1024&2048 & 70.21 & 0.000005 & 0.01296 \\\\\\\\\\n\",\n \"1024&4096 & 138.61 & 0.000003 & 0.01297 \\\\\\\\\\n\",\n \"2048&512 & 17.48 & 0.000004 & 0.0128 \\\\\\\\\\n\",\n \"2048&1024 & 34.78 & 0.000006 & 0.0129 \\\\\\\\\\n\",\n \"2048&2048 & 69.50 & 0.000003 & 0.01297 \\\\\\\\\\n\",\n \"2048&4096 & 138.59 & 0.000003 & 0.013 \\\\\\\\\\n\",\n \"4096&512 & 17.58 & 0.000002 & 0.013 \\\\\\\\\\n\",\n \"4096&1024 & 34.93 & 0.000004 & 0.0129 \\\\\\\\\\n\",\n \"4096&2048 & 69.65 & 0.000002 & 0.013 \\\\\\\\\\n\",\n \"4096&4096 & 138.87 & 0.000002 & 0.013 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Extra inference overhead of~\\\\method }\\n\",\n \"\\\\label{table:inference_overhead}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{ccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Prompt Length} & \\\\textbf{Generation Length} & \\\\textbf{H2O} & \\\\textbf{SnapKV} & \\\\textbf{StreamingLLM} & \\\\textbf{PyramidKV} \\\\\\\\ \\n\",\n \"\\\\midrule\\n\",\n \"512&512 & 18.47 & 18.25 & 18.96 & 18.26 \\\\\\\\\\n\",\n \"512&1024 & 35.10 & 34.76 & 36.20 & 34.69 \\\\\\\\\\n\",\n \"512&2048 & 70.21 & 69.60 & 72.35 & 70.69 \\\\\\\\ \\n\",\n \"512&4096 & 140.80 & 139.42 & 146.37 & 138.62 \\\\\\\\\\n\",\n \"1024&512 & 17.63 & 17.34 & 18.12 & 17.32 \\\\\\\\\\n\",\n \"1024&1024 & 35.16 & 34.61 & 36.17 & 34.67 \\\\\\\\\\n\",\n \"1024&2048 & 71.02 & 69.17 & 72.37 & 70.21 \\\\\\\\\\n\",\n \"1024&4096 & 140.51 & 138.83 & 146.09 & 138.61 \\\\\\\\ \\n\",\n \"2048&512 & 17.64 & 19.54 & 18.22 & 17.48 \\\\\\\\ \\n\",\n \"2048&1024 & 35.09 & 34.76 & 36.29 & 34.78 \\\\\\\\ \\n\",\n \"2048&2048 & 70.84 & 69.56 & 72.46 & 69.50 \\\\\\\\ \\n\",\n \"2048&4096 & 140.16 & 139.55 & 145.22 & 138.59 \\\\\\\\ \\n\",\n \"4096&512 & 17.75 & 17.67 & 18.40 & 17.58 \\\\\\\\ \\n\",\n \"4096&1024 & 35.20 & 35.08 & 36.46 & 34.93 \\\\\\\\ \\n\",\n \"4096&2048 & 70.02 & 69.26 & 72.58 & 69.65 \\\\\\\\ \\n\",\n \"4096&4096 & 139.87 & 138.57 & 144.98 & 138.87 \\\\\\\\ \\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Performance comparison across different configurations and methods.}\\n\",\n \"\\\\label{table:inference_speed_comparison}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 04.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 19.86 & 9.09 & 27.89 & \\\\textbf{37.34} & 28.35 & \\\\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\\\\\\n\",\n \"H2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\\\textbf{37.76} & \\\\textbf{5.63} & 69.33 & \\\\textbf{53.44} & \\\\textbf{50.15} & 33.89 \\\\\\\\\\n\",\n \"SLM & 17.44 & 8.68 & 22.25 & 35.37 & \\\\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\\\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.13} & \\\\textbf{14.18} & \\\\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\\\textbf{18.33} & \\\\textbf{21.65} & \\\\textbf{19.23} & \\\\textbf{58.00} & \\\\textbf{88.31} & 37.07 & 5.23 & \\\\textbf{69.50} & 52.61 & 45.74 & \\\\textbf{34.76} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 96} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 20.45 & 10.34 & 31.84 & 37.85 & 28.65 & \\\\textbf{18.52} & 17.90 & 21.26 & 19.07 & 41.50 & 86.95 & 37.82 & 5.08 & 69.12 & 54.69 & \\\\textbf{51.31} & 34.51 \\\\\\\\\\n\",\n \"H2O & 21.55 & 11.21 & 28.73 & 37.66 & 30.12 & 18.47 & 19.57 & 21.57 & 20.44 & 38.50 & \\\\textbf{87.63} & \\\\textbf{38.47} & 5.60 & 69.00 & 54.51 & 50.16 & 34.57 \\\\\\\\\\n\",\n \"SLM & 18.67 & 8.43 & 24.98 & 38.35 & \\\\textbf{30.59} & 16.37 & 17.33 & 19.84 & 18.41 & 41.00 & 73.92 & 29.38 & 5.80 & \\\\textbf{69.50} & 47.15 & 45.61 & 31.58 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.67} & \\\\textbf{15.10} & \\\\textbf{33.50} & \\\\textbf{39.73} & 26.48 & 17.47 & \\\\textbf{19.64} & \\\\textbf{22.28} & \\\\textbf{20.49} & \\\\textbf{61.50} & 87.38 & 38.18 & \\\\textbf{6.00} & 69.25 & \\\\textbf{55.30} & 46.78 & \\\\textbf{36.29} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 128} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"SKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\\\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\\\textbf{51.82} & 35.50 \\\\\\\\\\n\",\n \"H2O & \\\\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\\\textbf{32.71} & 18.45 & \\\\textbf{20.32} & 22.02 & \\\\textbf{21.10} & 38.50 & 87.75 & \\\\textbf{39.14} & 5.83 & \\\\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\\\\\\n\",\n \"SLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\\\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\\\\\\n\",\n \"Ours & 21.40 & \\\\textbf{16.92} & \\\\textbf{33.79} & \\\\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\\\textbf{22.48} & 20.95 & \\\\textbf{66.50} & \\\\textbf{89.35} & 38.39 & \\\\textbf{5.92} & 69.00 & \\\\textbf{56.49} & 47.95 & \\\\textbf{37.25} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & \\\\textbf{25.86} & 29.55 & \\\\textbf{41.10} & \\\\textbf{44.99} & \\\\textbf{35.80} & 21.81 & 25.98 & \\\\textbf{23.40} & 26.46 & \\\\textbf{73.50} & \\\\textbf{90.56} & 41.66 & 5.17 & \\\\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\\\\\\n\",\n \"SLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\\\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\\\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\\\\\\n\",\n \"H2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\\\textbf{90.56} & 41.84 & 4.91 & \\\\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\\\\\\n\",\n \"Ours & 25.40 & \\\\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\\\textbf{21.98} & \\\\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\\\textbf{90.56} & \\\\textbf{42.14} & 5.22 & \\\\textbf{69.25} & \\\\textbf{58.76} & \\\\textbf{51.18} & \\\\textbf{41.49} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\\n\",\n \"}\\n\",\n \"\\\\label{table:longbench_appendix_llama3_8b}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & 16.94&17.17&39.51&\\\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\\\\\\n\",\n \"SLM & 15.01&13.84&28.74&30.97&\\\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\\\\\\n\",\n \"H2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\\\textbf{21.52}&\\\\textbf{21.98}&37.00&81.02&\\\\textbf{38.62}&\\\\textbf{5.00}&\\\\textbf{66.03}&43.54&\\\\textbf{40.46}&30.88\\\\\\\\\\n\",\n \"Ours & \\\\textbf{20.91}&\\\\textbf{20.21}&\\\\textbf{39.94}&33.57&22.87&\\\\textbf{15.70}&\\\\textbf{17.31}&21.23&21.41&\\\\textbf{54.00}&81.98&36.96&3.58&60.83&\\\\textbf{44.52}&37.99&\\\\textbf{32.19}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 96} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & 19.92&18.80&\\\\textbf{43.29}&\\\\textbf{39.66}&23.08&\\\\textbf{15.94}&16.65&21.26&21.47&43.50&83.48&39.74&4.00&60.10&45.53&41.12&32.47\\\\\\\\\\n\",\n \"SLM & 15.15&15.48&31.44&30.03&\\\\textbf{23.93}&12.73&16.76&19.15&19.19&41.50&75.31&28.71&5.00&28.48&38.92&36.05&26.37\\\\\\\\\\n\",\n \"H2O & 19.44&20.81&38.78&32.39&21.51&14.43&17.68&\\\\textbf{22.40}&\\\\textbf{21.99}&38.00&82.51&\\\\textbf{39.94}&\\\\textbf{6.06}&\\\\textbf{77.48}&45.18&\\\\textbf{42.43}&32.67\\\\\\\\\\n\",\n \"Ours & \\\\textbf{20.35}&\\\\textbf{21.87}&41.15&34.94&21.85&15.81&\\\\textbf{18.21}&21.66&21.43&\\\\textbf{65.00}&\\\\textbf{83.60}&39.60&4.50&67.80&\\\\textbf{45.83}&39.38&\\\\textbf{34.08}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 128} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"\\n\",\n \"SKV & 19.16 & 21.46 & 43.52 & \\\\textbf{38.60} & \\\\textbf{23.35} & \\\\textbf{16.09} & 17.66 & 21.84 & 21.47 & 47.50 & \\\\textbf{84.15} & 40.24 & 5.00 & 69.31 & \\\\textbf{46.98} & \\\\textbf{42.97} & 34.96 \\\\\\\\\\n\",\n \"SLM & 16.57 & 14.68 & 32.40 & 30.19 & 22.64 & 12.34 & 18.08 & 18.96 & 19.19 & 43.50 & 74.22 & 29.02 & 4.50 & 29.48 & 39.23 & 36.16 & 27.57 \\\\\\\\\\n\",\n \"H2O & 21.20 & 21.90 & 41.55 & 33.56 & 21.28 & 12.93 & \\\\textbf{18.59} & \\\\textbf{22.61} & \\\\textbf{21.99} & 39.00 & 82.37 & \\\\textbf{40.44} & \\\\textbf{6.00} & \\\\textbf{83.19} & 46.41 & 42.66 & 34.73 \\\\\\\\\\n\",\n \"Ours & \\\\textbf{21.75} & \\\\textbf{22.03} & \\\\textbf{44.32} & 34.06 & 22.79 & 15.77 & 18.58 & 21.89 & 21.43 & \\\\textbf{66.00} & 83.46 & 39.75 & 4.50 & 66.90 & 46.96 & 41.28 & \\\\textbf{35.72} \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"\\n\",\n \"SKV &\\\\textbf{25.89} & \\\\textbf{32.93} & 48.56 & \\\\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\\\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\\\textbf{5.50} & \\\\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\\\\\\n\",\n \"SLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\\\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\\\\\\n\",\n \"H2O & 25.76 & 31.10 & \\\\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\\\textbf{86.35} & 42.48 & \\\\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\\\\\\n\",\n \"Ours & 25.53 & 32.21 & 48.97 & 42.26 & \\\\textbf{27.50} & \\\\textbf{19.36} & 26.60 & 23.97 & \\\\textbf{26.73} & \\\\textbf{71.00} & 86.25 & \\\\textbf{42.94} & 4.50 & 87.90 & \\\\textbf{53.12} & \\\\textbf{47.21} & \\\\textbf{41.63} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for Mistral-7B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\\n\",\n \"}\\n\",\n \"\\\\label{table:longbench_appendix_mistral}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \"\\n\",\n \"\\\\centering\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.05ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c@{\\\\hspace{0.6ex}}c}\\n\",\n \"\\n\",\n \"\\\\specialrule{1pt}{0pt}{2pt}\\n\",\n \"\\\\multirow{5}{*}{Method} & \\\\multicolumn{3}{c}{Single-Document QA} & \\\\multicolumn{3}{c}{Multi-Document QA}& \\\\multicolumn{3}{c}{Summarization}& \\\\multicolumn{3}{c}{Few-shot Learning}& \\\\multicolumn{2}{c}{Synthetic} & \\\\multicolumn{2}{c}{Code} & \\\\multirow{5}{*}{Avg.} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-4}\\\\cmidrule(lr){5-7}\\\\cmidrule(lr){8-10}\\\\cmidrule(lr){11-13}\\\\cmidrule(lr){14-15}\\\\cmidrule(lr){16-17}\\n\",\n \"& \\\\rotatebox[origin=c]{30}{NrtvQA} & \\\\rotatebox[origin=c]{30}{Qasper} & \\\\rotatebox[origin=c]{30}{MF-en} & \\\\rotatebox[origin=c]{30}{HotpotQA} & \\\\rotatebox[origin=c]{30}{2WikiMQA} & \\\\rotatebox[origin=c]{30}{Musique} & \\\\rotatebox[origin=c]{30}{GovReport} & \\\\rotatebox[origin=c]{30}{QMSum} & \\\\rotatebox[origin=c]{30}{MultiNews} & \\\\rotatebox[origin=c]{30}{TREC} & \\\\rotatebox[origin=c]{30}{TriviaQA} & \\\\rotatebox[origin=c]{30}{SAMSum} & \\\\rotatebox[origin=c]{30}{PCount} & \\\\rotatebox[origin=c]{30}{PRe} & \\\\rotatebox[origin=c]{30}{Lcc} & \\\\rotatebox[origin=c]{30}{RB-P} & \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-17}\\n\",\n \"&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"FKV & 27.75& \\t46.48& \\t49.45\\t& 52.04& \\t54.9& \\t30.42& \\t32.37& \\t22.27\\t& 27.58\\t& 73.5& \\t92.46& \\t45.73\\t& 12.5\\t& 72.5\\t& 40.96\\t& 63.91\\t& 46.55 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\\\textbf{91.06}&40.26&12.00&\\\\textbf{72.50}&43.33&57.62&39.45\\\\\\\\\\n\",\n \"SLM & 22.07&23.53&27.31&43.21&\\\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\\\textbf{72.50}&40.23&50.20&35.47\\\\\\\\\\n\",\n \"H2O & 25.45&34.64&33.23&\\\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\\\textbf{41.58}&12.00&71.50&43.83&\\\\textbf{58.16}&39.94\\\\\\\\\\n\",\n \"Ours & \\\\textbf{25.47}&\\\\textbf{36.71}&\\\\textbf{42.29}&47.08&46.21&\\\\textbf{28.30}&\\\\textbf{20.60}&\\\\textbf{21.62}&\\\\textbf{21.62}&\\\\textbf{64.50}&89.61&41.28&\\\\textbf{12.50}&\\\\textbf{72.50}&\\\\textbf{45.34}&56.50&\\\\textbf{42.01}\\\\\\\\\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 96} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"\\n\",\n \"SKV & \\\\textbf{25.78}&35.71&42.13&\\\\textbf{50.38}&\\\\textbf{51.46}&26.68&19.61&21.40&21.98&48.50&\\\\textbf{92.11}&41.21&12.00&72.00&44.85&59.05&41.55\\\\\\\\\\n\",\n \"SLM & 23.31&29.46&29.21&41.85&45.92&23.00&18.42&19.71&18.57&45.00&76.79&33.54&12.00&\\\\textbf{72.50}&40.49&50.73&36.28\\\\\\\\\\n\",\n \"H2O & 25.30&35.13&35.54&47.39&50.61&26.20&20.87&\\\\textbf{21.80}&\\\\textbf{22.93}&41.00&90.47&\\\\textbf{43.42}&12.00&72.00&43.84&\\\\textbf{59.86}&40.52\\\\\\\\\\n\",\n \"Ours & 25.47&\\\\textbf{37.61}&\\\\textbf{44.00}&47.33&45.36&\\\\textbf{27.91}&\\\\textbf{21.05}&21.60&22.31&\\\\textbf{66.00}&91.45&42.36&12.00&\\\\textbf{72.50}&\\\\textbf{45.12}&56.88&\\\\textbf{42.43}\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 128} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & \\\\textbf{26.22}&37.49&\\\\textbf{45.70}&\\\\textbf{50.86}&\\\\textbf{52.82}&28.50&20.38&21.72&22.56&53.00&91.61&41.43&12.00&71.50&45.06&\\\\textbf{60.50}&42.58 \\\\\\\\\\n\",\n \"SLM & 24.25&29.12&29.24&40.20&46.28&21.80&19.55&19.42&20.61&48.00&76.60&33.21&12.00&\\\\textbf{72.50}&40.65&51.03&36.53 \\\\\\\\\\n\",\n \"H2O & 25.61&35.02&37.74&47.77&51.16&26.87&20.57&20.78&23.33&42.00&91.65&43.85&12.00&\\\\textbf{72.50}&43.50&59.67&40.88 \\\\\\\\\\n\",\n \"Ours & 26.06&\\\\textbf{40.35}&45.67&50.20&52.78&\\\\textbf{29.36}&\\\\textbf{22.31}&\\\\textbf{22.02}&\\\\textbf{23.69}&\\\\textbf{71.00}&\\\\textbf{92.27}&\\\\textbf{44.33}&12.00&\\\\textbf{72.50}&\\\\textbf{45.90}&59.55&\\\\textbf{44.37} \\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\midrule\\n\",\n \"\\\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\\\\\\n\",\n \"\\\\arrayrulecolor{black!20}\\\\midrule\\n\",\n \"\\n\",\n \"SKV & 26.73&45.18&47.91&\\\\textbf{52.00}&\\\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\\\textbf{72.50}&\\\\textbf{41.52}&\\\\textbf{69.27}&46.36\\\\\\\\ \\n\",\n \"SLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\\\\\ \\n\",\n \"H2O & \\\\textbf{27.67}&\\\\textbf{46.51}&\\\\textbf{49.54}&51.49&53.85&29.97&28.57&\\\\textbf{22.79}&\\\\textbf{27.53}&59.00&\\\\textbf{92.63}&\\\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\\\\\ \\n\",\n \"Ours & 27.22&46.19&48.72&51.62&54.56&\\\\textbf{31.11}&\\\\textbf{29.76}&22.50&27.27&\\\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\\\textbf{46.55}\\\\\\\\ \\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\arrayrulecolor{black}\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Performance comparison of ~\\\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-70B-Instruct. ~\\\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\\n\",\n \"}\\n\",\n \"\\\\label{table:longbench_appendix_llama3_70b}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\small\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{lcccccc}\\n\",\n \"\\\\toprule\\n\",\n \" Model & Length & KV Cache & Full KV Acc. & PyramidKV Acc. & SnapKV Acc. & H2O Acc. \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \" Mistral-7B & 32k & 64 & 100.00 & 80.50 & 43.90 & 48.40 \\\\\\\\\\n\",\n \" Mistral-7B & 32k & 96 & 100.00 & 90.50 & 72.20 & 59.10 \\\\\\\\\\n\",\n \" Mistral-7B & 32k & 128 & 100.00 & 91.60 & 80.10 & 64.90 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" LLaMa-3-8B & 8k & 64 & 100.00 & 92.90 & 62.00 & 31.90 \\\\\\\\\\n\",\n \" LLaMa-3-8B & 8k & 96 & 100.00 & 95.80 & 80.70 & 44.20 \\\\\\\\\\n\",\n \" LLaMa-3-8B & 8k & 128 & 100.00 & 97.40 & 87.40 & 49.10 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"LLaMa-3-70B & 8k & 64 & 100.00 & 99.60 & 76.20 & 47.30 \\\\\\\\\\n\",\n \"LLaMa-3-70B & 8k & 96 & 100.00 & 98.60 & 94.40 & 69.90 \\\\\\\\\\n\",\n \"LLaMa-3-70B & 8k & 128 & 100.00 & 100.00 & 98.60 & 82.30 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\label{figure:needle}\\n\",\n \"\\\\caption{Recall Accuracy performance from Fact Retrieval Across Context Lengths (``Needle In A HayStack'')\\n\",\n \"}\\n\",\n \"\\\\vspace{-3mm}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_mistral_64.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{Mistral-7B-Instruct} with \\\\textbf{32k} context size in \\\\textbf{64} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_mistral_64}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_mistral_96.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{Mistral-7B-Instruct} with \\\\textbf{32k} context size in \\\\textbf{96} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_mistral_96}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_mistral_128.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{Mistral-7B-Instruct} with \\\\textbf{32k} context size in \\\\textbf{128} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_mistral_128}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama_64.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-8B-Instruct} with \\\\textbf{8k} context size in \\\\textbf{64} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama_64}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama_96.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-8B-Instruct} with \\\\textbf{8k} context size in \\\\textbf{96} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama_96}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama_128.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-8B-Instruct} with \\\\textbf{8k} context size in \\\\textbf{128} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama_128}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama70_64.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-70B} with \\\\textbf{8k} context size in \\\\textbf{64} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama70_64}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama70_96.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-70B} with \\\\textbf{8k} context size in \\\\textbf{96} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama70_96}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\columnwidth]{Figures/needle_llama70_128.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\\\textbf{LlaMa-3-70B} with \\\\textbf{8k} context size in \\\\textbf{128} KV cache size.\\n\",\n \" The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \\n\",\n \" ~\\\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\\n\",\n \" }\\n\",\n \" \\\\label{figure:needle_llama70_128}\\n\",\n \"\\\\end{figure}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\documentclass{article}\n\n\n\n% if you need to pass options to natbib, use, e.g.:\n% \\PassOptionsToPackage{numbers, compress}{natbib}\n% before loading neurips_2024\n\n\n% ready for submission\n% \\usepackage[preprint]{neurips_2024}\n\\usepackage{iclr2025_conference,times}\n\\iclrfinalcopy\n\n% \\usepackage{neurips_2024}\n% \\iclrfinalcopy\n% \\input{math_commands.tex}\n\n\n\n\\usepackage{xcolor}\n% to compile a preprint version, e.g., for submission to arXiv, add add the\n% [preprint] option:\n% \\usepackage[preprint]{neurips_2024}\n\n\n% to compile a camera-ready version, add the [final] option, e.g.:\n% \\usepackage[final]{neurips_2024}\n\n\n% to avoid loading the natbib package, add option nonatbib:\n% \\usepackage[nonatbib]{neurips_2024}\n\n\n\\usepackage[utf8]{inputenc} % allow utf-8 input\n\\usepackage[T1]{fontenc} % use 8-bit T1 fonts\n\\usepackage{hyperref} % hyperlinks\n\\usepackage{url} % simple URL typesetting\n\\usepackage{booktabs} % professional-quality tables\n\\usepackage{amsfonts} % blackboard math symbols\n\\usepackage{nicefrac} % compact symbols for 1/2, etc.\n\\usepackage{microtype} % microtypography\n% \\usepackage{xcolor} % colors\n% \\usepackage[table]{xcolor}\n\n\\usepackage{booktabs,tabularx, colortbl} \n\n\\usepackage{graphicx}\n% \\usepackage{hyperref}\n\\usepackage{multirow}\n\\usepackage{enumitem}\n\n\\usepackage{float}\n\n% \\usepackage{amsthm}\n\\usepackage{amsfonts} \n\\usepackage{bm}\n\\usepackage{mathtools}\n\\usepackage{amsmath}\n%%%%% NEW MATH DEFINITIONS %%%%%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n% Mark sections of captions for referring to divisions of figures\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em (Right)}}\n\\newcommand{\\figtop}{{\\em (Top)}}\n\\newcommand{\\figbottom}{{\\em (Bottom)}}\n\\newcommand{\\captiona}{{\\em (a)}}\n\\newcommand{\\captionb}{{\\em (b)}}\n\\newcommand{\\captionc}{{\\em (c)}}\n\\newcommand{\\captiond}{{\\em (d)}}\n\n% Highlight a newly defined term\n\\newcommand{\\newterm}[1]{{\\bf #1}}\n\n\n% Figure 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For start of sentence\n\\def\\Figref#1{Figure~\\ref{#1}}\n\\def\\twofigref#1#2{figures \\ref{#1} and \\ref{#2}}\n\\def\\quadfigref#1#2#3#4{figures \\ref{#1}, \\ref{#2}, \\ref{#3} and \\ref{#4}}\n% Section reference, lower-case.\n\\def\\secref#1{section~\\ref{#1}}\n% Section reference, capital.\n\\def\\Secref#1{Section~\\ref{#1}}\n% Reference to two sections.\n\\def\\twosecrefs#1#2{sections \\ref{#1} and \\ref{#2}}\n% Reference to three sections.\n\\def\\secrefs#1#2#3{sections \\ref{#1}, \\ref{#2} and \\ref{#3}}\n% Reference to an equation, lower-case.\n\\def\\eqref#1{equation~\\ref{#1}}\n% Reference to an equation, upper case\n\\def\\Eqref#1{Equation~\\ref{#1}}\n% A raw reference to an equation---avoid using if possible\n\\def\\plaineqref#1{\\ref{#1}}\n% Reference to a chapter, lower-case.\n\\def\\chapref#1{chapter~\\ref{#1}}\n% Reference to an equation, upper case.\n\\def\\Chapref#1{Chapter~\\ref{#1}}\n% Reference to a range of chapters\n\\def\\rangechapref#1#2{chapters\\ref{#1}--\\ref{#2}}\n% Reference to an algorithm, lower-case.\n\\def\\algref#1{algorithm~\\ref{#1}}\n% Reference to an algorithm, upper case.\n\\def\\Algref#1{Algorithm~\\ref{#1}}\n\\def\\twoalgref#1#2{algorithms \\ref{#1} and \\ref{#2}}\n\\def\\Twoalgref#1#2{Algorithms \\ref{#1} and \\ref{#2}}\n% Reference to a part, lower case\n\\def\\partref#1{part~\\ref{#1}}\n% Reference to a part, upper case\n\\def\\Partref#1{Part~\\ref{#1}}\n\\def\\twopartref#1#2{parts \\ref{#1} and \\ref{#2}}\n\n\\def\\ceil#1{\\lceil #1 \\rceil}\n\\def\\floor#1{\\lfloor #1 \\rfloor}\n\\def\\1{\\bm{1}}\n\\newcommand{\\train}{\\mathcal{D}}\n\\newcommand{\\valid}{\\mathcal{D_{\\mathrm{valid}}}}\n\\newcommand{\\test}{\\mathcal{D_{\\mathrm{test}}}}\n\n\\def\\eps{{\\epsilon}}\n\n\n% Random variables\n\\def\\reta{{\\textnormal{$\\eta$}}}\n\\def\\ra{{\\textnormal{a}}}\n\\def\\rb{{\\textnormal{b}}}\n\\def\\rc{{\\textnormal{c}}}\n\\def\\rd{{\\textnormal{d}}}\n\\def\\re{{\\textnormal{e}}}\n\\def\\rf{{\\textnormal{f}}}\n\\def\\rg{{\\textnormal{g}}}\n\\def\\rh{{\\textnormal{h}}}\n\\def\\ri{{\\textnormal{i}}}\n\\def\\rj{{\\textnormal{j}}}\n\\def\\rk{{\\textnormal{k}}}\n\\def\\rl{{\\textnormal{l}}}\n% rm is already a command, just don't name any random variables m\n\\def\\rn{{\\textnormal{n}}}\n\\def\\ro{{\\textnormal{o}}}\n\\def\\rp{{\\textnormal{p}}}\n\\def\\rq{{\\textnormal{q}}}\n\\def\\rr{{\\textnormal{r}}}\n\\def\\rs{{\\textnormal{s}}}\n\\def\\rt{{\\textnormal{t}}}\n\\def\\ru{{\\textnormal{u}}}\n\\def\\rv{{\\textnormal{v}}}\n\\def\\rw{{\\textnormal{w}}}\n\\def\\rx{{\\textnormal{x}}}\n\\def\\ry{{\\textnormal{y}}}\n\\def\\rz{{\\textnormal{z}}}\n\n% Random vectors\n\\def\\rvepsilon{{\\mathbf{\\epsilon}}}\n\\def\\rvtheta{{\\mathbf{\\theta}}}\n\\def\\rva{{\\mathbf{a}}}\n\\def\\rvb{{\\mathbf{b}}}\n\\def\\rvc{{\\mathbf{c}}}\n\\def\\rvd{{\\mathbf{d}}}\n\\def\\rve{{\\mathbf{e}}}\n\\def\\rvf{{\\mathbf{f}}}\n\\def\\rvg{{\\mathbf{g}}}\n\\def\\rvh{{\\mathbf{h}}}\n\\def\\rvu{{\\mathbf{i}}}\n\\def\\rvj{{\\mathbf{j}}}\n\\def\\rvk{{\\mathbf{k}}}\n\\def\\rvl{{\\mathbf{l}}}\n\\def\\rvm{{\\mathbf{m}}}\n\\def\\rvn{{\\mathbf{n}}}\n\\def\\rvo{{\\mathbf{o}}}\n\\def\\rvp{{\\mathbf{p}}}\n\\def\\rvq{{\\mathbf{q}}}\n\\def\\rvr{{\\mathbf{r}}}\n\\def\\rvs{{\\mathbf{s}}}\n\\def\\rvt{{\\mathbf{t}}}\n\\def\\rvu{{\\mathbf{u}}}\n\\def\\rvv{{\\mathbf{v}}}\n\\def\\rvw{{\\mathbf{w}}}\n\\def\\rvx{{\\mathbf{x}}}\n\\def\\rvy{{\\mathbf{y}}}\n\\def\\rvz{{\\mathbf{z}}}\n\n% Elements of random vectors\n\\def\\erva{{\\textnormal{a}}}\n\\def\\ervb{{\\textnormal{b}}}\n\\def\\ervc{{\\textnormal{c}}}\n\\def\\ervd{{\\textnormal{d}}}\n\\def\\erve{{\\textnormal{e}}}\n\\def\\ervf{{\\textnormal{f}}}\n\\def\\ervg{{\\textnormal{g}}}\n\\def\\ervh{{\\textnormal{h}}}\n\\def\\ervi{{\\textnormal{i}}}\n\\def\\ervj{{\\textnormal{j}}}\n\\def\\ervk{{\\textnormal{k}}}\n\\def\\ervl{{\\textnormal{l}}}\n\\def\\ervm{{\\textnormal{m}}}\n\\def\\ervn{{\\textnormal{n}}}\n\\def\\ervo{{\\textnormal{o}}}\n\\def\\ervp{{\\textnormal{p}}}\n\\def\\ervq{{\\textnormal{q}}}\n\\def\\ervr{{\\textnormal{r}}}\n\\def\\ervs{{\\textnormal{s}}}\n\\def\\ervt{{\\textnormal{t}}}\n\\def\\ervu{{\\textnormal{u}}}\n\\def\\ervv{{\\textnormal{v}}}\n\\def\\ervw{{\\textnormal{w}}}\n\\def\\ervx{{\\textnormal{x}}}\n\\def\\ervy{{\\textnormal{y}}}\n\\def\\ervz{{\\textnormal{z}}}\n\n% Random matrices\n\\def\\rmA{{\\mathbf{A}}}\n\\def\\rmB{{\\mathbf{B}}}\n\\def\\rmC{{\\mathbf{C}}}\n\\def\\rmD{{\\mathbf{D}}}\n\\def\\rmE{{\\mathbf{E}}}\n\\def\\rmF{{\\mathbf{F}}}\n\\def\\rmG{{\\mathbf{G}}}\n\\def\\rmH{{\\mathbf{H}}}\n\\def\\rmI{{\\mathbf{I}}}\n\\def\\rmJ{{\\mathbf{J}}}\n\\def\\rmK{{\\mathbf{K}}}\n\\def\\rmL{{\\mathbf{L}}}\n\\def\\rmM{{\\mathbf{M}}}\n\\def\\rmN{{\\mathbf{N}}}\n\\def\\rmO{{\\mathbf{O}}}\n\\def\\rmP{{\\mathbf{P}}}\n\\def\\rmQ{{\\mathbf{Q}}}\n\\def\\rmR{{\\mathbf{R}}}\n\\def\\rmS{{\\mathbf{S}}}\n\\def\\rmT{{\\mathbf{T}}}\n\\def\\rmU{{\\mathbf{U}}}\n\\def\\rmV{{\\mathbf{V}}}\n\\def\\rmW{{\\mathbf{W}}}\n\\def\\rmX{{\\mathbf{X}}}\n\\def\\rmY{{\\mathbf{Y}}}\n\\def\\rmZ{{\\mathbf{Z}}}\n\n% Elements of random matrices\n\\def\\ermA{{\\textnormal{A}}}\n\\def\\ermB{{\\textnormal{B}}}\n\\def\\ermC{{\\textnormal{C}}}\n\\def\\ermD{{\\textnormal{D}}}\n\\def\\ermE{{\\textnormal{E}}}\n\\def\\ermF{{\\textnormal{F}}}\n\\def\\ermG{{\\textnormal{G}}}\n\\def\\ermH{{\\textnormal{H}}}\n\\def\\ermI{{\\textnormal{I}}}\n\\def\\ermJ{{\\textnormal{J}}}\n\\def\\ermK{{\\textnormal{K}}}\n\\def\\ermL{{\\textnormal{L}}}\n\\def\\ermM{{\\textnormal{M}}}\n\\def\\ermN{{\\textnormal{N}}}\n\\def\\ermO{{\\textnormal{O}}}\n\\def\\ermP{{\\textnormal{P}}}\n\\def\\ermQ{{\\textnormal{Q}}}\n\\def\\ermR{{\\textnormal{R}}}\n\\def\\ermS{{\\textnormal{S}}}\n\\def\\ermT{{\\textnormal{T}}}\n\\def\\ermU{{\\textnormal{U}}}\n\\def\\ermV{{\\textnormal{V}}}\n\\def\\ermW{{\\textnormal{W}}}\n\\def\\ermX{{\\textnormal{X}}}\n\\def\\ermY{{\\textnormal{Y}}}\n\\def\\ermZ{{\\textnormal{Z}}}\n\n% Vectors\n\\def\\vzero{{\\bm{0}}}\n\\def\\vone{{\\bm{1}}}\n\\def\\vmu{{\\bm{\\mu}}}\n\\def\\vtheta{{\\bm{\\theta}}}\n\\def\\va{{\\bm{a}}}\n\\def\\vb{{\\bm{b}}}\n\\def\\vc{{\\bm{c}}}\n\\def\\vd{{\\bm{d}}}\n\\def\\ve{{\\bm{e}}}\n\\def\\vf{{\\bm{f}}}\n\\def\\vg{{\\bm{g}}}\n\\def\\vh{{\\bm{h}}}\n\\def\\vi{{\\bm{i}}}\n\\def\\vj{{\\bm{j}}}\n\\def\\vk{{\\bm{k}}}\n\\def\\vl{{\\bm{l}}}\n\\def\\vm{{\\bm{m}}}\n\\def\\vn{{\\bm{n}}}\n\\def\\vo{{\\bm{o}}}\n\\def\\vp{{\\bm{p}}}\n\\def\\vq{{\\bm{q}}}\n\\def\\vr{{\\bm{r}}}\n\\def\\vs{{\\bm{s}}}\n\\def\\vt{{\\bm{t}}}\n\\def\\vu{{\\bm{u}}}\n\\def\\vv{{\\bm{v}}}\n\\def\\vw{{\\bm{w}}}\n\\def\\vx{{\\bm{x}}}\n\\def\\vy{{\\bm{y}}}\n\\def\\vz{{\\bm{z}}}\n\n% Elements of vectors\n\\def\\evalpha{{\\alpha}}\n\\def\\evbeta{{\\beta}}\n\\def\\evepsilon{{\\epsilon}}\n\\def\\evlambda{{\\lambda}}\n\\def\\evomega{{\\omega}}\n\\def\\evmu{{\\mu}}\n\\def\\evpsi{{\\psi}}\n\\def\\evsigma{{\\sigma}}\n\\def\\evtheta{{\\theta}}\n\\def\\eva{{a}}\n\\def\\evb{{b}}\n\\def\\evc{{c}}\n\\def\\evd{{d}}\n\\def\\eve{{e}}\n\\def\\evf{{f}}\n\\def\\evg{{g}}\n\\def\\evh{{h}}\n\\def\\evi{{i}}\n\\def\\evj{{j}}\n\\def\\evk{{k}}\n\\def\\evl{{l}}\n\\def\\evm{{m}}\n\\def\\evn{{n}}\n\\def\\evo{{o}}\n\\def\\evp{{p}}\n\\def\\evq{{q}}\n\\def\\evr{{r}}\n\\def\\evs{{s}}\n\\def\\evt{{t}}\n\\def\\evu{{u}}\n\\def\\evv{{v}}\n\\def\\evw{{w}}\n\\def\\evx{{x}}\n\\def\\evy{{y}}\n\\def\\evz{{z}}\n\n% Matrix\n\\def\\mA{{\\bm{A}}}\n\\def\\mB{{\\bm{B}}}\n\\def\\mC{{\\bm{C}}}\n\\def\\mD{{\\bm{D}}}\n\\def\\mE{{\\bm{E}}}\n\\def\\mF{{\\bm{F}}}\n\\def\\mG{{\\bm{G}}}\n\\def\\mH{{\\bm{H}}}\n\\def\\mI{{\\bm{I}}}\n\\def\\mJ{{\\bm{J}}}\n\\def\\mK{{\\bm{K}}}\n\\def\\mL{{\\bm{L}}}\n\\def\\mM{{\\bm{M}}}\n\\def\\mN{{\\bm{N}}}\n\\def\\mO{{\\bm{O}}}\n\\def\\mP{{\\bm{P}}}\n\\def\\mQ{{\\bm{Q}}}\n\\def\\mR{{\\bm{R}}}\n\\def\\mS{{\\bm{S}}}\n\\def\\mT{{\\bm{T}}}\n\\def\\mU{{\\bm{U}}}\n\\def\\mV{{\\bm{V}}}\n\\def\\mW{{\\bm{W}}}\n\\def\\mX{{\\bm{X}}}\n\\def\\mY{{\\bm{Y}}}\n\\def\\mZ{{\\bm{Z}}}\n\\def\\mBeta{{\\bm{\\beta}}}\n\\def\\mPhi{{\\bm{\\Phi}}}\n\\def\\mLambda{{\\bm{\\Lambda}}}\n\\def\\mSigma{{\\bm{\\Sigma}}}\n\n% Tensor\n\\DeclareMathAlphabet{\\mathsfit}{\\encodingdefault}{\\sfdefault}{m}{sl}\n\\SetMathAlphabet{\\mathsfit}{bold}{\\encodingdefault}{\\sfdefault}{bx}{n}\n\\newcommand{\\tens}[1]{\\bm{\\mathsfit{#1}}}\n\\def\\tA{{\\tens{A}}}\n\\def\\tB{{\\tens{B}}}\n\\def\\tC{{\\tens{C}}}\n\\def\\tD{{\\tens{D}}}\n\\def\\tE{{\\tens{E}}}\n\\def\\tF{{\\tens{F}}}\n\\def\\tG{{\\tens{G}}}\n\\def\\tH{{\\tens{H}}}\n\\def\\tI{{\\tens{I}}}\n\\def\\tJ{{\\tens{J}}}\n\\def\\tK{{\\tens{K}}}\n\\def\\tL{{\\tens{L}}}\n\\def\\tM{{\\tens{M}}}\n\\def\\tN{{\\tens{N}}}\n\\def\\tO{{\\tens{O}}}\n\\def\\tP{{\\tens{P}}}\n\\def\\tQ{{\\tens{Q}}}\n\\def\\tR{{\\tens{R}}}\n\\def\\tS{{\\tens{S}}}\n\\def\\tT{{\\tens{T}}}\n\\def\\tU{{\\tens{U}}}\n\\def\\tV{{\\tens{V}}}\n\\def\\tW{{\\tens{W}}}\n\\def\\tX{{\\tens{X}}}\n\\def\\tY{{\\tens{Y}}}\n\\def\\tZ{{\\tens{Z}}}\n\n\n% Graph\n\\def\\gA{{\\mathcal{A}}}\n\\def\\gB{{\\mathcal{B}}}\n\\def\\gC{{\\mathcal{C}}}\n\\def\\gD{{\\mathcal{D}}}\n\\def\\gE{{\\mathcal{E}}}\n\\def\\gF{{\\mathcal{F}}}\n\\def\\gG{{\\mathcal{G}}}\n\\def\\gH{{\\mathcal{H}}}\n\\def\\gI{{\\mathcal{I}}}\n\\def\\gJ{{\\mathcal{J}}}\n\\def\\gK{{\\mathcal{K}}}\n\\def\\gL{{\\mathcal{L}}}\n\\def\\gM{{\\mathcal{M}}}\n\\def\\gN{{\\mathcal{N}}}\n\\def\\gO{{\\mathcal{O}}}\n\\def\\gP{{\\mathcal{P}}}\n\\def\\gQ{{\\mathcal{Q}}}\n\\def\\gR{{\\mathcal{R}}}\n\\def\\gS{{\\mathcal{S}}}\n\\def\\gT{{\\mathcal{T}}}\n\\def\\gU{{\\mathcal{U}}}\n\\def\\gV{{\\mathcal{V}}}\n\\def\\gW{{\\mathcal{W}}}\n\\def\\gX{{\\mathcal{X}}}\n\\def\\gY{{\\mathcal{Y}}}\n\\def\\gZ{{\\mathcal{Z}}}\n\n% Sets\n\\def\\sA{{\\mathbb{A}}}\n\\def\\sB{{\\mathbb{B}}}\n\\def\\sC{{\\mathbb{C}}}\n\\def\\sD{{\\mathbb{D}}}\n% Don't use a set called E, because this would be the same as our symbol\n% for expectation.\n\\def\\sF{{\\mathbb{F}}}\n\\def\\sG{{\\mathbb{G}}}\n\\def\\sH{{\\mathbb{H}}}\n\\def\\sI{{\\mathbb{I}}}\n\\def\\sJ{{\\mathbb{J}}}\n\\def\\sK{{\\mathbb{K}}}\n\\def\\sL{{\\mathbb{L}}}\n\\def\\sM{{\\mathbb{M}}}\n\\def\\sN{{\\mathbb{N}}}\n\\def\\sO{{\\mathbb{O}}}\n\\def\\sP{{\\mathbb{P}}}\n\\def\\sQ{{\\mathbb{Q}}}\n\\def\\sR{{\\mathbb{R}}}\n\\def\\sS{{\\mathbb{S}}}\n\\def\\sT{{\\mathbb{T}}}\n\\def\\sU{{\\mathbb{U}}}\n\\def\\sV{{\\mathbb{V}}}\n\\def\\sW{{\\mathbb{W}}}\n\\def\\sX{{\\mathbb{X}}}\n\\def\\sY{{\\mathbb{Y}}}\n\\def\\sZ{{\\mathbb{Z}}}\n\n% Entries of a matrix\n\\def\\emLambda{{\\Lambda}}\n\\def\\emA{{A}}\n\\def\\emB{{B}}\n\\def\\emC{{C}}\n\\def\\emD{{D}}\n\\def\\emE{{E}}\n\\def\\emF{{F}}\n\\def\\emG{{G}}\n\\def\\emH{{H}}\n\\def\\emI{{I}}\n\\def\\emJ{{J}}\n\\def\\emK{{K}}\n\\def\\emL{{L}}\n\\def\\emM{{M}}\n\\def\\emN{{N}}\n\\def\\emO{{O}}\n\\def\\emP{{P}}\n\\def\\emQ{{Q}}\n\\def\\emR{{R}}\n\\def\\emS{{S}}\n\\def\\emT{{T}}\n\\def\\emU{{U}}\n\\def\\emV{{V}}\n\\def\\emW{{W}}\n\\def\\emX{{X}}\n\\def\\emY{{Y}}\n\\def\\emZ{{Z}}\n\\def\\emSigma{{\\Sigma}}\n\n% entries of a tensor\n% Same font as tensor, without \\bm wrapper\n\\newcommand{\\etens}[1]{\\mathsfit{#1}}\n\\def\\etLambda{{\\etens{\\Lambda}}}\n\\def\\etA{{\\etens{A}}}\n\\def\\etB{{\\etens{B}}}\n\\def\\etC{{\\etens{C}}}\n\\def\\etD{{\\etens{D}}}\n\\def\\etE{{\\etens{E}}}\n\\def\\etF{{\\etens{F}}}\n\\def\\etG{{\\etens{G}}}\n\\def\\etH{{\\etens{H}}}\n\\def\\etI{{\\etens{I}}}\n\\def\\etJ{{\\etens{J}}}\n\\def\\etK{{\\etens{K}}}\n\\def\\etL{{\\etens{L}}}\n\\def\\etM{{\\etens{M}}}\n\\def\\etN{{\\etens{N}}}\n\\def\\etO{{\\etens{O}}}\n\\def\\etP{{\\etens{P}}}\n\\def\\etQ{{\\etens{Q}}}\n\\def\\etR{{\\etens{R}}}\n\\def\\etS{{\\etens{S}}}\n\\def\\etT{{\\etens{T}}}\n\\def\\etU{{\\etens{U}}}\n\\def\\etV{{\\etens{V}}}\n\\def\\etW{{\\etens{W}}}\n\\def\\etX{{\\etens{X}}}\n\\def\\etY{{\\etens{Y}}}\n\\def\\etZ{{\\etens{Z}}}\n\n% The true underlying data generating distribution\n\\newcommand{\\pdata}{p_{\\rm{data}}}\n% The empirical distribution defined by the training set\n\\newcommand{\\ptrain}{\\hat{p}_{\\rm{data}}}\n\\newcommand{\\Ptrain}{\\hat{P}_{\\rm{data}}}\n% The model distribution\n\\newcommand{\\pmodel}{p_{\\rm{model}}}\n\\newcommand{\\Pmodel}{P_{\\rm{model}}}\n\\newcommand{\\ptildemodel}{\\tilde{p}_{\\rm{model}}}\n% Stochastic autoencoder distributions\n\\newcommand{\\pencode}{p_{\\rm{encoder}}}\n\\newcommand{\\pdecode}{p_{\\rm{decoder}}}\n\\newcommand{\\precons}{p_{\\rm{reconstruct}}}\n\n\\newcommand{\\laplace}{\\mathrm{Laplace}} % Laplace distribution\n\n\\newcommand{\\E}{\\mathbb{E}}\n\\newcommand{\\Ls}{\\mathcal{L}}\n\\newcommand{\\R}{\\mathbb{R}}\n\\newcommand{\\emp}{\\tilde{p}}\n\\newcommand{\\lr}{\\alpha}\n\\newcommand{\\reg}{\\lambda}\n\\newcommand{\\rect}{\\mathrm{rectifier}}\n\\newcommand{\\softmax}{\\mathrm{softmax}}\n\\newcommand{\\sigmoid}{\\sigma}\n\\newcommand{\\softplus}{\\zeta}\n\\newcommand{\\KL}{D_{\\mathrm{KL}}}\n\\newcommand{\\Var}{\\mathrm{Var}}\n\\newcommand{\\standarderror}{\\mathrm{SE}}\n\\newcommand{\\Cov}{\\mathrm{Cov}}\n% Wolfram Mathworld says $L^2$ is for function spaces and $\\ell^2$ is for vectors\n% But then they seem to use $L^2$ for vectors throughout the site, and so does\n% wikipedia.\n\\newcommand{\\normlzero}{L^0}\n\\newcommand{\\normlone}{L^1}\n\\newcommand{\\normltwo}{L^2}\n\\newcommand{\\normlp}{L^p}\n\\newcommand{\\normmax}{L^\\infty}\n\n\\newcommand{\\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book.\n\n\\DeclareMathOperator*{\\argmax}{arg\\,max}\n\\DeclareMathOperator*{\\argmin}{arg\\,min}\n\n\\DeclareMathOperator{\\sign}{sign}\n\\DeclareMathOperator{\\Tr}{Tr}\n\\let\\ab\\allowbreak\n\n% \\newtheorem{definition}[theorem]{Definition}\n\n\\newcommand{\\tabincell}[2]{\\begin{tabular}{@{}#1@{}}#2\\end{tabular}} \n\n\\newcommand{\\draftonly}[1]{#1} \n\\newcommand{\\draftcomment}[3]{\\draftonly{{\\textcolor{#3}{[\\textbf{#1--\\textsc{#2}}]}}}}\n\\newcommand{\\jh}[1]{\\draftcomment{#1}{Junjie}{blue}}\n\\newcommand{\\wx}[1]{\\draftcomment{#1}{Wen}{olive}}\n\\newcommand{\\zc}[1]{\\draftcomment{#1}{Zefan}{red}}\n\\newcommand{\\yd}[1]{\\draftcomment{#1}{Yue}{purple}}\n\\newcommand{\\yc}[1]{\\draftcomment{#1}{Yichi}{pink}}\n\n\n\n\\usepackage{xspace}\n\\newcommand{\\pattern}[0]{RAG flow}\n\\newcommand{\\method}[0]{PyramidKV\\xspace}\n\n\\usepackage{cleveref}\n\\newcommand{\\Scref}[1]{\\S\\ref{#1}}\n\n\\title{PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling}\n\n\n% DinamicKV: Dynamic Layer-Wise Spasity-Aware KV Cache Compression\n% DinamicKV: Dynamic Spasity-based KV Cache Compression\n% RAG Flow: Understanding Retrieval-Augmented Generation in Information Flow Perspective\n% InstructKV: Instruciton-Aware KV Cache Pruning with Information Aggregation Flow\n\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to LaTeX to determine where to break the\n% lines. Using \\AND forces a line break at that point. So, if LaTeX puts 3 of 4\n% authors names on the first line, and the last on the second line, try using\n% \\AND instead of \\And before the third author name.\n\n\n\\author{%\nZefan Cai$^{1}$,\nYichi Zhang$^{2}$,\nBofei Gao$^{2}$,\nYuliang Liu$^{3}$, \nTianyu Liu$^{4}$, \n\\textbf{Keming Lu}$^4$, \\\\\n\\textbf{Wayne Xiong}$^{6}$,\n\\textbf{Yue Dong}$^{5}$,\n\\textbf{Baobao Chang}$^{2}$,\n\\textbf{Junjie Hu}$^{1}$,\n\\textbf{Wen Xiao}$^{6}$,\n\\\\\n$^1$University of Wisconsin - Madison \n$^2$Peking University \n$^3$Nanjing University \n$^4$Qwen \\\\\n$^5$University of California - Riverside \n$^6$Microsoft \\\\\n \\texttt{zefncai@gmail.com} \\\\\n % \\url{https://github.com/Zefan-Cai/PyramidKV} \\\\\n\\url{https://github.com/Zefan-Cai/PyramidKV} \\\\\n}\n\n\n\n\\begin{document}\n\n\n\\maketitle\n\\begin{abstract}\n%% \\yd{this pattern name can be changed}\\wx{I think this name makes sense, will replace the current one in the paper},\n\nIn this study, we investigate whether attention-based information flow inside large language models (LLMs) is aggregated through noticeable patterns for long context processing. Our observations reveal that LLMs aggregate information through \n\\textbf{Pyramidal} Information Funneling where attention is scattering widely in lower layers, progressively consolidating within specific contexts, and ultimately focusing on critical tokens (a.k.a massive activation or attention sink) in higher layers. Motivated by these insights, we developed \\method, a novel and effective KV cache compression method. This approach dynamically adjusts the KV cache size across different layers, allocating more cache in lower layers and less in higher ones, diverging from traditional methods that maintain a uniform KV cache size.\nOur experimental evaluations, utilizing the LongBench benchmark, show that \\method matches the performance of models with a full KV cache while retaining only 12\\% of the KV cache, thus significantly reducing memory usage. In scenarios emphasizing memory efficiency, where only 0.7\\% of the KV cache is maintained, \\method surpasses other KV cache compression techniques, achieving up to a 20.5 absolute accuracy improvement on TREC dataset. In the Needle-in-a-Haystack experiment, \\method outperforms competing methods in maintaining long-context comprehension in LLMs; notably, retaining just 128 KV cache entries enables the LLAMA-3-70B model to achieve 100.0 Acc. performance, matching that of a full KV cache.\n% \\zc{Need to mention we preserve full performance at LongBench at 2k and full performance at needle at 128}\n\n% In this study, we investigate whether attention-based information flow inside large language models (LLMs) is aggregated through noticeable patterns for long context processing. Our observations reveal that LLMs aggregate information through \n% Pyramidal Information Funneling where attention is scattering widely in lower layers, progressively consolidating within specific contexts, and ultimately focusing on critical tokens (a.k.a massive activation or attention sink) in higher layers. Motivated by these insights, we developed PyramidKV, a novel and effective KV cache compression method. This approach dynamically adjusts the KV cache size across different layers, allocating more cache in lower layers and less in higher ones, diverging from traditional methods that maintain a uniform KV cache size.\n% Our experimental evaluations, utilizing the LongBench benchmark, show that PyramidKV matches the performance of models with a full KV cache while retaining only 12\\% of the KV cache, thus significantly reducing memory usage. In scenarios emphasizing memory efficiency, where only 0.7\\% of the KV cache is maintained, PyramidKV surpasses other KV cache compression techniques, achieving up to a 20.5 absolute accuracy improvement on TREC dataset. In the Needle-in-a-Haystack experiment, PyramidKV outperforms competing methods in maintaining long-context comprehension in LLMs; notably, retaining just 128 KV cache entries enables the LLAMA-3-70B model to achieve 100\\% Acc. performance, matching that of a full KV cache.\n\n\n% In this work, we study the intrinsic attention patterns of Large Language Models (LLMs) when they answer questions based on long-context documents.\n% We discover that LLMs implicitly perform information aggregation from shallow layers to deeper ones. Specifically, in shallow layers, the information is first spread globally, and then aggregated within local context, and when it gets deeper, the information is further aggregated to few important tokens, which is so-called Massive Activation or Attention Sink in previous works. Insprired by the observation, we propose a novel and effective KV compression method called \\method. Different from the previous works in KV cache compression that retains the size of the maintained KV cache the same across different layers in LLM, we keep different numbers of KV cache for different layers, with lower layers retaining more while higher layers fewer.\n% In our experiments on LongBench, \\method shows a comparable performance with Full KV cache with only 5.8\\% KV cache kept, reducing the memory by xx\\%. In memory-efficient scenarios (when only 0.5\\% KV cache remaining), our model performs much better than other KV cache compression methods, leading up to 20\\% absolute improvement on the tasks.\n\n% The performance \n% ~\\method is xxx times faster than full KV cache technique while maintaining the same performance across LLM series (LlaMa and Mistral), sizes ($7$B, $13$B and $70$B) and architectures (Dense and MoE).\n% Our experiments also demonstrate that ~\\method is effective and efficient in streaming applications.\n\n% In shallow layers, the information flows from the context to the initial tokens for each document; in mature layers, the information flows from the initial tokens for each document to some abstract tokens. In the top layer, LLMs generate outputs almost solely rely on some global abstractive tokens with massive attention scores.\n% Based on the aforementioned study, we propose a plug-and-play method inference accelerate method ~\\method to perform KV cache compression.\n% Different from the KV cache compression that retains the size of the maintained key and value vectors the same across Transformer layers, we conduct a dynamic KV Cache compression method that \n% targeted profiling to discern the intrinsic structure of attention modules. \n% ~\\method is xxx times faster than full KV cache technique while maintaining the same performance across LLM series (LlaMa and Mistral), sizes ($7$B, $13$B and $70$B) and architectures (Dense and MoE).\n% Our experiments also demonstrate that ~\\method is effective and efficient in streaming applications.\n\\end{abstract}\n\n\n\n\\section{Introduction}\n\\label{section:introduction}\n% \\wx{I rewrite the introduction section below.}\n\nLarge language models (LLMs)~\\citep{achiam2023gpt,touvron2023llama,touvron2023llama2,jiang2023mistral} are integral to various natural language processing applications, including dialogue systems~\\citep{vicuna2023}, document summarization~\\citep{fabbri-etal-2019-multi}, and code completion~\\citep{roziere2023code}. These models have recently been scaled up to handle long contexts~\\citep{fu2024data, ding2024longrope, zhu2023pose, chen2023longlora}, with GPT-4 processing up to 128K tokens and Gemini-pro-1.5 handling 1M tokens. However, scaling LLMs to extremely long contexts naturally leads to a significant delay due to the quadratic computation of attention over long contexts. A common solution to mitigate such inference delays involves caching the key and value states (KV) of previous tokens~\\citep{waddington2013kv}, with the trade-off of requiring extensive GPU memory storage. For instance, maintaining a KV cache for 100K tokens in LLaMA-2 7B requires over 50GB of memory, while a 2K context requires less than 1GB of memory~\\citep{wu2024retrieval}.\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/dynamickv4.pdf}\n \\caption{\n Illustration of~\\method compared with existing KV cache compression methods.\n (a) Full KV has all tokens stored in the KV cache in each layer; cache size increases as the input length increases.\n (b) StreamingLLM~\\citep{xiao2023efficient} only keeps few initial tokens with a fixed cache size in each layer.\n (c) SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} keep a fixed cache size across Transformer layers, and their selection is based on the attention score.\n (d)~\\method maintains pyramid-like cache sizes, allocating more cache budget to lower layers and less to higher layers. This approach to KV cache selection better aligns with the increasing attention sparsity observed in multi-layer Transformers (\\Scref{section:observation}).\n }\n \\label{figure:comparison}\n\\end{figure}\n\nTo tackle these memory constraints, recent studies have explored the optimization of KV caching, including approaches such as low-rank decomposition of the KV cache~\\citep{dong2024get} or pruning non-essential KV cache~\\citep{zhang2024h2o, li2024snapkv, ge2023model}. Notably, it has been shown that maintaining merely 20\\% of the KV cache can preserve a substantial level of performance~\\citep{zhang2024h2o}. Moreover, extreme compression of the KV cache for tasks of longer contexts (e.g., retrieval augmented generation or RAG for short) can drastically improve efficiency and further reduce resource use. However, questions about the universal applicability of these strategies across all layers of an LLM remain open. (1) \\textit{Are these KV cache strategies applicable to all layers? }(2) \\textit{Is it computationally efficient to use the same KV cache size across layers as previous studies have done?} These considerations suggest a need for an in-depth, more nuanced understanding of KV cache optimization in LLMs. %\\jh{What is missing in the literature? we need one more sentence to motivate our research. Why do we perform this study? something like: ``However, a comprehensive understanding of the KV cache optimization is still missing.''}\\wx{Agree, added several sentences for motivation.}\n\nTo examine these questions, we aim to systematically investigate the design principles of the KV cache compression across different layers, specifically tailored to the behaviors of the attention mechanism. We first investigate how information flow is aggregated via attention mechanisms across different layers in multi-document question answering (QA), a classic task involving long contexts. Our analysis identifies a notable transition of attention distribution from a broad coverage of global contexts to a narrow focus of local tokens over layers in LLMs. This pattern suggests an aggregated information flow where information is initially gathered broadly and subsequently narrowed down to key tokens, epitomizing the massive attention phenomenon. Our findings provide unique insights beyond the previously documented ``massive activation''~\\citep{sun2024massive} that very few activations exhibit significantly larger values than others when calculating multi-head attention in LLMs and ``attention sink''~\\citep{xiao2023efficient} that keeping the KV of initial tokens will largely recover the performance of window attention.\n\nBuilding on these insights on how information flows are aggregated through a pyramid pattern, we design a novel and effective KV cache pruning approach that mirrors the geometric shape, named PyramidKV. As shown in \\autoref{figure:comparison}, unlike the fixed-and-same length KV cache pruning common in prior works~\\citep{zhang2024h2o, ge2023model, li2024snapkv}, PyramidKV allocates more KV cache to the lower layers where information is more dispersed and each KV holds less information while reducing the KV cache in higher layers where information becomes concentrated in fewer key tokens. To the best of our knowledge, PyramidKV is the first KV cache compression method with varied cache retention across layers, tailoring cache amounts to the informational needs of each layer and paving the way for future research.\n\n\nWe conducted comprehensive experiments on LongBench~\\citep{bai2023longbench} using 17 datasets across various tasks and domains with three backbone models (LLaMa-3-8B-Instruct, LLaMa-3-70B-Instruct and Mistral-7B~\\citep{jiang2023mistral}). The results show that \\method preserves performance using just 12.0\\% of the KV cache (KV Cache size = 2048) on the LongBench benchmark and significantly outperforms other methods in extreme conditions, retaining only 0.7\\% of the KV cache. Moreover, \\method outperforms baseline models (H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv}, StreamingLLM~\\citep{xiao2023efficient}) across all tested cache sizes (64, 96, 128, 256), with its advantages most pronounced at smaller cache sizes. In the Needle In A Haystack experiment, \\method effectively maintains the long-context comprehension in LLMs, outperforming than competing methods. Remarkably, with \\method, retaining only 128 KV cache entries allows the LLaMa-3-70B-Instruct model to achieve 100.0 Acc. performance, matching the performance of a full KV cache.\n% \\zc{Need to mention we preserve full performance at LongBench at 2k and full performance at needle at 128}\n\n\n\n\n\n\n\n\n% We conduct extensive experiments on LongBench~\\citep{bai2023longbench} (including 17 datasets across different tasks and domains) with two different base models (LLaMa-3-8B-Instruct and Mistral-7B~\\citep{jiang2023mistral}) in \\Scref{section:experiment}. The experiment results show that PyramidKV can preserve the performance with only 12.0\\% KV cache, and outperforms the baseline methods in extreme scenarios (with only 0.7\\% KV cache kept).\n% Our evaluation also shows that ~\\method outperforms baselines (i.e., H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv} and StreamingLLM~\\citep{xiao2023efficient}) across various cache sizes (64, 96, 128, 256, 512), and the performance strengths of PyramidKV are more evident in\n% small KV Cache sizes.\n% Our experiment on Needle In A HayStask demonstrates that~\\method preserves the long-context understanding ability of LLMs better than other compression methods, which may explain the superiority of ~\\method in LongBench.\n\n\n% \\jh{Check this link: \\url{https://cs.stanford.edu/people/widom/paper-writing.html}. Make sure you answer the five questions suggested in the blog post.}\n\n% Comment out \n% Large Language Models (LLMs)~\\citep{achiam2023gpt,touvron2023llama1,touvron2023llama} are now widely applied in many natural language processing applications, including dialog systems~\\citep{vicuna2023}, document summarization~\\citep{fabbri-etal-2019-multi}, code completion~\\citep{roziere2023code}.\n\n% Deploying and inferring with LLMs in a long context requires a significant waiting time. Caching previous tokens' Key and Value states (KV) ~\\citep{waddington2013kv} is a widely adopted technique for accelerating inference, but it will consume massive extensive memory scaling linearly with the sequence length and batch size. For example, for LLaMA 2 7B, the KV cache of 100K tokens requires more than 50GB memory,\n% while 2K context requires less than 1GB memory\\citep{} (cite retrieval head paper).\n% Existing works focus on KV cache compression to reduce memory consumption.\n% H2)~\\citep{zhang2024h2o}\n% FastGen~\\citep{ge2023model} decides separate KV cache compression strategies for each head in multi-head transformers.\n% StreamingLLM~\\citep{xiao2023efficient} keeps the very few initial tokens with extreme attention scores and the local window tokens based on the observation of Attention Sink.\n% However, StreamingLLM fails in lots of \n\n% To understand the failure of Streaming, we find an interesting phenomenon of autoregressive\n% LLMs: a surprisingly large amount of attention score is allocated to the initial tokens \\jh{Some existing works also find this pattern. Make sure we don't overclaim but also highlight the unique insight. Make a clear comparison.}\n\n% \\jh{Change ``initial tokens'' to ``first few tokens''}\n% In shallow layers (i.e., layer 0 to layer 16), LLMs implicitly perform document abstraction through multi-layer transformers.\n% For each document, the context of each document increases the attention score to the initial few tokens of the document as the information flows from shallow layers to deep layers.\n% The initial tokens inside each document serve as abstraction tokens to store the knowledge of the document.\n\n% \\paragraph{Multi-Document Abstraction}\n% In middle layers (i.e., layer 16 to layer 32), LLMs implicitly perform multi-document abstraction through multi-layer transformers.\n% Specifically, the context of each document decreases the attention score of the first few tokens and increases the attention scores of some global abstractive tokens as the information flows from shallow layers to deep layers.\n\n% \\jh{It's not very natural to see the transition from the observations above to the design of our KV cache. Need some smoothing. We need a compact sentence to summarize the key property of the KV cache method which is inspired from the observation.}\n\n% \\wx{agree, revised (replace text starting from 'To understand the failure of Streaming...'): \n% Through the investigation of attention matrices in large language models (LLMs), we observed that, in addition to the 'massive attention' noted in prior studies \\citep{}, the attention scores shift from a global to a local focus, ultimately concentrating on a few tokens as one moves from lower to higher layers. This pattern suggests an aggregated information flow within the model: information is first gathered locally from the context and then concentrated into a few tokens, leading to the massive attention phenomenon.}\n% Based on the aforementioned analysis, it is intuitive to explore the application of efficient inference methods, since the LLM generates outputs solely relying on the global abstractive tokens.\n% Based on the aforementioned patterns, we argue that KV Cache pruning should consistently compress the same tokens across layers and heads.\n\n% During the decoding stage, caching previous tokens' Key and Value states (KV) consumes extensive memory \n% ~\\citep{xiao2023efficient}\n\n\n\n% Fortunately, our preliminary obse has yielded intriguing observations about the empirical\n% properties of LLMs. These findings pave the way for the potential design of an efficient KV cache:\n\n% (1) Unlike the hypothesis of previous works that XXX\\jh{summarize the prior work}, we observe that the attention matrices of LLMs increase from less than 30\\% sparse in bottom layers to over 95\\% sparse across a wide range of LLMs and tasks.\n% This may weaken the previous conclusion that only a small percentage of the KV cache is sufficient for decoding the same output token at each generation step.\n% Therefore, the required KV cache may decrease as the layer increases.\n\n% Based on the aforementioned observations, we argue that\n% (1) the \n\n\n\\section{Related Work}\n\\label{section:related_work}\n\n% \\subsection{Attention Pattern of LLMs}\n% \\jh{my overall impression after reading this section is that it's not clear what new things we bring to the community. and in which aspects? }\\wx{added several sentences in each subsection.}\n\n% \\subsection*{Interpretation of LLMs}\n% \\wx{Done with this section}\n% Previous works have explored the attention mechanism in LLMs, and it has been found that the attention matrices are usually sparse - few tokens have been attended excessively while others receiving little attention - which is also in-line with our findings. For example, \\citet{xiao2023efficient} observes attention sink, that keeping the KV of initial tokens will largely recover the performance of window attention even if they are not semantically important. Similarly, \\citet{sun2024massive} discovers massive activations, that very few activations exhibit significantly larger values than others inside LLMs (but not necessarily the first few tokens) and the values largely stay constant regardless of the input, and they function as indispensable bias terms. In another line of work, researchers found that there are certain patterns existing across different attention heads or layers. \\citet{li2024snapkv} discovers that each attention head in the model consistently focuses on specific prompt attention features during generation. And \\citet{wang2023label} reveals that label words in the demonstration examples of In-Context Learning function as anchors - semantic information aggregates into label word representations during the shallow computation layers’ processing and then the consolidated\n% information in label words serves as a reference for LLMs’ final predictions. Beyond language models, \\citet{chen2024image} identifies the inefficient attention phenomena in Large Vision-Language Models (LVLMs), that the attention computation over visual tokens is of extreme inefficiency in the deep layers.\n\n\\paragraph{Interpretation of LLMs}\nPrior research has shown that attention matrices in LLMs are typically sparse~\\citep{chen2024image,xiao2023efficient,zhang2024h2o}, focusing disproportionately on a few tokens. For instance, \\citet{xiao2023efficient} identified an ``attention sink'' phenomenon, where maintaining the Key and Value (KV) states of the first few tokens can substantially restore the performance of windowed attention, despite these tokens not being semantically crucial. Similarly, \\citet{sun2024massive} identified a ``massive activations'' pattern, where a minority of activations show significantly larger values than others within LLMs. Interestingly, these values remain relatively constant across different inputs and act as critical bias terms in the model. %\\jh{As we have Sec 3. to analyze the attention pattern in the main paper, what are the new findings to the community compared to the literature? We should make a clear distinction and show the significance of our work}\\wx{added one sentence below.}\n\nFurther explorations in this field reveal distinct patterns across various attention heads and layers. \\citet{li2024snapkv} observed that certain attention heads consistently target specific prompt attention features during decoding. Additionally, \\citet{wang2023label} discovered that in In-Context Learning scenarios, label words in demonstration examples serve as semantic anchors. In the lower layers of an \nLLM, shallow semantic information coalesces around these label words, which subsequently guide the LLMs’ final output predictions by serving as reference points. Recently,\n\\citet{wu2024retrieval} revealed that a special type of attention head, the so-called retrieval head, is largely responsible for retrieving information. Inspired by these findings that the attention mechanism exhibits varying behaviors across different layers, we discovered that ``Massive Activation'' does not consistently manifest across all layers in long context sequences; instead, it predominantly occurs in the upper layers. Additionally, we identified a novel trend of information aggregation specific to long-context inputs, which will be further explained in \\Scref{section:observation}.\n\n% Extending beyond the realm of language models, \\citet{chen2024image} reported similar inefficiencies in Large Vision-Language Models (LVLMs), particularly noting that attention processing over visual tokens becomes markedly inefficient in deeper layers. These findings across different types of models highlight a broader pattern of specific, intense focus areas within attention mechanisms, which are pivotal for the models' processing and output generation capabilities. \\jh{This paragraph on VLM seems a bit distracting. Maybe omit if space is limited.}\\wx{agree, can be removed}\n\n\n\n\n% \\subsection{LLM Acceleration}\n% \\subsection*{KV Cache Compression}\n% As \n% FastGen~\\citep{ge2023model} constructs the KV cache in an adaptive manner: evicting long-range contexts on attention heads emphasizing local contexts, discarding non-special tokens on attention heads centered on special tokens, and only employing the standard KV cache for attention heads that broadly attend to all tokens.\n% \\wx{Need to add at least snapkv, h20 } \\zc{Done}\n% SnapKV~\\citep{li2024snapkv} automatically compresses KV caches by selecting clustered important KV positions for each attention head based on their attention scores.\n% ~\\citep{zhang2024h2o} proposes Heavy Hitter Oracle (H2O), a KV cache eviction policy that dynamically retains a balance of recent and H2 tokens.\n% StreamingLLM~\\citep{xiao2023efficient} proposes an efficient framework\n% that enables LLMs trained with a finite length attention window to generalize to infinite sequence length without any fine-tuning.\n\n\\paragraph{KV Cache Compression}\nThere has been a growing interest in addressing LLMs' memory constraints on processing long context inputs. FastGen~\\citep{ge2023model} introduces an adaptive KV cache management strategy that optimizes memory use by tailoring retention tactics to the specific nature of attention heads. This method involves evicting long-range contexts from heads that prioritize local interactions, discarding non-special tokens from heads focused on special tokens, and maintaining a standard KV cache for heads that engage broadly across tokens. SnapKV~\\citep{li2024snapkv} improves efficiency by compressing KV caches via selecting/clustering significant KV positions based on their attention scores. Heavy Hitter Oracle (H2O)~\\citep{zhang2024h2o} implements a dynamic eviction policy that effectively balances the retention of recent and historically significant tokens, optimizing memory usage while preserving essential information. StreamingLLM~\\citep{xiao2023efficient} enables LLMs trained on finite attention windows to handle infinite sequence lengths without fine-tuning, thus expanding the models' applicability to broader contexts. LM-Infinite~\\citep{han2023lm} allows LLMs pre-trained with 2K or 4K-long segments to generalize to up to 200M length inputs while retaining perplexity without parameter updates.\n\nWhile these approaches have significantly advanced the efficient management of memory for LLMs, they generally apply a fixed KV cache size across all layers. In contrast, our investigations into the attention mechanisms across different layers of LLMs reveal that the attention patterns vary from layer to layer, making a one-size-fits-all approach to KV cache management suboptimal. In response to this inefficiency, we propose a novel KV cache compression method, called \\method that allocates different KV cache budgets across different layers, tailored to the unique demands and operational logic of each layer's attention mechanism. This layer-specific strategy takes a significant step toward balancing both memory efficiency and model performance, addressing a key limitation in existing methodologies.\n\n\n\n% \\section{Aggregated Information Flow}\n\\section{Pyramidal Information Funneling}\n\\label{section:observation}\n% \\wx{I rewrite this section}\\yc{Fix the correspondence between Figure2 and text, But it seems like LLaMA3 doesn't have the \"massive activation\" pattern and \"attention sink\"} \n% \\zc{Got a solution: mention llama and cite llama-1 and llama-2 report.}\n\nTo systematically understand the attention mechanism over layers in LLMs for long-context inputs, we conduct a fine-grained study focusing on the multi-document question answering (QA) task. The model is presented with multiple interrelated documents and prompted to generate an answer for the given query. The main target is to investigate how the model aggregates dispersed information within these retrieved documents for accurate responses. \n\n\\begin{figure}[ht]\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/obs.pdf}\n \\caption{\n Attention patterns of retrieval-augmented generation across layers in LlaMa~\\citep{touvron2023llama, touvron2023llama2} reveal that in the lower layers, the model exhibits a broad-spectrum mode of attention, distributing attention scores uniformly across all content. In the middle layers, attention becomes more localized within each document, indicating refined information aggregation (dotted red triangular shapes in layers 6 and 10). This culminates in the upper layers, where ``massive attention'' focuses on a few key tokens (concentrated attention bars after layer 18), efficiently extracting essential information for answers.\n % \\footnote{The attention analysis is based on LlaMa-2-7B-chat.}\n }\n \\label{figure:rag_flow}\n\\end{figure}\n\n% \\begin{figure}[ht]\n% \\centering\n% \\includegraphics[width=\\columnwidth]{Figures/layers.pdf}\n% \\caption{\n% \\zc{To be done}\n% }\n% \\label{figure:rag_flow}\n% \\end{figure}\n\nIn particular, we focus on our analysis of the LLaMa~\\citep{touvron2023llama, touvron2023llama2} and visualize the distribution and behavior of attention scores over layers. %\\jh{How do you visualize the attention in MHA? Which attention head do you select for visualization?}\\wx{\nTo assess the distinct behaviors of each multi-head self-attention layer, we compute the average attention from all heads within each layer. \\autoref{figure:rag_flow} shows the attention patterns of one QA example over six different layers (i.e., 0, 6, 12, 18, 24, and 30).\n\nWe identify an approximately uniform distribution of attention scores from the lower layers (e.g., the 0th layer). This suggests that the model operates in a broad-spectrum mode at the lower layers, aggregating information globally from all available content without prioritizing its attention on specific input segments. Notably, a distinct transition to a more localized attention pattern within each document emerges, as the model progresses to encode information at the middle layers (6th to 18th layers). In this phase, attention is predominantly directed towards tokens within the same document, suggesting a more refined aggregation of information within individual contexts.\n\n\n\nThis trend continues and intensifies in the upper layers (from the 24th to the 30th layer), where we observed the emergence of `massive attention' phenomena. In these layers, the attention mechanism concentrates overwhelmingly on a few key tokens. This pattern of attention allocation, where extremely high attention scores are registered, signifies that the model has aggregated the essential information into these focal tokens. Such behavior underscores a sophisticated mechanism by which LLMs manage and streamline complex and voluminous information, culminating in the efficient extraction of the most pertinent data points necessary for generating accurate answers.\n\n%The primary objective was for the model to synthesize the dispersed information contained within these documents to formulate a coherent and accurate response, effectively simulating a typical real-life information retrieval scenario.\n% To delve deeper into the operational dynamics of the attention mechanism in LLMs, especially when dealing with lengthy contextual inputs, we initiated a comprehensive study centered on the task of multi-document question answering (QA). This experimental setup involved presenting the model with multiple interrelated documents alongside a specific query. The primary objective was for the model to synthesize the dispersed information contained within these documents to formulate a coherent and accurate response, effectively simulating a typical real-life information retrieval scenario.\n\n% Our analysis included a detailed investigation of the distribution and behavior of attention scores across various layers of the model. We show a real example with sampled layers - 5, 10, 15, 20, 25, and 30—as illustrated in \\autoref{figure:rag_flow}.\n\n% The findings from the lower layers (specifically, the 5th layer) indicated an approximately uniform distribution of attention scores. This suggests that at this stage, the model operates in a broad-spectrum mode, capturing and assimilating information globally from all available content without prioritizing specific sections of the input. As the model progresses to the middle layers (10th to 15th layers), there is a distinct transition to a more localized approach. In this phase, attention is predominantly directed towards tokens within the same document, suggesting a more refined aggregation of information within individual contexts.\n\n\n% \\autoref{figure:rag_flow} presents the information flow inside LLMs when they generate outputs based on external resources.\n% \\paragraph{Single-Document Aggregation}\n% In shallow layers (i.e., layer 0 to layer 16), LLMs implicitly perform document abstraction through multi-layer transformers.\n% For each document, the context of each document increases the attention score to the first few tokens of each document as the information flows from shallow layers to deep layers.\n% The first few tokens inside each document serve as abstraction tokens to store the knowledge of the document.\n% \\paragraph{Multi-Document Abstraction}\n% In middle layers (i.e., layer 16 to layer 32), LLMs implicitly perform multi-document abstraction through multi-layer transformers.\n% Specifically, the context of each document decreases the attention score of the initial few tokens and increases the attention scores of some global abstractive tokens as the information flows from shallow layers to deep layers.\\jh{How can we derive this conclusion? Are you referring to the vertical bars in the figure? We should explicitly point the reader to the pattern in the figure.}\n% \\paragraph{Generation based on Global Abstractive Tokens}\n% In upper layers, the attention score to the global abstractive tokens becomes really massive that the LLMs generate outputs even solely rely on the global abstractive tokens.\n\n\n\n% Based on the aforementioned analysis, it is intuitive to explore the application of efficient inference methods, since the LLM generates outputs solely relying on the global abstractive tokens.\n% Previous work~\\citep{li2024snapkv, ge2023model} that performs separate KV cache pruning strategies across attention heads and transformer layers.\n\n% Based on the aforementioned patterns, we propose three hypotheses for KV cache prune: \\jh{If we have experimental results to verify these hypotheses, we should mention to refer the readers to the later section.}\n\n% \\begin{enumerate}[leftmargin=15pt,topsep=1pt] \\itemsep-0.2em\n% \\item \\textbf{Consistent Prune} KV Cache pruning should consistently compress the same tokens across layers and attention heads. Otherwise, the pruning will cut off the information flow inside LLMs and decrease the performance.\n% \\item \\textbf{Deep Layer leads} Middle layers know which tokens the information is aggregated, while the attention patterns of shallow layers ignore the patterns of document abstractive tokens; the attention patterns of upper layers ignore the patterns of global abstractive tokens.\n% \\end{enumerate}\n\n\n% \\jh{TODO: need more mathematical formulation.}\n% \\zc{It is done. I believe the formulation and method part need some paraphrase to make it more clear. It is too detailed and long as for now.}\n\n\\section{PyramidKV}\n\\label{section:method} \n\\subsection{Preliminaries and Problem Formulation}\n% \\label{section:problem_formulation}\n\nIn an autoregressive transformer-based LLM, the generation of the \n$i$-th token requires that the attention module computes the query, key, and value vectors for all previous $i-1$ tokens. To speed up the inference process and avoid duplicate computations, the key and value matrices are typically stored in the GPU memory. While the KV cache enhances inference speed and reduces redundant computations, it can consume significant memory when dealing with long input contexts. To optimize memory usage, a strategy called KV cache compression is proposed~\\citep{zhang2024h2o, xiao2023efficient, li2024snapkv}, which involves retaining only a minimal amount of KV cache while preserving as much information as possible.\n\n% During the decoding stage, caching previous tokens' Key and Value states (KV) consumes extensive memory, especially when the input sequence and the generation output are long.\n% KV cache compression aims to alleviate this challenge by retaining the important key and value matrix with limited KV cache.\n\n% \\jh{The notation below is a bit complicated and unclear to me. Need a bit of simplification.}\n% \\jh{Formally, we should use $\\mK\\in \\R^{n\\times d}$ for a matrix and use $K$ for a scalar}\n\nIn a language model with $m$ transformer layers, we denote the key and value matrices in the $l$-th attention layer respectively as $\\mK^l, \\mV^l \\in \\R^{n\\times d}, \\forall l\\in [0, m-1]$ when encoding a sequence of $n$ tokens. The goal of KV cache compression is to seek two sub-matrices $\\mK^l_s, \\mV^l_s \\in \\R^{k^l \\times d}$ from the full matrices $\\mK^l$ and $\\mV^l$, given a cache budget $k^l<n$ for each layer $l\\in [0, m-1]$ while maximizing performance preservation. That is, a language model with KV cache compression only uses $\\mK^l_s$ and $\\mV^l_s$ in the GPU memory for inference on a dataset $\\gD$, and obtains a similar result to a full model according to an evaluation scoring metric, i.e., $\\text{score}(\\mK^l, \\mV^l, \\gD) \\approx \\text{score}(\\mK^l_s, \\mV^l_s, \\gD)$. \n\n% \\paragraph{KV Cache Compression for A Single-layer Transformer}\n% In the context of a single-layer transformer within one attention head, let $K$ and $V$ denote the full key and value matrices, respectively, each of dimension $\\mathbb{R}^{n \\times d}$. The objective of KV cache compression is to identify and retain smaller sub-matrices $K_s \\in \\mathbb{R}^{k \\times d}$ and $V_s \\in \\mathbb{R}^{k \\times d}$, where $k$ is less than $n$ and represents the number of key-value pairs retained. This approach aims to ensure that the outputs computed using these sub-matrices closely approximate those derived from the complete $K$ and $V$ matrices.\n% Formally, we define the generative process with KV cache size for a single layer transformer.\n\n\n% $K_{\\leq n,*}$ represents the first $n$-th row of $K \\in \\mathbb{R}^{n \\times d}$ and $V_{\\leq n, *}$ represents the first $n$ rows of $V \\in \\mathbb{R}^{n \\times d}$. Let $k$ denote the budget of space and $k < n$.\n\n% The selected rows $K_s \\in \\mathbb{R}^{k \\times d}$ denotes a sub-matrix of $K \\in \\mathbb{R}^{n \\times d}$ which selects $k$ rows from $K \\in \\mathbb{R}^{n \\times d}$, and the selected $V_s \\in \\mathbb{R}^{k \\times d}$ denotes a sub-matrix of $K \\in \\mathbb{R}^{n \\times d}$ which selects $k$ rows from $V \\in \\mathbb{R}^{n \\times d}$.\n\n% % For the non-selected rows $K_d \\in \\mathbb{R}^{k \\times d}$\n% The discarded rows $K_c \\in \\mathbb{R}^{n - k \\times d}$ denotes a sub-matrix of $K \\in \\mathbb{R}^{n - k \\times d}$ which were not selected, and the discarded rows $V_c \\in \\mathbb{R}^{n - k \\times d}$ denotes a sub-matrix of $V \\in \\mathbb{R}^{n - k \\times d}$ which were not selected, we do not keep that rows in the GPU memory.\n\n% % \\begin{definition}[KV cache compression policy, informal]\n% % \\label{definition:kv_cache_compression_policy}\n\n% Let $K$ and $V$ denote the source set. Let $K_s$ and $V_s$ denote the target set.\n% % Let $k$ denotes the budget of key and value matrix space.\n% Our goal is to find a KV cache compression method that the output $i$-th token of the generative process based on $K$ and $V$ is similar to the output of the generative process based on $K_s$ and $V_s$.\n% We defined the compression policy $p: K, V \\to K_s, V_s$.\n\n% For the generation of the $i$-th token, we have\n% \\begin{itemize}[itemsep=0.1pt,topsep=0pt,leftmargin=*]\n% \\item $|K_s| = k$ and $|V_s| = k$\n% \\item The standard multi-head attention output is $o_i = D_i^{-1} \\cdot exp(Q_i \\cdot (K_i)^T)$, where \n% \\item $| S_i \\backslash S_{i-1} | \\leq 1$ or equivalently $|S_i \\cap S_{i-1}| \\geq k-1$ (we can evict at most $1$ $\\kv$ in the $\\kv$ $\\cache$)\n% \\end{itemize}\n\n% \\end{definition}\n\n\n% \\paragraph{KV cache compression for multi-layer transformers} \\wx{I don't see any difference between these two settings, I think we can remove this paragraph.}\\jh{Agreed.}\n\n% Then we switch to define the generative process with limited KV cache size for multi-layer transformers.\n\n% The cache size limitation is defined as $K = {k^0, ..., k^m}$, where $k^l < n$ denotes the cache size limitation for layer $l$ and $m$ denotes the number of layers for transformers.\n\n% For layer $l < m$, $K^l_{\\leq n,*}$ represents the first $n$-th row of $K^l \\in \\mathbb{R}^{n \\times d}$ and $V^l_{\\leq n, *}$ represents the first $n$ rows of $V^l \\in \\mathbb{R}^{n \\times d}$.\n% The selected rows $K^l_s \\in \\mathbb{R}^{k \\times d}$ denotes a sub-matrix of $K^l \\in \\mathbb{R}^{n \\times d}$ which selects $k^l$ rows from $K^l \\in \\mathbb{R}^{n \\times d}$, and the selected $V^l_s \\in \\mathbb{R}^{k \\times d}$ denotes a sub-matrix of $K^l \\in \\mathbb{R}^{n \\times d}$ which selects $k^l$ rows from $V^l \\in \\mathbb{R}^{n \\times d}$.\n\n% For layer $l < m + 1$, the discarded rows $K^l_c \\in \\mathbb{R}^{n - k \\times d}$ denotes a sub-matrix of $K^l \\in \\mathbb{R}^{n - k \\times d}$ which were not selected, and the discarded rows $V^l_c \\in \\mathbb{R}^{n - k \\times d}$ denotes a sub-matrix of $V^l \\in \\mathbb{R}^{n - k \\times d}$ which were not selected, we do not keep that rows in the GPU memory.\n\n% For layer $l < m$, let $K^l$ and $V^l$ denote the source set. Let $K^l_s$ and $V^l_s$ denote the target set.\n% % Let $k^l$ denotes the budget of key and value matrix space.\n% Our goal is to find a KV cache compression method that the output $i$-th token of the generative process based on $K^l$ and $V^l$ is similar to the output of the generative process based on $K^l_s$ and $V^l_s$.\n\n% \\end{definition}\n\n\n% \\subsection{Ineffective Greedy Algorithm}\n\n% We empirically observe that local attention, which is calculated using local statistics at every decoding step\n% by summing up the attention scores of the previous tokens, is ineffective as taking into account\n% the attention of future tokens.\n% Formally,\n\n% Fortunately, the attention scores to the previous tokens are accessible when performing KV cache compression. Therefore, we build a layer-wise dynamic compression. Formally,\n\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/method2.pdf}\n \\caption{\n Illustration of~\\method. At the lower level of the transformer, the \\method selects more keys and values based on the exhibited average attention pattern. Fewer keys and values at the higher level are selected based on the massive activation pattern, where we observe that attention scores are concentrated over local regions.}\n \\label{figure:method}\n\\end{figure}\n\n\n\\subsection{Proposed Method}\n\\label{section:method}\n\n% \\jh{Zefan, could you follow the notation in Sec 4 to polish the method section? It seems a bit complicated. Please check this link for formal writing of math equations: \\url{http://demo.clab.cs.cmu.edu/cdyer/short-guide-typesetting.pdf}}\n% \\zc{I re-write this section based on the notation. The subsection \n% as two parts of this method should be re-named.}\n\nIn this section, we introduce our method, \\method, based on the pyramidal information funneling observed across different layers in \\Scref{section:observation}. \\method consists of two steps: (1) Dynamically allocating different KV cache sizes/budgets across different layers (\\Scref{subsection:pyramid_size_allocation}); and (2) Selecting important KV vectors in each attention head for caching (\\Scref{subsection:key_and_value_selection}).\n\n\\subsubsection{KV Cache Size/Budget Allocation}\n\\label{subsection:pyramid_size_allocation}\n% \\wx{I have rewritten this part}\nPrevious work on KV cache compression~\\citep{li2024snapkv,zhang2024h2o,xiao2023efficient} often allocates a fixed KV cache size across LLM layers. However, as our analysis in \\Scref{section:observation} demonstrates, attention patterns are not identical across different layers. Particularly dense attention is observed in the lower layers, and sparse attention in higher layers. Therefore, using a fixed KV cache size across different layers may lead to suboptimal performance. These approaches may retain many unimportant tokens in the higher layers of sparser attentions while potentially overlooking many crucial tokens in the lower layers of denser attentions.\n% SnapKV~\\citep{li2024snapkv}, H2O~\\citep{zhang2024h2o} and StreamingLLM~\\citep{xiao2023efficient} apply a fixed key and value matrix cache size $k$ across multi transformer layers.\n% Based on our observation at \\Scref{section:observation}, we find that the attention sparsity of LLMs increase from lower layers to upper layers.\n% The efficiency of aforementioned methods suffers a lot, because they retaining a large number of unimportant tokens in the sparse tiop layers while missing many important tokens in the dense bottom layers.\n\nThus, we propose to increase compression efficiency by dynamically allocating the cache budgets across layers to reflect the aggregated information flow based on attention patterns.\nSpecifically, \\method allocates more KV cache to the lower layers where information is\nmore dispersed and each KV state contains less information, while reducing the KV cache in higher layers where information becomes concentrated in a few key tokens.\n\n% (within a local window---a document for instance)\n% \\jh{Did you define what ``local window'' is? Is it a fixed-size text segment? Are you referring to a document in the multi-document QA?} \n% \\zc{local window is defined and used by h2o and snapKV, They use it to represent a fixed size Key and Value cache in the last few tokens of the input sequence.} \\wx{I still feel `local' window is a bit confusing in this context, instead we call them instruction tokens (which is referred as local window in (cite), dooes it sound good?'} \n% \\zc{instruction tokens (which is referred as local window in (cite) looks good.}\n\nFollowing the common practice in KV cache compression~\\citep{li2024snapkv, xiao2023efficient}, %\\wx{cite the work with local window} \\zc{Done}, \nwe first retain the KV cache for the last $\\alpha$ tokens of the input across all layers, as these tokens have been shown to contain the most immediate task-related information, where $\\alpha$ is a hyperparameter, controlling the number of last few tokens being included in the KV cache.\n% \\jh{It's confusing. Isn't $\\alpha$ denoting the last $\\alpha$ tokens to retain?}\n% \\zc{Yes, $\\alpha$ denoting the last $\\alpha$ tokens to retain, namely the size of local window.}\nFor simplicity, we call these tokens ``\\textit{instruction tokens}'', which is also referred to as ``\\textit{local window}'' in previous literature~\\citep{zhang2024h2o, li2024snapkv, xiao2023efficient}. \n\nSubsequently, given the remaining total cache budget $k^\\text{total} = \\sum_{l \\in [0, m-1]} k^l$ that can be used over all transformer layers (noted as $m$), we first determine the cache sizes for the top and bottom layers, and use an arithmetic sequence to compute the cache sizes for the intermediate layers to form the pyramidal shape. The key intuition is to follow the attention pattern in aggregated information flow, reflecting a monotonically decreasing pattern of important tokens for attention from lower layers to upper layers. We allocate $k^0 = (2 \\cdot k^\\text{total}) / m$ for the first bottom layer, and $k^{m-1} = k^\\text{total} / (\\beta \\cdot m) - k^0$ for the top layer, where $\\beta$ is a hyperparameter to adjust the pyramid's shape. Once the cache sizes of the bottom and top layers are determined, the cache sizes for all intermediate layers are set according to an arithmetic sequence, defined as \n\\begin{align} \\label{eq:budget}\nk^l = k^{m-1} - \\frac{k^{m-1} - k^0}{m} \\times l.\n\\end{align}\n\n% \\jh{use $\\times$ for scalar product, and $\\cdot$ for vector dot product} \n\n% Formally, given total key and value matrix limitation $\\sum_{l \\leq m}$ where $m$ denotes the number of layers,\n% the total key and value cache limitation is $\\sum_{l \\in [1, m]} k^l$.\n% Our goal is to allocate the cache limitation efficiently.\n% For bottom layer $l = 1$, we apply $k^1 = (2 \\cdot \\sum_{l \\in [1, m]} k^l) / m$, which is the maximum cache limitation across transformer layers.\n% For top layer $l = m$, we apply $k^m = \\sum_{l \\in [1, m]} k^l / (\\beta * m)$, which is the minimum cache limitation across transformer layers. $\\beta$ is a super parameter.\n% % The step size is calculated by $s = $.\n% The cache size for layer $l$ is calculated as below: $k^l = k^m - ((k^m - k^1) / m) \\cdot (l - 1)$.\n% We name this KV cache compression approach with dynamic cache size by mirroring the geometric shape, named PyramidKV. \n\n\n\n% for layer $l$ in multi-layer transformers, we have\n\n% \\begin{itemize}\n% \\item \n \n% The max limitation $k^0 = 2 \\cdot k$ is applied in the bottom layer $l = 0$;\n% \\item The minimum limitation $k^{m - 1} = k / \\beta$ is applied in the top layer $l = m - 1$, where $\\beta$ is a super parameter;\n% \\item The step size of layer $l$ is larger than that of layer $l-1$ is: $s = k^{m - 1} - k^1$;\n% \\item the cache size for layer $l$ is $k^l = k^m - s \\cdot l$.\n% \\end{itemize}\n% \\wx{This is not clear to me.. need to rewrite}\n\n\n\n\\subsubsection{KV Cache Selection}\n\\label{subsection:key_and_value_selection}\n\nOnce the KV cache budget is determined for each layer, our method needs to select specific KV states for caching within each layer in LLMs. As described in the previous section, the KV cache of the last $\\alpha$ tokens, referred to as instruction tokens, are retained across all layers. Following SnapKV~\\citep{li2024snapkv}, the selection of the remaining tokens is then guided by the attention scores derived from these instruction tokens---tokens receiving higher attention scores are deemed more relevant to the generation process and are thus their KV states are prioritized for retention in the GPU cache.\n\nIn a typical LLM, the attention mechanism in each head $h$ is calculated using the formula: \n\\begin{align} \\label{eq:Al}\n \\mA^h = \\text{softmax}(\\mQ^h \\cdot (\\mK^h)^\\top / \\sqrt{d_k}),\n\\end{align}\nwhere $d_k$ denotes the dimension of the key vectors. Following~\\citep{li2024snapkv}, we utilize a pooling layer at $\\mA^h$ to avoid the risk of being misled by some massive activation scores. %\\jh{Can you write down the pooling operation here?} \\jh{Pooling along which dimension? What is the exact pooling operation? Is it a max pooing or something else? what is the output shape after pooling?}\n\nTo quantify the importance of each token during the generation process, we measure the level of attention each token receives from the instruction tokens, and use this measurement to select important tokens for KV caching. Specifically, we compute the score of selecting $i$-th token for retention in the KV cache as $s^h_i$ in each attention head $h$ by: \n\\begin{align}\\label{eq:att_score}\n s^h_i = \\sum_{j\\in [n-\\alpha,n]} \\mA^h_{ij}\n\\end{align}\nwhere $[n-\\alpha, n]$ is the range of the instruction tokens. In each layer $l$ and for each head $h$, the top $k^l$ tokens with the highest scores are selected, and their respective KV caches are retained. All other KV caches are discarded and will not be utilized in any subsequent computations throughout the generation process.\n\n% \\jh{Why do you use this score? Need a sentence to explain your design rationale }\\wx{we have it in the paragraph above, do we need to repeat and rephrase here?}\n\n% \\zc{We also apply a pooling layer, as the same at Sec 4.2 at SnapKV. So I added this sentence to show the pooling.} \n% \\jh{$s^h_i$ is a scalar, how do you perform pooling? Do you stack the scores of all tokens together to form a vector $\\vs^h\\in\\R^{n}$ and then do pooling? This should be clearly written in the equation. }\\wx{need to be more clear here}\n% \\zc{The pooling is to the attention matrix. It was a typo.} \\jh{Pooling along which dimension? What is the exact pooling operation? Is it a max pooing or something else? what is the output shape after pooling?}\n\n\n\n% Based on the allocation method at \\Scref{subsection:pyramid_size_allocation}, the cache size limitation is $k^l = k^m - s \\cdot (l - 1)$ is for layer $l$.\n% We define a local window size $\\alpha < k^l$, where $\\alpha$ is a super parameter.\n% Given $\\mQ^l \\in \\mathbb{R}^{n - \\alpha \\times d}$, $\\mK^l \\in \\mathbb{R}^{n - \\alpha \\times d}$ and $\\mV^l \\in \\mathbb{R}^{n - \\alpha \\times d}$, we calculate the multi-head attention score:\n% \\begin{align} \\label{eq:Al}\n% \\mA^l = \\text{softmax}(\\mQ^l \\cdot (\\mK^l)^\\top / \\sqrt{d_\\text{head}}),\n% \\end{align}\n% where $d_{head}$ denotes the dimension of attention heads.\n\n% Then we sum up the attention score from each query $q$:\n% \\begin{align}\\label{eq:att_score}\n% \\mS^l = \\sum_{q \\leq n} \\mA^l\n% \\end{align}\n\n% \\jh{More importantly, you should also explain why you select the sub-matrics in this way. Highlight the key intuition.}\n% Finally we could select $\\mK_{k - \\alpha}^l \\in \\mathbb{R}^{k^l \\times d}$ and $\\mV_{k - \\alpha}^l \\in \\mathbb{R}^{k^l \\times d}$ by choosing the top $k - \\alpha$ scores and corresponding positions based on $Score^l$.\n% THen the chooses $\\mK_{k - \\alpha}^l \\in \\mathbb{R}^{k^l \\times d}$ and $\\mV_{k - \\alpha}^l \\in \\mathbb{R}^{k^l \\times d}$ would be concatenated with the local window $\\mK_\\alpha^l \\in \\mathbb{R}^{k^l \\times d}$ and $\\mV_\\alpha^l \\in \\mathbb{R}^{k^l \\times d}$ to get the selected Key Value cache $\\mK_k^l \\in \\mathbb{R}^{k^l \\times d}$ and $\\mV_k^l \\in \\mathbb{R}^{k^l \\times d}$.\n\n\n\n\n\n\\section{Experiment}\n\\label{section:experiment}\n\n% Trade-off between performance and memory reduction\n\nWe conduct comprehensive experiments to evaluate the effectiveness of \\method on performance preserving and memory reduction.\nFirst, we introduce the backbone LLMs (\\Scref{subsection:llms}), the evaluation datasets (\\Scref{subsection:datasets}), the baselines in comparison (\\Scref{subsection:baselines}), and the experiment setup (\\Scref{subsection:experiment_setup}).\nNext, we report the performance in a memory-oriented scenario and a performance-oriented scenario experiments in \\Scref{subsection:results}. We also test if the model can preserve the performance on long-context inputs on the Needle-in-the-haystack experiment (\\Scref{subsection:needle_in_the_haystack}). Finally, we discuss the trade-off between memory, time, and performance in \\Scref{subsection:memory}.\n\n% trade-off between memory reduction and performance on short-context tasks in \\Scref{subsection:short_context_results} and long-context tasks in \\Scref{subsection:long_context_results}.\n% Secondly, we perform an analysis of long-context ability of ~\\method based on a needle in a haystack.\n% Thirdly, we discuss the smallest compression ratio of ~\\method to maintain generation quality in \\Scref{subsection:memory}, the end-to-end latency improvement in \\Scref{subsection:latency} and the computation cost in \\Scref{subsection:profiling}.\n\n\\subsection{Backbone LLMs}\n\\label{subsection:llms}\n\nWe compare \\method against baselines using state-of-the-art open-sourced LLMs, namely LLaMa-3-8B-Instruct, Mistral-7B-Instruct~\\citep{jiang2023mistral} and LLaMa-3-70B-Instruct. Testing examples are evaluated in a generative format, with answers generated by greedy decoding across all tasks to ensure a fair comparison.\n\n\\subsection{Datasets}\n\\label{subsection:datasets}\n\n% \\paragraph{Factual knowledge} Factual knowledge is essential for language models to serve users’ information needs. We use the Massive Multitask Language Understanding dataset (MMLU) for measuring models’ factual knowledge. MMLU consists of a set of questions about 57 subjects ranging in difficulty from elementary levels to professional levels, and its multiple-choice format makes it suitable for probing models’ knowledge without worrying about the open-endedness of generations.\n% \\paragraph{Reasoning} Reasoning is another fundamental ability for models, especially for solving complex tasks. We use the test split of Grade School Math dataset (GSM) to evaluate models’ mathematical reasoning capabilities. We also adopt Big-Bench-Hard (BBH), which contains 23 challenging tasks from Big-Bench, to evaluate models’ general reasoning capabilities.\n% \\paragraph{Multilinguality} Multilinguality acts as an important perspective of models for serving people from different backgrounds. We use TyDiQA, a multilingual question answering benchmark covering 11 typologically diverse languages for testing how much models can process non-Engish text. We use the gold-passage setup where one passage containing the reference answer is given.\n% \\paragraph{Coding} Coding is a particular application that people have used language models for and might be important for integrating these models with external tools. We use the HumanEval dataset and MBPP dataset to evaluate the models’ capability to generate functionally correct programs from docstrings. To avoid ambiguity with our human evaluation, we call this dataset Codex-Eval in this paper.\n% \\paragraph{Open-ended instruction following} While the performance on the benchmarks above quantifies the models’ ability at specific skills, it may not reflect how well the models can handle instructions from real users, which cover highly diverse requests and are often open-ended. For example, the popular ShareGPT dataset contains instances of users asking for programming help, resume formatting tips, educational role-playing, pronunciation suggestion, fanfiction writing, and more. We evaluate such open-ended instructability of models using both model-based evaluation and human evaluation, both of which consist of multiple test sets from existing studies\n% \\paragraph{Safety} Safety is of particular concern regarding the fast-developing language models to ensure the ethical and proper use of them. Following LLaMa-2, we employ ToxiGen to measure the amount of toxic language and hate speech generation across different groups when the models are prompted to do so. We also adopt TruthfulQA to measure how well models can avoid generating known falsehoods due to misconceptions or false beliefs while providing useful information.\n% \\paragraph{Long-Context Question Answering}\n\nWe use LongBench~\\citep{bai2023longbench} to assess the performance of \\method on tasks involving long-context inputs. LongBench is a meticulously designed benchmark suite that tests the capabilities of language models in handling extended documents and complex information sequences. This benchmark was created for comprehensive multi-task evaluation of long context inputs. It includes 17 datasets covering tasks such as single-document QA~\\citep{kovcisky2018narrativeqa,dasigi2021dataset}, multi-document QA~\\citep{yang2018hotpotqa,ho2020constructing}, summarization~\\citep{huang2021efficient,zhong2021qmsum,fabbri2019multi}, few-shot learning~\\citep{li2002learning,gliwa2019samsum,joshi2017triviaqa}, synthetic, and code generation~\\citep{guo2023longcoder,liu2023repobench}. The datasets feature an average input length ranging from 1,235 to 18,409 tokens (detailed average lengths can be found in~\\autoref{table:longbench}), necessitating substantial memory for KV cache management. For all these tasks, we adhered to the standard metrics recommended by LongBench~\\citep{bai2023longbench} (i.e., F1 for QA, Rouge-L for summarization, Acc. for synthetic and Edit Sim. for code generation.) We refer readers to more details at~\\autoref{appendix:evaluation}.\n% We refer the reader to ~\\autoref{appendix:evaluation} for the evaluation details. \n% can be added in the next version, we don't have time on it.\n\n% comment version\n% We use LongBench\\citep{bai2023longbench} to assess the performance of \\method on tasks involving long-context inputs. LongBench is a meticulously designed benchmark suite that tests the capabilities of language models in handling extended documents and complex information sequences. This benchmark was created for multi-task evaluation of long context inputs. It includes 17 datasets covering tasks such as single-document QA, multi-document QA, summarization, few-shot learning\\jh{of what?} \\zc{QA and summerization}, synthetic \\jh{parsing?} \\zc{synthetic is like finding the pattern in the context, i.e. counting the passages in the input. LongBench called this task synthetic task.}, and code generation. The datasets feature an average input length ranging from 8,714 to 36,418 tokens (detailed average lengths can be found in~\\autoref{table:longbench}), necessitating substantial memory for KV cache management. For all these tasks, we adhered to the standard metrics recommended by LongBench~\\citep{bai2023longbench}.\\jh{Need a brief description of the evaluation metrics} \\zc{Each dataset has its own metrics, including F1, rouge, Acc. Can we add a table of metrics in Appendix? Then we do not describe metrics in this section.} We refer the reader to the Appendix XX\\jh{add the number}for the setup details. \n\n\n\n% We calculate F1 scores for GSM8k, NQ and TQA, and use the code execution Pass@1 rate for HumanEval.\n% while we subsample some benchmarks to a reasonable size to improve the efficiency of doing chain-of-thought reasoning.\n% For short tasks including Factuality, Reasoning, Multilinguality, Coding, Open-ended Instruction Following, Safety, we use KV Cache retained ratio as the variant.\n% For Long-Context context tasks, we use KV Cache retained size as the variant, because for long-context tasks generally have very long input length with up to $16000$ tokens. In this case, most of the tokens may be not important for generation, especially for LongBench, which is a question-answering benchmark targeted at generation the answer based on a large set of passages. We would like to show the performance of KV Cache compression methods in a extremely small retained size.\n\n\n\n\\subsection{Baselines}\n\\label{subsection:baselines}\nWe compare \\method with three baselines, all of which keep the same KV cache size across different layers, with different strategies for KV cache selection.\n% We refer readers to \\autoref{appendix:baselines} for more details.\n% \\paragraph{RandomKV (RKV)} is a naive baseline that randomly selects KV cache to retain. We use a fixed cache size across Transformer layers for this baseline. This baseline represents the bottom bound of KV cache compression methods.\n\n\\paragraph{StreamingLLM (SLM)}~\\citep{xiao2023efficient} is an efficient framework that enables LLMs trained with a finite length attention window to generalize to infinite sequence length without any fine-tuning. They propose StreamingLLM based on the attention sink phenomenon that keeping the KV of the first few tokens will largely recover the performance of window attention. StreamingLLM is a competitive method to solve long-context tasks. In our experiments, to be consistent with other methods, we simply keep the KV cache of the last $\\alpha$ tokens and the first $k-\\alpha$ tokens, as suggested in the paper.\n% \\paragraph{FastGen} constructs the KV cache in an adaptive manner: evicting long-range contexts on attention heads emphasizing local contexts, discarding non-special tokens on attention heads centered on special tokens, and only employing the standard KV cache for attention heads that broadly attend to all tokens.\n\n\\paragraph{Heavy Hitter Oracle (H2O)}~\\citep{zhang2024h2o} is a KV cache compression policy that dynamically retains a balance of recent and Heavy Hitter (H2) tokens. H2O keeps a fixed cache size of the Key and Value matrix across Transformer layers. The selection process for the KV cache is driven by attention scores, specifically utilizing the average attention scores from all queries across all tokens to guide the selection.\n\n\\paragraph{SnapKV (SKV)}~\\citep{li2024snapkv} automatically compresses KV caches by selecting clustered important tokens for each attention head. This method discerns the attention patterns of the Key and Value matrices using a localized observation window positioned at the end of the prompts. However, unlike H2O, SnapKV employs a more nuanced clustering algorithm that includes a pooling layer. Additionally, SnapKV captures attention signals using patterns from a localized window (Instruction Tokens), rather than aggregating attention across all queries, allowing for more targeted and efficient compression.\n\n% The same as H2O, SnapKV also keeps a fixed cache size of the Key and Value matrix across Transformer layers, and the selection of the Key and Value matrix is also based on the attention score.\n% \\wx{not clear, need to make it clear, as it is an important baseline}\n% \\zc{Done}\n% Different from H2O, SnapKV applies a fine-grained clustering algorithm utilizing a pooling layer, and they use the attention pattern from a local window to capture the attention signal instead of using the attention from all queries.\n\n\\paragraph{FullKV (FKV)} caches all keys and values for each input token in each layer. All methods are compared to the FullKV simultaneously.\n\n% In addition to the baseline models, we also benchmark our model against the gold standard, which utilizes the full KV cache.\n% \\paragraph{DynamicKV}\\wx{cite} is a baseline of using the attention sparsity as the exclusive signal to determine the number of Key and Value vectors to retain for each layer. Layers with greater sparsity would be allocated less tickets, while layers with weaker sparsity would be allocated more tickets.\n\n\n% All the baseline models keep the same KV cache size across different layers.\n% H2O, StreamingLLM, FastGen, SnapKV, DynamicKV and RandomKV keep a same KV Cache compression size across layers. None of them have dynamic compression size across layers, so their compression may be less efficient compared to ~\\method, because their compression on top layers be redundant as only a very small number of key and value tensors retained could could build up up to 90\\% of the Attention scores. So the redundant tickets could be alleviated to bottom layers.\n\n\\subsection{Experiment Setup}\n\\label{subsection:experiment_setup}\n\n% We compare ~\\method with baselines at this same KV cache size limitation for a fair comparison.\nWe maintain a fixed constant KV cache size for each layer for the baseline methods. In contrast, \\method employs varying KV cache sizes across different layers. To ensure a fair comparison, we adjusted the average KV cache size in \\method to match that of the baseline models, to keep the total memory consumption of all methods the same.\n% For each KV cache size limitation, we ensure that the total memory consumption of all methods are the same.\nIn our experiment, we set $\\beta=20$ and $\\alpha=8$. We use the same prompt for each dataset in all the experiments.\n\n% \\zc{We need to talk about how to ensure fair comparison.}\n\n% We compare the performance of KV Cache compression methods as below\n\n\n% \\subsection{Short Context Results}\n% \\label{subsection:short_context_results}\n\n% The evaluation results of short context tasks is presented at \\autoref{table:short}. We present the evaluation results for various KV Cache size retain ratios.\n% ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. Note that the performance strengths of ~\\method is more evident in small KV Cache sizes.\n% We also notice that ~\\method generally achieves stronger performance in larger models, showing the scaling potential of ~\\method.\n\n% \\input{Tables/short_results}\n\n\n% \\subsection{Results}\n\\subsection{\\method Excels in Memory-constrained Settings}\n\\label{subsection:results}\n\n\n% \\begin{figure}\n% \\centering\n% \\includegraphics[width=1.0\\columnwidth]{Figures/results_v2.pdf}\n% \\vspace{-3mm}\n% \\caption{\n% The evaluation results from LongBench\\citep{bai2023longbench} across 64, 96, 128, 256 and 512 cache sizes.\n% The evaluation metrics are the average score of LongBench across datasets.\n% ~\\method outperforms H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv} and StreamingLLM~\\citep{xiao2023efficient}, especially in small KV cache sizes.\n% % \\jh{What are the evaluation metrics? accuracy? this should be mentioned when introducing the LongBench in Sec 6.2}\n% }\n% \\vspace{-3mm}\n% \\label{figure:results2}\n% \\end{figure}\n\n\\begin{figure}\n \\centering\n \\begin{minipage}{0.33\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/result1.pdf}\n \\end{minipage}%\n \\hfill\n \\begin{minipage}{0.33\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/result2.pdf}\n \\end{minipage}%\n \\hfill\n \\begin{minipage}{0.33\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figures/result3.pdf}\n \\end{minipage}\n \\vspace{-3mm}\n \\caption{The evaluation results from LongBench~\\citep{bai2023longbench} across 64, 96, 128 and 256 cache sizes at LLaMa-3-8B-Instruct (Left), Mistral-7B-Instruct (Middle) and LLaMa-3-70B-Instruct (Right).\n The evaluation metrics are the average score of LongBench across datasets.\n ~\\method outperforms H2O~\\citep{zhang2024h2o}, SnapKV~\\citep{li2024snapkv} and StreamingLLM~\\citep{xiao2023efficient}, especially in small KV cache sizes.}\n \\label{figure:results}\n\\end{figure}\n\n\n\n\n\n\\begin{table*}[t]\n\n\\centering\n\n% \\wx{need to label the best in each block} \n% \\jh{the font size is too small. Suggestion: 1. write abbreviations for method names, e.g., RKV -> RKV, SLM -> SLM, SKV -> SKV, and write the full name in the caption. 2. Reduce the space between columns using ``c@{\\hspace{0.05ex}}c''}\n\n\n% credit to https://arxiv.org/abs/2401.01325\n% \\scalebox{0.48}{\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\cmidrule(lr){2-17}\n&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n\n\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV &25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 4.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n% \\midrule\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\nH2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\nSLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\nOurs & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 128} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n% % RKV & 3.22 & 6.97 & 8.87 & 22.92 & 15.53 & 7.83 & 1.75 & 6.57 & 1.36 & 32.5 & 22.13 & 6.92 & 6.0 & 60.4 & 10.13 & 10.72 & 13.98 \\\\\n% SKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\textbf{51.82} & 35.50 \\\\\n% SLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\n% H2O & \\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\textbf{32.71} & 18.45 & \\textbf{20.32} & 22.02 & \\textbf{21.10} & 38.50 & 87.75 & \\textbf{39.14} & 5.83 & \\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\n% Ours & 21.40 & \\textbf{16.92} & \\textbf{33.79} & \\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\textbf{22.48} & 20.95 & \\textbf{66.50} & \\textbf{89.35} & 38.39 & \\textbf{5.92} & 69.00 & \\textbf{56.49} & 47.95 & \\textbf{37.25} \\\\\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\nSLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\nH2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\nOurs & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nFKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\nSLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\nH2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\nOurs & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n\n\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 128} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n% % RKV & 2.04 & 2.22 & 3.23 & 5.25 & 5.18 & 0.33 & 0.8 & 1.8 & 2.42 & 32.0 & 3.24 & 1.8 & 0.62 & 1.8 & 17.41 & 15.88 & 6.00 \\\\\n% SKV & 19.16 & 21.46 & 43.52 & \\textbf{38.60} & 23.35 & \\textbf{16.09} & 17.66 & 21.84 & \\textbf{21.45} & 47.50 & \\textbf{84.15} & 40.24 & 5.00 & 69.31 & \\textbf{46.98} & \\textbf{42.97} & 34.96\\\\\n% SLM & 16.57 & 14.68 & 32.40 & 30.19 & 22.64 & 12.34 & 18.08 & 18.96 & 21.98 & 43.50 & 74.22 & 29.02 & 4.50 & 29.48 & 39.23 & 36.16 & 27.57 \\\\\n% H2O & 21.20 & 21.90 & 41.55 & 33.56 & 21.28 & 12.93 & \\textbf{18.59} & \\textbf{22.61} & 19.17 & 39.00 & 82.37 & \\textbf{40.44} & \\textbf{6.00} & \\textbf{83.19} & 46.41 & 42.66 & 34.73 \\\\\n% Ours & \\textbf{21.75} & \\textbf{22.03} & \\textbf{44.32} & 34.06 & \\textbf{22.79} & 15.77 & 18.58 & 21.89 & 21.41 & \\textbf{66.00} & 83.46 & 39.75 & 4.50 & 66.90 & 46.96 & 41.28 & \\textbf{35.72} \\\\\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\nSLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\nH2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\nOurs & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV & 27.75 & 46.48 & 49.45 & 52.04 & 54.90 & 30.42 & 32.37 & 22.27 & 27.58 & 73.50 & 92.46 & 45.73 & 12.50 & 72.50 & 40.96 & 63.91 & 46.55\\\\\n% \\midrule\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\nSLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\nH2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\nOurs & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 128} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n% % RKV & 3.22 & 6.97 & 8.87 & 22.92 & 15.53 & 7.83 & 1.75 & 6.57 & 1.36 & 32.5 & 22.13 & 6.92 & 6.0 & 60.4 & 10.13 & 10.72 & 13.98 \\\\\n% SKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\textbf{51.82} & 35.50 \\\\\n% SLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\n% H2O & \\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\textbf{32.71} & 18.45 & \\textbf{20.32} & 22.02 & \\textbf{21.10} & 38.50 & 87.75 & \\textbf{39.14} & 5.83 & \\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\n% Ours & 21.40 & \\textbf{16.92} & \\textbf{33.79} & \\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\textbf{22.48} & 20.95 & \\textbf{66.50} & \\textbf{89.35} & 38.39 & \\textbf{5.92} & 69.00 & \\textbf{56.49} & 47.95 & \\textbf{37.25} \\\\\n\n\n% \\arrayrulecolor{black}\\midrule\n\\arrayrulecolor{black!20}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n% RKV & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\\\\nSKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \nSLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \nH2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \nOurs & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n\n\n\n\n\n\n\\arrayrulecolor{black}\\bottomrule\n\\end{tabular}\n}\n\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct, Mistral-7B-Instruct and LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes (i.e. KV Size = 64). Bold text represents the best performance.}\n\\label{table:longbench}\n\\vspace{-3mm}\n\\end{table*}\nThe evaluation results from LongBench~\\citep{bai2023longbench} are shown in \\autoref{table:longbench} and \\autoref{figure:results}.\nIn \\autoref{figure:results}, we report the average score across datasets for 64, 96, 128, and 256 case sizes.\nIn \\autoref{table:longbench}, we report the results for two different KV cache sizes with 64 and 2048. These two sizes represent two distinct operational scenarios---the memory-efficient scenario and the performance-preserving scenario, respectively for a trade-off between memory and model performance. \nIn \\autoref{appendix:results}, we report the results of KV cache sizes with 64, 96, 128 and 2048.\n\nOverall, \\method preserves the performance with only 12\\% of the KV cache and it consistently surpasses other method across a range of KV cache sizes and different backbone models, with its performance advantages becoming particularly pronounced in memory-constrained environments where only about 0.7\\% of the KV cache from the prompt is retained. Upon examining specific tasks, \\method demonstrates a notably superior performance on the TREC task, a few-shot question answering challenge. This suggests that the model effectively aggregates information from the few-shot examples, highlighting the potential for further investigation into in-context learning tasks.\n\nNotably, we initially observe the pyramidal attention patterns from the visualization analysis on the multi-document QA task (\\autoref{figure:rag_flow}), but the pyramid heuristic has demonstrated its effectiveness on a range of other LongBench tasks (e.g., single-document QA, In-Context Learning), suggesting its promising generalizability beyond multi-document QA.\n% ~\\method preserves the performance with only 11\\% of the KV cache. \n\n\nThe performance advantage of \\method increases as the KV cache memory decreases. By focusing on optimizing budget allocation across layers, \\method accurately allocates resources in memory-constrained scenarios, ensuring that retained information is effectively preserved to maintain model performance. Moreover, as in long bench results shown in \\autoref{table:longbench}, even in the performance-preserving scenario (i.e., KV cache size = 2048), \\method still improves the performance over baseline methods and even outperforms the performance of FullKV.\n\n\n\n\n\n\n\n% Taking a win rate over 45\\% as little-to-no quality regression, ~\\method can achieve $\\sim$40\\% memory reduction in LLaMa 1-65B, $\\sim$30\\% in LLaMa 1-30B, $\\sim$20\\% in LLaMa 1-13B and LLaMa 1-7B. \n\n\n\n\\subsection{\\method Preserves the Long-Context Understanding Ability}\n\\label{subsection:needle_in_the_haystack}\n% \\jh{Key take-away message for the subsection title.}\n% \\zc{Done}\n\n% We perform Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test to see how \\method improves the long-context understanding of LLMs test in-context retrieval ability of long context LLMs\n\n\nWe conduct the \"Fact Retrieval Across Context Lengths\" (Needle In A Haystack) experiment~\\citep{liu2023lost,fu2024data}, which is a dataset designed to test whether a model can find key information in long input sequences, to evaluate the in-context retrieval capabilities of LLMs when utilizing various KV cache compression methods. For this purpose, we employ \\textbf{LlaMa-3-8B-Instruct} and \\textbf{LlaMa-3-70B-Instruct} as our base, with context lengths extending up to 8k. We compared several KV cache compression techniques (\\method, SnapKV~\\citep{li2024snapkv}, and H2O~\\citep{zhang2024h2o}) at cache sizes of \\textbf{128} and full cache. The results, presented in \\autoref{figure:needle_llama} \\footnote{Additional results with 64, 96 and 128 KV cache sizes with \\textbf{LlaMa-3-8B-Instruct} at 8k context length, \\textbf{LlaMa-3-70B-Instruct} at 8k context length, and \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} at 32k context length are available in \\autoref{appendix:needle}}. The results demonstrate that with only 128 KV cache retained, \\method effectively maintains the model's ability to understand short contexts, and shows only modest degradation for longer contexts. In contrast, other KV cache compression methods significantly hinder the performance of LLMs. Notably, for the larger model (\\textbf{LlaMa-3-70B-Instruct}), \\method achieves 100.0 Acc. performance, matching the results of FullKV, thereby demonstrating its ability to preserve long-context comprehension with a substantially reduced KV cache.\n\n\n% We perform Fact Retrieval Across Context Lengths (``Needle In A HayStack'')~\\citep{liu2023lost,fu2024data} to test the in-context retrieval ability of LLMs after leveraging different KV cache methods. \n% Specifically, we use \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} as the base model, with context length up to \\textbf{32k}. We compare KV cache compression methods (\\method, SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o}) with cache size 64 and the full cache, and the results are shown in \\autoref{figure:needle}. (More experiment results with different KV cache size can be found in \\autoref{appendix:needle})\n% The results show that \\method can preserve the model's long context understanding ability significantly more than other KV cache compression methods significantly hurt the performance of LLMs in the evaluation. \n\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_main.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} and \\textbf{LlaMa-3-70B-Instruct} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n \\textbf{PyramidKV with 128 KV cache size achieves the same 100.0 Acc. performance compared with FullKV with 8k context size for LLaMA-3-70B-Instruct.}\n }\n \\label{figure:needle_llama}\n\\end{figure}\n% final score: standard: 0.650 pyramid: 0.626 snapkv: 0.573\n\n% \\begin{figure}\n% \\centering\n% \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_64.pdf}\n% \\caption{\n% Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with \\textbf{32k} context size in \\textbf{64} KV cache size.\n% The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n% % (a) represents the results of Full KV cache size. \n% % (b) represents the results of ~\\method.\n% % (c) represents the results of SnapKV.\n% ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n% % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n% % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n% }\n% \\label{figure:needle_mistral}\n% \\end{figure}\n\n\n\n\n\n\n\\subsection{~\\method Significantly Reduces Memory with Limited Performance Drop}\n\\label{subsection:memory}\n% \\jh{Key take-away message for the subsection title.}\n% \\zc{Done}\n\nIn this section, we study how sensitive the methods are with different sizes of KV cache. \nWe report the KV cache memory reduction in Table \\ref{tab:memory_reduction}.\nWe evaluate the memory consumption of LLaMa-3-8B-Instruct.\nSpecifically, we evaluate the memory consumption of all methods with a fixed batch size of 1, a sequence length of 8192, and model weights in fp16 format.\nWe observe that \\method substantially reduces the KV cache memory across different numbers of cache sizes.\n\nWe also present that the allocation strategy and score-based selection add minimal complexity in the inference phase compared to the computation required for next-token predictions as~\\autoref{appendix:inference_overhead}.\n\n\n\\begin{table*}[h]\n\\small\n\\centering\n\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{ccc|cccccc}\n\\toprule\n cache size & Memory & Compression Ratio & QMSum & TREC & TriviaQA & PCount & PRe & Lcc \\\\\n\n\\midrule\n64 & 53M & 0.8\\% & 21.65 & 58.00 & 88.31 & 5.23 & 69.50 & 52.61 \\\\ \n128 & 107M & 1.6\\% & 22.48 & 66.50 & 89.35 & 5.92 & 69.00 & 56.49 \\\\ \n256 & 214M & 3.1\\% & 22.69 & 71.00 & 90.48 & 5.83 & 69.25 & 56.94 \\\\\n512 & 428M & 6.3\\% & 22.80 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\n1024 & 856M & 12.5\\% & 22.55 & 71.50 & 90.61 & 5.91 & 69.50 & 58.16 \\\\\n2048 & 1712M & 25.0\\% & 22.55 & 72.00 & 90.56 & 5.58 & 69.25 & 56.79 \\\\\nFull & 6848M & 100.0\\% & 23.30 & 73.00 & 90.56 & 5.22 & 69.25 & 58.76 \\\\\n\n\n\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Memory reduction effect and benchmark result by using \\method. We conducted a comparison of memory consumption between the Llama-3-8B-Instruct model utilizing the Full KV cache and the Llama-3-8B-Instruct model compressed with the \\method.\n}\n\n\n\n\\label{tab:memory_reduction}\n\\vspace{-3mm}\n\\end{table*}\n\n% 64 17150\n% 128 17132\n% 256 17122\n% 512 17336\n\n\n% step 214/256\n\n\n\n\n\n\n\n\n\n\n% \\subsection{End-to-end Latency Improvement}\n% \\label{subsection:latency}\n\n% \\input{Tables/latency}\n\n% \\subsection{Profiling Cost}\n% \\label{subsection:profiling}\n\n% \\input{Tables/profiling}\n\n% We implement a sparsity kernel for KV-cache compression and present the end-to-end latency improvement in Table.\n% For the Full-cache baseline, we use the widely used Hugging Face Accelerate (HF).\n\n% In the experiment, we record the total duration in seconds, measured from the start of prompt encoding, until the end of generation as the end-to-end latency.\n\n% For ~\\method, we implemented a customized kernel to handle the KV cache pruning operation. Specifically, we adapt the kernel from Deepspeed by adding the KV cache sparsity operation. All methods are tested on the same Nvidia V100 GPUs.\n\n% As shown in Table, we can observe that ~\\method achieves significant end-to-end speed-up across all the generation settings. For the least significant case, Fastgen can have a decent 16.04\\% latency improvement over the full-cache baseline on a short generation length of 512. In the best cases, we can achieve up to 55.0\\% latency reduction with Fastgen at a generation length of 16k.\n\n% We can also observe that the relative speedup is greater with longer generation length. For example, given $batch\\_size = 1$, FastGen’s relative speed-up rises from $16.04\\%$ to $55.0\\%$, as the generation length grows from $512$ to $16k$. The tendency can also be observed in other batch settings.\n\n% This analysis confirms that FastGen can achieve major speed-up in real development, especially in long generation settings. \n\n\n\n% \\input{Files/6_Discussion}\n\\section{Conclusion}\n\\label{section:conclusion}\nIn this study, we investigate the intrinsic attention patterns of Large Language Models (LLMs) when processing long context inputs. Our empirical analysis leads us to discover the existence of Pyramidal Information Funneling in the attention across layers: it distributes information broadly in lower layers, increasingly concentrates it within specific contexts, and ultimately focuses on critical tokens in higher layers with massive activation or attention sink. Motivated by this discovery, we design a novel KV cache compression approach \\method that utilizes this information flow pattern. It varies KV cache sizes across layers, uniquely designed to complement the attention behavior observed across different layers. By leveraging the Pyramidal Information Funneling into KV cache compression design, our method excels in memory-constrained settings, preserves long-context understanding ability, and significantly reduces memory usage with minimal performance trade-offs compared to the baselines.\n\n\n\n% employs a pyramidal sizing strategy for KV cache, which is tailored to the intrinsic behavior of the attention module.\n% % Experiments show that PyramidKV\n\n % Our experimental evaluations, conducted using the LongBench benchmark, demonstrate that \\method achieves performance comparable to models with a full KV cache while only retaining 11.7\\% of the KV cache, thereby significantly reducing memory usage by 75\\%. In scenarios that prioritize memory efficiency—where only 1.6\\% of the KV cache is maintained—\\method outperforms other KV cache compression techniques, delivering up to a 32.33\\% absolute improvement on specific tasks.\n \n% Looking ahead, there is potential to refine KV Cache Compression even further by dynamically adjusting it based on real-time analysis of the attention matrices, ensuring that the compression method remains perfectly aligned with the shifting patterns of attention within LLMs.\n\n% In this work, we study the intrinsic attention patterns of Large Language Models (LLMs) when they answer questions based on long-context documents.\n% We discover that LLMs implicitly perform information aggregation through multi-layer transformers.\n% In shallow layers, the information flows from the context to the initial tokens for each document; in mature layers, the information flows from the initial tokens for each document to some abstract tokens. In the top layer, LLMs generate outputs that almost solely rely on some global abstractive tokens with massive attention scores.\n% Based on the aforementioned study, we propose a plug-and-play method inference accelerate method ~\\method to perform KV cache compression.\n% Different from the KV cache compression that retains the size of the maintained key and value vectors the same across Transformer layers, we conduct a dynamic KV Cache compression method that \n% targeted profiling to discern the intrinsic structure of attention modules. \n% ~\\method is xxx times faster than full KV cache technique while maintaining the same performance across LLM series (LlaMa and Mistral), sizes ($7$B, $13$B and $70$B) and architectures (Dense and MoE).\n% Our experiments also demonstrate that ~\\method is effective and efficient in streaming applications.\n\\bibliographystyle{plainnat}\n\\bibliography{reference}\n\n% \\maketitle\n\\appendix\n% \\section{Limitations}\n% \\label{section:limitations}\n\n% Our study on KV cache compression, despite its advances, faces several limitations.\n% Our cache size allocation does not dynamically allocate the cache size based on the attention score, so the allocation would inevitably be sub-optimal.\n% Looking ahead, there is potential to refine KV Cache Compression even further by dynamically adjusting it based on real-time analysis of the attention matrices, ensuring that the compression method remains perfectly aligned with the shifting patterns of attention within LLMs.\n\\clearpage\n\\newpage\n\n\\section{Limitations}\n\\label{section:limitations}\nOur experiments were limited to three base models: LLAMA-3-8B-Instruct, LLAMA-3-70B-Instruct and Mistral-7B-Instruct. While these models demonstrated consistent trends, the robustness of our findings could be enhanced by testing a broader array of model families, should resources permit. Additionally, our research was conducted exclusively in English, with no investigations into how these findings might be transferred to other languages. Expanding the linguistic scope of our experiments could provide a more comprehensive understanding of the applicability of our results globally.\nBased on our results at LongBench and Needle-in-a-HayStack experiment, PyramidKV generally works decently in most of the language tasks (i.e., Single-Document QA, Multi-Document QA, Summerization, Few-Shot In-Context Learning, etc.). Although we observe that PyramidKV performs better in some tasks (i.e., Few-Shot In-Context Learning) compared with some other tasks (i.e., Summerization), we have not observed cases that the decoding result collapses at some tasks. This remains a new topic for future work to explore. \n\n\\section{Future Work}\n\\label{section:future_work}\nOur investigation on PyramidKV highlights considerable opportunities for optimizing KV cache compression by adjusting the number of KV caches retained according to the distinct attention patterns of each layer (or even for each head). For instance, the retention of KV cache for each layer could be dynamically modified based on real-time analysis of the attention matrices, ensuring that the compression strategy is consistently aligned with the changing attention dynamics within LLMs. Furthermore, our experiments indicate that PyramidKV significantly surpasses other methods in few-shot learning tasks, suggesting promising applications of KV cache in in-context learning. This approach could potentially enable the use of more shots within constrained memory limits.\n% Due to the resource limits, we only conduct experiments on two base models, LLAMA-3-8B-Instruct and Mistral-7B-Instruct. Although both models show the same trend, it could be more solid to conduct experiments on more model families if there is sufficient resource. In addition, all the experiments are in English only, no explorations are conducted in other languages.\n% Our study on KV cache compression, despite its advances, faces several limitations.\n% Our cache size allocation does not dynamically allocate the cache size based on the attention score, so the allocation would inevitably be sub-optimal.\n% % Looking ahead, there is potential to refine KV Cache Compression even further by dynamically adjusting it based on real-time analysis of the attention matrices, ensuring that the compression method remains perfectly aligned with the shifting patterns of attention within LLMs.\n\n\\section{Details of Evaluation}\n\\label{appendix:evaluation}\n\n\nWe use LongBench~\\citep{bai2023longbench} to assess the performance of \\method on tasks involving long-context inputs. LongBench is a meticulously designed benchmark suite that tests the capabilities of language models in handling extended documents and complex information sequences. This benchmark was created for multi-task evaluation of long context inputs.\n\nWe present the details of metrics, language and data for LongBench at \\autoref{table:stat}. \n\nWe run all the experiments on NVIDIA A100.\n\n\n\\begin{table}[htbp]\n\\centering \n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{llrccc}\n\\toprule\nDataset & Source & Avg len & Metric & Language & \\#data \\\\\n\\midrule\n\\emph{Single-Document QA} \\\\\nNarrativeQA & Literature, Film & 18,409 & F1 & English & 200 \\\\\nQasper & Science & 3,619 & F1 & English & 200 \\\\\nMultiFieldQA-en & Multi-field & 4,559 & F1 & English & 150 \\\\\n\\midrule\n\\emph{Multi-Document QA} \\\\\nHotpotQA & Wikipedia & 9,151 & F1 & English & 200 \\\\\n2WikiMultihopQA & Wikipedia & 4,887 & F1 & English & 200 \\\\\nMuSiQue & Wikipedia & 11,214 & F1 & English & 200 \\\\\n\\midrule\n\\emph{Summarization} \\\\\nGovReport & Government report & 8,734 & Rouge-L & English & 200 \\\\\nQMSum & Meeting & 10,614 & Rouge-L & English & 200 \\\\\nMultiNews & News & 2,113 & Rouge-L & English & 200 \\\\\n\\midrule\n\\emph{Few-shot Learning} \\\\\nTREC & Web question & 5,177 & Accuracy (CLS) & English & 200 \\\\\nTriviaQA & Wikipedia, Web & 8,209 & F1 & English & 200 \\\\\nSAMSum & Dialogue & 6,258 & Rouge-L & English & 200 \\\\\n\\midrule\n\\emph{Synthetic Task} \\\\\nPassageCount & Wikipedia & 11,141 & Accuracy (EM) & English & 200 \\\\\nPassageRetrieval-en & Wikipedia & 9,289 & Accuracy (EM) & English & 200 \\\\\n\\midrule\n\\emph{Code Completion} \\\\\nLCC & Github & 1,235 & Edit Sim & Python/C\\#/Java & 500 \\\\\nRepoBench-P & Github repository & 4,206 & Edit Sim & Python/Java & 500 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\caption{An overview of the dataset statistics in LongBench~\\citep{bai2023longbench}. `Source' denotes the origin of the context. `Accuracy (CLS)' refers to classification accuracy, while `Accuracy (EM)' refers to exact match accuracy.}\n\\label{table:stat}\n\\end{table}\n\n\n% \\section{Baselines}\n% \\label{appendix:baselines}\n\n\\section{Handle Rotary Embedding after Tokens are Removed in~\\method}\n\nWe keep the rotary embedding unchanged after tokens are removed, so that LLMs can still capture the exact position information even if the tokens are removed. StreamingLLM~\\citep{xiao2023efficient} shows that rolling kv cache with the correct relative position is crucial for maintaining performance. This is because StreamingLLM is designed to mainly handle unlimited context sizes, where contexts exceed the LLM’s fixed context length. Without changing the rotary embedding after token removal, LLMs would receive rotary embedding of a non-monotonic position sequence. For example, after the first KV cache compression, LLMs might receive the input position embedding as [$0, 1, 2, 3, 3096, 3097, \\cdots, 4096$], and the position embedding of the generated sequences could be [$1005, 1006, 1007, \\cdots$]. The position sequence of [$0, 1, 2, 3, 3096, …, 4096, 1005, 1006, 1007, \\cdots$] is a non-monotonic sequence, which may negatively hurts the performance. In contrast, our targeting settings will not process unlimited context size. For example, given a input sequence of $4012$ length, after KV cache compression, the position sequence would be [$0, 4, 6, 16, \\cdots, 3927, 3987, 4012$], and the position sequence of the generated tokens would be [$4013, 4014, \\cdots$]. By keeping the rotary embedding unchanged after the tokens are removed, the LLM avoids non-monotonic position sequences, and the LLM can capture the exact position information even if the tokens are shifted. Our preliminary results show that rolling KV cache with the correct relative position will slightly decrease the performance.\n\n\n\\section{Ablation Study}\n\n\\subsection{Hyper Parameter $\\alpha$}\n\nWe present the study of $\\alpha$ for LlaMa-3-8B-Instruct in 128 KV cache size budget at~\\autoref{table:ablation_step_a}.We find that a small alpha value (i.e., 8, 16) leads to better performance than a larger alpha value (i.e., 24, 32, 40, 48).\n\n\n\n\\begin{table*}[htbp]\n\n\\centering\n\n\n\n% credit to https://arxiv.org/abs/2401.01325\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{4}{*}{$\\alpha$} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & Avg. \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\midrule\n\n8 & 21.40 & 16.92 & 31.62 & 38.45 & 28.72 & 18.59 & 19.96 & 22.49 & 20.96 & 66.50 & 89.35 & 38.43 & 5.92 & 69.00 & 57.86 & 51.80 & 37.37 \\\\ \n16 & 23.37 & 16.21 & 33.93 & 38.24 & 27.28 & 20.57 & 19.71 & 21.93 & 20.86 & 60.00 & 88.75 & 38.34 & 5.48 & 69.12 & 57.84 & 53.42 & 37.19 \\\\ \n24 & 22.85 & 14.51 & 32.26 & 38.38 & 28.36 & 20.33 & 19.55 & 21.72 & 20.72 & 54.50 & 88.71 & 38.46 & 5.48 & 69.50 & 56.83 & 53.65 & 36.61 \\\\ \n32 & 23.01 & 14.54 & 31.68 & 38.86 & 29.90 & 19.16 & 19.20 & 21.83 & 20.52 & 49.50 & 87.01 & 38.01 & 5.75 & 69.50 & 57.02 & 54.54 & 36.25 \\\\ \n40 & 21.70 & 13.06 & 30.14 & 36.78 & 27.34 & 18.88 & 18.72 & 21.37 & 19.79 & 44.00 & 87.74 & 38.43 & 6.08 & 69.25 & 56.11 & 53.89 & 35.21 \\\\ \n48 & 21.51 & 12.30 & 29.77 & 39.04 & 26.76 & 17.97 & 18.65 & 21.20 & 20.29 & 44.50 & 87.73 & 38.44 & 5.51 & 69.25 & 56.73 & 53.88 & 35.22 \\\\ \n\n\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Ablation on $\\alpha$.}\n\\label{table:ablation_step_a}\n\\end{table*}\n\\subsection{Hyper Parameter $\\beta$}\n\nOne topic we want to analyze for our ablation study is the selection of $\\beta$, which can determine the staircase. The smaller $\\beta$ is, the gentler the staircase is; the larger $\\beta$ is, the steeper the staircase is. We want to investigate the effect of $\\beta$ step size on the final result. Results on 128 KV cache size and LlaMa-3-8B-Instruct are shown in \\autoref{table:ablation_step_b}. The results at \\autoref{table:ablation_step_b} show that using a relatively small value of $\\beta$ yields better outcomes, and~\\method is generally robust to the selection of $\\beta$.\n\n\n\n\\begin{table*}[htbp]\n\n\\centering\n\n\n\n% credit to https://arxiv.org/abs/2401.01325\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{4}{*}{$\\beta$} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & Avg. \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\midrule\n20 & 21.40 & 16.92 & 33.79 & 39.73 & 28.72 & 18.59 & 19.86 & 22.48 & 20.95 & 66.50 & 89.35 & 38.39 & 5.92 & 69.00 & 56.49 & 47.95 & 37.25 \\\\\n18 & 21.71 & 16.24 & 33.59 & 39.89 & 27.94 & 18.38 & 19.76 & 22.32 & 21.20 & 66.50 & 88.98 & 38.93 & 5.46 & 69.50 & 56.47 & 49.23 & 37.25 \\\\\n16 & 21.74 & 14.86 & 33.64 & 39.18 & 28.17 & 18.77 & 19.57 & 22.25 & 21.48 & 66.50 & 89.69 & 38.87 & 5.82 & 69.50 & 57.02 & 50.11 & 37.32 \\\\\n14 & 22.53 & 16.31 & 33.50 & 40.50 & 28.15 & 19.26 & 19.66 & 22.39 & 21.38 & 65.50 & 90.02 & 38.56 & 5.75 & 69.50 & 57.51 & 49.71 & 37.51 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Ablation on $\\beta$.}\n\\label{table:ablation_step_b}\n\\end{table*}\n\n% \\subsection{Attention from local window or global, H2 and Local}\n\n% Another topic we are interested in is the calculation method of attention and the ablation about attention-based selection and local window selection. The selection of vectors based on attention can be done through the attention of other tokens within a local window, or through the attention of all queries to all tokens.\n% We want to explore which type of attention is a more effective signal for selection,\n% % The key and value tensors selected based on attention are heavy hitters, \n% and we hope to analyze the impact of attention-based selection and the local window on the results.\n% Results show that local window and attention-based selection are both needed for a good performance, and the attention calculation based on local window or not make minor difference.\n\n% \\input{Tables/ablation_attention}\n\n\\section{License}\n\\label{appendix:license}\nLongBench: MIT\n\n\n\n\\section{PyramidKV will cause minimal extra inference overhead.}\n\\label{appendix:inference_overhead}\n\nThe allocation strategy and score-based selection add minimal complexity in the inference phase compared to the computation required for next-token predictions as~\\autoref{table:inference_overhead}. Each row shows the setting of using a specific “[Prompt length, Generation length]” combination. We show the inference speed comparison between total inference time, time for allocation strategy and time for score-based selection on LlaMa-3-8B-Instruct. Each cell is the latency measured in seconds. Furthermore, our budget allocation can be calculated before inference, requiring only a one-time computation. Thus, PyramidKV will cause minimal extra inference overhead.\n\n\n% \\include{Tables/inference_overhead}\n\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\begin{tabular}{ccccccccc}\n\\toprule\n\\textbf{Prompt Length} & \\textbf{Generation Length} & \\textbf{Inference Time} & \\textbf{Allocation Time} & \\textbf{Selection Time} \\\\\n\\midrule\n512&512 & 18.26 & 0.0000003 & 0.0194 \\\\\n512&1024 & 34.69 & 0.000002 & 0.0133 \\\\\n512&2048 & 70.69 & 0.000003 & 0.013 \\\\\n512&4096 & 138.62 & 0.000005 & 0.013 \\\\\n1024&512 & 17.32 & 0.000002 & 0.0131 \\\\\n1024&1024 & 34.67 & 0.000002 & 0.01288 \\\\\n1024&2048 & 70.21 & 0.000005 & 0.01296 \\\\\n1024&4096 & 138.61 & 0.000003 & 0.01297 \\\\\n2048&512 & 17.48 & 0.000004 & 0.0128 \\\\\n2048&1024 & 34.78 & 0.000006 & 0.0129 \\\\\n2048&2048 & 69.50 & 0.000003 & 0.01297 \\\\\n2048&4096 & 138.59 & 0.000003 & 0.013 \\\\\n4096&512 & 17.58 & 0.000002 & 0.013 \\\\\n4096&1024 & 34.93 & 0.000004 & 0.0129 \\\\\n4096&2048 & 69.65 & 0.000002 & 0.013 \\\\\n4096&4096 & 138.87 & 0.000002 & 0.013 \\\\\n\\bottomrule\n\\end{tabular}\n\\caption{Extra inference overhead of~\\method }\n\\label{table:inference_overhead}\n\\end{table}\n\n\\section{Inference Speed Comparison}\n\\label{appendix:inference_speed_comparison}\n\n\\method does not require extra computation time for budget allocation at inference by design. We show the inference speed comparison between~\\method and baselines on LlaMa-3-8B-Instruct as~\\autoref{table:inference_speed_comparison}. Each row shows the setting of using a specific “[Prompt length, Generation length]” combination. Each cell is the latency measured in seconds.~\\method does not sacrifice the speed.~\\method provides performance improvement and memory saving while runs at a comparable speed compared with baselines (i.e. SnapKV~\\citep{li2024snapkv}, StreamingLLM~\\citep{xiao2023efficient} and H2O~\\citep{zhang2024h2o}). That’s because the allocation strategy requires very limited additional complexity in the inference/generation phase compared with computation required for generation as~\\autoref{appendix:inference_overhead}.\n\n\n\\begin{table}[h!]\n\\centering\n\\small\n\\begin{tabular}{ccccccc}\n\\toprule\n\\textbf{Prompt Length} & \\textbf{Generation Length} & \\textbf{H2O} & \\textbf{SnapKV} & \\textbf{StreamingLLM} & \\textbf{PyramidKV} \\\\ \n\\midrule\n512&512 & 18.47 & 18.25 & 18.96 & 18.26 \\\\\n512&1024 & 35.10 & 34.76 & 36.20 & 34.69 \\\\\n512&2048 & 70.21 & 69.60 & 72.35 & 70.69 \\\\ \n512&4096 & 140.80 & 139.42 & 146.37 & 138.62 \\\\\n1024&512 & 17.63 & 17.34 & 18.12 & 17.32 \\\\\n1024&1024 & 35.16 & 34.61 & 36.17 & 34.67 \\\\\n1024&2048 & 71.02 & 69.17 & 72.37 & 70.21 \\\\\n1024&4096 & 140.51 & 138.83 & 146.09 & 138.61 \\\\ \n2048&512 & 17.64 & 19.54 & 18.22 & 17.48 \\\\ \n2048&1024 & 35.09 & 34.76 & 36.29 & 34.78 \\\\ \n2048&2048 & 70.84 & 69.56 & 72.46 & 69.50 \\\\ \n2048&4096 & 140.16 & 139.55 & 145.22 & 138.59 \\\\ \n4096&512 & 17.75 & 17.67 & 18.40 & 17.58 \\\\ \n4096&1024 & 35.20 & 35.08 & 36.46 & 34.93 \\\\ \n4096&2048 & 70.02 & 69.26 & 72.58 & 69.65 \\\\ \n4096&4096 & 139.87 & 138.57 & 144.98 & 138.87 \\\\ \n\\bottomrule\n\\end{tabular}\n\\caption{Performance comparison across different configurations and methods.}\n\\label{table:inference_speed_comparison}\n\\end{table}\n\n\n\n\\section{\\method Excels in all KV Cache Size Limitation}\n\\label{appendix:results}\n\n\n\nThe evaluation results from LongBench\\citep{bai2023longbench} are shown in \\autoref{table:longbench_appendix_llama3_8b}, \\autoref{table:longbench_appendix_mistral}, and\\autoref{table:longbench_appendix_llama3_70b}.\nWe report the results using LlaMa-3-8B-Instruct, LlaMa-3-70B-Instruct and Mistral-7B-Instruct\\citep{jiang2023mistral} for different KV cache sizes.\n\nOverall, \\method consistently surpasses other method across a range of KV cache sizes and different backbone models, with its performance advantages becoming particularly pronounced in memory-constrained environments. Upon examining specific tasks, \\method demonstrates a notably superior performance on the TREC task, a few-shot question answering challenge. This suggests that the model effectively aggregates information from the few-shot examples, highlighting the potential for further investigation into in-context learning tasks.\n\n\n\n\n\\begin{table*}\n\n\\centering\n\n% \\wx{need to label the best in each block} \n% \\jh{the font size is too small. Suggestion: 1. write abbreviations for method names, e.g., RKV -> RKV, SLM -> SLM, SKV -> SKV, and write the full name in the caption. 2. Reduce the space between columns using ``c@{\\hspace{0.05ex}}c''}\n\n\n% credit to https://arxiv.org/abs/2401.01325\n% \\scalebox{0.48}{\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\cmidrule(lr){2-17}\n&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n\n\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV & 25.70 & 29.75 & 41.12 & 45.55 & 35.87 & 22.35 & 25.63 & 23.03 & 26.21 & 73.00 & 90.56 & 41.88 & 04.67 & 69.25 & 58.05 & 50.77 & 41.46 \\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 19.86 & 9.09 & 27.89 & \\textbf{37.34} & 28.35 & \\textbf{18.17} & 15.86 & 20.80 & 16.41 & 38.50 & 85.92 & 36.32 & 5.22 & 69.00 & 51.78 & 48.38 & 33.05 \\\\\nH2O & 20.80 & 11.34 & 27.03 & 37.25 & 30.01 & 17.94 & 18.29 & 21.49 & 19.13 & 38.00 & 84.70 & \\textbf{37.76} & \\textbf{5.63} & 69.33 & \\textbf{53.44} & \\textbf{50.15} & 33.89 \\\\\nSLM & 17.44 & 8.68 & 22.25 & 35.37 & \\textbf{31.51} & 15.97 & 15.46 & 20.06 & 14.64 & 38.00 & 72.33 & 29.10 & 5.42 & \\textbf{69.50} & 46.14 & 45.09 & 30.43 \\\\\nOurs & \\textbf{21.13} & \\textbf{14.18} & \\textbf{30.26} & 35.12 & 23.76 & 16.17 & \\textbf{18.33} & \\textbf{21.65} & \\textbf{19.23} & \\textbf{58.00} & \\textbf{88.31} & 37.07 & 5.23 & \\textbf{69.50} & 52.61 & 45.74 & \\textbf{34.76} \\\\\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 96} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 20.45 & 10.34 & 31.84 & 37.85 & 28.65 & \\textbf{18.52} & 17.90 & 21.26 & 19.07 & 41.50 & 86.95 & 37.82 & 5.08 & 69.12 & 54.69 & \\textbf{51.31} & 34.51 \\\\\nH2O & 21.55 & 11.21 & 28.73 & 37.66 & 30.12 & 18.47 & 19.57 & 21.57 & 20.44 & 38.50 & \\textbf{87.63} & \\textbf{38.47} & 5.60 & 69.00 & 54.51 & 50.16 & 34.57 \\\\\nSLM & 18.67 & 8.43 & 24.98 & 38.35 & \\textbf{30.59} & 16.37 & 17.33 & 19.84 & 18.41 & 41.00 & 73.92 & 29.38 & 5.80 & \\textbf{69.50} & 47.15 & 45.61 & 31.58 \\\\\nOurs & \\textbf{21.67} & \\textbf{15.10} & \\textbf{33.50} & \\textbf{39.73} & 26.48 & 17.47 & \\textbf{19.64} & \\textbf{22.28} & \\textbf{20.49} & \\textbf{61.50} & 87.38 & 38.18 & \\textbf{6.00} & 69.25 & \\textbf{55.30} & 46.78 & \\textbf{36.29} \\\\\n\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 128} \\\\\n\\arrayrulecolor{black!20}\\midrule\nSKV & 21.19 & 13.55 & 32.64 & 38.75 & 29.64 & \\textbf{18.73} & 18.98 & 21.62 & 20.26 & 45.00 & 88.36 & 37.64 & 5.13 & 68.85 & 55.84 & \\textbf{51.82} & 35.50 \\\\\nH2O & \\textbf{22.12} & 13.20 & 31.61 & 37.79 & \\textbf{32.71} & 18.45 & \\textbf{20.32} & 22.02 & \\textbf{21.10} & 38.50 & 87.75 & \\textbf{39.14} & 5.83 & \\textbf{69.50} & 55.06 & 50.97 & 35.37 \\\\\nSLM & 18.61 & 9.65 & 25.99 & 37.95 & 29.39 & 16.34 & 18.03 & 20.11 & 20.08 & 43.50 & 74.08 & 29.86 & 5.90 & \\textbf{69.50} & 47.47 & 45.60 & 32.00 \\\\\nOurs & 21.40 & \\textbf{16.92} & \\textbf{33.79} & \\textbf{39.73} & 28.72 & 18.59 & 19.86 & \\textbf{22.48} & 20.95 & \\textbf{66.50} & \\textbf{89.35} & 38.39 & \\textbf{5.92} & 69.00 & \\textbf{56.49} & 47.95 & \\textbf{37.25} \\\\\n\n\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 256} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n\n% SKV & 24.03&18.00&36.56&42.73&32.73&20.25&20.52&21.97&22.48&61.50&90.14&39.48&5.75&69.50&55.73&51.05&\\textbf{38.28} \\\\\n% SLM & 18.36&9.62&28.56&38.52&30.38&16.03&19.40&20.30&22.70&52.50&73.33&30.37&5.86&69.50&45.52&43.87&32.80 \\\\\n% H2O & 23.82&16.61&16.61&39.04&31.72&20.05&21.27&22.25&22.23&39.00&89.22&39.45&5.57&69.50&54.48&49.00&34.99 \\\\\n% Ours & 23.99&20.61&38.28&\\textbf{43.23}&\\textbf{31.72}&\\textbf{20.94}&\\textbf{21.27}&\\textbf{22.69}&\\textbf{22.83}&\\textbf{71.00}&\\textbf{90.48}&\\textbf{39.86}&\\textbf{5.86}&\\textbf{69.50}&\\textbf{56.94}&\\textbf{50.16}&39.31 \\\\\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-8B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & \\textbf{25.86} & 29.55 & \\textbf{41.10} & \\textbf{44.99} & \\textbf{35.80} & 21.81 & 25.98 & \\textbf{23.40} & 26.46 & \\textbf{73.50} & \\textbf{90.56} & 41.66 & 5.17 & \\textbf{69.25} & 56.65 & 49.94 & 41.35 \\\\\nSLM & 21.71 & 25.78 & 38.13 & 40.12 & 32.01 & 16.86 & 23.14 & 22.64 & \\textbf{26.48} & 70.00 & 83.22 & 31.75 & \\textbf{5.74} & 68.50 & 53.50 & 45.58 & 37.82 \\\\\nH2O & 25.56 & 26.85 & 39.54 & 44.30 & 32.92 & 21.09 & 24.68 & 23.01 & 26.16 & 53.00 & \\textbf{90.56} & 41.84 & 4.91 & \\textbf{69.25} & 56.40 & 49.68 & 39.35 \\\\\nOurs & 25.40 & \\textbf{29.71} & 40.25 & 44.76 & 35.32 & \\textbf{21.98} & \\textbf{26.83} & 23.30 & 26.19 & 73.00 & \\textbf{90.56} & \\textbf{42.14} & 5.22 & \\textbf{69.25} & \\textbf{58.76} & \\textbf{51.18} & \\textbf{41.49} \\\\\n\n\n\\arrayrulecolor{black}\\bottomrule\n\\end{tabular}\n}\n\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-8B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n}\n\\label{table:longbench_appendix_llama3_8b}\n\\end{table*}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\begin{table*}\n\n\\centering\n\n% \\wx{need to label the best in each block} \n% \\jh{the font size is too small. Suggestion: 1. write abbreviations for method names, e.g., RKV -> RKV, SLM -> SLM, SKV -> SKV, and write the full name in the caption. 2. Reduce the space between columns using ``c@{\\hspace{0.05ex}}c''}\n\n\n% credit to https://arxiv.org/abs/2401.01325\n% \\scalebox{0.48}{\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\cmidrule(lr){2-17}\n&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n\n\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV & 26.90 & 33.07 & 49.20 & 43.02 & 27.33 & 18.78 & 32.91 & 24.21 & 26.99 & 71.00 & 86.23 & 42.65 & 2.75 & 86.98 & 56.96 & 54.52 & 42.71 \\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & 16.94&17.17&39.51&\\textbf{36.87}&22.26&15.18&14.75&20.35&21.45&37.50&\\textbf{84.16}&37.28&4.50&61.13&42.40&38.44&30.72\\\\\nSLM & 15.01&13.84&28.74&30.97&\\textbf{24.50}&13.42&13.25&19.46&19.17&35.50&76.91&29.61&4.67&27.33&38.71&35.29&25.60\\\\\nH2O & 18.19&19.04&37.40&30.18&22.22&13.77&16.60&\\textbf{21.52}&\\textbf{21.98}&37.00&81.02&\\textbf{38.62}&\\textbf{5.00}&\\textbf{66.03}&43.54&\\textbf{40.46}&30.88\\\\\nOurs & \\textbf{20.91}&\\textbf{20.21}&\\textbf{39.94}&33.57&22.87&\\textbf{15.70}&\\textbf{17.31}&21.23&21.41&\\textbf{54.00}&81.98&36.96&3.58&60.83&\\textbf{44.52}&37.99&\\textbf{32.19}\\\\\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 96} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & 19.92&18.80&\\textbf{43.29}&\\textbf{39.66}&23.08&\\textbf{15.94}&16.65&21.26&21.47&43.50&83.48&39.74&4.00&60.10&45.53&41.12&32.47\\\\\nSLM & 15.15&15.48&31.44&30.03&\\textbf{23.93}&12.73&16.76&19.15&19.19&41.50&75.31&28.71&5.00&28.48&38.92&36.05&26.37\\\\\nH2O & 19.44&20.81&38.78&32.39&21.51&14.43&17.68&\\textbf{22.40}&\\textbf{21.99}&38.00&82.51&\\textbf{39.94}&\\textbf{6.06}&\\textbf{77.48}&45.18&\\textbf{42.43}&32.67\\\\\nOurs & \\textbf{20.35}&\\textbf{21.87}&41.15&34.94&21.85&15.81&\\textbf{18.21}&21.66&21.43&\\textbf{65.00}&\\textbf{83.60}&39.60&4.50&67.80&\\textbf{45.83}&39.38&\\textbf{34.08}\\\\\n\n\n\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 128} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\n\nSKV & 19.16 & 21.46 & 43.52 & \\textbf{38.60} & \\textbf{23.35} & \\textbf{16.09} & 17.66 & 21.84 & 21.47 & 47.50 & \\textbf{84.15} & 40.24 & 5.00 & 69.31 & \\textbf{46.98} & \\textbf{42.97} & 34.96 \\\\\nSLM & 16.57 & 14.68 & 32.40 & 30.19 & 22.64 & 12.34 & 18.08 & 18.96 & 19.19 & 43.50 & 74.22 & 29.02 & 4.50 & 29.48 & 39.23 & 36.16 & 27.57 \\\\\nH2O & 21.20 & 21.90 & 41.55 & 33.56 & 21.28 & 12.93 & \\textbf{18.59} & \\textbf{22.61} & \\textbf{21.99} & 39.00 & 82.37 & \\textbf{40.44} & \\textbf{6.00} & \\textbf{83.19} & 46.41 & 42.66 & 34.73 \\\\\nOurs & \\textbf{21.75} & \\textbf{22.03} & \\textbf{44.32} & 34.06 & 22.79 & 15.77 & 18.58 & 21.89 & 21.43 & \\textbf{66.00} & 83.46 & 39.75 & 4.50 & 66.90 & 46.96 & 41.28 & \\textbf{35.72} \\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{Mistral-7B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\n\nSKV &\\textbf{25.89} & \\textbf{32.93} & 48.56 & \\textbf{42.96} & 27.42 & 19.02 & 26.56 & \\textbf{24.47} & 26.69 & 70.00 & 86.27 & 42.57 & \\textbf{5.50} & \\textbf{88.90} & 50.42 & 46.72 & 41.56 \\\\\nSLM & 20.31 & 26.64 & 45.72 & 35.25 & 24.31 & 12.20 & \\textbf{27.47} & 21.57 & 24.51 & 68.50 & 71.95 & 31.19 & 5.00 & 22.56 & 43.38 & 37.08 & 32.35 \\\\\nH2O & 25.76 & 31.10 & \\textbf{49.03} & 40.76 & 26.52 & 17.07 & 24.81 & 23.64 & 26.60 & 55.00 & \\textbf{86.35} & 42.48 & \\textbf{5.50} & 88.15 & 49.93 & 46.57 & 39.95 \\\\\nOurs & 25.53 & 32.21 & 48.97 & 42.26 & \\textbf{27.50} & \\textbf{19.36} & 26.60 & 23.97 & \\textbf{26.73} & \\textbf{71.00} & 86.25 & \\textbf{42.94} & 4.50 & 87.90 & \\textbf{53.12} & \\textbf{47.21} & \\textbf{41.63} \\\\\n\n\n\n\\arrayrulecolor{black}\\bottomrule\n\\end{tabular}\n}\n\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for Mistral-7B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n}\n\\label{table:longbench_appendix_mistral}\n\\end{table*}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\begin{table*}[!t]\n\n\\centering\n\n% \\wx{need to label the best in each block} \n% \\jh{the font size is too small. Suggestion: 1. write abbreviations for method names, e.g., RKV -> RKV, SLM -> SLM, SKV -> SKV, and write the full name in the caption. 2. Reduce the space between columns using ``c@{\\hspace{0.05ex}}c''}\n\n\n% credit to https://arxiv.org/abs/2401.01325\n% \\scalebox{0.48}{\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c@{\\hspace{0.6ex}}c}\n\n\\specialrule{1pt}{0pt}{2pt}\n\\multirow{5}{*}{Method} & \\multicolumn{3}{c}{Single-Document QA} & \\multicolumn{3}{c}{Multi-Document QA}& \\multicolumn{3}{c}{Summarization}& \\multicolumn{3}{c}{Few-shot Learning}& \\multicolumn{2}{c}{Synthetic} & \\multicolumn{2}{c}{Code} & \\multirow{5}{*}{Avg.} \\\\\n\\cmidrule(lr){2-4}\\cmidrule(lr){5-7}\\cmidrule(lr){8-10}\\cmidrule(lr){11-13}\\cmidrule(lr){14-15}\\cmidrule(lr){16-17}\n& \\rotatebox[origin=c]{30}{NrtvQA} & \\rotatebox[origin=c]{30}{Qasper} & \\rotatebox[origin=c]{30}{MF-en} & \\rotatebox[origin=c]{30}{HotpotQA} & \\rotatebox[origin=c]{30}{2WikiMQA} & \\rotatebox[origin=c]{30}{Musique} & \\rotatebox[origin=c]{30}{GovReport} & \\rotatebox[origin=c]{30}{QMSum} & \\rotatebox[origin=c]{30}{MultiNews} & \\rotatebox[origin=c]{30}{TREC} & \\rotatebox[origin=c]{30}{TriviaQA} & \\rotatebox[origin=c]{30}{SAMSum} & \\rotatebox[origin=c]{30}{PCount} & \\rotatebox[origin=c]{30}{PRe} & \\rotatebox[origin=c]{30}{Lcc} & \\rotatebox[origin=c]{30}{RB-P} & \\\\\n\\cmidrule(lr){2-17}\n&18409&3619&4559&9151&4887&11214&8734&10614&2113&5177&8209&6258&11141&9289&1235&4206& \\\\\n\n\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = Full} \\\\\n\\arrayrulecolor{black!20}\\midrule\nFKV & 27.75& \t46.48& \t49.45\t& 52.04& \t54.9& \t30.42& \t32.37& \t22.27\t& 27.58\t& 73.5& \t92.46& \t45.73\t& 12.5\t& 72.5\t& 40.96\t& 63.91\t& 46.55 \\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 64} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & 23.92&31.09&36.54&46.66&50.40&25.30&18.05&21.11&19.79&41.50&\\textbf{91.06}&40.26&12.00&\\textbf{72.50}&43.33&57.62&39.45\\\\\nSLM & 22.07&23.53&27.31&43.21&\\textbf{51.66}&23.85&16.62&19.74&15.20&39.50&76.89&33.06&12.00&\\textbf{72.50}&40.23&50.20&35.47\\\\\nH2O & 25.45&34.64&33.23&\\textbf{48.25}&50.30&24.88&20.03&21.50&21.39&42.00&90.36&\\textbf{41.58}&12.00&71.50&43.83&\\textbf{58.16}&39.94\\\\\nOurs & \\textbf{25.47}&\\textbf{36.71}&\\textbf{42.29}&47.08&46.21&\\textbf{28.30}&\\textbf{20.60}&\\textbf{21.62}&\\textbf{21.62}&\\textbf{64.50}&89.61&41.28&\\textbf{12.50}&\\textbf{72.50}&\\textbf{45.34}&56.50&\\textbf{42.01}\\\\\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 96} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\n\nSKV & \\textbf{25.78}&35.71&42.13&\\textbf{50.38}&\\textbf{51.46}&26.68&19.61&21.40&21.98&48.50&\\textbf{92.11}&41.21&12.00&72.00&44.85&59.05&41.55\\\\\nSLM & 23.31&29.46&29.21&41.85&45.92&23.00&18.42&19.71&18.57&45.00&76.79&33.54&12.00&\\textbf{72.50}&40.49&50.73&36.28\\\\\nH2O & 25.30&35.13&35.54&47.39&50.61&26.20&20.87&\\textbf{21.80}&\\textbf{22.93}&41.00&90.47&\\textbf{43.42}&12.00&72.00&43.84&\\textbf{59.86}&40.52\\\\\nOurs & 25.47&\\textbf{37.61}&\\textbf{44.00}&47.33&45.36&\\textbf{27.91}&\\textbf{21.05}&21.60&22.31&\\textbf{66.00}&91.45&42.36&12.00&\\textbf{72.50}&\\textbf{45.12}&56.88&\\textbf{42.43}\\\\\n\n\n\n\n\n\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 128} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & \\textbf{26.22}&37.49&\\textbf{45.70}&\\textbf{50.86}&\\textbf{52.82}&28.50&20.38&21.72&22.56&53.00&91.61&41.43&12.00&71.50&45.06&\\textbf{60.50}&42.58 \\\\\nSLM & 24.25&29.12&29.24&40.20&46.28&21.80&19.55&19.42&20.61&48.00&76.60&33.21&12.00&\\textbf{72.50}&40.65&51.03&36.53 \\\\\nH2O & 25.61&35.02&37.74&47.77&51.16&26.87&20.57&20.78&23.33&42.00&91.65&43.85&12.00&\\textbf{72.50}&43.50&59.67&40.88 \\\\\nOurs & 26.06&\\textbf{40.35}&45.67&50.20&52.78&\\textbf{29.36}&\\textbf{22.31}&\\textbf{22.02}&\\textbf{23.69}&\\textbf{71.00}&\\textbf{92.27}&\\textbf{44.33}&12.00&\\textbf{72.50}&\\textbf{45.90}&59.55&\\textbf{44.37} \\\\\n\n\n\n\n% \\arrayrulecolor{black}\\midrule\n% \\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 256} \\\\\n% \\arrayrulecolor{black!20}\\midrule\n\n% SKV & 26.44&40.96&45.44&51.00&54.49&29.97&23.04&22.05&24.47&66.00&91.53&43.97&12.00&72.50&45.03&62.96&\\textbf{44.49} \\\\\n% SLM & 24.75&27.99&30.01&41.40&46.55&21.51&21.78&18.99&23.88&55.00&77.49&33.67&12.00&72.50&40.82&50.66&37.44 \\\\\n% H2O & 27.95&38.12&43.33&49.41&53.58&28.23&23.60&22.20&24.60&44.00&92.73&45.08&12.00&72.50&42.74&62.73&42.68 \\\\\n% Ours & 27.14&\\textbf{42.61}&\\textbf{47.15}&\\textbf{50.60}&\\textbf{53.54}&\\textbf{30.60}&\\textbf{23.93}&\\textbf{22.19}&\\textbf{24.99}&\\textbf{73.00}&\\textbf{92.03}&\\textbf{44.82}&12.00&\\textbf{73.00}&\\textbf{44.56}&\\textbf{61.24}&45.21 \\\\\n\n\n\n\n\\arrayrulecolor{black}\\midrule\n\\multicolumn{18}{c}{LlaMa-3-70B-Instruct, KV Size = 2048} \\\\\n\\arrayrulecolor{black!20}\\midrule\n\nSKV & 26.73&45.18&47.91&\\textbf{52.00}&\\textbf{55.24}&30.48&28.76&22.35&27.31&72.50&92.38&45.58&12.00&\\textbf{72.50}&\\textbf{41.52}&\\textbf{69.27}&46.36\\\\ \nSLM & 26.69&41.01&35.97&46.55&52.98&25.71&27.81&20.81&27.16&69.00&91.55&44.02&12.00&72.00&41.44&68.73&43.96\\\\ \nH2O & \\textbf{27.67}&\\textbf{46.51}&\\textbf{49.54}&51.49&53.85&29.97&28.57&\\textbf{22.79}&\\textbf{27.53}&59.00&\\textbf{92.63}&\\textbf{45.94}&12.00&72.50&41.39&63.90&45.33\\\\ \nOurs & 27.22&46.19&48.72&51.62&54.56&\\textbf{31.11}&\\textbf{29.76}&22.50&27.27&\\textbf{73.50}&91.88&45.47&12.00&72.50&41.36&69.12&\\textbf{46.55}\\\\ \n\n\n\n\\arrayrulecolor{black}\\bottomrule\n\\end{tabular}\n}\n\\caption{Performance comparison of ~\\method (Ours) with SnapKV (SKV), H2O, StreamingLLM (SLM) and FullKV (FKV) on LongBench for LlaMa-3-70B-Instruct. ~\\method generally outperforms other KV Cache compression methods across various KV Cache sizes and LLMs. The performance strengths of ~\\method are more evident in small KV Cache sizes. Bold text represents the best performance.\n}\n\\label{table:longbench_appendix_llama3_70b}\n\\end{table*}\n\n\n\n\n\n\n\n\n\n\n\n\\clearpage\n\\newpage\n\n\n\n\n\\section{\\method Preserves the Long-Context Understanding Ability}\n\\label{appendix:needle}\n\n\n\nWe perform Fact Retrieval Across Context Lengths (``Needle In A HayStack'')~\\citep{liu2023lost,fu2024data} to test the in-context retrieval ability of LLMs after leveraging different KV cache methods. We conducted the Needle-in-a-Haystack experiment using various LLMs (i.e., Mistral-7B-Instruct-32k, LLaMA-3-8B-Instruct-8k, and LLaMA-3-70B-Instruct-8k), various KV cache sizes (i.e., 64, 96, and 128) and various methods (i.e., FullKV, PyramidKV, H2O and StreamingLLM). \\method achieves Acc. performance closest to FullKV, while other methods show significant decreases. It is worth noting that PyramidKV with 128 KV cache size achieves the same 100.0 Acc. performance compared with FullKV with 8k context size for LLaMA-3-70B-Instruct.\n\n\\autoref{figure:needle_mistral_64}, \\autoref{figure:needle_mistral_96}, \\autoref{figure:needle_mistral_128} show the results of \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with different cache size (64, 96 and 128, respectively).\n\n\\autoref{figure:needle_llama_64}, \\autoref{figure:needle_llama_96}, \\autoref{figure:needle_llama_128} show the results of \\textbf{LlaMa-3-8B-Instruct} with different cache size (64, 96 and 128, respectively).\n\n\\autoref{figure:needle_llama70_64}, \\autoref{figure:needle_llama70_96}, \\autoref{figure:needle_llama70_128} show the results of \\textbf{LlaMa-3-70B-Instruct} with different cache size (64, 96 and 128, respectively).\n\n% \\include{Tables/needle}\n\\begin{table*}[h]\n\\small\n\\centering\n\\begin{tabular}{lcccccc}\n\\toprule\n Model & Length & KV Cache & Full KV Acc. & PyramidKV Acc. & SnapKV Acc. & H2O Acc. \\\\\n\\midrule\n Mistral-7B & 32k & 64 & 100.00 & 80.50 & 43.90 & 48.40 \\\\\n Mistral-7B & 32k & 96 & 100.00 & 90.50 & 72.20 & 59.10 \\\\\n Mistral-7B & 32k & 128 & 100.00 & 91.60 & 80.10 & 64.90 \\\\\n \\midrule\n LLaMa-3-8B & 8k & 64 & 100.00 & 92.90 & 62.00 & 31.90 \\\\\n LLaMa-3-8B & 8k & 96 & 100.00 & 95.80 & 80.70 & 44.20 \\\\\n LLaMa-3-8B & 8k & 128 & 100.00 & 97.40 & 87.40 & 49.10 \\\\\n \\midrule\nLLaMa-3-70B & 8k & 64 & 100.00 & 99.60 & 76.20 & 47.30 \\\\\nLLaMa-3-70B & 8k & 96 & 100.00 & 98.60 & 94.40 & 69.90 \\\\\nLLaMa-3-70B & 8k & 128 & 100.00 & 100.00 & 98.60 & 82.30 \\\\\n\\bottomrule\n\\end{tabular}\n\\label{figure:needle}\n\\caption{Recall Accuracy performance from Fact Retrieval Across Context Lengths (``Needle In A HayStack'')\n}\n\\vspace{-3mm}\n\\end{table*}\n\n\n\n\n\n\n\n\n% \\autoref{figure:needle_mistral_64} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with \\textbf{32k} context size in a cache size of \\textbf{64} and a full KV cache size. \n\n% \\autoref{figure:needle_mistral_96} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with \\textbf{32k} context size in a cache size of \\textbf{96} and a full KV cache size. \n\n% \\autoref{figure:needle_mistral_128} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{Mistral-7B-Instruct}~\\citep{jiang2023mistral} with \\textbf{32k} context size in a cache size of \\textbf{128} and a full KV cache size. \n\n% \\autoref{figure:needle_llama_64} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{LlaMa-3-8B} with \\textbf{8k} context size in a cache size of \\textbf{64} and a full KV cache size. \n\n% \\autoref{figure:needle_llama_96} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{LlaMa-3-8B} with \\textbf{8k} context size in a cache size of \\textbf{96} and a full KV cache size. \n\n% \\autoref{figure:needle_llama_128} shows the quantitative result of \\method compared with SnapKV~\\citep{li2024snapkv} and H2O~\\citep{zhang2024h2o} sing \\textbf{LlaMa-3-8B} with \\textbf{8k} context size in a cache size of \\textbf{128} and a full KV cache size. \n\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_64.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{64} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_mistral_64}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_96.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{96} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_mistral_96}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_mistral_128.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{Mistral-7B-Instruct} with \\textbf{32k} context size in \\textbf{128} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_mistral_128}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama_64.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{64} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama_64}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama_96.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{96} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama_96}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama_128.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-8B-Instruct} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama_128}\n\\end{figure}\n\n\n\n\n\n\n\n\n\n\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_64.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{64} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama70_64}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_96.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{96} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama70_96}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n \\includegraphics[width=\\columnwidth]{Figures/needle_llama70_128.pdf}\n \\caption{\n Results of the Fact Retrieval Across Context Lengths (``Needle In A HayStack'') test in \\textbf{LlaMa-3-70B} with \\textbf{8k} context size in \\textbf{128} KV cache size.\n The vertical axis of the table represents the depth percentage, and the horizontal axis represents the token length. \n % (a) represents the results of Full KV cache size. \n % (b) represents the results of~\\method.\n % (c) represents the results of SnapKV.\n ~\\method mitigates the negative impact of KV cache compression on the long-context understanding capability of LLMs.\n % Higher scores indicate a better retrieval ability. For the average score across token length and depth percentage\n % the Full KV scores 65.0, PyramidKV scores 62.6, and SnapKV scores 57.3.\n }\n \\label{figure:needle_llama70_128}\n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\clearpage\n\\newpage\n\n% \\input{Files/0_Introduction}\n\n\n\n\n\n\\end{document}\n\n% \\end{document}"},"question":{"kind":"string","value":"When the proposed method is applied to Llama 70B models, is there a task where, for any of the data sets in it, the KV size of 64 outperforms both full KV cache and KV size of 2048. If so, name the task and the margin by which it outperforms KV size of 2048. If not, just say No."},"answer":{"kind":"string","value":"Code, 3.98"},"plan":{"kind":"string","value":"SELECT all tasks where method is authors' method AND base model is llama 70b\nLOOP for each task\n SELECT all datasets in this task\n LOOP for each dataset\n IF kv size 64 score > full kv cache score AND kv size 64 score > kv size 2048 score\n COMPUTE margin = kv size 64 score - kv size 2048 score\n RETURN task, margin\nRETURN No\n"}}},{"rowIdx":365,"cells":{"paper":{"kind":"string","value":"2510.24706"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t!]\n","\\centering\n","\\caption{Overall performance comparison of LLMs across VR games (5-shot setting). Best model performance per metric is \\textbf{bolded}, second best is \\underline{underlined}.}\n","\\label{tab:overall_performance_1}\n","\\resizebox{\\textwidth}{!}{\n","\\setlength{\\tabcolsep}{2pt}\n","\\begin{tabular}{l cccc cccc cccc cccc}\n","\\toprule\n","\\multirow{2}{*}{\\textbf{Model}} & \\multicolumn{4}{c}{\\textbf{Half-Life: Alyx}} & \\multicolumn{4}{c}{\\textbf{Into the Radius}} & \\multicolumn{4}{c}{\\textbf{Moss: Book II}} & \\multicolumn{4}{c}{\\textbf{Vivecraft}} \\\\\n","\\cmidrule(lr){2-5} \\cmidrule(lr){6-9} \\cmidrule(lr){10-13} \\cmidrule(lr){14-17}\n","& \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} \\\\\n","\\midrule\n","GPT-3.5 & \\textbf{0.858} & 0.123 & \\textbf{0.287} & 0.143 & 0.662 & 0.169 & 0.226 & 0.137 & 0.782 & 0.169 & 0.207 & 0.186 & 0.922 & 0.043 & 0.098 & 0.067 \\\\\n","GPT-4 & \\underline{0.853} & \\underline{0.125} & 0.258 & \\textbf{0.172} & \\underline{0.693} & 0.189 & \\underline{0.328} & 0.177 & \\textbf{0.824} & 0.218 & 0.336 & \\underline{0.220} & 0.927 & \\underline{0.137} & 0.437 & 0.081 \\\\\n","GPT-4o & 0.804 & 0.022 & 0.075 & \\underline{0.167} & \\textbf{0.698} & \\textbf{0.291} & \\textbf{0.414} & \\textbf{0.190} & \\textbf{0.824} & \\textbf{0.300} & \\underline{0.342} & \\textbf{0.222} & \\underline{0.931} & \\textbf{0.190} & \\textbf{0.489} & \\textbf{0.096} \\\\\n","Mixtral & 0.839 & \\textbf{0.126} & 0.246 & 0.147 & 0.666 & 0.123 & 0.228 & 0.097 & 0.756 & 0.117 & 0.191 & 0.121 & 0.926 & 0.060 & 0.239 & 0.070 \\\\\n","LLaMA-3 & 0.848 & \\textbf{0.126} & \\underline{0.279} & 0.162 & 0.644 & \\underline{0.242} & 0.317 & 0.168 & \\underline{0.823} & \\underline{0.283} & \\textbf{0.349} & 0.200 & 0.929 & 0.039 & 0.122 & 0.042 \\\\\n","GLM-4 & 0.836 & 0.076 & 0.183 & 0.149 & 0.618 & 0.096 & 0.186 & 0.149 & 0.749 & 0.087 & 0.174 & 0.165 & 0.909 & 0.000 & 0.045 & 0.061 \\\\\n","\\midrule\n","Human & 0.845 & 0.090 & 0.240 & 0.110 & 0.684 & 0.148 & 0.257 & \\underline{0.181} & 0.817 & 0.112 & 0.328 & 0.174 & \\textbf{0.935} & 0.122 & \\underline{0.482} & \\underline{0.084} \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Overall performance comparison of LLMs across VR games (5-shot setting). Best model performance per metric is \\\\textbf{bolded}, second best is \\\\underline{underlined}.}\\n\",\n \"\\\\label{tab:overall_performance_1}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\setlength{\\\\tabcolsep}{2pt}\\n\",\n \"\\\\begin{tabular}{l cccc cccc cccc cccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Model}} & \\\\multicolumn{4}{c}{\\\\textbf{Half-Life: Alyx}} & \\\\multicolumn{4}{c}{\\\\textbf{Into the Radius}} & \\\\multicolumn{4}{c}{\\\\textbf{Moss: Book II}} & \\\\multicolumn{4}{c}{\\\\textbf{Vivecraft}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-5} \\\\cmidrule(lr){6-9} \\\\cmidrule(lr){10-13} \\\\cmidrule(lr){14-17}\\n\",\n \"& \\\\textbf{NSAS}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SOP}\\\\ensuremath{\\\\uparrow} & \\\\textbf{F1$_{\\\\text{SOP}}$}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SSC}\\\\ensuremath{\\\\uparrow} & \\\\textbf{NSAS}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SOP}\\\\ensuremath{\\\\uparrow} & \\\\textbf{F1$_{\\\\text{SOP}}$}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SSC}\\\\ensuremath{\\\\uparrow} & \\\\textbf{NSAS}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SOP}\\\\ensuremath{\\\\uparrow} & \\\\textbf{F1$_{\\\\text{SOP}}$}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SSC}\\\\ensuremath{\\\\uparrow} & \\\\textbf{NSAS}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SOP}\\\\ensuremath{\\\\uparrow} & \\\\textbf{F1$_{\\\\text{SOP}}$}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SSC}\\\\ensuremath{\\\\uparrow} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"GPT-3.5 & \\\\textbf{0.858} & 0.123 & \\\\textbf{0.287} & 0.143 & 0.662 & 0.169 & 0.226 & 0.137 & 0.782 & 0.169 & 0.207 & 0.186 & 0.922 & 0.043 & 0.098 & 0.067 \\\\\\\\\\n\",\n \"GPT-4 & \\\\underline{0.853} & \\\\underline{0.125} & 0.258 & \\\\textbf{0.172} & \\\\underline{0.693} & 0.189 & \\\\underline{0.328} & 0.177 & \\\\textbf{0.824} & 0.218 & 0.336 & \\\\underline{0.220} & 0.927 & \\\\underline{0.137} & 0.437 & 0.081 \\\\\\\\\\n\",\n \"GPT-4o & 0.804 & 0.022 & 0.075 & \\\\underline{0.167} & \\\\textbf{0.698} & \\\\textbf{0.291} & \\\\textbf{0.414} & \\\\textbf{0.190} & \\\\textbf{0.824} & \\\\textbf{0.300} & \\\\underline{0.342} & \\\\textbf{0.222} & \\\\underline{0.931} & \\\\textbf{0.190} & \\\\textbf{0.489} & \\\\textbf{0.096} \\\\\\\\\\n\",\n \"Mixtral & 0.839 & \\\\textbf{0.126} & 0.246 & 0.147 & 0.666 & 0.123 & 0.228 & 0.097 & 0.756 & 0.117 & 0.191 & 0.121 & 0.926 & 0.060 & 0.239 & 0.070 \\\\\\\\\\n\",\n \"LLaMA-3 & 0.848 & \\\\textbf{0.126} & \\\\underline{0.279} & 0.162 & 0.644 & \\\\underline{0.242} & 0.317 & 0.168 & \\\\underline{0.823} & \\\\underline{0.283} & \\\\textbf{0.349} & 0.200 & 0.929 & 0.039 & 0.122 & 0.042 \\\\\\\\\\n\",\n \"GLM-4 & 0.836 & 0.076 & 0.183 & 0.149 & 0.618 & 0.096 & 0.186 & 0.149 & 0.749 & 0.087 & 0.174 & 0.165 & 0.909 & 0.000 & 0.045 & 0.061 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Human & 0.845 & 0.090 & 0.240 & 0.110 & 0.684 & 0.148 & 0.257 & \\\\underline{0.181} & 0.817 & 0.112 & 0.328 & 0.174 & \\\\textbf{0.935} & 0.122 & \\\\underline{0.482} & \\\\underline{0.084} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{table*}[t!]\n","\\centering\n","\\caption{Overall performance comparison of LLMs across VR games (5-shot setting). Best model performance per metric is \\textbf{bolded}, second best is \\underline{underlined}.}\n","\\label{tab:overall_performance_1}\n","\\resizebox{\\textwidth}{!}{\n","\\setlength{\\tabcolsep}{2pt}\n","\\begin{tabular}{l cccc cccc cccc cccc}\n","\\toprule\n","\\multirow{2}{*}{\\textbf{Model}} & \\multicolumn{4}{c}{\\textbf{Half-Life: Alyx}} & \\multicolumn{4}{c}{\\textbf{Into the Radius}} & \\multicolumn{4}{c}{\\textbf{Moss: Book II}} & \\multicolumn{4}{c}{\\textbf{Vivecraft}} \\\\\n","\\cmidrule(lr){2-5} \\cmidrule(lr){6-9} \\cmidrule(lr){10-13} \\cmidrule(lr){14-17}\n","& \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} \\\\\n","\\midrule\n","GPT-3.5 & \\textbf{0.858} & 0.123 & \\textbf{0.287} & 0.143 & 0.662 & 0.169 & 0.226 & 0.137 & 0.782 & 0.169 & 0.207 & 0.186 & 0.922 & 0.043 & 0.098 & 0.067 \\\\\n","GPT-4 & \\underline{0.853} & \\underline{0.125} & 0.258 & \\textbf{0.172} & \\underline{0.693} & 0.189 & \\underline{0.328} & 0.177 & \\textbf{0.824} & 0.218 & 0.336 & \\underline{0.220} & 0.927 & \\underline{0.137} & 0.437 & 0.081 \\\\\n","GPT-4o & 0.804 & 0.022 & 0.075 & \\underline{0.167} & \\textbf{0.698} & \\textbf{0.291} & \\textbf{0.414} & \\textbf{0.190} & \\textbf{0.824} & \\textbf{0.300} & \\underline{0.342} & \\textbf{0.222} & \\underline{0.931} & \\textbf{0.190} & \\textbf{0.489} & \\textbf{0.096} \\\\\n","Mixtral & 0.839 & \\textbf{0.126} & 0.246 & 0.147 & 0.666 & 0.123 & 0.228 & 0.097 & 0.756 & 0.117 & 0.191 & 0.121 & 0.926 & 0.060 & 0.239 & 0.070 \\\\\n","LLaMA-3 & 0.848 & \\textbf{0.126} & \\underline{0.279} & 0.162 & 0.644 & \\underline{0.242} & 0.317 & 0.168 & \\underline{0.823} & \\underline{0.283} & \\textbf{0.349} & 0.200 & 0.929 & 0.039 & 0.122 & 0.042 \\\\\n","GLM-4 & 0.836 & 0.076 & 0.183 & 0.149 & 0.618 & 0.096 & 0.186 & 0.149 & 0.749 & 0.087 & 0.174 & 0.165 & 0.909 & 0.000 & 0.045 & 0.061 \\\\\n","\\midrule\n","Human & 0.845 & 0.090 & 0.240 & 0.110 & 0.684 & 0.148 & 0.257 & \\underline{0.181} & 0.817 & 0.112 & 0.328 & 0.174 & \\textbf{0.935} & 0.122 & \\underline{0.482} & \\underline{0.084} \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\end{table*}\n"],["\\begin{table*}[t!]\n","\\caption{Overall performance across VR games and settings. We report the average scores for our four evaluation metrics: Strict Step-by-Step Matching (SSM), Normalized Step Alignment Score (NSAS), Sequential Order Preservation (SOP), and Semantic Step Coverage (SSC). Higher is better for all metrics. Bold indicates best model performance, underline indicates second best.}\n","\\label{tab:overall_performance_2}\n","\\resizebox{\\textwidth}{!}{\n","\\setlength{\\tabcolsep}{2pt}\n","\\begin{tabular}{l cccc cccc cccc}\n","\\toprule\n","\\multirow{2}{*}{\\textbf{Model}} & \\multicolumn{4}{c}{\\textbf{Average Across Settings}} & \\multicolumn{4}{c}{\\textbf{Zero-Shot}} & \\multicolumn{4}{c}{\\textbf{5-Shot}} \\\\\n"," & \\textbf{SSM (\\%)} & \\textbf{NSAS} & \\textbf{SOP} & \\textbf{SSC} & \\textbf{SSM (\\%)} & \\textbf{NSAS} & \\textbf{SOP} & \\textbf{SSC} & \\textbf{SSM (\\%)} & \\textbf{NSAS} & \\textbf{SOP} & \\textbf{SSC} \\\\\n","\\midrule\n","GPT-3.5 & 1.4 & 0.781 & 0.063 & 0.066 & 0.8 & 0.771 & 0.003 & 0.046 & 2.1 & 0.791 & 0.128 & 0.095 \\\\\n","GPT-4 & 3.7 & 0.806 & 0.107 & 0.124 & 1.0 & 0.788 & 0.015 & 0.107 & 8.8 & 0.825 & 0.184 & 0.140 \\\\\n","GPT-4o & \\underline{5.3} & 0.797 & 0.138 & \\underline{0.141} & 0.6 & 0.785 & 0.015 & 0.108 & \\underline{10.9} & 0.806 & 0.228 & \\underline{0.161} \\\\\n","Gemini-1.5 & \\textbf{5.8} & \\textbf{0.813} & \\textbf{0.146} & \\textbf{0.142} & \\textbf{2.1} & \\textbf{0.795} & 0.010 & \\textbf{0.124} & \\textbf{11.7} & \\textbf{0.832} & \\textbf{0.236} & \\textbf{0.162} \\\\\n","Mixtral & 1.1 & 0.784 & 0.068 & 0.079 & 0.0 & 0.777 & 0.002 & 0.040 & 2.2 & 0.796 & 0.105 & 0.107 \\\\\n","LLaMA-3 & 1.2 & 0.787 & 0.088 & 0.111 & 0.1 & 0.783 & 0.011 & 0.088 & 1.8 & 0.794 & 0.163 & 0.132 \\\\\n","GLM-4 & 0.0 & 0.761 & 0.038 & 0.077 & 0.0 & 0.762 & 0.006 & 0.052 & 0.0 & 0.765 & 0.071 & 0.120 \\\\\n","\\midrule\n","Human & 1.2 & 0.833 & 0.122 & 0.159 & -- & -- & -- & -- & -- & -- & -- & -- \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\end{table*}\n"],["\\begin{figure}[!htbp]\n"," \\centering\n"," \\includegraphics[width=0.8\\linewidth, height=0.20\\textheight, keepaspectratio]{Figures/strict_ssm.png}\n"," \\caption{Overview of Strict Step-by-Step Matching (SSM) Calculation}\n"," \\label{fig:ssm}\n","\\end{figure}\n"],["\\begin{figure}[!htbp]\n"," \\vspace{0.8em}\n"," \\centering\n"," \\includegraphics[width=1.0\\linewidth, height=0.48\\textheight, keepaspectratio]{Figures/longest_common_steps.png}\n"," \\caption{Overview of Common Subsequence Evaluation}\n"," \\label{fig:cse}\n","\\end{figure}\n"],["\\begin{table}[htbp!]\n","\\caption{Performance of LLMs across VR Games (Best Few-Shot Setting)}\n","\\label{tab:performance_llm_across_games}\n","\\centering\n","\\small\n","\\begin{tabular}{lccccc}\n","\\toprule\n","\\textbf{Model} & \\textbf{NSAS} & \\textbf{SOP} & \\textbf{SSC} & \\textbf{SSM} & \\textbf{Best FS} \\\\\n","\\midrule\n","Gemini-1.5-Pro & 0.845 & 0.251 & 0.151 & 0.087 & 5 \\\\\n","GPT-4o & 0.832 & 0.291 & 0.190 & 0.135 & 5 \\\\\n","GPT-4 & 0.824 & 0.218 & 0.177 & 0.095 & 5 \\\\\n","LLaMA-3-8B & 0.823 & 0.283 & 0.200 & 0.040 & 5 \\\\\n","Human & 0.817 & 0.124 & 0.174 & 0.021 & - \\\\\n","Mixtral-8x7B & 0.790 & 0.123 & 0.142 & 0.039 & 5 \\\\\n","GPT-3.5 & 0.778 & 0.169 & 0.137 & 0.037 & 5 \\\\\n","GLM-4-Flash & 0.749 & 0.096 & 0.165 & 0.000 & 5 \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[htbp!]\n","\\caption{Performance comparison across different VR games (5-shot setting). We report NSAS scores (primary metric) and SOP scores (in parentheses).}\n","\\label{tab:per_game}\n","\\centering\n","\\resizebox{0.75\\columnwidth}{!}{\n","\\begin{tabular}{l|cccc}\n","\\toprule\n","\\textbf{Model} & \\textbf{Half-Life: Alyx} & \\textbf{Radius} & \\textbf{Moss} & \\textbf{Vivecraft} \\\\\n","\\midrule\n","GPT-3.5-turbo & 0.858 (0.123) & 0.662 (0.169) & 0.782 (0.169) & 0.922 (0.043) \\\\\n","GPT-4-turbo & 0.852 (0.125) & 0.693 (0.189) & 0.824 (0.218) & 0.927 (0.137) \\\\\n","GPT-4o & 0.804 (0.022) & 0.698 (0.291) & 0.824 (0.300) & 0.931 (0.190) \\\\\n","Gemini-1.5-Pro & 0.863 (0.209) & 0.682 (0.102) & 0.848 (0.265) & 0.938 (0.250) \\\\\n","Mixtral-8x7B & 0.839 (0.126) & 0.666 (0.123) & 0.756 (0.117) & 0.926 (0.060) \\\\\n","LLaMA-3-8B & 0.848 (0.126) & 0.644 (0.242) & 0.823 (0.283) & 0.929 (0.039) \\\\\n","GLM-4-flash & 0.836 (0.076) & 0.618 (0.096) & 0.749 (0.087) & 0.909 (0.000) \\\\\n","\\midrule\n","Human & 0.845 (0.090) & 0.684 (0.148) & 0.817 (0.112) & 0.935 (0.122) \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\end{table}\n"],["\\begin{table}[t!]\n","\\caption{Impact of few-shot examples on model performance. We report F1 scores for Sequential Order Preservation (SOP) across different number of examples. Higher is better.}\n","\\label{tab:fewshot_impact}\n","\\centering\n","\\resizebox{0.73\\columnwidth}{!}{\n","\\begin{tabular}{l|cccc|c}\n","\\toprule\n","\\textbf{Model} & \\textbf{Zero-shot} & \\textbf{1-shot} & \\textbf{3-shot} & \\textbf{5-shot} & \\textbf{Relative Gain (\\%)} \\\\\n","\\midrule\n","GPT-3.5-turbo & 0.036 & 0.096 & 0.190 & 0.226 & 527.8 \\\\\n","GPT-4-turbo & 0.102 & 0.171 & 0.254 & 0.301 & 195.1 \\\\\n","GPT-4o & 0.112 & 0.224 & 0.257 & 0.287 & 156.3 \\\\\n","Gemini-1.5-Pro & 0.085 & 0.187 & 0.260 & \\textbf{0.330} & \\textbf{288.2} \\\\\n","Mixtral-8x7B & 0.031 & 0.110 & 0.204 & 0.201 & 548.4 \\\\\n","LLaMA-3-8B & 0.090 & 0.165 & 0.254 & 0.299 & 232.2 \\\\\n","GLM-4-flash & 0.033 & 0.069 & 0.121 & 0.146 & 342.4 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\end{table}\n"],["\\begin{table}[h!]\n"," \\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\textit{Vivecraft} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-shot} & 0.9258 & 0.0248 & 0.9255 & 0.0238 & 0.9191 & 0.0306 & 0.9209 & 0.0334 & 0.9312 & 0.0207 & 0.9244 & 0.0329 \\\\\n"," \\textbf{1-shot} & 0.921 & 0.0309 & 0.9349 & 0.0506 & 0.9358 & 0.0735 & 0.9362 & 0.0553 & 0.9219 & 0.0636 & 0.9101 & 0.0765 \\\\\n"," \\textbf{3-shot} & 0.9284 & 0.0734 & 0.914 & 0.1167 & 0.9212 & 0.1115 & 0.9381 & 0.0781 & 0.9005 & 0.1125 & 0.9022 & 0.1051 \\\\\n"," \\textbf{5-shot} & 0.9218 & 0.0385 & 0.9274 & 0.0674 & 0.9305 & 0.0689 & 0.9378 & 0.0708 & 0.9256 & 0.0477 & 0.9289 & 0.0364 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \n"," \\label{tab:vivecraft_nsas}\n","\\end{table}\n"],["\\begin{table}[h!]\n"," \\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores\n","comparison of LLMs on \\textit{Vivecraft} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.0029 & 0.0312 & 0.0007 & 0.0078 & 0.0012 & 0.0125 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0059 & 0.0624 \\\\\n"," \\textbf{1-shot} & 0.015 & 0.0734 & 0.1203 & 0.2157 & 0.1568 & 0.2337 & 0.1794 & 0.291 & 0.0812 & 0.164 & 0.0351 & 0.1215 \\\\\n"," \\textbf{3-shot} & 0.1302 & 0.2352 & 0.1143 & 0.2136 & 0.2826 & 0.3417 & 0.2335 & 0.3417 & 0.0986 & 0.2024 & 0.1124 & 0.2026 \\\\\n"," \\textbf{5-shot} & 0.0395 & 0.1226 & 0.1366 & 0.2388 & 0.1837 & 0.278 & 0.2495 & 0.3358 & 0.0553 & 0.158 & 0.0374 & 0.1371 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n","\n"," \\label{tab:vivecraft_sop}\n","\\end{table}\n"],["\\begin{table}[h!]\n"," \\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\textit{Vivecraft} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.049 & 0.11 & 0.1301 & 0.1443 & 0.1272 & 0.1511 & 0.2221 & 0.2151 & 0.024 & 0.0999 & 0.1088 & 0.1549\\\\\n"," \\textbf{1-shot}& 0.1274 & 0.1988 & 0.544 & 0.3672 & 0.6598 & 0.3322 & 0.5747 & 0.3359 & 0.4914 & 0.3617 & 0.3165 & 0.3415 \\\\\n"," \\textbf{3-shot} & 0.4755 & 0.3526 & 0.6486 & 0.3373 & 0.6817 & 0.3204 & 0.6538 & 0.3373 & 0.5414 & 0.37 & 0.5299 & 0.3785 \\\\\n"," \\textbf{5-shot} & 0.18 & 0.2337 & 0.5035 & 0.3772 & 0.6183 & 0.3416 & 0.608 & 0.3546 & 0.3579 & 0.3555 & 0.1606 & 0.2605 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \n"," \\label{tab:vivecraft_ssc}\n","\\end{table}\n"],["\\begin{table}[h!]\n"," \\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\textit{Half-Life: Alyx} under different shot settings}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.838 & 0.0413 & 0.8456 & 0.0366 & 0.8376 & 0.0424 & 0.8447 & 0.032 & 0.8376 & 0.0331 & 0.848 & 0.0317 \\\\\n"," \\textbf{1-shot} & 0.8354 & 0.0582 & 0.8427 & 0.0489 & 0.8472 & 0.0629 & 0.8627 & 0.0482 & 0.807 & 0.1099 & 0.8131 & 0.1289 \\\\\n"," \\textbf{3-shot} & 0.8452 & 0.0551 & 0.845 & 0.0467 & 0.838 & 0.0757 & 0.8701 & 0.0603 & 0.8255 & 0.0819 & 0.8449 & 0.0707 \\\\\n"," \\textbf{5-shot} & 0.8577 & 0.0773 & 0.8523 & 0.0613 & 0.8039 & 0.0694 & 0.8625 & 0.0691 & 0.8394 & 0.0834 & 0.848 & 0.0976 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \n"," \\label{tab:alyx_nsas}\n","\\end{table}\n"],["\\begin{table}[h!]\n"," \\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\textit{Half Life: Alyx} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.0098 & 0.0802 & 0.0252 & 0.1265 & 0.0396 & 0.1745 & 0.0082 & 0.0669 & 0.0019 & 0.0158 & 0.0123 & 0.0704 \\\\\n"," \\textbf{1-shot} & 0.0447 & 0.0764 & 0.0402 & 0.1224 & 0.024 & 0.0733 & 0.0198 & 0.1263 & 0.0425 & 0.0816 & 0.0447 & 0.0967 \\\\\n"," \\textbf{3-shot} & 0.0725 & 0.1159 & 0.0312 & 0.0725 & 0.0701 & 0.1261 & 0.1349 & 0.2187 & 0.0703 & 0.1094 & 0.087 & 0.1687 \\\\\n"," \\textbf{5-shot} & 0.123 & 0.1834 & 0.1248 & 0.2382 & 0.0216 & 0.0809 & 0.2089 & 0.2938 & 0.1257 & 0.2409 & 0.1259 & 0.2385 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n","\n"," \\label{tab:alyx_sop}\n","\\end{table}\n"],["\\begin{table} [htbp!]\n"," \\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\textit{Half Life: Alyx} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.0785 & 0.1843 & 0.2231 & 0.2089 & 0.2424 & 0.2111 & 0.1989 & 0.1982 & 0.0716 & 0.1187 & 0.1662 & 0.172\\\\\n"," \\textbf{1-shot}& 0.2562 & 0.235 & 0.3485 & 0.2336 & 0.4184 & 0.2413 & 0.3859 & 0.2654 & 0.3256 & 0.1934 & 0.3872 & 0.2058\\\\\n"," \\textbf{3-shot} & 0.3072 & 0.2444 & 0.3648 & 0.2414 & 0.5611 & 0.229 & 0.5494 & 0.2887 & 0.3544 & 0.2202 & 0.4599 & 0.2371 \\\\\n"," \\textbf{5-shot} & 0.425 & 0.2814 & 0.6127 & 0.2856 & 0.6934 & 0.2359 & 0.6299 & 0.315 & 0.4642 & 0.2957 & 0.5152 & 0.2708 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:alyx_ssc}\n","\\end{table}\n"],["\\begin{table} [htbp!]\n"," \\caption{Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\textit{ Moss: Book II} under different shot settings}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.7819 & 0.0403 & 0.8055 & 0.0717 & 0.7871 & 0.0596 & 0.7994 & 0.0548 & 0.7913 & 0.0595 & 0.7916 & 0.0572 \\\\\n"," \\textbf{1-shot}& 0.776 & 0.0616 & 0.7993 & 0.0771 & 0.803 & 0.0924 & 0.8139 & 0.0778 & 0.7663 & 0.0793 & 0.7938 & 0.0763 \\\\\n"," \\textbf{3-shot} & 0.7776 & 0.0889 & 0.818 & 0.0925 & 0.8016 & 0.1242 & 0.8302 & 0.0935 & 0.7613 & 0.1341 & 0.7895 & 0.1371\\\\\n"," \\textbf{5-shot} & 0.782 & 0.0952 & 0.8243 & 0.102 & 0.8237 & 0.1092 & 0.8478 & 0.1017 & 0.756 & 0.1469 & 0.8232 & 0.105\\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:moss_nsas}\n","\\end{table}\n"],["\\begin{table} [htbp!]\n"," \\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\textit{Moss: Book II} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.0091 & 0.0581 & 0.0263 & 0.1533 & 0.0113 & 0.0494 & 0.0197 & 0.1029 & 0.0052 & 0.033 & 0.0 & 0.0\\\\\n"," \\textbf{1-shot}& 0.034 & 0.1568 & 0.0663 & 0.2044 & 0.1084 & 0.2486 & 0.1145 & 0.2495 & 0.0739 & 0.1721 & 0.0578 & 0.1486 \\\\\n"," \\textbf{3-shot} & 0.1581 & 0.242 & 0.1678 & 0.2522 & 0.2324 & 0.3185 & 0.2272 & 0.3324 & 0.1351 & 0.252 & 0.2584 & 0.3089 \\\\\n"," \\textbf{5-shot} & 0.1686 & 0.244 & 0.2182 & 0.2801 & 0.2998 & 0.3062 & 0.2652 & 0.3596 & 0.1169 & 0.247 & 0.2831 & 0.3097 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:moss_sop}\n","\\end{table}\n"],["\\begin{table} [htbp!]\n"," \\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\textit{Moss: Book II} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.0715 & 0.1792 & 0.2491 & 0.2844 & 0.2313 & 0.2567 & 0.1763 & 0.221 & 0.0407 & 0.0991 & 0.1208 & 0.1779\\\\\n"," \\textbf{1-shot}& 0.0748 & 0.1719 & 0.259 & 0.2771 & 0.3682 & 0.3018 & 0.3449 & 0.3396 & 0.1749 & 0.2393 & 0.2319 & 0.293 \\\\\n"," \\textbf{3-shot} & 0.3349 & 0.3069 & 0.4593 & 0.3309 & 0.5001 & 0.3444 & 0.5238 & 0.3738 & 0.3207 & 0.3105 & 0.4689 & 0.3399 \\\\\n"," \\textbf{5-shot} & 0.3737 & 0.3213 & 0.4951 & 0.3373 & 0.5562 & 0.3319 & 0.6091 & 0.3476 & 0.2974 & 0.3385 & 0.4567 & 0.3173 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:moss_ssc}\n","\\end{table}\n"],["\\begin{table} [htbp!]\n"," \\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on VR game \\textit{Into the Radius} under different shot settings}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.6165 & 0.0755 & 0.6408 & 0.0955 & 0.5939 & 0.1306 & 0.6492 & 0.1018 & 0.6644 & 0.0718 & 0.6447 & 0.0882 \\\\\n"," \\textbf{1-shot} & 0.641 & 0.1177 & 0.6519 & 0.1421 & 0.6282 & 0.1687 & 0.6875 & 0.1159 & 0.6285 & 0.1684 & 0.6285 & 0.1346 \\\\\n"," \\textbf{3-shot} & 0.6305 & 0.128 & 0.6802 & 0.1645 & 0.6491 & 0.2057 & 0.6634 & 0.1638 & 0.618 & 0.1633 & 0.6479 & 0.1606 \\\\\n"," \\textbf{5-shot} & 0.6621 & 0.1291 & 0.6927 & 0.1721 & 0.6984 & 0.2136 & 0.6818 & 0.1191 & 0.666 & 0.1495 & 0.6443 & 0.211\\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n","\n"," \\label{tab:radius_nsas}\n","\\end{table}\n"],["\\begin{table} [htbp!]\n"," \\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\textit{Into the Radius} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.0091 & 0.0581 & 0.0263 & 0.1533 & 0.0113 & 0.0494 & 0.0197 & 0.1029 & 0.0052 & 0.033 & 0.0 & 0.0\\\\\n"," \\textbf{1-shot}& 0.034 & 0.1568 & 0.0663 & 0.2044 & 0.1084 & 0.2486 & 0.1145 & 0.2495 & 0.0739 & 0.1721 & 0.0578 & 0.1486 \\\\\n"," \\textbf{3-shot} & 0.1581 & 0.242 & 0.1678 & 0.2522 & 0.2324 & 0.3185 & 0.2272 & 0.3324 & 0.1351 & 0.252 & 0.2584 & 0.3089 \\\\\n"," \\textbf{5-shot} & 0.1686 & 0.244 & 0.2182 & 0.2801 & 0.2998 & 0.3062 & 0.2652 & 0.3596 & 0.1169 & 0.247 & 0.2831 & 0.3097 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n","\n"," \\label{tab:radius_sop}\n","\\end{table}\n"],["\\begin{table} [htbp!]\n"," \\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\textit{Into the Radius} under different shot settings.}\n"," \\centering\n"," \\resizebox{\\textwidth}{!}{%\n"," \\renewcommand{\\arraystretch}{1.5}\n"," \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n"," \\toprule\n"," \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n"," \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n"," \\midrule\n"," \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n"," \\midrule\n"," \\textbf{Zero-Shot} & 0.0354 & 0.0982 & 0.1528 & 0.1774 & 0.2199 & 0.1745 & 0.1783 & 0.2107 & 0.0406 & 0.0899 & 0.1243 & 0.1655\\\\\n"," \\textbf{1-shot}& 0.1511 & 0.2246 & 0.304 & 0.2983 & 0.4102 & 0.2585 & 0.2823 & 0.3277 & 0.2593 & 0.3249 & 0.3171 & 0.269\\\\\n"," \\textbf{3-shot}& 0.2321 & 0.2713 & 0.4463 & 0.3099 & 0.5623 & 0.2976 & 0.3402 & 0.3379 & 0.3544 & 0.2621 & 0.5319 & 0.2382\\\\\n"," \\textbf{5-shot}& 0.3302 & 0.3115 & 0.5082 & 0.3063 & 0.6194 & 0.2877 & 0.2971 & 0.3187 & 0.285 & 0.3384 & 0.5314 & 0.2886\\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\label{tab:radius_ssc}\n","\\end{table}\n"],["\\begin{figure} [htbp!]\n"," \\centering\n","\\includegraphics[width=1.2\\linewidth, height=0.9\\textheight, keepaspectratio]{Figures/nsas_barh_4x1.png}\n"," \\caption{LLMs NSAS (avg) by Different Shot Setting Across Four VR Games}\n"," \\vspace{0.8em}\n"," \\label{fig:nsas_barh}\n","\\end{figure}\n"],["\\begin{figure} [htbp!]\n","\\centering\n"," \\includegraphics[width=1.2\\linewidth, height=0.9\\textheight, keepaspectratio]{Figures/sop_barh_4x1.png}\n"," \\caption{LLMs SOP (avg) by Different Shot Setting Across Four VR Games}\n","\\vspace{0.8em}\n","\\label{fig:sop_barh}\n","\\end{figure}\n"],["\\begin{figure} [htbp!]\n","\\centering\n"," \\includegraphics[width=1.2\\linewidth, height=1.0\\textheight, keepaspectratio]{Figures/ssc_barh_4x1.png}\n"," \\caption{LLMs SSC (avg) by Different Shot Setting Across Four VR Games}\n","\\vspace{0.8em}\n","\\label{fig:ssc_barh}\n","\\end{figure}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t!]\\n\",\n \"\\\\centering\\n\",\n \"\\\\caption{Overall performance comparison of LLMs across VR games (5-shot setting). Best model performance per metric is \\\\textbf{bolded}, second best is \\\\underline{underlined}.}\\n\",\n \"\\\\label{tab:overall_performance_1}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\setlength{\\\\tabcolsep}{2pt}\\n\",\n \"\\\\begin{tabular}{l cccc cccc cccc cccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Model}} & \\\\multicolumn{4}{c}{\\\\textbf{Half-Life: Alyx}} & \\\\multicolumn{4}{c}{\\\\textbf{Into the Radius}} & \\\\multicolumn{4}{c}{\\\\textbf{Moss: Book II}} & \\\\multicolumn{4}{c}{\\\\textbf{Vivecraft}} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-5} \\\\cmidrule(lr){6-9} \\\\cmidrule(lr){10-13} \\\\cmidrule(lr){14-17}\\n\",\n \"& \\\\textbf{NSAS}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SOP}\\\\ensuremath{\\\\uparrow} & \\\\textbf{F1$_{\\\\text{SOP}}$}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SSC}\\\\ensuremath{\\\\uparrow} & \\\\textbf{NSAS}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SOP}\\\\ensuremath{\\\\uparrow} & \\\\textbf{F1$_{\\\\text{SOP}}$}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SSC}\\\\ensuremath{\\\\uparrow} & \\\\textbf{NSAS}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SOP}\\\\ensuremath{\\\\uparrow} & \\\\textbf{F1$_{\\\\text{SOP}}$}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SSC}\\\\ensuremath{\\\\uparrow} & \\\\textbf{NSAS}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SOP}\\\\ensuremath{\\\\uparrow} & \\\\textbf{F1$_{\\\\text{SOP}}$}\\\\ensuremath{\\\\uparrow} & \\\\textbf{SSC}\\\\ensuremath{\\\\uparrow} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"GPT-3.5 & \\\\textbf{0.858} & 0.123 & \\\\textbf{0.287} & 0.143 & 0.662 & 0.169 & 0.226 & 0.137 & 0.782 & 0.169 & 0.207 & 0.186 & 0.922 & 0.043 & 0.098 & 0.067 \\\\\\\\\\n\",\n \"GPT-4 & \\\\underline{0.853} & \\\\underline{0.125} & 0.258 & \\\\textbf{0.172} & \\\\underline{0.693} & 0.189 & \\\\underline{0.328} & 0.177 & \\\\textbf{0.824} & 0.218 & 0.336 & \\\\underline{0.220} & 0.927 & \\\\underline{0.137} & 0.437 & 0.081 \\\\\\\\\\n\",\n \"GPT-4o & 0.804 & 0.022 & 0.075 & \\\\underline{0.167} & \\\\textbf{0.698} & \\\\textbf{0.291} & \\\\textbf{0.414} & \\\\textbf{0.190} & \\\\textbf{0.824} & \\\\textbf{0.300} & \\\\underline{0.342} & \\\\textbf{0.222} & \\\\underline{0.931} & \\\\textbf{0.190} & \\\\textbf{0.489} & \\\\textbf{0.096} \\\\\\\\\\n\",\n \"Mixtral & 0.839 & \\\\textbf{0.126} & 0.246 & 0.147 & 0.666 & 0.123 & 0.228 & 0.097 & 0.756 & 0.117 & 0.191 & 0.121 & 0.926 & 0.060 & 0.239 & 0.070 \\\\\\\\\\n\",\n \"LLaMA-3 & 0.848 & \\\\textbf{0.126} & \\\\underline{0.279} & 0.162 & 0.644 & \\\\underline{0.242} & 0.317 & 0.168 & \\\\underline{0.823} & \\\\underline{0.283} & \\\\textbf{0.349} & 0.200 & 0.929 & 0.039 & 0.122 & 0.042 \\\\\\\\\\n\",\n \"GLM-4 & 0.836 & 0.076 & 0.183 & 0.149 & 0.618 & 0.096 & 0.186 & 0.149 & 0.749 & 0.087 & 0.174 & 0.165 & 0.909 & 0.000 & 0.045 & 0.061 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Human & 0.845 & 0.090 & 0.240 & 0.110 & 0.684 & 0.148 & 0.257 & \\\\underline{0.181} & 0.817 & 0.112 & 0.328 & 0.174 & \\\\textbf{0.935} & 0.122 & \\\\underline{0.482} & \\\\underline{0.084} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \"\\\\caption{Overall performance across VR games and settings. We report the average scores for our four evaluation metrics: Strict Step-by-Step Matching (SSM), Normalized Step Alignment Score (NSAS), Sequential Order Preservation (SOP), and Semantic Step Coverage (SSC). Higher is better for all metrics. Bold indicates best model performance, underline indicates second best.}\\n\",\n \"\\\\label{tab:overall_performance_2}\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\setlength{\\\\tabcolsep}{2pt}\\n\",\n \"\\\\begin{tabular}{l cccc cccc cccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multirow{2}{*}{\\\\textbf{Model}} & \\\\multicolumn{4}{c}{\\\\textbf{Average Across Settings}} & \\\\multicolumn{4}{c}{\\\\textbf{Zero-Shot}} & \\\\multicolumn{4}{c}{\\\\textbf{5-Shot}} \\\\\\\\\\n\",\n \" & \\\\textbf{SSM (\\\\%)} & \\\\textbf{NSAS} & \\\\textbf{SOP} & \\\\textbf{SSC} & \\\\textbf{SSM (\\\\%)} & \\\\textbf{NSAS} & \\\\textbf{SOP} & \\\\textbf{SSC} & \\\\textbf{SSM (\\\\%)} & \\\\textbf{NSAS} & \\\\textbf{SOP} & \\\\textbf{SSC} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"GPT-3.5 & 1.4 & 0.781 & 0.063 & 0.066 & 0.8 & 0.771 & 0.003 & 0.046 & 2.1 & 0.791 & 0.128 & 0.095 \\\\\\\\\\n\",\n \"GPT-4 & 3.7 & 0.806 & 0.107 & 0.124 & 1.0 & 0.788 & 0.015 & 0.107 & 8.8 & 0.825 & 0.184 & 0.140 \\\\\\\\\\n\",\n \"GPT-4o & \\\\underline{5.3} & 0.797 & 0.138 & \\\\underline{0.141} & 0.6 & 0.785 & 0.015 & 0.108 & \\\\underline{10.9} & 0.806 & 0.228 & \\\\underline{0.161} \\\\\\\\\\n\",\n \"Gemini-1.5 & \\\\textbf{5.8} & \\\\textbf{0.813} & \\\\textbf{0.146} & \\\\textbf{0.142} & \\\\textbf{2.1} & \\\\textbf{0.795} & 0.010 & \\\\textbf{0.124} & \\\\textbf{11.7} & \\\\textbf{0.832} & \\\\textbf{0.236} & \\\\textbf{0.162} \\\\\\\\\\n\",\n \"Mixtral & 1.1 & 0.784 & 0.068 & 0.079 & 0.0 & 0.777 & 0.002 & 0.040 & 2.2 & 0.796 & 0.105 & 0.107 \\\\\\\\\\n\",\n \"LLaMA-3 & 1.2 & 0.787 & 0.088 & 0.111 & 0.1 & 0.783 & 0.011 & 0.088 & 1.8 & 0.794 & 0.163 & 0.132 \\\\\\\\\\n\",\n \"GLM-4 & 0.0 & 0.761 & 0.038 & 0.077 & 0.0 & 0.762 & 0.006 & 0.052 & 0.0 & 0.765 & 0.071 & 0.120 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Human & 1.2 & 0.833 & 0.122 & 0.159 & -- & -- & -- & -- & -- & -- & -- & -- \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[!htbp]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.8\\\\linewidth, height=0.20\\\\textheight, keepaspectratio]{Figures/strict_ssm.png}\\n\",\n \" \\\\caption{Overview of Strict Step-by-Step Matching (SSM) Calculation}\\n\",\n \" \\\\label{fig:ssm}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[!htbp]\\n\",\n \" \\\\vspace{0.8em}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1.0\\\\linewidth, height=0.48\\\\textheight, keepaspectratio]{Figures/longest_common_steps.png}\\n\",\n \" \\\\caption{Overview of Common Subsequence Evaluation}\\n\",\n \" \\\\label{fig:cse}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[htbp!]\\n\",\n \"\\\\caption{Performance of LLMs across VR Games (Best Few-Shot Setting)}\\n\",\n \"\\\\label{tab:performance_llm_across_games}\\n\",\n \"\\\\centering\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{lccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Model} & \\\\textbf{NSAS} & \\\\textbf{SOP} & \\\\textbf{SSC} & \\\\textbf{SSM} & \\\\textbf{Best FS} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Gemini-1.5-Pro & 0.845 & 0.251 & 0.151 & 0.087 & 5 \\\\\\\\\\n\",\n \"GPT-4o & 0.832 & 0.291 & 0.190 & 0.135 & 5 \\\\\\\\\\n\",\n \"GPT-4 & 0.824 & 0.218 & 0.177 & 0.095 & 5 \\\\\\\\\\n\",\n \"LLaMA-3-8B & 0.823 & 0.283 & 0.200 & 0.040 & 5 \\\\\\\\\\n\",\n \"Human & 0.817 & 0.124 & 0.174 & 0.021 & - \\\\\\\\\\n\",\n \"Mixtral-8x7B & 0.790 & 0.123 & 0.142 & 0.039 & 5 \\\\\\\\\\n\",\n \"GPT-3.5 & 0.778 & 0.169 & 0.137 & 0.037 & 5 \\\\\\\\\\n\",\n \"GLM-4-Flash & 0.749 & 0.096 & 0.165 & 0.000 & 5 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[htbp!]\\n\",\n \"\\\\caption{Performance comparison across different VR games (5-shot setting). We report NSAS scores (primary metric) and SOP scores (in parentheses).}\\n\",\n \"\\\\label{tab:per_game}\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{0.75\\\\columnwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l|cccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Model} & \\\\textbf{Half-Life: Alyx} & \\\\textbf{Radius} & \\\\textbf{Moss} & \\\\textbf{Vivecraft} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"GPT-3.5-turbo & 0.858 (0.123) & 0.662 (0.169) & 0.782 (0.169) & 0.922 (0.043) \\\\\\\\\\n\",\n \"GPT-4-turbo & 0.852 (0.125) & 0.693 (0.189) & 0.824 (0.218) & 0.927 (0.137) \\\\\\\\\\n\",\n \"GPT-4o & 0.804 (0.022) & 0.698 (0.291) & 0.824 (0.300) & 0.931 (0.190) \\\\\\\\\\n\",\n \"Gemini-1.5-Pro & 0.863 (0.209) & 0.682 (0.102) & 0.848 (0.265) & 0.938 (0.250) \\\\\\\\\\n\",\n \"Mixtral-8x7B & 0.839 (0.126) & 0.666 (0.123) & 0.756 (0.117) & 0.926 (0.060) \\\\\\\\\\n\",\n \"LLaMA-3-8B & 0.848 (0.126) & 0.644 (0.242) & 0.823 (0.283) & 0.929 (0.039) \\\\\\\\\\n\",\n \"GLM-4-flash & 0.836 (0.076) & 0.618 (0.096) & 0.749 (0.087) & 0.909 (0.000) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Human & 0.845 (0.090) & 0.684 (0.148) & 0.817 (0.112) & 0.935 (0.122) \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{Impact of few-shot examples on model performance. We report F1 scores for Sequential Order Preservation (SOP) across different number of examples. Higher is better.}\\n\",\n \"\\\\label{tab:fewshot_impact}\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{0.73\\\\columnwidth}{!}{\\n\",\n \"\\\\begin{tabular}{l|cccc|c}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Model} & \\\\textbf{Zero-shot} & \\\\textbf{1-shot} & \\\\textbf{3-shot} & \\\\textbf{5-shot} & \\\\textbf{Relative Gain (\\\\%)} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"GPT-3.5-turbo & 0.036 & 0.096 & 0.190 & 0.226 & 527.8 \\\\\\\\\\n\",\n \"GPT-4-turbo & 0.102 & 0.171 & 0.254 & 0.301 & 195.1 \\\\\\\\\\n\",\n \"GPT-4o & 0.112 & 0.224 & 0.257 & 0.287 & 156.3 \\\\\\\\\\n\",\n \"Gemini-1.5-Pro & 0.085 & 0.187 & 0.260 & \\\\textbf{0.330} & \\\\textbf{288.2} \\\\\\\\\\n\",\n \"Mixtral-8x7B & 0.031 & 0.110 & 0.204 & 0.201 & 548.4 \\\\\\\\\\n\",\n \"LLaMA-3-8B & 0.090 & 0.165 & 0.254 & 0.299 & 232.2 \\\\\\\\\\n\",\n \"GLM-4-flash & 0.033 & 0.069 & 0.121 & 0.146 & 342.4 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \" \\\\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\\\textit{Vivecraft} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-shot} & 0.9258 & 0.0248 & 0.9255 & 0.0238 & 0.9191 & 0.0306 & 0.9209 & 0.0334 & 0.9312 & 0.0207 & 0.9244 & 0.0329 \\\\\\\\\\n\",\n \" \\\\textbf{1-shot} & 0.921 & 0.0309 & 0.9349 & 0.0506 & 0.9358 & 0.0735 & 0.9362 & 0.0553 & 0.9219 & 0.0636 & 0.9101 & 0.0765 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.9284 & 0.0734 & 0.914 & 0.1167 & 0.9212 & 0.1115 & 0.9381 & 0.0781 & 0.9005 & 0.1125 & 0.9022 & 0.1051 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.9218 & 0.0385 & 0.9274 & 0.0674 & 0.9305 & 0.0689 & 0.9378 & 0.0708 & 0.9256 & 0.0477 & 0.9289 & 0.0364 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\n\",\n \" \\\\label{tab:vivecraft_nsas}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \" \\\\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores\\n\",\n \"comparison of LLMs on \\\\textit{Vivecraft} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.0029 & 0.0312 & 0.0007 & 0.0078 & 0.0012 & 0.0125 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0059 & 0.0624 \\\\\\\\\\n\",\n \" \\\\textbf{1-shot} & 0.015 & 0.0734 & 0.1203 & 0.2157 & 0.1568 & 0.2337 & 0.1794 & 0.291 & 0.0812 & 0.164 & 0.0351 & 0.1215 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.1302 & 0.2352 & 0.1143 & 0.2136 & 0.2826 & 0.3417 & 0.2335 & 0.3417 & 0.0986 & 0.2024 & 0.1124 & 0.2026 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.0395 & 0.1226 & 0.1366 & 0.2388 & 0.1837 & 0.278 & 0.2495 & 0.3358 & 0.0553 & 0.158 & 0.0374 & 0.1371 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\n\",\n \" \\\\label{tab:vivecraft_sop}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \" \\\\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\\\textit{Vivecraft} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.049 & 0.11 & 0.1301 & 0.1443 & 0.1272 & 0.1511 & 0.2221 & 0.2151 & 0.024 & 0.0999 & 0.1088 & 0.1549\\\\\\\\\\n\",\n \" \\\\textbf{1-shot}& 0.1274 & 0.1988 & 0.544 & 0.3672 & 0.6598 & 0.3322 & 0.5747 & 0.3359 & 0.4914 & 0.3617 & 0.3165 & 0.3415 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.4755 & 0.3526 & 0.6486 & 0.3373 & 0.6817 & 0.3204 & 0.6538 & 0.3373 & 0.5414 & 0.37 & 0.5299 & 0.3785 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.18 & 0.2337 & 0.5035 & 0.3772 & 0.6183 & 0.3416 & 0.608 & 0.3546 & 0.3579 & 0.3555 & 0.1606 & 0.2605 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\n\",\n \" \\\\label{tab:vivecraft_ssc}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \" \\\\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\\\textit{Half-Life: Alyx} under different shot settings}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.838 & 0.0413 & 0.8456 & 0.0366 & 0.8376 & 0.0424 & 0.8447 & 0.032 & 0.8376 & 0.0331 & 0.848 & 0.0317 \\\\\\\\\\n\",\n \" \\\\textbf{1-shot} & 0.8354 & 0.0582 & 0.8427 & 0.0489 & 0.8472 & 0.0629 & 0.8627 & 0.0482 & 0.807 & 0.1099 & 0.8131 & 0.1289 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.8452 & 0.0551 & 0.845 & 0.0467 & 0.838 & 0.0757 & 0.8701 & 0.0603 & 0.8255 & 0.0819 & 0.8449 & 0.0707 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.8577 & 0.0773 & 0.8523 & 0.0613 & 0.8039 & 0.0694 & 0.8625 & 0.0691 & 0.8394 & 0.0834 & 0.848 & 0.0976 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\n\",\n \" \\\\label{tab:alyx_nsas}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[h!]\\n\",\n \" \\\\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\\\textit{Half Life: Alyx} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.0098 & 0.0802 & 0.0252 & 0.1265 & 0.0396 & 0.1745 & 0.0082 & 0.0669 & 0.0019 & 0.0158 & 0.0123 & 0.0704 \\\\\\\\\\n\",\n \" \\\\textbf{1-shot} & 0.0447 & 0.0764 & 0.0402 & 0.1224 & 0.024 & 0.0733 & 0.0198 & 0.1263 & 0.0425 & 0.0816 & 0.0447 & 0.0967 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.0725 & 0.1159 & 0.0312 & 0.0725 & 0.0701 & 0.1261 & 0.1349 & 0.2187 & 0.0703 & 0.1094 & 0.087 & 0.1687 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.123 & 0.1834 & 0.1248 & 0.2382 & 0.0216 & 0.0809 & 0.2089 & 0.2938 & 0.1257 & 0.2409 & 0.1259 & 0.2385 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\n\",\n \" \\\\label{tab:alyx_sop}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table} [htbp!]\\n\",\n \" \\\\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\\\textit{Half Life: Alyx} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.0785 & 0.1843 & 0.2231 & 0.2089 & 0.2424 & 0.2111 & 0.1989 & 0.1982 & 0.0716 & 0.1187 & 0.1662 & 0.172\\\\\\\\\\n\",\n \" \\\\textbf{1-shot}& 0.2562 & 0.235 & 0.3485 & 0.2336 & 0.4184 & 0.2413 & 0.3859 & 0.2654 & 0.3256 & 0.1934 & 0.3872 & 0.2058\\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.3072 & 0.2444 & 0.3648 & 0.2414 & 0.5611 & 0.229 & 0.5494 & 0.2887 & 0.3544 & 0.2202 & 0.4599 & 0.2371 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.425 & 0.2814 & 0.6127 & 0.2856 & 0.6934 & 0.2359 & 0.6299 & 0.315 & 0.4642 & 0.2957 & 0.5152 & 0.2708 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:alyx_ssc}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table} [htbp!]\\n\",\n \" \\\\caption{Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\\\textit{ Moss: Book II} under different shot settings}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.7819 & 0.0403 & 0.8055 & 0.0717 & 0.7871 & 0.0596 & 0.7994 & 0.0548 & 0.7913 & 0.0595 & 0.7916 & 0.0572 \\\\\\\\\\n\",\n \" \\\\textbf{1-shot}& 0.776 & 0.0616 & 0.7993 & 0.0771 & 0.803 & 0.0924 & 0.8139 & 0.0778 & 0.7663 & 0.0793 & 0.7938 & 0.0763 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.7776 & 0.0889 & 0.818 & 0.0925 & 0.8016 & 0.1242 & 0.8302 & 0.0935 & 0.7613 & 0.1341 & 0.7895 & 0.1371\\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.782 & 0.0952 & 0.8243 & 0.102 & 0.8237 & 0.1092 & 0.8478 & 0.1017 & 0.756 & 0.1469 & 0.8232 & 0.105\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:moss_nsas}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table} [htbp!]\\n\",\n \" \\\\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\\\textit{Moss: Book II} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.0091 & 0.0581 & 0.0263 & 0.1533 & 0.0113 & 0.0494 & 0.0197 & 0.1029 & 0.0052 & 0.033 & 0.0 & 0.0\\\\\\\\\\n\",\n \" \\\\textbf{1-shot}& 0.034 & 0.1568 & 0.0663 & 0.2044 & 0.1084 & 0.2486 & 0.1145 & 0.2495 & 0.0739 & 0.1721 & 0.0578 & 0.1486 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.1581 & 0.242 & 0.1678 & 0.2522 & 0.2324 & 0.3185 & 0.2272 & 0.3324 & 0.1351 & 0.252 & 0.2584 & 0.3089 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.1686 & 0.244 & 0.2182 & 0.2801 & 0.2998 & 0.3062 & 0.2652 & 0.3596 & 0.1169 & 0.247 & 0.2831 & 0.3097 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:moss_sop}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table} [htbp!]\\n\",\n \" \\\\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\\\textit{Moss: Book II} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.0715 & 0.1792 & 0.2491 & 0.2844 & 0.2313 & 0.2567 & 0.1763 & 0.221 & 0.0407 & 0.0991 & 0.1208 & 0.1779\\\\\\\\\\n\",\n \" \\\\textbf{1-shot}& 0.0748 & 0.1719 & 0.259 & 0.2771 & 0.3682 & 0.3018 & 0.3449 & 0.3396 & 0.1749 & 0.2393 & 0.2319 & 0.293 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.3349 & 0.3069 & 0.4593 & 0.3309 & 0.5001 & 0.3444 & 0.5238 & 0.3738 & 0.3207 & 0.3105 & 0.4689 & 0.3399 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.3737 & 0.3213 & 0.4951 & 0.3373 & 0.5562 & 0.3319 & 0.6091 & 0.3476 & 0.2974 & 0.3385 & 0.4567 & 0.3173 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:moss_ssc}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table} [htbp!]\\n\",\n \" \\\\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on VR game \\\\textit{Into the Radius} under different shot settings}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.6165 & 0.0755 & 0.6408 & 0.0955 & 0.5939 & 0.1306 & 0.6492 & 0.1018 & 0.6644 & 0.0718 & 0.6447 & 0.0882 \\\\\\\\\\n\",\n \" \\\\textbf{1-shot} & 0.641 & 0.1177 & 0.6519 & 0.1421 & 0.6282 & 0.1687 & 0.6875 & 0.1159 & 0.6285 & 0.1684 & 0.6285 & 0.1346 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.6305 & 0.128 & 0.6802 & 0.1645 & 0.6491 & 0.2057 & 0.6634 & 0.1638 & 0.618 & 0.1633 & 0.6479 & 0.1606 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.6621 & 0.1291 & 0.6927 & 0.1721 & 0.6984 & 0.2136 & 0.6818 & 0.1191 & 0.666 & 0.1495 & 0.6443 & 0.211\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\n\",\n \" \\\\label{tab:radius_nsas}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table} [htbp!]\\n\",\n \" \\\\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\\\textit{Into the Radius} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.0091 & 0.0581 & 0.0263 & 0.1533 & 0.0113 & 0.0494 & 0.0197 & 0.1029 & 0.0052 & 0.033 & 0.0 & 0.0\\\\\\\\\\n\",\n \" \\\\textbf{1-shot}& 0.034 & 0.1568 & 0.0663 & 0.2044 & 0.1084 & 0.2486 & 0.1145 & 0.2495 & 0.0739 & 0.1721 & 0.0578 & 0.1486 \\\\\\\\\\n\",\n \" \\\\textbf{3-shot} & 0.1581 & 0.242 & 0.1678 & 0.2522 & 0.2324 & 0.3185 & 0.2272 & 0.3324 & 0.1351 & 0.252 & 0.2584 & 0.3089 \\\\\\\\\\n\",\n \" \\\\textbf{5-shot} & 0.1686 & 0.244 & 0.2182 & 0.2801 & 0.2998 & 0.3062 & 0.2652 & 0.3596 & 0.1169 & 0.247 & 0.2831 & 0.3097 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\n\",\n \" \\\\label{tab:radius_sop}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table} [htbp!]\\n\",\n \" \\\\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\\\textit{Into the Radius} under different shot settings.}\\n\",\n \" \\\\centering\\n\",\n \" \\\\resizebox{\\\\textwidth}{!}{%\\n\",\n \" \\\\renewcommand{\\\\arraystretch}{1.5}\\n\",\n \" \\\\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Model} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-3.5-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4-turbo}} & \\\\multicolumn{2}{c|}{\\\\textbf{GPT-4o}} & \\\\multicolumn{2}{c|}{\\\\textbf{Gemini-1.5-Pro}} & \\\\multicolumn{2}{c|} {\\\\textbf{Mixtral-8x7B}} &\\n\",\n \" \\\\multicolumn{2}{c}{\\\\textbf{LLaMA-3-8b}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Metrics} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} & \\\\textbf{avg} & \\\\textbf{std} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\textbf{Zero-Shot} & 0.0354 & 0.0982 & 0.1528 & 0.1774 & 0.2199 & 0.1745 & 0.1783 & 0.2107 & 0.0406 & 0.0899 & 0.1243 & 0.1655\\\\\\\\\\n\",\n \" \\\\textbf{1-shot}& 0.1511 & 0.2246 & 0.304 & 0.2983 & 0.4102 & 0.2585 & 0.2823 & 0.3277 & 0.2593 & 0.3249 & 0.3171 & 0.269\\\\\\\\\\n\",\n \" \\\\textbf{3-shot}& 0.2321 & 0.2713 & 0.4463 & 0.3099 & 0.5623 & 0.2976 & 0.3402 & 0.3379 & 0.3544 & 0.2621 & 0.5319 & 0.2382\\\\\\\\\\n\",\n \" \\\\textbf{5-shot}& 0.3302 & 0.3115 & 0.5082 & 0.3063 & 0.6194 & 0.2877 & 0.2971 & 0.3187 & 0.285 & 0.3384 & 0.5314 & 0.2886\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\label{tab:radius_ssc}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure} [htbp!]\\n\",\n \" \\\\centering\\n\",\n \"\\\\includegraphics[width=1.2\\\\linewidth, height=0.9\\\\textheight, keepaspectratio]{Figures/nsas_barh_4x1.png}\\n\",\n \" \\\\caption{LLMs NSAS (avg) by Different Shot Setting Across Four VR Games}\\n\",\n \" \\\\vspace{0.8em}\\n\",\n \" \\\\label{fig:nsas_barh}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure} [htbp!]\\n\",\n \"\\\\centering\\n\",\n \" \\\\includegraphics[width=1.2\\\\linewidth, height=0.9\\\\textheight, keepaspectratio]{Figures/sop_barh_4x1.png}\\n\",\n \" \\\\caption{LLMs SOP (avg) by Different Shot Setting Across Four VR Games}\\n\",\n \"\\\\vspace{0.8em}\\n\",\n \"\\\\label{fig:sop_barh}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure} [htbp!]\\n\",\n \"\\\\centering\\n\",\n \" \\\\includegraphics[width=1.2\\\\linewidth, height=1.0\\\\textheight, keepaspectratio]{Figures/ssc_barh_4x1.png}\\n\",\n \" \\\\caption{LLMs SSC (avg) by Different Shot Setting Across Four VR Games}\\n\",\n \"\\\\vspace{0.8em}\\n\",\n \"\\\\label{fig:ssc_barh}\\n\",\n \"\\\\end{figure}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n\\documentclass{article} %\n\\usepackage{iclr2026_conference,times}\n\n%\n%\n\n\\usepackage{amsmath,amsfonts,bm}\n\n%\n\\newcommand{\\figleft}{{\\em (Left)}}\n\\newcommand{\\figcenter}{{\\em (Center)}}\n\\newcommand{\\figright}{{\\em 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#1]}}\n\n\\newcommand{\\mytodoteal}[1]{\\mytodocomment{teal}{{\\sf}~#1}}\n\\newcommand{\\mytodoviolet}[1]{\\mytodocomment{violet}{{\\sf}~#1}}\n\\newcommand{\\mytodoblue}[1]{\\mytodocomment{blue}{{\\sf}~#1}}\n\\newcommand{\\mytodored}[1]{\\mytodocommentred{red}{{\\sf}~#1}}\n\\newcommand{\\mytodomagenta}[1]{\\mytodocomment{magenta}{{\\sf}~#1}}\n\\newcommand{\\mytodoorange}[1]{\\mytodocomment{orange}{{\\sf}~#1}}\n\\newcommand{\\mytodopurple}[1]{\\mytodocomment{purple}{{\\sf}~#1}}\n\\newcommand{\\mytodocyan}[1]{\\mytodocomment{cyan}{{\\sf}~#1}}\n\n\\lstset{\n escapeinside={(*@}{@*)}\n}\n\\lstdefinelanguage{dsl}{\n morekeywords={program, statement_list, statement, time_constrained_statement, control_flow_statement, manipulation_statement, variable_declaration_statement, device, property, value, pose_property, orientation_property, button_property, axis_property, position_coordinate, orientation_coordinate, referenced_value, script_operator, arithmetic_operator, assignment_operator, if_statement, while_statement},\n morestring=[b]\",\n sensitive=false,\n morecomment=[l]{//},\n moredelim=*[s][\\color{blue}]{<}{>},\n moredelim=*[s][\\color{purple}]{:=}{:=},\n moredelim=*[s][\\color{orange}]{::}{::},\n keywordstyle=\\color{teal},\n stringstyle=\\color{red},\n commentstyle=\\color{gray},\n}\n\n\n\\title{\\llama~\\methodname: Can LLMs Manipulate Physical Devices to Play Virtual Reality Games?}\n\n%\n%\n%\n\n\\author{Shuqing Li$^1$ \\qquad Jiayi Yan$^1$$^*$ \\qquad \\quad Chenyu Niu$^1$\\thanks{Equal contributions.} \\qquad Jen-tse Huang$^1$ \\\\\n\\bf Yun Peng$^1$ \\qquad \\ \\ Wenxuan Wang$^1$\\thanks{Corresponding author.} \\quad Yepang Liu$^2$ \\qquad Michael R. Lyu$^1$ \\\\\n$^1$Chinese University of Hong Kong \\quad $^2$Southern University of Science and Technology\n}\n\n%\n%\n%\n%\n%\n%\n%\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\n\\iclrfinalcopy %\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\n%\n%\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n\nVirtual Reality (VR) games require players to translate high-level semantic actions into precise device manipulations using controllers and head-mounted displays (HMDs). While humans intuitively perform this translation based on common sense and embodied understanding, whether Large Language Models (LLMs) can effectively replicate this ability remains underexplored. This paper introduces a benchmark, \\methodname, evaluating LLMs' capability to translate semantic actions into VR device manipulation sequences across 262 scenarios from four popular VR games: Half-Life: Alyx, Into the Radius, Moss: Book II, and Vivecraft. We evaluate seven LLMs, including GPT-3.5, GPT-4, GPT-4o, Gemini-1.5-Pro, LLaMA-3-8B, Mixtral-8x7B, and GLM-4-Flash, compared against annotated ground truth and human performance. Our results reveal that while top-performing models like Gemini-1.5-Pro demonstrate strong task decomposition capabilities, they still struggle with procedural reasoning and spatial understanding compared to humans. Performance varies significantly across games, suggesting sensitivity to interaction complexity. Few-shot examples substantially improve performance, indicating potential for targeted enhancement of LLMs' VR manipulation capabilities.\nWe release all materials at \\url{https://sites.google.com/view/combobench}.\\end{abstract}\n\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n\n%\n%\n%\n\n%\n\n%\n\n%\n\n\\section{Introduction}\n\n%\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n%\n%\n%\n\nLarge Language Models (LLMs) have demonstrated remarkable proficiency in general-purpose task solving~\\cite{qin2023chatgpt}, conquering complex domains such as code~\\cite{lee2024unified, lam2025codecrash} or math~\\cite{lu2024mathvista} problems.\nWhile they exhibit increasingly more human-like characteristics~\\cite{huang2024humanity, liang2023encouraging}, an essential attribute of human intelligence is still underexplored: the ability to rapidly learn and apply unfamiliar concepts by leveraging common sense, prior experiences, and a repertoire of cognitive skills.\n\nThis is particularly evident in novel interactive environments like video games, where players quickly master device manipulations (atomic actions) and combine them to achieve complex semantic goals.\nVirtual Reality (VR) games elevate this challenge.\nThey demand not only the execution of atomic actions via physical devices (\\eg, Head-Mounted Displays (HMDs) and controllers) but also the inference of complex, often uninstructed, semantic actions.\nFor instance, in \\textit{Half-Life: Alyx}~\\cite{halflifealyx}, when asked to ``surrender,'' players might instinctively raise their controller-held hands even if not explicitly taught.\n\nSuch translation of high-level intent into a sequence of physical device manipulations engages a suite of cognitive abilities:\n(1) \\textit{Task decomposition}: Breaking down a high-level semantic action (\\eg, ``tame the horse'' and ``plant wheat'') into a coherent series of intermediate steps.\n(2) \\textit{Procedural reasoning}: Understanding the logical and temporal order of these steps, including prerequisite conditions or concurrent actions (\\eg, the need to till soil before planting seeds).\n(3) \\textit{Spatial reasoning \\& contextual awareness}: Interpreting instructions within a 3D spatial context (\\eg, ``move HMD towards the Creeper'' and ``crouch through the gap'') and understanding environmental cues or object states (\\eg, recognizing a door is open/closed and acting accordingly).\n(4) \\textit{Object interaction \\& tool use understanding}: Correctly mapping intended sub-actions to specific VR device manipulations (\\eg, knowing which button to press to ``use'' an item, and how to manipulate a controller to simulate ``swinging'' a tool like a pickaxe).\nThis involves understanding the affordances of virtual objects and tools.\n(5) \\textit{Motor action mapping \\& VR procedural transfer}: Translating abstract actions (\\eg, ``press,'' ``move,'' and ``trigger'') into specific, executable VR controller commands, potentially by adapting from provided examples or general knowledge of VR interaction paradigms.\nThis touches upon a form of simulated embodied reasoning.\n(6) \\textit{Judgment of termination/continuation conditions}: Recognizing when a sub-task or a looped action is complete (\\eg, ``mine until the block breaks'' and ``water until the plant grows'').\nTherefore, playing VR games serves as a rich testbed for evaluating if LLMs can bridge this gap between abstract understanding and grounded, physical interaction.\n\nTo systematically evaluate LLMs' ability to perform this crucial translation, we introduce \\methodname, which stands for Cognitive-Oriented Manipulation Benchmark for game combos using physical VR devices.\nIt comprises \\numberofscenarios scenarios derived from \\numberofgames popular VR games: \\textit{Vivecraft}~\\cite{vivecraft} (Minecraft in VR), \\textit{Half-Life: Alyx}~\\cite{halflifealyx}, \\textit{Moss: Book II}~\\cite{mossbookii}, and \\textit{Into the Radius}~\\cite{intotheradius}.\nEach scenario presents a high-level semantic action, and the ground truth consists of a fine-grained sequence of VR device manipulations required to achieve it.\nThese sequences are annotated by experienced VR players, allowing us to analyze LLM-generated outputs at the step-level and map their successes and failures to the aforementioned cognitive abilities.\nFor example, failing to ``press the X button'' after ``moving the HMD towards the Creeper'' might indicate a lapse in procedural reasoning or object interaction understanding for that specific step.\n\nWe evaluate seven LLMs, including GPT-3.5~\\cite{gpt35}, GPT-4~\\cite{gpt4}, GPT-4o~\\cite{gpt4o}, Gemini-1.5-Pro~\\cite{gemini15}, LLaMA-3-8B~\\cite{llama3}, Mixtral-8x7B~\\cite{mistral}, and GLM-4-Flash~\\cite{glm4}.\nWe design a multi-dimensional scoring approach that assesses: (1) high-level semantic action understanding, (2) procedural step correctness, and (3) device-specific manipulation accuracy, allowing for fine-grained analysis of where each model succeeds or struggles in the translation process.\nOur findings reveal significant variation in model performance across cognitive capabilities.\nAll models demonstrate strong task decomposition abilities but show pronounced weaknesses in motor action mapping and procedural reasoning. \nGemini-1.5-Pro exhibits the most balanced performance across capabilities, while even advanced models like GPT-4 struggle with spatial reasoning compared to human performance.\nFew-shot examples substantially improve outcomes, particularly for procedural understanding, with diminishing returns beyond three examples.\nPerformance also varies considerably across games, with models generally performing better in environments with more consistent interaction patterns (Vivecraft) than those requiring nuanced controller manipulations (Half-Life: Alyx).\nThese results highlight specific cognitive gaps in current LLMs' ability to perform simulated embodied reasoning for VR interactions and identify targeted areas for improvement toward more capable virtual agents.\nOur contributions are:\n\\begin{itemize}[leftmargin=*,nosep]\n\\item We introduce \\methodname, the first benchmark designed to evaluate LLMs' fine-grained cognitive abilities in translating high-level semantic actions into VR device manipulations, comprising \\numberofscenarios human-annotated scenarios from \\numberofgames diverse VR games.\n\\item We define a set of key cognitive abilities crucial for VR interaction and design \\methodname to enable step-level analysis of LLM performance against these dimensions.\n\\item We conduct a comprehensive evaluation of \\numberofllms state-of-the-art LLMs, providing a nuanced analysis of their strengths and weaknesses across these cognitive abilities and offering insights into the current frontiers of LLM-driven VR interaction.\n\\end{itemize}%\n%\n\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n%\n%\n%\n\n\n\n%\n%\n\n%\n%\n\n%\n\n%\n\n%\n%\n \n%\n \n%\n%\n\n%\n\n%\n%\n\n%\n\n%\n%\n%\n\n%\n\n\n\n\n%\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n%\n%\n\n%\n\n%\n\n\n\n\\section{\\methodname: Design and Curation}\n\\label{sec:dataset_design}\n\nThe \\methodname dataset is meticulously curated to evaluate the capability of LLMs in translating high-level semantic actions into sequences of physical VR device manipulations. This section details the game selection process, scenario definition, and the annotation methodology.\n\n\\subsection{Cognitive Capability Taxonomy Development}\n\\label{subsec:capability_taxonomy}\n\nTo establish a theoretically grounded framework for evaluating LLMs in VR contexts, we conducted structured interviews with three domain experts specializing in cognitive science and educational psychology. The experts were selected based on their research backgrounds in spatial cognition, procedural learning, and embodied interaction, which areas that are highly relevant to VR interaction.\n\n\\paragraph{Expert Interview.} Each expert participated in a 90-minute semi-structured interview focused on identifying and categorizing the cognitive abilities required for translating semantic goals into physical actions in virtual environments. The interviews followed a three-phase structure: (1) open-ended discussion about cognitive processes in VR interaction, (2) systematic review of preliminary capability categories identified from literature, and (3) expert suggestions for refinement and expansion of these categories.\n\n\\paragraph{Taxonomy Refinement.} Following the interviews, we synthesized the experts' insights through thematic analysis. Areas of consensus were directly incorporated into our taxonomy, while divergent perspectives were reconciled through follow-up consultations. This iterative process resulted in the identification of six core capability dimensions that comprehensively capture the cognitive demands of VR interaction:\n%\n(1) Task decomposition: The ability to break down high-level goals into sequentially ordered sub-tasks.\n(2) Procedural reasoning: Understanding causal relationships between actions and their temporal dependencies.\n(3) Spatial reasoning \\& contextual Awareness: Processing spatial relationships and interpreting environmental cues for action selection.\n(4) Object interaction \\& tool use understanding: Comprehending affordances and functional properties of virtual objects.\n(5) Motor action mapping \\& VR procedural transfer: Translating conceptual actions into specific physical device manipulations.\n(6) Judgment of termination/continuation conditions: Recognizing completion states or conditions requiring repeated action.\n%\n\n%\n\n\\subsection{Game Selection Criteria and Process}\n\\label{subsec:game_selection}\n\nTo ensure a diverse and relevant set of VR interaction paradigms, we selected games based on a systematic process.\nFirst, we queried the Steam store~\\cite{website:steam-app-store-vr} filtering for titles tagged as ``VR Only'' and available in ``English,'' sorting the results by user review scores in descending order.\nWe then iteratively examined games from this ranked list, focusing on their primary genre as categorized by Steam. To ensure genre diversity, we prioritized games from genres not yet represented in our collection.\nA crucial selection criterion was the availability of comprehensive textual walkthroughs. For each candidate game, we searched for detailed guides using keywords such as ``walkthrough,'' ``guide,'' or ``tutorial.'' A walkthrough was deemed sufficiently detailed if it provided unambiguous, step-by-step instructions enabling the completion of core game objectives or specific complex tasks.\nFollowing this methodology, we selected four popular and critically acclaimed VR games representing distinct genres and interaction styles for \\methodname:\n%\n(1) \\textit{Vivecraft}~\\cite{vivecraft} (Open-world sandbox, crafting)\n(2) \\textit{Half-Life: Alyx}~\\cite{halflifealyx} (First-person shooter, puzzle-solving, physics-based interaction)\n(3) \\textit{Moss: Book II}~\\cite{mossbookii} (Third-person action-adventure, puzzle-platformer)\n(4) \\textit{Into the Radius}~\\cite{intotheradius} (First-person survival shooter, exploration)\n%\nSuch selection provides a rich variety of control schemes and task complexities for evaluating LLMs.\n\n\\subsection{Scenario Definition: Semantic Action Identification}\n\\label{subsec:action_selection}\n\nFor all selected games, \\numberofhiredplayers data annotators, comprising undergraduate and postgraduate computer science students with at least two years of programming experience and sufficient knowledge about VR games, manually identified salient semantic actions from the collected textual walkthroughs.\nSemantic actions were defined as high-level, goal-oriented tasks described in the walkthroughs (e.g., ``tame the horse,'' ``kill the creeper,'' ``solve the gravity glove puzzle'') that necessitate a sequence of fine-grained VR device manipulations to accomplish.\nWe focused on scenarios that: (1) involve complex interactions not always explicitly detailed in in-game tutorials, (2) often constitute essential steps or objectives required for game progression.\n%\n%\n%\n%\nThis process resulted in the identification of \\numberofscenarios distinct scenarios across the four games.\n\n\\subsection{Annotation of VR Device Manipulations}\n\\label{subsec:manipulation_annotation} \n\nExperienced VR users from our annotation team then played through each identified semantic action in the respective games using Oculus Quest 2 VR hardware. The objective was to record the precise sequence of device manipulations required to complete each semantic action.\nThe annotation process captured the following details for each step within a manipulation sequence:\n\\begin{itemize}[leftmargin=*,nosep]\n \\item \\textbf{Device used:} Specification of whether the HMD or a controller was used.\n \\item \\textbf{Controller specificity:} If a controller was used, and the action was hand-specific (e.g., primary hand for a tool), the annotation indicated whether the left or right controller was required. If either controller could perform the action, this was noted as ``left or right controller.''\n \\item \\textbf{Operation type and parameters:}\n \\begin{itemize}[leftmargin=*,nosep]\n \\item \\textit{Movement:} For actions involving device movement (HMD or controller), the direction (e.g., ``towards the Creeper,'' ``upwards'') or target position was recorded.\n \\item \\textit{Button presses:} The specific button involved and the action (e.g., ``press X button,'' ``release trigger'') were noted.\n \\item \\textit{Joystick/thumbstick manipulation:} The direction of joystick push (e.g., ``push left thumbstick forward'') was recorded.\n \\end{itemize}\n \\item \\textbf{Sequential composition:} For complex semantic actions composed of multiple, distinct sub-actions that might have been annotated individually, the sequence and composition of these simpler actions were explicitly recorded.\n\\end{itemize}\n%\n\n\\subsection{Cognitive Capability Labeling Using LLMs}\n\\label{subsec:capability_labeling}\n\nA critical aspect of \\methodname is the annotation of each manipulation step with the specific cognitive capabilities it engages. This fine-grained labeling enables precise analysis of where LLMs succeed or fail in the VR interaction translation process.\n\n\\paragraph{Initial Human Annotation.} To begin, our annotators manually labeled a subset of 50 manipulation sequences (approximately 20\\% of the dataset), assigning relevant capability categories to each step based on the taxonomy described in Section~\\ref{subsec:capability_taxonomy}. For example, in the sequence required to \"tame a horse\" in Vivecraft, the step \"equip the saddle by pressing the Y button while looking at the inventory slot containing the saddle\" was labeled with \"Object Interaction \\& Tool Use Understanding\" and \"Motor Action Mapping.\"\n\n\\paragraph{LLM-Assisted Annotation Pipeline.} We then developed an LLM-assisted annotation pipeline to scale this process to the entire dataset. Specifically:\n\\ding{172} We used the human-annotated examples as few-shot demonstrations for GPT-4o.\n\\ding{173} For each unlabeled manipulation step, we provided the LLM with:\n[2.a] The semantic action context (e.g., \"taming a horse in Vivecraft\").\n[2.b] The specific manipulation step to label.\n[2.c] The preceding and following steps (when available).\n[2.d] Detailed descriptions of each capability category.\n[2.e] Three few-shot examples with explanations of why each capability was assigned.\n\\ding{174} The LLM generated capability labels along with justifications for each assignment.\n\\ding{175} Human annotators reviewed the LLM-generated labels, making corrections when necessary. The review process revealed an 89.7\\% agreement rate between LLM-assigned labels and human judgments.\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n\\paragraph{Multi-label Distribution.} Most manipulation steps engaged multiple cognitive capabilities simultaneously. On average, each step was associated with 2.3 capability categories ($\\sigma$ = 0.8). The most frequently co-occurring capabilities were \"Motor Action Mapping\" and \"Object Interaction \\& Tool Use Understanding\" (present together in 68\\% of steps), reflecting the inherent coupling between understanding virtual object affordances and translating this understanding into physical manipulations.\n\n%\n\n\\subsection{Contextualization and Verification}\n\\label{subsec:context_verification}\n\nTo further contextualize the annotated actions and aid in verification, we sourced or recorded gameplay videos corresponding to the textual walkthroughs for each game.\nFor each annotated semantic action and its constituent manipulation steps, we recorded the corresponding timestamps in these videos. This allows for visual verification of the annotated sequences and provides richer context for understanding the actions. If suitable public gameplay videos matching the exact walkthrough steps were unavailable, our annotators recorded their own gameplay sessions while performing the actions.\n\\section{Experiments}\n\n\\subsection{Model Selection}\n\n%\nWe evaluate \\numberofllms state-of-the-art LLMs: GPT-4o, GPT-4-turbo, GPT-3.5-turbo, Gemini-1.5-Pro, LLaMA-3-8B, and Mixtral-8x7B. We also perform human evaluation to validate the average human capabilities for comparison, when humans are given exactly the same input as LLMs.\nFor all experiments, we used the official APIs for proprietary models and Hugging Face implementations for open-source models. Temperature was set to 0 across all models to minimize non-deterministic outputs. For embedding calculations, we utilized OpenAI's text-embedding-3-large model via their API. \n%\n\n\\subsection{Evaluation Metrics}\n\nTo comprehensively evaluate the capability of LLMs in translating semantic actions into VR device manipulations, we propose a multi-dimensional evaluation framework with four distinct metrics. These metrics collectively capture different aspects of model performance in \\methodname, ranging from strict matching to more flexible semantic alignment.\n\n\\paragraph{Strict Step-by-Step Matching (SSM).}\n\nOur first metric evaluates the exact matching between model-generated and ground truth steps, enforcing both sequence length equivalence and semantic alignment:\n%\n$\\text{SSM} = \\frac{\\text{Number of correctly predicted sequences}}{\\text{Total number of sequences}}$.\n%\nA sequence is considered correctly predicted only when:\n%\nthe number of steps in the generated sequence equals that of the ground truth,\n and every step in the generated sequence has a cosine similarity above a threshold of 0.8387 with its corresponding step in the ground truth\n%\nThis strict metric serves as a measure of precision in reproducing exact device manipulation sequences and rewards models that can generate complete, step-accurate instructions.\n\n\\paragraph{Common Subsequence Evaluation.}\n\nWe further introduce two complementary metrics based on common subsequence alignment to assess partial correctness:\n(1) \\textbf{Normalized Step Alignment Score (NSAS)}\nThis metric quantifies the alignment between the model-generated sequence and ground truth while accounting for missing and additional steps:\n%\n$\\text{NSAS} = \\frac{(|C| - |M| - |A|) - \\text{min}_{\\text{all\\_samples}}}{|G| \\cdot (\\text{max}_{\\text{all\\_samples}} - \\text{min}_{\\text{all\\_samples}})}$,\n%\nwhere:\n%\n$|C|$ represents the count of correctly matched steps in the common subsequence,\n$|M|$ represents missing steps from the ground truth,\n$|A|$ represents additional steps generated by the model,\n$|G|$ represents the total number of steps in the ground truth,\n$\\text{min}_{\\text{all\\_samples}}$ and $\\text{max}_{\\text{all\\_samples}}$ represent the minimum and maximum raw scores across all evaluations, enabling consistent normalization\n%\nThis score is normalized across the entire dataset to ensure fair comparison across different models and scenarios.\n(2) \\textbf{Sequential Order Preservation (SOP)}\nThe SOP metric specifically assesses the model's ability to maintain the correct procedural ordering of steps:\n%\n$\\text{SOP} = \\frac{|\\text{Steps correctly ordered and matched}|}{|G|}$.\n%\nThis metric evaluates whether the steps in the matched subsequence maintain their ordinal positions (e.g., step 1 followed by step 2, etc.) in both the ground truth and model output, capturing the model's procedural reasoning capabilities.\n\n\\paragraph{Semantic Step Coverage (SSC).}\n\nOur final metric adopts a more flexible matching approach to evaluate semantic coverage of critical actions:\n%\n$\\text{SSC} = \\frac{|\\text{MR steps matched to any GT step}|}{|\\text{MR}|}$,\n%\nwhere a model result (MR) step is considered matched if it has a cosine similarity above the threshold (0.8387) with any step in the ground truth (GT). This metric computes the proportion of generated steps that semantically align with at least one ground truth step, regardless of position.\n\n%\n\n%\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n%\n\n\n\n\n\n\n\n\n\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n\\begin{table*}[t!]\n\\centering\n\\caption{Overall performance comparison of LLMs across VR games (5-shot setting). Best model performance per metric is \\textbf{bolded}, second best is \\underline{underlined}.}\n\\label{tab:overall_performance_1}\n\\resizebox{\\textwidth}{!}{\n\\setlength{\\tabcolsep}{2pt}\n\\begin{tabular}{l cccc cccc cccc cccc}\n\\toprule\n\\multirow{2}{*}{\\textbf{Model}} & \\multicolumn{4}{c}{\\textbf{Half-Life: Alyx}} & \\multicolumn{4}{c}{\\textbf{Into the Radius}} & \\multicolumn{4}{c}{\\textbf{Moss: Book II}} & \\multicolumn{4}{c}{\\textbf{Vivecraft}} \\\\\n\\cmidrule(lr){2-5} \\cmidrule(lr){6-9} \\cmidrule(lr){10-13} \\cmidrule(lr){14-17}\n& \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{F1$_{\\text{SOP}}$}\\ensuremath{\\uparrow} & \\textbf{SSC}\\ensuremath{\\uparrow} \\\\\n\\midrule\nGPT-3.5 & \\textbf{0.858} & 0.123 & \\textbf{0.287} & 0.143 & 0.662 & 0.169 & 0.226 & 0.137 & 0.782 & 0.169 & 0.207 & 0.186 & 0.922 & 0.043 & 0.098 & 0.067 \\\\\nGPT-4 & \\underline{0.853} & \\underline{0.125} & 0.258 & \\textbf{0.172} & \\underline{0.693} & 0.189 & \\underline{0.328} & 0.177 & \\textbf{0.824} & 0.218 & 0.336 & \\underline{0.220} & 0.927 & \\underline{0.137} & 0.437 & 0.081 \\\\\nGPT-4o & 0.804 & 0.022 & 0.075 & \\underline{0.167} & \\textbf{0.698} & \\textbf{0.291} & \\textbf{0.414} & \\textbf{0.190} & \\textbf{0.824} & \\textbf{0.300} & \\underline{0.342} & \\textbf{0.222} & \\underline{0.931} & \\textbf{0.190} & \\textbf{0.489} & \\textbf{0.096} \\\\\nMixtral & 0.839 & \\textbf{0.126} & 0.246 & 0.147 & 0.666 & 0.123 & 0.228 & 0.097 & 0.756 & 0.117 & 0.191 & 0.121 & 0.926 & 0.060 & 0.239 & 0.070 \\\\\nLLaMA-3 & 0.848 & \\textbf{0.126} & \\underline{0.279} & 0.162 & 0.644 & \\underline{0.242} & 0.317 & 0.168 & \\underline{0.823} & \\underline{0.283} & \\textbf{0.349} & 0.200 & 0.929 & 0.039 & 0.122 & 0.042 \\\\\nGLM-4 & 0.836 & 0.076 & 0.183 & 0.149 & 0.618 & 0.096 & 0.186 & 0.149 & 0.749 & 0.087 & 0.174 & 0.165 & 0.909 & 0.000 & 0.045 & 0.061 \\\\\n\\midrule\nHuman & 0.845 & 0.090 & 0.240 & 0.110 & 0.684 & 0.148 & 0.257 & \\underline{0.181} & 0.817 & 0.112 & 0.328 & 0.174 & \\textbf{0.935} & 0.122 & \\underline{0.482} & \\underline{0.084} \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\end{table*}\n\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n\\begin{table*}[t!]\n\\caption{Overall performance across VR games and settings. We report the average scores for our four evaluation metrics: Strict Step-by-Step Matching (SSM), Normalized Step Alignment Score (NSAS), Sequential Order Preservation (SOP), and Semantic Step Coverage (SSC). Higher is better for all metrics. Bold indicates best model performance, underline indicates second best.}\n\\label{tab:overall_performance_2}\n\\resizebox{\\textwidth}{!}{\n\\setlength{\\tabcolsep}{2pt}\n\\begin{tabular}{l cccc cccc cccc}\n\\toprule\n\\multirow{2}{*}{\\textbf{Model}} & \\multicolumn{4}{c}{\\textbf{Average Across Settings}} & \\multicolumn{4}{c}{\\textbf{Zero-Shot}} & \\multicolumn{4}{c}{\\textbf{5-Shot}} \\\\\n & \\textbf{SSM (\\%)} & \\textbf{NSAS} & \\textbf{SOP} & \\textbf{SSC} & \\textbf{SSM (\\%)} & \\textbf{NSAS} & \\textbf{SOP} & \\textbf{SSC} & \\textbf{SSM (\\%)} & \\textbf{NSAS} & \\textbf{SOP} & \\textbf{SSC} \\\\\n\\midrule\nGPT-3.5 & 1.4 & 0.781 & 0.063 & 0.066 & 0.8 & 0.771 & 0.003 & 0.046 & 2.1 & 0.791 & 0.128 & 0.095 \\\\\nGPT-4 & 3.7 & 0.806 & 0.107 & 0.124 & 1.0 & 0.788 & 0.015 & 0.107 & 8.8 & 0.825 & 0.184 & 0.140 \\\\\nGPT-4o & \\underline{5.3} & 0.797 & 0.138 & \\underline{0.141} & 0.6 & 0.785 & 0.015 & 0.108 & \\underline{10.9} & 0.806 & 0.228 & \\underline{0.161} \\\\\nGemini-1.5 & \\textbf{5.8} & \\textbf{0.813} & \\textbf{0.146} & \\textbf{0.142} & \\textbf{2.1} & \\textbf{0.795} & 0.010 & \\textbf{0.124} & \\textbf{11.7} & \\textbf{0.832} & \\textbf{0.236} & \\textbf{0.162} \\\\\nMixtral & 1.1 & 0.784 & 0.068 & 0.079 & 0.0 & 0.777 & 0.002 & 0.040 & 2.2 & 0.796 & 0.105 & 0.107 \\\\\nLLaMA-3 & 1.2 & 0.787 & 0.088 & 0.111 & 0.1 & 0.783 & 0.011 & 0.088 & 1.8 & 0.794 & 0.163 & 0.132 \\\\\nGLM-4 & 0.0 & 0.761 & 0.038 & 0.077 & 0.0 & 0.762 & 0.006 & 0.052 & 0.0 & 0.765 & 0.071 & 0.120 \\\\\n\\midrule\nHuman & 1.2 & 0.833 & 0.122 & 0.159 & -- & -- & -- & -- & -- & -- & -- & -- \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\end{table*}\n\n\n\n\\subsection{Experimental Results}\n\n%\n\n%\n\n%\n\nWe analyze and answer the following Research Questions (RQs):\n\\textbf{(RQ1)} How do state-of-the-art LLMs perform in translating semantic actions into VR device manipulations across different VR games?\n\\textbf{(RQ2)} How does the number of few-shot examples affect LLMs' ability to execute this translation?\n\\textbf{(RQ3)} Do LLM and human performance exhibit significant variations across the four different VR games, potentially indicating sensitivity to game mechanics and interaction complexity? \n\\textbf{(RQ4)} Which cognitive capabilities do current LLMs excel at, and where do they struggle?\n\\textbf{(RQ5)} How do LLMs compare to human performance in VR device manipulation tasks?\n\n\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n\n\\subsection{RQ1 \\& RQ3: LLM Performance Across VR Games}\n\n\\begin{wraptable}[12]{r}{0.5\\linewidth}\n\\centering\n\\vspace{-20pt}\n\\caption{Cross-game performance variation (standard deviation across games) w/ 5-shot examples.}\n\\label{tab:cross_game_variation}\n\\setlength{\\tabcolsep}{2pt}\n\\resizebox{0.5\\columnwidth}{!}{\n\\begin{tabular}{l ccc c}\n\\toprule\n\\textbf{Model} & \\textbf{NSAS \\ensuremath{\\sigma}}\\ensuremath{\\downarrow} & \\textbf{SOP \\ensuremath{\\sigma}}\\ensuremath{\\downarrow} & \\textbf{F1$_{\\text{SOP}}$ \\ensuremath{\\sigma}}\\ensuremath{\\downarrow} & \\textbf{Game Gap}\\ensuremath{\\downarrow} \\\\\n\\midrule\nGPT-3.5 & 0.110 & 0.061 & 0.084 & 0.085 \\\\\nGPT-4 & 0.059 & 0.051 & 0.081 & 0.074 \\\\\nGPT-4o & 0.068 & 0.137 & 0.184 & 0.127 \\\\\nGemini-1.5 & \\textbf{0.099} & \\textbf{0.093} & \\textbf{0.127} & \\textbf{0.095} \\\\\nMixtral & 0.114 & 0.031 & 0.065 & 0.070 \\\\\nLLaMA-3 & 0.112 & 0.103 & 0.120 & 0.113 \\\\\nGLM-4 & 0.135 & 0.049 & 0.069 & 0.084 \\\\\n\\midrule\nHuman & 0.105 & 0.029 & 0.117 & 0.084 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\end{wraptable}\n%\n%\n%\nTables~\\ref{tab:overall_performance_1}, \\ref{tab:overall_performance_2}, and \\ref{tab:cross_game_variation} present comprehensive performance metrics for all evaluated LLMs across the four VR games. Our analysis reveals substantial variations in model capabilities and game-specific challenges.\nGemini-1.5-Pro emerges as the strongest performer overall, achieving the highest NSAS scores in three of the four games (Half-Life: Alyx: 0.863, Moss: Book II: 0.848, Vivecraft: 0.938), while maintaining competitive performance in Into the Radius (0.682). GPT-4o demonstrates particular strength in Into the Radius with the highest SOP score (0.291) and F1$_{\\text{SOP}}$ (0.414), suggesting superior procedural reasoning capabilities in this specific game context. GPT-4-turbo maintains consistently strong performance across all games, positioning itself as a reliable general-purpose model for VR interaction translation.\n\nA striking pattern emerges in the SOP metrics, which vary dramatically across both models and games (0.00-0.30 range). While NSAS scores remain relatively high (mostly $>$0.75), indicating models can identify relevant steps, the low SOP values reveal fundamental difficulties in maintaining correct temporal ordering. This discrepancy is particularly pronounced in Vivecraft, where models achieve high NSAS scores (0.909-0.938) but struggle with step ordering (SOP: 0.00-0.19), suggesting that simpler interaction patterns may paradoxically lead to overconfidence in step sequencing.\n\nAnalysis of performance variations (Table~\\ref{tab:cross_game_variation}) reveals significant game-dependent effects. Vivecraft exhibits the highest average performance across models (NSAS: 0.922-0.938), likely due to its consistent block-based interaction paradigm inherited from Minecraft. In contrast, Into the Radius presents the greatest challenge, with notably lower NSAS scores (0.618-0.698) and high performance variance. This pattern suggests that games featuring realistic physics simulations and complex inventory management pose particular difficulties for current LLMs.\n\nInterestingly, different models exhibit distinct strengths across game types. GPT-4o shows remarkable adaptability in Into the Radius (SOP: 0.291) compared to other models, while struggling in Half-Life: Alyx (SOP: 0.022). Gemini-1.5-Pro maintains the most balanced performance profile across games (Game Gap: 0.095), suggesting more robust generalization capabilities. Smaller models like Mixtral-8x7B and GLM-4-flash show disproportionate performance degradation in complex environments, with GLM-4-flash achieving zero SOP in Vivecraft despite reasonable NSAS scores.\n%\nThe substantial performance variations across games highlight the impact of interaction design on LLM capabilities. Games with discrete, well-defined actions (Vivecraft) enable higher model performance, while those requiring nuanced controller manipulation and spatial reasoning (Half-Life: Alyx, Into the Radius) expose current limitations. The correlation between game complexity and performance degradation is non-linear, moderate complexity (Moss: Book II) sometimes yields better results than simpler environments, suggesting that models may benefit from richer contextual cues in certain scenarios.\n\nThese findings collectively demonstrate that while state-of-the-art LLMs have made significant progress in understanding VR interactions, their performance remains highly sensitive to specific game mechanics and interaction paradigms. The gap between high NSAS scores and low SOP values across all games indicates that current models can identify relevant actions but struggle with the procedural reasoning required to sequence them correctly, which is an important capability for successful VR interaction.\n\n\n\n\n\\subsection{RQ2: Impact of Few-Shot Examples}\n\n\\begin{wraptable}[11]{r}{0.65\\linewidth}\n\\vspace{-20pt}\n\\caption{Effect of few-shot examples on model performance (average across all games)}\n\\label{tab:few_shot_effect}\n\\centering\n\\resizebox{1.0\\linewidth}{!}{\n\\setlength{\\tabcolsep}{2pt}\n\\begin{tabular}{l ccc ccc ccc}\n\\toprule\n\\multirow{2}{*}{\\textbf{Model}} & \\multicolumn{3}{c}{\\textbf{Zero-shot}} & \\multicolumn{3}{c}{\\textbf{3-shot}} & \\multicolumn{3}{c}{\\textbf{5-shot}} \\\\\n\\cmidrule(lr){2-4} \\cmidrule(lr){5-7} \\cmidrule(lr){8-10}\n& \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{SSM}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{SSM}\\ensuremath{\\uparrow} & \\textbf{NSAS}\\ensuremath{\\uparrow} & \\textbf{SOP}\\ensuremath{\\uparrow} & \\textbf{SSM}\\ensuremath{\\uparrow} \\\\\n\\midrule\nGPT-3.5 & 0.781 & 0.003 & 0.006 & 0.783 & 0.113 & 0.013 & 0.806 & 0.128 & 0.022 \\\\\nGPT-4 & 0.799 & 0.015 & 0.012 & 0.807 & 0.106 & 0.039 & 0.824 & 0.167 & 0.066 \\\\\nGPT-4o & 0.785 & 0.015 & 0.012 & 0.802 & 0.166 & 0.059 & 0.815 & 0.159 & \\textbf{0.077} \\\\\nGemini-1.5 & 0.797 & 0.010 & 0.016 & 0.827 & 0.174 & 0.048 & \\textbf{0.833} & \\textbf{0.207} & 0.056 \\\\\nMixtral & 0.784 & 0.002 & 0.000 & 0.766 & 0.103 & 0.010 & 0.797 & 0.106 & 0.021 \\\\\nLLaMA-3 & 0.786 & 0.011 & 0.001 & 0.787 & 0.139 & 0.014 & 0.811 & 0.172 & 0.020 \\\\\nGLM-4 & 0.747 & 0.005 & 0.000 & 0.756 & 0.036 & 0.000 & 0.778 & 0.065 & 0.000 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\end{wraptable}\n%\n%\nTable~\\ref{tab:few_shot_effect} demonstrates that few-shot examples substantially improve LLM performance in VR device manipulation tasks, with the most dramatic gains observed in Sequential Order Preservation (SOP), where scores increase by 10--20x from near-zero baselines. All models benefit from in-context examples, though with diminishing returns, the improvement from zero-shot to 3-shot (average NSAS gain: 2.1\\%, SOP: 10-fold increase) significantly exceeds that from 3-shot to 5-shot (NSAS: 1.4\\%, SOP: 20-50\\% relative gain). Gemini-1.5-Pro exhibits the strongest adaptability, achieving the highest 5-shot performance (NSAS: 0.833, SOP: 0.207), while maintaining consistent improvements across all metrics. The differential impact across metrics reveals that few-shot examples primarily address procedural sequencing challenges (massive SOP improvements) more effectively than exact step matching (modest SSM gains), suggesting that demonstrations help models understand temporal dependencies in VR interactions but do not fully resolve the complexity of translating semantic actions into precise device manipulations.\n\n\n%\n\n%\n\n%\n%\n%\n%\n%\n%\n\n%\n\n\\subsection{RQ4: Cognitive Capabilities Analysis}\nWe analyzed model performance across six cognitive capabilities required for effective VR interaction (Figure~\\ref{fig:capabilities_radar}). By mapping evaluation metrics to capability scores (0-10 scale), we identified specific strengths and limitations in how LLMs approach spatial-mechanical reasoning tasks.\n\n\\textbf{Areas of Strength:} All evaluated LLMs demonstrate strong task decomposition capabilities (7.8-8.5), with minimal performance gap compared to humans (8.2). Gemini-1.5-Pro leads with a score of 8.5, while even smaller models like Mixtral-8x7B (8.0) and GLM-4-flash (7.8) perform admirably. This suggests that segmenting high-level actions into component steps aligns well with the sequential reasoning abilities developed during language model pre-training.\n\n\\textbf{Areas of Weakness:} Motor action mapping emerges as the most significant challenge (0.5-4.5), with all models struggling to precisely translate abstract actions into specific VR control manipulations. GPT-4o performs best in this dimension (4.5), but still falls short of robust capability. Procedural reasoning also shows substantial variation (2.3-7.0), with only Gemini-1.5-Pro approaching adequate performance. Judgment of termination conditions represents another challenge area, with most models scoring below 5.0 (except Gemini-1.5-Pro at 6.0), compared to human performance (6.5).\n\n\\textbf{Model Comparison:} Gemini-1.5-Pro demonstrates the most balanced performance profile, consistently outperforming other models in procedural reasoning (7.0), spatial reasoning (7.5), and termination judgment (6.0). GPT-4 variants show strong task decomposition and object interaction (5.3-5.7) but lag in procedural sequencing. LLaMA-3-8B shows surprisingly competitive performance in procedural reasoning (5.7), outperforming larger models like GPT-3.5-Turbo (4.3), suggesting architecture differences may be as important as scale.\n\n\n\n%\n\n%\n\n%\n\n%\n\n\\subsection{RQ5: Comparison with Human Performance}\n\n\\begin{wrapfigure}[17]{r}{0.5\\linewidth}\n\\vspace{-20pt}\n\\centering\n\\includegraphics[width=1.0\\linewidth]{Figures/vr_capabilities_radar_ICLR_fonts_xxl.pdf}\n\\caption{Cognitive capabilities of LLMs and humans in translating semantic actions to VR device manipulations. Higher scores (0-10 scale) indicate stronger abilities.}\n\\label{fig:capabilities_radar}\n\\end{wrapfigure}\nTo contextualize our findings, we compare LLM performance against human baselines across our evaluation metrics. As shown in Tables~\\ref{tab:overall_performance_1} and~\\ref{tab:overall_performance_2}, state-of-the-art LLMs demonstrate competitive performance with humans on several key dimensions.\n%\nOur results reveal a nuanced performance landscape. While top-performing models (Gemini-1.5-Pro, GPT-4o) achieve comparable or superior NSAS scores relative to humans in certain games (e.g., Vivecraft: 0.931-0.938 vs. 0.935 for humans), human participants maintain a decisive advantage in Sequential Order Preservation, particularly for games requiring complex interaction sequences. In Half-Life: Alyx, humans achieve only 0.090 SOP compared to the best model performance of 0.209 (Gemini-1.5-Pro), yet this reflects the challenging nature of the task rather than superior model performance, both humans and models struggle with the intricate procedural requirements of this game.\n%\n\nAnalysis of performance variance across games (Table~\\ref{tab:cross_game_variation}) reveals striking similarities between human and high-performing model behavior. The standard deviation of human performance (0.084) closely aligns with that of GPT-4 (0.074) and Mixtral-8x7B (0.070), suggesting that both humans and advanced LLMs exhibit similar sensitivity patterns to game-specific interaction complexities. This convergence is particularly evident in structured environments like Vivecraft, where the consistency gap between humans and LLMs has substantially narrowed.\n%\nFigure~\\ref{fig:capabilities_radar} illustrates the capability-wise performance comparison, revealing critical gaps in embodied reasoning. Humans maintain superior performance in spatial reasoning (8.3 vs. 7.5 for Gemini-1.5-Pro) and judgment of termination conditions (6.5 vs. 6.0). These differences are statistically significant ($p < 0.05$, Wilcoxon signed-rank test) and persist across all evaluated models. This performance gap suggests that while LLMs have achieved remarkable progress in understanding VR interaction semantics, they lack the grounded physical intuition that humans naturally apply when reasoning about three-dimensional manipulations and determining action completion states.\n\nThe convergence of human and LLM performance on certain metrics, coupled with persistent gaps in spatial and termination reasoning, indicates that current language models can effectively decompose VR tasks but struggle with aspects requiring embodied experience. This finding has important implications for the development of future VR-capable AI systems, suggesting the need for training paradigms that better incorporate spatial and physical reasoning capabilities.\n\n\n\n\n%\n\n%\n\n%\n\n%\n%\n%%\n\n%\n\n%%\n\n%\n\n%\n\n%\n\n\n\\section{Related Work}\n\nRecent work has explored the use of large language models (LLMs) as generalist agents for embodied and interactive reasoning tasks. In robotics, \\textit{SayCan}~\\cite{ahn2022can} and \\textit{PaLM-E}~\\cite{driess2023palm} combine LLMs with affordance-based skill models or multimodal inputs to plan and execute robot actions in real-world settings. These methods demonstrate that LLMs can decompose high-level goals into actionable steps when grounded in sensory input and executable primitives. Similar capabilities have been investigated in virtual domains such as Minecraft through agents like \\textit{Voyager}~\\cite{wang2023voyager} and simulation platforms like \\textit{MineDojo}~\\cite{fan2022minedojo}, which showcase in-context learning and autonomous skill acquisition by prompting LLMs to generate and refine code or sub-goals based on environmental feedback. However, these systems are typically tuned for code-level or symbolic outputs and do not focus on physical device manipulation or spatially grounded motor control as required in VR environments.\n\nTask decomposition and procedural reasoning have been studied extensively via prompting strategies such as Chain-of-Thought~\\cite{wei2022chain} and ReAct~\\cite{yao2022react}, which interleave reasoning with action selection to improve coherence in multi-step planning. LLMs have also been used to generate structured action sequences or API calls from natural instructions in domains like household tasks~\\cite{shridhar2020alfred} and scientific procedures~\\cite{wang2022scienceworld}. Code-as-policy paradigms~\\cite{liang2022code} show that LLMs can output executable policy code that integrates logical control flow, enabling conditional and iterative actions. However, these approaches often abstract away the complexity of physical or spatial execution, making them less suited for evaluating embodied skills involving real-time device input, object affordances, or 3D spatial constraints.\n\nTo assess grounded reasoning, several benchmarks have been proposed in interactive settings. Animal-AI~\\cite{mecattaf2024little} evaluates embodied cognition through physics-based tasks adapted from animal intelligence experiments, highlighting LLMs' partial competence in navigation, tool use, and physical causality. Similarly, platforms like ALFWorld~\\cite{shridhar2021alfworld} and ScienceWorld~\\cite{wang2022scienceworld} test instruction-following via text or symbolic interfaces, while MacGyver-style tasks~\\cite{tian2024macgyver} probe object-use innovation in constrained settings. These works underscore known limitations in spatial reasoning, persistence, and tool-use generalization among LLMs. \n\n%\nConcurrently, capability-oriented embodied evaluations for multimodal/embodied LLMs have emerged. EmbodiedBench~\\cite{embodiedbench2025} unifies high- and low-level tasks with fine-grained error taxonomies, while VLABench~\\cite{vlabench2024} targets long-horizon, language-conditioned manipulation for VLA policies; the Embodied Agent Interface (EAI)~\\cite{eai2024} standardizes modules and metrics for step-level diagnostics. In parallel, GUI/OS/mobile control benchmarks, including OSWorld~\\cite{osworld2024}, SPA-Bench~\\cite{spabench2024}, WebArena~\\cite{webarena2023}, Mind2Web~\\cite{mind2web2023}, AndroidEnv~\\cite{androidenv2021}, and AppAgent/AppAgent~v2~\\cite{appagent2023,appagentv2_2024}, evaluate precise, procedure-level device interactions (click/tap/drag/typing) with programmatic success checks, offering a complementary view of grounded action competence. On the robotics side, VLA policies such as RT-1/RT-2~\\cite{rt12022,rt22023} and OpenVLA~\\cite{openvla2024} map visual observations and language to action tokens, improving semantic generalization in manipulation; large-scale 3D suites like Habitat~2.0/HAB~\\cite{habitat2_2021}, BEHAVIOR-1K/OmniGibson~\\cite{behavior1k2024}, and CALVIN~\\cite{calvin2021} stress long-horizon rearrangement and physics. \n\nIn contrast, our benchmark, \\methodname, targets the translation of semantic goals into fine-grained, physically grounded VR device manipulations, enabling a more precise step-level analysis of embodied cognitive abilities critical for real-world interaction.\n\n\\section{Conclusion}\n\n%\n\n\n%\n%\n\nWe present \\methodname, a comprehensive benchmark evaluating seven state-of-the-art LLMs on their ability to translate semantic actions into VR device manipulations across 262 scenarios from four popular VR games. Our evaluation reveals that while advanced models like Gemini-1.5-Pro demonstrate strong task decomposition capabilities (NSAS > 0.8), they exhibit significant weaknesses in motor action mapping and procedural reasoning, with Sequential Order Preservation scores often below 0.3 even in the best cases. Few-shot examples dramatically improve procedural understanding (10-20x increase in SOP scores) but provide limited benefit for exact step matching, suggesting that in-context learning helps models understand action relationships but cannot fully bridge the gap in physical manipulation reasoning. The pronounced performance variations across games and cognitive capabilities indicate that current text-trained LLMs lack the embodied understanding necessary for reliable VR interaction, pointing to the need for multimodal training approaches that incorporate spatial, visual, and haptic information. These findings highlight fundamental limitations in how language models represent physical interactions and suggest that achieving human-level VR manipulation capabilities will require architectural innovations beyond scaling current approaches, with important implications for the development of embodied AI systems in virtual and augmented reality applications.\n\\bibliography{iclr2026_conference, model}\n\\bibliographystyle{iclr2026_conference}\n\n%\n\n%\n\n%\n%\n\n%\n%\n\n%\n\n%\n\n%\n%\n \n%\n \n%\n%\n\n%\n\n%\n\n%\n%\n\n%\n\n%\n%\n \n%\n \n%\n \n%\n%\n\n%\n\n%\n%\n\n%\n\n%\n%\n \n%\n \n%\n%\n\n%\n\n%\n%\n\n%\n\n%\n%\n \n%\n \n%\n \n%\n%\n\n%\n\n\n%\n\n%\n\n%\n\n%\n%\n%\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\clearpage\n\n\\appendix\n\n\n\\section{Preliminaries on Virtual Reality}\n\\label{sec:background}\n\nVirtual Reality (VR) represents a fundamentally distinct paradigm of human-computer interaction that transcends traditional interface boundaries. Unlike conventional computing systems that rely on indirect manipulation through keyboards, mice, and two-dimensional displays, VR creates immersive digital environments where users experience presence and embodiment. This paradigm shift necessitates a comprehensive understanding of both the technological infrastructure and the cognitive demands placed on users who must translate abstract intentions into concrete physical manipulations within virtual spaces.\n\nThe evolution of VR technology has progressed through several generations, from early tethered systems requiring substantial computational infrastructure to modern standalone devices that integrate processing, display, and tracking capabilities within compact form factors. Contemporary VR systems can be broadly categorized into three architectural approaches. PC-tethered headsets leverage external computational resources to deliver high-fidelity experiences with complex graphics and physics simulations. Standalone headsets, exemplified by devices like the Meta Quest series, incorporate integrated processors that balance performance with portability. Mobile-phone-based solutions represent an accessible entry point, utilizing smartphones as both display and processor, though with inherent limitations in tracking precision and computational capability.\n\nThe core hardware components enabling VR interaction form an integrated ecosystem of sensory input and output devices. Head-Mounted Displays (HMDs) serve as the primary visual interface, providing stereoscopic rendering that creates depth perception while simultaneously tracking head orientation and position through integrated sensors. This tracking enables natural viewing behaviors where users can examine virtual objects by physically moving their heads, mirroring real-world visual exploration patterns. Motion controllers, typically deployed in pairs to represent both hands, enable direct manipulation of virtual objects through a combination of positional tracking, button inputs, trigger mechanisms, and thumbstick controls. These devices must balance ergonomic considerations with functional complexity, providing sufficient input channels while maintaining intuitive operation. Spatial tracking systems, whether implemented through external sensors (outside-in tracking) or integrated cameras (inside-out tracking), monitor user movements with six degrees of freedom, capturing both translational and rotational motion to enable natural locomotion and interaction within virtual environments.\n\nThe ongoing evolution of VR hardware continues to introduce novel interaction modalities. Haptic gloves promise to deliver tactile feedback through actuators that simulate texture, resistance, and temperature. Full-body tracking systems capture skeletal motion to enable more nuanced avatar control and gesture recognition. Specialized peripherals, from steering wheels for racing simulations to weapon replicas for combat games, demonstrate the trend toward application-specific controllers that enhance immersion through physical affordances that match virtual interactions.\n\n\\subsection{Interaction Paradigms and Design Principles}\n\\label{subsec:interaction_paradigms}\n\nThe design of VR interaction paradigms represents a delicate balance between leveraging users' existing motor skills and introducing novel control schemes that exploit the unique capabilities of virtual environments. Direct manipulation forms the foundation of most VR interactions, where users employ hand controllers to simulate natural actions like grasping, throwing, and pushing. This approach capitalizes on users' lifetime of experience with physical object manipulation but requires careful calibration of virtual physics to match expectations. The mapping between controller inputs and virtual hand movements must account for the absence of tactile feedback, often employing visual or auditory cues to confirm successful interactions.\n\nRay-casting emerged as an elegant solution to the fundamental challenge of interacting with objects beyond physical reach. By projecting virtual rays from controllers, users can select, manipulate, and activate distant objects without locomotion. This technique exemplifies how VR interaction design often augments natural human capabilities rather than strictly simulating physical constraints. Advanced ray-casting implementations incorporate features like ray curvature for improved ergonomics, variable ray length based on context, and visual feedback mechanisms that indicate interaction possibilities.\n\nGesture recognition systems interpret temporal patterns of controller or hand movement as discrete commands, enabling a rich vocabulary of interactions without relying on button combinations. These systems must balance recognition accuracy with user comfort, avoiding gestures that cause fatigue or require precise movements difficult to perform consistently. Machine learning approaches have enhanced gesture recognition capabilities, allowing for more natural and varied input patterns while maintaining reliable detection rates.\n\nSymbolic input mechanisms address scenarios where direct physical analogues are impractical or inefficient. Virtual keyboards present unique challenges in VR, as users lack tactile feedback and must rely on visual confirmation of key presses. Solutions range from laser-pointer selection of virtual keys to gesture-based text entry systems that map hand movements to characters. Voice commands offer an alternative input modality that bypasses manual interaction entirely, though they introduce considerations around recognition accuracy, latency, and social acceptability in shared spaces.\n\n\\subsection{Development Platforms and Technical Considerations}\n\\label{subsec:development}\n\nThe creation of VR applications relies on sophisticated development ecosystems that abstract hardware complexity while providing fine-grained control over interaction mechanics. Unity and Unreal Engine have emerged as dominant platforms, offering comprehensive toolsets that handle rendering pipelines, physics simulation, spatial audio, and cross-platform deployment. These engines provide specialized VR interaction frameworks that standardize common patterns like object grabbing, teleportation, and menu systems, significantly reducing development complexity.\n\nHardware software development kits (SDKs) serve as the bridge between high-level application logic and device-specific capabilities. Meta's OpenXR initiative represents an industry effort to standardize VR/AR interfaces, enabling applications to target multiple hardware platforms without extensive modifications. Platform-specific SDKs like SteamVR and Oculus SDK continue to play important roles, offering access to proprietary features and optimizations that enhance performance on particular hardware.\n\nTechnical constraints fundamentally shape VR interaction design decisions. Maintaining consistent frame rates above 72Hz (and preferably 90Hz or higher) prevents motion sickness and ensures responsive interactions. This performance requirement influences every aspect of application design, from polygon counts and texture resolution to the complexity of physics simulations. Tracking precision varies across hardware platforms and environmental conditions, necessitating interaction designs that accommodate occasional tracking losses or reduced accuracy. Developers must also consider the diverse computational capabilities across the VR ecosystem, implementing scalable solutions that provide acceptable experiences on entry-level hardware while leveraging the capabilities of high-end systems.\n\n\\subsection{Challenges in VR Interaction}\n\\label{subsec:challenges}\n\nDespite remarkable technological progress, VR interaction continues to face fundamental challenges that impact user experience and limit application domains. The locomotion problem exemplifies the tension between physical and virtual spaces. While users may explore vast virtual environments, they remain constrained by finite physical play areas. Teleportation offers a practical solution but breaks immersion and can cause spatial disorientation. Artificial locomotion through thumbstick control risks motion sickness in susceptible users. More exotic solutions like omnidirectional treadmills or redirected walking techniques remain impractical for consumer applications.\n\nThe absence of comprehensive haptic feedback represents perhaps the most significant limitation in current VR systems. While controllers provide basic vibration feedback, they cannot simulate the rich tactile experiences of real-world interaction: the weight of objects, surface textures, temperature variations, or resistance to movement. This sensory gap creates a fundamental disconnect between visual expectations and physical sensations, requiring users to adapt their interaction strategies and often leading to reduced precision in manipulation tasks.\n\nInteraction discoverability poses ongoing challenges as VR applications lack standardized interface conventions comparable to desktop or mobile platforms. Users encountering new VR experiences must often learn application-specific control schemes, gesture sets, and interaction patterns. The absence of persistent visual UI elements (to maintain immersion) exacerbates this challenge, as users cannot easily reference control schemes during gameplay. This lack of standardization increases cognitive load and creates barriers to entry for new users.\n\nPrecision manipulation tasks highlight the limitations of current tracking systems and input devices. Tasks requiring fine motor control, such as threading a virtual needle or manipulating small components, prove challenging due to tracking jitter, lack of physical surfaces for hand stabilization, and absence of tactile confirmation. These limitations restrict the types of applications suitable for VR and influence interaction design toward larger, more forgiving target sizes and simplified manipulation schemes.\n\n\\begin{figure}[!htbp]\n \\centering\n \\includegraphics[width=0.8\\linewidth, height=0.20\\textheight, keepaspectratio]{Figures/strict_ssm.png}\n \\caption{Overview of Strict Step-by-Step Matching (SSM) Calculation}\n \\label{fig:ssm}\n\\end{figure}\n\n\\begin{figure}[!htbp]\n \\vspace{0.8em}\n \\centering\n \\includegraphics[width=1.0\\linewidth, height=0.48\\textheight, keepaspectratio]{Figures/longest_common_steps.png}\n \\caption{Overview of Common Subsequence Evaluation}\n \\label{fig:cse}\n\\end{figure}\n\n\\section{Explanation of Evaluation Metrics}\n\n\\subsection{Strict Step-by-Step Matching (SSM)}\n\nFigure~\\ref{fig:ssm} illustrates the Strict Step-by-Step Matching (SSM) calculation process. SSM represents our most stringent evaluation metric, requiring exact correspondence between model-generated sequences and ground truth annotations. The calculation process operates as follows:\n\nIn the left panel, we observe a scenario where the ground truth contains 4 steps while the model result contains 5 steps. For SSM to register a match, two conditions must be satisfied: (1) the number of steps must be identical between ground truth and model output, and (2) each step must have a cosine similarity score above our threshold of 0.8387 with its corresponding ground truth step. In this example, the length mismatch alone disqualifies the sequence from being counted as correct, resulting in an SSM score of 0. The orange X symbol on the fifth model step visually indicates this length mismatch failure.\n\nThe right panel demonstrates a successful SSM match where both sequences contain 4 steps. Each model step is compared with its corresponding ground truth step using cosine similarity of their text embeddings. The green checkmarks indicate that all four step pairs exceed the similarity threshold, resulting in a successful match and contributing 1 to the SSM score. This metric's strictness explains why even high-performing models achieve relatively low SSM scores—any deviation in sequence length or individual step similarity results in complete failure for that sequence.\n\n\\subsection{Common Subsequence Evaluation}\n\nFigure~\\ref{fig:cse} details our Common Subsequence Evaluation approach, which underlies the Normalized Step Alignment Score (NSAS) and Sequential Order Preservation (SOP) metrics. This evaluation method provides more nuanced assessment than SSM by identifying partial matches and preserved ordering within sequences.\n\nThe process begins with comparing each step in the ground truth and model result sequences using cosine similarity, as shown by the crossing blue lines in the leftmost panel. Unlike SSM's strict position-based matching, this approach allows steps to match regardless of their positions in the sequences. The algorithm then identifies the top 3 longest common subsequences where matched steps maintain their relative ordering. \n\nIn the example shown, multiple candidate subsequences are generated, each representing different ways steps from both sequences can be aligned while preserving order. The model (shown as GPT-4o) then selects the most matching subsequence based on the highest cumulative similarity scores. The final selected subsequence shows GT Steps 2, 3, and 4 matching with MR Steps 1, 4, and 5 respectively. This flexible matching approach allows the metrics to capture semantic correctness even when models include additional steps or present steps in slightly different positions.\n\nThe NSAS metric is calculated by considering the correctly matched steps (|C|), missing steps from ground truth (|M|), and additional steps in the model output (|A|), normalized by the total ground truth steps and scaled across the dataset. The SOP metric specifically evaluates whether matched steps maintain their sequential order, providing insight into the model's procedural reasoning capabilities.\n\n%\n\n%\n\n%\n\n%\n\n%\n\n\n\n\n%\n\n\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n\n\n\n\n\n\n\n\n\n\n\\section{Detailed Experiment Results}\n\\label{sec:detailed_results}\n\nThis section provides comprehensive analysis of our experimental results, including detailed performance breakdowns across models, games, and experimental conditions. We present both aggregated metrics and fine-grained analyses that illuminate specific strengths and weaknesses in current LLMs' ability to reason about VR device manipulations.\n\n\\subsection{Overall Performance Analysis}\n\nThe table~\\ref{tab:performance_llm_across_games} below presents a holistic view of model performance across all experimental conditions. The results reveal a clear performance hierarchy, with Gemini-1.5-Pro achieving the highest average Normalized Step Alignment Score (NSAS) of 0.845, followed closely by GPT-4o (0.832) and GPT-4 (0.824). Notably, even the best-performing models achieve relatively modest Strict Step-by-Step Matching (SSM) scores, with Gemini-1.5-Pro reaching only 8.7\\% exact sequence matches. This discrepancy between NSAS and SSM scores indicates that while models can identify appropriate actions, they struggle with precise sequencing and complete reproduction of manipulation sequences.\n\nThe Sequential Order Preservation (SOP) scores reveal perhaps the most significant challenge facing current LLMs. Even top-performing models achieve SOP scores below 0.3, indicating difficulty in maintaining correct procedural ordering of steps. This limitation is particularly pronounced in zero-shot settings, where SOP scores approach zero for most models, suggesting that procedural reasoning for VR interactions requires exposure to examples rather than emerging from general language understanding.\n\nHuman performance provides an important baseline for contextualizing model achievements. While humans achieve comparable NSAS scores (0.817) to top LLMs, they show notably lower SOP scores (0.124) than leading models. This counterintuitive result reflects the challenging nature of the tasks even for experienced VR users and suggests that perfect procedural recall may be less important than adaptive problem-solving in real-world VR interaction.\n\n\\begin{table}[htbp!]\n\\caption{Performance of LLMs across VR Games (Best Few-Shot Setting)}\n\\label{tab:performance_llm_across_games}\n\\centering\n\\small\n\\begin{tabular}{lccccc}\n\\toprule\n\\textbf{Model} & \\textbf{NSAS} & \\textbf{SOP} & \\textbf{SSC} & \\textbf{SSM} & \\textbf{Best FS} \\\\\n\\midrule\nGemini-1.5-Pro & 0.845 & 0.251 & 0.151 & 0.087 & 5 \\\\\nGPT-4o & 0.832 & 0.291 & 0.190 & 0.135 & 5 \\\\\nGPT-4 & 0.824 & 0.218 & 0.177 & 0.095 & 5 \\\\\nLLaMA-3-8B & 0.823 & 0.283 & 0.200 & 0.040 & 5 \\\\\nHuman & 0.817 & 0.124 & 0.174 & 0.021 & - \\\\\nMixtral-8x7B & 0.790 & 0.123 & 0.142 & 0.039 & 5 \\\\\nGPT-3.5 & 0.778 & 0.169 & 0.137 & 0.037 & 5 \\\\\nGLM-4-Flash & 0.749 & 0.096 & 0.165 & 0.000 & 5 \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\\subsection{Game-Specific Performance Patterns}\n\nThe table~\\ref{tab:per_game} below reveals substantial variations in model performance across different VR games, highlighting how game design and interaction complexity influence LLM reasoning capabilities. Vivecraft consistently yields the highest performance across all models, with NSAS scores ranging from 0.909 to 0.938. This strong performance likely reflects the game's discrete, block-based interaction paradigm inherited from Minecraft, which provides clear action-object mappings that align well with linguistic descriptions.\n\nIn contrast, Into the Radius proves most challenging, with NSAS scores dropping to 0.618-0.698 across models. This game's emphasis on realistic physics simulation, complex inventory management, and weapon manipulation requires understanding of nuanced spatial relationships and multi-step procedures that current LLMs struggle to capture. The high standard deviation in performance (0.135 for GLM-4-flash) indicates inconsistent model behavior when confronting complex interaction scenarios.\n\nHalf-Life: Alyx and Moss: Book II occupy intermediate positions in the difficulty spectrum. Half-Life: Alyx's physics-based puzzles and combat scenarios require precise timing and spatial reasoning, reflected in extremely low SOP scores (0.022 for GPT-4o). Moss: Book II's third-person perspective and puzzle-platforming elements introduce unique challenges in translating camera-relative directions into controller movements, though models show more consistent performance than in Half-Life: Alyx.\n\n\\begin{table}[htbp!]\n\\caption{Performance comparison across different VR games (5-shot setting). We report NSAS scores (primary metric) and SOP scores (in parentheses).}\n\\label{tab:per_game}\n\\centering\n\\resizebox{0.75\\columnwidth}{!}{\n\\begin{tabular}{l|cccc}\n\\toprule\n\\textbf{Model} & \\textbf{Half-Life: Alyx} & \\textbf{Radius} & \\textbf{Moss} & \\textbf{Vivecraft} \\\\\n\\midrule\nGPT-3.5-turbo & 0.858 (0.123) & 0.662 (0.169) & 0.782 (0.169) & 0.922 (0.043) \\\\\nGPT-4-turbo & 0.852 (0.125) & 0.693 (0.189) & 0.824 (0.218) & 0.927 (0.137) \\\\\nGPT-4o & 0.804 (0.022) & 0.698 (0.291) & 0.824 (0.300) & 0.931 (0.190) \\\\\nGemini-1.5-Pro & 0.863 (0.209) & 0.682 (0.102) & 0.848 (0.265) & 0.938 (0.250) \\\\\nMixtral-8x7B & 0.839 (0.126) & 0.666 (0.123) & 0.756 (0.117) & 0.926 (0.060) \\\\\nLLaMA-3-8B & 0.848 (0.126) & 0.644 (0.242) & 0.823 (0.283) & 0.929 (0.039) \\\\\nGLM-4-flash & 0.836 (0.076) & 0.618 (0.096) & 0.749 (0.087) & 0.909 (0.000) \\\\\n\\midrule\nHuman & 0.845 (0.090) & 0.684 (0.148) & 0.817 (0.112) & 0.935 (0.122) \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\end{table}\n\n\n\\subsection{Impact of Few-Shot Learning}\n\nThe table~\\ref{tab:fewshot_impact} below demonstrates the transformative effect of few-shot examples on model performance. The most dramatic improvements occur in SOP scores, which increase by factors of 10-20x from zero-shot to 5-shot settings. GPT-3.5-turbo exemplifies this pattern, improving from 0.036 to 0.226 in SOP F1 score, representing a 527.8\\% relative gain. This massive improvement suggests that examples primarily help models understand the expected format and level of detail for procedural instructions rather than teaching fundamental VR interaction principles.\n\nThe diminishing returns pattern is consistent across models, with the largest gains occurring between zero-shot and 1-shot conditions. The jump from 3-shot to 5-shot provides minimal additional benefit, indicating that models quickly extract relevant patterns from limited examples. Gemini-1.5-Pro shows the most efficient few-shot learning, achieving top performance with fewer examples than competing models, suggesting superior in-context learning capabilities for procedural tasks.\n\nInterestingly, few-shot examples have differential effects across game types. Complex games like Into the Radius show continued improvement with additional examples, while simpler environments like Vivecraft plateau quickly. This pattern indicates that few-shot learning is most beneficial when dealing with diverse interaction patterns and complex procedural sequences.\n\n\\begin{table}[t!]\n\\caption{Impact of few-shot examples on model performance. We report F1 scores for Sequential Order Preservation (SOP) across different number of examples. Higher is better.}\n\\label{tab:fewshot_impact}\n\\centering\n\\resizebox{0.73\\columnwidth}{!}{\n\\begin{tabular}{l|cccc|c}\n\\toprule\n\\textbf{Model} & \\textbf{Zero-shot} & \\textbf{1-shot} & \\textbf{3-shot} & \\textbf{5-shot} & \\textbf{Relative Gain (\\%)} \\\\\n\\midrule\nGPT-3.5-turbo & 0.036 & 0.096 & 0.190 & 0.226 & 527.8 \\\\\nGPT-4-turbo & 0.102 & 0.171 & 0.254 & 0.301 & 195.1 \\\\\nGPT-4o & 0.112 & 0.224 & 0.257 & 0.287 & 156.3 \\\\\nGemini-1.5-Pro & 0.085 & 0.187 & 0.260 & \\textbf{0.330} & \\textbf{288.2} \\\\\nMixtral-8x7B & 0.031 & 0.110 & 0.204 & 0.201 & 548.4 \\\\\nLLaMA-3-8B & 0.090 & 0.165 & 0.254 & 0.299 & 232.2 \\\\\nGLM-4-flash & 0.033 & 0.069 & 0.121 & 0.146 & 342.4 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\end{table}\n\n\\subsection{Cognitive Capability Analysis}\nThe figure~\\ref{fig:capabilities_radar} shows model performance across six cognitive dimensions, revealing distinct capability profiles. All models demonstrate strong task decomposition abilities (7.8-8.5), indicating that breaking down high-level goals into subtasks aligns well with LLMs' training on hierarchical text structures. Gemini-1.5-Pro leads in this dimension with a score of 8.5, though even smaller models like Mixtral-8x7B achieve respectable scores of 8.0.\n\nMotor action mapping emerges as the most challenging capability across all models (0.5-4.5), highlighting the difficulty of translating abstract action concepts into specific button presses and controller movements. This limitation likely stems from the absence of embodied experience in text-based training data. GPT-4o performs best in this dimension but still falls far short of human-level capability, suggesting a fundamental gap in current architectures.\n\nProcedural reasoning shows high variance across models (2.3-7.0), with Gemini-1.5-Pro again leading. The correlation between procedural reasoning scores and few-shot learning gains suggests that this capability can be partially addressed through examples, though the ceiling remains well below human performance. Spatial reasoning capabilities (4.8-7.5) reveal another significant gap, particularly evident in games requiring 3D navigation and object manipulation.\n\n\\subsection{Statistical Significance and Variance Analysis}\n\nThe tables~\\ref{tab:vivecraft_nsas},~\\ref{tab:vivecraft_sop},~\\ref{tab:vivecraft_ssc},~\\ref{tab:alyx_nsas},~\\ref{tab:alyx_sop},~\\ref{tab:alyx_ssc},~\\ref{tab:moss_nsas},~\\ref{tab:moss_sop},~\\ref{tab:moss_ssc},~\\ref{tab:radius_nsas},~\\ref{tab:radius_sop}, and~\\ref{tab:radius_ssc} below provide detailed statistical analyses of model performance, revealing important patterns in consistency and reliability. And the figures~\\ref{fig:nsas_barh},~\\ref{fig:sop_barh},~\\ref{fig:ssc_barh} The standard deviation measurements across different games and shot settings illuminate which models maintain stable performance versus those exhibiting high variability. For instance, in Vivecraft, GPT-3.5-turbo shows remarkably consistent NSAS scores in zero-shot settings (std = 0.0248), but this consistency deteriorates with few-shot examples (std = 0.0734 at 3-shot), suggesting that additional examples introduce uncertainty in the model's approach to task completion.\n\nThe variance patterns differ significantly between metrics. NSAS scores generally show lower standard deviations (0.02-0.21 range) compared to SOP scores (0.00-0.34 range), indicating that models more consistently identify relevant steps than maintain proper ordering. This pattern is particularly pronounced in complex games like Into the Radius, where SOP standard deviations exceed 0.3 for several models in few-shot settings. Such high variance suggests that models employ different strategies across different runs, sometimes achieving correct ordering by chance rather than through systematic understanding.\n\nComparison with human variance provides crucial context for interpreting model stability. Human annotators show standard deviations comparable to mid-tier models (0.084 in cross-game performance), suggesting that some degree of variance is inherent to the task rather than a model limitation. However, humans maintain more consistent SOP performance (std = 0.029) compared to all models except Mixtral-8x7B, indicating more reliable procedural reasoning despite overall lower scores.\n\n\\begin{table}[h!]\n \\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\textit{Vivecraft} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-shot} & 0.9258 & 0.0248 & 0.9255 & 0.0238 & 0.9191 & 0.0306 & 0.9209 & 0.0334 & 0.9312 & 0.0207 & 0.9244 & 0.0329 \\\\\n \\textbf{1-shot} & 0.921 & 0.0309 & 0.9349 & 0.0506 & 0.9358 & 0.0735 & 0.9362 & 0.0553 & 0.9219 & 0.0636 & 0.9101 & 0.0765 \\\\\n \\textbf{3-shot} & 0.9284 & 0.0734 & 0.914 & 0.1167 & 0.9212 & 0.1115 & 0.9381 & 0.0781 & 0.9005 & 0.1125 & 0.9022 & 0.1051 \\\\\n \\textbf{5-shot} & 0.9218 & 0.0385 & 0.9274 & 0.0674 & 0.9305 & 0.0689 & 0.9378 & 0.0708 & 0.9256 & 0.0477 & 0.9289 & 0.0364 \\\\\n \\bottomrule\n \\end{tabular}\n }\n \n \\label{tab:vivecraft_nsas}\n\\end{table}\n\n%\n\n\\begin{table}[h!]\n \\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores\ncomparison of LLMs on \\textit{Vivecraft} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.0029 & 0.0312 & 0.0007 & 0.0078 & 0.0012 & 0.0125 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0059 & 0.0624 \\\\\n \\textbf{1-shot} & 0.015 & 0.0734 & 0.1203 & 0.2157 & 0.1568 & 0.2337 & 0.1794 & 0.291 & 0.0812 & 0.164 & 0.0351 & 0.1215 \\\\\n \\textbf{3-shot} & 0.1302 & 0.2352 & 0.1143 & 0.2136 & 0.2826 & 0.3417 & 0.2335 & 0.3417 & 0.0986 & 0.2024 & 0.1124 & 0.2026 \\\\\n \\textbf{5-shot} & 0.0395 & 0.1226 & 0.1366 & 0.2388 & 0.1837 & 0.278 & 0.2495 & 0.3358 & 0.0553 & 0.158 & 0.0374 & 0.1371 \\\\\n \\bottomrule\n \\end{tabular}\n }\n\n \\label{tab:vivecraft_sop}\n\\end{table}\n\n\\begin{table}[h!]\n \\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\textit{Vivecraft} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.049 & 0.11 & 0.1301 & 0.1443 & 0.1272 & 0.1511 & 0.2221 & 0.2151 & 0.024 & 0.0999 & 0.1088 & 0.1549\\\\\n \\textbf{1-shot}& 0.1274 & 0.1988 & 0.544 & 0.3672 & 0.6598 & 0.3322 & 0.5747 & 0.3359 & 0.4914 & 0.3617 & 0.3165 & 0.3415 \\\\\n \\textbf{3-shot} & 0.4755 & 0.3526 & 0.6486 & 0.3373 & 0.6817 & 0.3204 & 0.6538 & 0.3373 & 0.5414 & 0.37 & 0.5299 & 0.3785 \\\\\n \\textbf{5-shot} & 0.18 & 0.2337 & 0.5035 & 0.3772 & 0.6183 & 0.3416 & 0.608 & 0.3546 & 0.3579 & 0.3555 & 0.1606 & 0.2605 \\\\\n \\bottomrule\n \\end{tabular}\n }\n \n \\label{tab:vivecraft_ssc}\n\\end{table}\n\n\n\\begin{table}[h!]\n \\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\textit{Half-Life: Alyx} under different shot settings}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.838 & 0.0413 & 0.8456 & 0.0366 & 0.8376 & 0.0424 & 0.8447 & 0.032 & 0.8376 & 0.0331 & 0.848 & 0.0317 \\\\\n \\textbf{1-shot} & 0.8354 & 0.0582 & 0.8427 & 0.0489 & 0.8472 & 0.0629 & 0.8627 & 0.0482 & 0.807 & 0.1099 & 0.8131 & 0.1289 \\\\\n \\textbf{3-shot} & 0.8452 & 0.0551 & 0.845 & 0.0467 & 0.838 & 0.0757 & 0.8701 & 0.0603 & 0.8255 & 0.0819 & 0.8449 & 0.0707 \\\\\n \\textbf{5-shot} & 0.8577 & 0.0773 & 0.8523 & 0.0613 & 0.8039 & 0.0694 & 0.8625 & 0.0691 & 0.8394 & 0.0834 & 0.848 & 0.0976 \\\\\n \\bottomrule\n \\end{tabular}\n }\n \n \\label{tab:alyx_nsas}\n\\end{table}\n\n\\begin{table}[h!]\n \\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\textit{Half Life: Alyx} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.0098 & 0.0802 & 0.0252 & 0.1265 & 0.0396 & 0.1745 & 0.0082 & 0.0669 & 0.0019 & 0.0158 & 0.0123 & 0.0704 \\\\\n \\textbf{1-shot} & 0.0447 & 0.0764 & 0.0402 & 0.1224 & 0.024 & 0.0733 & 0.0198 & 0.1263 & 0.0425 & 0.0816 & 0.0447 & 0.0967 \\\\\n \\textbf{3-shot} & 0.0725 & 0.1159 & 0.0312 & 0.0725 & 0.0701 & 0.1261 & 0.1349 & 0.2187 & 0.0703 & 0.1094 & 0.087 & 0.1687 \\\\\n \\textbf{5-shot} & 0.123 & 0.1834 & 0.1248 & 0.2382 & 0.0216 & 0.0809 & 0.2089 & 0.2938 & 0.1257 & 0.2409 & 0.1259 & 0.2385 \\\\\n \\bottomrule\n \\end{tabular}\n }\n\n \\label{tab:alyx_sop}\n\\end{table}\n\n\n\n\\begin{table} [htbp!]\n \\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\textit{Half Life: Alyx} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.0785 & 0.1843 & 0.2231 & 0.2089 & 0.2424 & 0.2111 & 0.1989 & 0.1982 & 0.0716 & 0.1187 & 0.1662 & 0.172\\\\\n \\textbf{1-shot}& 0.2562 & 0.235 & 0.3485 & 0.2336 & 0.4184 & 0.2413 & 0.3859 & 0.2654 & 0.3256 & 0.1934 & 0.3872 & 0.2058\\\\\n \\textbf{3-shot} & 0.3072 & 0.2444 & 0.3648 & 0.2414 & 0.5611 & 0.229 & 0.5494 & 0.2887 & 0.3544 & 0.2202 & 0.4599 & 0.2371 \\\\\n \\textbf{5-shot} & 0.425 & 0.2814 & 0.6127 & 0.2856 & 0.6934 & 0.2359 & 0.6299 & 0.315 & 0.4642 & 0.2957 & 0.5152 & 0.2708 \\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{tab:alyx_ssc}\n\\end{table}\n\n\n\\begin{table} [htbp!]\n \\caption{Normalized Step Alignment Score (NSAS) scores comparison of LLMs on \\textit{ Moss: Book II} under different shot settings}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.7819 & 0.0403 & 0.8055 & 0.0717 & 0.7871 & 0.0596 & 0.7994 & 0.0548 & 0.7913 & 0.0595 & 0.7916 & 0.0572 \\\\\n \\textbf{1-shot}& 0.776 & 0.0616 & 0.7993 & 0.0771 & 0.803 & 0.0924 & 0.8139 & 0.0778 & 0.7663 & 0.0793 & 0.7938 & 0.0763 \\\\\n \\textbf{3-shot} & 0.7776 & 0.0889 & 0.818 & 0.0925 & 0.8016 & 0.1242 & 0.8302 & 0.0935 & 0.7613 & 0.1341 & 0.7895 & 0.1371\\\\\n \\textbf{5-shot} & 0.782 & 0.0952 & 0.8243 & 0.102 & 0.8237 & 0.1092 & 0.8478 & 0.1017 & 0.756 & 0.1469 & 0.8232 & 0.105\\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{tab:moss_nsas}\n\\end{table}\n\n\\newpage\n\\begin{table} [htbp!]\n \\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\textit{Moss: Book II} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.0091 & 0.0581 & 0.0263 & 0.1533 & 0.0113 & 0.0494 & 0.0197 & 0.1029 & 0.0052 & 0.033 & 0.0 & 0.0\\\\\n \\textbf{1-shot}& 0.034 & 0.1568 & 0.0663 & 0.2044 & 0.1084 & 0.2486 & 0.1145 & 0.2495 & 0.0739 & 0.1721 & 0.0578 & 0.1486 \\\\\n \\textbf{3-shot} & 0.1581 & 0.242 & 0.1678 & 0.2522 & 0.2324 & 0.3185 & 0.2272 & 0.3324 & 0.1351 & 0.252 & 0.2584 & 0.3089 \\\\\n \\textbf{5-shot} & 0.1686 & 0.244 & 0.2182 & 0.2801 & 0.2998 & 0.3062 & 0.2652 & 0.3596 & 0.1169 & 0.247 & 0.2831 & 0.3097 \\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{tab:moss_sop}\n\\end{table}\n\n\\begin{table} [htbp!]\n \\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\textit{Moss: Book II} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.0715 & 0.1792 & 0.2491 & 0.2844 & 0.2313 & 0.2567 & 0.1763 & 0.221 & 0.0407 & 0.0991 & 0.1208 & 0.1779\\\\\n \\textbf{1-shot}& 0.0748 & 0.1719 & 0.259 & 0.2771 & 0.3682 & 0.3018 & 0.3449 & 0.3396 & 0.1749 & 0.2393 & 0.2319 & 0.293 \\\\\n \\textbf{3-shot} & 0.3349 & 0.3069 & 0.4593 & 0.3309 & 0.5001 & 0.3444 & 0.5238 & 0.3738 & 0.3207 & 0.3105 & 0.4689 & 0.3399 \\\\\n \\textbf{5-shot} & 0.3737 & 0.3213 & 0.4951 & 0.3373 & 0.5562 & 0.3319 & 0.6091 & 0.3476 & 0.2974 & 0.3385 & 0.4567 & 0.3173 \\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{tab:moss_ssc}\n\\end{table}\n\n\n\\begin{table} [htbp!]\n \\caption{Average and standard deviation of Normalized Step Alignment Score (NSAS) scores comparison of LLMs on VR game \\textit{Into the Radius} under different shot settings}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.6165 & 0.0755 & 0.6408 & 0.0955 & 0.5939 & 0.1306 & 0.6492 & 0.1018 & 0.6644 & 0.0718 & 0.6447 & 0.0882 \\\\\n \\textbf{1-shot} & 0.641 & 0.1177 & 0.6519 & 0.1421 & 0.6282 & 0.1687 & 0.6875 & 0.1159 & 0.6285 & 0.1684 & 0.6285 & 0.1346 \\\\\n \\textbf{3-shot} & 0.6305 & 0.128 & 0.6802 & 0.1645 & 0.6491 & 0.2057 & 0.6634 & 0.1638 & 0.618 & 0.1633 & 0.6479 & 0.1606 \\\\\n \\textbf{5-shot} & 0.6621 & 0.1291 & 0.6927 & 0.1721 & 0.6984 & 0.2136 & 0.6818 & 0.1191 & 0.666 & 0.1495 & 0.6443 & 0.211\\\\\n \\bottomrule\n \\end{tabular}\n }\n\n \\label{tab:radius_nsas}\n\\end{table}\n\n\\begin{table} [htbp!]\n \\caption{Average and standard deviation of Sequential Order Preservation (SOP) scores comparison of LLMs on \\textit{Into the Radius} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.0091 & 0.0581 & 0.0263 & 0.1533 & 0.0113 & 0.0494 & 0.0197 & 0.1029 & 0.0052 & 0.033 & 0.0 & 0.0\\\\\n \\textbf{1-shot}& 0.034 & 0.1568 & 0.0663 & 0.2044 & 0.1084 & 0.2486 & 0.1145 & 0.2495 & 0.0739 & 0.1721 & 0.0578 & 0.1486 \\\\\n \\textbf{3-shot} & 0.1581 & 0.242 & 0.1678 & 0.2522 & 0.2324 & 0.3185 & 0.2272 & 0.3324 & 0.1351 & 0.252 & 0.2584 & 0.3089 \\\\\n \\textbf{5-shot} & 0.1686 & 0.244 & 0.2182 & 0.2801 & 0.2998 & 0.3062 & 0.2652 & 0.3596 & 0.1169 & 0.247 & 0.2831 & 0.3097 \\\\\n \\bottomrule\n \\end{tabular}\n }\n\n \\label{tab:radius_sop}\n\\end{table}\n\n\\begin{table} [htbp!]\n \\caption{Average and standard deviation of Semantic Step Coverage (SSC) scores comparison of LLMs on \\textit{Into the Radius} under different shot settings.}\n \\centering\n \\resizebox{\\textwidth}{!}{%\n \\renewcommand{\\arraystretch}{1.5}\n \\begin{tabular}{l|cc|cc|cc|cc|cc|cc}\n \\toprule\n \\textbf{Model} & \\multicolumn{2}{c|}{\\textbf{GPT-3.5-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4-turbo}} & \\multicolumn{2}{c|}{\\textbf{GPT-4o}} & \\multicolumn{2}{c|}{\\textbf{Gemini-1.5-Pro}} & \\multicolumn{2}{c|} {\\textbf{Mixtral-8x7B}} &\n \\multicolumn{2}{c}{\\textbf{LLaMA-3-8b}} \\\\\n \\midrule\n \\textbf{Metrics} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} & \\textbf{avg} & \\textbf{std} \\\\\n \\midrule\n \\textbf{Zero-Shot} & 0.0354 & 0.0982 & 0.1528 & 0.1774 & 0.2199 & 0.1745 & 0.1783 & 0.2107 & 0.0406 & 0.0899 & 0.1243 & 0.1655\\\\\n \\textbf{1-shot}& 0.1511 & 0.2246 & 0.304 & 0.2983 & 0.4102 & 0.2585 & 0.2823 & 0.3277 & 0.2593 & 0.3249 & 0.3171 & 0.269\\\\\n \\textbf{3-shot}& 0.2321 & 0.2713 & 0.4463 & 0.3099 & 0.5623 & 0.2976 & 0.3402 & 0.3379 & 0.3544 & 0.2621 & 0.5319 & 0.2382\\\\\n \\textbf{5-shot}& 0.3302 & 0.3115 & 0.5082 & 0.3063 & 0.6194 & 0.2877 & 0.2971 & 0.3187 & 0.285 & 0.3384 & 0.5314 & 0.2886\\\\\n \\bottomrule\n \\end{tabular}\n }\n \\label{tab:radius_ssc}\n\\end{table}\n\n\\newpage\n\\begin{figure} [htbp!]\n \\centering\n\\includegraphics[width=1.2\\linewidth, height=0.9\\textheight, keepaspectratio]{Figures/nsas_barh_4x1.png}\n \\caption{LLMs NSAS (avg) by Different Shot Setting Across Four VR Games}\n \\vspace{0.8em}\n \\label{fig:nsas_barh}\n\\end{figure}\n\n\\begin{figure} [htbp!]\n\\centering\n \\includegraphics[width=1.2\\linewidth, height=0.9\\textheight, keepaspectratio]{Figures/sop_barh_4x1.png}\n \\caption{LLMs SOP (avg) by Different Shot Setting Across Four VR Games}\n\\vspace{0.8em}\n\\label{fig:sop_barh}\n\\end{figure}\n\n\\begin{figure} [htbp!]\n\\centering\n \\includegraphics[width=1.2\\linewidth, height=1.0\\textheight, keepaspectratio]{Figures/ssc_barh_4x1.png}\n \\caption{LLMs SSC (avg) by Different Shot Setting Across Four VR Games}\n\\vspace{0.8em}\n\\label{fig:ssc_barh}\n\\end{figure}\n\n\\FloatBarrier\n\\subsection{Cross-Game Generalization Patterns}\n\nThe cross-game performance analysis reveals important insights about model generalization capabilities. Models that perform well on one game do not necessarily maintain their advantage across others. For example, while GPT-4o achieves the highest SOP score in Into the Radius (0.291), it performs poorly in Half-Life: Alyx (0.022). This game-specific variation suggests that models may overfit to particular interaction patterns rather than developing general VR manipulation capabilities.\n\nThe \"Game Gap\" metric in the table~\\ref{tab:cross_game_variation} quantifies this generalization challenge. Lower values indicate more consistent cross-game performance. Mixtral-8x7B achieves the lowest Game Gap (0.070), despite not leading in any individual game. This consistency might make it more suitable for applications requiring reliable performance across diverse VR experiences. In contrast, GPT-4o's high Game Gap (0.127) reflects its specialized strengths and weaknesses across different interaction paradigms.\n\nAnalysis of confusion patterns reveals that models struggle most when transitioning between games with different control schemes. The shift from Vivecraft's discrete block interactions to Half-Life: Alyx's continuous physics manipulation represents a fundamental change in how actions map to controller inputs. Models trained primarily on text lack the embodied experience to navigate these transitions smoothly, often applying inappropriate interaction patterns learned from one context to another.\n\n\\subsection{Temporal Dynamics in Sequential Tasks}\n\nDetailed examination of step-by-step performance reveals how models handle temporal dependencies in VR interactions. Early steps in sequences generally show higher accuracy (NSAS > 0.9) across all models, with performance degrading for later steps. This degradation is particularly severe for steps that depend on the successful completion of previous actions. For instance, in a sequence like \"pick up object, aim at target, throw object,\" models may correctly identify all three actions but fail to recognize that aiming requires successfully completing the pickup action first.\n\nThe SOP metric specifically captures these temporal dependencies, and the low scores across all models highlight a fundamental limitation in current architectures. Even with few-shot examples that demonstrate correct ordering, models struggle to internalize the causal relationships between steps. This suggests that improved performance may require architectural innovations that better capture temporal and causal reasoning, rather than simply scaling existing approaches.\n\nError analysis reveals common patterns in temporal mistakes. Models frequently suggest parallel actions that must be performed sequentially (e.g., \"press trigger while reaching for object\" when the trigger can only be meaningfully pressed after grasping). They also struggle with iterative processes, often omitting loop conditions or termination criteria. These patterns indicate that models lack an understanding of the physical constraints that govern VR interactions.\n\n\\subsection{Detailed Performance Tables and Visualizations}\n\nThe table~\\ref{tab:overall_performance_2} provides granular data for researchers seeking to understand specific model behaviors. These tables reveal several noteworthy patterns. First, the relationship between different metrics is non-linear. High NSAS scores do not guarantee good SOP performance, and models with similar average scores may achieve them through different strengths. This multidimensional performance landscape suggests that selecting models for specific applications requires careful consideration of which capabilities are most critical.\n\nThe table~\\ref{tab:overall_performance_2} illustrates the strict matching process, highlighting why SSM scores remain low even for generally capable models. The requirement for exact sequence length and step-by-step correspondence proves extremely demanding. Even minor variations in phrasing or step granularity result in match failures. This visualization helps explain why SSM may be overly strict for practical applications, where functional equivalence matters more than exact replication.\n\nThe table~\\ref{tab:overall_performance_2} demonstrates the more nuanced evaluation approach that underlies our NSAS and SOP metrics. By identifying the longest common subsequences with semantic matching, these metrics better capture functional understanding while still penalizing significant deviations from ground truth. The visualization shows how models might achieve reasonable NSAS scores by identifying most relevant actions while still failing SOP evaluation due to ordering errors.\n\nThe heat maps of model performance across game-task combinations reveal clustering of difficulty. Certain task types (e.g., combat sequences in Half-Life: Alyx, inventory management in Into the Radius) consistently challenge all models, while others (e.g., block placement in Vivecraft) show near-ceiling performance. These patterns suggest that targeted improvements for specific interaction types might yield better results than general capability enhancement.\n\n\\subsection{Implications for Future Research}\n\nThe detailed experimental results paint a complex picture of current LLM capabilities and limitations in VR interaction reasoning. While models demonstrate competence in identifying relevant actions and decomposing high-level goals, they consistently struggle with the procedural and embodied aspects of VR interaction. The strong effect of few-shot examples suggests that current models possess latent capabilities that can be activated through appropriate prompting, but fundamental architectural limitations prevent them from achieving human-like understanding of physical manipulation sequences.\n\nThe high variance in performance across games and tasks indicates that robustness remains a significant challenge. Models that excel in one context may fail dramatically in another, limiting their practical applicability. This brittleness likely stems from the discrete nature of text-based training, which lacks the continuous, embodied experience that humans leverage when learning new physical tasks.\n\nMoving forward, these results suggest several promising research directions. Multimodal models that incorporate visual and proprioceptive information alongside text may better capture the embodied nature of VR interactions. Explicit modeling of temporal and causal relationships could address the procedural reasoning gaps identified in our experiments. Finally, training on synthetic VR interaction data or through simulated embodiment might provide models with the experiential knowledge currently lacking in text-only approaches.\n\nThe detailed results also highlight the importance of comprehensive evaluation frameworks that assess multiple dimensions of capability. Single metrics fail to capture the complexity of VR interaction reasoning, and future benchmarks should continue to embrace multidimensional evaluation approaches that can identify specific strengths and weaknesses in model capabilities.\n\n\n\n\n\n\n\\section{Discussion, Limitations \\& Broader Impacts}\n\\label{subsec:discussion}\n\nOur investigation into LLMs' ability to translate semantic actions into VR device manipulations reveals both promising capabilities and fundamental limitations that reflect broader challenges in bridging linguistic understanding and embodied interaction. The relatively low Sequential Order Preservation (SOP) scores across all evaluated models indicate that current LLMs struggle with the temporal reasoning required for complex procedural tasks. This limitation suggests that while LLMs can identify relevant actions and understand their purposes, they lack the embodied experience necessary to accurately sequence physical manipulations.\n\nThe substantial performance variations across different VR games highlight how interaction complexity and consistency impact model performance. Games with standardized, discrete actions (like Vivecraft's block-based interactions) prove more amenable to LLM reasoning than those requiring nuanced controller movements or complex spatial reasoning (like Half-Life: Alyx). This pattern suggests that current language models may benefit from more structured representations of physical actions and explicit training on procedural sequences.\n\nThe significant improvement from few-shot examples demonstrates that LLMs possess latent capabilities for VR interaction reasoning that can be activated through appropriate prompting. However, the fact that performance plateaus with additional examples indicates fundamental architectural limitations rather than simple lack of exposure to relevant examples. This finding suggests that advances in VR-capable AI may require new training paradigms that incorporate spatial and temporal reasoning more directly.\n\nFrom a broader perspective, this work carries important implications for the future of human-computer interaction and AI development. On the positive side, LLMs that can effectively reason about VR interactions could dramatically improve accessibility for users with motor impairments, enable more intuitive natural language interfaces for VR applications, and accelerate the development of intelligent tutoring systems for VR training scenarios. The potential transfer of these capabilities to robotic systems could enable more sophisticated human-robot collaboration in both virtual and physical environments.\n\nHowever, we must also consider potential negative implications. As LLMs gain greater agency in controlling virtual (and potentially physical) systems, questions of safety, security, and user autonomy become paramount. The ability to translate high-level commands into detailed manipulation sequences could be exploited for unauthorized system control or social engineering attacks. Additionally, the computational resources required for training and deploying such models raise environmental concerns that must be balanced against their benefits.\n\nThe digital divide may be exacerbated as advanced VR-AI systems require substantial hardware investments and technical expertise. Ensuring equitable access to these technologies will require conscious effort from researchers, developers, and policymakers. Privacy concerns also emerge as these systems necessarily monitor and analyze detailed user movement patterns and interaction behaviors.\n\nMoving forward, the field must pursue responsible development practices that prioritize user safety, privacy, and autonomy while advancing the technical capabilities of VR-AI systems. This includes developing robust evaluation frameworks that assess not only task performance but also failure modes, implementing transparent systems that users can understand and control, and ensuring that advances in VR interaction AI serve to augment rather than replace human agency in virtual environments.\n\n\n\\section{Large Language Models Usage Statement}\n\nThis work incorporated LLMs to aid in editorial refinement and linguistic improvement of the manuscript. The models provided assistance with stylistic enhancements and clarity optimization, including tasks such as rephrasing sentences and correcting grammatical errors.\n\nWe explicitly note that LLMs played no role in the conceptualization, theoretical development, or experimental design aspects of this research. The authors retain full responsibility for the entirety of the manuscript's content, including sections improved with LLM support. All LLM-assisted text has been carefully reviewed to ensure adherence to academic standards and ethical research practices.\n\\end{document}\n"},"question":{"kind":"string","value":"Among model rows (excluding Human), identify all model-game pairs where the same model has at least one best and one second best metric within that game. Which pair has the highest value for the sum of NSAS-SSC and F1_SOP-SOP? For that model, how many of its metrics exceed the Human row?"},"answer":{"kind":"string","value":"GPT-4o -- Vivecraft, 12"},"plan":{"kind":"string","value":"SELECT all models except Human\nLOOP for each model\n SELECT all games\n LOOP for each game\n COMPUTE best_metrics_in_game = number of metric types where this model is bolded in this game\n COMPUTE second_metrics_in_game = number of metric types where this model is underlined in this game\n IF best_metrics_in_game > 0 AND second_metrics_in_game > 0\n COMPUTE combined_score = (NSAS-SSC) + (F1_SOP-SOP)\nCOMPUTE target_model–target_game = argmax model–game pair over combined_score\n\n\nCOMPUTE exceed_count = 0\nSELECT all metrics\nLOOP for each metric\n IF target_model metric value > Human metric value\n COMPUTE increase exceed_count\n\n\nRETURN target_model–target_game, exceed_count\n"}}},{"rowIdx":366,"cells":{"paper":{"kind":"string","value":"2511.01815"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t!]\n"," \\caption{\\small Accuracy of KV cache compression methods. Results within $1$ score point of vanilla are in \\textbf{bold}. See Appendix \\ref{sec:appendix_stderr} for standard error analysis. \\methodopcrdef{}{\\mathrm{CR}} denotes \\Method{} set for $\\mathrm{CR}\\times$ compression before applying DEFLATE.}\n"," \\label{tab:nonthinking-results}\n"," \\centering\n"," \\setlength{\\tabcolsep}{1mm}\n"," \\resizebox{0.85\\textwidth}{!}{%\n"," \\begin{tabular}{lc|cccccccccc}\n"," \\toprule\n"," & Vanilla & \\makecell{GEAR$_\\text{2-bit}$} & \\makecell{KIVI$_\\text{2-bit}$} & \\HTO{} & \\TOVA{} & xKV & FP8 & \\methodopcrdef{4}{8} & \\methodopcrdef{4}{16} & \\methodopcrdef{4}{32} & \\methodopcrdef{4}{64} \\\\\n"," \\midrule\n"," \\multicolumn{12}{c}{\\tabwithinbest{}Llama 3.1 8B}\\\\\n"," CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{9}{10} & \\crinterval{18}{22} & \\crinterval{34}{44} & \\crinterval{60}{88} \\\\\n"," GSM8K & \\textbf{56.8} & 52.8 & 52.8 & 54.3 & 54.5 & \\textbf{56.6} & 55.2 & \\textbf{57.0} & \\textbf{56.9} & \\textbf{57.8} & \\textbf{57.2} \\\\\n"," MMLU & \\textbf{60.5} & \\textbf{59.6} & \\textbf{59.6} & 44.3 & 44.8 & \\textbf{59.5} & \\textbf{60.1} & \\textbf{59.8} & \\textbf{60.1} & \\textbf{60.6} & \\textbf{60.7} \\\\\n"," QASPER & \\textbf{40.4} & \\textbf{40.4} & 39.1 & 34.3 & 38.6 & 35.6 & \\textbf{40.8} & \\textbf{40.1} & \\textbf{40.7} & \\textbf{39.4} & 37.8 \\\\\n"," LITM & \\textbf{99.4} & 96.9 & 88.8 & 20.2 & 1.2 & \\textbf{99.9} & \\textbf{99.4} & \\textbf{99.3} & \\textbf{99.3} & \\textbf{99.1} & 90.2 \\\\\n"," RULER-VT & \\textbf{99.8} & \\textbf{99.8} & \\textbf{98.9} & 50.4 & \\textbf{99.7} & \\textbf{99.8} & \\textbf{99.9} & \\textbf{99.1} & \\textbf{99.1} & \\textbf{98.9} & 95.9 \\\\\n"," \\midrule\n"," \\multicolumn{12}{c}{\\tabwithinbest{}MN‑Minitron 8B}\\\\\n"," CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{10}{11} & \\crinterval{17}{21} & \\crinterval{32}{46} & \\crinterval{53}{95} \\\\\n"," GSM8K & \\textbf{59.1} & 57.9 & 58.0 & 55.3 & \\textbf{59.2} & \\textbf{59.3} & \\textbf{60.1} & \\textbf{60.6} & \\textbf{60.3} & \\textbf{59.1} & 57.8 \\\\\n"," MMLU & \\textbf{64.3} & \\textbf{63.6} & \\textbf{63.2} & 43.5 & 48.1 & 63.1 & \\textbf{64.3} & \\textbf{64.2} & \\textbf{64.1} & \\textbf{63.7} & 62.1 \\\\\n"," QASPER & \\textbf{38.2} & \\textbf{38.2} & \\textbf{38.2} & 30.0 & 33.9 & 34.5 & \\textbf{38.3} & \\textbf{39.1} & \\textbf{38.6} & \\textbf{37.7} & \\textbf{38.1} \\\\\n"," LITM & \\textbf{99.8} & 96.0 & 86.3 & 16.6 & 0.3 & \\textbf{99.6} & \\textbf{99.8} & \\textbf{99.4} & \\textbf{99.3} & 86.9 & 59.5 \\\\\n"," RULER-VT & \\textbf{99.4} & 98.3 & 96.8 & 39.2 & \\textbf{99.3} & \\textbf{99.1} & \\textbf{99.2} & \\textbf{98.8} & \\textbf{98.8} & 96.0 & 93.4 \\\\\n"," \\midrule\n","\\multicolumn{12}{c}{\\tabwithinbest{}Mistral NeMo 12B}\\\\\n"," CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{10}{11} & \\crinterval{17}{20} & \\crinterval{31}{43} & \\crinterval{51}{87} \\\\\n"," GSM8K & \\textbf{61.9} & 59.8 & 59.7 & 57.0 & 60.3 & \\textbf{61.9} & \\textbf{61.7} & \\textbf{62.5} & \\textbf{62.0} & \\textbf{62.2} & \\textbf{61.9} \\\\\n"," MMLU & \\textbf{64.5} & \\textbf{64.0} & \\textbf{64.3} & 45.4 & 49.0 & \\textbf{63.9} & \\textbf{64.5} & \\textbf{64.6} & \\textbf{64.4} & \\textbf{63.8} & 61.4 \\\\\n"," QASPER & \\textbf{38.4} & \\textbf{38.6} & \\textbf{38.2} & 29.5 & 36.0 & 33.5 & \\textbf{37.9} & \\textbf{37.6} & \\textbf{37.6} & \\textbf{37.5} & \\textbf{38.0} \\\\\n"," LITM & \\textbf{99.5} & 96.9 & 91.9 & 16.2 & 8.7 & 97.9 & \\textbf{99.0} & \\textbf{99.9} & \\textbf{99.8} & \\textbf{99.6} & 95.3 \\\\\n"," RULER-VT & \\textbf{99.8} & \\textbf{99.4} & 98.3 & 35.2 & \\textbf{99.6} & \\textbf{99.4} & \\textbf{99.8} & \\textbf{99.5} & \\textbf{99.5} & \\textbf{98.9} & 98.0 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\caption{\\\\small Accuracy of KV cache compression methods. Results within $1$ score point of vanilla are in \\\\textbf{bold}. See Appendix \\\\ref{sec:appendix_stderr} for standard error analysis. \\\\methodopcrdef{}{\\\\mathrm{CR}} denotes \\\\Method{} set for $\\\\mathrm{CR}\\\\times$ compression before applying DEFLATE.}\\n\",\n \" \\\\label{tab:nonthinking-results}\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \" \\\\resizebox{0.85\\\\textwidth}{!}{%\\n\",\n \" \\\\begin{tabular}{lc|cccccccccc}\\n\",\n \" \\\\toprule\\n\",\n \" & Vanilla & \\\\makecell{GEAR$_\\\\text{2-bit}$} & \\\\makecell{KIVI$_\\\\text{2-bit}$} & \\\\HTO{} & \\\\TOVA{} & xKV & FP8 & \\\\methodopcrdef{4}{8} & \\\\methodopcrdef{4}{16} & \\\\methodopcrdef{4}{32} & \\\\methodopcrdef{4}{64} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{12}{c}{\\\\tabwithinbest{}Llama 3.1 8B}\\\\\\\\\\n\",\n \" CR & $1$ & \\\\gearcr{} & \\\\kivicr{} & $8$ & $8$ & \\\\crinterval{1}{5} & 2 & \\\\crinterval{9}{10} & \\\\crinterval{18}{22} & \\\\crinterval{34}{44} & \\\\crinterval{60}{88} \\\\\\\\\\n\",\n \" GSM8K & \\\\textbf{56.8} & 52.8 & 52.8 & 54.3 & 54.5 & \\\\textbf{56.6} & 55.2 & \\\\textbf{57.0} & \\\\textbf{56.9} & \\\\textbf{57.8} & \\\\textbf{57.2} \\\\\\\\\\n\",\n \" MMLU & \\\\textbf{60.5} & \\\\textbf{59.6} & \\\\textbf{59.6} & 44.3 & 44.8 & \\\\textbf{59.5} & \\\\textbf{60.1} & \\\\textbf{59.8} & \\\\textbf{60.1} & \\\\textbf{60.6} & \\\\textbf{60.7} \\\\\\\\\\n\",\n \" QASPER & \\\\textbf{40.4} & \\\\textbf{40.4} & 39.1 & 34.3 & 38.6 & 35.6 & \\\\textbf{40.8} & \\\\textbf{40.1} & \\\\textbf{40.7} & \\\\textbf{39.4} & 37.8 \\\\\\\\\\n\",\n \" LITM & \\\\textbf{99.4} & 96.9 & 88.8 & 20.2 & 1.2 & \\\\textbf{99.9} & \\\\textbf{99.4} & \\\\textbf{99.3} & \\\\textbf{99.3} & \\\\textbf{99.1} & 90.2 \\\\\\\\\\n\",\n \" RULER-VT & \\\\textbf{99.8} & \\\\textbf{99.8} & \\\\textbf{98.9} & 50.4 & \\\\textbf{99.7} & \\\\textbf{99.8} & \\\\textbf{99.9} & \\\\textbf{99.1} & \\\\textbf{99.1} & \\\\textbf{98.9} & 95.9 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{12}{c}{\\\\tabwithinbest{}MN‑Minitron 8B}\\\\\\\\\\n\",\n \" CR & $1$ & \\\\gearcr{} & \\\\kivicr{} & $8$ & $8$ & \\\\crinterval{1}{5} & 2 & \\\\crinterval{10}{11} & \\\\crinterval{17}{21} & \\\\crinterval{32}{46} & \\\\crinterval{53}{95} \\\\\\\\\\n\",\n \" GSM8K & \\\\textbf{59.1} & 57.9 & 58.0 & 55.3 & \\\\textbf{59.2} & \\\\textbf{59.3} & \\\\textbf{60.1} & \\\\textbf{60.6} & \\\\textbf{60.3} & \\\\textbf{59.1} & 57.8 \\\\\\\\\\n\",\n \" MMLU & \\\\textbf{64.3} & \\\\textbf{63.6} & \\\\textbf{63.2} & 43.5 & 48.1 & 63.1 & \\\\textbf{64.3} & \\\\textbf{64.2} & \\\\textbf{64.1} & \\\\textbf{63.7} & 62.1 \\\\\\\\\\n\",\n \" QASPER & \\\\textbf{38.2} & \\\\textbf{38.2} & \\\\textbf{38.2} & 30.0 & 33.9 & 34.5 & \\\\textbf{38.3} & \\\\textbf{39.1} & \\\\textbf{38.6} & \\\\textbf{37.7} & \\\\textbf{38.1} \\\\\\\\\\n\",\n \" LITM & \\\\textbf{99.8} & 96.0 & 86.3 & 16.6 & 0.3 & \\\\textbf{99.6} & \\\\textbf{99.8} & \\\\textbf{99.4} & \\\\textbf{99.3} & 86.9 & 59.5 \\\\\\\\\\n\",\n \" RULER-VT & \\\\textbf{99.4} & 98.3 & 96.8 & 39.2 & \\\\textbf{99.3} & \\\\textbf{99.1} & \\\\textbf{99.2} & \\\\textbf{98.8} & \\\\textbf{98.8} & 96.0 & 93.4 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\\\multicolumn{12}{c}{\\\\tabwithinbest{}Mistral NeMo 12B}\\\\\\\\\\n\",\n \" CR & $1$ & \\\\gearcr{} & \\\\kivicr{} & $8$ & $8$ & \\\\crinterval{1}{5} & 2 & \\\\crinterval{10}{11} & \\\\crinterval{17}{20} & \\\\crinterval{31}{43} & \\\\crinterval{51}{87} \\\\\\\\\\n\",\n \" GSM8K & \\\\textbf{61.9} & 59.8 & 59.7 & 57.0 & 60.3 & \\\\textbf{61.9} & \\\\textbf{61.7} & \\\\textbf{62.5} & \\\\textbf{62.0} & \\\\textbf{62.2} & \\\\textbf{61.9} \\\\\\\\\\n\",\n \" MMLU & \\\\textbf{64.5} & \\\\textbf{64.0} & \\\\textbf{64.3} & 45.4 & 49.0 & \\\\textbf{63.9} & \\\\textbf{64.5} & \\\\textbf{64.6} & \\\\textbf{64.4} & \\\\textbf{63.8} & 61.4 \\\\\\\\\\n\",\n \" QASPER & \\\\textbf{38.4} & \\\\textbf{38.6} & \\\\textbf{38.2} & 29.5 & 36.0 & 33.5 & \\\\textbf{37.9} & \\\\textbf{37.6} & \\\\textbf{37.6} & \\\\textbf{37.5} & \\\\textbf{38.0} \\\\\\\\\\n\",\n \" LITM & \\\\textbf{99.5} & 96.9 & 91.9 & 16.2 & 8.7 & 97.9 & \\\\textbf{99.0} & \\\\textbf{99.9} & \\\\textbf{99.8} & \\\\textbf{99.6} & 95.3 \\\\\\\\\\n\",\n \" RULER-VT & \\\\textbf{99.8} & \\\\textbf{99.4} & 98.3 & 35.2 & \\\\textbf{99.6} & \\\\textbf{99.4} & \\\\textbf{99.8} & \\\\textbf{99.5} & \\\\textbf{99.5} & \\\\textbf{98.9} & 98.0 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}[t]\n"," \\centering\n"," \\subfloat[Keys]{\n"," \\centering\n"," \\includegraphics[width=0.48\\linewidth]{figures/cosine_keys.pdf}\n"," \\label{fig:kv-cache-between-heads-key}\n"," }\n"," \\subfloat[Values]{\n"," \\centering\n"," \\includegraphics[width=0.48\\linewidth]{figures/cosine_values.pdf}\n"," \\label{fig:kv-cache-between-heads-value}\n"," }\n"," \\caption{Cosine similarity before and after alignment between key (a) and value (b) heads calculated using Llama 3.1 8B on inputs from Qasper \\citep{dasigi2021datasetinformationseekingquestionsanswers,shaham2022scrollsstandardizedcomparisonlong}. For each example, we calculate cosine similarity between all keys/values from the same position and then average across the batch. Orthonormal alignment matrices were produced using 20 samples from the RedPajama v2 \\citep{weber2024redpajama}.}\n"," \\label{fig:kv-cache-between-heads}\n","\\end{figure*}\n"],["\\begin{figure*}[t]\n"," \\centering %\n"," \\subfloat[Attention sink compression ablation]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/ablations/omit_compression_of_sinks.pdf}\n"," }\n"," \\subfloat[Sliding window compression ablation]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/ablations/kvtc_vs_kvtc_without_sliding_window.pdf}\n"," }\n"," \\caption{\n","Ablation of \\Method{} with compression ratio 64$\\times$ on Llama 3.1 8B: (a) compression disabled for attention sink tokens; (b) compression disabled for the final 128 tokens. All other settings are fixed. Additional ablations are provided in \\cref{sec:appendix:ablate_sink,sec:appendix:sec-kvtc-ws-ablate}.\n","}\n"," \\label{fig:kv-ablate-sinks-and-sw}\n","\\end{figure*}\n"],["\\begin{figure*}[t]\n"," \\centering\n"," \\includegraphics[scale=0.62]{figures/pca_dataset_error.pdf}\n"," \\hspace{-3mm}\n"," \\includegraphics[scale=0.62]{figures/pca_reconstruct_error.pdf}\n"," \\includegraphics[scale=0.62]{figures/bit_assignment2.pdf}\n"," \\caption{Calibration of Llama 3.1 8B with \\Method{}. \\textbf{Left:} Reconstruction error as a function of the size of calibration set. The arrow $A\\rightarrow B$ denotes fitting PCA on dataset A and calculating the error on B.\n"," \\textbf{Middle:} The reconstruction error as a function of position in the context. The error is higher for the sink tokens. \\textbf{Right:} Bit assignment computed via dynamic programming, counting in the per-group scaling factors.}\n"," \\label{fig:kv-pca-train}\n","\\end{figure*}\n"],["\\begin{table*}[t!]\n"," \\caption{\\small Accuracy of KV cache compression methods. Results within $1$ score point of vanilla are in \\textbf{bold}. See Appendix \\ref{sec:appendix_stderr} for standard error analysis. \\methodopcrdef{}{\\mathrm{CR}} denotes \\Method{} set for $\\mathrm{CR}\\times$ compression before applying DEFLATE.}\n"," \\label{tab:nonthinking-results}\n"," \\centering\n"," \\setlength{\\tabcolsep}{1mm}\n"," \\resizebox{0.85\\textwidth}{!}{%\n"," \\begin{tabular}{lc|cccccccccc}\n"," \\toprule\n"," & Vanilla & \\makecell{GEAR$_\\text{2-bit}$} & \\makecell{KIVI$_\\text{2-bit}$} & \\HTO{} & \\TOVA{} & xKV & FP8 & \\methodopcrdef{4}{8} & \\methodopcrdef{4}{16} & \\methodopcrdef{4}{32} & \\methodopcrdef{4}{64} \\\\\n"," \\midrule\n"," \\multicolumn{12}{c}{\\tabwithinbest{}Llama 3.1 8B}\\\\\n"," CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{9}{10} & \\crinterval{18}{22} & \\crinterval{34}{44} & \\crinterval{60}{88} \\\\\n"," GSM8K & \\textbf{56.8} & 52.8 & 52.8 & 54.3 & 54.5 & \\textbf{56.6} & 55.2 & \\textbf{57.0} & \\textbf{56.9} & \\textbf{57.8} & \\textbf{57.2} \\\\\n"," MMLU & \\textbf{60.5} & \\textbf{59.6} & \\textbf{59.6} & 44.3 & 44.8 & \\textbf{59.5} & \\textbf{60.1} & \\textbf{59.8} & \\textbf{60.1} & \\textbf{60.6} & \\textbf{60.7} \\\\\n"," QASPER & \\textbf{40.4} & \\textbf{40.4} & 39.1 & 34.3 & 38.6 & 35.6 & \\textbf{40.8} & \\textbf{40.1} & \\textbf{40.7} & \\textbf{39.4} & 37.8 \\\\\n"," LITM & \\textbf{99.4} & 96.9 & 88.8 & 20.2 & 1.2 & \\textbf{99.9} & \\textbf{99.4} & \\textbf{99.3} & \\textbf{99.3} & \\textbf{99.1} & 90.2 \\\\\n"," RULER-VT & \\textbf{99.8} & \\textbf{99.8} & \\textbf{98.9} & 50.4 & \\textbf{99.7} & \\textbf{99.8} & \\textbf{99.9} & \\textbf{99.1} & \\textbf{99.1} & \\textbf{98.9} & 95.9 \\\\\n"," \\midrule\n"," \\multicolumn{12}{c}{\\tabwithinbest{}MN‑Minitron 8B}\\\\\n"," CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{10}{11} & \\crinterval{17}{21} & \\crinterval{32}{46} & \\crinterval{53}{95} \\\\\n"," GSM8K & \\textbf{59.1} & 57.9 & 58.0 & 55.3 & \\textbf{59.2} & \\textbf{59.3} & \\textbf{60.1} & \\textbf{60.6} & \\textbf{60.3} & \\textbf{59.1} & 57.8 \\\\\n"," MMLU & \\textbf{64.3} & \\textbf{63.6} & \\textbf{63.2} & 43.5 & 48.1 & 63.1 & \\textbf{64.3} & \\textbf{64.2} & \\textbf{64.1} & \\textbf{63.7} & 62.1 \\\\\n"," QASPER & \\textbf{38.2} & \\textbf{38.2} & \\textbf{38.2} & 30.0 & 33.9 & 34.5 & \\textbf{38.3} & \\textbf{39.1} & \\textbf{38.6} & \\textbf{37.7} & \\textbf{38.1} \\\\\n"," LITM & \\textbf{99.8} & 96.0 & 86.3 & 16.6 & 0.3 & \\textbf{99.6} & \\textbf{99.8} & \\textbf{99.4} & \\textbf{99.3} & 86.9 & 59.5 \\\\\n"," RULER-VT & \\textbf{99.4} & 98.3 & 96.8 & 39.2 & \\textbf{99.3} & \\textbf{99.1} & \\textbf{99.2} & \\textbf{98.8} & \\textbf{98.8} & 96.0 & 93.4 \\\\\n"," \\midrule\n","\\multicolumn{12}{c}{\\tabwithinbest{}Mistral NeMo 12B}\\\\\n"," CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{10}{11} & \\crinterval{17}{20} & \\crinterval{31}{43} & \\crinterval{51}{87} \\\\\n"," GSM8K & \\textbf{61.9} & 59.8 & 59.7 & 57.0 & 60.3 & \\textbf{61.9} & \\textbf{61.7} & \\textbf{62.5} & \\textbf{62.0} & \\textbf{62.2} & \\textbf{61.9} \\\\\n"," MMLU & \\textbf{64.5} & \\textbf{64.0} & \\textbf{64.3} & 45.4 & 49.0 & \\textbf{63.9} & \\textbf{64.5} & \\textbf{64.6} & \\textbf{64.4} & \\textbf{63.8} & 61.4 \\\\\n"," QASPER & \\textbf{38.4} & \\textbf{38.6} & \\textbf{38.2} & 29.5 & 36.0 & 33.5 & \\textbf{37.9} & \\textbf{37.6} & \\textbf{37.6} & \\textbf{37.5} & \\textbf{38.0} \\\\\n"," LITM & \\textbf{99.5} & 96.9 & 91.9 & 16.2 & 8.7 & 97.9 & \\textbf{99.0} & \\textbf{99.9} & \\textbf{99.8} & \\textbf{99.6} & 95.3 \\\\\n"," RULER-VT & \\textbf{99.8} & \\textbf{99.4} & 98.3 & 35.2 & \\textbf{99.6} & \\textbf{99.4} & \\textbf{99.8} & \\textbf{99.5} & \\textbf{99.5} & \\textbf{98.9} & 98.0 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," }\n","\\end{table*}\n"],["\\begin{table}[t]\n"," \\centering\n"," \\begin{minipage}[t]{0.46\\textwidth}\n"," \\caption{Compression applied to a model which is split across four GPUs (pipeline parallel), with KV cache chunks being compressed separately with \\Method{}.\n"," In certain scenarios, like offloading to CPU RAM, these chunks could be compressed jointly for higher accuracy.\n"," }\n"," \\label{tab:llama-33-70b}\n"," \\small\n"," \\centering\n","\\vspace{0.4cm}\n"," \\begin{tabular}{l|ccc}\n"," \\toprule\n"," \\multirow{1}{*}{Method} & MATH-500 & NIAH & LITM\\\\\n"," \\midrule\n"," \\multicolumn{4}{c}{\\tabwithinbest{}Llama 3.3 70B Instruct} \\\\\n"," Vanilla & $75.6_{1.92}$ & 100.0 & 100.0 \\\\\n"," \\methodopcrdef{4}{8} & $73.2_{1.98}$ & 100.0 & 100.0 \\\\\n"," \\methodopcrdef{4}{10} & $74.4_{1.95}$ & 100.0 & 100.0 \\\\\n"," \\methodopcrdef{4}{16} & $73.2_{1.98}$ & 100.0 & 100.0 \\\\\n"," \\methodopcrdef{4}{20} & $72.6_{1.99}$ & 100.0 & 100.0 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n"," \n"," \\end{minipage}\\hfill\n"," \\begin{minipage}[t]{0.50\\textwidth}\n","\\small\n"," \\caption{Latency of a simple implementation based on the Transformers library \\citep{transformers}, measured on an NVIDIA H100 GPU using Mistral NeMo 12B in bfloat16. In addition, we compare TTFT during recomputation of KV caches with decompression of compressed caches. BF denotes batch size, CTX context length.\n","}\n","\\label{tab:latency-mistral}\n","\\centering\n","\\vspace{0.4cm}\n","\\small\n","\\resizebox{1.00\\linewidth}{!}{%\n","\\begin{tabular}{l r r | r r} \n","\\toprule \n"," \\text{Module} & \\multicolumn{2}{c|}{BS=8 CTX=8K} & \\multicolumn{2}{c}{BS=2 CTX=16K} \\\\\n"," & \\text{Comp} & \\text{Decomp} & \\text{Comp} & \\text{Decomp} \\\\\n"," \\midrule\n"," Project & $153\\,$ ms & $156\\,$ ms & $78\\,$ ms & $75\\,$ ms \\\\\n"," Quantize & $67\\,$ ms & $37\\,$ ms & $39\\,$ ms & $27\\,$ ms \\\\\n"," Deflate & $137\\,$ ms & $64\\,$ ms & $66\\,$ ms & $36\\,$ ms \\\\\n"," \\midrule\n"," Total & {\\bf 379$\\,$ ms }& {\\bf 267$\\,$ ms } & {\\bf 194$\\,$ ms } & {\\bf 143$\\,$ ms} \\\\\n"," \\midrule\n"," \\midrule\n","\\multicolumn{2}{l}{Vanilla recompute TTFT} & {\\bf 3098 ms} & & {\\bf 1780 ms} \\\\ \n","\\multicolumn{2}{l}{\\Method{} decomp TTFT} & {\\bf 380 ms} & & {\\bf 208 ms} \\\\ \n"," \n"," \\bottomrule\n"," \\end{tabular}\n"," }\n"," \\end{minipage}\n","\\end{table}\n"],["\\begin{figure}\n"," \\centering\n"," \\subfloat[]{\n"," \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_fineweb_ablate_niter_key.pdf}\n"," }\n"," \\hfill\n"," \\subfloat[]{\n"," \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_fineweb_ablate_niter_key.pdf}\n"," }\n"," \\hfill\n"," \\subfloat[]{\n"," \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_fineweb_ablate_niter_value.pdf}\n"," }\n"," \\hfill\n"," \\subfloat[]{\n"," \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_fineweb_ablate_niter_value.pdf}\n"," }\n"," \\caption{Relative reconstruction error when calibrating \\Method{} decorrelation step - ablation of the number of algorithm \\citep{halko2010findingstructurerandomnessprobabilistic} iterations. Figures (a)-(b) show key reconstruction error, whereas (c)-(d) show value reconstruction error. Other parameters as in Figure \\ref{fig:kv-pca-train}. We note that the larger number of iterations provides slight improvements.}\n"," \\label{fig:kv-pca-train-more}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n"," \\subfloat[]{\n"," \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_openr1.pdf}\n"," }\n"," \\hfill\n"," \\subfloat[]{\n"," \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_openr1.pdf}\n"," }\n"," \\caption{Relative reconstruction error when calibrating \\Method{} decorrelation step on OpenR1Math \\citep{OpenR1Math220k} traces with the error calculation on FineWeb \\citep{penedo2024the}. Parameters as in Figure \\ref{fig:kv-pca-train}. We note that OpenR1Math traces were published after the release of Llama 3.1 $8$B and Mistral NeMo $12$B, and possibly due to their specificity result in higher generalization error.}\n"," \\label{fig:kv-pca-train-openr1}\n","\\end{figure}\n"],["\\begin{figure}[ht]\n"," \\centering\n"," \\subfloat[Relative (within head) Absolute Activations]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_llama3.1_8b_base_fp16.pdf}\n"," }\n"," \\subfloat[\\centering Relative (within head) Variance of Activations]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_llama3.1_8b_base_fp16_var.pdf}\n"," }\\\\\n"," \\subfloat[Relative (within head) Absolute Activations]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_mistral_nemo_12b_base_bf16.pdf}\n"," }\n"," \\subfloat[\\centering Relative (within head) Variance of Activations]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_mistral_nemo_12b_base_bf16_var.pdf}\n"," }\\\\\n"," \\caption{For key/value head $i$ and channel $j$, we define per-channel mean absolute activation $\\mathrm{a}_{i,j} = \\frac{1}{n}\\sum_{t=1}^{n}{|\\mathrm{channel}_{t, i,j}|}$ and plot the relative activation $\\mathrm{heatmap}_{i,j} = \\mathrm{a}_{i,j}/\\max_b{\\{\\mathrm{a}_{i,b}\\}}$ --- Panels (a),(c)(e). \n"," Panels (b),(d),(f) show $\\frac{\\mathrm{varc}_{i,j}}{\\max_c{\\{\\mathrm{varc}_{i,c}\\}}}$ where $\\mathrm{varc}_{i,j}$ is the variance of $\\mathrm{channel}_{t, i,j}$ over $t$ .}\n"," \\label{fig:kv-cache-norms-ex}\n","\\end{figure}\n"],["\\begin{figure}[ht]\n"," \\centering\n"," \\subfloat[Relative (within head) Absolute Activations]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_1.5B_bf16.pdf}\n"," }\n"," \\subfloat[\\centering Relative (within head) Variance of Activations]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_1.5B_bf16_var.pdf}\n"," }\\\\\n"," \\subfloat[Relative (within head) Absolute Activations]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_7B_bf16.pdf}\n"," }\n"," \\subfloat[\\centering Relative (within head) Variance of Activations]{\n"," \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_7B_bf16_var.pdf}\n"," }\\\\\n"," \\caption{For key/value head $i$ and channel $j$, we define per-channel mean absolute activation $\\mathrm{a}_{i,j} = \\frac{1}{n}\\sum_{t=1}^{n}{|\\mathrm{channel}_{t, i,j}|}$ and plot the relative activation $\\mathrm{heatmap}_{i,j} = \\mathrm{a}_{i,j}/\\max_b{\\{\\mathrm{a}_{i,b}\\}}$ --- Panels (a),(c)(e). \n"," Panels (b),(d),(f) show $\\frac{\\mathrm{varc}_{i,j}}{\\max_c{\\{\\mathrm{varc}_{i,c}\\}}}$ where $\\mathrm{varc}_{i,j}$ is the variance of $\\mathrm{channel}_{t, i,j}$ over $t$ .}\n"," \\label{fig:kv-cache-norms-ex-p2}\n","\\end{figure}\n"],["\\begin{table}[ht]\n","\\caption{Ablation on the skipping compression of the first four tokens. We note that the difference starts to be visible with larger compression ratios, and that it is in favor of skipping compression of potential attention sinks \\citep{xiao2024efficientstreaminglanguagemodels}. Results are presented as $\\mathrm{score}_{\\mathrm{stderr}}$ where ${\\mathrm{stderr}}$ is bootstraped by LM Evaluation Harness (where available) \\citep{eval-harness}. The differences in compression ratios, are due to the fact that we count the skipped tokens into compression ratio.}\\label{tab:ablate-skipping-first-four-tokens}\n","\\small\n","\\centering\n","\\begin{tabular}{cccccccc}\n","\\toprule\n","\n","\\multirow{2}{*}{Model} & \\multirow{2}{*}{Method} & \\multirow{2}{*}{CR} & GSM8K & MMLU & QASPER & LITM 100 & RULER-VT \\\\\n"," & & & \\multicolumn{2}{c}{Math \\& Knowledge} & \\multicolumn{3}{c}{Long Context} \\\\\n","\\midrule\n","\\multirow{4}{*}{Llama 3.1 8B} & \\methodopcr{0}{16} & \\crinterval{19}{22} & $56.8_{ 1.4}$ & $60.3_{ 0.4}$ & $40.2$ & $99.2_{ 0.1}$ & $98.2_{0.4}$ \\\\\n","& \\methodopcr{4}{16} & \\crinterval{18}{22} & $56.9_{ 1.4}$ & $60.1_{ 0.4}$ & $40.7$ & $99.3_{ 0.1}$ &$99.1_{0.3}$\\\\\n","& \\methodopcr{0}{64} & \\crinterval{76}{90} & $1.6_{ 0.3}$ & $9.9_{ 0.2}$ & $27.6$ & $0.0_{ 0.0}$ &$61.8_{1.5}$\\\\\n","& \\methodopcr{4}{64} & \\crinterval{60}{88} & $57.2_{ 1.4}$ & $60.7_{ 0.4}$ & $37.8$ & $90.2_{ 0.4}$ &$95.9_{0.6}$\\\\\n","\n","\\midrule\n","\\multirow{2}{*}{MN-Minitron 8B}\n","& \\methodopcr{0}{64} & \\crinterval{79}{97} & $59.5_{ 1.4}$ & $61.9_{0.4}$ & $37.9$ & $55.1_{ 0.6}$ &$91.5_{0.9}$\\\\\n","& \\methodopcr{4}{64} & \\crinterval{53}{95} & $57.8_{ 1.4}$ & $62.1_{ 0.4}$ & $38.1$ & $59.5_{ 0.6}$ &$93.4_{0.8}$\\\\\n","\\midrule\n","\\multirow{2}{*}{Mistral NeMo 12B}\n","\n","& \\methodopcr{0}{64} & \\crinterval{77}{89} & $61.9_{1.3}$ & $62.4_{0.4}$ & $37.5$ & $84.8_{0.4}$ &$95.8_{0.6}$\\\\\n","& \\methodopcr{4}{64} & \\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[ht]\n","\\caption{Ablation of key/value compressibility with \\Method{}. We use the same \\Method{} configuration as in Table \\ref{tab:nonthinking-results}, but independently change key and value lossy compression rates. To denote that value compression ratio was set to $32$ and key was set to $64$ we use \\methodopcrk{64}}\\label{tab:nonthinking-ablate-key-vs-value}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{lc|ccccc}\n","\\toprule\n","\n","\\multirow{1}{*}{Method} & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n","\\midrule\n","\\multicolumn{7}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n","\\methodopcrkl{256} & \\crinterval{55}{80} &$57.1_{1.4}$& 57.4 & 36.6 &$48.6_{1.6}$&$91.9_{0.9}$\\\\\n","\\methodopcrvl{256} & \\crinterval{55}{77} &$56.8_{1.4}$& 57.5 & 36.3 &$71.9_{1.4}$&$95.9_{0.6}$\\\\\n","\n","\n","\\midrule\n","\\multicolumn{7}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n","\\methodopcrk{256} & \\crinterval{69}{79} &$62.2_{1.3}$& 61.7 & 34.6 &$73.2_{1.4}$&$90.4_{0.9}$\\\\\n","\\methodopcrv{256} & \\crinterval{69}{77} &$57.1_{1.4}$& 59.8 & 35.2 &$77.5_{1.3}$&$89.5_{1.0}$\\\\\n","\n","\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\\clearpage\n"],["\\begin{table}[ht]\n","\\caption{Ablation of the number of tokens used for \\Method{} calibration, along with respective PCA and DP calibration times. PCA calibration was performed using single H100 $80$GB GPU, calculation of DP tables (except simulation of quantization) was offloaded to the node cpu. We additionally limit DP calibration data to first 32K tokens, therefore we do not see increase in dp time after 40k calibration tokens. All calibration datapieces come from a 50/50 mixture of FineWeb \\citep{penedo2024the} and OpenMathR1 \\citep{OpenR1Math220k} traces between 1K and 8K tokens.}\\label{tab:nonthinking-ablate-num-tokens}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{lc|cccccccc}\n","\\toprule\n","\n"," \\multirow{1}{*}{Method} & Data & PCA Calib & DP Calib & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n","\\midrule\n","\\multicolumn{10}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n","\\methodopcrdef{4}{32} & \\multirow{3}{*}{20K} & \\multirow{3}{*}{41.3s} & 6.5 min & \\crinterval{31}{42} & $63.0_{1.3}$ & $63.9_{0.4}$ & $34.8$ & $97.3_{0.2}$ &$98.9_{0.3}$\\\\\n","\\methodopcrdef{4}{64} & & & 5.4 min & \\crinterval{63}{87} & $63.9_{1.3}$ & $61.7_{0.4}$ & $31.8$ & $88.8_{0.4}$ &$96.9_{0.5}$\\\\\n","\\methodopcrdef{4}{256} & & & 3.9 min & \\crinterval{148}{340} & $59.6_{1.4}$ & $51.5_{0.4}$ & $23.3$ & $10.4_{0.4}$ &$66.8_{1.5}$\\\\\n","\\hline\n","\\methodopcrdef{4}{32} & \\multirow{3}{*}{40K} & \\multirow{3}{*}{47.8s} & 7.2 min & \\crinterval{31}{43} & $64.2_{1.3}$ & $63.0_{0.4}$ & $35.3$ & $98.7_{0.1}$ &$99.5_{0.2}$\\\\\n","\\methodopcrdef{4}{64} & & & 6.1 min & \\crinterval{63}{88} & $63.7_{1.3}$ & $61.9_{0.4}$ & $32.4$ & $95.7_{0.3}$ &$97.8_{0.5}$\\\\\n","\\methodopcrdef{4}{256} & & & 4.6 min & \\crinterval{148}{344} & $58.3_{1.4}$ & $50.1_{0.4}$ & $23.7$ & $9.2_{0.4}$ &$70.6_{1.4}$\\\\\n","\\hline\n","\n","\\methodopcrdef{4}{32} & \\multirow{3}{*}{80K} & \\multirow{3}{*}{60.4s} & 7.2 min & \\crinterval{31}{43} & $63.6_{1.3}$ & $63.9_{0.4}$ & $36.0$ & $98.0_{0.2}$ &$99.3_{0.3}$\\\\\n","\\methodopcrdef{4}{64} & & & 6.1 min & \\crinterval{63}{88} & $63.3_{1.3}$ & $62.0_{0.4}$ & $32.2$ & $94.5_{0.3}$ &$97.8_{0.5}$\\\\\n","\\methodopcrdef{4}{256} & & & 4.6 min & \\crinterval{148}{339} & $60.5_{1.3}$ & $51.7_{0.4}$ & $23.3$ & $13.6_{0.4}$ &$83.7_{1.2}$\\\\\n","\n","\\hline\n","\\methodopcrdef{4}{32} & \\multirow{3}{*}{160K} & \\multirow{3}{*}{85.6s} & 7.2 min & \\crinterval{31}{43} & $63.2_{1.3}$ & $64.3_{0.4}$ & $36.6$ & $99.5_{0.1}$ &$99.4_{0.3}$\\\\\n","\\methodopcrdef{4}{64} & & & 6.1 min & \\crinterval{63.2}{87} & $64.6_{1.3}$ & $62.2_{0.4}$ & $32.8$ & $96.9_{0.2}$ &$97.7_{0.5}$\\\\\n","\\methodopcrdef{4}{256} & & & 4.6 min & \\crinterval{148}{341} & $61.4_{1.3}$ & $55.5_{0.4}$ & $24.3$ & $34.2_{0.6}$ &$79.5_{1.3}$\\\\\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\\clearpage\n"],["\\begin{table}[ht]\n","\\caption{Ablation of the source of data. We consider \\Method{} calibrated fully on FineWeb \\citep{penedo2024the}, fully on OpenMathR1 \\citep{OpenR1Math220k} and a 50/50 mixture. For all cases we utilize a 50/50 mix of documents between 1K and 8K tokens along with documents between 8K and 32K tokens. We calibrate using 160K tokens.}\\label{tab:nonthinking-ablate-data-source}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{lc|cccccc}\n","\\toprule\n","\n"," \\multirow{1}{*}{Method} & Data & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n","\\midrule\n","\\multicolumn{8}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n","\\multirow{3}{*}{\\methodopcrdef{4}{32}} & FineWeb + OpenR1Math & \\crinterval{31}{43} & $62.2_{1.3}$ & $63.8_{0.4}$ & $37.5$ & $99.6_{0.1}$ &$98.7_{0.4}$\\\\\n"," & FineWeb & \\crinterval{31}{43} & $63.5_{1.3}$ & $63.5_{0.4}$ & $37.5$ & $98.5_{0.2}$ &$98.9_{0.3}$\\\\\n"," & OpenR1Math & \\crinterval{31}{43} & $63.5_{1.3}$ & $64.8_{0.4}$ & $37.8$ & $99.7_{0.1}$ &$99.3_{0.3}$\\\\\n","\\hline\n","\\multirow{3}{*}{\\methodopcrdef{4}{64}} & FineWeb + OpenR1Math & \\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\n"," & FineWeb & \\crinterval{63}{87} & $63.2_{1.3}$ & $59.9_{0.4}$ & $36.5$ & $92.0_{0.3}$ &$97.4_{0.5}$\\\\\n"," & OpenR1Math & \\crinterval{63}{86} & $62.2_{1.3}$ & $63.7_{0.4}$ & $38.2$ & $98.5_{0.2}$ &$96.5_{0.6}$\\\\\n","\\hline\n","\\multirow{3}{*}{\\methodopcrdef{4}{256}} & FineWeb + OpenR1Math & \\crinterval{148}{340} & $60.0_{1.3}$ & $52.2_{0.4}$ & $31.6$ & $40.0_{0.6}$ &$84.3_{1.1}$\\\\\n"," & FineWeb & \\crinterval{148}{343} & $57.9_{1.4}$ & $51.5_{0.4}$ & $31.0$ & $14.1_{0.4}$ &$74.5_{1.4}$\\\\\n"," & OpenR1Math & \\crinterval{156}{342} & $56.6_{1.4}$ & $54.0_{0.4}$ & $29.4$ & $21.0_{0.5}$ &$81.3_{1.2}$\\\\\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[ht]\n","\\caption{Mean and standard deviation of downstream performance measured on 5 different calibrations sets (50/50 mixture of OpenR1Math \\citep{OpenR1Math220k} and FineWeb \\citep{penedo2024the}, 160K tokens, documents between 1K and 8K tokens). Results presented as $\\mathrm{mean}_{\\pm \\mathrm{std}}$}\\label{tab:nonthinking-ablate-data-source-std}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{l|cccccc}\n","\\toprule\n","\n"," \\multirow{1}{*}{Method} & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n","\\midrule\n","\\multicolumn{7}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n","Vanilla & 1 & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\n","\\multirow{1}{*}{\\methodopcrdef{4}{16}} & \\crinterval{17}{20} & $63.5_{\\pm 0.9}$ & $64.7_{\\pm 0.3}$ & $37.2_{\\pm 0.4}$ & $99.6_{\\pm 0.3}$ & $99.7_{\\pm 0.0}$ \\\\\n","\\multirow{1}{*}{\\methodopcrdef{4}{32}} & \\crinterval{31}{43} & $63.1_{\\pm 0.5}$ & $64.4_{\\pm 0.6}$ & $36.1_{\\pm 0.7}$ & $98.1_{\\pm 2.0}$ & $99.2_{\\pm 0.3}$ \\\\\n","\\multirow{1}{*}{\\methodopcrdef{4}{64}} & \\crinterval{50}{88} & $63.1_{\\pm 1.3}$ & $63.3_{\\pm 0.9}$ & $32.9_{\\pm 0.7}$ & $93.1_{\\pm 3.6}$ & $98.1_{\\pm 0.4}$ \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[ht]\n","\\caption{Ablation of out of distribution source of data. We consider \\Method{} calibrated on a 50/50 mixture of FineWeb \\citep{penedo2024the} and OpenMathR1 \\citep{OpenR1Math220k} along with calibration on Python/C/Assembly from the StarCoder dataset \\citep{li2023starcodersourceyou}. In all cases we utilize files between 1K and 8K tokens and calibrate on 160K tokens. For configurations that were tested using several seeds we report $\\mathrm{score}_{\\pm \\mathrm{std}}$, whereas for others we report $\\mathrm{score}_{\\mathrm{stderr}}$}\\label{tab:nonthinking-ablate-data-source-code}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{lc|cccccc}\n","\\toprule\n","\n"," \\multirow{1}{*}{Method} & Calibration Data & CR & GSM & MMLU & QASPER & LITM & RULER-VT \\\\\n","\\midrule\n","\n","\\multicolumn{8}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n","Vanilla & \\multirow{3}{*}{-} & 1 & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\n","GEAR 2bit & & 5 & $59.8_{1.4}$ & $64.0_{0.4}$ & $38.6$ & $96.9_{0.2}$ &$99.4_{0.3}$\\\\\n","KIVI 2bit & & 5 & $59.7_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $91.9_{0.3}$ &$98.3_{0.4}$\\\\\n","\\hline\n","\\multirow{2}{*}{\\methodopcrdef{4}{16}} & FineWeb + OpenR1Math & \\crinterval{17}{20} & $63.5_{\\pm 0.9}$ & $64.7_{\\pm 0.3}$ & $37.2_{\\pm 0.4}$ & $99.6_{\\pm 0.3}$ & $99.7_{\\pm 0.0}$ \\\\\n","& Python & \\crinterval{17}{20} & $59.4_{1.4}$ & $65.2_{0.4}$ & $37.4$ & $99.9_{0.0}$ &$99.7_{0.2}$\\\\\n","& C & \\crinterval{17}{20} & $55.0_{1.4}$ & $65.4_{0.4}$ & $38.0$ & $99.2_{0.1}$ &$99.3_{0.3}$\\\\\n","& Assembly & \\crinterval{17}{20} & $58.9_{1.4}$ & $65.2_{0.4}$ & $37.0$ & $99.9_{0.0}$ &$99.7_{0.2}$\\\\\n","\\hline\n","\\multirow{2}{*}{\\methodopcrdef{4}{32}} & FineWeb + OpenR1Math & \\crinterval{31}{43} & $63.1_{\\pm 0.5}$ & $64.4_{\\pm 0.6}$ & $36.1_{\\pm 0.7}$ & $98.1_{\\pm 2.0}$ & $99.2_{\\pm 0.3}$ \\\\\n","& Python & \\crinterval{35}{43} & $59.0_{1.4}$ & $64.3_{0.4}$ & $36.3$ & $99.7_{0.1}$ &$99.2_{0.3}$\\\\\n","& C & \\crinterval{31}{43} & $50.2_{1.4}$ & $64.7_{0.4}$ & $36.8$ & $96.2_{0.2}$ &$99.3_{0.3}$\\\\\n","& Assembly & \\crinterval{31}{43} & $55.2_{1.4}$ & $64.2_{0.4}$ & $36.7$ & $99.6_{0.1}$ &$99.4_{0.3}$\\\\\n","\\hline\n","\\multirow{2}{*}{\\methodopcrdef{4}{64}} & FineWeb + OpenR1Math & \\crinterval{50}{88} & $63.1_{\\pm 1.3}$ & $63.3_{\\pm 0.9}$ & $32.9_{\\pm 0.7}$ & $93.1_{\\pm 3.6}$ & $98.1_{\\pm 0.4}$ \\\\\n","& Python & \\crinterval{63}{87} & $56.3_{1.4}$ & $62.0_{0.4}$ & $33.9$ & $98.0_{0.2}$ &$97.4_{0.5}$\\\\\n","& C & \\crinterval{63}{87} & $54.4_{1.4}$ & $63.3_{0.4}$ & $34.5$ & $95.4_{0.3}$ &$97.8_{0.5}$\\\\\n","& Assembly & \\crinterval{50}{86} & $60.9_{1.3}$ & $62.2_{0.4}$ & $33.0$ & $99.1_{0.1}$ &$98.3_{0.4}$\\\\\n"," \n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[ht]\n","\\caption{Ablation of the sliding window size of recent tokens that are not compressed. For a fair compression in this table we simulate a sequence of short conversations by running compressing/eviction on the cache every $s=1$ instead every $s=16$ tokens. Therefore, the $w=16$ token window is left int the range $15$-$16$ instead of $0$-$16$.}\\label{tab:kvtc-ablate-ws}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{lc|cccccc}\n","\\toprule\n","\n"," \\multirow{1}{*}{Method} & Window Size & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n","\n"," \n","\\midrule\n","\\multicolumn{8}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n","\\multirow{4}{*}{\\methodopcrdef{4}{64}} & 1 & \\crinterval{59}{88} & $41.2_{1.4}$ & $53.8_{0.4}$ & $36.5$ & $68.3_{0.6}$ &$87.7_{1.0}$\\\\\n","& 16 & \\crinterval{58}{88} & $53.0_{1.4}$ & $56.0_{0.4}$ & $38.1$ & $80.0_{0.5}$ &$88.0_{1.0}$\\\\\n","& 64 & \\crinterval{57}{88} & $55.8_{1.4}$ & $59.2_{0.4}$ & $37.7$ & $89.8_{0.4}$ &$95.8_{0.6}$\\\\\n"," & 128 & \\crinterval{60}{88} & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\n","\n","\\midrule\n","\n","\\multicolumn{8}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n","\n","\\multirow{4}{*}{\\methodopcrdef{4}{64}} & 1 & \\crinterval{61}{87} & $53.0_{1.4}$ & $54.9_{0.4}$ & $36.4$ & $88.6_{0.4}$ &$90.7_{0.9}$\\\\\n","& 16 & \\crinterval{60}{87} & $60.1_{1.3}$ & $56.4_{0.4}$ & $37.7$ & $88.9_{0.4}$ &$95.8_{0.6}$\\\\\n","& 64 & \\crinterval{59}{87} & $62.2_{1.3}$ & $59.0_{0.4}$ & $37.8$ & $93.0_{0.3}$ &$98.0_{0.4}$\\\\\n"," & 128 & \\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\\clearpage\n"],["\\begin{table}[ht]\n","\\caption{Ablation of the lossless compression algorithms, performed using Mistral Nemo 12B with \\methodopcrdef{4}{32}. Identity stands for no additional lossless compression (just PCA + DP Quantization; note that we count the omitted sinks into compression ratio, what is notable for tasks with shorter contexts). We mark results that have compression ratio advantage over Identity smaller than 1 in red.}\\label{tab:kvtc-ablate-deflate}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{l|ccccc}\n","\\toprule\n","\n","\\multirow{2}{*}{Algorithm} & \\multicolumn{5}{c}{Compression Ratio} \\\\\n"," & Min-Max & GSM8K & QASPER & LITM & RULER-VT \\\\\n","\\midrule\n"," ANS & \\crinterval{32.8}{37.6} & 32.8 & 37.6 & 36.8 & 37.0 \\\\\n"," Bitcomp & \\crinterval{29.6}{32.3} & \\badresult{}29.6 & \\badresult{}32.3 & \\badresult{}32.2 & \\badresult{}32.2 \\\\\n"," DEFLATE & \\crinterval{34.7}{42.9} & 34.7 & 39.5 & 39.7 & 42.9 \\\\\n"," GDeflate & \\crinterval{34.6}{42.8} & 34.6 & 39.4 & 39.6 & 42.8 \\\\\n"," Identity & \\crinterval{29.6}{32.4} & \\badresult{}29.6 & \\badresult{}32.4 & \\badresult{}32.2 & \\badresult{}32.3 \\\\\n"," LZ4 & \\crinterval{29.5}{35.5} & \\badresult{}29.5 & \\badresult{}32.4 & \\badresult{}32.7 & 35.5 \\\\\n"," Snappy & \\crinterval{29.4}{34.5} & \\badresult{}29.4 & \\badresult{}32.2 & \\badresult{}32.4 & 34.5 \\\\\n"," zStandard & \\crinterval{34.6}{46.3} & 34.6 & 39.4 & 39.9 & 46.3 \\\\\n","\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[ht]\n","\\caption{Ablation of the importance of DP quantization over pure PCA. For alteration of sliding window size we follow the protocol from Appendix~\\ref{sec:appendix:sec-kvtc-ws-ablate}.}\\label{tab:kvtc-ablate-dp-pca}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{lcc|cccccc}\n","\\toprule\n","\n"," \\multirow{1}{*}{Window Size} & Method & Modification & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n","\n"," \n","\\midrule\n","\\multicolumn{9}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n","\\multirow{8}{*}{16} & \\multirow{2}{*}{\\methodopcrdef{4}{8}} & - & \\crinterval{9}{10} & $57.5_{1.4}$ & $59.4_{0.4}$ & $40.1$ & $99.1_{0.1}$ &$98.2_{0.4}$\\\\\n","& & -DPQ & \\crinterval{8}{9} & $56.9_{1.4}$ & $57.5_{0.4}$ & $40.1$ & $98.6_{0.1}$ &$93.0_{0.8}$\\\\\n","\\cmidrule{2-9}\n","& \\multirow{2}{*}{\\methodopcrdef{4}{16}} & - & \\crinterval{18}{22} & $57.2_{1.4}$ & $59.5_{0.4}$ & $40.6$ & $99.4_{0.1}$ &$98.3_{0.4}$\\\\\n","& & -DPQ & \\crinterval{16}{17} & $52.0_{1.4}$ & $53.8_{0.4}$ & $36.9$ & $69.2_{0.6}$ &$87.0_{1.1}$\\\\\n","\\cmidrule{2-9}\n","& \\multirow{2}{*}{\\methodopcrdef{4}{32}} & - & \\crinterval{34}{44} & $55.5_{1.4}$ & $58.2_{0.4}$ & $39.6$ & $98.8_{0.1}$ &$94.8_{0.7}$\\\\\n","& & -DPQ & \\crinterval{31}{34} & $42.9_{1.4}$ & $36.8_{0.4}$ & $34.2$ & $44.4_{0.6}$ &$83.0_{1.2}$\\\\\n","\\cmidrule{2-9}\n","& \\multirow{2}{*}{\\methodopcrdef{4}{64}} & - & \\crinterval{58}{88} & $53.0_{1.4}$ & $56.0_{0.4}$ & $38.1$ & $80.0_{0.5}$ &$88.0_{1.0}$\\\\\n","& & -DPQ & \\crinterval{52}{68} & $21.8_{1.1}$ & $6.5_{0.2}$ & $26.7$ & $5.1_{0.3}$ &$55.5_{1.6}$\\\\\n","\\midrule\n","\\multirow{8}{*}{128} & \\multirow{2}{*}{\\methodopcrdef{4}{8}} & - & \\crinterval{9}{10} & $56.7_{1.4}$ & $59.9_{0.4}$ & $40.0$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\n","& & -DPQ & \\crinterval{8}{9} & $57.0_{1.4}$ & $60.7_{0.4}$ & $40.2$ & $99.5_{0.1}$ &$98.5_{0.4}$\\\\\n","\\cmidrule{2-9}\n","& \\multirow{2}{*}{\\methodopcrdef{4}{16}} & - & \\crinterval{17}{22} & $57.1_{1.4}$ & $60.1_{0.4}$ & $40.7$ & $99.3_{0.1}$ &$99.0_{0.3}$\\\\\n","& & -DPQ & \\crinterval{16}{17} & $55.7_{1.4}$ & $59.7_{0.4}$ & $37.1$ & $85.0_{0.4}$ &$95.5_{0.7}$\\\\\n","\\cmidrule{2-9}\n","\n","& \\multirow{2}{*}{\\methodopcrdef{4}{32}} & - & \\crinterval{33}{44} & $58.4_{1.4}$ & $60.8_{0.4}$ & $39.3$ & $99.1_{0.1}$ &$98.9_{0.3}$\\\\\n","& & -DPQ & \\crinterval{31}{34} & $55.1_{1.4}$ & $56.9_{0.4}$ & $35.3$ & $64.5_{0.6}$ &$89.6_{1.0}$\\\\\n","\\cmidrule{2-9}\n","& \\multirow{2}{*}{\\methodopcrdef{4}{64}} & - & \\crinterval{60}{88} & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\n","& & -DPQ & \\crinterval{47}{68} & $57.2_{1.4}$ & $49.3_{0.4}$ & $28.1$ & $13.1_{0.4}$ &$58.7_{1.5}$\\\\\n","\n","\n","\n","\n","\n","\n","\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[ht]\n","\\caption{Ablation of the number of layers used for PCA. To better isolate the influence of the number of concatenated key/value heads, we run \\Method{} without dynamic programming quantization (that is, we run \\Method{}-DPQ introduced in Appendix \\ref{sec:appendix:ablate_dp}) and with a sliding window $w=16$.}\\label{tab:kvtc-ablate-pca-input-features}\n","\\centering\n","\\setlength{\\tabcolsep}{1mm}\n","\\small\n","\\begin{tabular}{lc|ccccc}\n","\\toprule\n","\n"," \\multirow{1}{*}{Method} & PCA Layers & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n","\n"," \n","\\midrule\n","\\multicolumn{7}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n","\\multirow{6}{*}{\\methodopcrdef{4}{8}-DPQ} & 1 & $27.5_{1.2}$ & $24.3_{0.3}$ & $28.2$ & $49.1_{0.6}$ &$70.8_{1.4}$\\\\\n","& 2 & $44.8_{1.4}$ & $41.1_{0.4}$ & $34.2$ & $77.6_{0.5}$ &$84.9_{1.1}$\\\\\n","& 4 & $53.3_{1.4}$ & $51.9_{0.4}$ & $37.5$ & $95.9_{0.2}$ &$93.0_{0.8}$\\\\\n","& 8 & $55.9_{1.4}$ & $55.3_{0.4}$ & $39.7$ & $99.2_{0.1}$ &$90.7_{0.9}$\\\\\n","& 16 & $56.0_{1.4}$ & $57.1_{0.4}$ & $38.8$ & $98.8_{0.1}$ &$92.8_{0.8}$\\\\\n"," & 32 & $56.9_{1.4}$ & $57.5_{0.4}$ & $40.1$ & $98.6_{0.1}$ &$93.0_{0.8}$\\\\\n","\\midrule\n","\\multirow{6}{*}{\\methodopcrdef{4}{16}-DPQ} & 1 & $2.5_{0.4}$ & $0.2_{0.0}$ & $18.4$ & $0.0_{0.0}$ &$0.5_{0.2}$\\\\\n","& 2 & $13.9_{1.0}$ & $2.3_{0.1}$ & $22.1$ & $0.7_{0.1}$ &$12.9_{1.0}$\\\\\n","& 4 & $33.3_{1.3}$ & $19.3_{0.3}$ & $29.1$ & $32.0_{0.6}$ &$62.7_{1.5}$\\\\\n","& 8 & $49.6_{1.4}$ & $43.4_{0.4}$ & $34.4$ & $60.7_{0.6}$ &$85.8_{1.1}$\\\\\n","& 16 & $51.6_{1.4}$ & $49.1_{0.4}$ & $36.0$ & $72.7_{0.6}$ &$89.0_{1.0}$\\\\\n"," & 32 & $52.0_{1.4}$ & $53.8_{0.4}$ & $36.9$ & $69.2_{0.6}$ &$87.0_{1.1}$\\\\\n","\\midrule\n","\\multirow{6}{*}{\\methodopcrdef{4}{32}-DPQ} & 1 & $1.1_{0.3}$ & $0.1_{0.0}$ & $17.8$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\n","& 2 & $1.5_{0.3}$ & $0.2_{0.0}$ & $18.1$ & $0.0_{0.0}$ &$0.2_{0.1}$\\\\\n","& 4 & $3.9_{0.5}$ & $0.9_{0.1}$ & $20.0$ & $0.0_{0.0}$ &$1.6_{0.4}$\\\\\n","& 8 & $28.0_{1.2}$ & $6.4_{0.2}$ & $24.7$ & $2.6_{0.2}$ &$33.0_{1.5}$\\\\\n","& 16 & $40.1_{1.4}$ & $26.0_{0.4}$ & $31.2$ & $24.6_{0.5}$ &$60.4_{1.5}$\\\\\n"," & 32 & $42.9_{1.4}$ & $36.8_{0.4}$ & $34.2$ & $44.4_{0.6}$ &$83.0_{1.2}$\\\\\n","\\midrule\n","\\multirow{6}{*}{\\methodopcrdef{4}{64}-DPQ} & 1 & $0.9_{0.3}$ & $0.3_{0.0}$ & $18.0$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\n","& 2 & $1.4_{0.3}$ & $0.1_{0.0}$ & $17.7$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\n","& 4 & $1.5_{0.3}$ & $0.1_{0.0}$ & $18.1$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\n","& 8 & $2.4_{0.4}$ & $0.6_{0.1}$ & $19.4$ & $0.0_{0.0}$ &$0.2_{0.1}$\\\\\n","& 16 & $13.9_{1.0}$ & $1.9_{0.1}$ & $22.1$ & $0.0_{0.0}$ &$10.0_{0.9}$\\\\\n"," & 32 & $21.8_{1.1}$ & $6.5_{0.2}$ & $26.7$ & $5.1_{0.3}$ &$55.5_{1.6}$\\\\\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[ht]\n","\\caption{Downstream task results, presented also in Table \\ref{tab:nonthinking-results}, here shown with standard error as reported by LM Evaluation Harness (where available).}\\label{tab:nonthinking-results-std}\n","\\centering\n","\\small\n","\\begin{tabular}{l|ccccc}\n","\\toprule\n","\n"," \\multirow{2}{*}{Method} & GSM8K & MMLU & QASPER & LITM 100 & RULER-VT \\\\\n"," & \\multicolumn{2}{c}{Math \\& Knowledge} & \\multicolumn{3}{c}{Long Context} \\\\\n","\\midrule\n","\\multicolumn{6}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n"," vanilla & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\n"," GEAR 2bit & $52.8_{1.4}$ & $59.6_{0.4}$ & $40.4$ & $96.9_{0.2}$ &$99.8_{0.2}$\\\\\n"," KIVI 2bit & $52.8_{1.4}$ & $59.6_{0.4}$ & $39.1$ & $88.8_{0.4}$ &$98.9_{0.3}$\\\\\n"," xKV$^{2/16 \\;4\\mathrm{key}}_{3/16 \\;4\\mathrm{value}}$ & $56.6_{1.4}$ & $59.5_{0.4}$ & $35.6$ & $99.9_{0.0}$ &$99.8_{0.2}$\\\\\n"," FP8 & $55.2_{1.4}$ & $60.1_{0.4}$ & $40.8$ & $99.4_{0.1}$ & $99.9_{0.1}$ \\\\\n"," \\methodopcrdef{4}{8} & $57.0_{1.4}$ & $59.8_{0.4}$ & $40.1$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\n"," \\methodopcrdef{4}{16} & $56.9_{1.4}$ & $60.1_{0.4}$ & $40.7$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\n"," \\methodopcrdef{4}{32} & $57.8_{1.4}$ & $60.6_{0.4}$ & $39.4$ & $99.1_{0.1}$ &$98.9_{0.3}$\\\\\n"," \\methodopcrdef{4}{64} & $57.2_{1.4}$ & $60.7_{0.4}$ & $37.8$ & $90.2_{0.4}$ &$95.9_{0.6}$\\\\\n","\n"," \\HTO{}$_{{1/16} \\;\\mathrm{past}}^{{1/16} \\;\\mathrm{recent}}$ & $54.3_{1.4}$ & $44.3_{0.4}$ & $34.3$ & $20.2_{0.5}$ &$50.4_{1.6}$\\\\\n"," \\TOVA{}{$\\frac{1}{8}$} & $54.5_{1.4}$ & $44.8_{0.4}$ & $38.6$ & $1.2_{0.1}$ &$99.7_{0.2}$\\\\\n","\n","\n","\\midrule\n","\\multicolumn{6}{c}{\\tabwithinbest{}MN-Minitron 8B} \\\\\n"," Vanilla & $59.1_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $99.8_{0.0}$ &$99.4_{0.3}$\\\\\n"," GEAR 2bit & $57.9_{1.4}$ & $63.6_{0.4}$ & $38.2$ & $96.0_{0.2}$ &$98.3_{0.4}$\\\\\n"," KIVI 2bit & $58.0_{1.4}$ & $63.2_{0.4}$ & $38.2$ & $86.3_{0.4}$ &$96.8_{0.6}$\\\\\n"," xKV$^{2/16 \\;5\\mathrm{key}}_{3/16 \\;5\\mathrm{value}}$ & $59.3_{1.4}$ & $63.1_{0.4}$ & $34.5$ & $99.6_{0.1}$ &$99.1_{0.3}$\\\\\n"," FP8 & $60.1_{1.3}$ & $64.3_{0.4}$ & $38.3$ & $99.8_{0.1}$ & $99.2_{0.3}$ \\\\\n"," \\methodopcrdef{4}{8} & $60.6_{1.3}$ & $64.2_{0.4}$ & $39.1$ & $99.4_{0.1}$ &$98.8_{0.3}$\\\\\n"," \\methodopcrdef{4}{16} & $60.3_{1.3}$ & $64.1_{0.4}$ & $38.6$ & $99.3_{0.1}$ &$98.8_{0.3}$\\\\\n"," \\methodopcrdef{4}{32} & $59.1_{1.4}$ & $63.7_{0.4}$ & $37.7$ & $86.9_{0.4}$ &$96.0_{0.6}$\\\\\n"," \\methodopcrdef{4}{64} & $57.8_{1.4}$ & $62.1_{0.4}$ & $38.1$ & $59.5_{0.6}$ &$93.4_{0.8}$\\\\\n"," \\HTO{}$_{{1/16} \\;\\mathrm{past}}^{{1/16} \\;\\mathrm{recent}}$ & $55.3_{1.4}$ & $43.5_{0.4}$ & $30.0$ & $16.6_{0.5}$ &$39.2_{1.5}$\\\\\n"," \\TOVA{}{$\\frac{1}{8}$} & $59.2_{1.4}$ & $48.1_{0.4}$ & $33.9$ & $0.3_{0.1}$ &$99.3_{0.3}$\\\\\n","\n","\\midrule\n","\\multicolumn{6}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n"," Vanilla & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\n"," GEAR 2bit & $59.8_{1.4}$ & $64.0_{0.4}$ & $38.6$ & $96.9_{0.2}$ &$99.4_{0.3}$\\\\\n"," KIVI 2bit & $59.7_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $91.9_{0.3}$ &$98.3_{0.4}$\\\\\n"," xKV$^{2/16 \\;5\\mathrm{key}}_{3/16 \\;5\\mathrm{value}}$ & $61.9_{1.3}$ & $63.9_{0.4}$ & $33.5$ & $97.9_{0.2}$ &$99.4_{0.3}$\\\\\n"," FP8 & $61.7_{1.3}$ & $64.5_{0.4}$ & $37.9$ & $99.0_{0.1}$ & $99.8_{0.2}$ \\\\\n"," \\methodopcrdef{4}{8} & $62.5_{1.3}$ & $64.6_{0.4}$ & $37.6$ & $99.9_{0.0}$ &$99.5_{0.2}$\\\\\n"," \\methodopcrdef{4}{16} & $62.0_{1.3}$ & $64.4_{0.4}$ & $37.6$ & $99.8_{0.0}$ &$99.5_{0.2}$\\\\\n"," \\methodopcrdef{4}{32} & $62.2_{1.3}$ & $63.8_{0.4}$ & $37.5$ & $99.6_{0.1}$ &$98.7_{0.4}$\\\\\n"," \\methodopcrdef{4}{64} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\n"," \\HTO{}$_{{1/16} \\;\\mathrm{past}}^{{1/16} \\;\\mathrm{recent}}$ & $57.0_{1.4}$ & $45.4_{0.4}$ & $29.5$ & $16.2_{0.5}$ &$35.2_{1.5}$\\\\\n"," \\TOVA{}{$\\frac{1}{8}$} & $60.3_{1.3}$ & $49.0_{0.4}$ & $36.0$ & $8.7_{0.4}$ &$99.6_{0.2}$\\\\\n","\n","\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"],["\\begin{table}[ht]\n","\\caption{Number of parameters used by PCA matrices, before DP, for the tested models. We note that despite treating keys and values separately, while using feature capacity for the efficient \\citep{halko2010findingstructurerandomnessprobabilistic} PCA calculation algorithm. For example, Llama 3.1 8B has 32 layers, each with 8 key/value heads, each head of size 128. Therefore, after cross-head concatenation, each key/value has $32\\times8\\times128 = 32768$ features. The PCA projection $V$ is cut to the first $10$K principal components by \\citep{halko2010findingstructurerandomnessprobabilistic} algorithm for efficiency, resulting in $32768 \\times 10000 \\simeq 328M$ parameters. Further DP bit allocation can remove additional principal directions depending on the desired compression ratio. Both models and PCA projection matrices are stored in 16bit precision.\n","}\\label{tab:model-kv-pca-size}\n","\n","\\small\n","\\centering\n","\\begin{tabular}{lcl|ccc}\n","\\toprule\n","Model & \\makecell{\\#Params} &\\makecell{Key/Value\\\\Features} & \\makecell{Key/Value\\\\PCA Cap} & \\makecell{Key/Value\\\\PCA Params} & $\\frac{\\mathrm{TotalPCAParams}}{\\mathrm{Model Params}}$ \\\\\n","\\midrule\n","Qwen 2.5 R1 1.5B & $1.5$B & $28\\times2\\times128 = 7168$ & \\multirow{2}{*}{8K} & 51M & $6.8$\\% \\\\\n","Qwen 2.5 R1 7B & $7.1$B & $28\\times4\\times128 = 14336$ & & 115M & $3.2$\\% \\\\\n","\\midrule\n","Llama 3.1 8B & $7.5$B & $32\\times8\\times128 = 32768$ & \\multirow{3}{*}{10K} & 328M & $8.7$\\% \\\\\n","Llama 3.3 70B & $69.5$B & $80\\times8\\times128 = 81920$ & & 819M & $2.4$\\% \\\\\n","Mistral NeMo 12B & $11.6$B & $40\\times8\\times128 = 40960$ & & 410M & $7.1$\\% \\\\\n","\\bottomrule\n","\\end{tabular}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\subfloat[Keys]{\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/cosine_keys.pdf}\\n\",\n \" \\\\label{fig:kv-cache-between-heads-key}\\n\",\n \" }\\n\",\n \" \\\\subfloat[Values]{\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/cosine_values.pdf}\\n\",\n \" \\\\label{fig:kv-cache-between-heads-value}\\n\",\n \" }\\n\",\n \" \\\\caption{Cosine similarity before and after alignment between key (a) and value (b) heads calculated using Llama 3.1 8B on inputs from Qasper \\\\citep{dasigi2021datasetinformationseekingquestionsanswers,shaham2022scrollsstandardizedcomparisonlong}. For each example, we calculate cosine similarity between all keys/values from the same position and then average across the batch. Orthonormal alignment matrices were produced using 20 samples from the RedPajama v2 \\\\citep{weber2024redpajama}.}\\n\",\n \" \\\\label{fig:kv-cache-between-heads}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \" \\\\centering %\\n\",\n \" \\\\subfloat[Attention sink compression ablation]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/ablations/omit_compression_of_sinks.pdf}\\n\",\n \" }\\n\",\n \" \\\\subfloat[Sliding window compression ablation]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/ablations/kvtc_vs_kvtc_without_sliding_window.pdf}\\n\",\n \" }\\n\",\n \" \\\\caption{\\n\",\n \"Ablation of \\\\Method{} with compression ratio 64$\\\\times$ on Llama 3.1 8B: (a) compression disabled for attention sink tokens; (b) compression disabled for the final 128 tokens. All other settings are fixed. Additional ablations are provided in \\\\cref{sec:appendix:ablate_sink,sec:appendix:sec-kvtc-ws-ablate}.\\n\",\n \"}\\n\",\n \" \\\\label{fig:kv-ablate-sinks-and-sw}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[scale=0.62]{figures/pca_dataset_error.pdf}\\n\",\n \" \\\\hspace{-3mm}\\n\",\n \" \\\\includegraphics[scale=0.62]{figures/pca_reconstruct_error.pdf}\\n\",\n \" \\\\includegraphics[scale=0.62]{figures/bit_assignment2.pdf}\\n\",\n \" \\\\caption{Calibration of Llama 3.1 8B with \\\\Method{}. \\\\textbf{Left:} Reconstruction error as a function of the size of calibration set. The arrow $A\\\\rightarrow B$ denotes fitting PCA on dataset A and calculating the error on B.\\n\",\n \" \\\\textbf{Middle:} The reconstruction error as a function of position in the context. The error is higher for the sink tokens. \\\\textbf{Right:} Bit assignment computed via dynamic programming, counting in the per-group scaling factors.}\\n\",\n \" \\\\label{fig:kv-pca-train}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \" \\\\caption{\\\\small Accuracy of KV cache compression methods. Results within $1$ score point of vanilla are in \\\\textbf{bold}. See Appendix \\\\ref{sec:appendix_stderr} for standard error analysis. \\\\methodopcrdef{}{\\\\mathrm{CR}} denotes \\\\Method{} set for $\\\\mathrm{CR}\\\\times$ compression before applying DEFLATE.}\\n\",\n \" \\\\label{tab:nonthinking-results}\\n\",\n \" \\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \" \\\\resizebox{0.85\\\\textwidth}{!}{%\\n\",\n \" \\\\begin{tabular}{lc|cccccccccc}\\n\",\n \" \\\\toprule\\n\",\n \" & Vanilla & \\\\makecell{GEAR$_\\\\text{2-bit}$} & \\\\makecell{KIVI$_\\\\text{2-bit}$} & \\\\HTO{} & \\\\TOVA{} & xKV & FP8 & \\\\methodopcrdef{4}{8} & \\\\methodopcrdef{4}{16} & \\\\methodopcrdef{4}{32} & \\\\methodopcrdef{4}{64} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{12}{c}{\\\\tabwithinbest{}Llama 3.1 8B}\\\\\\\\\\n\",\n \" CR & $1$ & \\\\gearcr{} & \\\\kivicr{} & $8$ & $8$ & \\\\crinterval{1}{5} & 2 & \\\\crinterval{9}{10} & \\\\crinterval{18}{22} & \\\\crinterval{34}{44} & \\\\crinterval{60}{88} \\\\\\\\\\n\",\n \" GSM8K & \\\\textbf{56.8} & 52.8 & 52.8 & 54.3 & 54.5 & \\\\textbf{56.6} & 55.2 & \\\\textbf{57.0} & \\\\textbf{56.9} & \\\\textbf{57.8} & \\\\textbf{57.2} \\\\\\\\\\n\",\n \" MMLU & \\\\textbf{60.5} & \\\\textbf{59.6} & \\\\textbf{59.6} & 44.3 & 44.8 & \\\\textbf{59.5} & \\\\textbf{60.1} & \\\\textbf{59.8} & \\\\textbf{60.1} & \\\\textbf{60.6} & \\\\textbf{60.7} \\\\\\\\\\n\",\n \" QASPER & \\\\textbf{40.4} & \\\\textbf{40.4} & 39.1 & 34.3 & 38.6 & 35.6 & \\\\textbf{40.8} & \\\\textbf{40.1} & \\\\textbf{40.7} & \\\\textbf{39.4} & 37.8 \\\\\\\\\\n\",\n \" LITM & \\\\textbf{99.4} & 96.9 & 88.8 & 20.2 & 1.2 & \\\\textbf{99.9} & \\\\textbf{99.4} & \\\\textbf{99.3} & \\\\textbf{99.3} & \\\\textbf{99.1} & 90.2 \\\\\\\\\\n\",\n \" RULER-VT & \\\\textbf{99.8} & \\\\textbf{99.8} & \\\\textbf{98.9} & 50.4 & \\\\textbf{99.7} & \\\\textbf{99.8} & \\\\textbf{99.9} & \\\\textbf{99.1} & \\\\textbf{99.1} & \\\\textbf{98.9} & 95.9 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{12}{c}{\\\\tabwithinbest{}MN‑Minitron 8B}\\\\\\\\\\n\",\n \" CR & $1$ & \\\\gearcr{} & \\\\kivicr{} & $8$ & $8$ & \\\\crinterval{1}{5} & 2 & \\\\crinterval{10}{11} & \\\\crinterval{17}{21} & \\\\crinterval{32}{46} & \\\\crinterval{53}{95} \\\\\\\\\\n\",\n \" GSM8K & \\\\textbf{59.1} & 57.9 & 58.0 & 55.3 & \\\\textbf{59.2} & \\\\textbf{59.3} & \\\\textbf{60.1} & \\\\textbf{60.6} & \\\\textbf{60.3} & \\\\textbf{59.1} & 57.8 \\\\\\\\\\n\",\n \" MMLU & \\\\textbf{64.3} & \\\\textbf{63.6} & \\\\textbf{63.2} & 43.5 & 48.1 & 63.1 & \\\\textbf{64.3} & \\\\textbf{64.2} & \\\\textbf{64.1} & \\\\textbf{63.7} & 62.1 \\\\\\\\\\n\",\n \" QASPER & \\\\textbf{38.2} & \\\\textbf{38.2} & \\\\textbf{38.2} & 30.0 & 33.9 & 34.5 & \\\\textbf{38.3} & \\\\textbf{39.1} & \\\\textbf{38.6} & \\\\textbf{37.7} & \\\\textbf{38.1} \\\\\\\\\\n\",\n \" LITM & \\\\textbf{99.8} & 96.0 & 86.3 & 16.6 & 0.3 & \\\\textbf{99.6} & \\\\textbf{99.8} & \\\\textbf{99.4} & \\\\textbf{99.3} & 86.9 & 59.5 \\\\\\\\\\n\",\n \" RULER-VT & \\\\textbf{99.4} & 98.3 & 96.8 & 39.2 & \\\\textbf{99.3} & \\\\textbf{99.1} & \\\\textbf{99.2} & \\\\textbf{98.8} & \\\\textbf{98.8} & 96.0 & 93.4 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\\\multicolumn{12}{c}{\\\\tabwithinbest{}Mistral NeMo 12B}\\\\\\\\\\n\",\n \" CR & $1$ & \\\\gearcr{} & \\\\kivicr{} & $8$ & $8$ & \\\\crinterval{1}{5} & 2 & \\\\crinterval{10}{11} & \\\\crinterval{17}{20} & \\\\crinterval{31}{43} & \\\\crinterval{51}{87} \\\\\\\\\\n\",\n \" GSM8K & \\\\textbf{61.9} & 59.8 & 59.7 & 57.0 & 60.3 & \\\\textbf{61.9} & \\\\textbf{61.7} & \\\\textbf{62.5} & \\\\textbf{62.0} & \\\\textbf{62.2} & \\\\textbf{61.9} \\\\\\\\\\n\",\n \" MMLU & \\\\textbf{64.5} & \\\\textbf{64.0} & \\\\textbf{64.3} & 45.4 & 49.0 & \\\\textbf{63.9} & \\\\textbf{64.5} & \\\\textbf{64.6} & \\\\textbf{64.4} & \\\\textbf{63.8} & 61.4 \\\\\\\\\\n\",\n \" QASPER & \\\\textbf{38.4} & \\\\textbf{38.6} & \\\\textbf{38.2} & 29.5 & 36.0 & 33.5 & \\\\textbf{37.9} & \\\\textbf{37.6} & \\\\textbf{37.6} & \\\\textbf{37.5} & \\\\textbf{38.0} \\\\\\\\\\n\",\n \" LITM & \\\\textbf{99.5} & 96.9 & 91.9 & 16.2 & 8.7 & 97.9 & \\\\textbf{99.0} & \\\\textbf{99.9} & \\\\textbf{99.8} & \\\\textbf{99.6} & 95.3 \\\\\\\\\\n\",\n \" RULER-VT & \\\\textbf{99.8} & \\\\textbf{99.4} & 98.3 & 35.2 & \\\\textbf{99.6} & \\\\textbf{99.4} & \\\\textbf{99.8} & \\\\textbf{99.5} & \\\\textbf{99.5} & \\\\textbf{98.9} & 98.0 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{minipage}[t]{0.46\\\\textwidth}\\n\",\n \" \\\\caption{Compression applied to a model which is split across four GPUs (pipeline parallel), with KV cache chunks being compressed separately with \\\\Method{}.\\n\",\n \" In certain scenarios, like offloading to CPU RAM, these chunks could be compressed jointly for higher accuracy.\\n\",\n \" }\\n\",\n \" \\\\label{tab:llama-33-70b}\\n\",\n \" \\\\small\\n\",\n \" \\\\centering\\n\",\n \"\\\\vspace{0.4cm}\\n\",\n \" \\\\begin{tabular}{l|ccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{1}{*}{Method} & MATH-500 & NIAH & LITM\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{4}{c}{\\\\tabwithinbest{}Llama 3.3 70B Instruct} \\\\\\\\\\n\",\n \" Vanilla & $75.6_{1.92}$ & 100.0 & 100.0 \\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{8} & $73.2_{1.98}$ & 100.0 & 100.0 \\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{10} & $74.4_{1.95}$ & 100.0 & 100.0 \\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{16} & $73.2_{1.98}$ & 100.0 & 100.0 \\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{20} & $72.6_{1.99}$ & 100.0 & 100.0 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" \\n\",\n \" \\\\end{minipage}\\\\hfill\\n\",\n \" \\\\begin{minipage}[t]{0.50\\\\textwidth}\\n\",\n \"\\\\small\\n\",\n \" \\\\caption{Latency of a simple implementation based on the Transformers library \\\\citep{transformers}, measured on an NVIDIA H100 GPU using Mistral NeMo 12B in bfloat16. In addition, we compare TTFT during recomputation of KV caches with decompression of compressed caches. BF denotes batch size, CTX context length.\\n\",\n \"}\\n\",\n \"\\\\label{tab:latency-mistral}\\n\",\n \"\\\\centering\\n\",\n \"\\\\vspace{0.4cm}\\n\",\n \"\\\\small\\n\",\n \"\\\\resizebox{1.00\\\\linewidth}{!}{%\\n\",\n \"\\\\begin{tabular}{l r r | r r} \\n\",\n \"\\\\toprule \\n\",\n \" \\\\text{Module} & \\\\multicolumn{2}{c|}{BS=8 CTX=8K} & \\\\multicolumn{2}{c}{BS=2 CTX=16K} \\\\\\\\\\n\",\n \" & \\\\text{Comp} & \\\\text{Decomp} & \\\\text{Comp} & \\\\text{Decomp} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Project & $153\\\\,$ ms & $156\\\\,$ ms & $78\\\\,$ ms & $75\\\\,$ ms \\\\\\\\\\n\",\n \" Quantize & $67\\\\,$ ms & $37\\\\,$ ms & $39\\\\,$ ms & $27\\\\,$ ms \\\\\\\\\\n\",\n \" Deflate & $137\\\\,$ ms & $64\\\\,$ ms & $66\\\\,$ ms & $36\\\\,$ ms \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Total & {\\\\bf 379$\\\\,$ ms }& {\\\\bf 267$\\\\,$ ms } & {\\\\bf 194$\\\\,$ ms } & {\\\\bf 143$\\\\,$ ms} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\midrule\\n\",\n \"\\\\multicolumn{2}{l}{Vanilla recompute TTFT} & {\\\\bf 3098 ms} & & {\\\\bf 1780 ms} \\\\\\\\ \\n\",\n \"\\\\multicolumn{2}{l}{\\\\Method{} decomp TTFT} & {\\\\bf 380 ms} & & {\\\\bf 208 ms} \\\\\\\\ \\n\",\n \" \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \" }\\n\",\n \" \\\\end{minipage}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\subfloat[]{\\n\",\n \" \\\\includegraphics[width=0.45\\\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_fineweb_ablate_niter_key.pdf}\\n\",\n \" }\\n\",\n \" \\\\hfill\\n\",\n \" \\\\subfloat[]{\\n\",\n \" \\\\includegraphics[width=0.45\\\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_fineweb_ablate_niter_key.pdf}\\n\",\n \" }\\n\",\n \" \\\\hfill\\n\",\n \" \\\\subfloat[]{\\n\",\n \" \\\\includegraphics[width=0.45\\\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_fineweb_ablate_niter_value.pdf}\\n\",\n \" }\\n\",\n \" \\\\hfill\\n\",\n \" \\\\subfloat[]{\\n\",\n \" \\\\includegraphics[width=0.45\\\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_fineweb_ablate_niter_value.pdf}\\n\",\n \" }\\n\",\n \" \\\\caption{Relative reconstruction error when calibrating \\\\Method{} decorrelation step - ablation of the number of algorithm \\\\citep{halko2010findingstructurerandomnessprobabilistic} iterations. Figures (a)-(b) show key reconstruction error, whereas (c)-(d) show value reconstruction error. Other parameters as in Figure \\\\ref{fig:kv-pca-train}. We note that the larger number of iterations provides slight improvements.}\\n\",\n \" \\\\label{fig:kv-pca-train-more}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \" \\\\subfloat[]{\\n\",\n \" \\\\includegraphics[width=0.45\\\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_openr1.pdf}\\n\",\n \" }\\n\",\n \" \\\\hfill\\n\",\n \" \\\\subfloat[]{\\n\",\n \" \\\\includegraphics[width=0.45\\\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_openr1.pdf}\\n\",\n \" }\\n\",\n \" \\\\caption{Relative reconstruction error when calibrating \\\\Method{} decorrelation step on OpenR1Math \\\\citep{OpenR1Math220k} traces with the error calculation on FineWeb \\\\citep{penedo2024the}. Parameters as in Figure \\\\ref{fig:kv-pca-train}. We note that OpenR1Math traces were published after the release of Llama 3.1 $8$B and Mistral NeMo $12$B, and possibly due to their specificity result in higher generalization error.}\\n\",\n \" \\\\label{fig:kv-pca-train-openr1}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\subfloat[Relative (within head) Absolute Activations]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/kv_norm/head_norm_llama3.1_8b_base_fp16.pdf}\\n\",\n \" }\\n\",\n \" \\\\subfloat[\\\\centering Relative (within head) Variance of Activations]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/kv_norm/head_norm_llama3.1_8b_base_fp16_var.pdf}\\n\",\n \" }\\\\\\\\\\n\",\n \" \\\\subfloat[Relative (within head) Absolute Activations]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/kv_norm/head_norm_mistral_nemo_12b_base_bf16.pdf}\\n\",\n \" }\\n\",\n \" \\\\subfloat[\\\\centering Relative (within head) Variance of Activations]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/kv_norm/head_norm_mistral_nemo_12b_base_bf16_var.pdf}\\n\",\n \" }\\\\\\\\\\n\",\n \" \\\\caption{For key/value head $i$ and channel $j$, we define per-channel mean absolute activation $\\\\mathrm{a}_{i,j} = \\\\frac{1}{n}\\\\sum_{t=1}^{n}{|\\\\mathrm{channel}_{t, i,j}|}$ and plot the relative activation $\\\\mathrm{heatmap}_{i,j} = \\\\mathrm{a}_{i,j}/\\\\max_b{\\\\{\\\\mathrm{a}_{i,b}\\\\}}$ --- Panels (a),(c)(e). \\n\",\n \" Panels (b),(d),(f) show $\\\\frac{\\\\mathrm{varc}_{i,j}}{\\\\max_c{\\\\{\\\\mathrm{varc}_{i,c}\\\\}}}$ where $\\\\mathrm{varc}_{i,j}$ is the variance of $\\\\mathrm{channel}_{t, i,j}$ over $t$ .}\\n\",\n \" \\\\label{fig:kv-cache-norms-ex}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\subfloat[Relative (within head) Absolute Activations]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_1.5B_bf16.pdf}\\n\",\n \" }\\n\",\n \" \\\\subfloat[\\\\centering Relative (within head) Variance of Activations]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_1.5B_bf16_var.pdf}\\n\",\n \" }\\\\\\\\\\n\",\n \" \\\\subfloat[Relative (within head) Absolute Activations]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_7B_bf16.pdf}\\n\",\n \" }\\n\",\n \" \\\\subfloat[\\\\centering Relative (within head) Variance of Activations]{\\n\",\n \" \\\\includegraphics[width=0.48\\\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_7B_bf16_var.pdf}\\n\",\n \" }\\\\\\\\\\n\",\n \" \\\\caption{For key/value head $i$ and channel $j$, we define per-channel mean absolute activation $\\\\mathrm{a}_{i,j} = \\\\frac{1}{n}\\\\sum_{t=1}^{n}{|\\\\mathrm{channel}_{t, i,j}|}$ and plot the relative activation $\\\\mathrm{heatmap}_{i,j} = \\\\mathrm{a}_{i,j}/\\\\max_b{\\\\{\\\\mathrm{a}_{i,b}\\\\}}$ --- Panels (a),(c)(e). \\n\",\n \" Panels (b),(d),(f) show $\\\\frac{\\\\mathrm{varc}_{i,j}}{\\\\max_c{\\\\{\\\\mathrm{varc}_{i,c}\\\\}}}$ where $\\\\mathrm{varc}_{i,j}$ is the variance of $\\\\mathrm{channel}_{t, i,j}$ over $t$ .}\\n\",\n \" \\\\label{fig:kv-cache-norms-ex-p2}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation on the skipping compression of the first four tokens. We note that the difference starts to be visible with larger compression ratios, and that it is in favor of skipping compression of potential attention sinks \\\\citep{xiao2024efficientstreaminglanguagemodels}. Results are presented as $\\\\mathrm{score}_{\\\\mathrm{stderr}}$ where ${\\\\mathrm{stderr}}$ is bootstraped by LM Evaluation Harness (where available) \\\\citep{eval-harness}. The differences in compression ratios, are due to the fact that we count the skipped tokens into compression ratio.}\\\\label{tab:ablate-skipping-first-four-tokens}\\n\",\n \"\\\\small\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{cccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \"\\\\multirow{2}{*}{Model} & \\\\multirow{2}{*}{Method} & \\\\multirow{2}{*}{CR} & GSM8K & MMLU & QASPER & LITM 100 & RULER-VT \\\\\\\\\\n\",\n \" & & & \\\\multicolumn{2}{c}{Math \\\\& Knowledge} & \\\\multicolumn{3}{c}{Long Context} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multirow{4}{*}{Llama 3.1 8B} & \\\\methodopcr{0}{16} & \\\\crinterval{19}{22} & $56.8_{ 1.4}$ & $60.3_{ 0.4}$ & $40.2$ & $99.2_{ 0.1}$ & $98.2_{0.4}$ \\\\\\\\\\n\",\n \"& \\\\methodopcr{4}{16} & \\\\crinterval{18}{22} & $56.9_{ 1.4}$ & $60.1_{ 0.4}$ & $40.7$ & $99.3_{ 0.1}$ &$99.1_{0.3}$\\\\\\\\\\n\",\n \"& \\\\methodopcr{0}{64} & \\\\crinterval{76}{90} & $1.6_{ 0.3}$ & $9.9_{ 0.2}$ & $27.6$ & $0.0_{ 0.0}$ &$61.8_{1.5}$\\\\\\\\\\n\",\n \"& \\\\methodopcr{4}{64} & \\\\crinterval{60}{88} & $57.2_{ 1.4}$ & $60.7_{ 0.4}$ & $37.8$ & $90.2_{ 0.4}$ &$95.9_{0.6}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multirow{2}{*}{MN-Minitron 8B}\\n\",\n \"& \\\\methodopcr{0}{64} & \\\\crinterval{79}{97} & $59.5_{ 1.4}$ & $61.9_{0.4}$ & $37.9$ & $55.1_{ 0.6}$ &$91.5_{0.9}$\\\\\\\\\\n\",\n \"& \\\\methodopcr{4}{64} & \\\\crinterval{53}{95} & $57.8_{ 1.4}$ & $62.1_{ 0.4}$ & $38.1$ & $59.5_{ 0.6}$ &$93.4_{0.8}$\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multirow{2}{*}{Mistral NeMo 12B}\\n\",\n \"\\n\",\n \"& \\\\methodopcr{0}{64} & \\\\crinterval{77}{89} & $61.9_{1.3}$ & $62.4_{0.4}$ & $37.5$ & $84.8_{0.4}$ &$95.8_{0.6}$\\\\\\\\\\n\",\n \"& \\\\methodopcr{4}{64} & \\\\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation of key/value compressibility with \\\\Method{}. We use the same \\\\Method{} configuration as in Table \\\\ref{tab:nonthinking-results}, but independently change key and value lossy compression rates. To denote that value compression ratio was set to $32$ and key was set to $64$ we use \\\\methodopcrk{64}}\\\\label{tab:nonthinking-ablate-key-vs-value}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{lc|ccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \"\\\\multirow{1}{*}{Method} & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{7}{c}{\\\\tabwithinbest{}Llama 3.1 8B} \\\\\\\\\\n\",\n \"\\\\methodopcrkl{256} & \\\\crinterval{55}{80} &$57.1_{1.4}$& 57.4 & 36.6 &$48.6_{1.6}$&$91.9_{0.9}$\\\\\\\\\\n\",\n \"\\\\methodopcrvl{256} & \\\\crinterval{55}{77} &$56.8_{1.4}$& 57.5 & 36.3 &$71.9_{1.4}$&$95.9_{0.6}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{7}{c}{\\\\tabwithinbest{}Mistral NeMo 12B} \\\\\\\\\\n\",\n \"\\\\methodopcrk{256} & \\\\crinterval{69}{79} &$62.2_{1.3}$& 61.7 & 34.6 &$73.2_{1.4}$&$90.4_{0.9}$\\\\\\\\\\n\",\n \"\\\\methodopcrv{256} & \\\\crinterval{69}{77} &$57.1_{1.4}$& 59.8 & 35.2 &$77.5_{1.3}$&$89.5_{1.0}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\\\clearpage\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation of the number of tokens used for \\\\Method{} calibration, along with respective PCA and DP calibration times. PCA calibration was performed using single H100 $80$GB GPU, calculation of DP tables (except simulation of quantization) was offloaded to the node cpu. We additionally limit DP calibration data to first 32K tokens, therefore we do not see increase in dp time after 40k calibration tokens. All calibration datapieces come from a 50/50 mixture of FineWeb \\\\citep{penedo2024the} and OpenMathR1 \\\\citep{OpenR1Math220k} traces between 1K and 8K tokens.}\\\\label{tab:nonthinking-ablate-num-tokens}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{lc|cccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \" \\\\multirow{1}{*}{Method} & Data & PCA Calib & DP Calib & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{10}{c}{\\\\tabwithinbest{}Mistral NeMo 12B} \\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{32} & \\\\multirow{3}{*}{20K} & \\\\multirow{3}{*}{41.3s} & 6.5 min & \\\\crinterval{31}{42} & $63.0_{1.3}$ & $63.9_{0.4}$ & $34.8$ & $97.3_{0.2}$ &$98.9_{0.3}$\\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{64} & & & 5.4 min & \\\\crinterval{63}{87} & $63.9_{1.3}$ & $61.7_{0.4}$ & $31.8$ & $88.8_{0.4}$ &$96.9_{0.5}$\\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{256} & & & 3.9 min & \\\\crinterval{148}{340} & $59.6_{1.4}$ & $51.5_{0.4}$ & $23.3$ & $10.4_{0.4}$ &$66.8_{1.5}$\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\methodopcrdef{4}{32} & \\\\multirow{3}{*}{40K} & \\\\multirow{3}{*}{47.8s} & 7.2 min & \\\\crinterval{31}{43} & $64.2_{1.3}$ & $63.0_{0.4}$ & $35.3$ & $98.7_{0.1}$ &$99.5_{0.2}$\\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{64} & & & 6.1 min & \\\\crinterval{63}{88} & $63.7_{1.3}$ & $61.9_{0.4}$ & $32.4$ & $95.7_{0.3}$ &$97.8_{0.5}$\\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{256} & & & 4.6 min & \\\\crinterval{148}{344} & $58.3_{1.4}$ & $50.1_{0.4}$ & $23.7$ & $9.2_{0.4}$ &$70.6_{1.4}$\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\methodopcrdef{4}{32} & \\\\multirow{3}{*}{80K} & \\\\multirow{3}{*}{60.4s} & 7.2 min & \\\\crinterval{31}{43} & $63.6_{1.3}$ & $63.9_{0.4}$ & $36.0$ & $98.0_{0.2}$ &$99.3_{0.3}$\\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{64} & & & 6.1 min & \\\\crinterval{63}{88} & $63.3_{1.3}$ & $62.0_{0.4}$ & $32.2$ & $94.5_{0.3}$ &$97.8_{0.5}$\\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{256} & & & 4.6 min & \\\\crinterval{148}{339} & $60.5_{1.3}$ & $51.7_{0.4}$ & $23.3$ & $13.6_{0.4}$ &$83.7_{1.2}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\\\hline\\n\",\n \"\\\\methodopcrdef{4}{32} & \\\\multirow{3}{*}{160K} & \\\\multirow{3}{*}{85.6s} & 7.2 min & \\\\crinterval{31}{43} & $63.2_{1.3}$ & $64.3_{0.4}$ & $36.6$ & $99.5_{0.1}$ &$99.4_{0.3}$\\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{64} & & & 6.1 min & \\\\crinterval{63.2}{87} & $64.6_{1.3}$ & $62.2_{0.4}$ & $32.8$ & $96.9_{0.2}$ &$97.7_{0.5}$\\\\\\\\\\n\",\n \"\\\\methodopcrdef{4}{256} & & & 4.6 min & \\\\crinterval{148}{341} & $61.4_{1.3}$ & $55.5_{0.4}$ & $24.3$ & $34.2_{0.6}$ &$79.5_{1.3}$\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\\\clearpage\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation of the source of data. We consider \\\\Method{} calibrated fully on FineWeb \\\\citep{penedo2024the}, fully on OpenMathR1 \\\\citep{OpenR1Math220k} and a 50/50 mixture. For all cases we utilize a 50/50 mix of documents between 1K and 8K tokens along with documents between 8K and 32K tokens. We calibrate using 160K tokens.}\\\\label{tab:nonthinking-ablate-data-source}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{lc|cccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \" \\\\multirow{1}{*}{Method} & Data & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{8}{c}{\\\\tabwithinbest{}Mistral NeMo 12B} \\\\\\\\\\n\",\n \"\\\\multirow{3}{*}{\\\\methodopcrdef{4}{32}} & FineWeb + OpenR1Math & \\\\crinterval{31}{43} & $62.2_{1.3}$ & $63.8_{0.4}$ & $37.5$ & $99.6_{0.1}$ &$98.7_{0.4}$\\\\\\\\\\n\",\n \" & FineWeb & \\\\crinterval{31}{43} & $63.5_{1.3}$ & $63.5_{0.4}$ & $37.5$ & $98.5_{0.2}$ &$98.9_{0.3}$\\\\\\\\\\n\",\n \" & OpenR1Math & \\\\crinterval{31}{43} & $63.5_{1.3}$ & $64.8_{0.4}$ & $37.8$ & $99.7_{0.1}$ &$99.3_{0.3}$\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{3}{*}{\\\\methodopcrdef{4}{64}} & FineWeb + OpenR1Math & \\\\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\\\\\\n\",\n \" & FineWeb & \\\\crinterval{63}{87} & $63.2_{1.3}$ & $59.9_{0.4}$ & $36.5$ & $92.0_{0.3}$ &$97.4_{0.5}$\\\\\\\\\\n\",\n \" & OpenR1Math & \\\\crinterval{63}{86} & $62.2_{1.3}$ & $63.7_{0.4}$ & $38.2$ & $98.5_{0.2}$ &$96.5_{0.6}$\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{3}{*}{\\\\methodopcrdef{4}{256}} & FineWeb + OpenR1Math & \\\\crinterval{148}{340} & $60.0_{1.3}$ & $52.2_{0.4}$ & $31.6$ & $40.0_{0.6}$ &$84.3_{1.1}$\\\\\\\\\\n\",\n \" & FineWeb & \\\\crinterval{148}{343} & $57.9_{1.4}$ & $51.5_{0.4}$ & $31.0$ & $14.1_{0.4}$ &$74.5_{1.4}$\\\\\\\\\\n\",\n \" & OpenR1Math & \\\\crinterval{156}{342} & $56.6_{1.4}$ & $54.0_{0.4}$ & $29.4$ & $21.0_{0.5}$ &$81.3_{1.2}$\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Mean and standard deviation of downstream performance measured on 5 different calibrations sets (50/50 mixture of OpenR1Math \\\\citep{OpenR1Math220k} and FineWeb \\\\citep{penedo2024the}, 160K tokens, documents between 1K and 8K tokens). Results presented as $\\\\mathrm{mean}_{\\\\pm \\\\mathrm{std}}$}\\\\label{tab:nonthinking-ablate-data-source-std}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{l|cccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \" \\\\multirow{1}{*}{Method} & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{7}{c}{\\\\tabwithinbest{}Mistral NeMo 12B} \\\\\\\\\\n\",\n \"Vanilla & 1 & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\\\\\\n\",\n \"\\\\multirow{1}{*}{\\\\methodopcrdef{4}{16}} & \\\\crinterval{17}{20} & $63.5_{\\\\pm 0.9}$ & $64.7_{\\\\pm 0.3}$ & $37.2_{\\\\pm 0.4}$ & $99.6_{\\\\pm 0.3}$ & $99.7_{\\\\pm 0.0}$ \\\\\\\\\\n\",\n \"\\\\multirow{1}{*}{\\\\methodopcrdef{4}{32}} & \\\\crinterval{31}{43} & $63.1_{\\\\pm 0.5}$ & $64.4_{\\\\pm 0.6}$ & $36.1_{\\\\pm 0.7}$ & $98.1_{\\\\pm 2.0}$ & $99.2_{\\\\pm 0.3}$ \\\\\\\\\\n\",\n \"\\\\multirow{1}{*}{\\\\methodopcrdef{4}{64}} & \\\\crinterval{50}{88} & $63.1_{\\\\pm 1.3}$ & $63.3_{\\\\pm 0.9}$ & $32.9_{\\\\pm 0.7}$ & $93.1_{\\\\pm 3.6}$ & $98.1_{\\\\pm 0.4}$ \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation of out of distribution source of data. We consider \\\\Method{} calibrated on a 50/50 mixture of FineWeb \\\\citep{penedo2024the} and OpenMathR1 \\\\citep{OpenR1Math220k} along with calibration on Python/C/Assembly from the StarCoder dataset \\\\citep{li2023starcodersourceyou}. In all cases we utilize files between 1K and 8K tokens and calibrate on 160K tokens. For configurations that were tested using several seeds we report $\\\\mathrm{score}_{\\\\pm \\\\mathrm{std}}$, whereas for others we report $\\\\mathrm{score}_{\\\\mathrm{stderr}}$}\\\\label{tab:nonthinking-ablate-data-source-code}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{lc|cccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \" \\\\multirow{1}{*}{Method} & Calibration Data & CR & GSM & MMLU & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\n\",\n \"\\\\multicolumn{8}{c}{\\\\tabwithinbest{}Mistral NeMo 12B} \\\\\\\\\\n\",\n \"Vanilla & \\\\multirow{3}{*}{-} & 1 & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\\\\\\n\",\n \"GEAR 2bit & & 5 & $59.8_{1.4}$ & $64.0_{0.4}$ & $38.6$ & $96.9_{0.2}$ &$99.4_{0.3}$\\\\\\\\\\n\",\n \"KIVI 2bit & & 5 & $59.7_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $91.9_{0.3}$ &$98.3_{0.4}$\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{2}{*}{\\\\methodopcrdef{4}{16}} & FineWeb + OpenR1Math & \\\\crinterval{17}{20} & $63.5_{\\\\pm 0.9}$ & $64.7_{\\\\pm 0.3}$ & $37.2_{\\\\pm 0.4}$ & $99.6_{\\\\pm 0.3}$ & $99.7_{\\\\pm 0.0}$ \\\\\\\\\\n\",\n \"& Python & \\\\crinterval{17}{20} & $59.4_{1.4}$ & $65.2_{0.4}$ & $37.4$ & $99.9_{0.0}$ &$99.7_{0.2}$\\\\\\\\\\n\",\n \"& C & \\\\crinterval{17}{20} & $55.0_{1.4}$ & $65.4_{0.4}$ & $38.0$ & $99.2_{0.1}$ &$99.3_{0.3}$\\\\\\\\\\n\",\n \"& Assembly & \\\\crinterval{17}{20} & $58.9_{1.4}$ & $65.2_{0.4}$ & $37.0$ & $99.9_{0.0}$ &$99.7_{0.2}$\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{2}{*}{\\\\methodopcrdef{4}{32}} & FineWeb + OpenR1Math & \\\\crinterval{31}{43} & $63.1_{\\\\pm 0.5}$ & $64.4_{\\\\pm 0.6}$ & $36.1_{\\\\pm 0.7}$ & $98.1_{\\\\pm 2.0}$ & $99.2_{\\\\pm 0.3}$ \\\\\\\\\\n\",\n \"& Python & \\\\crinterval{35}{43} & $59.0_{1.4}$ & $64.3_{0.4}$ & $36.3$ & $99.7_{0.1}$ &$99.2_{0.3}$\\\\\\\\\\n\",\n \"& C & \\\\crinterval{31}{43} & $50.2_{1.4}$ & $64.7_{0.4}$ & $36.8$ & $96.2_{0.2}$ &$99.3_{0.3}$\\\\\\\\\\n\",\n \"& Assembly & \\\\crinterval{31}{43} & $55.2_{1.4}$ & $64.2_{0.4}$ & $36.7$ & $99.6_{0.1}$ &$99.4_{0.3}$\\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\multirow{2}{*}{\\\\methodopcrdef{4}{64}} & FineWeb + OpenR1Math & \\\\crinterval{50}{88} & $63.1_{\\\\pm 1.3}$ & $63.3_{\\\\pm 0.9}$ & $32.9_{\\\\pm 0.7}$ & $93.1_{\\\\pm 3.6}$ & $98.1_{\\\\pm 0.4}$ \\\\\\\\\\n\",\n \"& Python & \\\\crinterval{63}{87} & $56.3_{1.4}$ & $62.0_{0.4}$ & $33.9$ & $98.0_{0.2}$ &$97.4_{0.5}$\\\\\\\\\\n\",\n \"& C & \\\\crinterval{63}{87} & $54.4_{1.4}$ & $63.3_{0.4}$ & $34.5$ & $95.4_{0.3}$ &$97.8_{0.5}$\\\\\\\\\\n\",\n \"& Assembly & \\\\crinterval{50}{86} & $60.9_{1.3}$ & $62.2_{0.4}$ & $33.0$ & $99.1_{0.1}$ &$98.3_{0.4}$\\\\\\\\\\n\",\n \" \\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation of the sliding window size of recent tokens that are not compressed. For a fair compression in this table we simulate a sequence of short conversations by running compressing/eviction on the cache every $s=1$ instead every $s=16$ tokens. Therefore, the $w=16$ token window is left int the range $15$-$16$ instead of $0$-$16$.}\\\\label{tab:kvtc-ablate-ws}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{lc|cccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \" \\\\multirow{1}{*}{Method} & Window Size & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\n\",\n \" \\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{8}{c}{\\\\tabwithinbest{}Llama 3.1 8B} \\\\\\\\\\n\",\n \"\\\\multirow{4}{*}{\\\\methodopcrdef{4}{64}} & 1 & \\\\crinterval{59}{88} & $41.2_{1.4}$ & $53.8_{0.4}$ & $36.5$ & $68.3_{0.6}$ &$87.7_{1.0}$\\\\\\\\\\n\",\n \"& 16 & \\\\crinterval{58}{88} & $53.0_{1.4}$ & $56.0_{0.4}$ & $38.1$ & $80.0_{0.5}$ &$88.0_{1.0}$\\\\\\\\\\n\",\n \"& 64 & \\\\crinterval{57}{88} & $55.8_{1.4}$ & $59.2_{0.4}$ & $37.7$ & $89.8_{0.4}$ &$95.8_{0.6}$\\\\\\\\\\n\",\n \" & 128 & \\\\crinterval{60}{88} & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\n\",\n \"\\\\multicolumn{8}{c}{\\\\tabwithinbest{}Mistral NeMo 12B} \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\multirow{4}{*}{\\\\methodopcrdef{4}{64}} & 1 & \\\\crinterval{61}{87} & $53.0_{1.4}$ & $54.9_{0.4}$ & $36.4$ & $88.6_{0.4}$ &$90.7_{0.9}$\\\\\\\\\\n\",\n \"& 16 & \\\\crinterval{60}{87} & $60.1_{1.3}$ & $56.4_{0.4}$ & $37.7$ & $88.9_{0.4}$ &$95.8_{0.6}$\\\\\\\\\\n\",\n \"& 64 & \\\\crinterval{59}{87} & $62.2_{1.3}$ & $59.0_{0.4}$ & $37.8$ & $93.0_{0.3}$ &$98.0_{0.4}$\\\\\\\\\\n\",\n \" & 128 & \\\\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\\\clearpage\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation of the lossless compression algorithms, performed using Mistral Nemo 12B with \\\\methodopcrdef{4}{32}. Identity stands for no additional lossless compression (just PCA + DP Quantization; note that we count the omitted sinks into compression ratio, what is notable for tasks with shorter contexts). We mark results that have compression ratio advantage over Identity smaller than 1 in red.}\\\\label{tab:kvtc-ablate-deflate}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{l|ccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \"\\\\multirow{2}{*}{Algorithm} & \\\\multicolumn{5}{c}{Compression Ratio} \\\\\\\\\\n\",\n \" & Min-Max & GSM8K & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \" ANS & \\\\crinterval{32.8}{37.6} & 32.8 & 37.6 & 36.8 & 37.0 \\\\\\\\\\n\",\n \" Bitcomp & \\\\crinterval{29.6}{32.3} & \\\\badresult{}29.6 & \\\\badresult{}32.3 & \\\\badresult{}32.2 & \\\\badresult{}32.2 \\\\\\\\\\n\",\n \" DEFLATE & \\\\crinterval{34.7}{42.9} & 34.7 & 39.5 & 39.7 & 42.9 \\\\\\\\\\n\",\n \" GDeflate & \\\\crinterval{34.6}{42.8} & 34.6 & 39.4 & 39.6 & 42.8 \\\\\\\\\\n\",\n \" Identity & \\\\crinterval{29.6}{32.4} & \\\\badresult{}29.6 & \\\\badresult{}32.4 & \\\\badresult{}32.2 & \\\\badresult{}32.3 \\\\\\\\\\n\",\n \" LZ4 & \\\\crinterval{29.5}{35.5} & \\\\badresult{}29.5 & \\\\badresult{}32.4 & \\\\badresult{}32.7 & 35.5 \\\\\\\\\\n\",\n \" Snappy & \\\\crinterval{29.4}{34.5} & \\\\badresult{}29.4 & \\\\badresult{}32.2 & \\\\badresult{}32.4 & 34.5 \\\\\\\\\\n\",\n \" zStandard & \\\\crinterval{34.6}{46.3} & 34.6 & 39.4 & 39.9 & 46.3 \\\\\\\\\\n\",\n \"\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation of the importance of DP quantization over pure PCA. For alteration of sliding window size we follow the protocol from Appendix~\\\\ref{sec:appendix:sec-kvtc-ws-ablate}.}\\\\label{tab:kvtc-ablate-dp-pca}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{lcc|cccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \" \\\\multirow{1}{*}{Window Size} & Method & Modification & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\n\",\n \" \\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{9}{c}{\\\\tabwithinbest{}Llama 3.1 8B} \\\\\\\\\\n\",\n \"\\\\multirow{8}{*}{16} & \\\\multirow{2}{*}{\\\\methodopcrdef{4}{8}} & - & \\\\crinterval{9}{10} & $57.5_{1.4}$ & $59.4_{0.4}$ & $40.1$ & $99.1_{0.1}$ &$98.2_{0.4}$\\\\\\\\\\n\",\n \"& & -DPQ & \\\\crinterval{8}{9} & $56.9_{1.4}$ & $57.5_{0.4}$ & $40.1$ & $98.6_{0.1}$ &$93.0_{0.8}$\\\\\\\\\\n\",\n \"\\\\cmidrule{2-9}\\n\",\n \"& \\\\multirow{2}{*}{\\\\methodopcrdef{4}{16}} & - & \\\\crinterval{18}{22} & $57.2_{1.4}$ & $59.5_{0.4}$ & $40.6$ & $99.4_{0.1}$ &$98.3_{0.4}$\\\\\\\\\\n\",\n \"& & -DPQ & \\\\crinterval{16}{17} & $52.0_{1.4}$ & $53.8_{0.4}$ & $36.9$ & $69.2_{0.6}$ &$87.0_{1.1}$\\\\\\\\\\n\",\n \"\\\\cmidrule{2-9}\\n\",\n \"& \\\\multirow{2}{*}{\\\\methodopcrdef{4}{32}} & - & \\\\crinterval{34}{44} & $55.5_{1.4}$ & $58.2_{0.4}$ & $39.6$ & $98.8_{0.1}$ &$94.8_{0.7}$\\\\\\\\\\n\",\n \"& & -DPQ & \\\\crinterval{31}{34} & $42.9_{1.4}$ & $36.8_{0.4}$ & $34.2$ & $44.4_{0.6}$ &$83.0_{1.2}$\\\\\\\\\\n\",\n \"\\\\cmidrule{2-9}\\n\",\n \"& \\\\multirow{2}{*}{\\\\methodopcrdef{4}{64}} & - & \\\\crinterval{58}{88} & $53.0_{1.4}$ & $56.0_{0.4}$ & $38.1$ & $80.0_{0.5}$ &$88.0_{1.0}$\\\\\\\\\\n\",\n \"& & -DPQ & \\\\crinterval{52}{68} & $21.8_{1.1}$ & $6.5_{0.2}$ & $26.7$ & $5.1_{0.3}$ &$55.5_{1.6}$\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multirow{8}{*}{128} & \\\\multirow{2}{*}{\\\\methodopcrdef{4}{8}} & - & \\\\crinterval{9}{10} & $56.7_{1.4}$ & $59.9_{0.4}$ & $40.0$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\\\\\\n\",\n \"& & -DPQ & \\\\crinterval{8}{9} & $57.0_{1.4}$ & $60.7_{0.4}$ & $40.2$ & $99.5_{0.1}$ &$98.5_{0.4}$\\\\\\\\\\n\",\n \"\\\\cmidrule{2-9}\\n\",\n \"& \\\\multirow{2}{*}{\\\\methodopcrdef{4}{16}} & - & \\\\crinterval{17}{22} & $57.1_{1.4}$ & $60.1_{0.4}$ & $40.7$ & $99.3_{0.1}$ &$99.0_{0.3}$\\\\\\\\\\n\",\n \"& & -DPQ & \\\\crinterval{16}{17} & $55.7_{1.4}$ & $59.7_{0.4}$ & $37.1$ & $85.0_{0.4}$ &$95.5_{0.7}$\\\\\\\\\\n\",\n \"\\\\cmidrule{2-9}\\n\",\n \"\\n\",\n \"& \\\\multirow{2}{*}{\\\\methodopcrdef{4}{32}} & - & \\\\crinterval{33}{44} & $58.4_{1.4}$ & $60.8_{0.4}$ & $39.3$ & $99.1_{0.1}$ &$98.9_{0.3}$\\\\\\\\\\n\",\n \"& & -DPQ & \\\\crinterval{31}{34} & $55.1_{1.4}$ & $56.9_{0.4}$ & $35.3$ & $64.5_{0.6}$ &$89.6_{1.0}$\\\\\\\\\\n\",\n \"\\\\cmidrule{2-9}\\n\",\n \"& \\\\multirow{2}{*}{\\\\methodopcrdef{4}{64}} & - & \\\\crinterval{60}{88} & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\\\\\\n\",\n \"& & -DPQ & \\\\crinterval{47}{68} & $57.2_{1.4}$ & $49.3_{0.4}$ & $28.1$ & $13.1_{0.4}$ &$58.7_{1.5}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Ablation of the number of layers used for PCA. To better isolate the influence of the number of concatenated key/value heads, we run \\\\Method{} without dynamic programming quantization (that is, we run \\\\Method{}-DPQ introduced in Appendix \\\\ref{sec:appendix:ablate_dp}) and with a sliding window $w=16$.}\\\\label{tab:kvtc-ablate-pca-input-features}\\n\",\n \"\\\\centering\\n\",\n \"\\\\setlength{\\\\tabcolsep}{1mm}\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{lc|ccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \" \\\\multirow{1}{*}{Method} & PCA Layers & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\\\\\\n\",\n \"\\n\",\n \" \\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{7}{c}{\\\\tabwithinbest{}Llama 3.1 8B} \\\\\\\\\\n\",\n \"\\\\multirow{6}{*}{\\\\methodopcrdef{4}{8}-DPQ} & 1 & $27.5_{1.2}$ & $24.3_{0.3}$ & $28.2$ & $49.1_{0.6}$ &$70.8_{1.4}$\\\\\\\\\\n\",\n \"& 2 & $44.8_{1.4}$ & $41.1_{0.4}$ & $34.2$ & $77.6_{0.5}$ &$84.9_{1.1}$\\\\\\\\\\n\",\n \"& 4 & $53.3_{1.4}$ & $51.9_{0.4}$ & $37.5$ & $95.9_{0.2}$ &$93.0_{0.8}$\\\\\\\\\\n\",\n \"& 8 & $55.9_{1.4}$ & $55.3_{0.4}$ & $39.7$ & $99.2_{0.1}$ &$90.7_{0.9}$\\\\\\\\\\n\",\n \"& 16 & $56.0_{1.4}$ & $57.1_{0.4}$ & $38.8$ & $98.8_{0.1}$ &$92.8_{0.8}$\\\\\\\\\\n\",\n \" & 32 & $56.9_{1.4}$ & $57.5_{0.4}$ & $40.1$ & $98.6_{0.1}$ &$93.0_{0.8}$\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multirow{6}{*}{\\\\methodopcrdef{4}{16}-DPQ} & 1 & $2.5_{0.4}$ & $0.2_{0.0}$ & $18.4$ & $0.0_{0.0}$ &$0.5_{0.2}$\\\\\\\\\\n\",\n \"& 2 & $13.9_{1.0}$ & $2.3_{0.1}$ & $22.1$ & $0.7_{0.1}$ &$12.9_{1.0}$\\\\\\\\\\n\",\n \"& 4 & $33.3_{1.3}$ & $19.3_{0.3}$ & $29.1$ & $32.0_{0.6}$ &$62.7_{1.5}$\\\\\\\\\\n\",\n \"& 8 & $49.6_{1.4}$ & $43.4_{0.4}$ & $34.4$ & $60.7_{0.6}$ &$85.8_{1.1}$\\\\\\\\\\n\",\n \"& 16 & $51.6_{1.4}$ & $49.1_{0.4}$ & $36.0$ & $72.7_{0.6}$ &$89.0_{1.0}$\\\\\\\\\\n\",\n \" & 32 & $52.0_{1.4}$ & $53.8_{0.4}$ & $36.9$ & $69.2_{0.6}$ &$87.0_{1.1}$\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multirow{6}{*}{\\\\methodopcrdef{4}{32}-DPQ} & 1 & $1.1_{0.3}$ & $0.1_{0.0}$ & $17.8$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\\\\\\n\",\n \"& 2 & $1.5_{0.3}$ & $0.2_{0.0}$ & $18.1$ & $0.0_{0.0}$ &$0.2_{0.1}$\\\\\\\\\\n\",\n \"& 4 & $3.9_{0.5}$ & $0.9_{0.1}$ & $20.0$ & $0.0_{0.0}$ &$1.6_{0.4}$\\\\\\\\\\n\",\n \"& 8 & $28.0_{1.2}$ & $6.4_{0.2}$ & $24.7$ & $2.6_{0.2}$ &$33.0_{1.5}$\\\\\\\\\\n\",\n \"& 16 & $40.1_{1.4}$ & $26.0_{0.4}$ & $31.2$ & $24.6_{0.5}$ &$60.4_{1.5}$\\\\\\\\\\n\",\n \" & 32 & $42.9_{1.4}$ & $36.8_{0.4}$ & $34.2$ & $44.4_{0.6}$ &$83.0_{1.2}$\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multirow{6}{*}{\\\\methodopcrdef{4}{64}-DPQ} & 1 & $0.9_{0.3}$ & $0.3_{0.0}$ & $18.0$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\\\\\\n\",\n \"& 2 & $1.4_{0.3}$ & $0.1_{0.0}$ & $17.7$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\\\\\\n\",\n \"& 4 & $1.5_{0.3}$ & $0.1_{0.0}$ & $18.1$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\\\\\\n\",\n \"& 8 & $2.4_{0.4}$ & $0.6_{0.1}$ & $19.4$ & $0.0_{0.0}$ &$0.2_{0.1}$\\\\\\\\\\n\",\n \"& 16 & $13.9_{1.0}$ & $1.9_{0.1}$ & $22.1$ & $0.0_{0.0}$ &$10.0_{0.9}$\\\\\\\\\\n\",\n \" & 32 & $21.8_{1.1}$ & $6.5_{0.2}$ & $26.7$ & $5.1_{0.3}$ &$55.5_{1.6}$\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Downstream task results, presented also in Table \\\\ref{tab:nonthinking-results}, here shown with standard error as reported by LM Evaluation Harness (where available).}\\\\label{tab:nonthinking-results-std}\\n\",\n \"\\\\centering\\n\",\n \"\\\\small\\n\",\n \"\\\\begin{tabular}{l|ccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\n\",\n \" \\\\multirow{2}{*}{Method} & GSM8K & MMLU & QASPER & LITM 100 & RULER-VT \\\\\\\\\\n\",\n \" & \\\\multicolumn{2}{c}{Math \\\\& Knowledge} & \\\\multicolumn{3}{c}{Long Context} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{6}{c}{\\\\tabwithinbest{}Llama 3.1 8B} \\\\\\\\\\n\",\n \" vanilla & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\\\\\\n\",\n \" GEAR 2bit & $52.8_{1.4}$ & $59.6_{0.4}$ & $40.4$ & $96.9_{0.2}$ &$99.8_{0.2}$\\\\\\\\\\n\",\n \" KIVI 2bit & $52.8_{1.4}$ & $59.6_{0.4}$ & $39.1$ & $88.8_{0.4}$ &$98.9_{0.3}$\\\\\\\\\\n\",\n \" xKV$^{2/16 \\\\;4\\\\mathrm{key}}_{3/16 \\\\;4\\\\mathrm{value}}$ & $56.6_{1.4}$ & $59.5_{0.4}$ & $35.6$ & $99.9_{0.0}$ &$99.8_{0.2}$\\\\\\\\\\n\",\n \" FP8 & $55.2_{1.4}$ & $60.1_{0.4}$ & $40.8$ & $99.4_{0.1}$ & $99.9_{0.1}$ \\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{8} & $57.0_{1.4}$ & $59.8_{0.4}$ & $40.1$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{16} & $56.9_{1.4}$ & $60.1_{0.4}$ & $40.7$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{32} & $57.8_{1.4}$ & $60.6_{0.4}$ & $39.4$ & $99.1_{0.1}$ &$98.9_{0.3}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{64} & $57.2_{1.4}$ & $60.7_{0.4}$ & $37.8$ & $90.2_{0.4}$ &$95.9_{0.6}$\\\\\\\\\\n\",\n \"\\n\",\n \" \\\\HTO{}$_{{1/16} \\\\;\\\\mathrm{past}}^{{1/16} \\\\;\\\\mathrm{recent}}$ & $54.3_{1.4}$ & $44.3_{0.4}$ & $34.3$ & $20.2_{0.5}$ &$50.4_{1.6}$\\\\\\\\\\n\",\n \" \\\\TOVA{}{$\\\\frac{1}{8}$} & $54.5_{1.4}$ & $44.8_{0.4}$ & $38.6$ & $1.2_{0.1}$ &$99.7_{0.2}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{6}{c}{\\\\tabwithinbest{}MN-Minitron 8B} \\\\\\\\\\n\",\n \" Vanilla & $59.1_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $99.8_{0.0}$ &$99.4_{0.3}$\\\\\\\\\\n\",\n \" GEAR 2bit & $57.9_{1.4}$ & $63.6_{0.4}$ & $38.2$ & $96.0_{0.2}$ &$98.3_{0.4}$\\\\\\\\\\n\",\n \" KIVI 2bit & $58.0_{1.4}$ & $63.2_{0.4}$ & $38.2$ & $86.3_{0.4}$ &$96.8_{0.6}$\\\\\\\\\\n\",\n \" xKV$^{2/16 \\\\;5\\\\mathrm{key}}_{3/16 \\\\;5\\\\mathrm{value}}$ & $59.3_{1.4}$ & $63.1_{0.4}$ & $34.5$ & $99.6_{0.1}$ &$99.1_{0.3}$\\\\\\\\\\n\",\n \" FP8 & $60.1_{1.3}$ & $64.3_{0.4}$ & $38.3$ & $99.8_{0.1}$ & $99.2_{0.3}$ \\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{8} & $60.6_{1.3}$ & $64.2_{0.4}$ & $39.1$ & $99.4_{0.1}$ &$98.8_{0.3}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{16} & $60.3_{1.3}$ & $64.1_{0.4}$ & $38.6$ & $99.3_{0.1}$ &$98.8_{0.3}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{32} & $59.1_{1.4}$ & $63.7_{0.4}$ & $37.7$ & $86.9_{0.4}$ &$96.0_{0.6}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{64} & $57.8_{1.4}$ & $62.1_{0.4}$ & $38.1$ & $59.5_{0.6}$ &$93.4_{0.8}$\\\\\\\\\\n\",\n \" \\\\HTO{}$_{{1/16} \\\\;\\\\mathrm{past}}^{{1/16} \\\\;\\\\mathrm{recent}}$ & $55.3_{1.4}$ & $43.5_{0.4}$ & $30.0$ & $16.6_{0.5}$ &$39.2_{1.5}$\\\\\\\\\\n\",\n \" \\\\TOVA{}{$\\\\frac{1}{8}$} & $59.2_{1.4}$ & $48.1_{0.4}$ & $33.9$ & $0.3_{0.1}$ &$99.3_{0.3}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{6}{c}{\\\\tabwithinbest{}Mistral NeMo 12B} \\\\\\\\\\n\",\n \" Vanilla & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\\\\\\n\",\n \" GEAR 2bit & $59.8_{1.4}$ & $64.0_{0.4}$ & $38.6$ & $96.9_{0.2}$ &$99.4_{0.3}$\\\\\\\\\\n\",\n \" KIVI 2bit & $59.7_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $91.9_{0.3}$ &$98.3_{0.4}$\\\\\\\\\\n\",\n \" xKV$^{2/16 \\\\;5\\\\mathrm{key}}_{3/16 \\\\;5\\\\mathrm{value}}$ & $61.9_{1.3}$ & $63.9_{0.4}$ & $33.5$ & $97.9_{0.2}$ &$99.4_{0.3}$\\\\\\\\\\n\",\n \" FP8 & $61.7_{1.3}$ & $64.5_{0.4}$ & $37.9$ & $99.0_{0.1}$ & $99.8_{0.2}$ \\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{8} & $62.5_{1.3}$ & $64.6_{0.4}$ & $37.6$ & $99.9_{0.0}$ &$99.5_{0.2}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{16} & $62.0_{1.3}$ & $64.4_{0.4}$ & $37.6$ & $99.8_{0.0}$ &$99.5_{0.2}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{32} & $62.2_{1.3}$ & $63.8_{0.4}$ & $37.5$ & $99.6_{0.1}$ &$98.7_{0.4}$\\\\\\\\\\n\",\n \" \\\\methodopcrdef{4}{64} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\\\\\\n\",\n \" \\\\HTO{}$_{{1/16} \\\\;\\\\mathrm{past}}^{{1/16} \\\\;\\\\mathrm{recent}}$ & $57.0_{1.4}$ & $45.4_{0.4}$ & $29.5$ & $16.2_{0.5}$ &$35.2_{1.5}$\\\\\\\\\\n\",\n \" \\\\TOVA{}{$\\\\frac{1}{8}$} & $60.3_{1.3}$ & $49.0_{0.4}$ & $36.0$ & $8.7_{0.4}$ &$99.6_{0.2}$\\\\\\\\\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[ht]\\n\",\n \"\\\\caption{Number of parameters used by PCA matrices, before DP, for the tested models. We note that despite treating keys and values separately, while using feature capacity for the efficient \\\\citep{halko2010findingstructurerandomnessprobabilistic} PCA calculation algorithm. For example, Llama 3.1 8B has 32 layers, each with 8 key/value heads, each head of size 128. Therefore, after cross-head concatenation, each key/value has $32\\\\times8\\\\times128 = 32768$ features. The PCA projection $V$ is cut to the first $10$K principal components by \\\\citep{halko2010findingstructurerandomnessprobabilistic} algorithm for efficiency, resulting in $32768 \\\\times 10000 \\\\simeq 328M$ parameters. Further DP bit allocation can remove additional principal directions depending on the desired compression ratio. Both models and PCA projection matrices are stored in 16bit precision.\\n\",\n \"}\\\\label{tab:model-kv-pca-size}\\n\",\n \"\\n\",\n \"\\\\small\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{tabular}{lcl|ccc}\\n\",\n \"\\\\toprule\\n\",\n \"Model & \\\\makecell{\\\\#Params} &\\\\makecell{Key/Value\\\\\\\\Features} & \\\\makecell{Key/Value\\\\\\\\PCA Cap} & \\\\makecell{Key/Value\\\\\\\\PCA Params} & $\\\\frac{\\\\mathrm{TotalPCAParams}}{\\\\mathrm{Model Params}}$ \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Qwen 2.5 R1 1.5B & $1.5$B & $28\\\\times2\\\\times128 = 7168$ & \\\\multirow{2}{*}{8K} & 51M & $6.8$\\\\% \\\\\\\\\\n\",\n \"Qwen 2.5 R1 7B & $7.1$B & $28\\\\times4\\\\times128 = 14336$ & & 115M & $3.2$\\\\% \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Llama 3.1 8B & $7.5$B & $32\\\\times8\\\\times128 = 32768$ & \\\\multirow{3}{*}{10K} & 328M & $8.7$\\\\% \\\\\\\\\\n\",\n \"Llama 3.3 70B & $69.5$B & $80\\\\times8\\\\times128 = 81920$ & & 819M & $2.4$\\\\% \\\\\\\\\\n\",\n \"Mistral NeMo 12B & $11.6$B & $40\\\\times8\\\\times128 = 40960$ & & 410M & $7.1$\\\\% \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n%\n%\n\\documentclass[10pt, logo]{nvidiatechreport} %\n\n%\n%\n\n\\usepackage{natbib}\n\\usepackage{xurl} %\n\\usepackage{hyperref}\n\\usepackage{url}\n\n%\n%\n%\n%\n%\n%\n\\usepackage{graphicx} %\n\\usepackage{wrapfig}\n%\n%\n%\n\\usepackage{caption} %\n%\n%\n%\n%\n%\n\\usepackage{algorithm}\n\\usepackage{algorithmic}\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n%\n\\usepackage{todonotes}\n\\makeatletter\n\\newcommand*\\iftodonotes{\\if@todonotes@disabled\\expandafter\\@secondoftwo\\else\\expandafter\\@firstoftwo\\fi}\n\\makeatother\n\\newcommand{\\noindentaftertodo}{\\iftodonotes{\\noindent}{}}\n\\newcommand{\\fixme}[2][]{\\todo[color=yellow,size=\\scriptsize,fancyline,caption={},#1]{#2}}\n\\newcommand{\\note}[4][]{\\todo[author=#2,color=#3,size=\\scriptsize,fancyline,caption={},#1]{#4}}\n\\newcommand{\\notewho}[3][]{\\note[#1]{#2}{blue!40}{#3}}\n\\newcommand{\\Fixme}[2][]{\\fixme[inline,#1]{#2}\\noindentaftertodo}\n\\newcommand{\\Notewho}[3][]{\\notewho[inline,#1]{#2}{#3}\\noindentaftertodo}\n\\definecolor{edolime}{rgb}{0.9,1,0.3}\n\\newcommand{\\adr}[2][]{\\note[#1]{todo}{edolime!70}{#2}}\n\\newcommand{\\Adr}[2][]{\\adr[inline,#1]{#2}\\noindentaftertodo}\n\n\\usepackage{custom_macros}\n\\usepackage{colortbl}\n\\usepackage{xcolor}\n\n\\usepackage[noabbrev,capitalise]{cleveref}\n\n%\n\n%\n%\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n%\n%\n%\n\n\\usepackage{pifont} %\n\\usepackage{enumitem}\n\\setlist{nosep}\n\n\\captionsetup[subfloat]{justification=centering,singlelinecheck=false}\n\n\\title{KV Cache Transform Coding\\\\for Compact Storage in LLM Inference}\n\\runningtitle{KV Cache Transform Coding for Compact Storage in LLM Inference}\n\n%\n%\n%\n\n\\author{Konrad Staniszewski \\& Adrian Łańcucki\\\\\nNVIDIA\\\\\n\\texttt{kstaniszewsk@nvidia.com}\n}\n\n%\n%\n%\n%\n%\n%\n%\n\n\\newcommand{\\fix}{\\marginpar{FIX}}\n\\newcommand{\\new}{\\marginpar{NEW}}\n\n%\n\n%\n%\n\n\\begin{abstract}\nServing large language models (LLMs) at scale necessitates efficient key-value (KV) cache management. KV caches can be reused across conversation turns via shared-prefix prompts that are common in iterative code editing and chat. However, stale caches consume scarce GPU memory, require offloading, or force recomputation. We present \\Method{}, a lightweight transform coder that compresses KV caches for compact on-GPU and off-GPU storage. Drawing on classical media compression, \\Method{} combines PCA-based feature decorrelation, adaptive quantization, and entropy coding. It requires only a brief initial calibration and leaves model parameters unchanged. By exploiting redundancies in KV caches, \\Method{} achieves up to 20$\\times$ compression while maintaining reasoning and long-context accuracy, and 40$\\times$ or higher for specific use cases. We test \\Method{} with Llama 3, Mistral NeMo, and R1-Qwen 2.5 models across benchmarks\n%\nincluding AIME25, LiveCodeBench, GSM8K, MMLU, Qasper, RULER, and MATH-500.\nIt consistently outperforms inference-time baselines such as token eviction, quantization, and SVD-based methods, while achieving higher compression ratios. These results support \\Method{} as a practical building block for memory-efficient LLM serving with reusable KV caches.\n\\end{abstract}\n\\begin{document}\n\\maketitle\n\n\\section{Introduction}\n\n\\begin{wrapfigure}{r}{0.47\\textwidth}\n\\vspace{-0.24cm}\n \\begin{center}\n %\n \\includegraphics[width=0.45\\textwidth]{figures/kvtc_outline.drawio.pdf}\n \\end{center}\n\\caption{\nThe \\Method{} transform-coding pipeline.\n%\n%\nFeatures are linearly decorrelated via PCA, and the resulting PCA coefficients are quantized using variable bit widths. The PCA basis $V$ is computed once on a calibration dataset and reused for all caches. Key and value caches are compressed separately.}\n \\label{fig:alg-description}\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n \\begin{center}\n \\includegraphics[width=0.75\\linewidth]{figures/kvtc-cr-breakdown.pdf}\n \\end{center}\n \\vspace{-0.4cm}\n \\caption{KV cache compression ratios contributed by parts of the \\Method{} pipeline for Llama 3.1 8B. DEFLATE's variability is marked with black stripes.}\n \\label{fig:cr-breakdown}\n\\vspace{-0.5cm}\n\\end{wrapfigure}\n\n\nChat-based interfaces, commonly used for interacting with large language models (LLMs), enable users to iteratively refine answers across open-domain dialogues and specialized tasks, such as code generation \\citep{chiang2024chatbotarenaopenplatform,köpf2023openassistantconversationsdemocratizing}. Each conversational turn extends the key--value (KV) cache associated with a conversation, storing hidden activations for every previous token. For modern Transformer models, this cache can easily occupy multiple gigabytes.\nAs models scale up in size and reasoning capability, generating increasingly long reasoning chains \\citep{openai2024openaio1card}, the KV cache footprint increases, posing a significant bottleneck for throughput and latency.\nDuring user turns, stale KV caches left on-chip occupy memory, which is needed for serving other users, yet ensure the fastest responses in the future. Conversely, caches could be discarded, incurring the cost of recomputation, or offloaded to CPU DRAM or local/network storage, leading to transfer overheads. This tension creates a latency--throughput dilemma in production systems and necessitates careful configuration.\n\nCrucially, inference frameworks view the local KV caches as databases. Strategies such as block-level paging and prefix sharing promote reuse of caches whenever prompt prefix matches \\citep{kwon2023efficientmemorymanagementlarge}.\nScaling LLM serving increasingly hinges on KV cache management and reuse \\citep{liu2024cachegenkvcachecompression,cheng2024large,yao2025cacheblend}, but current systems struggle to store, move, and refresh these caches efficiently. CacheGen \\citep{liu2024cachegenkvcachecompression} compresses caches for transmission, \noffering at most 8.6$\\times$ KV cache reduction in comparison to a 16-bit baseline. \nSVDq \\citep{yankun2025svdq125bit410xkey} and xKV \\citep{chang2025xkvcrosslayersvdkvcache} pursue low-rank compression during prefill, but both require calculation of per-prompt SVD. Long and frequently used prompts may justify investing more compute for offline training of corpus-specific caches \\citep{eyuboglu2025cartridgeslightweightgeneralpurposelong}.\n\n\nMeanwhile, intensively studied KV cache compression methods, aimed at improving the runtime efficiency of autoregressive generation, offer interim measures to the cache retention problem\n\\citep{yuan2024kvcachecompressionreturn}.\nPrior work hinges on observations that KV cache can be quantized \\citep{frantar2023gptqaccurateposttrainingquantization}\n%\nsparsified \\citep{kivi,hooper2024kvquant10millioncontext}, average-pooled \\citep{nawrot2024dynamicmemorycompressionretrofitting},\nor shared between layers \\citep{brandon2024reducingtransformerkeyvaluecache}; the cache itself is compressible \\citep{yuan2024kvcachecompressionreturn}, and dimensions of keys and values for separate heads show a high degree of correlation \\citep{\n%\nzhang2023h2oheavyhitteroracleefficient}. For long contexts, these methods offer substantial throughput and latency improvements, by lowering KV cache sizes and thus the memory traffic during next token prediction.\nHowever, due to tight latency constraints, often coupled with refraining from modifying weights of the model, these techniques tend to be brittle \\citep{tang2024questqueryawaresparsityefficient}, and accuracy degradation prohibits combining methods for compounded benefits. Finally, these methods seldom exploit the strong low‑rank structure of KV tensors.\n\nIn this paper, we introduce \\Method{}: a simple yet powerful transform coding scheme, compressing KV caches for storage.\nInspired by classical image codecs, it applies a learned orthonormal transform followed by channel‑wise scalar quantization, which dynamically allocates bits, and entropy coding. The resulting bitstream is on average 20$\\times$ smaller than the original 16-bit one, while maintaining comparable accuracy. The method also exposes a smooth compression--accuracy trade-off, with 40$\\times$ or higher compression attainable at modest accuracy decrease. Thus, \\Method{} largely mitigates the problem of KV cache management: lowering the cost of its on-chip retention and the bandwidth required for offloading, without compromising interactive latency.\n\n\\begin{figure*}[t]\n \\centering\n \\subfloat[Keys]{\n \\centering\n \\includegraphics[width=0.48\\linewidth]{figures/cosine_keys.pdf}\n \\label{fig:kv-cache-between-heads-key}\n }\n \\subfloat[Values]{\n \\centering\n \\includegraphics[width=0.48\\linewidth]{figures/cosine_values.pdf}\n \\label{fig:kv-cache-between-heads-value}\n }\n \\caption{Cosine similarity before and after alignment between key (a) and value (b) heads calculated using Llama 3.1 8B on inputs from Qasper \\citep{dasigi2021datasetinformationseekingquestionsanswers,shaham2022scrollsstandardizedcomparisonlong}. For each example, we calculate cosine similarity between all keys/values from the same position and then average across the batch. Orthonormal alignment matrices were produced using 20 samples from the RedPajama v2 \\citep{weber2024redpajama}.}\n \\label{fig:kv-cache-between-heads}\n\\end{figure*}\n\n\\section{Preliminaries}\\label{sec:preliminaries}\n\n\\begin{wraptable}{r}{0.35\\textwidth}\n\\vspace{-0.72cm}\n\\caption{KV cache size in 16 bits for 1K tokens of context.\n}\\label{tab:model-kv-cache-size}\n\\small\n\\centering\n\\resizebox{0.32\\textwidth}{!}{%\n\\begin{tabular}{lr}\n\\toprule\nModel & Size \\\\\n\\midrule\nQwen 2.5 R1 1.5B \n%\n& $28\\,$MiB\\\\\nQwen 2.5 R1 7B\n%\n& $56\\,$MiB \\\\\nLlama 3.1 8B\n%\n& $128\\,$MiB \\\\ \nLlama 3.3 70B Instruct\n%\n& $320\\,$MiB\\\\\nMistral NeMo 12B\n%\n& $160\\,$MiB \\\\\nMN-Minitron 8B\n%\n& $160\\,$MiB \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\vspace{-0.8cm}\n\\end{wraptable}\n\\paragraph{KV Cache Structure}\\label{sec:rotations}\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\nDuring decoding in autoregressive Transformers with multi-head self-attention, the keys and values produced for each processed token are cached to avoid recomputation. The collection of these tensors is the \\emph{KV cache}.\n%\nFor $l$ layers, $h$ heads, head dimension $d_{\\mathrm{head}}$ and sequence length $t$, a 16-bit KV cache occupies\n%\n$(4\\,l\\,h\\,d_{\\mathrm{head}}\\,t)$ bytes.\n\n%\n\nMotivated by work on cross-layer KV cache sharing and compression \\citep{brandon2024reducingtransformerkeyvaluecache,chang2025xkvcrosslayersvdkvcache},\nwe ask whether keys from different attention heads, and analogously values, lie in a shared latent space.\n%\n%\nTo be more precise, we examine if it is possible to align key or value caches, produced by different attention heads, via linear transformations. Specifically, for each pair of attention heads $h_i, h_j$ in the model, \nwe attempt to align their caches $K_i,K_j\\in \\mathbb{R}^{t\\times d_{\\textit{head}}}$ with an orthogonal map found by solving the Procrustes problem \\citep{gower2004procrustes}: \n\\begin{equation}\nR^{\\star}=\\text{arg min}_{R}\\ %\n\\norm{K_i - K_j R}_F \\quad \\text{s.t. } R^\\top R = I.\n\\end{equation}\nWe then compute token-wise cosine similarity between $K_i$ and $K_j$ before alignment, and between $K_i$ and $K_j R^\\star$ after alignment. We repeat the same procedure for values using $V_i, V_j$.\n%\nBefore alignment, inter-head cosine similarity is typically below 0.2. After orthogonal alignment, similarity increases substantially for keys and moderately for values (\\cref{fig:kv-cache-between-heads}). This pattern suggests that key heads largely inhabit a common subspace up to an orthogonal transformation; their dissimilarity before alignment likely stems from random initialization of key and value projection matrices.\nWe note that for a data matrix $A \\in \\mathbb{R}^{n \\times d}$, if $k$ directions suffice to explain all of the variance of $A$, then $k$ directions suffice to explain all of the variance of $B = [A, AR] \\in \\mathbb{R}^{n \\times (d+d')}$, for $R \\in \\mathbb{R}^{d \\times d'}$. This motivates our choice of PCA as a dimensionality reduction method.\n%\n\n%\n%\n%\n\n%\n\n%\n%\n%\n%\n%\n\n%\n%\n%\n%\n%\n%\n\nAnother motivation comes from the work on efficient attention kernels \\citep{jiang2024minference}. \nTo be more precise, from the observation that different attention heads can show similar attention patterns. \nIn a simplified setting without RoPE \\citep{su2023roformerenhancedtransformerrotary}, where keys are equal to queries and we assume the exact equality of dot products that create the attention patterns, the key spaces are equal up to an orthogonal transform by the uniqueness of Gram realizations \\citep{Horn2013MatrixAnalysis}.\n\n\\paragraph{Sliding Windows and Sink Tokens}\n\nWe avoid compressing both the $w$ most recent tokens and $s$ oldest tokens (attention sinks) due to their disproportionately high contribution to typical attention patterns \\citep{jiang2024minference}.\nIn transform coding for vision and audio, bits are allocated to transform coefficients so that quantization induces minimal perceptual distortion. By loose analogy, the attention mass allocated to a token can be viewed as a proxy for its importance.\nIn addition, when PCA is used to reduce the dimensionality of keys and values, the sink tokens yield higher reconstruction errors, as shown in Figure \\ref{fig:kv-pca-train}. \n\n%\n\nForeshadowing the experiments described in \\cref{sec:exp}, we have chosen $w=128$ and $s=4$ for evaluation. To illustrate their influence on accuracy, we ablate on their compression by setting either $w=0$ or $s=0$, as shown in \\cref{fig:kv-ablate-sinks-and-sw}. \n%\nThese experiments show that compressing these tokens can significantly lower, or even entirely collapse the accuracy at high compression ratios.\n\n%\n\n%\n%\n%\n%\n%\n%\n%\n%\n%\n%\n\n\\begin{figure*}[t]\n \\centering %\n \\subfloat[Attention sink compression ablation]{\n \\includegraphics[width=0.48\\linewidth]{figures/ablations/omit_compression_of_sinks.pdf}\n }\n \\subfloat[Sliding window compression ablation]{\n \\includegraphics[width=0.48\\linewidth]{figures/ablations/kvtc_vs_kvtc_without_sliding_window.pdf}\n }\n \\caption{\nAblation of \\Method{} with compression ratio 64$\\times$ on Llama 3.1 8B: (a) compression disabled for attention sink tokens; (b) compression disabled for the final 128 tokens. All other settings are fixed. Additional ablations are provided in \\cref{sec:appendix:ablate_sink,sec:appendix:sec-kvtc-ws-ablate}.\n}\n \\label{fig:kv-ablate-sinks-and-sw}\n\\end{figure*}\n%\n\n\n\\paragraph{Multi-Turn Conversations}\nLet a conversation be an ordered sequence\n\\begin{equation*}\n\\mathcal{C}= ((x_0,\\,y_0),\\,(x_1,\\,y_1),\\dots),\n\\end{equation*}\nwhere $x_t$ denotes the user (or system) input at turn $t$ and $y_t$ the generated reply. Generation of $y_t$ consists of a prefill pass, which produces the KV cache for all preceding tokens $(x_0,y_0,\\dots,x_t)$, followed by iterative decoding, which generates the tokens of $y_t$ one at a time.\n\nWhen a new user prompt $x_i$ is received,\nthe existing KV cache can be re-used and only newly added tokens have to be forwarded through the model, reducing computation and time-to-first-token (TTFT). However, if the cache has been deleted, the model must reprocess the entire conversation as a prompt, resulting in quadratic recomputation of attention across the input. \n\n\\begin{wrapfigure}{r}{0.45\\textwidth}\n\\vspace{-0.4cm}\n \\centering\n \\includegraphics[width=1.0\\linewidth]{figures/serving_times.drawio.pdf}\n \\caption{A high-level architecture of KV-cache-aware LLM serving environment.}\n \\label{fig:serving-arch}\n\\vspace{-0.2cm}\n\\end{wrapfigure}\n\n\\paragraph{KV Cache Management while Serving}\nEfficient LLM deployments often split prefill and decode across separate nodes due to their distinct performance profiles \\citep{zhong2024distserve}, as shown in \\cref{fig:serving-arch}. The prefill node produces the KV cache and transmits it to the decode node over a high-speed fabric, typically RDMA-capable such as InfiniBand or RoCE, minimizing latency and CPU overhead on the host. Both nodes may maintain tiered KV caches: GPU HBM (hot), CPU DRAM (warm), and NVMe/SSD (cold), managed with a retention policy.\n%\nLong-term storage might require sending caches to a remote location.\nCrucially, the decision to select a node for either prefill or decode of a certain input can be dictated by the already-held KV cache with a matching prefix. In such setups, KV cache transfers are typically the dominant cross-node traffic.\n\n%\n%\n%\n\n%\n\nWhy compress KV caches after the prefill or decode phase?\nCompression can: (i) extend the effective capacity of a KV cache database, and thus the lifetimes of caches, roughly in proportion to the compression ratio, and (ii) reduce network traffic. We discuss both angles below.\n\n\\begin{enumerate}[leftmargin=*,label=(\\roman*)]\n \\item Extending KV cache lifetimes increases cache hit rates in higher tiers (HBM/DRAM), often avoiding or substantially reducing prefill time for prompts with long, recently processed prefixes. For example, during a session with a coding assistant, a single 1{,}000-line file tokenized at $\\sim\\!10$ tokens per line and processed by Llama~3.3~70B yields about 1.6$\\,$GiB of 8-bit KV cache. Subsequent conversation turns, or a few parallel conversations about this file, might reuse the corresponding cache. However, on a node which serves multiple clients, the volume of generated KV cache might shorten its hot/warm residency even at moderate batch sizes. A 20$\\times$ lifetime extension via compression might determine whether a KV cache remains hot/warm until it becomes useful, or needs to be recomputed from scratch.\n \\item Prefill time scales as $\\mathcal{O}(n^2)$ with prompt length and typically dominates transfer time. In addition, KV caches can be streamed by layer during prefill in order to further reduce TTFT \\citep{qin2025mooncake}. However, KV cache compression reduces memory traffic proportionally to the compression ratio, which might be critical when the network bandwidth is saturated and becomes the bottleneck.\n\\end{enumerate}\n\n%\n%\n%\n%\n%\n%\n%\n%\n\n\\begin{figure*}[t]\n \\centering\n \\includegraphics[scale=0.62]{figures/pca_dataset_error.pdf}\n \\hspace{-3mm}\n \\includegraphics[scale=0.62]{figures/pca_reconstruct_error.pdf}\n \\includegraphics[scale=0.62]{figures/bit_assignment2.pdf}\n \\caption{Calibration of Llama 3.1 8B with \\Method{}. \\textbf{Left:} Reconstruction error as a function of the size of calibration set. The arrow $A\\rightarrow B$ denotes fitting PCA on dataset A and calculating the error on B.\n %\n \\textbf{Middle:} The reconstruction error as a function of position in the context. The error is higher for the sink tokens. \\textbf{Right:} Bit assignment computed via dynamic programming, counting in the per-group scaling factors.}\n \\label{fig:kv-pca-train}\n\\end{figure*}\n\n\\section{Method}\n\nOur \\Methodfull{} (\\Method{}), shown in \\cref{fig:alg-description}, builds upon the transform-coding framework \\citep{1672377,952802}, a widely adopted methodology for designing image and video compression algorithms such as JPEG \\citep{jpeg_standard}. It applies\nfeature decorrelation by projecting onto an orthonormal basis matrix $V$ obtained via the singular value decomposition (SVD) of centered calibration data (i.e., principal component analysis, PCA). Quantization parameters are selected using a dynamic programming algorithm, and the resulting symbols are entropy-coded with DEFLATE \\citep{deflate_patent}.\n%\nThe three modes of operation of \\Method{} are:\n%\n\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{Calibration }\n This step is performed only once for every model and compression ratio.\n During calibration, we obtain the key and value caches for the calibration dataset, calculate $\\mathrm{SVD}(C - \\mu) = U \\Sigma V^\\top$ where $\\mu$ is the mean of the data, and store the projection matrices $V^\\top$ (for key and value caches separately). Next, we run a dynamic programming algorithm that produces the optimal bit allocation for each of the principal components.\n %\n This step is fast; for instance, calibration for a 12B model can be completed within 10 minutes on an H100 GPU (Appendix \\ref{sec:appendix:sec-kvtc-data-vs-time-and-results}). In Appendix \\ref{sec:appendix:sec-kvtc-pca-sizes} we show that the additional amount of data stored per model is relatively small ($2.4$\\% of model parameters for Llama 3.3 70B). In Appendix~\\ref{sec:appendix:ablate_pca_input_size} we perform an ablation study on the number of layers over which we concatenate the KV caches.\n \\item \\textbf{Compression }\n Keys and values are compressed independently using the $(V, \\mu)$ parameters and bit allocation obtained during calibration. Compression is performed between inference phases (e.g., after decoding or between prefill and decoding) and can be executed on either GPU (affecting TTFT) or CPU (if the cache is already in storage). Importantly, during decoding, the model operates on decompressed KV caches; compression is used only for storage or transfer.\n \\item \\textbf{Decompression }\n Decompression reverses the compression steps. The most computationally intensive operation---the inverse projection using $V^\\top$---can be performed layer-by-layer using sub-matrices of $V^\\top$, allowing generation to begin early.\n\\end{itemize}\nIn the following sections we describe in detail the components of \\Method{} during calibration, compression and decompression.\n%\n\n\\subsection{Feature decorrelation}\nUnlike prior SVD-based methods that calculate a separate decomposition for each prompt \\citep{yankun2025svdq125bit410xkey,chang2025xkvcrosslayersvdkvcache}, we compute the KV cache projection matrices {\\bf once}\nusing a calibration dataset $\\mathcal{C}$, and reuse them across all requests at inference time.\n%\nPreparing a single, generalizable $V$ rests on three observations.\nFirst, SVD must be computed on a large, representative sample; sampling token positions from a diverse calibration set suffices for generalization and is computationally tractable. Second, excluding keys and values corresponding to the most recent tokens and attention sinks improves the achievable compression ratio (see \\cref{tab:ablate-skipping-first-four-tokens,tab:kvtc-ablate-ws} in \\cref{sec:appendix:ablations-plus-details}).\nThird, positional embeddings %\ndistort the apparent low-rank structure of keys and should be removed before compression \\citep{sun2025shadowkvkvcacheshadows}. \n\nDuring calibration,\nwe forward all sequences from $\\mathcal{C}$ through the model and collect their KV caches. For each sequence, cache entries are concatenated along the time dimension to form a global pool of positions. We then sample $n$ token positions from this pool, excluding attention sinks.\nFor each sampled position, we take the corresponding keys (and, equivalently, values) from $l$ layers and $h$ heads, undo positional rotations, and concatenate them along the hidden dimension $d_{\\text{head}}$. This yields a data matrix $C\\in\\mathbb{R}^{n\\times p}$ with $p=l\\,h\\,d_{\\text{head}}$, whose rows index sampled token positions.\n%\nLet $\\mu\\in\\mathbb{R}^p$ be the per-feature mean of $C$. We compute the SVD of the centered matrix,\n%\n\\begin{equation}\nC-\\mu = U\\,\\Sigma\\,V^\\top,\n\\end{equation}\n%\nwith singular values on $\\mathrm{diag}(\\Sigma)$ sorted in descending order (equivalently, PCA of $C$).\n%\nFor any $X\\in\\mathbb{R}^{m\\times p}$, the decorrelated representation and its inverse are\n%\n\\begin{equation}\nD=(X-\\mu)\\,V,\\qquad X = D\\,V^\\top+\\mu,\n\\end{equation}\n%\nwhere the equality holds when all $p$ components are used. When $r<p$ and the basis is truncated to $V\\in\\mathbb{R}^{p\\times r}$, then $X\\approx D\\,V^\\top+\\mu$.\n%\nFor scalability, we use randomized SVD \\citep{halko2010findingstructurerandomnessprobabilistic} calculated on a GPU with target rank $r<p$, substantially reducing runtime and memory. \n%\n%\nResults for this variant are shown in Figure~\\ref{fig:kv-pca-train}, with additional details and ablations in Appendix \\ref{sec:appendix:ablations-pca}.\n\n\n\\subsection{Quantization}\n\nPCA orders principal components by explained variance. We exploit this ordering to allocate a fixed bit budget across PCA coordinates so that high-variance components receive more bits. The allocation is computed once on a calibration set and reused at inference.\nWe quantize $D$ coordinate-wise to obtain $D^{q_1,\\ldots,q_d}$, where $q_i\\in\\mathbb{Z}_{\\ge 0}$ is the bit width assigned to the $i$-th principal component. Under a global bit budget, we minimize the Frobenius reconstruction error\n\\begin{equation}\n \\norm{D V^\\top - D^{q_1, \\ldots, q_k} V^\\top}_F^2\\ .\n\\end{equation}\nBecause right-multiplication by an orthonormal matrix preserves the Frobenius norm, we have\n\\begin{equation}\n\\norm{D V^\\top - D^{q_1, \\ldots, q_k} V^\\top}_F^2 = \\norm{(D - D^{q_1, \\ldots, q_k}) V^\\top}_F^2 = \\norm{D - D^{q_1, \\ldots, q_k}}_F^2\\ .\n\\end{equation}\n%\nThus, optimal bit allocation can be found directly in the decorrelated domain.\n\nWe solve the constrained allocation with a simple dynamic programming (DP) algorithm that keeps two tables:\n(1) the minimum reconstruction error achievable using the first $i$ principal components under a payload of $b$ bits; and\n(2) a backpointer storing the optimal local decision.\n%\nPseudocode and a proof sketch of optimality under these constraints are in \\cref{sec:appendix_dp_proof_sketch}.\n%\nFurthermore, inspired by the Microscaling data formats \\citep{rouhani2023microscaling}, we quantize groups of \\emph{subsequent} PCA coordinates together, each group with shared 16-bit shift and scaling factors. The DP optimizes both the per-group bit width and group size, restricted to $\\{1, 16, 64, 256, 1024\\}$ components per group. The total budget equals the sum of payload bits across all coordinates plus per-group shift and scaling factors.\n\nAn example allocation is shown in \\cref{fig:kv-pca-train}. As expected, the learned bit widths decrease monotonically for subsequent principal components. Crucially, the DP assigns zero bits to a substantial number of trailing principal components. This observation motivates reducing the dimensionality early during the calculation of PCA, lowering the cost of calibration, and trimming $V$ to the dimensions with nonzero bit widths for faster compression/decompression during inference. We show the benefits of DP guided quantization over pure PCA in \\cref{sec:appendix:ablate_dp}.\n\n\\subsection{Entropy coding}\n\n\nFinally, the quantized values are packed into a single byte array and further compressed using the DEFLATE algorithm \\citep{deflate_patent}. Crucially, we leverage \\NVCOMP{} \\citep{nvcomp_github}, which enables parallel operation directly on a GPU. This step is lossless, but the added compression ratio is content-dependent. We ablate the choice of the lossless compression algorithm and the influence on final compression in Appendix \\ref{sec:appendix:sec-kvtc-deflate-ablate}.\n\n\n\\section{Experiments}\n\\label{sec:exp}\n\n\\paragraph{Models}\nWe use models from three families: Llama 3~\\citep{grattafiori2024llama3herdmodels}, Mistral NeMo \\citep{mistral_nemo,sreenivas2024llmpruningdistillationpractice}, and R1-distilled Qwen 2.5 \\citep{deepseekai2025deepseekr1incentivizingreasoningcapability}.\nThe selection includes models ranging from 1.5B to 70B parameters of base, instruct, and reasoning kind.\nTable \\ref{tab:model-kv-cache-size} lists the models along with their KV cache sizes.\nNotably, MN-Minitron 8B has been pruned from the Mistral NeMo 12B base, retaining the original KV cache size.\n\n\\paragraph{Methods}\nWe compare our method against KIVI \\citep{kivi}, GEAR \\citep{kang2024gearefficientkvcache} and an FP8 quantization of KV cache to the E4M3 format \\citep{micikevicius2022fp8formatsdeeplearning}. For eviction baselines, we compare with \\TOVA{} \\citep{oren2024transformersmultistaternns} and \\HTO{} \\citep{zhang2023h2oheavyhitteroracleefficient}. For SVD baselines, we compare our method with xKV \\citep{chang2025xkvcrosslayersvdkvcache}. \nFinally, we compare \\Method{} with DMS\n\\citep{lancucki2025inferencetimehyperscalingkvcache},\na trained token eviction method, on reasoning tasks.\n\nFor all methods, we follow their original intended protocols, performing prefill in the vanilla mode and compressing the KV cache only after the self-attention has been calculated. For every method except xKV, we simulate a sequence of short conversations by running compression/eviction on the cache every $c$ tokens, where $c$ depends on the method's original sliding window policy. For \\Method{} which is run with a sliding window $w=128$, we compress/decompress every $c=16$ tokens, leaving the window in the 112--128 token range. In the case of xKV, we compress only the prefill tokens, providing it with an advantage, since xKV is specifically designed for prefill optimization, and re-computing SVD matrices for newly decoded tokens would be prohibitively time-consuming. For a fair comparison, we only report the prefill compression ratios for non-Qwen models.\n\nNotation-wise, \\methodopcrdef{\\mathrm{t}}{\\mathrm{CR}} denotes \\Method{} in the default setting, where\n%\n$\\mathrm{CR}$ is the target compression for the DP.\n%\n%\nFor all methods, we calculate CR only on the compressed tokens, not counting the sliding window tokens.\n\n \\paragraph{Tasks}\nWe evaluate compression effects on Llama 3.1 8B, MN-Minitron 8B and Mistral NeMo 12B across the following task categories, with results presented in Table \\ref{tab:nonthinking-results}:\n\\begin{itemize}[leftmargin=*]\n \\item \\textbf{Math \\& Knowledge}: 8-shot Chain of Thought (CoT) GSM8K \\citep{cobbe2021trainingverifierssolvemath}, 4-shot CoT MMLU \\citep{hendrycks2021measuringmassivemultitasklanguage}\n \\item \\textbf{Long Context Performance}: 0-shot key-value retrieval task from \\citep{liu2023lostmiddlelanguagemodels} (denoted LITM), 1-shot RULER \\citep{hsieh2024ruler} Variable Tracking (denoted RULER-VT), and 2-shot Qasper \\citep{shaham2022scrollsstandardizedcomparisonlong}\n\\end{itemize}\n\n%\nWe evaluate R1-distilled models on challenging mathematical competitions AIME 2024-2025 \\citep{aime} and coding tasks from LiveCodeBench \\citep{jain2024livecodebenchholisticcontaminationfree}, with results presented in Table \\ref{tab:thinking-results}.\n%\nWe additionally evaluate \\Method{} with Llama 3.3 70B Instruct on MATH-500 \\citep{hendrycks2021measuringmathematicalproblemsolving,prm800k}, the key-value retrieval task from \\citep{liu2023lostmiddlelanguagemodels} and Needle In A Haystack (NIAH) \\citep{kamradt2023needlehaystack,hsieh2024ruler}, with results presented in Table \\ref{tab:llama-33-70b}.\nDetailed evaluation protocols can be found in Appendix \\ref{appendix:evaluation-details}, \nand ablations and details about parameter choices for \\Method{}\nin Appendix \\ref{sec:appendix:ablations-plus-details}.\n\n\\paragraph{Calibration Data}\nWe sample a 1:1 mixture of short and long documents, with lengths in the 1--8K and 8--32K ranges, respectively. Rotary positional embeddings are removed for calibration; further details are provided in Appendix \\ref{sec:appendix:ablations-pca}. Ablations showing \\Method{} stability and generalization across domains of the calibration data are provided in Appendices \\ref{sec:appendix:sec-kvtc-data-vs-time-and-results} and \\ref{sec:appendix:sec-kvtc-data-vsdomain-and-results}.\n\n\\subsection{Results}\n\n\\begin{table*}[t!]\n \\caption{\\small Accuracy of KV cache compression methods. Results within $1$ score point of vanilla are in \\textbf{bold}. See Appendix \\ref{sec:appendix_stderr} for standard error analysis. \\methodopcrdef{}{\\mathrm{CR}} denotes \\Method{} set for $\\mathrm{CR}\\times$ compression before applying DEFLATE.}\n \\label{tab:nonthinking-results}\n \\centering\n %\n \\setlength{\\tabcolsep}{1mm}\n \\resizebox{0.85\\textwidth}{!}{%\n \\begin{tabular}{lc|cccccccccc}\n \\toprule\n & Vanilla & \\makecell{GEAR$_\\text{2-bit}$} & \\makecell{KIVI$_\\text{2-bit}$} & \\HTO{} & \\TOVA{} & xKV & FP8 & \\methodopcrdef{4}{8} & \\methodopcrdef{4}{16} & \\methodopcrdef{4}{32} & \\methodopcrdef{4}{64} \\\\\n \\midrule\n \\multicolumn{12}{c}{\\tabwithinbest{}Llama 3.1 8B}\\\\\n CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{9}{10} & \\crinterval{18}{22} & \\crinterval{34}{44} & \\crinterval{60}{88} \\\\\n GSM8K & \\textbf{56.8} & 52.8 & 52.8 & 54.3 & 54.5 & \\textbf{56.6} & 55.2 & \\textbf{57.0} & \\textbf{56.9} & \\textbf{57.8} & \\textbf{57.2} \\\\\n MMLU & \\textbf{60.5} & \\textbf{59.6} & \\textbf{59.6} & 44.3 & 44.8 & \\textbf{59.5} & \\textbf{60.1} & \\textbf{59.8} & \\textbf{60.1} & \\textbf{60.6} & \\textbf{60.7} \\\\\n QASPER & \\textbf{40.4} & \\textbf{40.4} & 39.1 & 34.3 & 38.6 & 35.6 & \\textbf{40.8} & \\textbf{40.1} & \\textbf{40.7} & \\textbf{39.4} & 37.8 \\\\\n LITM & \\textbf{99.4} & 96.9 & 88.8 & 20.2 & 1.2 & \\textbf{99.9} & \\textbf{99.4} & \\textbf{99.3} & \\textbf{99.3} & \\textbf{99.1} & 90.2 \\\\\n RULER-VT & \\textbf{99.8} & \\textbf{99.8} & \\textbf{98.9} & 50.4 & \\textbf{99.7} & \\textbf{99.8} & \\textbf{99.9} & \\textbf{99.1} & \\textbf{99.1} & \\textbf{98.9} & 95.9 \\\\\n \\midrule\n \\multicolumn{12}{c}{\\tabwithinbest{}MN‑Minitron 8B}\\\\\n CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{10}{11} & \\crinterval{17}{21} & \\crinterval{32}{46} & \\crinterval{53}{95} \\\\\n GSM8K & \\textbf{59.1} & 57.9 & 58.0 & 55.3 & \\textbf{59.2} & \\textbf{59.3} & \\textbf{60.1} & \\textbf{60.6} & \\textbf{60.3} & \\textbf{59.1} & 57.8 \\\\\n MMLU & \\textbf{64.3} & \\textbf{63.6} & \\textbf{63.2} & 43.5 & 48.1 & 63.1 & \\textbf{64.3} & \\textbf{64.2} & \\textbf{64.1} & \\textbf{63.7} & 62.1 \\\\\n QASPER & \\textbf{38.2} & \\textbf{38.2} & \\textbf{38.2} & 30.0 & 33.9 & 34.5 & \\textbf{38.3} & \\textbf{39.1} & \\textbf{38.6} & \\textbf{37.7} & \\textbf{38.1} \\\\\n LITM & \\textbf{99.8} & 96.0 & 86.3 & 16.6 & 0.3 & \\textbf{99.6} & \\textbf{99.8} & \\textbf{99.4} & \\textbf{99.3} & 86.9 & 59.5 \\\\\n RULER-VT & \\textbf{99.4} & 98.3 & 96.8 & 39.2 & \\textbf{99.3} & \\textbf{99.1} & \\textbf{99.2} & \\textbf{98.8} & \\textbf{98.8} & 96.0 & 93.4 \\\\\n \\midrule\n\\multicolumn{12}{c}{\\tabwithinbest{}Mistral NeMo 12B}\\\\\n CR & $1$ & \\gearcr{} & \\kivicr{} & $8$ & $8$ & \\crinterval{1}{5} & 2 & \\crinterval{10}{11} & \\crinterval{17}{20} & \\crinterval{31}{43} & \\crinterval{51}{87} \\\\\n GSM8K & \\textbf{61.9} & 59.8 & 59.7 & 57.0 & 60.3 & \\textbf{61.9} & \\textbf{61.7} & \\textbf{62.5} & \\textbf{62.0} & \\textbf{62.2} & \\textbf{61.9} \\\\\n MMLU & \\textbf{64.5} & \\textbf{64.0} & \\textbf{64.3} & 45.4 & 49.0 & \\textbf{63.9} & \\textbf{64.5} & \\textbf{64.6} & \\textbf{64.4} & \\textbf{63.8} & 61.4 \\\\\n QASPER & \\textbf{38.4} & \\textbf{38.6} & \\textbf{38.2} & 29.5 & 36.0 & 33.5 & \\textbf{37.9} & \\textbf{37.6} & \\textbf{37.6} & \\textbf{37.5} & \\textbf{38.0} \\\\\n LITM & \\textbf{99.5} & 96.9 & 91.9 & 16.2 & 8.7 & 97.9 & \\textbf{99.0} & \\textbf{99.9} & \\textbf{99.8} & \\textbf{99.6} & 95.3 \\\\\n RULER-VT & \\textbf{99.8} & \\textbf{99.4} & 98.3 & 35.2 & \\textbf{99.6} & \\textbf{99.4} & \\textbf{99.8} & \\textbf{99.5} & \\textbf{99.5} & \\textbf{98.9} & 98.0 \\\\\n \\bottomrule\n \\end{tabular}\n }\n\\end{table*}\nIn all experiments, \\Method{} applies the same compression ratio to both the key and value caches. An ablation of their individual compressibility is presented in Table \\ref{tab:nonthinking-ablate-key-vs-value} (Appendix \\ref{sec:appendix:ablations-plus-details}), suggesting that further adjustments could yield additional gains.\n\n\\paragraph{General-Purpose Base Models}\nWe evaluate \\Method{} on general-purpose models at the 8--12B scale, featuring three GQA-enabled models (Table \\ref{tab:nonthinking-results}). The compression ratio of \\Method{} varies due to the data-dependent nature of the DEFLATE algorithm, which, on average, achieves a compression ratio of approximately $1.23\\times$ \\textbf{on top} of quantization. Crucially, \\Method{} maintains high accuracy across tested tasks, even at substantial compression ratios of $32\\times$ and $64\\times$. Conversely, quantization methods---GEAR and KIVI---exhibit signs of performance degradation on GSM8K and Lost in the Middle tasks only at $5\\times$ CR; cache eviction methods such as \\HTO{} and \\TOVA{} perform poorly as generic KV cache compressors. We also note that xKV performs well across most tasks, except for Qasper. Interestingly, in certain cases, \\Method{} at very high compression ratios even surpasses the performance of the vanilla models, likely due to inherent variability in the CoT setup. Crucially, \\Method{} at $16\\times$ compression (approximately $20\\times$ after DEFLATE) consistently maintains results within $<1$ score point (accuracy or F1, depending on the task) of the vanilla models. \nThe standard errors for these results are reported in Table \\ref{tab:nonthinking-results-std} (Appendix \\ref{sec:appendix_stderr}).\n\n\\begin{wraptable}{r}{0.47\\textwidth}\n\\vspace{-1.45em}\n\\caption{\\small Reasoning quality (sampling temp $0.6$, top-p $95\\%$) of DeepSeek-R1-distilled Qwen2.5.\n DMS results taken from \\citep{lancucki2025inferencetimehyperscalingkvcache}.}\n \\label{tab:thinking-results}\n \\centering\n \\small\n%\n\\resizebox{0.47\\textwidth}{!}{%\n\\begin{tabular}{lc|ccc}\n\\toprule\n \\multirow{2}{*}{Method} & \\multirow{2}{*}{CR} & AIME24 & AIME25 & LCB \\\\\n & & \\multicolumn{2}{c}{Competition Math} & Coding \\\\\n\\midrule\n\\multicolumn{5}{c}{\\tabwithinbest{}Qwen 2.5 R1 1.5B} \\\\\n Vanilla & 1 & $26.2_{\\pm 4.8}$ & $21.7_{\\pm 2.9}$ & $16.4$ \\\\\n \\methodopcrdef{4}{8} & 9 & $25.4_{\\pm 5.7}$ & $24.2_{\\pm 4.0}$ & $16.1$ \\\\\n \\methodopcrdef{4}{16} & 18 & $27.9_{\\pm 6.7}$ & $22.5_{\\pm 5.2}$ & $13.3$ \\\\\n DMS$_{8\\times}$ & - & 23.3 & N/A & 16.1 \\\\\n\\midrule\n\\multicolumn{5}{c}{\\tabwithinbest{}Qwen 2.5 R1 7B} \\\\\n Vanilla & 1 & $50.9_{\\pm 4.9}$ & $40.8_{\\pm 4.3}$ & $36.7$ \\\\\n \\methodopcrdef{4}{8} & \\crinterval{9}{11} & $52.5_{\\pm 3.6}$ & $40.8_{\\pm 5.2}$ & $36.5$ \\\\\n \\methodopcrdef{4}{16} & \\crinterval{18}{21} & $50.9_{\\pm 6.8}$ & $38.3_{\\pm 5.5}$ & $31.6$ \\\\\n DMS$_{8\\times}$ & - & 50.0 & N/A & 33.4 \\\\\n\\bottomrule\n\\end{tabular}\n}\n%\n\\vspace{-3.0em}\n\\end{wraptable}\\paragraph{Reasoning Models}\nIn order to test \\Method{} under more challenging conditions where context plays a critical role, we use complex math and coding tasks (Table \\ref{tab:thinking-results}). Due to high variability, AIME results are averaged over eight independent runs with results reported as ${\\mathrm{score}}_{\\pm \\mathrm{std}}$. On coding tasks, \\methodopcrdef{}{8} shows minor accuracy drops of $0.3$pp for the 1.5B model and $0.2$pp for the 7B model.\nNotably, the KV cache size of the 1.5B model is already small at $29\\,$KiB/token, compared to $131\\,$KiB/token for Llama 3.1 8B, and a 9$\\times$ compression shrinks it to only $3.2\\,$KiB/token. We also compare our method against DMS, a state-of-the-art autoregressive KV cache token eviction method. DMS achieves competitive results, and since it employs token eviction, it could potentially be combined with \\Method{} for even lower KV cache footprint.\n\n\\begin{table}[t]\n \\centering\n \\begin{minipage}[t]{0.46\\textwidth}\n \\caption{Compression applied to a model which is split across four GPUs (pipeline parallel), with KV cache chunks being compressed separately with \\Method{}.\n In certain scenarios, like offloading to CPU RAM, these chunks could be compressed jointly for higher accuracy.\n }\n %\n%\n %\n \\label{tab:llama-33-70b}\n \\small\n \\centering\n\\vspace{0.4cm}\n \\begin{tabular}{l|ccc}\n \\toprule\n \\multirow{1}{*}{Method} & MATH-500 & NIAH & LITM\\\\\n \\midrule\n \\multicolumn{4}{c}{\\tabwithinbest{}Llama 3.3 70B Instruct} \\\\\n Vanilla & $75.6_{1.92}$ & 100.0 & 100.0 \\\\\n \\methodopcrdef{4}{8} & $73.2_{1.98}$ & 100.0 & 100.0 \\\\\n \\methodopcrdef{4}{10} & $74.4_{1.95}$ & 100.0 & 100.0 \\\\\n \\methodopcrdef{4}{16} & $73.2_{1.98}$ & 100.0 & 100.0 \\\\\n \\methodopcrdef{4}{20} & $72.6_{1.99}$ & 100.0 & 100.0 \\\\\n \\bottomrule\n \\end{tabular}\n \n \\end{minipage}\\hfill\n \\begin{minipage}[t]{0.50\\textwidth}\n\\small\n \\caption{Latency of a simple implementation based on the Transformers library \\citep{transformers}, measured on an NVIDIA H100 GPU using Mistral NeMo 12B in bfloat16. In addition, we compare TTFT during recomputation of KV caches with decompression of compressed caches. BF denotes batch size, CTX context length.\n}\n%\n\\label{tab:latency-mistral}\n%\n\\centering\n\\vspace{0.4cm}\n\\small\n\\resizebox{1.00\\linewidth}{!}{%\n\\begin{tabular}{l r r | r r} \n\\toprule \n%\n \\text{Module} & \\multicolumn{2}{c|}{BS=8 CTX=8K} & \\multicolumn{2}{c}{BS=2 CTX=16K} \\\\\n & \\text{Comp} & \\text{Decomp} & \\text{Comp} & \\text{Decomp} \\\\\n \\midrule\n %\n Project & $153\\,$ ms & $156\\,$ ms & $78\\,$ ms & $75\\,$ ms \\\\\n Quantize & $67\\,$ ms & $37\\,$ ms & $39\\,$ ms & $27\\,$ ms \\\\\n Deflate & $137\\,$ ms & $64\\,$ ms & $66\\,$ ms & $36\\,$ ms \\\\\n \\midrule\n Total & {\\bf 379$\\,$ ms }& {\\bf 267$\\,$ ms } & {\\bf 194$\\,$ ms } & {\\bf 143$\\,$ ms} \\\\\n \\midrule\n \\midrule\n\\multicolumn{2}{l}{Vanilla recompute TTFT} & {\\bf 3098 ms} & & {\\bf 1780 ms} \\\\ \n\\multicolumn{2}{l}{\\Method{} decomp TTFT} & {\\bf 380 ms} & & {\\bf 208 ms} \\\\ \n \n %\n %\n \\bottomrule\n \\end{tabular}\n }\n \\end{minipage}\n\\end{table}\n\\paragraph{Multi-GPU Inference}\nTo investigate attainable compression ratios for models distributed across multiple GPUs, we evaluate \\Method{} using Llama 3.3 70B (Table \\ref{tab:llama-33-70b}). The model runs in a pipeline-parallel setting \\citep{hu2021pipelineparallelisminferenceheterogeneous} on four GPUs, each handling 20 layers. We maintain a local KV cache on each GPU, applying \\Method{} separately. Accuracy drops on the MATH-500 task are within $1.5\\times\\mathrm{stderr}$, with accuracy decreasing by $1.2$pp at $10\\times$ compression and $3.0$pp at $20\\times$.\n\n\\paragraph{Latency}\nWe calculate the latency of elements of the compression pipeline and provide the results in Table \\ref{tab:latency-mistral}. In contrast to full re-computation of KV cache for 8K context length, \\methodopcrdef{4}{16} can reduce time-to-first-token (TTFT) up to 8$\\times$.\n\n\\section{Limitations and future work}\n\n\\paragraph{Online Compression and Composability with Other Methods}\n\\Method{} was designed for efficient storage and reducing time-to-first-token. However, the advantage of having a single, generalizable PCA matrix for initial compression of cache renders it suitable for further exploration of inference directly in the principal component space.\n%\nWe leave this as future work.\n\nNotably, \\Method{} does not alter the structure of KV cache and does not change how the attention is calculated. Consequently, it is directly compatible with token eviction methods, including but not limited to these used in the experimental section, such as \\TOVA{}, \\HTO{}, and DMS. Finally, \\Method{} could be used to compress the latent state in Multi-head Latent Attention \\citep{deepseekai2024deepseekv2strongeconomicalefficient}.\n%\n\\paragraph{Scalability and Generalization Limits}\nWe approximate deployment by evaluating \\Method{} on benchmark tasks in simulated multi-turn settings, which may not fully reflect real content distributions or interaction patterns. Our experiments cover dense decoder-only models from 1.5B to 70B parameters; evaluating larger models under conditions that more accurately mirror production is left for future work. For calibration, we process approximately 200K tokens on a single NVIDIA H100 SXM 80GB GPU. Under these settings, computing the PCA basis with the randomized algorithm of \\citet{halko2010findingstructurerandomnessprobabilistic} completes within minutes. As shown in \\cref{fig:kv-pca-train,fig:kv-pca-train-more,fig:kv-pca-train-openr1}, increasing the calibration set size consistently reduces the Frobenius-norm reconstruction error. Scaling \\Method{} beyond 200K tokens, primarily a matter of scaling the computation of PCA, is left for future work. Finally, we report Frobenius-norm reconstruction error as a proxy for downstream task accuracy. While convenient, this metric does not guarantee task-level gains and its predictive power may be task-dependent. We provide an initial correlation analysis in \\cref{sec:appendix:sec-kvtc-data-vs-time-and-results} and defer a systematic study of alternative proxies to future work.\n\nFinally, the compression and decompression times of \\Method{} can be substantially reduced via kernel fusion and hierarchical PCA: first at the level of individual layers, then across groups of layers. Nevertheless, even a simple implementation yields substantial benefits and, in many cases, incurs only marginal overhead.\n%\n\n\n\\section{Related work}\nThe challenge of KV cache compression has garnered significant attention, with approaches broadly categorized into the following domains:\n\n\\paragraph{Tuning-Free Quantization}\nQuantization-based methods that avoid model fine-tuning offer a straightforward path to KV cache compression \\citep{zhao2024atomlowbitquantizationefficient, sheng2023flexgenhighthroughputgenerativeinference}. Works such as KIVI \\citep{kivi} and KVQuant \\citep{hooper2024kvquant10millioncontext} have advanced this direction by developing separate quantization strategies for key and value embeddings. These methods leverage the observation that keys benefit from per-channel quantization, while values are better suited to per-token quantization. \nOur approach diverges from these methods by first projecting concatenated embeddings from attention layers using SVD matrices derived from a calibration set. Quantization is then applied in this transformed space, with the precision dynamically optimized via dynamic programming bit allocation. While we adopt KIVI's uniform quantization scheme, our application occurs in the SVD-transformed domain. Similar to KVQuant, we apply compression before RoPE \\citep{su2023roformerenhancedtransformerrotary} to preserve model quality. \n\n\\paragraph{Tuning-Based Quantization}\nA complementary approach to post-training quantization involves fine-tuning models to adapt to quantized activations. LLM-QAT \\citep{liu2023llmqatdatafreequantizationaware} leverages generations from the pre-quantized model for fine-tuning, while BitDistiller \\citep{du2024bitdistillerunleashingpotentialsub4bit} merges Quantization Aware Training \\citep{\n%\njacob2017quantizationtrainingneuralnetworks} with Knowledge Distillation \\citep{hinton2015distillingknowledgeneuralnetwork}\n%\nIn contrast, our method eliminates the need for parameter modifications.\n\n\\paragraph{Singular Value Decomposition Approaches}\nSVD has emerged as a straightforward method for removing the redundancy in KV caches and exploiting its low-rank structure.\n%\nGEAR \\citep{kang2024gearefficientkvcache} improves quantization through low-rank correction mechanisms, whereas LoRC \\citep{zhang2024lorclowrankcompressionllms} minimizes computational overhead by directly reducing the rank of key and value matrices.\n%\nEigen Attention \\citep{saxena2024eigenattentionattentionlowrank} restructures attention computation by projecting into a truncated subspace defined by SVD, enabling efficient operations. A similar mechanism could be devised for value vectors in \\Method{}, and key vectors for layers that do not employ positional embeddings.\nGEAR \\citep{kang2024gearefficientkvcache} improves KIVI quantization through low-rank correction mechanisms.\n%\nBuilding on ShadowKV \\citep{sun2025shadowkvkvcacheshadows}, SVDq \\citep{yankun2025svdq125bit410xkey} integrates SVD with quantization, leveraging singular value magnitudes for a simple precision allocation; xKV \\citep{chang2025xkvcrosslayersvdkvcache} aggregates KV caches across multiple layers before decomposition.\n%\nThis work differs in three respects: (i) it models rotational relationships between non-adjacent layers to enable cross-layer concatenation before decomposition; (ii) it selects ranks and bitwidths via a dynamic program under a compression budget; and (iii) it applies entropy coding to the quantized factors. Empirical comparisons and ablations (e.g., treatment of early sink tokens) are reported in Appendix \\ref{sec:appendix:ablations-plus-details}.\n\n%\n%\n%\n\n\\paragraph{Sparse Attention Strategies}\nSparse attention mechanisms provide a complementary paradigm for managing sequence length dimensions by selectively discarding non-essential keys/values during inference. Techniques such as \\HTO{} \\citep{zhang2023h2oheavyhitteroracleefficient} and \\TOVA{} \\citep{oren2024transformersmultistaternns} employ prioritization strategies to dynamically prune less informative elements from the KV cache. In contrast, chunk-based approaches like Quest \\citep{tang2024questqueryawaresparsityefficient}, Landmark Attention \\citep{mohtashami2023landmarkattentionrandomaccessinfinite}, and Native Sparse Attention \\citep{yuan2025nativesparseattentionhardwarealigned} construct compressed representations of the KV cache by partitioning sequences into chunks. These methods retrieve only the most critical chunks during attention computation, significantly reducing the number of memory transfers.\nConcurrently, dynamic compression techniques such as Dynamic Memory Compression \\citep{nawrot2024dynamicmemorycompressionretrofitting} and Dynamic Memory Sparsification \\citep{lancucki2025inferencetimehyperscalingkvcache} optimize KV cache memory usage through pooling/eviction of keys/values. These strategies can be potentially integrated with quantization and SVD methods to achieve higher compression ratios and improved inference latency \\citep{yankun2025svdq125bit410xkey}.\n\n\\paragraph{Cache Management Systems}\nFinally, cache management systems address the operational challenges of KV cache handling in production environments. Paged Attention \\citep{kwon2023efficientmemorymanagementlarge} mitigates memory overhead by introducing chunked memory allocation for KV caches. Continuous batching techniques, as implemented in systems like vLLM \\citep{kwon2023efficientmemorymanagementlarge} and FasterTransformer \\citep{nvidiafastertransformer}, optimize device utilization by enabling parallel processing of multiple sequences. CacheGen \\citep{liu2024cachegenkvcachecompression} advanced the field with a distributed framework for long-term KV cache management, incorporating compression, streaming, and cross-node coordination. Our approach extends these systems by integrating fine-grained compression capabilities, enabling token-level compression without compromising distributed architecture advantages. \n%\n\n\n%\n%\n\n\\section{Conclusion}\nWe introduce \\Method{}, a method for compressing KV cache up to 20$\\times$ with negligible quality degradation, and higher compression ratios of 40$\\times$ or more available for specific use cases. We empirically show that key and value caches exhibit substantial redundancy, which\n$\\Method{}$ exploits through a simple, transform coding pipeline. It is built around linear dimensionality reduction and a dynamic programming algorithm, which assigns variable numbers of bits to principal components.\nWe demonstrate the effectiveness of \\Method{} across both regular and thinking model families, evaluating models from 1.5B to 70B. We believe that \\Method{} paves the way towards more efficient LLM deployments, lowering the cost of LLM-assisted iterative workflows.\n\n\\section*{Reproducibility} \nTo foster reproducibility of our results, we provide extensive details about the calibration of PCA matrices in Appendix \\ref{sec:appendix:ablations-pca} along with ablations regarding \\Method{} parameters in Appendices \\ref{sec:appendix:ablate_sink} (sink tokens), \\ref{sec:appendix:sep-key-value-comp} (key vs value compressibility), \\ref{sec:appendix:sec-kvtc-data-vs-time-and-results} (amount of calibration data), \\ref{sec:appendix:sec-kvtc-data-vsdomain-and-results} (effect of calibration data domain) and \\ref{sec:appendix:sec-kvtc-ws-ablate} (sliding window).\nIn Appendix \\ref{appendix:evaluation-details}, we present the details about the evaluation setup --- tasks, used prompts, and baseline configuration. We note that we utilize LM Eval Harness \\citep{eval-harness} and RULER \\citep{hsieh2024ruler} for evaluation, which are publicly available. In Appendix \\ref{sec:appendix_dp_proof_sketch} we provide the pseudocode for the dynamic programming precision assignment algorithm along with the sketch of the optimality proof and complexity analysis. \n%\n\n\n\\section*{Ethical statement} \nAs a method that aims to improve aspects regarding LLM usage, \\Method{} does not introduce new risks. However, we note that it can amplify existing ones. Therefore, we refer to the existing body of knowledge on the ethical risks of LLM development, such as Ethics Threats in LLM-Based Agents \\citep{gan2024navigatingriskssurveysecurity}, potential reversal of safety alignment \\citep{NEURIPS2024_d3a230d7}, and more general risks regarding LLMs \\citep{li2025securityconcernslargelanguage}.\n\n%\n%\n%\n\n%\n%\n%\n\n\\section*{Acknowledgments}\nThe authors thank Mikołaj Błaż, Przemysław Podczasi, Piotr Tarasiewicz, and Przemysław Strzelczyk for many helpful discussions; Kevin Shih and Dima Zhylko for valuable comments on earlier versions of the manuscript; Szymon Migacz for assistance with computing infrastructure; and Alex Fit-Florea and Michael Lightstone for their support for the publication of this work.\n\n\\bibliography{references}\n\\bibliographystyle{iclr2026_conference}\n\n\\appendix\n\\clearpage\n\\onecolumn\n\\section*{Appendix}\n%\n%\n\n\n\n\n\\section{Evaluation details}\\label{appendix:evaluation-details}\n\n\\subsection{Tasks}\nFor evaluation, we utilize Language Model Evaluation Harness \\citep{eval-harness} and RULER \\citep{hsieh2024ruler} with the Transformers library \\citep{transformers} serving as an inference backend.\n\n\n\\subsubsection{GSM8K}\nGSM8K \\citep{cobbe2021trainingverifierssolvemath} is an established task for the evaluation of the reasoning of non-reasoning models (models without thinking phase (\\texttt{<think>...</think>}) before answer) \\citep{yang2025qwen3technicalreport}.\nWe evaluate it in an 8-shot CoT setting with few-shot examples from \\citep{wei2023chainofthoughtpromptingelicitsreasoning}. Following \\citep{llama3_3_eval} we allow for the generation of up to $1024$ tokens. Task name in LM Eval Harness is \\texttt{gsm8k\\_cot}.\n\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small GSM8K 8-shot prompt example]\n\\begin{small}\n \\begin{Verbatim}[breaklines=true]\nQ: There are 15 trees in the grove. Grove workers will plant trees in the grove today. After they are done, there will be 21 trees. How many trees did the grove workers plant today?\nA: There are 15 trees originally. Then there were 21 trees after some more were planted. So there must have been 21 - 15 = 6. The answer is 6.\n\nQ: If there are 3 cars in the parking lot and 2 more cars arrive, how many cars are in the parking lot?\nA: There are originally 3 cars. 2 more cars arrive. 3 + 2 = 5. The answer is 5.\n\nQ: Leah had 32 chocolates and her sister had 42. If they ate 35, how many pieces do they have left in total?\nA: Originally, Leah had 32 chocolates. Her sister had 42. So in total they had 32 + 42 = 74. After eating 35, they had 74 - 35 = 39. The answer is 39.\n\nQ: Jason had 20 lollipops. He gave Denny some lollipops. Now Jason has 12 lollipops. How many lollipops did Jason give to Denny?\nA: Jason started with 20 lollipops. Then he had 12 after giving some to Denny. So he gave Denny 20 - 12 = 8. The answer is 8.\n\nQ: Shawn has five toys. For Christmas, he got two toys each from his mom and dad. How many toys does he have now?\nA: Shawn started with 5 toys. If he got 2 toys each from his mom and dad, then that is 4 more toys. 5 + 4 = 9. The answer is 9.\n\nQ: There were nine computers in the server room. Five more computers were installed each day, from monday to thursday. How many computers are now in the server room?\nA: There were originally 9 computers. For each of 4 days, 5 more computers were added. So 5 * 4 = 20 computers were added. 9 + 20 is 29. The answer is 29.\n\nQ: Michael had 58 golf balls. On tuesday, he lost 23 golf balls. On wednesday, he lost 2 more. How many golf balls did he have at the end of wednesday?\nA: Michael started with 58 golf balls. After losing 23 on tuesday, he had 58 - 23 = 35. After losing 2 more, he had 35 - 2 = 33 golf balls. The answer is 33.\n\nQ: Olivia has $23. She bought five bagels for $3 each. How much money does she have left?\nA: Olivia had 23 dollars. 5 bagels for 3 dollars each will be 5 x 3 = 15 dollars. So she has 23 - 15 dollars left. 23 - 15 is 8. The answer is 8.\n\nQ: {QUESTION}\nA:\n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\n\\clearpage\n\\subsubsection{MMLU}\nMMLU \\citep{hendrycks2021measuringmassivemultitasklanguage} is a collection of multiple-choice questions spanning $57$ subjects.\nFor MMLU evaluation, we use 4-shot \\texttt{mmlu\\_flan\\_cot\\_fewshot} from LM Eval Harness, allowing for generation of up to $256$ tokens. We pick this setup instead of the perplexity-based forward-pass evaluation of MMLU, because our baselines perform a prefill using full precision KV cache. Therefore, for a fair evaluation, we need to make the model generate a non-zero number of tokens before providing the answer, as otherwise the performance would be identical to vanilla.\n\n\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small MMLU 4-shot prompt example]\n\\begin{small}\n \\begin{Verbatim}[breaklines=true]\nThe following are multiple choice questions (with answers) about abstract algebra.Q: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n(A) True, True (B) False, False (C) True, False (D) False, True\nA: Let's think step by step. A cyclic group is a group that is generated by a single element. Hence a subgroup generated by a single element of a group is cyclic and Statement 1 is True. The answer is (C).\n\nQ: The symmetric group $S_n$ has $\nactorial{n}$ elements, hence it is not true that $S_{10}$ has 10 elements.\nFind the characteristic of the ring 2Z.\n(A) 0 (B) 3 (C) 12 (D) 30\nA: Let's think step by step. A characteristic of a ring is R is $n$ if the statement $ka = 0$ for all $a\\in 2Z$ implies that $k$ is a multiple of $n$. Assume that $ka = 0$ for all $a\\in 2Z$ for some $k$. In particular $2k = 0$. Hence $k=0$ and $n=0$. The answer is (A).\n\nQ: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n(A) True, True (B) False, False (C) True, False (D) False, True\nA: Let's think step by step. Statement 1 is true. Let $S$ be a finite set. If $f:S \nightarrow S$ is a onto function, then $|S| = |f(S)|$. If $f$ was not one to one, then for finite domain $S$ the image would have less than $S$ elements, a contradiction.\nStatement 2 is true. Let $G$ be an abelian group and $H$ be a subgroup of $G$. We need to show that $H$ is abelian. Let $a,b \\in H$. Then $a,b \\in G$ and $ab=ba$. Since $G$ is abelian, $ab=ba$. Since $H$ is a subgroup of $G$, $ab \\in H$. Therefore, $ab=ba$ and $H$ is abelian. The answer is (A).\n\nQ: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n(A) True, True (B) False, False (C) True, False (D) False, True\nA: Let's think step by step. Statement 2 is false. Let $H$ be a subgroup of $S_3$ generated by the cycle $(1,2)$ and $K$ be a subgroup of $S_3$ generated by the cycle $(1,3)$. Both $H$ and $K$ have two elements, the generators and the identity. However $HK$ contains cycles (1,2), (1,3) and (2,3,1), but the inverse of (2,3,1) is (2,1,3) and it does not belong to HK, hence HK is not a subgroup. The answer is (B).\n\nQ: {QUESTION}\nA: Let's think step by step.\n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\n\\clearpage\n\\subsubsection{Lost in the Middle}\nLost in the Middle \\citep{liu2023lostmiddlelanguagemodels} is evaluated in a 0-shot 100-keys (300 keys for Llama 3.3 70B) setup, allowing generation of 64 tokens using the prompt presented below. We implement the evaluation using the LM Eval Harness framework and utilize the UUID strings and code from \\citep{liu2023lostmiddlelanguagemodels}. This benchmark allows for methodical testing of the model's ability to access the input context. As an evaluation metric, we utilize the exact match between the UUID returned by the model and the gold answer.\n\n\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small Lost in the Middle question example (base models)]\n\\begin{small}\n \\begin{Verbatim}[breaklines=true]\nExtract the value corresponding to the specified key in the JSON object below.\n\nJSON data:\n{\"1afcec1f-1acd-42e3-b833-e7882d5daada\": \"25f1a78d-a2f6-4c7d-8bd6-51226b263cbe\",\n \"94071d67-86df-455c-8ee9-691e492ff740\": \"0d7ba717-e034-410e-88ab-c13d37cc6499\",\n \"88b322bb-571c-4e55-9934-aa8df11b3349\": \"c54095cf-9931-460b-8a6b-e1f09afb2f72\",\n...\n \"5a729e1f-6956-4c1d-b024-10b317ed5657\": \"cea37ae5-84e1-4deb-b4c6-19d04134d664\",\n \"aaed65fc-f80c-4090-a0a9-90592140b9de\": \"ffc2e314-2d0f-4b20-be32-916ba96d1ea9\",\n \"90b7fe08-8708-451a-badf-34cabe7930a4\": \"7bebff53-05c7-4ca3-9314-bca68bd65c04\"}\n \"1afcec1f-1acd-42e3-b833-e7882d5daada\":\n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\n\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small Lost in the Middle question example (Llama 3.3 70B instruct)]\n\\begin{small}\n \\begin{Verbatim}[breaklines=true, breakanywhere=true]\n<|begin_of_text|><|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26 Jul 2024\n\n<|eot_id|><|start_header_id|>user<|end_header_id|>\n\nExtract the value corresponding to the specified key in the JSON object below.\n\nJSON data:\n{\"2a85047d-fe61-4c53-8844-1d85668d6a7d\": \"a4852ee7-d94f-40ce-8c2f-f14e95377e79\",\n \"1698320e-2ba6-499f-b119-b8ffd74d53db\": \"e212083b-22f5-4d27-87d3-5c3cfcf9542f\",\n ...\n \"90ef90b0-7972-46d0-9a73-4b07be2f5aae\": \"ebb84b27-9156-4d23-8a7d-a34aef606f28\",\n \"c1736979-584d-4b93-8e25-a206770fcdae\": \"dcb5aace-7fb2-4288-bfc2-c5faacf89469\"}\n What is the value associated with the key \"2a85047d-fe61-4c53-8844-1d85668d6a7d\"? Answer using the following format:\n\n`The value associated with the key \"2a85047d-fe61-4c53-8844-1d85668d6a7d\" is ANSWER_HERE.`\n\nWhere ANSWER_HERE is the value associated with the key \"2a85047d-fe61-4c53-8844-1d85668d6a7d\".<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n\n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\n\\clearpage\n\\subsubsection{Variable Tracking}\nVariable Tracking is evaluated in 1-shot (with a relatively short example shown below) using RULER \\citep{hsieh2024ruler} with context length 8K, limiting the generation to $128$ tokens. The benchmark tests the model's ability to track variable assignments across unrelated contexts.\n%\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small Variable Tracking prompt and question example]\n \\begin{small}\n \\begin{Verbatim}[breaklines=true, breakanywhere=true]\nMemorize and track the chain(s) of variable assignment hidden in the following text.\n\nThe grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n VAR JUP = 97498 The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n VAR AGD = VAR JUP The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n VAR KCB = VAR AGD The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n VAR LJP = VAR KCB The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n VAR LFP = VAR LJP The grass is green. The sky is blue. The sun is yellow. Here we go. There and back again.\n\nQuestion: Find all variables that are assigned the value 97498 in the text above. Answer: According to the chain(s) of variable assignment in the text above, 5 variables are assgined the value 97498, they are: JUP AGD KCB LJP LFP\n\n\n\nMemorize and track the chain(s) of variable assignment hidden in the following text.\n\n...\nQuestion: Find all variables that are assigned the value 79092 in the text above. Answer: According to the chain(s) of variable assignment in the text above, 5 variables are assgined the value 79092, they are: \n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\\clearpage\n\n\n\\subsubsection{Needle In A Haystack}\nNeedle In A Haystack (NIAH) \\citep{kamradt2023needlehaystack} is evaluated 0-shot using RULER \\citep{hsieh2024ruler} with context length 100K, limiting the generation to $128$ tokens. The benchmark tests the model's ability to retrieve information hidden in long text. The name of the task in the RULER is \\texttt{niah\\_single\\_2}.\n%\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small NIAH prompt example]\n \\begin{small}\n \\begin{Verbatim}[breaklines=true, breakanywhere=true]\n<|begin_of_text|><|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\\nToday Date: 26 Jul 2024\n\n<|eot_id|><|start_header_id|>user<|end_header_id|>\n\nA special magic number is hidden within the following text. Make sure to memorize it. I will quiz you about the number afterwards.\n\n<essay text prefix>\n<needle>\n<essay text suffix>\nWhat is the special magic number for abrasive-pathology mentioned in th\ne provided text? The special magic number for abrasive-pathology mentioned in the provided text is<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n\\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\n\n\\subsubsection{Qasper}\nQasper \\citep{dasigi2021datasetinformationseekingquestionsanswers,shaham2022scrollsstandardizedcomparisonlong} is evaluated in 2-shot using LM Eval Harness task \\texttt{scrolls\\_qasper} with full autoregressive generation and F1 score (same reasons as with MMLU evaluation). We limit the generation to $128$ tokens.\nThis benchmark evaluates the model's ability to answer questions about a paper presented as part of the input.\n\\clearpage\n\n\\subsubsection{AIME 2024-2025}\nWe implement AIME evaluation using LM Eval Harness. Following \\citep{lancucki2025inferencetimehyperscalingkvcache} we utilize prompts adopted from the Open-R1 repository \\citep{openr1} and limit the generation to $30$K tokens.\nAIME competitions are popular for the evaluation of reasoning models such as DeepSeek R1 \\citep{deepseekai2025deepseekr1incentivizingreasoningcapability}.\nTo check the correctness of an answer, we utilize the following code with Math-Verify \\citep{math_verify}:\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small AIME 2024-2025 evaluation code]\n \\begin{small}\n \\begin{Verbatim}[breaklines=true, breakanywhere=true]\nfrom math_verify.metric import math_metric\nfrom math_verify.parser import LatexExtractionConfig, ExprExtractionConfig\n\ndef grade_answer(problem, model_answer):\n gold_is_latex = False\n verify_func = math_metric(\n gold_extraction_target=(\n LatexExtractionConfig() if gold_is_latex else ExprExtractionConfig(),\n ),\n pred_extraction_target=(ExprExtractionConfig(), LatexExtractionConfig()),\n aggregation_function=max,\n precision=6,\n )\n gold_answer = problem[\"answer\"]\n\n try:\n with timeout(seconds=30): # custom class to throw and exception if code does not complete under 30 seconds\n grade, extracted_answers = verify_func([gold_answer], [model_answer])\n return grade == 1\n except:\n return False\n\n \n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\n\\clearpage\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small AIME 2024-2025 prompt]\n \\begin{small}\n \\begin{Verbatim}[breaklines=true, breakanywhere=true]\n<|begin_of_sentence|><|User|>Solve the following math problem efficiently and clearly:\n\n- For simple problems (2 steps or fewer):\nProvide a concise solution with minimal explanation.\n\n- For complex problems (3 steps or more):\nUse this step-by-step format:\n\n## Step 1: [Concise description]\n[Brief explanation and calculations]\n\n## Step 2: [Concise description]\n[Brief explanation and calculations]\n\n...\n\nRegardless of the approach, always conclude with:\n\nTherefore, the final answer is: $\\boxed{answer}$. I hope it is correct.\n\nWhere [answer] is just the final number or expression that solves the problem.\n\nProblem: {PROBLEM}\n\n<|Assistant|><think>\n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\n\n\n\\subsubsection{LiveCodeBench}\nFor LiveCodeBench \\citep{jain2024livecodebenchholisticcontaminationfree} evaluation, we utilize the official repository and, following \\citep{lancucki2025inferencetimehyperscalingkvcache}, limit the generation to $16$K tokens and data range from 2024-08-01 to 2025-01-31.\nThe benchmark consists of problems from sites like leetcode.com and codeforces.com.\n\\clearpage\n\n\\subsubsection{MATH-500}\nFor evaluation on MATH-500 \\citep{prm800k}, a subset of MATH \\citep{hendrycks2021measuringmathematicalproblemsolving} introduced by \\citet{prm800k}, we limit the generation to $5120$ tokens following \\citep{llama3_3_eval}. We also change the sliding window size to $w=256$. We utilize the following prompt adopted from MATH-500 evaluation, and the following code optimized for reproduction of Llama 3.3 70B results without the LLM judge:\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small MATH-500 eval code]\n \\begin{small}\n \\begin{Verbatim}[breaklines=true, breakanywhere=true]\nfrom math_verify import parse, verify\n\ndef answer_normalize(answer: str) -> str:\n answer = answer.split(r\"\\boxed{\")[-1].split(\"}$\")[0].strip()\n answer = answer.replace(r\"\\left\", \"\")\n answer = answer.replace(r\"\\right\", \"\")\n answer = answer.replace(r\"\\begin{align}\", \"\")\n answer = answer.replace(r\"\\end{align}\", \"\")\n answer = answer.replace(r\"\\begin{equation}\", \"\")\n answer = answer.replace(r\"\\end{equation}\", \"\")\n answer = answer.replace(\" \", \"\")\n answer = answer.replace(r\"\\$\", \"\")\n if answer.startswith(r\"\\text\"):\n answer = answer.replace(r\"\\text{\", \"\")\n answer = answer.replace(r\"}\", \"\")\n\n if answer.startswith(r\"x\\in\"):\n answer = answer.replace(r\"x\\in\", \"\")\n\n if answer.startswith(r\"y=\"):\n answer = answer.replace(r\"y=\", \"\")\n \n return answer\n\n\ndef compare_answers(answer: str, model_answer: str) -> bool:\n gold = parse(answer)\n model = parse(model_answer)\n res = verify(gold, model)\n if not res:\n answer = answer_normalize(answer)\n model_answer = answer_normalize(model_answer)\n print(answer, model_answer)\n gold = parse(answer)\n model = parse(model_answer)\n if not verify(gold, model): # sometimes fails for improper expressions\n res = verify(answer, model_answer)\n gold = answer\n model = model_answer\n if res:\n return True\n else:\n return False\n else:\n return res\n\n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\n\\clearpage\n\\begin{tcolorbox}[colback=green!5!white,colframe=black!50!green,title=\\small MATH-500 prompt]\n \\begin{small}\n \\begin{Verbatim}[breaklines=true, breakanywhere=true]\n<|begin_of_text|><|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26 Jul 2024\n\n<|eot_id|><|start_header_id|>user<|end_header_id|>\n\nSolve the following math problem efficiently and clearly:\n\n- For simple problems (2 steps or fewer):\nProvide a concise solution with minimal explanation.\n\n- For complex problems (3 steps or more):\nUse this step-by-step format:\n\n## Step 1: [Concise description]\n[Brief explanation and calculations]\n\n## Step 2: [Concise description]\n[Brief explanation and calculations]\n\n...\n\nRegardless of the approach, always conclude with:\n\nTherefore, the final answer is: $\\boxed{answer}$. I hope it is correct.\n\nWhere [answer] is just the final number or expression that solves the problem.\n\nProblem: {PROBLEM}<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n \\end{Verbatim}\n\\end{small}\n\\end{tcolorbox}\n\\clearpage\n\n\\subsection{Baselines configuration}\\label{sec:appendix_baselines_config}\n\n\\subsubsection{KIVI} \nWe follow \\cite[Section 4.1]{kivi} and use \\texttt{group size} = $32$ and \\texttt{residual length} = $128$, with $2$-bits per key and $2$-bits per value.\nWe utilize the official implementation.\n\n\\subsubsection{GEAR}\nWe follow \\citep{kang2024gearefficientkvcache} github repository and set underlying quantization to KIVI with \\texttt{group size} = $64$, \\texttt{streaming gap} = $64$, $2$-bit keys and values.\nAdditionally, we set the rank of key/value correction to $4$ for prefill and $2$ for generation.\nWe utilize the official implementation.\n\n\n\n\n\\subsubsection{xKV} \nWe follow \\citep{chang2025xkvcrosslayersvdkvcache}.\nFor Llama 3.1 $8$B we group layers by $4$ and set the pre-RoPE key rank to $512$ (compression ratio $8$) and value rank to $768$ (compression rank $5 \\frac{1}{3}$).\nFor Mistral NeMo and MN-Minitron, we group layers by $5$ (those models have $1.25$ more layers than Llama 3.1 $8$B) and set the pre-RoPE key rank to $640$ (compression ratio $8$) and value rank to $960$ (compression rank $5 \\frac{1}{3}$).\nWe utilize the official implementation.\n\n\n\\subsubsection{H2O}\nWe utilize the official implementation of \\citep{zhang2023h2oheavyhitteroracleefficient} and set the recent and heavy hitter fractions to $\\frac{1}{16}$ of (input + max possible output size). This results in up to an 8x compression ratio. Lower compression ratios occur when the model produces shorter outputs than the maximal specified value. We note that this can give an advantage to H2O over other methods.\n\n\\subsubsection{TOVA}\nWe utilize the official implementation of \\citep{oren2024transformersmultistaternns} and set the max cache size to $\\frac{1}{8}$ of (input + possible output size). This results in up to an 8x compression ratio. Lower compression ratios occur when the model produces shorter outputs than the maximal specified value. We note that this can give an advantage to TOVA over other methods.\n\n\\subsubsection{DMS}\nWe copy the results from the Inference-Time Hyper-Scaling \\citep{lancucki2025inferencetimehyperscalingkvcache}.\n\n\n\\subsection{Hardware} \\label{appendix:hardware}\nExperiments were run on a node with 8 $\\times$ NVIDIA H100 GPUs (80 GB each). All jobs finished within 4 h, except MMLU and Llama-3.3-70B ($\\le$ 8 h) and xKV ($\\le$ 12 h). For baselines (KIVI, GEAR, xKV, TOVA, H2O) we used the authors' public code. All runs used batch size 1 (except Qwen evaluations) to prevent padding that could bias some of the baselines.\n\n\n\\clearpage\n\\section{Ablations and additional details}\\label{sec:appendix:ablations-plus-details}\n\nWe present additional details and ablations regarding \\Method{} in the following appendices:\n\\begin{itemize}\n %\n \\item Appendix \\ref{sec:appendix:ablations-pca} --- additional details about the hyperparameters of \\Method{}, along with justifications and references to relevant ablation studies.\n \\item Appendix, \\ref{sec:appendix:ablations-kv-props} --- properties of key and value channels.\n \\item Appendix \\ref{sec:appendix:ablate_sink} --- omitting sink tokens for KV cache compression can result in significant gains at higher compression ratios.\n \\item Appendix \\ref{sec:appendix:sep-key-value-comp} --- the difference in compressibility between keys and values suggests that long-context retrieval tasks may benefit from using higher precision for keys.\n \\item Appendix \\ref{sec:appendix:sec-kvtc-data-vs-time-and-results} --- increasing the amount of calibration data helps preserve performance at higher compression ratios, while smaller amounts remain competitive for lower compression.\n \\item Appendix \\ref{sec:appendix:sec-kvtc-data-vsdomain-and-results} --- influence of the calibration data domain on downstream performance.\n \\item Appendix \\ref{sec:appendix:sec-kvtc-ws-ablate} --- influence of the sliding window size on downstream performance.\n \\item Appendix \\ref{sec:appendix:sec-kvtc-deflate-ablate} --- ablation of lossless compression algorithms.\n \\item Appendix \\ref{sec:appendix:ablate_dp} --- benefits of DP quantization over pure PCA.\n \\item Appendix \\ref{sec:appendix:ablate_pca_input_size} --- benefits of cross layer PCA.\n \\item Appendix \\ref{sec:appendix_stderr} --- results from Table \\ref{tab:nonthinking-results}, with standard errors computed by LM Eval Harness \\citep{eval-harness}.\n \\item Appendix \\ref{sec:appendix:sec-kvtc-pca-sizes} --- sizes of PCA projection matrices (stored per model), with an emphasis on the fact that their size is only a small fraction of the model parameters. \n\n \\item Appendix \\ref{sec:appendix_dp_proof_sketch} --- pseudocode for the Dynamic Programming (DP) precision assignment algorithm, along with complexity analysis and a sketch of the optimality proof.\n \n\\end{itemize}\n\\clearpage\n\n\n%\n%\n%\n%\n%\n\n%\n\n\n%\n%\n%\n%\n\n\n\n\n\\clearpage\n\n\n\n\n\\subsection{PCA calculation parameters}\\label{sec:appendix:ablations-pca}\nAs mentioned in the main text, we utilize $8$ iterations of the randomized algorithm from \\citep{halko2010findingstructurerandomnessprobabilistic} for PCA. We utilize 160K calibration tokens for Llama 3.1 8B, Llama 3.3 70B instruct, Mistral NeMo 12B, and MN-Minitron 8B with a dimensionality cut-off of $10$K. \nThis choice is motivated by memory efficiency and the results presented in Figures \\ref{fig:kv-pca-train}, \\ref{fig:kv-pca-train-more} and \\ref{fig:kv-pca-train-openr1}, where the initial boost from the increase in the number of calibration tokens from $10$K to $100$K is relatively large compared to the boost attained when increasing from $100$K to $160$K. We leave the exploration of larger calibration sets for future work. In Appendix \\ref{sec:appendix:sec-kvtc-data-vs-time-and-results} we ablate the influence of the amount of the calibration data on downstream results. In Appendix \\ref{sec:appendix:sec-kvtc-pca-sizes} we provide the sizes of the projection matrices, noting that they are relatively small when compared to the model size ($2.4$\\% of model parameters for Llama 3.3 70B) .\n\nFor Qwen models, due to their smaller number of KV heads, we utilize $200$K calibration tokens and dimensionality reduction of $8$K. For all models, we utilize a 50/50 mixture of FineWeb \\citep{penedo2024the} and OpenR1Math traces \\citep{OpenR1Math220k} due to the duality of our benchmarks (reasoning and general purpose; see Appendix \\ref{sec:appendix:sec-kvtc-data-vsdomain-and-results} for an ablation on calibration data source). We take samples from both datasets with the only filters being minimum and maximum length (1K and 32K, respectively) for both datasets and quality score ($\\geq$ 0.95) for FineWeb (the quality score is attached to the dataset). Additionally, we ensure that the number of tokens from documents below 8000 and above 8000 tokens is roughly the same (except in the MN-Minitron case, as this model supports up to $8$K context length). Token counts and cutoffs are chosen so that a single calculation of PCA fits on a single H100 GPU with $80$GB of memory and completes within 10 minutes (for details see Appendix \\ref{sec:appendix:sec-kvtc-data-vs-time-and-results}). \n\nWe emphasize that for a given model, we use the same PCA matrix for all compression ratios. The only change between compression ratios is the precision assignment, which is done automatically via a dynamic programming algorithm. Additionally, we note that the manual adjustment needed by a practitioner to adapt \\Method{} to a new model is limited to choosing the initial PCA dimensionality cutoff (if the practitioner decides to use the efficient algorithm by \\citep{halko2010findingstructurerandomnessprobabilistic}), the number of samples that the chosen PCA implementation can handle (based on GPU/CPU memory) and the calibration sample choice if special scenarios are desired for increased compression. In this paper, we note that across a wide range of tasks, the choice of a 50/50 mixture of both short and long context FineWeb \\citep{penedo2024the} (for generic text) and OpenR1Math \\citep{OpenR1Math220k} (for thinking traces) data is sufficient for Llama, Mistral, and R1-distilled Qwen models for a variety of applications. In particular, we note that our method is not harder to adjust than xKV or SVDq, due to automatic precision assignment via dynamic programming. In particular, instead of aiming for the best reconstruction error for a specific compression ratio, the user can easily alter the algorithm to aim for the highest compression ratio within a given reconstruction error constraint.\n\n\n\n\n\\begin{figure}\n \\centering\n \\subfloat[]{\n \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_fineweb_ablate_niter_key.pdf}\n }\n \\hfill\n \\subfloat[]{\n \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_fineweb_ablate_niter_key.pdf}\n }\n \\hfill\n \\subfloat[]{\n \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_fineweb_ablate_niter_value.pdf}\n }\n \\hfill\n \\subfloat[]{\n \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_fineweb_ablate_niter_value.pdf}\n }\n \\caption{Relative reconstruction error when calibrating \\Method{} decorrelation step - ablation of the number of algorithm \\citep{halko2010findingstructurerandomnessprobabilistic} iterations. Figures (a)-(b) show key reconstruction error, whereas (c)-(d) show value reconstruction error. Other parameters as in Figure \\ref{fig:kv-pca-train}. We note that the larger number of iterations provides slight improvements.}\n \\label{fig:kv-pca-train-more}\n\\end{figure}\n\n\n\\begin{figure}\n \\centering\n \\subfloat[]{\n \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Llama_3.1_8B_openr1.pdf}\n }\n \\hfill\n \\subfloat[]{\n \\includegraphics[width=0.45\\textwidth]{figures/pca_train/ablate/Mistral-NeMo_12B_openr1.pdf}\n }\n \\caption{Relative reconstruction error when calibrating \\Method{} decorrelation step on OpenR1Math \\citep{OpenR1Math220k} traces with the error calculation on FineWeb \\citep{penedo2024the}. Parameters as in Figure \\ref{fig:kv-pca-train}. We note that OpenR1Math traces were published after the release of Llama 3.1 $8$B and Mistral NeMo $12$B, and possibly due to their specificity result in higher generalization error.}\n \\label{fig:kv-pca-train-openr1}\n\\end{figure}\n\\clearpage\n\n\n\\subsection{Additional Details About KV Cache Properties}\\label{sec:appendix:ablations-kv-props}\nWe study the relative channel activation patterns of Llama 3.1 8B, Mistral-Nemo 12B and Qwen 2.5 R1 (Figures \\ref{fig:kv-cache-norms-ex} and \\ref{fig:kv-cache-norms-ex-p2}). The relative activation results are computed on a 50/50 mixture of FineWeb \\citep{penedo2024the} and OpenR1Math \\citep{OpenR1Math220k}, with document lengths between 1K and 8K tokens. We observe that keys and values of all models show potential for dimensionality reduction and quantization (low absolute activations and variance).\n\\begin{figure}[ht]\n \\centering\n \\subfloat[Relative (within head) Absolute Activations]{\n \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_llama3.1_8b_base_fp16.pdf}\n %\n }\n \\subfloat[\\centering Relative (within head) Variance of Activations]{\n \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_llama3.1_8b_base_fp16_var.pdf}\n %\n }\\\\\n \\subfloat[Relative (within head) Absolute Activations]{\n \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_mistral_nemo_12b_base_bf16.pdf}\n %\n }\n \\subfloat[\\centering Relative (within head) Variance of Activations]{\n \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_mistral_nemo_12b_base_bf16_var.pdf}\n %\n }\\\\\n \\caption{For key/value head $i$ and channel $j$, we define per-channel mean absolute activation $\\mathrm{a}_{i,j} = \\frac{1}{n}\\sum_{t=1}^{n}{|\\mathrm{channel}_{t, i,j}|}$ and plot the relative activation $\\mathrm{heatmap}_{i,j} = \\mathrm{a}_{i,j}/\\max_b{\\{\\mathrm{a}_{i,b}\\}}$ --- Panels (a),(c)(e). \n Panels (b),(d),(f) show $\\frac{\\mathrm{varc}_{i,j}}{\\max_c{\\{\\mathrm{varc}_{i,c}\\}}}$ where $\\mathrm{varc}_{i,j}$ is the variance of $\\mathrm{channel}_{t, i,j}$ over $t$ .}\n \\label{fig:kv-cache-norms-ex}\n\\end{figure}\n\n\n\\begin{figure}[ht]\n \\centering\n \\subfloat[Relative (within head) Absolute Activations]{\n \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_1.5B_bf16.pdf}\n %\n }\n \\subfloat[\\centering Relative (within head) Variance of Activations]{\n \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_1.5B_bf16_var.pdf}\n %\n }\\\\\n \\subfloat[Relative (within head) Absolute Activations]{\n \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_7B_bf16.pdf}\n %\n }\n \\subfloat[\\centering Relative (within head) Variance of Activations]{\n \\includegraphics[width=0.48\\linewidth]{figures/kv_norm/head_norm_qwen2.5R1_7B_bf16_var.pdf}\n %\n }\\\\\n \\caption{For key/value head $i$ and channel $j$, we define per-channel mean absolute activation $\\mathrm{a}_{i,j} = \\frac{1}{n}\\sum_{t=1}^{n}{|\\mathrm{channel}_{t, i,j}|}$ and plot the relative activation $\\mathrm{heatmap}_{i,j} = \\mathrm{a}_{i,j}/\\max_b{\\{\\mathrm{a}_{i,b}\\}}$ --- Panels (a),(c)(e). \n Panels (b),(d),(f) show $\\frac{\\mathrm{varc}_{i,j}}{\\max_c{\\{\\mathrm{varc}_{i,c}\\}}}$ where $\\mathrm{varc}_{i,j}$ is the variance of $\\mathrm{channel}_{t, i,j}$ over $t$ .}\n \\label{fig:kv-cache-norms-ex-p2}\n\\end{figure}\n\n\\clearpage\n\n\\subsection{Excluding sink tokens from compression}\\label{sec:appendix:ablate_sink}\nWe consider the first four tokens of key and value caches (i.e., tokens at positions 0, 1, 2, and 3) to be sink tokens, motivated by the experimental results reported by \\citep{xia2024shearedllamaacceleratinglanguage}.\nReducing the dimensionality of key and value caches with PCA causes larger information loss of the sink tokens than the remaining ones, as shown in Figure \\ref{fig:kv-pca-train}. In order to assess the influence, we compare two setups: one that excludes first four tokens from compression (denoted \\Method{}$^{\\skiptokens 4}$) and one that compresses them along with other tokens (denoted \\Method{}$^{\\skiptokens 0}$).\nThe results are shown in Table \\ref{tab:ablate-skipping-first-four-tokens}. High compression ratio of $64\\times$ drastically reduces downstream task scores for the Llama 3.1 8B in the \\Method{}$^{\\skiptokens 0}$ case; for MN-Minitron 8B and Mistral NeMo 12B it causes regression on the long context tasks (Lost in the Middle and Variable Tracking) when compared with \\Method{}$^{\\skiptokens 4}$.\n%\n\n\\begin{table}[ht]\n\\caption{Ablation on the skipping compression of the first four tokens. We note that the difference starts to be visible with larger compression ratios, and that it is in favor of skipping compression of potential attention sinks \\citep{xiao2024efficientstreaminglanguagemodels}. Results are presented as $\\mathrm{score}_{\\mathrm{stderr}}$ where ${\\mathrm{stderr}}$ is bootstraped by LM Evaluation Harness (where available) \\citep{eval-harness}. The differences in compression ratios, are due to the fact that we count the skipped tokens into compression ratio.}\\label{tab:ablate-skipping-first-four-tokens}\n\\small\n\\centering\n\\begin{tabular}{cccccccc}\n\\toprule\n\n\\multirow{2}{*}{Model} & \\multirow{2}{*}{Method} & \\multirow{2}{*}{CR} & GSM8K & MMLU & QASPER & LITM 100 & RULER-VT \\\\\n & & & \\multicolumn{2}{c}{Math \\& Knowledge} & \\multicolumn{3}{c}{Long Context} \\\\\n\\midrule\n\\multirow{4}{*}{Llama 3.1 8B} & \\methodopcr{0}{16} & \\crinterval{19}{22} & $56.8_{ 1.4}$ & $60.3_{ 0.4}$ & $40.2$ & $99.2_{ 0.1}$ & $98.2_{0.4}$ \\\\\n& \\methodopcr{4}{16} & \\crinterval{18}{22} & $56.9_{ 1.4}$ & $60.1_{ 0.4}$ & $40.7$ & $99.3_{ 0.1}$ &$99.1_{0.3}$\\\\\n& \\methodopcr{0}{64} & \\crinterval{76}{90} & $1.6_{ 0.3}$ & $9.9_{ 0.2}$ & $27.6$ & $0.0_{ 0.0}$ &$61.8_{1.5}$\\\\\n& \\methodopcr{4}{64} & \\crinterval{60}{88} & $57.2_{ 1.4}$ & $60.7_{ 0.4}$ & $37.8$ & $90.2_{ 0.4}$ &$95.9_{0.6}$\\\\\n\n\\midrule\n\\multirow{2}{*}{MN-Minitron 8B}\n& \\methodopcr{0}{64} & \\crinterval{79}{97} & $59.5_{ 1.4}$ & $61.9_{0.4}$ & $37.9$ & $55.1_{ 0.6}$ &$91.5_{0.9}$\\\\\n& \\methodopcr{4}{64} & \\crinterval{53}{95} & $57.8_{ 1.4}$ & $62.1_{ 0.4}$ & $38.1$ & $59.5_{ 0.6}$ &$93.4_{0.8}$\\\\\n\\midrule\n\\multirow{2}{*}{Mistral NeMo 12B}\n\n& \\methodopcr{0}{64} & \\crinterval{77}{89} & $61.9_{1.3}$ & $62.4_{0.4}$ & $37.5$ & $84.8_{0.4}$ &$95.8_{0.6}$\\\\\n& \\methodopcr{4}{64} & \\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\subsection{Separate adjustment of compression ratios for key and value caches}\\label{sec:appendix:sep-key-value-comp}\nAll experimental results of \\Method{} (unless stated otherwise) have been obtained with 1:1 compression of keys and values. We present additional results of manually adjusting the compression ratio separately for keys and values (Table \\ref{tab:nonthinking-ablate-key-vs-value}).\nThe results suggest that for long-context retrieval tasks, the value cache could be compressed more than the key cache. We attribute this phenomenon to the necessity to precisely attend to selected tokens in the cache, which hinges on the high accuracy of key vectors. On the other hand, stronger compression of values shows a noticeable degradation on the GSM8K and MMLU tasks.\n\n\\begin{table}[ht]\n\\caption{Ablation of key/value compressibility with \\Method{}. We use the same \\Method{} configuration as in Table \\ref{tab:nonthinking-results}, but independently change key and value lossy compression rates. To denote that value compression ratio was set to $32$ and key was set to $64$ we use \\methodopcrk{64}}\\label{tab:nonthinking-ablate-key-vs-value}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{lc|ccccc}\n\\toprule\n\n\\multirow{1}{*}{Method} & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n\\midrule\n\\multicolumn{7}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n\\methodopcrkl{256} & \\crinterval{55}{80} &$57.1_{1.4}$& 57.4 & 36.6 &$48.6_{1.6}$&$91.9_{0.9}$\\\\\n\\methodopcrvl{256} & \\crinterval{55}{77} &$56.8_{1.4}$& 57.5 & 36.3 &$71.9_{1.4}$&$95.9_{0.6}$\\\\\n\n\n\\midrule\n\\multicolumn{7}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n\\methodopcrk{256} & \\crinterval{69}{79} &$62.2_{1.3}$& 61.7 & 34.6 &$73.2_{1.4}$&$90.4_{0.9}$\\\\\n\\methodopcrv{256} & \\crinterval{69}{77} &$57.1_{1.4}$& 59.8 & 35.2 &$77.5_{1.3}$&$89.5_{1.0}$\\\\\n\n\n\\bottomrule\n\\end{tabular}\n\\end{table}\\clearpage\n\n\n\n\\subsection{Calibration data tokens vs downstream performance}\\label{sec:appendix:sec-kvtc-data-vs-time-and-results}\nWe test how the amount of calibration data affects calibration times and the downstream performance.\nFrom Figures \\ref{fig:kv-pca-train-more} and \\ref{fig:kv-pca-train-openr1} we already know that increasing the amount of the calibration data can bring down the reconstruction error. The question that remains is how such an increase correlates with the downstream performance. In Table \\ref{tab:nonthinking-ablate-num-tokens} we show that an increase in calibration data clearly benefits a high compression ratio of $256\\times$, with more moderate returns for smaller ($64\\times$, $32\\times$) compression ratios. This is a positive result, as it allows for trading calibration stage complexity for improved downstream performance, with 40K token budget bringing already competitive results for $64\\times$ ratio. We additionally note that PCA calibration can be completed within 1.5 minutes for 160K tokens using \\citep{halko2010findingstructurerandomnessprobabilistic} algorithm, and that the DP calculation time (performed once per model and compression ratio) can be finalized within 8 minutes.\n\n\\begin{table}[ht]\n\\caption{Ablation of the number of tokens used for \\Method{} calibration, along with respective PCA and DP calibration times. PCA calibration was performed using single H100 $80$GB GPU, calculation of DP tables (except simulation of quantization) was offloaded to the node cpu. We additionally limit DP calibration data to first 32K tokens, therefore we do not see increase in dp time after 40k calibration tokens. All calibration datapieces come from a 50/50 mixture of FineWeb \\citep{penedo2024the} and OpenMathR1 \\citep{OpenR1Math220k} traces between 1K and 8K tokens.}\\label{tab:nonthinking-ablate-num-tokens}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{lc|cccccccc}\n\\toprule\n\n \\multirow{1}{*}{Method} & Data & PCA Calib & DP Calib & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n\\midrule\n\\multicolumn{10}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n\\methodopcrdef{4}{32} & \\multirow{3}{*}{20K} & \\multirow{3}{*}{41.3s} & 6.5 min & \\crinterval{31}{42} & $63.0_{1.3}$ & $63.9_{0.4}$ & $34.8$ & $97.3_{0.2}$ &$98.9_{0.3}$\\\\\n\\methodopcrdef{4}{64} & & & 5.4 min & \\crinterval{63}{87} & $63.9_{1.3}$ & $61.7_{0.4}$ & $31.8$ & $88.8_{0.4}$ &$96.9_{0.5}$\\\\\n\\methodopcrdef{4}{256} & & & 3.9 min & \\crinterval{148}{340} & $59.6_{1.4}$ & $51.5_{0.4}$ & $23.3$ & $10.4_{0.4}$ &$66.8_{1.5}$\\\\\n\\hline\n\\methodopcrdef{4}{32} & \\multirow{3}{*}{40K} & \\multirow{3}{*}{47.8s} & 7.2 min & \\crinterval{31}{43} & $64.2_{1.3}$ & $63.0_{0.4}$ & $35.3$ & $98.7_{0.1}$ &$99.5_{0.2}$\\\\\n\\methodopcrdef{4}{64} & & & 6.1 min & \\crinterval{63}{88} & $63.7_{1.3}$ & $61.9_{0.4}$ & $32.4$ & $95.7_{0.3}$ &$97.8_{0.5}$\\\\\n\\methodopcrdef{4}{256} & & & 4.6 min & \\crinterval{148}{344} & $58.3_{1.4}$ & $50.1_{0.4}$ & $23.7$ & $9.2_{0.4}$ &$70.6_{1.4}$\\\\\n\\hline\n\n\\methodopcrdef{4}{32} & \\multirow{3}{*}{80K} & \\multirow{3}{*}{60.4s} & 7.2 min & \\crinterval{31}{43} & $63.6_{1.3}$ & $63.9_{0.4}$ & $36.0$ & $98.0_{0.2}$ &$99.3_{0.3}$\\\\\n\\methodopcrdef{4}{64} & & & 6.1 min & \\crinterval{63}{88} & $63.3_{1.3}$ & $62.0_{0.4}$ & $32.2$ & $94.5_{0.3}$ &$97.8_{0.5}$\\\\\n\\methodopcrdef{4}{256} & & & 4.6 min & \\crinterval{148}{339} & $60.5_{1.3}$ & $51.7_{0.4}$ & $23.3$ & $13.6_{0.4}$ &$83.7_{1.2}$\\\\\n\n\\hline\n\\methodopcrdef{4}{32} & \\multirow{3}{*}{160K} & \\multirow{3}{*}{85.6s} & 7.2 min & \\crinterval{31}{43} & $63.2_{1.3}$ & $64.3_{0.4}$ & $36.6$ & $99.5_{0.1}$ &$99.4_{0.3}$\\\\\n\\methodopcrdef{4}{64} & & & 6.1 min & \\crinterval{63.2}{87} & $64.6_{1.3}$ & $62.2_{0.4}$ & $32.8$ & $96.9_{0.2}$ &$97.7_{0.5}$\\\\\n\\methodopcrdef{4}{256} & & & 4.6 min & \\crinterval{148}{341} & $61.4_{1.3}$ & $55.5_{0.4}$ & $24.3$ & $34.2_{0.6}$ &$79.5_{1.3}$\\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\\clearpage\n\\subsection{Calibration data domain vs downstream performance}\\label{sec:appendix:sec-kvtc-data-vsdomain-and-results}\nTo examine how the calibration data domain influences downstream performance, we prepare two additional versions of \\Method{} for Mistral NeMo $12$B: one using only FineWeb data and the other using only OpenR1Math data. Table \\ref{tab:nonthinking-ablate-data-source} shows that using OpenR1Math calibration data better maintains MMLU and key-value retrieval scores than FineWeb at higher compression rates. This improvement is likely related to the question-think-answer structure of OpenR1Math, which may be more aligned with the evaluation tasks, compared to the more general web collection nature of FineWeb. However, for $32\\times$ compression, both choices remain competitive. We note that for $256\\times$ compression, the 50/50 mixture of FineWeb and OpenR1Math results in the best scores. For reconstruction errors, regarding calibrating on OpenR1Math/FineWeb and testing on FineWeb/OpenR1Math, see Figures \\ref{fig:kv-pca-train-more} and \\ref{fig:kv-pca-train-openr1}.\n\nWe additionally check the standard deviation of task scores when sampling different calibration sets (see Table \\ref{tab:nonthinking-ablate-data-source-std}). We observe that \\Method{} is relatively stable when sampling 160K tokens --- a 50/50 mixture of FineWeb and OpenR1Math data --- as a calibration set. \n\n\nIn Table \\ref{tab:nonthinking-ablate-data-source-code}, we test \\Method{} calibration under strong domain shifts. We observe that using Python, C, or Assembly from StarCoder \\citep{li2023starcodersourceyou} instead of a 50/50 mixture of FineWeb and OpenR1Math data results in performance degradation on GSM8K. However, we note that despite a strong domain shift (code vs natural language), the model retains in-context retrieval abilities (LITM, RULER-VT) and for cr $16\\times$ obtains scores that are either on par or better than KIVI/GEAR 2-bit (except the case when we calibrate on C).\nWe note that files contained in StarCoder consist of both code and comments, which can potentially explain retention of lingual abilities.\n\n\\begin{table}[ht]\n\\caption{Ablation of the source of data. We consider \\Method{} calibrated fully on FineWeb \\citep{penedo2024the}, fully on OpenMathR1 \\citep{OpenR1Math220k} and a 50/50 mixture. For all cases we utilize a 50/50 mix of documents between 1K and 8K tokens along with documents between 8K and 32K tokens. We calibrate using 160K tokens.}\\label{tab:nonthinking-ablate-data-source}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{lc|cccccc}\n\\toprule\n\n \\multirow{1}{*}{Method} & Data & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n\\midrule\n\\multicolumn{8}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n\\multirow{3}{*}{\\methodopcrdef{4}{32}} & FineWeb + OpenR1Math & \\crinterval{31}{43} & $62.2_{1.3}$ & $63.8_{0.4}$ & $37.5$ & $99.6_{0.1}$ &$98.7_{0.4}$\\\\\n & FineWeb & \\crinterval{31}{43} & $63.5_{1.3}$ & $63.5_{0.4}$ & $37.5$ & $98.5_{0.2}$ &$98.9_{0.3}$\\\\\n & OpenR1Math & \\crinterval{31}{43} & $63.5_{1.3}$ & $64.8_{0.4}$ & $37.8$ & $99.7_{0.1}$ &$99.3_{0.3}$\\\\\n\\hline\n\\multirow{3}{*}{\\methodopcrdef{4}{64}} & FineWeb + OpenR1Math & \\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\n & FineWeb & \\crinterval{63}{87} & $63.2_{1.3}$ & $59.9_{0.4}$ & $36.5$ & $92.0_{0.3}$ &$97.4_{0.5}$\\\\\n & OpenR1Math & \\crinterval{63}{86} & $62.2_{1.3}$ & $63.7_{0.4}$ & $38.2$ & $98.5_{0.2}$ &$96.5_{0.6}$\\\\\n\\hline\n\\multirow{3}{*}{\\methodopcrdef{4}{256}} & FineWeb + OpenR1Math & \\crinterval{148}{340} & $60.0_{1.3}$ & $52.2_{0.4}$ & $31.6$ & $40.0_{0.6}$ &$84.3_{1.1}$\\\\\n & FineWeb & \\crinterval{148}{343} & $57.9_{1.4}$ & $51.5_{0.4}$ & $31.0$ & $14.1_{0.4}$ &$74.5_{1.4}$\\\\\n & OpenR1Math & \\crinterval{156}{342} & $56.6_{1.4}$ & $54.0_{0.4}$ & $29.4$ & $21.0_{0.5}$ &$81.3_{1.2}$\\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{table}[ht]\n\\caption{Mean and standard deviation of downstream performance measured on 5 different calibrations sets (50/50 mixture of OpenR1Math \\citep{OpenR1Math220k} and FineWeb \\citep{penedo2024the}, 160K tokens, documents between 1K and 8K tokens). Results presented as $\\mathrm{mean}_{\\pm \\mathrm{std}}$}\\label{tab:nonthinking-ablate-data-source-std}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{l|cccccc}\n\\toprule\n\n \\multirow{1}{*}{Method} & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n\\midrule\n\\multicolumn{7}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\nVanilla & 1 & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\n\\multirow{1}{*}{\\methodopcrdef{4}{16}} & \\crinterval{17}{20} & $63.5_{\\pm 0.9}$ & $64.7_{\\pm 0.3}$ & $37.2_{\\pm 0.4}$ & $99.6_{\\pm 0.3}$ & $99.7_{\\pm 0.0}$ \\\\\n\\multirow{1}{*}{\\methodopcrdef{4}{32}} & \\crinterval{31}{43} & $63.1_{\\pm 0.5}$ & $64.4_{\\pm 0.6}$ & $36.1_{\\pm 0.7}$ & $98.1_{\\pm 2.0}$ & $99.2_{\\pm 0.3}$ \\\\\n\\multirow{1}{*}{\\methodopcrdef{4}{64}} & \\crinterval{50}{88} & $63.1_{\\pm 1.3}$ & $63.3_{\\pm 0.9}$ & $32.9_{\\pm 0.7}$ & $93.1_{\\pm 3.6}$ & $98.1_{\\pm 0.4}$ \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\begin{table}[ht]\n\\caption{Ablation of out of distribution source of data. We consider \\Method{} calibrated on a 50/50 mixture of FineWeb \\citep{penedo2024the} and OpenMathR1 \\citep{OpenR1Math220k} along with calibration on Python/C/Assembly from the StarCoder dataset \\citep{li2023starcodersourceyou}. In all cases we utilize files between 1K and 8K tokens and calibrate on 160K tokens. For configurations that were tested using several seeds we report $\\mathrm{score}_{\\pm \\mathrm{std}}$, whereas for others we report $\\mathrm{score}_{\\mathrm{stderr}}$}\\label{tab:nonthinking-ablate-data-source-code}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{lc|cccccc}\n\\toprule\n\n \\multirow{1}{*}{Method} & Calibration Data & CR & GSM & MMLU & QASPER & LITM & RULER-VT \\\\\n\\midrule\n\n\\multicolumn{8}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\nVanilla & \\multirow{3}{*}{-} & 1 & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\nGEAR 2bit & & 5 & $59.8_{1.4}$ & $64.0_{0.4}$ & $38.6$ & $96.9_{0.2}$ &$99.4_{0.3}$\\\\\nKIVI 2bit & & 5 & $59.7_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $91.9_{0.3}$ &$98.3_{0.4}$\\\\\n\\hline\n\\multirow{2}{*}{\\methodopcrdef{4}{16}} & FineWeb + OpenR1Math & \\crinterval{17}{20} & $63.5_{\\pm 0.9}$ & $64.7_{\\pm 0.3}$ & $37.2_{\\pm 0.4}$ & $99.6_{\\pm 0.3}$ & $99.7_{\\pm 0.0}$ \\\\\n& Python & \\crinterval{17}{20} & $59.4_{1.4}$ & $65.2_{0.4}$ & $37.4$ & $99.9_{0.0}$ &$99.7_{0.2}$\\\\\n& C & \\crinterval{17}{20} & $55.0_{1.4}$ & $65.4_{0.4}$ & $38.0$ & $99.2_{0.1}$ &$99.3_{0.3}$\\\\\n& Assembly & \\crinterval{17}{20} & $58.9_{1.4}$ & $65.2_{0.4}$ & $37.0$ & $99.9_{0.0}$ &$99.7_{0.2}$\\\\\n\\hline\n\\multirow{2}{*}{\\methodopcrdef{4}{32}} & FineWeb + OpenR1Math & \\crinterval{31}{43} & $63.1_{\\pm 0.5}$ & $64.4_{\\pm 0.6}$ & $36.1_{\\pm 0.7}$ & $98.1_{\\pm 2.0}$ & $99.2_{\\pm 0.3}$ \\\\\n& Python & \\crinterval{35}{43} & $59.0_{1.4}$ & $64.3_{0.4}$ & $36.3$ & $99.7_{0.1}$ &$99.2_{0.3}$\\\\\n& C & \\crinterval{31}{43} & $50.2_{1.4}$ & $64.7_{0.4}$ & $36.8$ & $96.2_{0.2}$ &$99.3_{0.3}$\\\\\n& Assembly & \\crinterval{31}{43} & $55.2_{1.4}$ & $64.2_{0.4}$ & $36.7$ & $99.6_{0.1}$ &$99.4_{0.3}$\\\\\n\\hline\n\\multirow{2}{*}{\\methodopcrdef{4}{64}} & FineWeb + OpenR1Math & \\crinterval{50}{88} & $63.1_{\\pm 1.3}$ & $63.3_{\\pm 0.9}$ & $32.9_{\\pm 0.7}$ & $93.1_{\\pm 3.6}$ & $98.1_{\\pm 0.4}$ \\\\\n& Python & \\crinterval{63}{87} & $56.3_{1.4}$ & $62.0_{0.4}$ & $33.9$ & $98.0_{0.2}$ &$97.4_{0.5}$\\\\\n& C & \\crinterval{63}{87} & $54.4_{1.4}$ & $63.3_{0.4}$ & $34.5$ & $95.4_{0.3}$ &$97.8_{0.5}$\\\\\n& Assembly & \\crinterval{50}{86} & $60.9_{1.3}$ & $62.2_{0.4}$ & $33.0$ & $99.1_{0.1}$ &$98.3_{0.4}$\\\\\n \n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\\subsection{Sliding window size vs downstream performance}\\label{sec:appendix:sec-kvtc-ws-ablate}\nWe ablate the influence of sliding window of recent not-compressed tokens on downstream performance in Table \\ref{tab:kvtc-ablate-ws}. We observe that increasing the length of sliding window improves downstream performance of the model, with most noticeable difference between sliding windows $\\leq 16$ and sliding windows $\\geq 64$.\n\n\n\\begin{table}[ht]\n\\caption{Ablation of the sliding window size of recent tokens that are not compressed. For a fair compression in this table we simulate a sequence of short conversations by running compressing/eviction on the cache every $s=1$ instead every $s=16$ tokens. Therefore, the $w=16$ token window is left int the range $15$-$16$ instead of $0$-$16$.}\\label{tab:kvtc-ablate-ws}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{lc|cccccc}\n\\toprule\n\n \\multirow{1}{*}{Method} & Window Size & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n\n \n\\midrule\n\\multicolumn{8}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n\\multirow{4}{*}{\\methodopcrdef{4}{64}} & 1 & \\crinterval{59}{88} & $41.2_{1.4}$ & $53.8_{0.4}$ & $36.5$ & $68.3_{0.6}$ &$87.7_{1.0}$\\\\\n& 16 & \\crinterval{58}{88} & $53.0_{1.4}$ & $56.0_{0.4}$ & $38.1$ & $80.0_{0.5}$ &$88.0_{1.0}$\\\\\n& 64 & \\crinterval{57}{88} & $55.8_{1.4}$ & $59.2_{0.4}$ & $37.7$ & $89.8_{0.4}$ &$95.8_{0.6}$\\\\\n & 128 & \\crinterval{60}{88} & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\n\n\\midrule\n\n\\multicolumn{8}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n%\n%\n%\n%\n\n\\multirow{4}{*}{\\methodopcrdef{4}{64}} & 1 & \\crinterval{61}{87} & $53.0_{1.4}$ & $54.9_{0.4}$ & $36.4$ & $88.6_{0.4}$ &$90.7_{0.9}$\\\\\n& 16 & \\crinterval{60}{87} & $60.1_{1.3}$ & $56.4_{0.4}$ & $37.7$ & $88.9_{0.4}$ &$95.8_{0.6}$\\\\\n& 64 & \\crinterval{59}{87} & $62.2_{1.3}$ & $59.0_{0.4}$ & $37.8$ & $93.0_{0.3}$ &$98.0_{0.4}$\\\\\n & 128 & \\crinterval{51}{87} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\\clearpage\n\n\\subsection{Ablations of lossless compression}\\label{sec:appendix:sec-kvtc-deflate-ablate}\nWe ablate the differences between:\n\\begin{itemize}\n \\item ANS~\\citep{duda2014asymmetricnumeralsystemsentropy}\n \\item Bitcomp with default nvCOMP settings~\\citep{nvcomp_github}\n \\item DEFLATE~\\citep{deflate_patent} (Huffman~\\citep{4051119} + LZ77~\\citep{lz77_1997}) \n \\item GDeflate~\\citep{nvidia_gdeflate_ds}\n \\item LZ4~\\citep{lz4}\n \\item Snappy~\\citep{snappy}\n \\item Zstandard~\\citep{zstd}\n \\item Identity --- no additional lossless compression\n\\end{itemize}\nWe present the results in Table \\ref{tab:kvtc-ablate-deflate}. We note that DEFLATE can be easily substituted by a faster GDeflate optimized for GPUs, as the highest measured difference in compression ratio is $\\leq0.1$. We observe that the cache generated for RULER Variable Tracking is significantly more compressible than the cache generated for other tasks. We hypothesize that it may be an effect of repeated noise used as context filler by the authors (see Appendix~\\ref{appendix:evaluation-details}). We observe that ANS, DEFLATE, GDeflate, and Zstandard improve significantly over Identity in all studied cases. For a detailed study of throughput vs compression ratio of tested algorithms, we refer to \\citep{nvidia_nvcomp_benchmarks}.\n\n\\begin{table}[ht]\n\\caption{Ablation of the lossless compression algorithms, performed using Mistral Nemo 12B with \\methodopcrdef{4}{32}. Identity stands for no additional lossless compression (just PCA + DP Quantization; note that we count the omitted sinks into compression ratio, what is notable for tasks with shorter contexts). We mark results that have compression ratio advantage over Identity smaller than 1 in red.}\\label{tab:kvtc-ablate-deflate}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{l|ccccc}\n\\toprule\n\n\\multirow{2}{*}{Algorithm} & \\multicolumn{5}{c}{Compression Ratio} \\\\\n & Min-Max & GSM8K & QASPER & LITM & RULER-VT \\\\\n\\midrule\n ANS & \\crinterval{32.8}{37.6} & 32.8 & 37.6 & 36.8 & 37.0 \\\\\n Bitcomp & \\crinterval{29.6}{32.3} & \\badresult{}29.6 & \\badresult{}32.3 & \\badresult{}32.2 & \\badresult{}32.2 \\\\\n DEFLATE & \\crinterval{34.7}{42.9} & 34.7 & 39.5 & 39.7 & 42.9 \\\\\n GDeflate & \\crinterval{34.6}{42.8} & 34.6 & 39.4 & 39.6 & 42.8 \\\\\n Identity & \\crinterval{29.6}{32.4} & \\badresult{}29.6 & \\badresult{}32.4 & \\badresult{}32.2 & \\badresult{}32.3 \\\\\n LZ4 & \\crinterval{29.5}{35.5} & \\badresult{}29.5 & \\badresult{}32.4 & \\badresult{}32.7 & 35.5 \\\\\n Snappy & \\crinterval{29.4}{34.5} & \\badresult{}29.4 & \\badresult{}32.2 & \\badresult{}32.4 & 34.5 \\\\\n zStandard & \\crinterval{34.6}{46.3} & 34.6 & 39.4 & 39.9 & 46.3 \\\\\n\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\\clearpage\n\\subsection{Benefits of DP quantization}\\label{sec:appendix:ablate_dp}\nWe compare \\Method{} to a variant that does not use DP quantization, but instead removes a fraction of the least important principal components (denoted -DPQ). The results are presented in Table \\ref{tab:kvtc-ablate-dp-pca}. We observe that removing PCA components, rather than applying DP quantization, leads to significant performance degradation on long context tasks. Additionally, the performance of DPQ on short context tasks deteriorates further as the length of the sliding window of uncompressed elements is reduced. We also note that DEFLATE can be much more efficient on quantized data. In general, our findings demonstrate that quantization is a crucial component of \\Method{}, and omitting it hinders scaling to larger compression ratios.\n\\begin{table}[ht]\n\\caption{Ablation of the importance of DP quantization over pure PCA. For alteration of sliding window size we follow the protocol from Appendix~\\ref{sec:appendix:sec-kvtc-ws-ablate}.}\\label{tab:kvtc-ablate-dp-pca}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{lcc|cccccc}\n\\toprule\n\n \\multirow{1}{*}{Window Size} & Method & Modification & CR & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n\n \n\\midrule\n\\multicolumn{9}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n\\multirow{8}{*}{16} & \\multirow{2}{*}{\\methodopcrdef{4}{8}} & - & \\crinterval{9}{10} & $57.5_{1.4}$ & $59.4_{0.4}$ & $40.1$ & $99.1_{0.1}$ &$98.2_{0.4}$\\\\\n& & -DPQ & \\crinterval{8}{9} & $56.9_{1.4}$ & $57.5_{0.4}$ & $40.1$ & $98.6_{0.1}$ &$93.0_{0.8}$\\\\\n\\cmidrule{2-9}\n& \\multirow{2}{*}{\\methodopcrdef{4}{16}} & - & \\crinterval{18}{22} & $57.2_{1.4}$ & $59.5_{0.4}$ & $40.6$ & $99.4_{0.1}$ &$98.3_{0.4}$\\\\\n& & -DPQ & \\crinterval{16}{17} & $52.0_{1.4}$ & $53.8_{0.4}$ & $36.9$ & $69.2_{0.6}$ &$87.0_{1.1}$\\\\\n\\cmidrule{2-9}\n& \\multirow{2}{*}{\\methodopcrdef{4}{32}} & - & \\crinterval{34}{44} & $55.5_{1.4}$ & $58.2_{0.4}$ & $39.6$ & $98.8_{0.1}$ &$94.8_{0.7}$\\\\\n& & -DPQ & \\crinterval{31}{34} & $42.9_{1.4}$ & $36.8_{0.4}$ & $34.2$ & $44.4_{0.6}$ &$83.0_{1.2}$\\\\\n\\cmidrule{2-9}\n& \\multirow{2}{*}{\\methodopcrdef{4}{64}} & - & \\crinterval{58}{88} & $53.0_{1.4}$ & $56.0_{0.4}$ & $38.1$ & $80.0_{0.5}$ &$88.0_{1.0}$\\\\\n& & -DPQ & \\crinterval{52}{68} & $21.8_{1.1}$ & $6.5_{0.2}$ & $26.7$ & $5.1_{0.3}$ &$55.5_{1.6}$\\\\\n\\midrule\n\\multirow{8}{*}{128} & \\multirow{2}{*}{\\methodopcrdef{4}{8}} & - & \\crinterval{9}{10} & $56.7_{1.4}$ & $59.9_{0.4}$ & $40.0$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\n& & -DPQ & \\crinterval{8}{9} & $57.0_{1.4}$ & $60.7_{0.4}$ & $40.2$ & $99.5_{0.1}$ &$98.5_{0.4}$\\\\\n\\cmidrule{2-9}\n& \\multirow{2}{*}{\\methodopcrdef{4}{16}} & - & \\crinterval{17}{22} & $57.1_{1.4}$ & $60.1_{0.4}$ & $40.7$ & $99.3_{0.1}$ &$99.0_{0.3}$\\\\\n& & -DPQ & \\crinterval{16}{17} & $55.7_{1.4}$ & $59.7_{0.4}$ & $37.1$ & $85.0_{0.4}$ &$95.5_{0.7}$\\\\\n\\cmidrule{2-9}\n\n& \\multirow{2}{*}{\\methodopcrdef{4}{32}} & - & \\crinterval{33}{44} & $58.4_{1.4}$ & $60.8_{0.4}$ & $39.3$ & $99.1_{0.1}$ &$98.9_{0.3}$\\\\\n& & -DPQ & \\crinterval{31}{34} & $55.1_{1.4}$ & $56.9_{0.4}$ & $35.3$ & $64.5_{0.6}$ &$89.6_{1.0}$\\\\\n\\cmidrule{2-9}\n& \\multirow{2}{*}{\\methodopcrdef{4}{64}} & - & \\crinterval{60}{88} & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\n& & -DPQ & \\crinterval{47}{68} & $57.2_{1.4}$ & $49.3_{0.4}$ & $28.1$ & $13.1_{0.4}$ &$58.7_{1.5}$\\\\\n\n%\n%\n%\n%\n\n%\n%\n\n%\n%\n\n%\n%\n%\n%\n%\n\n%\n%\n\n%\n%\n\n%\n%\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\\clearpage\n\n\\subsection{PCA feature concat size vs performance}\\label{sec:appendix:ablate_pca_input_size}\nWe study how the number of layers over which we concatenate key/value heads influences the performance of \\Method{}. We present the results in Table \\ref{tab:kvtc-ablate-pca-input-features}. To better isolate the influence of the number of concatenated key/value heads, we run \\Method{} without dynamic programming quantization (that is, we run \\Method{}-DPQ introduced in Appendix \\ref{sec:appendix:ablate_dp}) and with a sliding window $w=16$. We note that results support our hypothesis about cross-layer similarity between key/value heads from Section \\ref{sec:preliminaries}, as the more layers we concatenate for calibration (PCA), the better the downstream performance. \n\n\\begin{table}[ht]\n\\caption{Ablation of the number of layers used for PCA. To better isolate the influence of the number of concatenated key/value heads, we run \\Method{} without dynamic programming quantization (that is, we run \\Method{}-DPQ introduced in Appendix \\ref{sec:appendix:ablate_dp}) and with a sliding window $w=16$.}\\label{tab:kvtc-ablate-pca-input-features}\n\\centering\n\\setlength{\\tabcolsep}{1mm}\n\\small\n\\begin{tabular}{lc|ccccc}\n\\toprule\n\n \\multirow{1}{*}{Method} & PCA Layers & GSM8K & MMLU & QASPER & LITM & RULER-VT \\\\\n\n \n\\midrule\n\\multicolumn{7}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n\\multirow{6}{*}{\\methodopcrdef{4}{8}-DPQ} & 1 & $27.5_{1.2}$ & $24.3_{0.3}$ & $28.2$ & $49.1_{0.6}$ &$70.8_{1.4}$\\\\\n& 2 & $44.8_{1.4}$ & $41.1_{0.4}$ & $34.2$ & $77.6_{0.5}$ &$84.9_{1.1}$\\\\\n& 4 & $53.3_{1.4}$ & $51.9_{0.4}$ & $37.5$ & $95.9_{0.2}$ &$93.0_{0.8}$\\\\\n& 8 & $55.9_{1.4}$ & $55.3_{0.4}$ & $39.7$ & $99.2_{0.1}$ &$90.7_{0.9}$\\\\\n& 16 & $56.0_{1.4}$ & $57.1_{0.4}$ & $38.8$ & $98.8_{0.1}$ &$92.8_{0.8}$\\\\\n & 32 & $56.9_{1.4}$ & $57.5_{0.4}$ & $40.1$ & $98.6_{0.1}$ &$93.0_{0.8}$\\\\\n\\midrule\n\\multirow{6}{*}{\\methodopcrdef{4}{16}-DPQ} & 1 & $2.5_{0.4}$ & $0.2_{0.0}$ & $18.4$ & $0.0_{0.0}$ &$0.5_{0.2}$\\\\\n& 2 & $13.9_{1.0}$ & $2.3_{0.1}$ & $22.1$ & $0.7_{0.1}$ &$12.9_{1.0}$\\\\\n& 4 & $33.3_{1.3}$ & $19.3_{0.3}$ & $29.1$ & $32.0_{0.6}$ &$62.7_{1.5}$\\\\\n& 8 & $49.6_{1.4}$ & $43.4_{0.4}$ & $34.4$ & $60.7_{0.6}$ &$85.8_{1.1}$\\\\\n& 16 & $51.6_{1.4}$ & $49.1_{0.4}$ & $36.0$ & $72.7_{0.6}$ &$89.0_{1.0}$\\\\\n & 32 & $52.0_{1.4}$ & $53.8_{0.4}$ & $36.9$ & $69.2_{0.6}$ &$87.0_{1.1}$\\\\\n\\midrule\n\\multirow{6}{*}{\\methodopcrdef{4}{32}-DPQ} & 1 & $1.1_{0.3}$ & $0.1_{0.0}$ & $17.8$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\n& 2 & $1.5_{0.3}$ & $0.2_{0.0}$ & $18.1$ & $0.0_{0.0}$ &$0.2_{0.1}$\\\\\n& 4 & $3.9_{0.5}$ & $0.9_{0.1}$ & $20.0$ & $0.0_{0.0}$ &$1.6_{0.4}$\\\\\n& 8 & $28.0_{1.2}$ & $6.4_{0.2}$ & $24.7$ & $2.6_{0.2}$ &$33.0_{1.5}$\\\\\n& 16 & $40.1_{1.4}$ & $26.0_{0.4}$ & $31.2$ & $24.6_{0.5}$ &$60.4_{1.5}$\\\\\n & 32 & $42.9_{1.4}$ & $36.8_{0.4}$ & $34.2$ & $44.4_{0.6}$ &$83.0_{1.2}$\\\\\n\\midrule\n\\multirow{6}{*}{\\methodopcrdef{4}{64}-DPQ} & 1 & $0.9_{0.3}$ & $0.3_{0.0}$ & $18.0$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\n& 2 & $1.4_{0.3}$ & $0.1_{0.0}$ & $17.7$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\n& 4 & $1.5_{0.3}$ & $0.1_{0.0}$ & $18.1$ & $0.0_{0.0}$ &$0.1_{0.1}$\\\\\n& 8 & $2.4_{0.4}$ & $0.6_{0.1}$ & $19.4$ & $0.0_{0.0}$ &$0.2_{0.1}$\\\\\n& 16 & $13.9_{1.0}$ & $1.9_{0.1}$ & $22.1$ & $0.0_{0.0}$ &$10.0_{0.9}$\\\\\n & 32 & $21.8_{1.1}$ & $6.5_{0.2}$ & $26.7$ & $5.1_{0.3}$ &$55.5_{1.6}$\\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\\clearpage\n\n\n\\subsection{Standard error of the main results}\\label{sec:appendix_stderr}\nIn Table \\ref{tab:nonthinking-results-std} we attach the results from Table \\ref{tab:nonthinking-results} with their standard error, as bootstrapped by LM Evaluation Harness (where available) \\citep{eval-harness}. We note that downstream evaluation runs, except the Qwen models, were performed using $1$ seed and greedy evaluation.\n\n\n\\begin{table}[ht]\n\\caption{Downstream task results, presented also in Table \\ref{tab:nonthinking-results}, here shown with standard error as reported by LM Evaluation Harness (where available).}\\label{tab:nonthinking-results-std}\n\\centering\n\\small\n\\begin{tabular}{l|ccccc}\n\\toprule\n\n \\multirow{2}{*}{Method} & GSM8K & MMLU & QASPER & LITM 100 & RULER-VT \\\\\n & \\multicolumn{2}{c}{Math \\& Knowledge} & \\multicolumn{3}{c}{Long Context} \\\\\n\\midrule\n\\multicolumn{6}{c}{\\tabwithinbest{}Llama 3.1 8B} \\\\\n vanilla & $56.8_{1.4}$ & $60.5_{0.4}$ & $40.4$ & $99.4_{0.1}$ &$99.8_{0.2}$\\\\\n GEAR 2bit & $52.8_{1.4}$ & $59.6_{0.4}$ & $40.4$ & $96.9_{0.2}$ &$99.8_{0.2}$\\\\\n KIVI 2bit & $52.8_{1.4}$ & $59.6_{0.4}$ & $39.1$ & $88.8_{0.4}$ &$98.9_{0.3}$\\\\\n xKV$^{2/16 \\;4\\mathrm{key}}_{3/16 \\;4\\mathrm{value}}$ & $56.6_{1.4}$ & $59.5_{0.4}$ & $35.6$ & $99.9_{0.0}$ &$99.8_{0.2}$\\\\\n FP8 & $55.2_{1.4}$ & $60.1_{0.4}$ & $40.8$ & $99.4_{0.1}$ & $99.9_{0.1}$ \\\\\n \\methodopcrdef{4}{8} & $57.0_{1.4}$ & $59.8_{0.4}$ & $40.1$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\n \\methodopcrdef{4}{16} & $56.9_{1.4}$ & $60.1_{0.4}$ & $40.7$ & $99.3_{0.1}$ &$99.1_{0.3}$\\\\\n \\methodopcrdef{4}{32} & $57.8_{1.4}$ & $60.6_{0.4}$ & $39.4$ & $99.1_{0.1}$ &$98.9_{0.3}$\\\\\n \\methodopcrdef{4}{64} & $57.2_{1.4}$ & $60.7_{0.4}$ & $37.8$ & $90.2_{0.4}$ &$95.9_{0.6}$\\\\\n\n \\HTO{}$_{{1/16} \\;\\mathrm{past}}^{{1/16} \\;\\mathrm{recent}}$ & $54.3_{1.4}$ & $44.3_{0.4}$ & $34.3$ & $20.2_{0.5}$ &$50.4_{1.6}$\\\\\n \\TOVA{}{$\\frac{1}{8}$} & $54.5_{1.4}$ & $44.8_{0.4}$ & $38.6$ & $1.2_{0.1}$ &$99.7_{0.2}$\\\\\n\n\n\\midrule\n\\multicolumn{6}{c}{\\tabwithinbest{}MN-Minitron 8B} \\\\\n Vanilla & $59.1_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $99.8_{0.0}$ &$99.4_{0.3}$\\\\\n GEAR 2bit & $57.9_{1.4}$ & $63.6_{0.4}$ & $38.2$ & $96.0_{0.2}$ &$98.3_{0.4}$\\\\\n KIVI 2bit & $58.0_{1.4}$ & $63.2_{0.4}$ & $38.2$ & $86.3_{0.4}$ &$96.8_{0.6}$\\\\\n xKV$^{2/16 \\;5\\mathrm{key}}_{3/16 \\;5\\mathrm{value}}$ & $59.3_{1.4}$ & $63.1_{0.4}$ & $34.5$ & $99.6_{0.1}$ &$99.1_{0.3}$\\\\\n FP8 & $60.1_{1.3}$ & $64.3_{0.4}$ & $38.3$ & $99.8_{0.1}$ & $99.2_{0.3}$ \\\\\n \\methodopcrdef{4}{8} & $60.6_{1.3}$ & $64.2_{0.4}$ & $39.1$ & $99.4_{0.1}$ &$98.8_{0.3}$\\\\\n \\methodopcrdef{4}{16} & $60.3_{1.3}$ & $64.1_{0.4}$ & $38.6$ & $99.3_{0.1}$ &$98.8_{0.3}$\\\\\n \\methodopcrdef{4}{32} & $59.1_{1.4}$ & $63.7_{0.4}$ & $37.7$ & $86.9_{0.4}$ &$96.0_{0.6}$\\\\\n \\methodopcrdef{4}{64} & $57.8_{1.4}$ & $62.1_{0.4}$ & $38.1$ & $59.5_{0.6}$ &$93.4_{0.8}$\\\\\n \\HTO{}$_{{1/16} \\;\\mathrm{past}}^{{1/16} \\;\\mathrm{recent}}$ & $55.3_{1.4}$ & $43.5_{0.4}$ & $30.0$ & $16.6_{0.5}$ &$39.2_{1.5}$\\\\\n \\TOVA{}{$\\frac{1}{8}$} & $59.2_{1.4}$ & $48.1_{0.4}$ & $33.9$ & $0.3_{0.1}$ &$99.3_{0.3}$\\\\\n\n\\midrule\n\\multicolumn{6}{c}{\\tabwithinbest{}Mistral NeMo 12B} \\\\\n Vanilla & $61.9_{1.3}$ & $64.5_{0.4}$ & $38.4$ & $99.5_{0.1}$ &$99.8_{0.2}$\\\\\n GEAR 2bit & $59.8_{1.4}$ & $64.0_{0.4}$ & $38.6$ & $96.9_{0.2}$ &$99.4_{0.3}$\\\\\n KIVI 2bit & $59.7_{1.4}$ & $64.3_{0.4}$ & $38.2$ & $91.9_{0.3}$ &$98.3_{0.4}$\\\\\n xKV$^{2/16 \\;5\\mathrm{key}}_{3/16 \\;5\\mathrm{value}}$ & $61.9_{1.3}$ & $63.9_{0.4}$ & $33.5$ & $97.9_{0.2}$ &$99.4_{0.3}$\\\\\n FP8 & $61.7_{1.3}$ & $64.5_{0.4}$ & $37.9$ & $99.0_{0.1}$ & $99.8_{0.2}$ \\\\\n \\methodopcrdef{4}{8} & $62.5_{1.3}$ & $64.6_{0.4}$ & $37.6$ & $99.9_{0.0}$ &$99.5_{0.2}$\\\\\n \\methodopcrdef{4}{16} & $62.0_{1.3}$ & $64.4_{0.4}$ & $37.6$ & $99.8_{0.0}$ &$99.5_{0.2}$\\\\\n \\methodopcrdef{4}{32} & $62.2_{1.3}$ & $63.8_{0.4}$ & $37.5$ & $99.6_{0.1}$ &$98.7_{0.4}$\\\\\n \\methodopcrdef{4}{64} & $61.9_{1.3}$ & $61.4_{0.4}$ & $38.0$ & $95.3_{0.3}$ &$98.0_{0.4}$\\\\\n \\HTO{}$_{{1/16} \\;\\mathrm{past}}^{{1/16} \\;\\mathrm{recent}}$ & $57.0_{1.4}$ & $45.4_{0.4}$ & $29.5$ & $16.2_{0.5}$ &$35.2_{1.5}$\\\\\n \\TOVA{}{$\\frac{1}{8}$} & $60.3_{1.3}$ & $49.0_{0.4}$ & $36.0$ & $8.7_{0.4}$ &$99.6_{0.2}$\\\\\n\n\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\\clearpage\n\n\\subsection{PCA matrix sizes}\\label{sec:appendix:sec-kvtc-pca-sizes}\nIn Table \\ref{tab:model-kv-pca-size} we present the sizes of PCA projection matrices ($V$ from $U \\Sigma V^\\top$) after being computed via \\citep{halko2010findingstructurerandomnessprobabilistic} algorithm.\nWe note that the sizes are only a relatively small fraction of the model parameters, and that they can be further reduced by the DP algorithm depending on the desired compression ratio.\n\n\\begin{table}[ht]\n\\caption{Number of parameters used by PCA matrices, before DP, for the tested models. We note that despite treating keys and values separately, while using feature capacity for the efficient \\citep{halko2010findingstructurerandomnessprobabilistic} PCA calculation algorithm. For example, Llama 3.1 8B has 32 layers, each with 8 key/value heads, each head of size 128. Therefore, after cross-head concatenation, each key/value has $32\\times8\\times128 = 32768$ features. The PCA projection $V$ is cut to the first $10$K principal components by \\citep{halko2010findingstructurerandomnessprobabilistic} algorithm for efficiency, resulting in $32768 \\times 10000 \\simeq 328M$ parameters. Further DP bit allocation can remove additional principal directions depending on the desired compression ratio. Both models and PCA projection matrices are stored in 16bit precision.\n}\\label{tab:model-kv-pca-size}\n\n\\small\n\\centering\n\\begin{tabular}{lcl|ccc}\n\\toprule\nModel & \\makecell{\\#Params} &\\makecell{Key/Value\\\\Features} & \\makecell{Key/Value\\\\PCA Cap} & \\makecell{Key/Value\\\\PCA Params} & $\\frac{\\mathrm{TotalPCAParams}}{\\mathrm{Model Params}}$ \\\\\n\\midrule\nQwen 2.5 R1 1.5B & $1.5$B & $28\\times2\\times128 = 7168$ & \\multirow{2}{*}{8K} & 51M & $6.8$\\% \\\\\nQwen 2.5 R1 7B & $7.1$B & $28\\times4\\times128 = 14336$ & & 115M & $3.2$\\% \\\\\n\\midrule\nLlama 3.1 8B & $7.5$B & $32\\times8\\times128 = 32768$ & \\multirow{3}{*}{10K} & 328M & $8.7$\\% \\\\\nLlama 3.3 70B & $69.5$B & $80\\times8\\times128 = 81920$ & & 819M & $2.4$\\% \\\\\nMistral NeMo 12B & $11.6$B & $40\\times8\\times128 = 40960$ & & 410M & $7.1$\\% \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\n\\clearpage\n\n\\subsection{Dynamic programming algorithm}\\label{sec:appendix_dp_proof_sketch}\nBelow, we present the pseudocode for the dynamic programming precision assignment along with a proof sketch.\n\n\\begin{tcolorbox}[colback=blue!5!white,colframe=white!50!blue,title=\\small Dynamic Programming Precision Assignment Pseudocode]\n \\begin{tiny}\n \\begin{Verbatim}[breaklines=true, breakanywhere=true]\nD # calibration data matrix of shape (batch, num_features)\nm = D.mean(dim=0, keepdim=True) # of each feature across the batch dimension\n\nU, S, V = svd(D - m) # D - m = U @ S @ V.T\n\nP = U@S # assume columns sorted by singular values\nbatch, num_considered_features = P.shape\n\n# initial_reconstruction_error corresponds to quantizing everything with zero bits\ninitial_reconstruction_error = (P*P).sum() # squared Frobenius norm\n\n# set to initial_reconstruction_error as we assume that the data is initially quantized with 0 bits\n# and we progressively consider non-zero quantization of more and more features\nbest_error = tensor(shape=(num_considered_features + 1, max_bit_budget + 1), values=initial_reconstruction_error)\nbest_error_type = array(shape=(num_considered_features + 1, max_bit_budget + 1), values=0)\nbest_error_block_size = tensor(shape=(num_considered_features + 1, max_bit_budget + 1), values=0)\nbest_error_bit_cost = tensor(shape=(num_considered_features + 1, max_bit_budget + 1), values=0)\n\n# we assume that block sizes are > 0\nallowed_block_sizes = [1, 16, 64, 256, 1024] \n\n# We assume the presence of a None type that quantizes data to the array of zeros.\n# We count bit usage of this type as 0, \n# because it directly corresponds to the removal of principal components.\ntypes = [None, int2, int4, fp8] \n\nfor i in range(1, num_considered_features + 1): \n for block_size in allowed_block_sizes:\n if block_size <= i:\n assert block_size > 0\n # the loop below can be parallelized\n for budget in range(1, max_bit_budget + 1): \n if best_error[i, budget] > best_error[i, budget - 1]:\n best_error[i, budget] = best_error[i, budget - 1]\n best_error_type[i, budget] = best_error_type[i, budget - 1]\n best_error_block_size[i, budget] = best_error_block_size[i, budget - 1]\n best_error_bit_cost[i, budget] = best_error_bit_cost[i, budget - 1]\n\n for t in types:\n\n block_to_quantize = P[:, i - block_size:i]\n\n quantized_data, used_bits = simulate_quantization(block_to_quantize, t)\n if used_bits <= budget:\n zero_bit_quantize_error = (block_to_quantize * block_to_quantize).sum()\n quantization_error = block_to_quantize - quantized_data\n quantization_error = (quantization_error * quantization_error).sum()\n\n error_change = -zero_bit_quantize_error + quantization_error\n\n if best_error[i, budget] > error_change + best_error[i - block_size, budget - used_bits]:\n best_error[i, budget] = error_change + best_error[i - block_size, budget - used_bits]\n best_error_type[i, budget] = t\n best_error_block_size[i, budget] = block_size\n best_error_bit_cost[i, budget] = used_bits\n\n# we can use best_error, best_error_type, best_error_block_size and best_error_bit_cost tables to get the quantization for a given budget\n \\end{Verbatim}\n\\end{tiny}\n\\end{tcolorbox}\nThe proof of the optimality follows by simple induction on \\texttt{i} and \\texttt{budget}.\nTo be more precise we want to prove that \\texttt{best\\_error[j, q]} is the smallest reconstruction error (squared Frobenius norm) one can achieve when considering first j features of P (setting other features to 0 -- 0-bit quantization) and quantization restricted to types from \\texttt{types} that can only be used to quantize blocks of contiguous features of sizes in \\texttt{allowed\\_block\\_sizes} sizes, while utilizing no more than \\texttt{budget} bits. For simplicity we assume that the smallest reconstruction error (squared Frobenius norm) for \\texttt{q=0} budget cases is \\texttt{initial\\_reconstruction\\_error = (P*P).sum()}.\nThen the proof by induction can be conducted as follows:\n\\begin{itemize}\n \\item For \\texttt{i=0} or \\texttt{budget=0} we have that if we consider quantization of the first $0$ features and leave other features as zeros or budget of size $0$, then the reconstruction error is indeed \\texttt{(P*P).sum()}.\n \\item Then to prove for \\texttt{i>0} and \\texttt{budget>0} we assume the optimality of \\texttt{best\\_error[j, q]} for \\texttt{j<i}, and for \\texttt{j=i} and \\texttt{q<budget}. Then we note that the algorithm enumerates all possible quantization blocks that the quantization of the first \\texttt{i} features can end with within the budget \\texttt{budget}.\n\\end{itemize}\n\nComputational complexity can be directly inferred from the pseudo-code:\n\\begin{align*}\n\\mathcal{O}(\\mathrm{num\\_considered\\_features} \\times \\\\\n\\mathrm{|allowed\\_block\\_sizes|} \\times\\\\\n\\mathrm{max\\_bit\\_budget} \\times\n\\\\ \\mathrm{|types|} \\times \\\\\nq_{\\mathrm{sim}}(\\mathrm{max}\\{\\mathrm{allowed\\_block\\_sizes}\\}, \\mathrm{batch}))\n\\end{align*}\nwhere \n\\[q_{\\mathrm{sim}}(\\mathrm{max}\\{\\mathrm{allowed\\_block\\_sizes}\\}, \\mathrm{batch})\n\\]\nis the time taken to simulate quantization.\nAssuming that $\\mathrm{|allowed\\_block\\_sizes|}$ and $\\mathrm{|types|}$ are constant and \nquantization simulation can be performed in\n\\[\\mathcal{O}(\\mathrm{\\mathrm{max}\\{allowed\\_block\\_sizes}\\} \\times \\mathrm{batch})\\]\nwe can write the asymptotic bound on the algorithm runtime as:\n\\begin{align*}\n\\mathcal{O}(\\mathrm{num\\_considered\\_features} \\times \\mathrm{max\\_bit\\_budget} \\times \\mathrm{batch})\n\\end{align*}\nWe additionally provide the runtime of the algorithm in Table \\ref{tab:nonthinking-ablate-num-tokens} in Appendix \\ref{sec:appendix:sec-kvtc-data-vs-time-and-results}.\n\n\n\n\n\n\n\n\\clearpage\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"Among methods with compression ratios of at least 30×, for each base model choose the method whose GSM8K/MMLU average is closest to that model’s vanilla GSM8K/MMLU average. Across these chosen methods, which base model’s method has the greatest number of bolded scores across all datasets, and what are that count and its total score difference from vanilla?"},"answer":{"kind":"string","value":"Mistral NeMo 12B, 5, -2.1"},"plan":{"kind":"string","value":"SELECT all base models\nLOOP for each base model\n COMPUTE vanilla_average = average of vanilla GSM8K and MMLU\n SELECT all methods with compression ratio ≥ 30×\n LOOP for each method\n COMPUTE method_average = average of this method’s GSM8K and MMLU\n COMPUTE distance = absolute(method_average − vanilla_average )\n COMPUTE chosen_method_for_model = argmin method over distance\n\n\nSELECT all base models\nLOOP for each base model\n COMPUTE bold_count = number of bolded scores of chosen_method_for_model\n COMPUTE difference = sum(chosen_method_for_model score - vanilla score) over all datasets\nCOMPUTE target_model = argmax model over bold_count\n\n\nRETURN target_model, bold_count of target_model, difference of target_model\n"}}},{"rowIdx":367,"cells":{"paper":{"kind":"string","value":"2505.16986"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lcccc|cccc|c|cc|c}\n"," \\toprule\n"," \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n"," & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 83.51 & 89.98 & 92.08 & 91.02 & 58.02 & 66.38 & 82.18 & 73.44 & 85.26 & 39.19 & 86.44 & 62.07 \\\\\n"," Hotels & 78.18 & 84.87 & 90.84 & 87.75 & 60.40 & 67.29 & 85.53 & 75.32 & 72.13 & 48.30 & 80.91 & 71.35 \\\\\n"," Restaurants & 72.76 & 80.40 & 88.44 & 84.23 & 57.49 & 66.69 & 80.64 & 73.00 & 95.16 & 95.14 & 98.63 & 65.32 \\\\\n"," Attractions & 90.50 & 97.87 & 92.33 & 95.02 & 75.54 & 91.34 & 81.37 & 86.07 & 98.15 & N/A & N/A &83.00 \\\\ \\midrule\n"," \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 80.27 & 91.31 & 86.91 & 89.05 & 57.76 & 74.51 & 71.99 & 73.23 & 89.25 & 24.04 & 80.63 & 57.01 \\\\\n"," H-R & 82.02 & 91.03 & 89.23 & 90.12 & 68.44 & 77.95 & 84.86 & 81.26 & 83.67 & 29.12 & 87.58 & 64.42 \\\\\n"," H-A & 62.30 & 72.67 & 81.35 & 76.77 & 59.22 & 68.73 & 81.05 & 74.39 & 71.41 & 27.87 & 82.80 & 65.70 \\\\\n"," F-H-A & 77.19 & 87.50 & 86.76 & 87.13 & 59.63 & 74.16 & 75.27 & 74.71 & 81.15 & 22.65 & 83.45 & 52.76 \\\\\n"," F-H-R & 71.53 & 86.05 & 80.91 & 83.40 & 54.39 & 71.99 & 68.99 & 70.45 & 82.47 & 46.32 & 84.40 & 53.88 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Results using Llama 3.1 8B Instruct after SFT.}\n","\\label{table:llama3.1-8b-sft}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lcccc|cccc|c|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\multicolumn{4}{c}{\\\\textbf{Tool Call}} & \\\\multicolumn{4}{|c|}{\\\\textbf{Parameter Matching}} & \\\\textbf{Code Exec. Rate} & \\\\multicolumn{2}{|c|}{\\\\textbf{Information Seeking}} & \\\\multicolumn{1}{c}{\\\\textbf{Cache Summary}} \\\\\\\\ \\n\",\n \" & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\\\\\ \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 83.51 & 89.98 & 92.08 & 91.02 & 58.02 & 66.38 & 82.18 & 73.44 & 85.26 & 39.19 & 86.44 & 62.07 \\\\\\\\\\n\",\n \" Hotels & 78.18 & 84.87 & 90.84 & 87.75 & 60.40 & 67.29 & 85.53 & 75.32 & 72.13 & 48.30 & 80.91 & 71.35 \\\\\\\\\\n\",\n \" Restaurants & 72.76 & 80.40 & 88.44 & 84.23 & 57.49 & 66.69 & 80.64 & 73.00 & 95.16 & 95.14 & 98.63 & 65.32 \\\\\\\\\\n\",\n \" Attractions & 90.50 & 97.87 & 92.33 & 95.02 & 75.54 & 91.34 & 81.37 & 86.07 & 98.15 & N/A & N/A &83.00 \\\\\\\\ \\\\midrule\\n\",\n \" \\\\multicolumn{10}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 80.27 & 91.31 & 86.91 & 89.05 & 57.76 & 74.51 & 71.99 & 73.23 & 89.25 & 24.04 & 80.63 & 57.01 \\\\\\\\\\n\",\n \" H-R & 82.02 & 91.03 & 89.23 & 90.12 & 68.44 & 77.95 & 84.86 & 81.26 & 83.67 & 29.12 & 87.58 & 64.42 \\\\\\\\\\n\",\n \" H-A & 62.30 & 72.67 & 81.35 & 76.77 & 59.22 & 68.73 & 81.05 & 74.39 & 71.41 & 27.87 & 82.80 & 65.70 \\\\\\\\\\n\",\n \" F-H-A & 77.19 & 87.50 & 86.76 & 87.13 & 59.63 & 74.16 & 75.27 & 74.71 & 81.15 & 22.65 & 83.45 & 52.76 \\\\\\\\\\n\",\n \" F-H-R & 71.53 & 86.05 & 80.91 & 83.40 & 54.39 & 71.99 & 68.99 & 70.45 & 82.47 & 46.32 & 84.40 & 53.88 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Results using Llama 3.1 8B Instruct after SFT.}\\n\",\n \"\\\\label{table:llama3.1-8b-sft}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure*}[!t]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{assets/pipeline.png}\n"," \\caption{Illustrative example from the $\\benchmarkname$ dataset. This example showcases a multi-domain scenario involving both flights and hotels, where the user is planning a trip and attempting to book relevant services. The dialogue is constructed by retrieving entities from a knowledge base, and tool calls are executed using a predefined toolbox, simulating realistic, tool-augmented agent behavior.}\n"," \\label{fig:architecture}\n","\\end{figure*}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lccccccc}\n"," \\toprule\n"," \\textbf{Dataset} & \\textbf{Deployed} & \\textbf{Human Annotated} & \\textbf{Execution Result} & \\textbf{Multi-turn Context} & \\textbf{Multi-Domain} \\\\\n"," & \\textbf{Tools} & \\textbf{Tool Planning} & \\textbf{Evaluation} & \\textbf{Planning} & \\textbf{Tool Planning}\\\\\n"," \\midrule\n"," APIBank~\\cite{li2023api} & \\cmark & \\cmark & \\cmark & \\cmark & & \\\\\n"," APIBench~\\cite{patil2024gorilla} & & & \\cmark & & \\\\\n"," GAIA~\\cite{mialon2023gaia} & & \\cmark & \\cmark & & \\\\\n"," GTA~\\cite{wang2024gta} & \\cmark & \\cmark & \\cmark & \\cmark & \\\\\n"," m\\&m's~\\cite{ma2024m} & \\cmark & \\cmark & \\cmark & \\cmark & \\\\\n"," ToolBench~\\cite{qin2023toolllm} & \\cmark & & \\cmark & & \\\\\n"," Toolformer~\\cite{schick2023toolformer} & \\cmark & \\cmark & \\cmark & & \\\\\n"," TravelPlanner~\\cite{xie2024travelplanner} & \\cmark & \\cmark & \\cmark & & \\cmark & \\\\ \n"," \\midrule\n"," $\\textbf{\\benchmarkname}$ & \\cmark & \\cmark & \\cmark & \\cmark & \\cmark \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Comparison of datasets for the LLM-based agent systems.}\n","\\end{table*}\n"],["\\begin{figure*}[!t]\n"," \\centering\n"," \\includegraphics[width=\\textwidth]{assets/data_generation.png}\n"," \\caption{$\\benchmarkname$ generates data by populating delexicalized entities with corresponding entries from the knowledge base.}\n"," \\label{fig:data_generation}\n","\\end{figure*}\n"],["\\begin{table*}[!t]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lcccc|cc|c|c}\n"," \\toprule \n"," & \\multicolumn{4}{c|}{\\textbf{Single-domain}} & \\multicolumn{2}{c|}{\\textbf{Multi-domain}}\n"," & \\textbf{Common} & \\textbf{Total} \\\\ \n"," & \\textbf{Flights} & \\textbf{Hotels} & \\textbf{Restaurants} & \\textbf{Attractions} & \\textbf{2 Domains} & \\textbf{3 Domains} & \\\\ \\midrule\n"," \\textbf{\\# Attributes} & 35 & 43 & 21 & 7 & N/A & N/A & N/A & 106 \\\\\n"," \\textbf{\\# Tools} & 2 & 2 & 2 & 2 & 1 & N/A & 5 & 14 \\\\ \n"," \\textbf{\\# Dialogues} & 1.5k & 1.5k & 1.5k & 1.5k & 4.5k & 3k & N/A & 13.5k \\\\ \n"," \\textbf{Avg. \\# turns} & 8.2 & 8.0 & 9.0 & 6.0 & 11.3 & 9.7 & N/A & N/A \\\\ \n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Dataset statistics detailing the number of attributes, tools, dialogues, and the average number of turns, categorized by each individual domain, multi-domain, and common categories. \"N/A\" indicates that the metric is not applicable in the given context.} \n","\\label{tab:baseline-results-one-epoch}\n","\\end{table*}\n"],["\\begin{figure}[!ht]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{assets/domain_adaptation.png}\n"," \\caption{\\textbf{Left:} Tool Call F1 performance and \\textbf{Right:} Parameter Matching F1 performance.}\n"," \\label{fig:enter-label}\n","\\end{figure}\n"],["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lcccc|cccc|c|cc|c}\n"," \\toprule\n"," \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec.} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache}} \\\\ \n"," & & & & & & & & & \\textbf{Rate} & & & \\textbf{Summary} \\\\\n"," & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n"," \\multicolumn{8}{l}{\\texttt{Single-Domain}} \\\\\n"," \\midrule\n"," Flights & 25.12 & 30.90 & 57.34 & 40.16 & 15.57 & 17.34 & 60.30 & 26.94 & 26.24 & 14.41 & 82.36 & 36.63 \\\\\n"," Hotels & 42.86 & 49.89 & 75.25 & 60.00 & 17.57 & 23.59 & 40.80 & 29.89 & 48.13 & 47.01 & 80.38 & 33.70 \\\\\n"," Restaurants & 40.40 & 52.97 & 63.00 & 57.55 & 31.47 & 36.07 & 71.12 & 47.87 & \\textbf{56.99} & 28.91 & 75.68 & 35.49 \\\\\n"," Attractions & 33.03 & 48.49 & 50.90 & 49.66 & 14.11 & 25.11 & 24.36 & 24.73 & 40.40 & N/A & N/A & 43.87 \\\\ \\midrule\n"," \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 33.09 & 40.89 & 63.44 & 49.73 & 16.11 & 19.28 & 49.48 & 27.75 & 38.43 & 26.54 & 82.00 & 21.85 \\\\\n"," H-R & 51.06 & 59.21 & 78.77 & 67.61 & 26.62 & 33.52 & 56.37 & 42.05 & 51.82 & 28.60 & 84.07 & 9.95 \\\\\n"," H-A & 38.75 & 45.46 & 72.39 & 55.85 & 16.11 & 20.02 & 45.12 & 27.74 & 48.88 & 26.03 & 81.77 & 32.75 \\\\\n"," F-H-A & 27.76 & 36.24 & 54.24 & 43.45 & 16.21 & 21.18 & 40.88 & 27.90 & 28.76 & 14.15 & 78.58 & 24.37 \\\\\n"," F-H-R & 29.04 & 34.65 & 64.19 & 45.00 & 18.53 & 21.77 & 55.44 & 31.26 & 36.79 & 33.28 & 82.84 & 27.47 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall results using Llama 3.1 8B Instruct with few-shot in-context learning.}\n","\\label{table:llama3.1-8b}\n","\\end{table*}\n"],["\\begin{figure}[!ht]\n"," \\centering\n"," \\includegraphics[width=0.9\\linewidth]{assets/flight_shot_learning.png}\n"," \\caption{Few-shot performance on Flight domain.}\n"," \\label{fig:few-shot}\n","\\end{figure}\n"],["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lcccc|cccc|c|cc|c}\n"," \\toprule\n"," \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n"," & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 83.51 & 89.98 & 92.08 & 91.02 & 58.02 & 66.38 & 82.18 & 73.44 & 85.26 & 39.19 & 86.44 & 62.07 \\\\\n"," Hotels & 78.18 & 84.87 & 90.84 & 87.75 & 60.40 & 67.29 & 85.53 & 75.32 & 72.13 & 48.30 & 80.91 & 71.35 \\\\\n"," Restaurants & 72.76 & 80.40 & 88.44 & 84.23 & 57.49 & 66.69 & 80.64 & 73.00 & 95.16 & 95.14 & 98.63 & 65.32 \\\\\n"," Attractions & 90.50 & 97.87 & 92.33 & 95.02 & 75.54 & 91.34 & 81.37 & 86.07 & 98.15 & N/A & N/A &83.00 \\\\ \\midrule\n"," \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 80.27 & 91.31 & 86.91 & 89.05 & 57.76 & 74.51 & 71.99 & 73.23 & 89.25 & 24.04 & 80.63 & 57.01 \\\\\n"," H-R & 82.02 & 91.03 & 89.23 & 90.12 & 68.44 & 77.95 & 84.86 & 81.26 & 83.67 & 29.12 & 87.58 & 64.42 \\\\\n"," H-A & 62.30 & 72.67 & 81.35 & 76.77 & 59.22 & 68.73 & 81.05 & 74.39 & 71.41 & 27.87 & 82.80 & 65.70 \\\\\n"," F-H-A & 77.19 & 87.50 & 86.76 & 87.13 & 59.63 & 74.16 & 75.27 & 74.71 & 81.15 & 22.65 & 83.45 & 52.76 \\\\\n"," F-H-R & 71.53 & 86.05 & 80.91 & 83.40 & 54.39 & 71.99 & 68.99 & 70.45 & 82.47 & 46.32 & 84.40 & 53.88 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Results using Llama 3.1 8B Instruct after SFT.}\n","\\label{table:llama3.1-8b-sft}\n","\\end{table*}\n"],["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lcccc|cccc|c|cc|c}\n"," \\toprule\n"," \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n"," & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 58.42 & 78.26 & 69.75 & 73.76 & 32.11 & 40.51 & 60.76 & 48.61 & 83.32 & 20.25 & 82.90 & 53.80 \\\\\n"," Hotels & 92.42 & 96.03 & 96.10 & 96.07 & 75.33 & 80.85 & 91.69 & 85.93 & 98.55 & 46.98 & 80.27 & 75.00 \\\\\n"," Restaurants & 94.23 & 96.63 & 97.43 & 97.03 & 85.51 & 93.62 & 90.80 & 92.19 & 99.54 & 37.90 & 79.95 & 90.78 \\\\\n"," Attractions & 79.14 & 92.16 & 84.86 & 88.36 & 71.17 & 87.04 & 79.60 & 83.16 & 63.70 & N/A & N/A & 78.59 \\\\ \\midrule\n"," \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 43.48 & 53.73 & 69.52 & 60.61 & 22.28 & 25.94 & 61.24 & 36.44 & 95.02 & 27.39 & 83.42 & 37.15 \\\\\n"," H-R & 60.50 & 70.91 & 80.46 & 78.29 & 50.94 & 60.08 & 76.99 & 67.50 & 99.60 & 22.97 & 84.11 & 38.43 \\\\\n"," H-A & 64.91 & 68.93 & 91.75 & 78.72 & 59.24 & 66.59 & 84.29 & 74.40 & 97.01 & 30.02 & 82.71 & 57.03 \\\\\n"," F-H-A & 60.46 & 70.77 & 80.59 & 75.36 & 44.27 & 51.19 & 76.58 & 61.37 & 94.81 & 19.16 & 82.27 & 44.29 \\\\\n"," F-H-R & 52.97 & 62.22 & 78.07 & 69.25 & 42.93 & 50.66 & 73.76 & 60.07 & 91.30 & 40.45 & 85.62 & 45.37 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Results using Llama 3.3 70B Instruct.}\n","\\label{table:llama3.3-70b}\n","\\end{table*}\n"],["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lcccc|cccc|c|cc|c}\n"," \\toprule\n"," \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n"," & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 77.59 & 87.87 & 86.90 & 87.38 & 49.53 & 58.04 & 77.15 & 66.25 & 57.20 & 29.65 & 83.12 & 57.46\n"," \\\\\n"," Hotels & 89.33 & 95.33 & 93.41 & 94.36 & 65.27 & 70.52 & 89.77 & 78.99 & 63.95 & 18.07 & 79.56 & 57.23\n"," \\\\\n"," Restaurants & 87.77 & 92.65 & 94.35 & 93.49 & 71.59 & 77.69 & 90.11 & 83.44 & 69.82 & 7.16 & 69.91 & 69.22\n"," \\\\\n"," Attractions & 65.76 & 80.16 & 78.54 & 79.34 & 44.92 & 53.04 & 74.59 & 62.00 & 72.57 & N/A & N/A & 63.87\n","\\\\ \\midrule\n"," \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 69.87 & 78.42 & 86.51 & 82.27 & 42.38 & 50.39 & 72.71 & 59.53 & 66.89 & 9.72 & 78.43 & 47.49\n"," \\\\\n"," H-R & 59.10 & 65.62 & 85.60 & 74.29 & 51.91 & 58.54 & 82.10 & 68.35 & 49.72 & 19.69 & 85.40 & 32.55\n"," \\\\\n"," H-A & 63.46 & 67.81 & 90.83 & 77.65 & 65.22 & 72.53 & 86.60 & 78.95 & 44.39 & 21.41 & 81.95 & 56.64\n"," \\\\\n"," F-H-A & 68.41 & 75.27 & 88.25 & 81.24 & 50.21 & 61.04 & 73.88 & 66.85 & 60.86 & 27.00 & 82.48 & 50.42\n"," \\\\\n"," F-H-R & 67.22 & 73.80 & 88.30 & 80.40 & 58.97 & 71.66 & 76.91 & 74.19 & 61.47 & 10.08 & 78.32 & 53.74\n"," \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Results using S1.1 32B.}\n","\\label{table:s1.1}\n","\\end{table*}\n"],["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lcccc|cccc|c|cc|c}\n"," \\toprule\n"," \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n"," & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 36.66 & 67.30 & 44.61 & 53.66 & 15.74 & 56.10 & 17.95 & 27.20 & 72.76 & 13.91 & 81.60 & 39.73\n"," \\\\\n"," Hotels & 83.96 & 91.74 & 90.82 & 91.28 & 53.22 & 63.09 & 77.30 & 69.47 & 93.05 & 46.95 & 80.47 & 46.52\n"," \\\\\n"," Restaurants & 64.13 & 83.60 & 73.36 & 78.14 & 47.10 & 61.89 & 66.34 & 64.04 & 93.49 & 28.27 & 69.74 & 50.53\n"," \\\\\n"," Attractions & 35.78 & 61.67 & 46.02 & 52.71 & 22.90 & 66.92 & 25.82 & 37.27 & 66.25 & N/A & N/A & 50.79\n","\\\\ \\midrule\n"," \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 57.79 & 88.12 & 62.67 & 73.25 & 29.91 & 59.20 & 37.68 & 46.05 & 83.37 & 27.96 & 83.02 & 32.53\n"," \\\\\n"," H-R & 54.07 & 70.71 & 69.67 & 70.18 & 35.42 & 50.91 & 53.79 & 52.31 & 96.04 & 23.19 & 84.83 & 21.72\n"," \\\\\n"," H-A & 65.81 & 78.69 & 80.08 & 79.38 & 48.58 & 61.78 & 69.45 & 65.39 & 96.04 & 27.92 & 82.97 & 53.52\n"," \\\\\n"," F-H-A & 37.83 & 62.18 & 49.14 & 54.90 & 32.73 & 64.59 & 39.89 & 49.32 & 84.49 & 15.42 & 81.00 & 32.33\n"," \\\\\n"," F-H-R & 46.79 & 72.75 & 56.74 & 63.75 & 33.99 & 59.56 & 44.18 & 50.73 & 91.86 & 36.30 & 84.63 & 37.65\n"," \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Results using Phi-4-reasoning-plus.}\n","\\label{table:phi-4-reasoning-plus}\n","\\end{table*}\n"],["\\begin{figure}[!ht]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{assets/all_model_f1_scores.png}\n"," \\caption{\\textbf{Above:} Tool Call F1 performance and \\textbf{Below:} Parameter Matching F1 performance.}\n"," \\label{fig:compare-models}\n","\\end{figure}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lccccccc}\n"," \\toprule\n"," \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n"," \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 8,200 & 737 & 830 & 0 & 468 \\\\\n"," Hotels & 8,000 & 417 & 218 & 0 & 820 \\\\\n"," Restaurants & 7,900 & 513 & 14 & 1 & 183 \\\\\n"," Attractions & 5,975 & 507 & 1 & 0 & 243 \\\\\n"," \\midrule\n"," \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 11,700 & 834 & 1087 & 0 & 408 \\\\\n"," H-R & 10,950 & 1532 & 18 & 1 & 522 \\\\\n"," H-A & 11,000 & 1024 & 167 & 0 & 308 \\\\\n"," F-H-A & 9,775 & 1163 & 990 & 0 & 575 \\\\\n"," F-H-R & 8,575 & 812 & 761 & 3 & 495 \\\\\n"," \\midrule\n"," \\texttt{Total} & - & 7539 & 4086 & 5 & 4022\\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Error Analysis Results using Llama 3.1 8B Instruct.}\n","\\end{table*}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lccccccc}\n"," \\toprule\n"," \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n"," \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 8,200 & 408 & 176 & 42 & 26 \\\\\n"," Hotels & 8,000 & 1,099 & 16 & 0 & 0 \\\\\n"," Restaurants & 7,900 & 209 & 5 & 0 & 2 \\\\\n"," Attractions & 5,975 & 18 & 9 & 0 & 8 \\\\\n"," \\midrule\n"," \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 11,700 & 454 & 149 & 0 & 22 \\\\\n"," H-R & 10,950 & 692 & 185 & 0 & 17 \\\\\n"," H-A & 11,000 & 1248 & 315 & 0 & 1 \\\\\n"," F-H-A & 9,775 & 789 & 124 & 9 & 27 \\\\\n"," F-H-R & 8,575 & 541 & 109 & 0 & 101 \\\\\n"," \\midrule\n"," \\texttt{Total} & - & 5458 & 1088 & 51 & 204 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Error Analysis Results using Llama 3.1 8B SFT Instruct.}\n","\\end{table*}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lccccccc}\n"," \\toprule\n"," \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n"," \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 8,200 & 518 & 2 & 30 & 0 \\\\\n"," Hotels & 8,000 & 41 & 0 & 0 & 0 \\\\\n"," Restaurants & 7,900 & 29 & 0 & 0 & 0 \\\\\n"," Attractions & 5,975 & 4 & 2 & 0 & 1 \\\\\n"," \\midrule\n"," \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 11,700 & 158 & 28 & 0 & 0\n"," \\\\\n"," H-R & 10,950 & 14 & 2 & 0 & 1\n"," \\\\\n"," H-A & 11,000 & 48 & 33 & 0 & 48\n"," \\\\\n"," F-H-A & 9,775 & 148 & 6 & 7 & 3\n"," \\\\\n"," F-H-R & 8,575 & 330 & 5 & 1 & 7\n"," \\\\\n"," \\midrule\n"," \\texttt{Total} & - & 1290 & 78 & 38 & 60 \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Error Analysis Results using Llama 3.3 70B Instruct.}\n","\\end{table*}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lccccccc}\n"," \\toprule\n"," \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n"," \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 8,200 & 559 & 16 & 3 & 40\n"," \\\\\n"," Hotels & 8,000 & 92 & 1 & 39 & 27\n"," \\\\\n"," Restaurants & 7,900 & 20 & 7 & 0 & 28\n"," \\\\\n"," Attractions & 5,975 & 11 & 27 & 0 & 76\n"," \\\\\n"," \\midrule\n"," \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 11,700 & 24 & 34 & 114 & 63\n"," \\\\\n"," H-R & 10,950 & 54 & 895 & 102 & 34\n"," \\\\\n"," H-A & 11,000 & 3 & 1071 & 43 & 23\n"," \\\\\n"," F-H-A & 9,775 & 89 & 579 & 25 & 49\n"," \\\\\n"," F-H-R & 8,575 & 85 & 241 & 7 & 28\n"," \\\\\n"," \\midrule\n"," \\texttt{Total} & - & 937 & 2871 & 333 & 368\n"," \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Error Analysis Results using S1.1.}\n","\\end{table*}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lccccccc}\n"," \\toprule\n"," \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n"," \\midrule\n"," \\texttt{Single-Domain} \\\\\n"," \\midrule\n"," Flights & 8,200 & 103 & 7 & 1 & 1\n"," \\\\\n"," Hotels & 8,000 & 277 & 0 & 0 & 1\n"," \\\\\n"," Restaurants & 7,900 & 259 & 0 & 0 & 19\n"," \\\\\n"," Attractions & 5,975 & 0 & 0 & 0 & 0\n"," \\\\\n"," \\midrule\n"," \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n"," F-H & 11,700 & 212 & 2 & 0 & 7\n"," \\\\\n"," H-R & 10,950 & 212 & 0 & 0 & 1\n"," \\\\\n"," H-A & 11,000 & 162 & 0 & 0 & 6\n"," \\\\\n"," F-H-A & 9,775 & 120 & 3 & 0 & 5\n"," \\\\\n"," F-H-R & 8,575 & 153 & 4 & 0 & 32\n"," \\\\\n"," \\midrule\n"," \\texttt{Total} & - & 1498 & 16 & 1 & 72\\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Overall Error Analysis Results using Phi-4-reasoning-plus.}\n","\\end{table*}\n"],["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lllll}\n"," \\toprule \n"," \\textbf{Domain} & \\textbf{Attributes} \\\\ \\midrule\n"," Flight & airline, flight\\_id, start\\_airport, start\\_airport\\_latitude, start\\_airport\\_longitude, \\\\\n"," & start\\_airport\\_code, end\\_airport, end\\_airport\\_latitude, end\\_airport\\_longitude, \\\\\n"," & end\\_airport\\_code, economy\\_class\\_option\\_present, business\\_class\\_option\\_present, \\\\\n"," & first\\_class\\_option\\_present, distance\\_miles, duration\\_minutes, \\\\\n"," & departure\\_time, arrival\\_time, number\\_of\\_layovers, first\\_layover\\_airport, \\\\\n"," Hotel & hotel\\_name, city, state, neighborhood, latitude, longitude, rating, \\\\ & stars, max\\_occupancy, gym\\_present, pool\\_present, price\\_per\\_night, num\\_rooms\\_available, \\\\ & breakfast\\_included, smoking\\_allowed, air\\_conditioning\\_present, \\\\\n"," & heating\\_present, free\\_wifi\\_included, airport\\_shuttle\\_present, \\\\ &\n"," is\\_pet\\_friendly, has\\_spa\\_services, has\\_room\\_service, \\\\ & has\\_beach\\_access, has\\_fitness\\_class, has\\_laundry\\_service, \\\\ & has\\_valet\\_parking, has\\_balcony, has\\_rooftop\\_bar, has\\_inroom\\_Kitchen, \\\\ & has\\_kids\\_club, has\\_meeting\\_rooms, has\\_electric\\_vehicle\\_charging, \\\\ & has\\_hot\\_tub, has\\_sauna, has\\_free\\_parking, is\\_wheelchair\\_accessible, \\\\ & has\\_skiing\\_lodging, has\\_ocean\\_view\\_rooms\\_present, has\\_city\\_view\\_rooms\\_present, \\\\ & start\\_date\\_available, end\\_date\\_available \\\\\n"," Attraction & city, state, name, type, latitude, longitude, neighborhood \\\\\n"," Restaurant & restaurant\\_name, city, state, neighborhood, \\\\\n"," & latitude, longitude, rating, price, price\\_per\\_person, has\\_nut\\_allergy\\_options, has\\_dairy\\_allergy\\_options, has\\_shell\\_fish\\_allergy\\_options, \\\\ & has\\_tomato\\_allergy\\_options, has\\_nightshade\\_allergy\\_options, \\\\ & has\\_gluten\\_free\\_options, has\\_vegetarian\\_options, has\\_vegan\\_options, \\\\ & has\\_kosher\\_options, has\\_halal\\_options, cuisine \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Domains and Attributes.} \n","\\label{tab:domains-and-attributes}\n","\\end{table*}\n"],["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{ll}\n"," \\toprule \n"," \\textbf{Domain} & \\textbf{Tools}\n"," \\\\\n"," \\textbf{Flights} & search\\_flights, filter\\_flights \\\\\n"," \\textbf{Hotels} & search\\_hotels, filter\\_hotels \\\\\n"," \\textbf{Restaurants} & search\\_restaurants, filter\\_restaurants \\\\\n"," \\textbf{Attractions} & search\\_attractions, filter\\_attractions \\\\\n"," \\textbf{Multi-domain} & search\\_nearest \\\\\n"," \\textbf{Common} & save\\_to\\_cache, get\\_results\\_from\\_cache, sort\\_results, seek\\_information, adjust\\_date \\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{List of Tools.} \n","\\label{tab:defined-tools-domain}\n","\\end{table*}\n"],["\\begin{table*}[!ht]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lll}\n"," \\toprule \n"," \\textbf{Attribute} & \\textbf{Type} & \\textbf{Description} \\\\ \\midrule\n"," airline & string & Airline of the flight, \\\\\n"," flight\\_classes & string & Classes for the flight (economy, business, first) \\\\\n"," num\\_layovers & integer & Number of layovers for the flight, between 0 and 2 \\\\\n"," layover\\_duration\\_amount & integer & Duration of a layover flight. Between 1 and 6 hours \\\\\n"," airports & list & Airport information for each flight including the city, state, airport code and airport name. \\\\\n"," \n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Flight Ontology Attributes.} \n","\\label{tab:flight-ontology-attributes}\n","\\end{table*}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lll}\n"," \\toprule \n"," \\textbf{Attribute} & \\textbf{Type} & \\textbf{Description} \\\\ \\midrule\n"," city & string & City that the hotel is in \\\\\n"," state & string & State that the hotel is in \\\\\n"," neighborhood & string & Neighborhood within the city that the hotel is in\\\\\n"," stars & integer & Star rating of the hotel between 1 and 5 \\\\\n"," rating & float & Customer rating of the hotel between 1.0 and 5.0, incremented by 0.1 \\\\\n"," price\\_per\\_night & integer & Price per night of the hotel ranging between 20 to 2000 dollars \\\\\n"," max\\_occupancy & integer & Maximum occupancy per room ranging between 1 and 7 \\\\\n"," gym\\_present & boolean & Whether or not the hotel has a gym \\\\\n"," pool\\_present & boolean & Whether or not the hotel has a pool \\\\\n"," breakfast\\_included & boolean & Whether or not the hotel has breakfast included \\\\\n"," smoking\\_allowed & boolean & Whether or not the hotel allows smoking \\\\\n"," air\\_conditioning\\_present & boolean & Whether or not the hotel has air conditioning \\\\\n"," heating\\_present & boolean & Whether or not the hotel has heating \\\\\n"," free\\_wifi\\_included & boolean & Whether or not the hotel includes free WiFi \\\\\n"," airport\\_shuttle\\_present & boolean & Whether or not the hotel has an airport shuffle \\\\\n"," is\\_pet\\_friendly & boolean & Whether or not the hotel allows pets \\\\\n"," has\\_spa\\_services & boolean & Whether or not the hotel has spa services \\\\\n"," has\\_room\\_service & boolean & Whether or not the hotel has room service \\\\\n"," has\\_beach\\_access & boolean & Whether or not the hotel has access to a beach \\\\\n"," has\\_business\\_center & boolean & Whether or not the hotel has a business center \\\\\n"," has\\_fitness\\_classes & boolean & Whether or not the hotel has fitness classes \\\\\n"," has\\_laundry\\_service & boolean & Whether or not the hotel has laundry services \\\\\n"," has\\_valet\\_parking & boolean & Whether or not the hotel has valet parking \\\\\n"," has\\_balcony & boolean & Whether or not the hotel has a balcony \\\\\n"," has\\_rooftop\\_bar & boolean & Whether or not the hotel has a rooftop bar \\\\\n"," has\\_inroom\\_kitchen & boolean & Whether or not the hotel has an inroom kitchen \\\\\n"," has\\_kids\\_club & boolean & Whether or not the hotel has a kids club \\\\\n"," has\\_meeting\\_rooms & boolean & Whether or not the hotel has meeting rooms \\\\\n"," has\\_electric\\_vehicle\\_charging & boolean & Whether or not the hotel has electric vehicle charging \\\\\n"," has\\_hot\\_tub & boolean & Whether or not the hotel has a hot tub \\\\\n"," has\\_sauna & boolean & Whether or not the hotel has a sauna \\\\ \n"," has\\_free\\_parking & boolean & Whether or not the hotel has free parking\\\\ \n"," is\\_wheelchair\\_accessible& boolean & Whether or not the hotel is wheelchair accessible \\\\ \n"," has\\_skiing\\_lodging & boolean & Whether or not the hotel has skiing and lodging \\\\ \n"," ocean\\_view\\_rooms\\_present & boolean & Whether or not the hotel has rooms with a view of the ocean \\\\\n"," city\\_view\\_rooms\\_present & boolean & Whether or not the hotel has rooms with views of the city\\\\\n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Hotel Ontology Attributes.} \n","\\label{tab:hotel-ontology-attributes}\n","\\end{table*}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n"," \\begin{tabular}{lll}\n"," \\toprule \n"," \\textbf{Attribute} & \\textbf{Type} & \\textbf{Description} \\\\ \\midrule\n"," city & string & City that the restaurant is in \\\\\n"," state & string & State that the restaurant is in \\\\\n"," neighborhood & string & Neighborhood within the city that the restaurant is in\\\\\n"," rating & float & Customer rating of the restaurant between 1.0 and 5.0, incremented by 0.1 \\\\\n"," price\\_per\\_person & integer & Average price per person at the restaurant \\\\\n"," cuisine & string & Cuisine of the restaurant \\\\\n"," has\\_nut\\_allergy\\_options & boolean & Whether or not the restaurant has any options for individuals with an allergy to nuts \\\\\n"," has\\_dairy\\_allergy\\_options & boolean & Whether or not restaurant has any options for individuals with an allergy to dairy products \\\\\n"," has\\_shell\\_fish\\_allergy\\_options & boolean & Whether or not the restaurant has any options for individuals with an allergy to shell fish \\\\\n"," has\\_tomato\\_allergy\\_options & boolean & Whether or not the restaurant has options for individuals with an allergy to tomatoes \\\\\n"," has\\_nightshade\\_allergy\\_options & boolean & Whether or not the restaurant has options for individuals with an allergy to nightshades \\\\\n"," has\\_gluten\\_free\\_options & boolean & Whether or not the restaurant has gluten free options \\\\\n"," has\\_vegetarian\\_options & boolean & Whether or not the restaurant has vegetarian options \\\\\n"," has\\_vegan\\_options & boolean & Whether or not the restaurant has vegan options \\\\\n"," has\\_halal\\_options & boolean & Whether or not the restaurant has halal options \\\\\n"," has\\_kosher\\_options & boolean & Whether or not the hotel has kosher options \\\\ \n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Restaurant Ontology Attributes.} \n","\\label{tab:restaurant-ontology-attributes}\n","\\end{table*}\n"],["\\begin{table*}[!htbp]\n","\\centering\n","\\resizebox{0.8\\textwidth}{!}{\n"," \\begin{tabular}{lll}\n"," \\toprule \n"," \\textbf{Attribute} & \\textbf{Type} & \\textbf{Description} \\\\ \\midrule\n"," city & string & City that the attraction is in \\\\\n"," state & string & State that the attraction is in \\\\\n"," neighborhood & string & Neighborhood within the city that the attraction is in\\\\\n"," type & string & Type of the attraction \\\\ \n"," \\bottomrule\n"," \\end{tabular}\n","}\n","\\caption{Attraction Ontology Attributes.} \n","\\label{tab:attraction-ontology-attributes}\n","\\end{table*}\n"],["\\begin{table}[!ht]\n","\\centering\n","\\small\n","\\renewcommand{\\arraystretch}{1.3}\n","\\begin{tabular}{|l|p{5.5cm}|p{7.5cm}|}\n","\\hline\n","\\textbf{Domain} & \\textbf{Placeholders Used} & \\textbf{Required Scenarios} \\\\\n","\\hline\n","\\textbf{Flight} & \n","\\texttt{<CITY\\_x>}, \\texttt{<CLASS\\_x>}, \\texttt{<DEPARTURE\\_DATE\\_x>}, \\texttt{<DEPARTURE\\_TIME\\_x>}, \\texttt{<ARRIVAL\\_DATE\\_x>}, \\texttt{<ARRIVAL\\_TIME\\_x>}, \\texttt{<AIRLINE\\_x>}, \\texttt{<PRICE\\_x>}, \\texttt{<AIRPORT\\_x>}, \\texttt{<NUM\\_TRAVELERS\\_x>} & \n","Round trip (with 2 departure dates), one-way, multi-city, strict arrival time, flexible dates, large group bookings, solo/business/family travel, weekend getaways, budget constraints, special occasions (e.g., birthdays) \\\\\n","\\hline\n","\n","\\textbf{Hotel} & \n","\\texttt{<CHECK\\_IN\\_DATE\\_x>}, \\texttt{<CHECK\\_OUT\\_DATE\\_x>}, \\texttt{<CITY\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>}, \\texttt{<STAR\\_x>}, \\texttt{<RATING\\_x>}, \\texttt{<PRICE\\_x>}, \\texttt{<NUM\\_ROOMS\\_x>}, \\texttt{<NUM\\_TRAVELERS\\_x>} & \n","Multi-city trips, multiple hotels in one city, specific neighborhoods, special occasions, last-minute reservations, business vs. leisure, extended stays, view/accessibility/pet-friendly requests, family and group accommodations \\\\\n","\\hline\n","\n","\\textbf{Attraction} & \n","\\texttt{<ATTRACTION\\_TYPE\\_x>}, \\texttt{<CITY\\_x>}, \\texttt{<STATE\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>} & \n","Multi-type attraction queries, across cities/states, neighborhood-specific exploration, curiosity about state-level offerings. Assistant must ask open-ended questions and only mention placeholders if user provides them. \\\\\n","\\hline\n","\n","\\textbf{Restaurant} & \n","\\texttt{<RESTAURANT\\_RATING\\_x>}, \\texttt{<RESTAURANT\\_PRICE\\_x>}, \\texttt{<RESTAURANT\\_CUISINE\\_x>}, \\texttt{<CITY\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>} & \n","Multi-city dining, cuisine preferences, dietary restrictions (e.g., nut-free, vegan, halal), budget vs. premium, special occasion dining, rating-focused or casual vs. upscale preferences \\\\\n","\\hline\n","\\end{tabular}\n","\\vspace{1mm}\n","\\caption{Domain-specific customization for template generation. Each domain builds on the shared prompt instructions with unique placeholders and required conversation scenarios.}\n","\\label{tab:domain-customization}\n","\\end{table}\n"],["\\begin{table}[!ht]\n","\\centering\n","\\small\n","\\renewcommand{\\arraystretch}{1.2}\n","\\begin{tabularx}{\\textwidth}{|l|X|X|}\n","\\hline\n","\\textbf{Domains} & \\textbf{Placeholders Used} & \\textbf{Required Scenarios} \\\\\n","\\hline\n","\n","\\textbf{Flight + Hotel} & \n","\\texttt{<CITY\\_x>}, \\texttt{<CLASS\\_x>}, \\texttt{<DEPARTURE\\_DATE\\_x>}, \\texttt{<CHECK\\_IN\\_DATE\\_x>}, \\texttt{<CHECK\\_OUT\\_DATE\\_x>}, \\texttt{<NUM\\_TRAVELERS\\_x>} & \n","Trip planning involving both air travel and accommodation. Includes round-trip and one-way flights, hotel stays across one or more cities, budget and luxury travelers, group vs. solo travel, flexible dates, specific preferences like nonstop flights or hotels with amenities (e.g., pool, gym, pet-friendly). \\\\\n","\\hline\n","\n","\\textbf{Flight + Hotel + Attraction} & \n","All flight, hotel, and attraction placeholders (e.g., \\texttt{<CITY\\_x>}, \\texttt{<CHECK\\_IN\\_DATE\\_x>}, \\texttt{<ATTRACTION\\_TYPE\\_x>}) & \n","User planning a full trip involving flights, hotel stays, and sightseeing. Must include: round-trip and one-way flights, multi-city stays, hotels near attractions, flexible schedules, user-provided attraction types or specific attraction names (only when linking to hotel proximity), and special constraints (e.g., group travel, business trips, anniversaries). Assistant must never use placeholder names before user introduces them. Includes amenity discussions and attraction-type grammar handling (e.g., cultural vs. \\texttt{<ATTRACTION\\_TYPE\\_1>} attraction). \\\\\n","\\hline\n","\n","\\textbf{Flight + Hotel + Restaurant} & \n","All flight, hotel, and restaurant placeholders (e.g., \\texttt{<RESTAURANT\\_CUISINE\\_x>}, \\texttt{<RESTAURANT\\_PRICE\\_x>}) & \n","End-to-end trip planning including flights, accommodation, and dining. Required scenarios include: dietary restrictions, cuisine-first or city-first planning, restaurant proximity to hotel, multiple hotels or restaurants in one city, round-trip and one-way flights, and amenities like pet-friendly or spa. Must feature diverse language, nonlinear flows, and varied user personas. Includes explicit handling of dietary needs (e.g., halal, nut-free, vegetarian), and placeholder logic as per prompt. \\\\\n","\\hline\n","\n","\\textbf{Hotel + Attraction} & \n","\\texttt{<CITY\\_x>}, \\texttt{<CHECK\\_IN\\_DATE\\_x>}, \\texttt{<ATTRACTION\\_TYPE\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>} & \n","User looking for accommodations and nearby attractions. Includes: specific neighborhoods, family-friendly vs. solo travel, themed vacations, extended stays, proximity to cultural or outdoor attractions, and cases where attraction type drives hotel location. \\\\\n","\\hline\n","\n","\\textbf{Hotel + Restaurant} & \n","\\texttt{<RESTAURANT\\_CUISINE\\_x>}, \\texttt{<HOTEL\\_PRICE\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>} & \n","Combines hotel booking with dining preferences. Includes cuisine-specific searches, budget dining vs. fine dining, dietary needs (gluten-free, halal), special events (anniversaries), restaurant proximity to hotel, and group size considerations. Templates vary in planning flow—some start with hotel, others with restaurants. \\\\\n","\\hline\n","\n","\\end{tabularx}\n","\\vspace{1mm}\n","\\caption{Multi-domain combinations and scenario requirements. Each configuration builds on the unified instructions with additional placeholder logic and domain-specific complexity.}\n","\\label{tab:multi-domain-customization}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{assets/pipeline.png}\\n\",\n \" \\\\caption{Illustrative example from the $\\\\benchmarkname$ dataset. This example showcases a multi-domain scenario involving both flights and hotels, where the user is planning a trip and attempting to book relevant services. The dialogue is constructed by retrieving entities from a knowledge base, and tool calls are executed using a predefined toolbox, simulating realistic, tool-augmented agent behavior.}\\n\",\n \" \\\\label{fig:architecture}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lccccccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Dataset} & \\\\textbf{Deployed} & \\\\textbf{Human Annotated} & \\\\textbf{Execution Result} & \\\\textbf{Multi-turn Context} & \\\\textbf{Multi-Domain} \\\\\\\\\\n\",\n \" & \\\\textbf{Tools} & \\\\textbf{Tool Planning} & \\\\textbf{Evaluation} & \\\\textbf{Planning} & \\\\textbf{Tool Planning}\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" APIBank~\\\\cite{li2023api} & \\\\cmark & \\\\cmark & \\\\cmark & \\\\cmark & & \\\\\\\\\\n\",\n \" APIBench~\\\\cite{patil2024gorilla} & & & \\\\cmark & & \\\\\\\\\\n\",\n \" GAIA~\\\\cite{mialon2023gaia} & & \\\\cmark & \\\\cmark & & \\\\\\\\\\n\",\n \" GTA~\\\\cite{wang2024gta} & \\\\cmark & \\\\cmark & \\\\cmark & \\\\cmark & \\\\\\\\\\n\",\n \" m\\\\&m's~\\\\cite{ma2024m} & \\\\cmark & \\\\cmark & \\\\cmark & \\\\cmark & \\\\\\\\\\n\",\n \" ToolBench~\\\\cite{qin2023toolllm} & \\\\cmark & & \\\\cmark & & \\\\\\\\\\n\",\n \" Toolformer~\\\\cite{schick2023toolformer} & \\\\cmark & \\\\cmark & \\\\cmark & & \\\\\\\\\\n\",\n \" TravelPlanner~\\\\cite{xie2024travelplanner} & \\\\cmark & \\\\cmark & \\\\cmark & & \\\\cmark & \\\\\\\\ \\n\",\n \" \\\\midrule\\n\",\n \" $\\\\textbf{\\\\benchmarkname}$ & \\\\cmark & \\\\cmark & \\\\cmark & \\\\cmark & \\\\cmark \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Comparison of datasets for the LLM-based agent systems.}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure*}[!t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\textwidth]{assets/data_generation.png}\\n\",\n \" \\\\caption{$\\\\benchmarkname$ generates data by populating delexicalized entities with corresponding entries from the knowledge base.}\\n\",\n \" \\\\label{fig:data_generation}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lcccc|cc|c|c}\\n\",\n \" \\\\toprule \\n\",\n \" & \\\\multicolumn{4}{c|}{\\\\textbf{Single-domain}} & \\\\multicolumn{2}{c|}{\\\\textbf{Multi-domain}}\\n\",\n \" & \\\\textbf{Common} & \\\\textbf{Total} \\\\\\\\ \\n\",\n \" & \\\\textbf{Flights} & \\\\textbf{Hotels} & \\\\textbf{Restaurants} & \\\\textbf{Attractions} & \\\\textbf{2 Domains} & \\\\textbf{3 Domains} & \\\\\\\\ \\\\midrule\\n\",\n \" \\\\textbf{\\\\# Attributes} & 35 & 43 & 21 & 7 & N/A & N/A & N/A & 106 \\\\\\\\\\n\",\n \" \\\\textbf{\\\\# Tools} & 2 & 2 & 2 & 2 & 1 & N/A & 5 & 14 \\\\\\\\ \\n\",\n \" \\\\textbf{\\\\# Dialogues} & 1.5k & 1.5k & 1.5k & 1.5k & 4.5k & 3k & N/A & 13.5k \\\\\\\\ \\n\",\n \" \\\\textbf{Avg. \\\\# turns} & 8.2 & 8.0 & 9.0 & 6.0 & 11.3 & 9.7 & N/A & N/A \\\\\\\\ \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Dataset statistics detailing the number of attributes, tools, dialogues, and the average number of turns, categorized by each individual domain, multi-domain, and common categories. \\\"N/A\\\" indicates that the metric is not applicable in the given context.} \\n\",\n \"\\\\label{tab:baseline-results-one-epoch}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[!ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{assets/domain_adaptation.png}\\n\",\n \" \\\\caption{\\\\textbf{Left:} Tool Call F1 performance and \\\\textbf{Right:} Parameter Matching F1 performance.}\\n\",\n \" \\\\label{fig:enter-label}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lcccc|cccc|c|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\multicolumn{4}{c}{\\\\textbf{Tool Call}} & \\\\multicolumn{4}{|c|}{\\\\textbf{Parameter Matching}} & \\\\textbf{Code Exec.} & \\\\multicolumn{2}{|c|}{\\\\textbf{Information Seeking}} & \\\\multicolumn{1}{c}{\\\\textbf{Cache}} \\\\\\\\ \\n\",\n \" & & & & & & & & & \\\\textbf{Rate} & & & \\\\textbf{Summary} \\\\\\\\\\n\",\n \" & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\\\\\ \\\\midrule\\n\",\n \" \\\\multicolumn{8}{l}{\\\\texttt{Single-Domain}} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 25.12 & 30.90 & 57.34 & 40.16 & 15.57 & 17.34 & 60.30 & 26.94 & 26.24 & 14.41 & 82.36 & 36.63 \\\\\\\\\\n\",\n \" Hotels & 42.86 & 49.89 & 75.25 & 60.00 & 17.57 & 23.59 & 40.80 & 29.89 & 48.13 & 47.01 & 80.38 & 33.70 \\\\\\\\\\n\",\n \" Restaurants & 40.40 & 52.97 & 63.00 & 57.55 & 31.47 & 36.07 & 71.12 & 47.87 & \\\\textbf{56.99} & 28.91 & 75.68 & 35.49 \\\\\\\\\\n\",\n \" Attractions & 33.03 & 48.49 & 50.90 & 49.66 & 14.11 & 25.11 & 24.36 & 24.73 & 40.40 & N/A & N/A & 43.87 \\\\\\\\ \\\\midrule\\n\",\n \" \\\\multicolumn{10}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 33.09 & 40.89 & 63.44 & 49.73 & 16.11 & 19.28 & 49.48 & 27.75 & 38.43 & 26.54 & 82.00 & 21.85 \\\\\\\\\\n\",\n \" H-R & 51.06 & 59.21 & 78.77 & 67.61 & 26.62 & 33.52 & 56.37 & 42.05 & 51.82 & 28.60 & 84.07 & 9.95 \\\\\\\\\\n\",\n \" H-A & 38.75 & 45.46 & 72.39 & 55.85 & 16.11 & 20.02 & 45.12 & 27.74 & 48.88 & 26.03 & 81.77 & 32.75 \\\\\\\\\\n\",\n \" F-H-A & 27.76 & 36.24 & 54.24 & 43.45 & 16.21 & 21.18 & 40.88 & 27.90 & 28.76 & 14.15 & 78.58 & 24.37 \\\\\\\\\\n\",\n \" F-H-R & 29.04 & 34.65 & 64.19 & 45.00 & 18.53 & 21.77 & 55.44 & 31.26 & 36.79 & 33.28 & 82.84 & 27.47 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall results using Llama 3.1 8B Instruct with few-shot in-context learning.}\\n\",\n \"\\\\label{table:llama3.1-8b}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[!ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.9\\\\linewidth]{assets/flight_shot_learning.png}\\n\",\n \" \\\\caption{Few-shot performance on Flight domain.}\\n\",\n \" \\\\label{fig:few-shot}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lcccc|cccc|c|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\multicolumn{4}{c}{\\\\textbf{Tool Call}} & \\\\multicolumn{4}{|c|}{\\\\textbf{Parameter Matching}} & \\\\textbf{Code Exec. Rate} & \\\\multicolumn{2}{|c|}{\\\\textbf{Information Seeking}} & \\\\multicolumn{1}{c}{\\\\textbf{Cache Summary}} \\\\\\\\ \\n\",\n \" & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\\\\\ \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 83.51 & 89.98 & 92.08 & 91.02 & 58.02 & 66.38 & 82.18 & 73.44 & 85.26 & 39.19 & 86.44 & 62.07 \\\\\\\\\\n\",\n \" Hotels & 78.18 & 84.87 & 90.84 & 87.75 & 60.40 & 67.29 & 85.53 & 75.32 & 72.13 & 48.30 & 80.91 & 71.35 \\\\\\\\\\n\",\n \" Restaurants & 72.76 & 80.40 & 88.44 & 84.23 & 57.49 & 66.69 & 80.64 & 73.00 & 95.16 & 95.14 & 98.63 & 65.32 \\\\\\\\\\n\",\n \" Attractions & 90.50 & 97.87 & 92.33 & 95.02 & 75.54 & 91.34 & 81.37 & 86.07 & 98.15 & N/A & N/A &83.00 \\\\\\\\ \\\\midrule\\n\",\n \" \\\\multicolumn{10}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 80.27 & 91.31 & 86.91 & 89.05 & 57.76 & 74.51 & 71.99 & 73.23 & 89.25 & 24.04 & 80.63 & 57.01 \\\\\\\\\\n\",\n \" H-R & 82.02 & 91.03 & 89.23 & 90.12 & 68.44 & 77.95 & 84.86 & 81.26 & 83.67 & 29.12 & 87.58 & 64.42 \\\\\\\\\\n\",\n \" H-A & 62.30 & 72.67 & 81.35 & 76.77 & 59.22 & 68.73 & 81.05 & 74.39 & 71.41 & 27.87 & 82.80 & 65.70 \\\\\\\\\\n\",\n \" F-H-A & 77.19 & 87.50 & 86.76 & 87.13 & 59.63 & 74.16 & 75.27 & 74.71 & 81.15 & 22.65 & 83.45 & 52.76 \\\\\\\\\\n\",\n \" F-H-R & 71.53 & 86.05 & 80.91 & 83.40 & 54.39 & 71.99 & 68.99 & 70.45 & 82.47 & 46.32 & 84.40 & 53.88 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Results using Llama 3.1 8B Instruct after SFT.}\\n\",\n \"\\\\label{table:llama3.1-8b-sft}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lcccc|cccc|c|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\multicolumn{4}{c}{\\\\textbf{Tool Call}} & \\\\multicolumn{4}{|c|}{\\\\textbf{Parameter Matching}} & \\\\textbf{Code Exec. Rate} & \\\\multicolumn{2}{|c|}{\\\\textbf{Information Seeking}} & \\\\multicolumn{1}{c}{\\\\textbf{Cache Summary}} \\\\\\\\ \\n\",\n \" & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\\\\\ \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 58.42 & 78.26 & 69.75 & 73.76 & 32.11 & 40.51 & 60.76 & 48.61 & 83.32 & 20.25 & 82.90 & 53.80 \\\\\\\\\\n\",\n \" Hotels & 92.42 & 96.03 & 96.10 & 96.07 & 75.33 & 80.85 & 91.69 & 85.93 & 98.55 & 46.98 & 80.27 & 75.00 \\\\\\\\\\n\",\n \" Restaurants & 94.23 & 96.63 & 97.43 & 97.03 & 85.51 & 93.62 & 90.80 & 92.19 & 99.54 & 37.90 & 79.95 & 90.78 \\\\\\\\\\n\",\n \" Attractions & 79.14 & 92.16 & 84.86 & 88.36 & 71.17 & 87.04 & 79.60 & 83.16 & 63.70 & N/A & N/A & 78.59 \\\\\\\\ \\\\midrule\\n\",\n \" \\\\multicolumn{10}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 43.48 & 53.73 & 69.52 & 60.61 & 22.28 & 25.94 & 61.24 & 36.44 & 95.02 & 27.39 & 83.42 & 37.15 \\\\\\\\\\n\",\n \" H-R & 60.50 & 70.91 & 80.46 & 78.29 & 50.94 & 60.08 & 76.99 & 67.50 & 99.60 & 22.97 & 84.11 & 38.43 \\\\\\\\\\n\",\n \" H-A & 64.91 & 68.93 & 91.75 & 78.72 & 59.24 & 66.59 & 84.29 & 74.40 & 97.01 & 30.02 & 82.71 & 57.03 \\\\\\\\\\n\",\n \" F-H-A & 60.46 & 70.77 & 80.59 & 75.36 & 44.27 & 51.19 & 76.58 & 61.37 & 94.81 & 19.16 & 82.27 & 44.29 \\\\\\\\\\n\",\n \" F-H-R & 52.97 & 62.22 & 78.07 & 69.25 & 42.93 & 50.66 & 73.76 & 60.07 & 91.30 & 40.45 & 85.62 & 45.37 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Results using Llama 3.3 70B Instruct.}\\n\",\n \"\\\\label{table:llama3.3-70b}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lcccc|cccc|c|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\multicolumn{4}{c}{\\\\textbf{Tool Call}} & \\\\multicolumn{4}{|c|}{\\\\textbf{Parameter Matching}} & \\\\textbf{Code Exec. Rate} & \\\\multicolumn{2}{|c|}{\\\\textbf{Information Seeking}} & \\\\multicolumn{1}{c}{\\\\textbf{Cache Summary}} \\\\\\\\ \\n\",\n \" & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\\\\\ \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 77.59 & 87.87 & 86.90 & 87.38 & 49.53 & 58.04 & 77.15 & 66.25 & 57.20 & 29.65 & 83.12 & 57.46\\n\",\n \" \\\\\\\\\\n\",\n \" Hotels & 89.33 & 95.33 & 93.41 & 94.36 & 65.27 & 70.52 & 89.77 & 78.99 & 63.95 & 18.07 & 79.56 & 57.23\\n\",\n \" \\\\\\\\\\n\",\n \" Restaurants & 87.77 & 92.65 & 94.35 & 93.49 & 71.59 & 77.69 & 90.11 & 83.44 & 69.82 & 7.16 & 69.91 & 69.22\\n\",\n \" \\\\\\\\\\n\",\n \" Attractions & 65.76 & 80.16 & 78.54 & 79.34 & 44.92 & 53.04 & 74.59 & 62.00 & 72.57 & N/A & N/A & 63.87\\n\",\n \"\\\\\\\\ \\\\midrule\\n\",\n \" \\\\multicolumn{10}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 69.87 & 78.42 & 86.51 & 82.27 & 42.38 & 50.39 & 72.71 & 59.53 & 66.89 & 9.72 & 78.43 & 47.49\\n\",\n \" \\\\\\\\\\n\",\n \" H-R & 59.10 & 65.62 & 85.60 & 74.29 & 51.91 & 58.54 & 82.10 & 68.35 & 49.72 & 19.69 & 85.40 & 32.55\\n\",\n \" \\\\\\\\\\n\",\n \" H-A & 63.46 & 67.81 & 90.83 & 77.65 & 65.22 & 72.53 & 86.60 & 78.95 & 44.39 & 21.41 & 81.95 & 56.64\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-A & 68.41 & 75.27 & 88.25 & 81.24 & 50.21 & 61.04 & 73.88 & 66.85 & 60.86 & 27.00 & 82.48 & 50.42\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-R & 67.22 & 73.80 & 88.30 & 80.40 & 58.97 & 71.66 & 76.91 & 74.19 & 61.47 & 10.08 & 78.32 & 53.74\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Results using S1.1 32B.}\\n\",\n \"\\\\label{table:s1.1}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lcccc|cccc|c|cc|c}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\multicolumn{4}{c}{\\\\textbf{Tool Call}} & \\\\multicolumn{4}{|c|}{\\\\textbf{Parameter Matching}} & \\\\textbf{Code Exec. Rate} & \\\\multicolumn{2}{|c|}{\\\\textbf{Information Seeking}} & \\\\multicolumn{1}{c}{\\\\textbf{Cache Summary}} \\\\\\\\ \\n\",\n \" & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\\\\\ \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 36.66 & 67.30 & 44.61 & 53.66 & 15.74 & 56.10 & 17.95 & 27.20 & 72.76 & 13.91 & 81.60 & 39.73\\n\",\n \" \\\\\\\\\\n\",\n \" Hotels & 83.96 & 91.74 & 90.82 & 91.28 & 53.22 & 63.09 & 77.30 & 69.47 & 93.05 & 46.95 & 80.47 & 46.52\\n\",\n \" \\\\\\\\\\n\",\n \" Restaurants & 64.13 & 83.60 & 73.36 & 78.14 & 47.10 & 61.89 & 66.34 & 64.04 & 93.49 & 28.27 & 69.74 & 50.53\\n\",\n \" \\\\\\\\\\n\",\n \" Attractions & 35.78 & 61.67 & 46.02 & 52.71 & 22.90 & 66.92 & 25.82 & 37.27 & 66.25 & N/A & N/A & 50.79\\n\",\n \"\\\\\\\\ \\\\midrule\\n\",\n \" \\\\multicolumn{10}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 57.79 & 88.12 & 62.67 & 73.25 & 29.91 & 59.20 & 37.68 & 46.05 & 83.37 & 27.96 & 83.02 & 32.53\\n\",\n \" \\\\\\\\\\n\",\n \" H-R & 54.07 & 70.71 & 69.67 & 70.18 & 35.42 & 50.91 & 53.79 & 52.31 & 96.04 & 23.19 & 84.83 & 21.72\\n\",\n \" \\\\\\\\\\n\",\n \" H-A & 65.81 & 78.69 & 80.08 & 79.38 & 48.58 & 61.78 & 69.45 & 65.39 & 96.04 & 27.92 & 82.97 & 53.52\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-A & 37.83 & 62.18 & 49.14 & 54.90 & 32.73 & 64.59 & 39.89 & 49.32 & 84.49 & 15.42 & 81.00 & 32.33\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-R & 46.79 & 72.75 & 56.74 & 63.75 & 33.99 & 59.56 & 44.18 & 50.73 & 91.86 & 36.30 & 84.63 & 37.65\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Results using Phi-4-reasoning-plus.}\\n\",\n \"\\\\label{table:phi-4-reasoning-plus}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{figure}[!ht]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{assets/all_model_f1_scores.png}\\n\",\n \" \\\\caption{\\\\textbf{Above:} Tool Call F1 performance and \\\\textbf{Below:} Parameter Matching F1 performance.}\\n\",\n \" \\\\label{fig:compare-models}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lccccccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\textbf{ \\\\# Turns} & \\\\textbf{\\\\# Validation Error} & \\\\textbf{\\\\# Variable Not Defined} & \\\\textbf{\\\\# Index Out Of Range} & \\\\textbf{\\\\# Other} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 8,200 & 737 & 830 & 0 & 468 \\\\\\\\\\n\",\n \" Hotels & 8,000 & 417 & 218 & 0 & 820 \\\\\\\\\\n\",\n \" Restaurants & 7,900 & 513 & 14 & 1 & 183 \\\\\\\\\\n\",\n \" Attractions & 5,975 & 507 & 1 & 0 & 243 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{6}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 11,700 & 834 & 1087 & 0 & 408 \\\\\\\\\\n\",\n \" H-R & 10,950 & 1532 & 18 & 1 & 522 \\\\\\\\\\n\",\n \" H-A & 11,000 & 1024 & 167 & 0 & 308 \\\\\\\\\\n\",\n \" F-H-A & 9,775 & 1163 & 990 & 0 & 575 \\\\\\\\\\n\",\n \" F-H-R & 8,575 & 812 & 761 & 3 & 495 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Total} & - & 7539 & 4086 & 5 & 4022\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Error Analysis Results using Llama 3.1 8B Instruct.}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lccccccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\textbf{ \\\\# Turns} & \\\\textbf{\\\\# Validation Error} & \\\\textbf{\\\\# Variable Not Defined} & \\\\textbf{\\\\# Index Out Of Range} & \\\\textbf{\\\\# Other} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 8,200 & 408 & 176 & 42 & 26 \\\\\\\\\\n\",\n \" Hotels & 8,000 & 1,099 & 16 & 0 & 0 \\\\\\\\\\n\",\n \" Restaurants & 7,900 & 209 & 5 & 0 & 2 \\\\\\\\\\n\",\n \" Attractions & 5,975 & 18 & 9 & 0 & 8 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{6}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 11,700 & 454 & 149 & 0 & 22 \\\\\\\\\\n\",\n \" H-R & 10,950 & 692 & 185 & 0 & 17 \\\\\\\\\\n\",\n \" H-A & 11,000 & 1248 & 315 & 0 & 1 \\\\\\\\\\n\",\n \" F-H-A & 9,775 & 789 & 124 & 9 & 27 \\\\\\\\\\n\",\n \" F-H-R & 8,575 & 541 & 109 & 0 & 101 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Total} & - & 5458 & 1088 & 51 & 204 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Error Analysis Results using Llama 3.1 8B SFT Instruct.}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lccccccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\textbf{ \\\\# Turns} & \\\\textbf{\\\\# Validation Error} & \\\\textbf{\\\\# Variable Not Defined} & \\\\textbf{\\\\# Index Out Of Range} & \\\\textbf{\\\\# Other} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 8,200 & 518 & 2 & 30 & 0 \\\\\\\\\\n\",\n \" Hotels & 8,000 & 41 & 0 & 0 & 0 \\\\\\\\\\n\",\n \" Restaurants & 7,900 & 29 & 0 & 0 & 0 \\\\\\\\\\n\",\n \" Attractions & 5,975 & 4 & 2 & 0 & 1 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{6}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 11,700 & 158 & 28 & 0 & 0\\n\",\n \" \\\\\\\\\\n\",\n \" H-R & 10,950 & 14 & 2 & 0 & 1\\n\",\n \" \\\\\\\\\\n\",\n \" H-A & 11,000 & 48 & 33 & 0 & 48\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-A & 9,775 & 148 & 6 & 7 & 3\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-R & 8,575 & 330 & 5 & 1 & 7\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Total} & - & 1290 & 78 & 38 & 60 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Error Analysis Results using Llama 3.3 70B Instruct.}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lccccccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\textbf{ \\\\# Turns} & \\\\textbf{\\\\# Validation Error} & \\\\textbf{\\\\# Variable Not Defined} & \\\\textbf{\\\\# Index Out Of Range} & \\\\textbf{\\\\# Other} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 8,200 & 559 & 16 & 3 & 40\\n\",\n \" \\\\\\\\\\n\",\n \" Hotels & 8,000 & 92 & 1 & 39 & 27\\n\",\n \" \\\\\\\\\\n\",\n \" Restaurants & 7,900 & 20 & 7 & 0 & 28\\n\",\n \" \\\\\\\\\\n\",\n \" Attractions & 5,975 & 11 & 27 & 0 & 76\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{6}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 11,700 & 24 & 34 & 114 & 63\\n\",\n \" \\\\\\\\\\n\",\n \" H-R & 10,950 & 54 & 895 & 102 & 34\\n\",\n \" \\\\\\\\\\n\",\n \" H-A & 11,000 & 3 & 1071 & 43 & 23\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-A & 9,775 & 89 & 579 & 25 & 49\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-R & 8,575 & 85 & 241 & 7 & 28\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Total} & - & 937 & 2871 & 333 & 368\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Error Analysis Results using S1.1.}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lccccccc}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\textbf{Domain} & \\\\textbf{ \\\\# Turns} & \\\\textbf{\\\\# Validation Error} & \\\\textbf{\\\\# Variable Not Defined} & \\\\textbf{\\\\# Index Out Of Range} & \\\\textbf{\\\\# Other} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Single-Domain} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Flights & 8,200 & 103 & 7 & 1 & 1\\n\",\n \" \\\\\\\\\\n\",\n \" Hotels & 8,000 & 277 & 0 & 0 & 1\\n\",\n \" \\\\\\\\\\n\",\n \" Restaurants & 7,900 & 259 & 0 & 0 & 19\\n\",\n \" \\\\\\\\\\n\",\n \" Attractions & 5,975 & 0 & 0 & 0 & 0\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{6}{l}{\\\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\\\\\ \\\\midrule\\n\",\n \" F-H & 11,700 & 212 & 2 & 0 & 7\\n\",\n \" \\\\\\\\\\n\",\n \" H-R & 10,950 & 212 & 0 & 0 & 1\\n\",\n \" \\\\\\\\\\n\",\n \" H-A & 11,000 & 162 & 0 & 0 & 6\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-A & 9,775 & 120 & 3 & 0 & 5\\n\",\n \" \\\\\\\\\\n\",\n \" F-H-R & 8,575 & 153 & 4 & 0 & 32\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\texttt{Total} & - & 1498 & 16 & 1 & 72\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Overall Error Analysis Results using Phi-4-reasoning-plus.}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lllll}\\n\",\n \" \\\\toprule \\n\",\n \" \\\\textbf{Domain} & \\\\textbf{Attributes} \\\\\\\\ \\\\midrule\\n\",\n \" Flight & airline, flight\\\\_id, start\\\\_airport, start\\\\_airport\\\\_latitude, start\\\\_airport\\\\_longitude, \\\\\\\\\\n\",\n \" & start\\\\_airport\\\\_code, end\\\\_airport, end\\\\_airport\\\\_latitude, end\\\\_airport\\\\_longitude, \\\\\\\\\\n\",\n \" & end\\\\_airport\\\\_code, economy\\\\_class\\\\_option\\\\_present, business\\\\_class\\\\_option\\\\_present, \\\\\\\\\\n\",\n \" & first\\\\_class\\\\_option\\\\_present, distance\\\\_miles, duration\\\\_minutes, \\\\\\\\\\n\",\n \" & departure\\\\_time, arrival\\\\_time, number\\\\_of\\\\_layovers, first\\\\_layover\\\\_airport, \\\\\\\\\\n\",\n \" Hotel & hotel\\\\_name, city, state, neighborhood, latitude, longitude, rating, \\\\\\\\ & stars, max\\\\_occupancy, gym\\\\_present, pool\\\\_present, price\\\\_per\\\\_night, num\\\\_rooms\\\\_available, \\\\\\\\ & breakfast\\\\_included, smoking\\\\_allowed, air\\\\_conditioning\\\\_present, \\\\\\\\\\n\",\n \" & heating\\\\_present, free\\\\_wifi\\\\_included, airport\\\\_shuttle\\\\_present, \\\\\\\\ &\\n\",\n \" is\\\\_pet\\\\_friendly, has\\\\_spa\\\\_services, has\\\\_room\\\\_service, \\\\\\\\ & has\\\\_beach\\\\_access, has\\\\_fitness\\\\_class, has\\\\_laundry\\\\_service, \\\\\\\\ & has\\\\_valet\\\\_parking, has\\\\_balcony, has\\\\_rooftop\\\\_bar, has\\\\_inroom\\\\_Kitchen, \\\\\\\\ & has\\\\_kids\\\\_club, has\\\\_meeting\\\\_rooms, has\\\\_electric\\\\_vehicle\\\\_charging, \\\\\\\\ & has\\\\_hot\\\\_tub, has\\\\_sauna, has\\\\_free\\\\_parking, is\\\\_wheelchair\\\\_accessible, \\\\\\\\ & has\\\\_skiing\\\\_lodging, has\\\\_ocean\\\\_view\\\\_rooms\\\\_present, has\\\\_city\\\\_view\\\\_rooms\\\\_present, \\\\\\\\ & start\\\\_date\\\\_available, end\\\\_date\\\\_available \\\\\\\\\\n\",\n \" Attraction & city, state, name, type, latitude, longitude, neighborhood \\\\\\\\\\n\",\n \" Restaurant & restaurant\\\\_name, city, state, neighborhood, \\\\\\\\\\n\",\n \" & latitude, longitude, rating, price, price\\\\_per\\\\_person, has\\\\_nut\\\\_allergy\\\\_options, has\\\\_dairy\\\\_allergy\\\\_options, has\\\\_shell\\\\_fish\\\\_allergy\\\\_options, \\\\\\\\ & has\\\\_tomato\\\\_allergy\\\\_options, has\\\\_nightshade\\\\_allergy\\\\_options, \\\\\\\\ & has\\\\_gluten\\\\_free\\\\_options, has\\\\_vegetarian\\\\_options, has\\\\_vegan\\\\_options, \\\\\\\\ & has\\\\_kosher\\\\_options, has\\\\_halal\\\\_options, cuisine \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Domains and Attributes.} \\n\",\n \"\\\\label{tab:domains-and-attributes}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{ll}\\n\",\n \" \\\\toprule \\n\",\n \" \\\\textbf{Domain} & \\\\textbf{Tools}\\n\",\n \" \\\\\\\\\\n\",\n \" \\\\textbf{Flights} & search\\\\_flights, filter\\\\_flights \\\\\\\\\\n\",\n \" \\\\textbf{Hotels} & search\\\\_hotels, filter\\\\_hotels \\\\\\\\\\n\",\n \" \\\\textbf{Restaurants} & search\\\\_restaurants, filter\\\\_restaurants \\\\\\\\\\n\",\n \" \\\\textbf{Attractions} & search\\\\_attractions, filter\\\\_attractions \\\\\\\\\\n\",\n \" \\\\textbf{Multi-domain} & search\\\\_nearest \\\\\\\\\\n\",\n \" \\\\textbf{Common} & save\\\\_to\\\\_cache, get\\\\_results\\\\_from\\\\_cache, sort\\\\_results, seek\\\\_information, adjust\\\\_date \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{List of Tools.} \\n\",\n \"\\\\label{tab:defined-tools-domain}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lll}\\n\",\n \" \\\\toprule \\n\",\n \" \\\\textbf{Attribute} & \\\\textbf{Type} & \\\\textbf{Description} \\\\\\\\ \\\\midrule\\n\",\n \" airline & string & Airline of the flight, \\\\\\\\\\n\",\n \" flight\\\\_classes & string & Classes for the flight (economy, business, first) \\\\\\\\\\n\",\n \" num\\\\_layovers & integer & Number of layovers for the flight, between 0 and 2 \\\\\\\\\\n\",\n \" layover\\\\_duration\\\\_amount & integer & Duration of a layover flight. Between 1 and 6 hours \\\\\\\\\\n\",\n \" airports & list & Airport information for each flight including the city, state, airport code and airport name. \\\\\\\\\\n\",\n \" \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Flight Ontology Attributes.} \\n\",\n \"\\\\label{tab:flight-ontology-attributes}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lll}\\n\",\n \" \\\\toprule \\n\",\n \" \\\\textbf{Attribute} & \\\\textbf{Type} & \\\\textbf{Description} \\\\\\\\ \\\\midrule\\n\",\n \" city & string & City that the hotel is in \\\\\\\\\\n\",\n \" state & string & State that the hotel is in \\\\\\\\\\n\",\n \" neighborhood & string & Neighborhood within the city that the hotel is in\\\\\\\\\\n\",\n \" stars & integer & Star rating of the hotel between 1 and 5 \\\\\\\\\\n\",\n \" rating & float & Customer rating of the hotel between 1.0 and 5.0, incremented by 0.1 \\\\\\\\\\n\",\n \" price\\\\_per\\\\_night & integer & Price per night of the hotel ranging between 20 to 2000 dollars \\\\\\\\\\n\",\n \" max\\\\_occupancy & integer & Maximum occupancy per room ranging between 1 and 7 \\\\\\\\\\n\",\n \" gym\\\\_present & boolean & Whether or not the hotel has a gym \\\\\\\\\\n\",\n \" pool\\\\_present & boolean & Whether or not the hotel has a pool \\\\\\\\\\n\",\n \" breakfast\\\\_included & boolean & Whether or not the hotel has breakfast included \\\\\\\\\\n\",\n \" smoking\\\\_allowed & boolean & Whether or not the hotel allows smoking \\\\\\\\\\n\",\n \" air\\\\_conditioning\\\\_present & boolean & Whether or not the hotel has air conditioning \\\\\\\\\\n\",\n \" heating\\\\_present & boolean & Whether or not the hotel has heating \\\\\\\\\\n\",\n \" free\\\\_wifi\\\\_included & boolean & Whether or not the hotel includes free WiFi \\\\\\\\\\n\",\n \" airport\\\\_shuttle\\\\_present & boolean & Whether or not the hotel has an airport shuffle \\\\\\\\\\n\",\n \" is\\\\_pet\\\\_friendly & boolean & Whether or not the hotel allows pets \\\\\\\\\\n\",\n \" has\\\\_spa\\\\_services & boolean & Whether or not the hotel has spa services \\\\\\\\\\n\",\n \" has\\\\_room\\\\_service & boolean & Whether or not the hotel has room service \\\\\\\\\\n\",\n \" has\\\\_beach\\\\_access & boolean & Whether or not the hotel has access to a beach \\\\\\\\\\n\",\n \" has\\\\_business\\\\_center & boolean & Whether or not the hotel has a business center \\\\\\\\\\n\",\n \" has\\\\_fitness\\\\_classes & boolean & Whether or not the hotel has fitness classes \\\\\\\\\\n\",\n \" has\\\\_laundry\\\\_service & boolean & Whether or not the hotel has laundry services \\\\\\\\\\n\",\n \" has\\\\_valet\\\\_parking & boolean & Whether or not the hotel has valet parking \\\\\\\\\\n\",\n \" has\\\\_balcony & boolean & Whether or not the hotel has a balcony \\\\\\\\\\n\",\n \" has\\\\_rooftop\\\\_bar & boolean & Whether or not the hotel has a rooftop bar \\\\\\\\\\n\",\n \" has\\\\_inroom\\\\_kitchen & boolean & Whether or not the hotel has an inroom kitchen \\\\\\\\\\n\",\n \" has\\\\_kids\\\\_club & boolean & Whether or not the hotel has a kids club \\\\\\\\\\n\",\n \" has\\\\_meeting\\\\_rooms & boolean & Whether or not the hotel has meeting rooms \\\\\\\\\\n\",\n \" has\\\\_electric\\\\_vehicle\\\\_charging & boolean & Whether or not the hotel has electric vehicle charging \\\\\\\\\\n\",\n \" has\\\\_hot\\\\_tub & boolean & Whether or not the hotel has a hot tub \\\\\\\\\\n\",\n \" has\\\\_sauna & boolean & Whether or not the hotel has a sauna \\\\\\\\ \\n\",\n \" has\\\\_free\\\\_parking & boolean & Whether or not the hotel has free parking\\\\\\\\ \\n\",\n \" is\\\\_wheelchair\\\\_accessible& boolean & Whether or not the hotel is wheelchair accessible \\\\\\\\ \\n\",\n \" has\\\\_skiing\\\\_lodging & boolean & Whether or not the hotel has skiing and lodging \\\\\\\\ \\n\",\n \" ocean\\\\_view\\\\_rooms\\\\_present & boolean & Whether or not the hotel has rooms with a view of the ocean \\\\\\\\\\n\",\n \" city\\\\_view\\\\_rooms\\\\_present & boolean & Whether or not the hotel has rooms with views of the city\\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Hotel Ontology Attributes.} \\n\",\n \"\\\\label{tab:hotel-ontology-attributes}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lll}\\n\",\n \" \\\\toprule \\n\",\n \" \\\\textbf{Attribute} & \\\\textbf{Type} & \\\\textbf{Description} \\\\\\\\ \\\\midrule\\n\",\n \" city & string & City that the restaurant is in \\\\\\\\\\n\",\n \" state & string & State that the restaurant is in \\\\\\\\\\n\",\n \" neighborhood & string & Neighborhood within the city that the restaurant is in\\\\\\\\\\n\",\n \" rating & float & Customer rating of the restaurant between 1.0 and 5.0, incremented by 0.1 \\\\\\\\\\n\",\n \" price\\\\_per\\\\_person & integer & Average price per person at the restaurant \\\\\\\\\\n\",\n \" cuisine & string & Cuisine of the restaurant \\\\\\\\\\n\",\n \" has\\\\_nut\\\\_allergy\\\\_options & boolean & Whether or not the restaurant has any options for individuals with an allergy to nuts \\\\\\\\\\n\",\n \" has\\\\_dairy\\\\_allergy\\\\_options & boolean & Whether or not restaurant has any options for individuals with an allergy to dairy products \\\\\\\\\\n\",\n \" has\\\\_shell\\\\_fish\\\\_allergy\\\\_options & boolean & Whether or not the restaurant has any options for individuals with an allergy to shell fish \\\\\\\\\\n\",\n \" has\\\\_tomato\\\\_allergy\\\\_options & boolean & Whether or not the restaurant has options for individuals with an allergy to tomatoes \\\\\\\\\\n\",\n \" has\\\\_nightshade\\\\_allergy\\\\_options & boolean & Whether or not the restaurant has options for individuals with an allergy to nightshades \\\\\\\\\\n\",\n \" has\\\\_gluten\\\\_free\\\\_options & boolean & Whether or not the restaurant has gluten free options \\\\\\\\\\n\",\n \" has\\\\_vegetarian\\\\_options & boolean & Whether or not the restaurant has vegetarian options \\\\\\\\\\n\",\n \" has\\\\_vegan\\\\_options & boolean & Whether or not the restaurant has vegan options \\\\\\\\\\n\",\n \" has\\\\_halal\\\\_options & boolean & Whether or not the restaurant has halal options \\\\\\\\\\n\",\n \" has\\\\_kosher\\\\_options & boolean & Whether or not the hotel has kosher options \\\\\\\\ \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Restaurant Ontology Attributes.} \\n\",\n \"\\\\label{tab:restaurant-ontology-attributes}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[!htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{0.8\\\\textwidth}{!}{\\n\",\n \" \\\\begin{tabular}{lll}\\n\",\n \" \\\\toprule \\n\",\n \" \\\\textbf{Attribute} & \\\\textbf{Type} & \\\\textbf{Description} \\\\\\\\ \\\\midrule\\n\",\n \" city & string & City that the attraction is in \\\\\\\\\\n\",\n \" state & string & State that the attraction is in \\\\\\\\\\n\",\n \" neighborhood & string & Neighborhood within the city that the attraction is in\\\\\\\\\\n\",\n \" type & string & Type of the attraction \\\\\\\\ \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Attraction Ontology Attributes.} \\n\",\n \"\\\\label{tab:attraction-ontology-attributes}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\small\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.3}\\n\",\n \"\\\\begin{tabular}{|l|p{5.5cm}|p{7.5cm}|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Domain} & \\\\textbf{Placeholders Used} & \\\\textbf{Required Scenarios} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Flight} & \\n\",\n \"\\\\texttt{<CITY\\\\_x>}, \\\\texttt{<CLASS\\\\_x>}, \\\\texttt{<DEPARTURE\\\\_DATE\\\\_x>}, \\\\texttt{<DEPARTURE\\\\_TIME\\\\_x>}, \\\\texttt{<ARRIVAL\\\\_DATE\\\\_x>}, \\\\texttt{<ARRIVAL\\\\_TIME\\\\_x>}, \\\\texttt{<AIRLINE\\\\_x>}, \\\\texttt{<PRICE\\\\_x>}, \\\\texttt{<AIRPORT\\\\_x>}, \\\\texttt{<NUM\\\\_TRAVELERS\\\\_x>} & \\n\",\n \"Round trip (with 2 departure dates), one-way, multi-city, strict arrival time, flexible dates, large group bookings, solo/business/family travel, weekend getaways, budget constraints, special occasions (e.g., birthdays) \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\textbf{Hotel} & \\n\",\n \"\\\\texttt{<CHECK\\\\_IN\\\\_DATE\\\\_x>}, \\\\texttt{<CHECK\\\\_OUT\\\\_DATE\\\\_x>}, \\\\texttt{<CITY\\\\_x>}, \\\\texttt{<CITY\\\\_x\\\\_NEIGHBORHOOD\\\\_y>}, \\\\texttt{<STAR\\\\_x>}, \\\\texttt{<RATING\\\\_x>}, \\\\texttt{<PRICE\\\\_x>}, \\\\texttt{<NUM\\\\_ROOMS\\\\_x>}, \\\\texttt{<NUM\\\\_TRAVELERS\\\\_x>} & \\n\",\n \"Multi-city trips, multiple hotels in one city, specific neighborhoods, special occasions, last-minute reservations, business vs. leisure, extended stays, view/accessibility/pet-friendly requests, family and group accommodations \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\textbf{Attraction} & \\n\",\n \"\\\\texttt{<ATTRACTION\\\\_TYPE\\\\_x>}, \\\\texttt{<CITY\\\\_x>}, \\\\texttt{<STATE\\\\_x>}, \\\\texttt{<CITY\\\\_x\\\\_NEIGHBORHOOD\\\\_y>} & \\n\",\n \"Multi-type attraction queries, across cities/states, neighborhood-specific exploration, curiosity about state-level offerings. Assistant must ask open-ended questions and only mention placeholders if user provides them. \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\textbf{Restaurant} & \\n\",\n \"\\\\texttt{<RESTAURANT\\\\_RATING\\\\_x>}, \\\\texttt{<RESTAURANT\\\\_PRICE\\\\_x>}, \\\\texttt{<RESTAURANT\\\\_CUISINE\\\\_x>}, \\\\texttt{<CITY\\\\_x>}, \\\\texttt{<CITY\\\\_x\\\\_NEIGHBORHOOD\\\\_y>} & \\n\",\n \"Multi-city dining, cuisine preferences, dietary restrictions (e.g., nut-free, vegan, halal), budget vs. premium, special occasion dining, rating-focused or casual vs. upscale preferences \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\vspace{1mm}\\n\",\n \"\\\\caption{Domain-specific customization for template generation. Each domain builds on the shared prompt instructions with unique placeholders and required conversation scenarios.}\\n\",\n \"\\\\label{tab:domain-customization}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[!ht]\\n\",\n \"\\\\centering\\n\",\n \"\\\\small\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.2}\\n\",\n \"\\\\begin{tabularx}{\\\\textwidth}{|l|X|X|}\\n\",\n \"\\\\hline\\n\",\n \"\\\\textbf{Domains} & \\\\textbf{Placeholders Used} & \\\\textbf{Required Scenarios} \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\textbf{Flight + Hotel} & \\n\",\n \"\\\\texttt{<CITY\\\\_x>}, \\\\texttt{<CLASS\\\\_x>}, \\\\texttt{<DEPARTURE\\\\_DATE\\\\_x>}, \\\\texttt{<CHECK\\\\_IN\\\\_DATE\\\\_x>}, \\\\texttt{<CHECK\\\\_OUT\\\\_DATE\\\\_x>}, \\\\texttt{<NUM\\\\_TRAVELERS\\\\_x>} & \\n\",\n \"Trip planning involving both air travel and accommodation. Includes round-trip and one-way flights, hotel stays across one or more cities, budget and luxury travelers, group vs. solo travel, flexible dates, specific preferences like nonstop flights or hotels with amenities (e.g., pool, gym, pet-friendly). \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\textbf{Flight + Hotel + Attraction} & \\n\",\n \"All flight, hotel, and attraction placeholders (e.g., \\\\texttt{<CITY\\\\_x>}, \\\\texttt{<CHECK\\\\_IN\\\\_DATE\\\\_x>}, \\\\texttt{<ATTRACTION\\\\_TYPE\\\\_x>}) & \\n\",\n \"User planning a full trip involving flights, hotel stays, and sightseeing. Must include: round-trip and one-way flights, multi-city stays, hotels near attractions, flexible schedules, user-provided attraction types or specific attraction names (only when linking to hotel proximity), and special constraints (e.g., group travel, business trips, anniversaries). Assistant must never use placeholder names before user introduces them. Includes amenity discussions and attraction-type grammar handling (e.g., cultural vs. \\\\texttt{<ATTRACTION\\\\_TYPE\\\\_1>} attraction). \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\textbf{Flight + Hotel + Restaurant} & \\n\",\n \"All flight, hotel, and restaurant placeholders (e.g., \\\\texttt{<RESTAURANT\\\\_CUISINE\\\\_x>}, \\\\texttt{<RESTAURANT\\\\_PRICE\\\\_x>}) & \\n\",\n \"End-to-end trip planning including flights, accommodation, and dining. Required scenarios include: dietary restrictions, cuisine-first or city-first planning, restaurant proximity to hotel, multiple hotels or restaurants in one city, round-trip and one-way flights, and amenities like pet-friendly or spa. Must feature diverse language, nonlinear flows, and varied user personas. Includes explicit handling of dietary needs (e.g., halal, nut-free, vegetarian), and placeholder logic as per prompt. \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\textbf{Hotel + Attraction} & \\n\",\n \"\\\\texttt{<CITY\\\\_x>}, \\\\texttt{<CHECK\\\\_IN\\\\_DATE\\\\_x>}, \\\\texttt{<ATTRACTION\\\\_TYPE\\\\_x>}, \\\\texttt{<CITY\\\\_x\\\\_NEIGHBORHOOD\\\\_y>} & \\n\",\n \"User looking for accommodations and nearby attractions. Includes: specific neighborhoods, family-friendly vs. solo travel, themed vacations, extended stays, proximity to cultural or outdoor attractions, and cases where attraction type drives hotel location. \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\textbf{Hotel + Restaurant} & \\n\",\n \"\\\\texttt{<RESTAURANT\\\\_CUISINE\\\\_x>}, \\\\texttt{<HOTEL\\\\_PRICE\\\\_x>}, \\\\texttt{<CITY\\\\_x\\\\_NEIGHBORHOOD\\\\_y>} & \\n\",\n \"Combines hotel booking with dining preferences. Includes cuisine-specific searches, budget dining vs. fine dining, dietary needs (gluten-free, halal), special events (anniversaries), restaurant proximity to hotel, and group size considerations. Templates vary in planning flow—some start with hotel, others with restaurants. \\\\\\\\\\n\",\n \"\\\\hline\\n\",\n \"\\n\",\n \"\\\\end{tabularx}\\n\",\n \"\\\\vspace{1mm}\\n\",\n \"\\\\caption{Multi-domain combinations and scenario requirements. Each configuration builds on the unified instructions with additional placeholder logic and domain-specific complexity.}\\n\",\n \"\\\\label{tab:multi-domain-customization}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\documentclass{article}\n\n% if you need to pass options to natbib, use, e.g.:\n % \\PassOptionsToPackage{numbers, compress}{natbib}\n% before loading neurips_2024\n\n\\usepackage[square,numbers]{natbib}\n\\bibliographystyle{abbrvnat}\n\n% ready for submission\n% \\usepackage[]{neurips_2025}\n\\usepackage[preprint]{neurips_2025}\n\n\n% to compile a preprint version, e.g., for submission to arXiv, add add the\n% [preprint] option:\n% \\usepackage[preprint]{neurips_2024}\n\n\n% to compile a camera-ready version, add the [final] option, e.g.:\n% \\usepackage[final]{neurips_2024}\n\n\n% to avoid loading the natbib package, add option nonatbib:\n% \\usepackage[nonatbib]{neurips_2024}\n\n\n\\usepackage[utf8]{inputenc} % allow utf-8 input\n\\usepackage[T1]{fontenc} % use 8-bit T1 fonts\n\\usepackage{hyperref} % hyperlinks\n\\usepackage{url} % simple URL typesetting\n\\usepackage{booktabs} % professional-quality tables\n\\usepackage{amsfonts} % blackboard math symbols\n\\usepackage{nicefrac} % compact symbols for 1/2, etc.\n\\usepackage{microtype} % microtypography\n\\usepackage{xcolor} % colors\n\\usepackage{float}\n\\usepackage[breakable]{tcolorbox}\n\\usepackage{listings}\n\n\\lstset{\n basicstyle=\\ttfamily\\small,\n breaklines=true,\n breakatwhitespace=true,\n columns=fullflexible,\n frame=single\n}\n\\usepackage{tabularx} % Add in preamble\n% \\usepackage[table]{xcolor}\n% \\usepackage{tabularx}\n\\usepackage{amssymb} % for \\checkmark\n\\usepackage{hyperref}\n\\usepackage{url}\n\\usepackage{multirow}\n\\usepackage{bbm}\n\\usepackage{graphicx}\n\\usepackage{amssymb}\n\\usepackage{amsmath}\n\\usepackage{amsthm}\n\\usepackage{booktabs}\n\\usepackage{lscape}\n\\usepackage{pifont}\n\\usepackage{multirow}\n\\usepackage{booktabs}\n\\usepackage{textcomp}\n\\usepackage{lscape}\n\\usepackage{pifont}\n\\usepackage{algorithm}\n\\usepackage{graphicx}\n\\usepackage{caption}\n\\usepackage{subcaption}\n\\usepackage{CJKutf8}\n\\usepackage{algorithm}\n\\usepackage{algpseudocode}\n\\usepackage{enumitem}\n\\usepackage{wrapfig}\n\\usepackage{tabularx}\n\\usepackage{booktabs}\n\\usepackage{array}\n\\usepackage{pifont}\n\\usepackage{xcolor}\n\\newcommand{\\cmark}{\\ding{51}}\n\\newcommand{\\gcmark}{{\\color{green!60!black}\\fontsize{10}{10}\\selectfont\\ding{51}}}\n\\newcommand\\benchmarkname{\\textcolor{black}{\\textsc{T1}}}\n\\newcommand\\agentname{\\textcolor{black}{\\textsc{T1-Agent}}}\n\\newcommand\\dascomment[1]{\\textcolor{red}{das: \\textit{#1}}}\n\n\\title{$\\benchmarkname$: A Tool-Oriented Conversational Dataset for Multi-Turn Agentic Planning}\n\n% \\title{T$^2$ (ToolTalk): A Dataset for Tool-Oriented, Multi-Turn Agentic Planning}\n% \\title{ToolAgents: Tool-Driven Agents for Solving Multi-Domain Problems}\n\n\n% The \\author macro works with any number of authors. There are two commands\n% used to separate the names and addresses of multiple authors: \\And and \\AND.\n%\n% Using \\And between authors leaves it to LaTeX to determine where to break the\n% lines. Using \\AND forces a line break at that point. So, if LaTeX puts 3 of 4\n% authors names on the first line, and the last on the second line, try using\n% \\AND instead of \\And before the third author name.\n\n\n\\author{%\n Amartya Chakraborty\\thanks{The authors contributed equally.} \\text{ }, Paresh Dashore$^*$, Nadia Bathaee$^*$, Anmol Jain$^*$, \\\\\n \\textbf{Anirban Das}, \\textbf{Shi-Xiong Zhang}, \\textbf{Sambit Sahu}, \\textbf{Milind Naphade}, \\textbf{Genta Indra Winata$^*$} \\\\\n Capital One \\\\\n \\texttt{\\{amartya.chakraborty, paresh.dashore, nadia.bathaee\\}@capitalone.com} \\\\\n \\texttt{\\{anmol.jain, genta.winata\\}@capitalone.com}\n}\n\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\nLarge Language Models (LLMs) have demonstrated impressive capabilities as intelligent agents capable of solving complex problems. However, effective planning in scenarios involving dependencies between API or tool calls-particularly in multi-turn conversations-remains a significant challenge. To address this, we introduce $\\benchmarkname$, a tool-augmented, multi-domain, multi-turn conversational dataset specifically designed to capture and manage inter-tool dependencies across diverse domains. $\\benchmarkname$ enables rigorous evaluation of agents' ability to coordinate tool use across nine distinct domains (4 single domain and 5 multi-domain) with the help of an integrated caching mechanism for both short- and long-term memory, while supporting dynamic replanning-such as deciding whether to recompute or reuse cached results. Beyond facilitating research on tool use and planning, $\\benchmarkname$ also serves as a benchmark for evaluating the performance of open-source language models. We present results powered by $\\agentname$, highlighting their ability to plan and reason in complex, tool-dependent scenarios.\n\\end{abstract}\n\n\n\\section{Introduction}\nLeveraging external tools using Large Language Models (LLMs) to solve diverse conversational tasks has emerged as a promising direction in the development of intelligent agents~\\cite{tang2023toolalpaca}. Despite recent advances, task oriented llm based dialogue systems perform poorly over long conversational context~\\cite{laban2025llms}, and there remains a lack of comprehensive resources for training and evaluating multi-turn, multi-domain conversational agents that emphasizes on complex user needs. Existing datasets primarily focus on single-turn conversations for planning tasks—such as executing APIs or code~\\cite{schick2023toolformer, xie2024travelplanner}—and do not capture realistic multi-turn scenarios that require reasoning over long contexts, coordination across multiple tools, and adherence to complex constraints. Tool calling in realistic scenarios often involves interdependent tools, where the correctness and efficiency of task completion depend heavily on the order and context in which tools are invoked. An effective agent must therefore understand when, which, and in what sequence to call tools in order to successfully complete complex tasks. \n\nTo address this gap, we introduce $\\benchmarkname$, a new dataset and evaluation framework for assessing agent performance in multi-turn dialogues, with a particular focus on tool usage and reasoning about inter-tool dependencies. The dataset spans multiple domains and features complex, goal-oriented interactions between users and a travel assistant. Alongside the dataset, we propose $\\agentname$, an agent designed to interpret nuanced user intents and generate executable code using a predefined set of tools. $\\benchmarkname$ is specifically designed to evaluate the ability of LLM-based agents to plan tool use effectively and leverage a caching mechanism to efficiently reuse previously retrieved information. To support this, we incorporate dedicated tools for accessing and managing the cache.\n% Furthermore, we incorporate a novel caching mechanism on the agent side during code generation: before generating new outputs, the agent checks whether the current user query relates to any previously cached results. If a match is found, it retrieves the cached data and applies further filtering as needed.\n\n\\begin{figure*}[!t]\n \\centering\n \\includegraphics[width=\\textwidth]{assets/pipeline.png}\n \\caption{Illustrative example from the $\\benchmarkname$ dataset. This example showcases a multi-domain scenario involving both flights and hotels, where the user is planning a trip and attempting to book relevant services. The dialogue is constructed by retrieving entities from a knowledge base, and tool calls are executed using a predefined toolbox, simulating realistic, tool-augmented agent behavior.}\n \\label{fig:architecture}\n\\end{figure*}\n\nOur contributions can be summarized as follows:\n\\begin{itemize}\n \\item We introduce $\\benchmarkname$, a comprehensive multi-turn dataset consisting of 13.5k dialogues designed to evaluate tool-using, LLM-based agents across nine key domains—comprising four single-domain and five multi-domain settings. The dataset covers a wide range of interaction scenarios, including single-domain, mixed-domain, and fully multi-domain conversations. It incorporates 14 distinct tools, enabling realistic and fine-grained assessment of agent capabilities in complex, tool-driven dialogue tasks.\n \\item To enhance the complexity and realism of the evaluation, the dataset includes cross-domain tasks and interdependent tool calls, requiring agents to reason about tool selection and execution order within context. This evaluation framework assesses the ability of LLM-based agents to think critically, reason effectively, and make context-aware decisions.\n \\item We evaluate our dataset using an LLM-based agent, $\\agentname$, a code-generation system built on open-source language models and equipped with a caching mechanism for improved performance. This architecture enables scalable evaluation and provides a robust, efficient framework for tool-using agents.\n \\item We will publicly release our code and dataset to facilitate future research.\n\\end{itemize}\n\n\\section{T1 Dataset}\n\n$\\benchmarkname$ is a dataset specifically designed to evaluate LLM-based agents on tool usage and complex planning tasks over multi-turn conversational context. This dataset simulates multi-turn conversations spanning both four single-domain and five multi-domain settings: \\textit{flights}, \\textit{restaurants}, \\textit{hotels}, \\textit{attractions}, \\textit{flights-hotels}, \\textit{hotels-restaurants}, \\textit{hotels-attractions}, \\textit{flights-hotels-attractions}, and \\textit{flights-hotels-restaurants}.\n% \\dascomment{sentence abruptly ends}.\nPlanning tasks are formulated as code, where function calls to external tools are used to accomplish specific goals.\n\n\\subsection{Tasks and Notations}\n\nWe define a dialogue \\( D \\) as an alternating sequence of assistant and user turns: \n\\begin{align}\nD = \\{A_1, U_1, A_2, U_2, \\ldots, A_n\\},\n\\end{align}\nwhere each \\( A_i \\) represents an assistant turn and \\( U_i \\) a user turn. The dialogue always starts with an assistant turn and proceeds in a strictly alternating order. We provide a set of tools \\( \\mathcal{T} \\), where each tool \\( t \\in \\mathcal{T} \\) encapsulates logic to perform a specific function. These tools can be categorized as follows:\n\\begin{itemize}\n \\item \\textbf{Domain-specific tools}: Designed to handle operations tied to a particular application domain.\n \\item \\textbf{Interdependent tools}: Used to identify or reason about dependencies across domains.\n \\item \\textbf{Generic tools}: Domain-independent or auxiliary utilities applicable across tasks.\n\\end{itemize}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lccccccc}\n \\toprule\n \\textbf{Dataset} & \\textbf{Deployed} & \\textbf{Human Annotated} & \\textbf{Execution Result} & \\textbf{Multi-turn Context} & \\textbf{Multi-Domain} \\\\\n & \\textbf{Tools} & \\textbf{Tool Planning} & \\textbf{Evaluation} & \\textbf{Planning} & \\textbf{Tool Planning}\\\\\n \\midrule\n APIBank~\\cite{li2023api} & \\cmark & \\cmark & \\cmark & \\cmark & & \\\\\n APIBench~\\cite{patil2024gorilla} & & & \\cmark & & \\\\\n GAIA~\\cite{mialon2023gaia} & & \\cmark & \\cmark & & \\\\\n GTA~\\cite{wang2024gta} & \\cmark & \\cmark & \\cmark & \\cmark & \\\\\n m\\&m's~\\cite{ma2024m} & \\cmark & \\cmark & \\cmark & \\cmark & \\\\\n ToolBench~\\cite{qin2023toolllm} & \\cmark & & \\cmark & & \\\\\n Toolformer~\\cite{schick2023toolformer} & \\cmark & \\cmark & \\cmark & & \\\\\n TravelPlanner~\\cite{xie2024travelplanner} & \\cmark & \\cmark & \\cmark & & \\cmark & \\\\ \n \\midrule\n $\\textbf{\\benchmarkname}$ & \\cmark & \\cmark & \\cmark & \\cmark & \\cmark \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Comparison of datasets for the LLM-based agent systems.}\n\\end{table*}\n\n\\begin{figure*}[!t]\n \\centering\n \\includegraphics[width=\\textwidth]{assets/data_generation.png}\n \\caption{$\\benchmarkname$ generates data by populating delexicalized entities with corresponding entries from the knowledge base.}\n \\label{fig:data_generation}\n\\end{figure*}\n\n% In this paper, we study four fundamental tasks involving tool usage:\n% \\begin{enumerate}\n% \\item \\textbf{Tool Calling}: Invoking the appropriate tool(s) based on the current dialogue context.\n% \\item \\textbf{Parameter Extraction}:\n% \\item \\textbf{Information Seeking}: Gathering missing or clarifying information required for successful tool execution.\n% \\item \\textbf{Data Caching}: Reusing previously generated results to improve efficiency and maintain continuity.\n% \\end{enumerate}\n\n\\subsection{Dataset Construction}\nWe construct our dataset by manually collecting data from Wikipedia to gather entities and metadata. For this task, we define four domains: flights, hotels, restaurants, and attractions. Additionally, we compile a list of 128 airports and 321 cities within the United States, along with up to 15 neighborhoods for each city. Some information—such as airline names, hotel names, and hotel star ratings—is synthesized to avoid inaccuracies and to prevent the LLMs from relying on its internal knowledge of real-world named entities.\n\n\\subsubsection{Ontology}\nWe have a total of 5 ontologies, one for each of the four defined domains and another one for city. For each ontology, we curated a list of key attributes that would be relevant such as the airline or number of layovers for a flight, the cuisine of a restaurant or the number of stars or customer rating for a hotel. For each of these attributes, we defined the possible values and then used the ontology to generate synthetic data for flights, hotels and restaurants which would subsequently be used by the tools we defined. \n\n\\begin{table*}[!t]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lcccc|cc|c|c}\n \\toprule \n & \\multicolumn{4}{c|}{\\textbf{Single-domain}} & \\multicolumn{2}{c|}{\\textbf{Multi-domain}}\n & \\textbf{Common} & \\textbf{Total} \\\\ \n & \\textbf{Flights} & \\textbf{Hotels} & \\textbf{Restaurants} & \\textbf{Attractions} & \\textbf{2 Domains} & \\textbf{3 Domains} & \\\\ \\midrule\n \\textbf{\\# Attributes} & 35 & 43 & 21 & 7 & N/A & N/A & N/A & 106 \\\\\n \\textbf{\\# Tools} & 2 & 2 & 2 & 2 & 1 & N/A & 5 & 14 \\\\ \n \\textbf{\\# Dialogues} & 1.5k & 1.5k & 1.5k & 1.5k & 4.5k & 3k & N/A & 13.5k \\\\ \n \\textbf{Avg. \\# turns} & 8.2 & 8.0 & 9.0 & 6.0 & 11.3 & 9.7 & N/A & N/A \\\\ \n \\bottomrule\n \\end{tabular}\n}\n\\caption{Dataset statistics detailing the number of attributes, tools, dialogues, and the average number of turns, categorized by each individual domain, multi-domain, and common categories. \"N/A\" indicates that the metric is not applicable in the given context.} \n\\label{tab:baseline-results-one-epoch}\n\\end{table*}\n\n\\paragraph{Flights.}\nThe ontology includes the airline, flight class (economy, business and first), number of layovers ranging between 0-2 stops, the duration of a layover ranging from 1-6 hours and a list of the possible airports to depart from and arrive to. To see the full table, go to Table~\\ref{tab:flight-ontology-attributes}.\n\n\\paragraph{Hotels.}\nThe ontology includes the number of stars ranging between 1 to 5 stars, the customer rating of the hotel ranging from 1.0 to 5.0, the cost of the hotel as well as whether or not the hotel includes a number of amenities such as the presence of a gym or pool. To see the full table, go to Table~\\ref{tab:hotel-ontology-attributes}.\n\n\\paragraph{Restaurants.}\nThe ontology includes the type of cuisine, the customer rating of the hotel ranging from 1.0 to 5.0, the price per person and whether or not the restaurant served any particular dietary options such as vegetarian, vegan, or halal. To see a full list of dietary restrictions, taken into consideration, go to Table~\\ref{tab:restaurant-ontology-attributes}.\n\n\\paragraph{Attractions.}\nThe ontology includes the type of attraction which is one of the following: touristy, culinary, historical, scenic, social, art, cultural, guided, and sporting.\n\n\\paragraph{Cities.}\nThe ontology includes a list of cities in the United States of America (US) that was collected through Wikipedia. For each city, we then extracted up to 15 neighborhoods as well as the approximate geographical coordinates of each neighborhood.\n\n\\subsubsection{Knowledge Bases}\n\\paragraph{Attractions.}\nFrom the list of 321 cities, we collect up to 15 attractions for 85 cities through the usage of Llama-3.3 70B Instruct and conduct quality assurance by human annotators to ensure the data correctness. We also collect the city neighborhood for each attraction as well as the geographical coordinates. In total, there are 728 attractions that were collected from the 85 cities for this dataset.\n\n\\paragraph{Flights.}\nFor flights, there are a total of 128 airports that are used to generate synthetic flight data. Each flight generated has an airline that was randomly selected from the ontology and the start and end airport are randomly selected from the list of airports in the ontology. Additionally, the departure time is randomly generated, however the arrival time is computed based on the geographical distance between the departure and arrival airports assuming the average speed of the flight to be 450 miles per hour. 480,410 synthetic flights were generated as part of this dataset\n\n\\paragraph{Hotels.}\nHotels are generated for all 321 cities in the ontology. For a particular city, a neighborhood is assigned and additionally, synthetic latitude and longitude coordinates are generated for each hotel in a city as the coordinates would be used for distance computing purposes. Each hotel is also provided a star and a synthetic customer rating that would be correlated to the amenities offered by the establishment as well as the price per night. 47,589 hotels were generated as part of this dataset. \n\n\n\\paragraph{Restaurants.}\nRestaurants are generated for all 321 cities in the ontology. Just like for hotels, in a particular city, a neighborhood is assigned to a restaurant and additionally, synthetic latitude and longitude coordinates are generated. Each restaurant also is given a user rating which was synthetically generated, a cuisine provided by the ontology as well as whether particular dietary options are supported and the average cost per person. 17,975 restaurants are generated as part of this dataset.\n\n\\subsubsection{Data Annotation and Quality Assurance}\nTo ensure high-quality and natural data, we employ five human annotators, with each data sample reviewed by both an annotator and a quality assurance (QA) reviewer. The annotators were selected to represent a diverse set of background and perspectives, while maintaining a high technical bar. All annotators have at least a Master's degree in Computer Science and demonstrated proficiency in Python, enabling them to handle complex annotation tasks requiring logical reasoning and scripting. The QA specialist also has a strong background in programming. Annotators are assigned a category of templates and are responsible for writing the appropriate code using the tools defined for this project. Afterward, the QA reviewer evaluates the annotated code and provides feedback, which is used to make necessary corrections and improvements.\n\n\\subsubsection{Dialogue Generation}\nWe create a total of nine data categories, as discussed in Section~\\ref{sec:distinct-domains}. The data construction follows a three-step process: first, we generate templates with placeholder values; second, we annotate the templates with code using the provided tools; and third, we programmatically fill in the placeholder values for each template.\n\\paragraph{Generating Dialogue Templates.}\nFor each of the 9 dialogue categories, we generate 60 dialogue templates using Llama-3.3 70B Instruct. These templates are then reviewed and refined by human annotators to ensure accurate dialogue flow, as well as high coherence and fluency. The model is prompted to generate synthetic dialogues for both single and multi-domain. Each template consists of a conversation between the assistant and user. To learn more about the prompt used, go to Appendix~\\ref{appendix:prompt-design-user-planner} and ~\\ref{appendix:multi-domain-prompt-design}. Additionally, the templates consist of placeholders for attributes such as a city or neighborhood name, cuisine of a restaurant, rating of a hotel or the type of an attraction. As the dataset is related to the area of travel, some placeholder values are tied to a particular city such as the neighborhood (\\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_x>}, airport name (\\texttt{<CITY\\_x\\_AIRPORT\\_x>}), hotel name (\\texttt{<CITY\\_x\\_HOTEL\\_NAME\\_x>}) and restaurant name (\\texttt{<CITY\\_x\\_RESTAURANT\\_NAME\\_x>}). \n\n\\paragraph{Template Lexicalization.}\nWithin each dialogue category, 25 dialogues are generated with the placeholder values filled with the actual values present within the ontology. In addition to the dialogues, the ground-truth code which is part of the annotation has the placeholder values replaced with actual values. The dataset is split into three partitions: training, validation and test. To limit data contamination among these three partitions, the cities that are to be used for filling in the placeholder are also assigned to a particular partition only to be used there. Hence, for example if the city of Boston is assigned to the training partition, it will never be present in any of the validation or test dialogue conversations.\n\\label{sec:dialogue-template-creation}\nAdditionally, for fields such as the check-in and checkout dates for hotels or departure and return flight dates, particular methods are taken to ensure that any dates or times follow chronological order and there is no instance where a check-in date at a hotel would be after the checkout date.\n\n\\paragraph{Generated Dialogue and Ground Truth Validation.}\nOnce the placeholders are filled for both the dialogues and ground truth code samples, each block of code is executed to identify any potential errors in annotation including an improper use of a placeholder or a syntax error. The validation assists the team in correcting any annotations and ensures that the resulting code is runnable and correct. \n\n\\section{T1-Agent}\nWe build an LLM powered $\\agentname$ to evaluate and simulate our $\\benchmarkname$ agentic dataset and measure its performance across three tasks: information seeking, parameter extraction, and tool calling.\n\n\\subsection{Information Seeking}\nEach tool has a mandatory set of parameters that must be provided before running the tool successfully. Information seeking is the task of gathering this mandatory set of parameters for any of the respective tools. We want to evaluate the capability of the agent to understand both the intent of the user's query and which parameters to ask the user about as a follow-up. Figure~\\ref{fig:architecture} shows an example of how information seeking is used by the agent. When the user inquires about a flight from New York to San Jose and a hotel in San Jose, the agent understands that the user would like to search for flights but needs to provide the departure date of the flight and the check-in date of the hotel. Thus, the agent infers that in followup discussion, it needs to ask for these details from the user.\n\n\\subsection{Parameter Extraction}\nAfter the agent understands the tools to call and the necessary parameters to collect, it works to extract those parameters from the user dialogue. From Figure~\\ref{fig:architecture}, when the user mentions that they want a flight from New York to San Jose for 3 nights, the agent is able to extract the starting and ending airport city for the flight as well as the number of nights to stay at the hotel. However, neither \\texttt{search\\_flights} or \\texttt{search\\_hotels} can be called yet since the departure date of the flight and the check-in and check-out date of the hotel have not yet been provided.\n\n\\subsection{Tool Calling}\nOnce the agent understands the necessary tool(s) to call and is provided the necessary parameters for each tool, the agent will make calls to each tool. In Figure~\\ref{fig:architecture}, once the user provides the departure date for the flight to San Jose, the agent calls the \\texttt{search\\_flights} tool with the departure and arrival cities as well as the departure date. Next, before the agent can call the \\texttt{search\\_hotels} tool, it must first compute the check-out date for the hotel. The check-in date provided is May 9 and the user provided the context that the duration of the hotel stay is 3 nights. Hence, the \\texttt{adjust\\_date} tool is called to compute the check-out date of the hotel. Once this is calculated, the agent will call the \\texttt{search\\_hotels} tool with the check-in and check-out dates as well as the city of the hotel. Additionally, both the flight and hotels that came up in the results will be saved to the cache, for further possible usage.\n\n\\subsection{Data Caching}\n% Unlike prior work such as \\textit{CodeAct} \\cite{wang2024executable}, which generates fresh tool calls at each user turn, \nWe introduce a data caching mechanism that enables $\\agentname$ to reuse the outputs of earlier tool calls when handling subsequent user requests. This reduces redundant computation and improves response efficiency in multi-turn interactions. After each user turn, any search results retrieved by a tool are cached for potential reuse in later turns. The \\texttt{save\\_to\\_cache} tool is used to store these results. As illustrated in Figure~\\ref{fig:architecture}, after the user provides the departure date for a flight to San Jose, the agent calls both \\texttt{search\\_flights} and \\texttt{search\\_hotels}, and then stores the results using the \\texttt{save\\_to\\_cache} tool. Later, when the user requests flights from a specific airline, the agent retrieves the cached flight results using the \\texttt{get\\_results\\_from\\_cache} tool and filters them using the \\texttt{filter\\_flights} tool based on the user's airline preference. This caching approach helps avoid unnecessary API calls by reusing existing search results and applying filtering when appropriate.\n\n\\paragraph{Example: Refining a Flight Search.}\nSuppose a previous user query fetched flights from NYC to Boston, and the result was cached with the key \\texttt{\"flights\\_nyc\\_bos\"}. Later, the user asks to see only flights priced under \\$500. The LLM, using the cache summary, generates the following plan:\n\n\\begin{verbatim}\nflights = get_results_from_cache(key=\"flights_nyc_bos\")\naffordable_flights = filter_flights(prior_result=flights, budget=500)\n\\end{verbatim}\n\nThis illustrates how the LLM composes new logic by combining previously retrieved results with downstream tools, without repeating expensive API operations. Our approach enables more efficient, coherent, and stateful plan generation in realistic, multi-turn assistant conversations.\n\n\n\\section{Experimental Setup}\n\n\\subsection{Datasets}\n\\label{sec:distinct-domains}\nEach category contains 60 dialogue templates and a pool of 54 cities used to populate placeholder values. We split both the templates and cities into 25\\% for training, 9\\% for validation, and 66\\% for testing, resulting in 15 training templates, 5 validation templates, and 40 test templates per category. Similarly, 13 cities are allocated for training, 4 for validation, and 37 for testing. Dialogues are randomly sampled within each partition. After partitioning, a script fills all placeholders in each template using the corresponding cities from the assigned split, ensuring no data leakage or overlap of templates and entities between the training and test sets. Each template is instantiated into 25 unique dialogues after substituting the placeholders in the dialogue templates with entities defined in the ontology, yielding a total of 1,500 fully generated dialogues.\n\n\n\n% We generate 25 dialogues for each single-domain and multi-domain template. The dataset is further divided into training, validation, and test splits. For more details, please refer to Section~\\ref{sec:dialogue-template-creation}.\n\n\\subsection{Domain Adaptation using SFT} \nWe perform a simple instruction tuning with the train dataset in order to showcase that the performance on such complex conversational tool calling can be improved over zero or few shot prompting. We train a Llama 3.1 8B Instruct model for one epoch on the training dataset. The training dataset is structured as a list of \\texttt{(prompt, completions)} pairs. The SFT thereafter follows standard next token prediction with cross-entropy loss. We use LoRA~\\cite{lora} on 8 A100 SXM gpus instead of full finetuning. For reproducibility, we use the widely adopted Huggingface TRL library~\\cite{vonwerra2022trl} and include the exact command to replicate the training in Section~\\ref{SFTScript}. \n\n\\subsection{Inference Procedure}\nDuring inference, for each user turn in a dialogue, the $\\agentname$ generates executable Python code that fulfills the user request at that point in the conversation. Before generating any code, the agent will check an \\textbf{execution cache} to determine if a similar request has been previously resolved. If a cached result is available, the agent will write code that fetches and reuses the cached object to prevent redundant computation and tool invocation.\n\nTo do this, the agent constructs a prompt that includes the conversation history along with the current user turn. Instead of including the full execution cache—which can be large and token-intensive—the prompt incorporates a \\textbf{summary} of the cached results.\nThese summaries are generated using a deterministic, rule-based function that transforms each cached result into a concise representation. This approach significantly reduces the token load in the prompt, making it feasible to include relevant past results without exceeding model input limits.\n\nThis design enables the agent to consider past outcomes and reuse relevant information during code generation. Even in cases where the user’s current query differs slightly from earlier queries, the agent is able to fetch a prior result from the cache and use that as a starting point for the current user turn. By introducing summarization at the \\textit{planning stage}, we shift caching responsibilities from the tool-execution layer to the agent’s decision-making process. Our approach allows the agent to selectively reuse and adapt cached outputs, leading to improved latency and broader generalization.\n\nThe generated code is executed in a sandboxed environment, and the cache is updated with the new results on each user turn. Our dataset also includes the corresponding ground truth code and post-execution cache, which are used for performance evaluation.\n\n\\section{Results and Analysis}\nIn this section, we present the performance of various LLMs on both single-domain and multi-domain tasks. Single-domain tasks involve conversations focused exclusively on one domain—such as flights, hotels, restaurants, or attractions. In contrast, multi-domain tasks involve interactions spanning multiple domains, such as a user requesting both flight bookings and nearby hotel recommendations within the same dialogue. \n\n\\subsection{Overall Results}\nTable~\\ref{table:llama3.1-8b} presents the overall performance of \\texttt{Llama 3.1 8B Instruct} in a few-shot in-context learning setting. The model performs significantly worse on multi-domain tasks compared to single-domain ones. Additionally, much of the generated code—particularly in multi-domain scenarios—is not executable. Despite the inclusion of few-shot examples, the model struggles with accurate tool invocation. Parameter matching is even more challenging, as it requires the model not only to identify the correct tool but also to extract the appropriate parameter values from the user’s utterance.\n\n\\subsection{Analysis}\n\n\\paragraph{The Impact of Domain Adaptation on Performance.}\nFigure~\\ref{fig:enter-label} presents the tool call F1 and parameter matching F1 scores. Overall, the SFT models outperform the base model and even surpass the performance of the 70B model by a substantial margin across all domains.\n\n\\begin{figure}[!ht]\n \\centering\n \\includegraphics[width=\\linewidth]{assets/domain_adaptation.png}\n \\caption{\\textbf{Left:} Tool Call F1 performance and \\textbf{Right:} Parameter Matching F1 performance.}\n \\label{fig:enter-label}\n\\end{figure}\n\n\\begin{table*}[!ht]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lcccc|cccc|c|cc|c}\n \\toprule\n \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec.} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache}} \\\\ \n & & & & & & & & & \\textbf{Rate} & & & \\textbf{Summary} \\\\\n & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n \\multicolumn{8}{l}{\\texttt{Single-Domain}} \\\\\n \\midrule\n Flights & 25.12 & 30.90 & 57.34 & 40.16 & 15.57 & 17.34 & 60.30 & 26.94 & 26.24 & 14.41 & 82.36 & 36.63 \\\\\n Hotels & 42.86 & 49.89 & 75.25 & 60.00 & 17.57 & 23.59 & 40.80 & 29.89 & 48.13 & 47.01 & 80.38 & 33.70 \\\\\n Restaurants & 40.40 & 52.97 & 63.00 & 57.55 & 31.47 & 36.07 & 71.12 & 47.87 & \\textbf{56.99} & 28.91 & 75.68 & 35.49 \\\\\n Attractions & 33.03 & 48.49 & 50.90 & 49.66 & 14.11 & 25.11 & 24.36 & 24.73 & 40.40 & N/A & N/A & 43.87 \\\\ \\midrule\n \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 33.09 & 40.89 & 63.44 & 49.73 & 16.11 & 19.28 & 49.48 & 27.75 & 38.43 & 26.54 & 82.00 & 21.85 \\\\\n H-R & 51.06 & 59.21 & 78.77 & 67.61 & 26.62 & 33.52 & 56.37 & 42.05 & 51.82 & 28.60 & 84.07 & 9.95 \\\\\n H-A & 38.75 & 45.46 & 72.39 & 55.85 & 16.11 & 20.02 & 45.12 & 27.74 & 48.88 & 26.03 & 81.77 & 32.75 \\\\\n F-H-A & 27.76 & 36.24 & 54.24 & 43.45 & 16.21 & 21.18 & 40.88 & 27.90 & 28.76 & 14.15 & 78.58 & 24.37 \\\\\n F-H-R & 29.04 & 34.65 & 64.19 & 45.00 & 18.53 & 21.77 & 55.44 & 31.26 & 36.79 & 33.28 & 82.84 & 27.47 \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall results using Llama 3.1 8B Instruct with few-shot in-context learning.}\n\\label{table:llama3.1-8b}\n\\end{table*}\n\n% \\begin{table*}[!ht]\n% \\centering\n% \\resizebox{\\textwidth}{!}{\n% \\begin{tabular}{lcccc|ccccccccc}\n% \\toprule\n% \\textbf{Model} & \\multicolumn{4}{c|}{\\textbf{Single Domain}} & \\multicolumn{5}{c}{\\textbf{Multi-Domain}} \\\\\n% & Flight & Hotel & Attraction & Restaurant & F-H & H-R & H-A & F-H-A & F-H-R \\\\ \\midrule\n% Llama 3.1 8B \\\\\n% $\\quad$+ Fine-tune \\\\\n% Llama 3.3 70B \\\\ \\midrule\n% Phi-4 R$^+$ 14B \\\\\n% S1.1 32B \\\\\n% \\bottomrule\n% \\end{tabular}\n% }\n% \\caption{F1 Results on Fine-grained Tool Call.}\n% \\end{table*}\n\n\\paragraph{Model Performance.}\nOur qualitative evaluation shows that the \\texttt{LLaMA 3.3 70B Instruct} model consistently delivers the strongest performance across tasks. In contrast, the \\texttt{LLaMA 3.1 8B Instruct} model, without any fine-tuning, struggles significantly. It often fails to utilize available cache effectively and generates an incorrect code.\n\n\\paragraph{Impact of Fine-Tuning.}\nWhile the 70B and the non-fine-tuned 8B models were prompted to generate answers with reasoning, a fine-tuned variant—despite not being instructed to provide reasoning—achieved performance comparable to the 70B Instruct model. This indicates the strong potential of task-specific fine-tuning in enhancing model performance.\n\n\\paragraph{Few-Shot Evaluation.}\nAs shown in Figure~\\ref{fig:few-shot}, we evaluate model performance on the \\textit{flights} domain under 0-shot, 5-shot, and 13-shot settings. Performance is notably poor in the 0-shot setting, with improvements observed in 5-shot and 13-shot configurations—though the gains plateau beyond 5 shots. Qualitative analysis suggests that without sufficient context, models continue to struggle with generalization in complex, multi-domain scenarios.\n\\begin{figure}[!ht]\n \\centering\n \\includegraphics[width=0.9\\linewidth]{assets/flight_shot_learning.png}\n \\caption{Few-shot performance on Flight domain.}\n \\label{fig:few-shot}\n\\end{figure}\n\n\\paragraph{Need for Complex Evaluation.}\nEven with the state-of-the-art model, \\texttt{LLaMA 3.3 70B Instruct}, which performs well on standard code generation tasks, we observe that it continues to struggle in complex, multi-turn scenarios involving advanced planning. The $\\benchmarkname$ dataset is designed to fill this gap by serving as a benchmark for evaluating model performance in such challenging settings.\n\n\\section{Related Work}\n\\subsection{Large Language Model Agents}\nLLM-based agents have emerged as foundational components in AI systems, capable of performing complex, multi-step tasks through reasoning, memory integration, and tool use. These agents often combine a pre-trained LLM with structured modules such as long-term memory, tool calling capabilities, and self-reflective feedback loops. Frameworks such as {AutoGPT}~\\cite{yang2023auto}, and {AgentGPT} allow LLMs to autonomously decompose user goals into subgoals and execute them sequentially using external APIs. More structured systems like {HuggingGPT}~\\cite{shen2023hugginggpt}, {CrewAI}, and {AutoGen}~\\cite{wu2023autogen} facilitate collaboration between multiple LLM agents, each specializing in roles such as planning, execution, or critique.\n\nDespite significant progress, planning within task-oriented dialogue systems—particularly over long horizons—remains a fundamental challenge. Previous paradigms such as \\textit{plan-observe-execute} (e.g., ReAct~\\cite{yao2023react}, ADaPT~\\cite{prasad2023adapt}) enable the model to interleave tool calls with reasoning steps. However, most frameworks focus on linear execution paths where each step invokes a single tool. These approaches often lack the ability to manage inter-tool dependencies, reuse intermediate results, or revise plans based on partial tool failures. Further, a lot of these systems performs single turn planning, i.e. the user of the system submits a request with all the information in the first turn. Multi-turn conversational planning is a nascent field. For example, in multi-turn workflows like conversational trip planning, agents need to collect information across multiple steps, then plan and coordinate across tools like flight search, visa information, and calendar APIs—something most current systems struggle to handle.\n\n\\subsection{Tool-Based Agents and Benchmarks}\n\nTool usage extends the scope of LLM capabilities beyond language modeling ~\\citep{team2024chameleon, schick2023toolformer} to real-world actionability, enabling interactions with APIs, web tools, and external software. To evaluate this ability, several benchmarks have been proposed, including {APIBank}~\\cite{li2023api}, {Tau-Bench}~\\cite{yao2024tau},\n{GAIA}~\\cite{mialon2023gaia}, {ALFWorld}~\\cite{shridhar2020alfworld}, {GTA}~\\cite{wang2024gta},\n{TravelPlanner}~\\cite{xie2024travelplanner}, and {ToolBench}~\\cite{qin2023toolllm}. Although these benchmarks each emphasize different strengths, such as breadth of API coverage, realism, or reasoning complexity—they often treat tool use as a series of isolated atomic actions without requiring coordinated planning between multiple tools. Further, there\n\nIn contrast, our work introduces $\\benchmarkname$, a tool-driven benchmark designed to evaluate LLM agents in multi-turn, multi-domain dialogue settings with inter-tool dependencies. $\\benchmarkname$ features an integrated caching mechanism that supports both short- and long-term memory of tool call results, allowing agents to make intelligent decisions about whether to replan or reuse cached outputs. Unlike prior benchmarks, it tests an agent’s ability to perform dynamic replanning, handle branching workflows, and compose tools in a realistic, dialog-driven environment. Thus, $\\benchmarkname$ not only challenges existing tool-use agents but also provides a diagnostic sandbox for evaluating the reasoning capabilities of open-source LLMs under realistic constraints.\n\n\n\n% \\section{Related Work }\n\n% \\subsection{Large Language Model Agents} AI Agents or Large Language model agents are now ubiquitously being used in various complex workflows~\\cite{tang2023toolalpaca}. The ability to utilize memory, tools alongside planning, reasoning and self reflection abilities have led to the enhancement in their abilities. Many tool calling frameworks such as AutoGPT~\\citep{}, HuggingGPT~\\citep{}, CrewAI~\\citep{}, AutoGen~\\citep{} etc, has sprung into existence that allows building of single or multi agent systems. However planning in task oriented dialogue systems, both long and short horizon, is not yet solved~\\citep{}. Prior work has looked into \\textit{plan-observe-execute} type paradigms to do planning in the presence of tools or functions~\\citep{react, rewoo, adapt} where each next action in the plan depends on the outcome of the previous execution. In this case however the plan at each step consists of calling an single tool. \n\n% \\paragraph{Tool-based Agents}\n% Tools give the AI agents ability to perform tasks. However in many cases, performing a single task may need multiple tools to be called with some application logic. Several benchmarks aims at assessing the performance of tool calling ability of AI Agents. APIBench, GTA, Tau-Bench, GAIA, OsWorld, Alfworld, Alfbench, TravelPlanner, Toolbench etc. \n% https://arxiv.org/pdf/2406.12045\n% %https://proceedings.neurips.cc/paper_files/paper/2024/file/bfd082c452dffb450d5a5202b0419205-Paper-Datasets_and_Benchmarks_Track.pdf\n% https://arxiv.org/pdf/2402.01622\n% https://arxiv.org/pdf/2406.14283?\n% https://aclanthology.org/2025.coling-main.672.pdf\n% https://arxiv.org/abs/2410.01440\n% https://openreview.net/pdf?id=dCPF1wlqj8\n% https://arxiv.org/pdf/2502.11221\n% https://aclanthology.org/2025.naacl-long.36.pdf\n% https://arxiv.org/pdf/2408.00764?\n% https://neurips.cc/virtual/2024/poster/97620\n\n\\newcolumntype{Y}{>{\\centering\\arraybackslash}X}\n\n\\section{Conclusion}\n\nWe introduce $\\benchmarkname$, a comprehensive dataset for evaluating planning, reasoning, and tool-usage in LLM-based agents through complex, multi-turn dialogues. By introducing inter-tool dependencies, dynamic replanning, and caching, it supports rigorous assessment across single- and multi-domain settings. Experiments with $\\agentname$ highlight both the strengths and limitations of open-source LLMs: while the \\texttt{LLaMA 3.3 70B Instruct} model performs best, the non-fine-tuned \\texttt{LLaMA 3.1 8B} struggles with caching and code generation. A fine-tuned 8B variant matches 70B performance, emphasizing the value of task-specific tuning. Despite improvements with few-shot learning, models still face generalization challenges in multi-domain scenarios.\n\\bibliography{main}\n\n\\appendix\n\n\\newpage\n% \\section*{NeurIPS Paper Checklist}\n% \\begin{enumerate}\n\n% \\item {\\bf Claims}\n% \\item[] Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?\n% \\item[] Answer: \\answerYes{} % Replace by \\answerYes{}, \\answerNo{}, or \\answerNA{}.\n% \\item[] Justification: The claim is supported by the abstract and introduction and aligns with the contributions outlined throughout the paper.\n% \\item[] Guidelines:\n% \\begin{itemize}\n% \\item The answer NA means that the abstract and introduction do not include the claims made in the paper.\n% \\item The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. 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Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.\n% %this research? \n% \\item[] Answer: \\answerYes{}, % Replace by \\answerYes{}, \\answerNo{}, or \\answerNA{}.\n% \\item[] Justification: We declared during the submission.\n% \\item[] Guidelines:\n% \\begin{itemize}\n% \\item The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.\n% \\item Please refer to our LLM policy (\\url{https://neurips.cc/Conferences/2025/LLM}) for what should or should not be described.\n% \\end{itemize}\n \n\\section{Limitations}\nIn this work, we focus on constructing and introducing a new dataset as a benchmark for evaluating agentic workflows in multi-turn conversational dialogue settings, with an emphasis on tool calling for planning. Our evaluations are limited to open-source models, as proprietary models are not included due to resource constraints. We use Llama 3.1 8B Instruct, Llama 3.3 70B Instruct, S1.1 32B, and Phi4 Reasoning Plus. We will release $\\benchmarkname$ dataset publicly and hope it will encourage future research that includes evaluations on proprietary models as well.\n\n\\section{Additional Results}\n\\subsection{Detailed Results for Llama 3.1 8B Instruct with SFT and Llama 3.3 70B Instruct}\nTable~\\ref{table:llama3.1-8b-sft} shows the results for Llama 3.1 8B Instruct with Domain Adaptation and Table~\\ref{table:llama3.3-70b} shows the results for Llama 3.3 70B Instruct.\n\n\\begin{table*}[!ht]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lcccc|cccc|c|cc|c}\n \\toprule\n \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 83.51 & 89.98 & 92.08 & 91.02 & 58.02 & 66.38 & 82.18 & 73.44 & 85.26 & 39.19 & 86.44 & 62.07 \\\\\n Hotels & 78.18 & 84.87 & 90.84 & 87.75 & 60.40 & 67.29 & 85.53 & 75.32 & 72.13 & 48.30 & 80.91 & 71.35 \\\\\n Restaurants & 72.76 & 80.40 & 88.44 & 84.23 & 57.49 & 66.69 & 80.64 & 73.00 & 95.16 & 95.14 & 98.63 & 65.32 \\\\\n Attractions & 90.50 & 97.87 & 92.33 & 95.02 & 75.54 & 91.34 & 81.37 & 86.07 & 98.15 & N/A & N/A &83.00 \\\\ \\midrule\n \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 80.27 & 91.31 & 86.91 & 89.05 & 57.76 & 74.51 & 71.99 & 73.23 & 89.25 & 24.04 & 80.63 & 57.01 \\\\\n H-R & 82.02 & 91.03 & 89.23 & 90.12 & 68.44 & 77.95 & 84.86 & 81.26 & 83.67 & 29.12 & 87.58 & 64.42 \\\\\n H-A & 62.30 & 72.67 & 81.35 & 76.77 & 59.22 & 68.73 & 81.05 & 74.39 & 71.41 & 27.87 & 82.80 & 65.70 \\\\\n F-H-A & 77.19 & 87.50 & 86.76 & 87.13 & 59.63 & 74.16 & 75.27 & 74.71 & 81.15 & 22.65 & 83.45 & 52.76 \\\\\n F-H-R & 71.53 & 86.05 & 80.91 & 83.40 & 54.39 & 71.99 & 68.99 & 70.45 & 82.47 & 46.32 & 84.40 & 53.88 \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Results using Llama 3.1 8B Instruct after SFT.}\n\\label{table:llama3.1-8b-sft}\n\\end{table*}\n\n\\begin{table*}[!ht]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lcccc|cccc|c|cc|c}\n \\toprule\n \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 58.42 & 78.26 & 69.75 & 73.76 & 32.11 & 40.51 & 60.76 & 48.61 & 83.32 & 20.25 & 82.90 & 53.80 \\\\\n Hotels & 92.42 & 96.03 & 96.10 & 96.07 & 75.33 & 80.85 & 91.69 & 85.93 & 98.55 & 46.98 & 80.27 & 75.00 \\\\\n Restaurants & 94.23 & 96.63 & 97.43 & 97.03 & 85.51 & 93.62 & 90.80 & 92.19 & 99.54 & 37.90 & 79.95 & 90.78 \\\\\n Attractions & 79.14 & 92.16 & 84.86 & 88.36 & 71.17 & 87.04 & 79.60 & 83.16 & 63.70 & N/A & N/A & 78.59 \\\\ \\midrule\n \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 43.48 & 53.73 & 69.52 & 60.61 & 22.28 & 25.94 & 61.24 & 36.44 & 95.02 & 27.39 & 83.42 & 37.15 \\\\\n H-R & 60.50 & 70.91 & 80.46 & 78.29 & 50.94 & 60.08 & 76.99 & 67.50 & 99.60 & 22.97 & 84.11 & 38.43 \\\\\n H-A & 64.91 & 68.93 & 91.75 & 78.72 & 59.24 & 66.59 & 84.29 & 74.40 & 97.01 & 30.02 & 82.71 & 57.03 \\\\\n F-H-A & 60.46 & 70.77 & 80.59 & 75.36 & 44.27 & 51.19 & 76.58 & 61.37 & 94.81 & 19.16 & 82.27 & 44.29 \\\\\n F-H-R & 52.97 & 62.22 & 78.07 & 69.25 & 42.93 & 50.66 & 73.76 & 60.07 & 91.30 & 40.45 & 85.62 & 45.37 \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Results using Llama 3.3 70B Instruct.}\n\\label{table:llama3.3-70b}\n\\end{table*}\n\n\\subsection{Detailed Results for Reasoning Models}\nAdditionally, we also experiment with medium-sized reasoning models to see how they perform. We work with S1.1 32B~\\cite{muennighoff2025s1} and Phi-4-reasoning-plus 14B~\\cite{abdin2025phi}. The decoding configuration for both models includes a maximum token limit of 4,000, a temperature of 0.1, and max token length is 7,000. We host our models using vLLM in a A100 40GB x 8 node.\n\n\\begin{table*}[!ht]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lcccc|cccc|c|cc|c}\n \\toprule\n \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 77.59 & 87.87 & 86.90 & 87.38 & 49.53 & 58.04 & 77.15 & 66.25 & 57.20 & 29.65 & 83.12 & 57.46\n \\\\\n Hotels & 89.33 & 95.33 & 93.41 & 94.36 & 65.27 & 70.52 & 89.77 & 78.99 & 63.95 & 18.07 & 79.56 & 57.23\n \\\\\n Restaurants & 87.77 & 92.65 & 94.35 & 93.49 & 71.59 & 77.69 & 90.11 & 83.44 & 69.82 & 7.16 & 69.91 & 69.22\n \\\\\n Attractions & 65.76 & 80.16 & 78.54 & 79.34 & 44.92 & 53.04 & 74.59 & 62.00 & 72.57 & N/A & N/A & 63.87\n\\\\ \\midrule\n \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 69.87 & 78.42 & 86.51 & 82.27 & 42.38 & 50.39 & 72.71 & 59.53 & 66.89 & 9.72 & 78.43 & 47.49\n \\\\\n H-R & 59.10 & 65.62 & 85.60 & 74.29 & 51.91 & 58.54 & 82.10 & 68.35 & 49.72 & 19.69 & 85.40 & 32.55\n \\\\\n H-A & 63.46 & 67.81 & 90.83 & 77.65 & 65.22 & 72.53 & 86.60 & 78.95 & 44.39 & 21.41 & 81.95 & 56.64\n \\\\\n F-H-A & 68.41 & 75.27 & 88.25 & 81.24 & 50.21 & 61.04 & 73.88 & 66.85 & 60.86 & 27.00 & 82.48 & 50.42\n \\\\\n F-H-R & 67.22 & 73.80 & 88.30 & 80.40 & 58.97 & 71.66 & 76.91 & 74.19 & 61.47 & 10.08 & 78.32 & 53.74\n \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Results using S1.1 32B.}\n\\label{table:s1.1}\n\\end{table*}\n\n\\begin{table*}[!ht]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lcccc|cccc|c|cc|c}\n \\toprule\n \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & \\multicolumn{2}{|c|}{\\textbf{Information Seeking}} & \\multicolumn{1}{c}{\\textbf{Cache Summary}} \\\\ \n & Acc. & Prec. & Rec. & F1 & Acc. & Prec. & Rec. & F1 & Acc. & SacreBLEU & BERTScore & EM \\\\ \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 36.66 & 67.30 & 44.61 & 53.66 & 15.74 & 56.10 & 17.95 & 27.20 & 72.76 & 13.91 & 81.60 & 39.73\n \\\\\n Hotels & 83.96 & 91.74 & 90.82 & 91.28 & 53.22 & 63.09 & 77.30 & 69.47 & 93.05 & 46.95 & 80.47 & 46.52\n \\\\\n Restaurants & 64.13 & 83.60 & 73.36 & 78.14 & 47.10 & 61.89 & 66.34 & 64.04 & 93.49 & 28.27 & 69.74 & 50.53\n \\\\\n Attractions & 35.78 & 61.67 & 46.02 & 52.71 & 22.90 & 66.92 & 25.82 & 37.27 & 66.25 & N/A & N/A & 50.79\n\\\\ \\midrule\n \\multicolumn{10}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 57.79 & 88.12 & 62.67 & 73.25 & 29.91 & 59.20 & 37.68 & 46.05 & 83.37 & 27.96 & 83.02 & 32.53\n \\\\\n H-R & 54.07 & 70.71 & 69.67 & 70.18 & 35.42 & 50.91 & 53.79 & 52.31 & 96.04 & 23.19 & 84.83 & 21.72\n \\\\\n H-A & 65.81 & 78.69 & 80.08 & 79.38 & 48.58 & 61.78 & 69.45 & 65.39 & 96.04 & 27.92 & 82.97 & 53.52\n \\\\\n F-H-A & 37.83 & 62.18 & 49.14 & 54.90 & 32.73 & 64.59 & 39.89 & 49.32 & 84.49 & 15.42 & 81.00 & 32.33\n \\\\\n F-H-R & 46.79 & 72.75 & 56.74 & 63.75 & 33.99 & 59.56 & 44.18 & 50.73 & 91.86 & 36.30 & 84.63 & 37.65\n \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Results using Phi-4-reasoning-plus.}\n\\label{table:phi-4-reasoning-plus}\n\\end{table*}\n\nBetween these two models, the S1.1 model mostly outperforms the Phi-4-reasoning-plus model when it comes to Tool Call and Parameter Matching metrics.\n\n\\section{Performance Comparison Between Models}\nWe observe that the S1.1 model performance performs reasonably well especially compared to the Llama 3.3 70B model that we observe to produce the best results. The Phi-4-reasoning-plus model did well with some domains but overall it does not perform as well as the S1.1 and Llama 3.3 70B models. Figure~\\ref{fig:compare-models} shows the performance comparison between models.\n\n\\begin{figure}[!ht]\n \\centering\n \\includegraphics[width=\\linewidth]{assets/all_model_f1_scores.png}\n \\caption{\\textbf{Above:} Tool Call F1 performance and \\textbf{Below:} Parameter Matching F1 performance.}\n \\label{fig:compare-models}\n\\end{figure}\n\n% \\section{Reproducibility}\n% Our dataset has been anonymized and please find the dataset on Kaggle \\url{https://kaggle.com/datasets/b47e52b440ccaf964009a3f4a3bdfdb92de205249fae87c3c3db7b615c29490c}. Details on how to reproduce our experiments using TRL are provided in the Appendix of our submission and we also included here for your perusal in Section~\\ref{SFTScript}. \n% For additional instructions and implementation details, please refer to this anonymous repository at: \\url{https://anonymous.4open.science/r/T1-code-38C8/README.md}.\n\n\\section{Error Analysis}\n\nWhen we look closer at the errors found during inferencing, we first break down the errors into a total of 4 categories:\n\\begin{itemize}\n\\item \\textbf{Validation Error}: Errors related to improper arguments being passed to the defined tools. \n\\item \\textbf{Variable Not Defined}: Error indicating code uses an underfined variable. \n\\item \\textbf{Index Out Of Range}: Error indicating generated code involves an index out of range, usually corresponding to the list data structure in Python.\n\\item \\textbf{Other}: Other errors present within the generated code.\n\\end{itemize}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lccccccc}\n \\toprule\n \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 8,200 & 737 & 830 & 0 & 468 \\\\\n Hotels & 8,000 & 417 & 218 & 0 & 820 \\\\\n Restaurants & 7,900 & 513 & 14 & 1 & 183 \\\\\n Attractions & 5,975 & 507 & 1 & 0 & 243 \\\\\n \\midrule\n \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 11,700 & 834 & 1087 & 0 & 408 \\\\\n H-R & 10,950 & 1532 & 18 & 1 & 522 \\\\\n H-A & 11,000 & 1024 & 167 & 0 & 308 \\\\\n F-H-A & 9,775 & 1163 & 990 & 0 & 575 \\\\\n F-H-R & 8,575 & 812 & 761 & 3 & 495 \\\\\n \\midrule\n \\texttt{Total} & - & 7539 & 4086 & 5 & 4022\\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Error Analysis Results using Llama 3.1 8B Instruct.}\n\\end{table*}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lccccccc}\n \\toprule\n \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 8,200 & 408 & 176 & 42 & 26 \\\\\n Hotels & 8,000 & 1,099 & 16 & 0 & 0 \\\\\n Restaurants & 7,900 & 209 & 5 & 0 & 2 \\\\\n Attractions & 5,975 & 18 & 9 & 0 & 8 \\\\\n \\midrule\n \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 11,700 & 454 & 149 & 0 & 22 \\\\\n H-R & 10,950 & 692 & 185 & 0 & 17 \\\\\n H-A & 11,000 & 1248 & 315 & 0 & 1 \\\\\n F-H-A & 9,775 & 789 & 124 & 9 & 27 \\\\\n F-H-R & 8,575 & 541 & 109 & 0 & 101 \\\\\n \\midrule\n \\texttt{Total} & - & 5458 & 1088 & 51 & 204 \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Error Analysis Results using Llama 3.1 8B SFT Instruct.}\n\\end{table*}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lccccccc}\n \\toprule\n \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 8,200 & 518 & 2 & 30 & 0 \\\\\n Hotels & 8,000 & 41 & 0 & 0 & 0 \\\\\n Restaurants & 7,900 & 29 & 0 & 0 & 0 \\\\\n Attractions & 5,975 & 4 & 2 & 0 & 1 \\\\\n \\midrule\n \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 11,700 & 158 & 28 & 0 & 0\n \\\\\n H-R & 10,950 & 14 & 2 & 0 & 1\n \\\\\n H-A & 11,000 & 48 & 33 & 0 & 48\n \\\\\n F-H-A & 9,775 & 148 & 6 & 7 & 3\n \\\\\n F-H-R & 8,575 & 330 & 5 & 1 & 7\n \\\\\n \\midrule\n \\texttt{Total} & - & 1290 & 78 & 38 & 60 \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Error Analysis Results using Llama 3.3 70B Instruct.}\n\\end{table*}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lccccccc}\n \\toprule\n \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 8,200 & 559 & 16 & 3 & 40\n \\\\\n Hotels & 8,000 & 92 & 1 & 39 & 27\n \\\\\n Restaurants & 7,900 & 20 & 7 & 0 & 28\n \\\\\n Attractions & 5,975 & 11 & 27 & 0 & 76\n \\\\\n \\midrule\n \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 11,700 & 24 & 34 & 114 & 63\n \\\\\n H-R & 10,950 & 54 & 895 & 102 & 34\n \\\\\n H-A & 11,000 & 3 & 1071 & 43 & 23\n \\\\\n F-H-A & 9,775 & 89 & 579 & 25 & 49\n \\\\\n F-H-R & 8,575 & 85 & 241 & 7 & 28\n \\\\\n \\midrule\n \\texttt{Total} & - & 937 & 2871 & 333 & 368\n \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Error Analysis Results using S1.1.}\n\\end{table*}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lccccccc}\n \\toprule\n \\textbf{Domain} & \\textbf{ \\# Turns} & \\textbf{\\# Validation Error} & \\textbf{\\# Variable Not Defined} & \\textbf{\\# Index Out Of Range} & \\textbf{\\# Other} \\\\\n \\midrule\n \\texttt{Single-Domain} \\\\\n \\midrule\n Flights & 8,200 & 103 & 7 & 1 & 1\n \\\\\n Hotels & 8,000 & 277 & 0 & 0 & 1\n \\\\\n Restaurants & 7,900 & 259 & 0 & 0 & 19\n \\\\\n Attractions & 5,975 & 0 & 0 & 0 & 0\n \\\\\n \\midrule\n \\multicolumn{6}{l}{\\texttt{Multi-Domain.} F: Flights, H: Hotels, R: Restaurants, A: Attractions} \\\\ \\midrule\n F-H & 11,700 & 212 & 2 & 0 & 7\n \\\\\n H-R & 10,950 & 212 & 0 & 0 & 1\n \\\\\n H-A & 11,000 & 162 & 0 & 0 & 6\n \\\\\n F-H-A & 9,775 & 120 & 3 & 0 & 5\n \\\\\n F-H-R & 8,575 & 153 & 4 & 0 & 32\n \\\\\n \\midrule\n \\texttt{Total} & - & 1498 & 16 & 1 & 72\\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Overall Error Analysis Results using Phi-4-reasoning-plus.}\n\\end{table*}\n\nOverall, we notice that validation errors are consistently present within the results of all of the models we evaluated.\n\n\\subsection{Llama 3.3 70B Instruct} The Llama 3.3 70B instruct model contains the fewest number of overall errors among the five models evaluated with a total of 1,466. This supports the idea that the larger number of parameters helps the model better understand the task as well passing in the proper parameters to the tools to generate high quality code. \n\n\\subsection{Llama 3.1 8B Instruct} The Llama 3.1 8B Instruct model consists of the most number of total errors among all 4 categories which were tracked. The only category it performs well in was the \\texttt{Index Out Of Range} error where there are only 5 instances.\n\n\\subsection{Llama 3.1 8B Instruct SFT}\nThe Llama 3.1 8B Instruct SFT does drastically improve on the number of \\texttt{Validation}, \\texttt{Variable Not Defined} and \\texttt{Other} categorized errors compared to the original model. This indicates that the model is able to better learn about calling the tools and writing higher quality code than the original model.\n\n\n\\subsection{S1.1} Overall, the S1.1 model performs the best when it comes to \\texttt{Validation} errors with a total of 937 errors. However, it also consists of the highest amount of \\texttt{Index Out of Range} errors and the 2nd highest amount of \\texttt{Variable Not Defined} errors.\n\n\\subsection{Phi-4-reasoning-plus}\nThe Phi-4-reasoning-plus has 1498 validation errors which is the third most among the 5 models. The model does perform reasonably well with the other error categories and has the fewest number of \\texttt{Index Out Of Range} and \\texttt{Variable Not Defined} errors with 1 and 16 respectively.\n\n\\section{Model and Prompt Configuration}\nWe use the Llama 3.1 8B Instruct and Llama 3.3 70B Instruct models, and fine-tune Llama 3.1 8B Instruct to evaluate the effectiveness of domain adaptation on the $\\benchmarkname$ dataset. We evaluate all the models in a \\textit{few-shot} setting, where several example turns are included in the prompt to guide the model’s behavior. The full prompts used for inference are provided in Section~\\ref{system-plan-generation-prompt} and Section~\\ref{user-plan-generation-prompt}. The decoding configuration for both models includes a maximum token limit of 4000, top-k sampling of 10, and a temperature of 0.1.\n\n\\section{Evaluation Protocol}\nWe evaluate the model's performance at every user turn by comparing the model’s output with the ground truth across the following facets.\n\\paragraph{Tool Call.} We evaluate the correctness of each tool call from the generated code against the ground truth code by comparing the number of times each tool is called using four metrics: accuracy, precision, recall, and F1.\n\\paragraph{Parameter Matching.} For each tool call in the ground truth, we identify the corresponding tool call in the generated code with the same name and the highest parameter overlap. We then calculate the accuracy, precision, recall, and F1 for the identified match. Parameter values are standardized to enable robust comparison; for example, lists are treated as sets to make them insensitive to ordering. Certain tool calls such as \\texttt{save\\_to\\_cache}, \\texttt{get\\_results\\_from\\_cache}, and \\texttt{seek\\_information} are excluded from this evaluation, as they depend on external artifacts (e.g., intermediate dataframes) and variable keys or identifiers that cannot be reliably matched. Similarly, certain parameter names (e.g., \\texttt{prior\\_results}) are also excluded. \n\\paragraph{Code Execution Success Rate.} We calculate the percentage of instances in which the model generates a code when expected and the code is executable without any errors in a sandbox environment.\n\\paragraph{Handling Information Seeking.} If both the model output and the ground truth include \\texttt{seek\\_information}, we evaluate the similarity of the strings inside the function using SacreBLEU~\\cite{post2018call} and BERTScore F1~\\cite{zhang2019bertscore}, capturing both sub-word overlap and semantic similarity of the requested information.\n\\paragraph{Cache Summary.} To assess how well the model serves complete requests, we compare the execution cache summary results of the generated code and ground truth using exact match (EM) to determine if the model-generated solution is functionally equivalent to the ground truth.\n\n\\section{More Information on T1 Dataset}\nTable~\\ref{tab:domains-and-attributes} shows the attributes for each domain. Table~\\ref{tab:defined-tools-domain} shows the tools used for each domain.\n\n\\begin{table*}[!ht]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lllll}\n \\toprule \n \\textbf{Domain} & \\textbf{Attributes} \\\\ \\midrule\n Flight & airline, flight\\_id, start\\_airport, start\\_airport\\_latitude, start\\_airport\\_longitude, \\\\\n & start\\_airport\\_code, end\\_airport, end\\_airport\\_latitude, end\\_airport\\_longitude, \\\\\n & end\\_airport\\_code, economy\\_class\\_option\\_present, business\\_class\\_option\\_present, \\\\\n & first\\_class\\_option\\_present, distance\\_miles, duration\\_minutes, \\\\\n & departure\\_time, arrival\\_time, number\\_of\\_layovers, first\\_layover\\_airport, \\\\\n Hotel & hotel\\_name, city, state, neighborhood, latitude, longitude, rating, \\\\ & stars, max\\_occupancy, gym\\_present, pool\\_present, price\\_per\\_night, num\\_rooms\\_available, \\\\ & breakfast\\_included, smoking\\_allowed, air\\_conditioning\\_present, \\\\\n & heating\\_present, free\\_wifi\\_included, airport\\_shuttle\\_present, \\\\ &\n is\\_pet\\_friendly, has\\_spa\\_services, has\\_room\\_service, \\\\ & has\\_beach\\_access, has\\_fitness\\_class, has\\_laundry\\_service, \\\\ & has\\_valet\\_parking, has\\_balcony, has\\_rooftop\\_bar, has\\_inroom\\_Kitchen, \\\\ & has\\_kids\\_club, has\\_meeting\\_rooms, has\\_electric\\_vehicle\\_charging, \\\\ & has\\_hot\\_tub, has\\_sauna, has\\_free\\_parking, is\\_wheelchair\\_accessible, \\\\ & has\\_skiing\\_lodging, has\\_ocean\\_view\\_rooms\\_present, has\\_city\\_view\\_rooms\\_present, \\\\ & start\\_date\\_available, end\\_date\\_available \\\\\n Attraction & city, state, name, type, latitude, longitude, neighborhood \\\\\n Restaurant & restaurant\\_name, city, state, neighborhood, \\\\\n & latitude, longitude, rating, price, price\\_per\\_person, has\\_nut\\_allergy\\_options, has\\_dairy\\_allergy\\_options, has\\_shell\\_fish\\_allergy\\_options, \\\\ & has\\_tomato\\_allergy\\_options, has\\_nightshade\\_allergy\\_options, \\\\ & has\\_gluten\\_free\\_options, has\\_vegetarian\\_options, has\\_vegan\\_options, \\\\ & has\\_kosher\\_options, has\\_halal\\_options, cuisine \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Domains and Attributes.} \n\\label{tab:domains-and-attributes}\n\\end{table*}\n\n\\begin{table*}[!ht]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{ll}\n \\toprule \n \\textbf{Domain} & \\textbf{Tools}\n \\\\\n \\textbf{Flights} & search\\_flights, filter\\_flights \\\\\n \\textbf{Hotels} & search\\_hotels, filter\\_hotels \\\\\n \\textbf{Restaurants} & search\\_restaurants, filter\\_restaurants \\\\\n \\textbf{Attractions} & search\\_attractions, filter\\_attractions \\\\\n \\textbf{Multi-domain} & search\\_nearest \\\\\n \\textbf{Common} & save\\_to\\_cache, get\\_results\\_from\\_cache, sort\\_results, seek\\_information, adjust\\_date \\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{List of Tools.} \n\\label{tab:defined-tools-domain}\n\\end{table*}\n\n\\newpage\n\\section{Sample Conversation from T1 Dataset}\n\n\n\\begin{table*}[!ht]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lll}\n \\toprule \n \\textbf{Attribute} & \\textbf{Type} & \\textbf{Description} \\\\ \\midrule\n airline & string & Airline of the flight, \\\\\n flight\\_classes & string & Classes for the flight (economy, business, first) \\\\\n num\\_layovers & integer & Number of layovers for the flight, between 0 and 2 \\\\\n layover\\_duration\\_amount & integer & Duration of a layover flight. Between 1 and 6 hours \\\\\n airports & list & Airport information for each flight including the city, state, airport code and airport name. \\\\\n \n \\bottomrule\n \\end{tabular}\n}\n\\caption{Flight Ontology Attributes.} \n\\label{tab:flight-ontology-attributes}\n\\end{table*}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lll}\n \\toprule \n \\textbf{Attribute} & \\textbf{Type} & \\textbf{Description} \\\\ \\midrule\n city & string & City that the hotel is in \\\\\n state & string & State that the hotel is in \\\\\n neighborhood & string & Neighborhood within the city that the hotel is in\\\\\n stars & integer & Star rating of the hotel between 1 and 5 \\\\\n rating & float & Customer rating of the hotel between 1.0 and 5.0, incremented by 0.1 \\\\\n price\\_per\\_night & integer & Price per night of the hotel ranging between 20 to 2000 dollars \\\\\n max\\_occupancy & integer & Maximum occupancy per room ranging between 1 and 7 \\\\\n gym\\_present & boolean & Whether or not the hotel has a gym \\\\\n pool\\_present & boolean & Whether or not the hotel has a pool \\\\\n breakfast\\_included & boolean & Whether or not the hotel has breakfast included \\\\\n smoking\\_allowed & boolean & Whether or not the hotel allows smoking \\\\\n air\\_conditioning\\_present & boolean & Whether or not the hotel has air conditioning \\\\\n heating\\_present & boolean & Whether or not the hotel has heating \\\\\n free\\_wifi\\_included & boolean & Whether or not the hotel includes free WiFi \\\\\n airport\\_shuttle\\_present & boolean & Whether or not the hotel has an airport shuffle \\\\\n is\\_pet\\_friendly & boolean & Whether or not the hotel allows pets \\\\\n has\\_spa\\_services & boolean & Whether or not the hotel has spa services \\\\\n has\\_room\\_service & boolean & Whether or not the hotel has room service \\\\\n has\\_beach\\_access & boolean & Whether or not the hotel has access to a beach \\\\\n has\\_business\\_center & boolean & Whether or not the hotel has a business center \\\\\n has\\_fitness\\_classes & boolean & Whether or not the hotel has fitness classes \\\\\n has\\_laundry\\_service & boolean & Whether or not the hotel has laundry services \\\\\n has\\_valet\\_parking & boolean & Whether or not the hotel has valet parking \\\\\n has\\_balcony & boolean & Whether or not the hotel has a balcony \\\\\n has\\_rooftop\\_bar & boolean & Whether or not the hotel has a rooftop bar \\\\\n has\\_inroom\\_kitchen & boolean & Whether or not the hotel has an inroom kitchen \\\\\n has\\_kids\\_club & boolean & Whether or not the hotel has a kids club \\\\\n has\\_meeting\\_rooms & boolean & Whether or not the hotel has meeting rooms \\\\\n has\\_electric\\_vehicle\\_charging & boolean & Whether or not the hotel has electric vehicle charging \\\\\n has\\_hot\\_tub & boolean & Whether or not the hotel has a hot tub \\\\\n has\\_sauna & boolean & Whether or not the hotel has a sauna \\\\ \n has\\_free\\_parking & boolean & Whether or not the hotel has free parking\\\\ \n is\\_wheelchair\\_accessible& boolean & Whether or not the hotel is wheelchair accessible \\\\ \n has\\_skiing\\_lodging & boolean & Whether or not the hotel has skiing and lodging \\\\ \n ocean\\_view\\_rooms\\_present & boolean & Whether or not the hotel has rooms with a view of the ocean \\\\\n city\\_view\\_rooms\\_present & boolean & Whether or not the hotel has rooms with views of the city\\\\\n \\bottomrule\n \\end{tabular}\n}\n\\caption{Hotel Ontology Attributes.} \n\\label{tab:hotel-ontology-attributes}\n\\end{table*}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{\\textwidth}{!}{\n \\begin{tabular}{lll}\n \\toprule \n \\textbf{Attribute} & \\textbf{Type} & \\textbf{Description} \\\\ \\midrule\n city & string & City that the restaurant is in \\\\\n state & string & State that the restaurant is in \\\\\n neighborhood & string & Neighborhood within the city that the restaurant is in\\\\\n rating & float & Customer rating of the restaurant between 1.0 and 5.0, incremented by 0.1 \\\\\n price\\_per\\_person & integer & Average price per person at the restaurant \\\\\n cuisine & string & Cuisine of the restaurant \\\\\n has\\_nut\\_allergy\\_options & boolean & Whether or not the restaurant has any options for individuals with an allergy to nuts \\\\\n has\\_dairy\\_allergy\\_options & boolean & Whether or not restaurant has any options for individuals with an allergy to dairy products \\\\\n has\\_shell\\_fish\\_allergy\\_options & boolean & Whether or not the restaurant has any options for individuals with an allergy to shell fish \\\\\n has\\_tomato\\_allergy\\_options & boolean & Whether or not the restaurant has options for individuals with an allergy to tomatoes \\\\\n has\\_nightshade\\_allergy\\_options & boolean & Whether or not the restaurant has options for individuals with an allergy to nightshades \\\\\n has\\_gluten\\_free\\_options & boolean & Whether or not the restaurant has gluten free options \\\\\n has\\_vegetarian\\_options & boolean & Whether or not the restaurant has vegetarian options \\\\\n has\\_vegan\\_options & boolean & Whether or not the restaurant has vegan options \\\\\n has\\_halal\\_options & boolean & Whether or not the restaurant has halal options \\\\\n has\\_kosher\\_options & boolean & Whether or not the hotel has kosher options \\\\ \n \\bottomrule\n \\end{tabular}\n}\n\\caption{Restaurant Ontology Attributes.} \n\\label{tab:restaurant-ontology-attributes}\n\\end{table*}\n\n\\begin{table*}[!htbp]\n\\centering\n\\resizebox{0.8\\textwidth}{!}{\n \\begin{tabular}{lll}\n \\toprule \n \\textbf{Attribute} & \\textbf{Type} & \\textbf{Description} \\\\ \\midrule\n city & string & City that the attraction is in \\\\\n state & string & State that the attraction is in \\\\\n neighborhood & string & Neighborhood within the city that the attraction is in\\\\\n type & string & Type of the attraction \\\\ \n \\bottomrule\n \\end{tabular}\n}\n\\caption{Attraction Ontology Attributes.} \n\\label{tab:attraction-ontology-attributes}\n\\end{table*}\n\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 1. Sample conversation for attractions,breakable]\n\\textbf{assistant}: Hello! Are you looking for something to do in your free time?\\\\\n\\\\\n\\textbf{user}: Yeah, I am thinking of visiting some scenic attractions in San Antonio.\n\\\\\n\\\\\n\\textbf{assistant}: San Antonio has a lot of great Scenic spots. Have you considered Downtown San Antonio?\n\\\\\n\\\\\n\\textbf{user}: Actually, I haven't. What's there?\n\\\\\n\\\\\n\\textbf{assistant}: It's a great area with a lot of Scenic attractions. I can give you some recommendations.\n\\\\\n\\\\ \n\\textbf{user}: Okay, that sounds good.\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 2. Sample conversation for flights,breakable]\n\\textbf{assistant}: Welcome! What can I help you with today?\\\\\n\\\\\n\\textbf{user}: I need to book a flight from Colorado Springs to San Antonio for my anniversary, and I'm looking for something special.\n\\\\\n\\\\\n\\textbf{assistant}: Happy anniversary! What date are you planning to travel?\n\\\\\n\\\\\n\\textbf{user}: We're thinking of May 21, 2025.\n\\\\\n\\\\\n\\textbf{assistant}: That's great! What kind of flight experience are you looking for? Luxury, perhaps?\n\\\\\n\\\\ \n\\textbf{user}: Yes, something luxurious. And we'd like to depart from COS.\n\\\\\n\\\\\n\\textbf{assistant}: I'll look into that. What's your budget for the flight?\n\\\\\n\\\\ \n\\textbf{user}: We're looking to spend around 1100.\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 3. Sample conversation for hotels,breakable]\n\\textbf{assistant}: Hello, what brings you here today?\\\\\n\\\\\n\\textbf{user}: I'm looking for a hotel in St. Louis for my anniversary, can you help me?\n\\\\\n\\\\\n\\textbf{assistant}: Congratulations on your anniversary! What are your check-in and check-out dates?\n\\\\\n\\\\\n\\textbf{user}: We're planning to check-in on May 18, 2025 and check-out on May 29, 2025.\n\\\\\n\\\\\n\\textbf{assistant}: That's great! How many rooms do you need and what's your budget per night?\n\\\\\n\\\\ \n\\textbf{user}: We need 3 room and our budget is around 550 per night.\n\\\\\n\\\\\n\\textbf{assistant}: I see. What kind of amenities are you looking for in a hotel?\n\\\\\n\\\\ \n\\textbf{user}: We'd like a hotel with a gym, pool, and air conditioning.\n\\\\\n\\\\\n\\textbf{assistant}: Got it. Would you prefer a hotel in a specific neighborhood in St. Louis?\n\\\\\n\\\\ \n\\textbf{user}: Yes, we'd like to stay in Downtown St. Louis.\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 4. Sample conversation for restaurants,breakable]\n\\textbf{assistant}: assistant: Welcome, what brings you here today?\\\\\n\\\\\n\\textbf{user}: I'm gluten-free and I'm looking for a restaurant that can accommodate my dietary needs.\n\\\\\n\\\\\n\\textbf{assistant}: Don't worry, I'm here to help. What kind of cuisine are you interested in?\n\\\\\n\\\\\n\\textbf{user}: I'm really craving Livonian.\n\\\\\n\\\\\n\\textbf{assistant}: There are some great Livonian places that offer gluten-free options. Are you looking for something in a specific neighborhood?\n\\\\\n\\\\ \n\\textbf{user}: Yeah, I'd love something in Las Vegas somewhere in Summerlin.\n\\\\\n\\\\\n\\textbf{assistant}: I can check what's available in Summerlin. What's your budget for this meal?\n\\\\\n\\\\ \n\\textbf{user}: I'm looking to spend around 120 per person.\n\\\\\n\\\\\n\\textbf{assistant}: That helps. Would you like me to recommend a few places that fit your criteria?\n\\\\\n\\\\ \n\\textbf{user}: Please do.\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 5. Sample conversation for flight and hotels,breakable]\n\\textbf{assistant}: assistant: Hello, how can I assist you today?\n\\\\\n\\\\\n\\textbf{user}: I'm looking for a flight from Atlanta to Memphis and a hotel in Memphis\n\\\\\n\\\\\n\\textbf{assistant}: What are your travel dates?\n\\\\\n\\\\\n\\textbf{user}: My departure date is May 18, 2025 and I'd like to return on June 1, 2025\n\\\\\n\\\\\n\\textbf{assistant}: What class of flight are you interested in?\n\\\\\n\\\\ \n\\textbf{user}: user: I'd prefer business\n\\\\\n\\\\\n\\textbf{assistant}: And for your hotel, what star rating are you looking for?\n\\\\\n\\\\ \n\\textbf{user}: I'd like a 2 star hotel in Downtown Memphis\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 6. Sample conversation for hotel and restaurant,breakable]\n\\textbf{assistant}: assistant: Hello! How can I assist you today?\n\\\\\n\\\\\n\\textbf{user}: I'm looking for a hotel in San Antonio and a restaurant that serves Turkish.\n\\\\\n\\\\\n\\textbf{assistant}: That sounds like a great plan! Can you tell me a bit more about your hotel preferences, such as the number of rooms and check-in date?\n\\\\\n\\\\\n\\textbf{user}: I need 3 rooms for 5 people, checking in on May 22, 2025 and checking out on May 27, 2025.\n\\\\\n\\\\\n\\textbf{assistant}: I'd be happy to help you with that. What's your budget per night for the hotel?\n\\\\\n\\\\ \n\\textbf{user}: I'm looking to spend around 50 per night.\n\\\\\n\\\\\n\\textbf{assistant}: That's helpful to know. For the restaurant, are you looking for something with a specific rating or price range?\n\\\\\n\\\\ \n\\textbf{user}: Yes, I'd like a restaurant with a rating of at least 3.5 and a price range of around 85.\n\\\\\n\\\\\n\\textbf{assistant}: I'll keep that in mind. Would you like the hotel to have any specific amenities, such as a gym or pool?\n\\\\\n\\\\ \n\\textbf{user}: Yes, a pool would be great. And can you recommend a restaurant with Turkish near the hotel?\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 7. Sample conversation for hotel and attraction,breakable]\n\\textbf{assistant}: Hi there! What brings you here today?\n\\\\\n\\\\\n\\textbf{user}: I'm planning a last-minute trip to Portland for 2 people.\n\\\\\n\\\\\n\\textbf{assistant}: Last-minute trips can be exciting! What's your budget for the hotel?\n\\\\\n\\\\\n\\textbf{user}: We're looking to spend around 55 per night.\n\\\\\n\\\\\n\\textbf{assistant}: Okay, that helps. What's your check-in and check-out date?\n\\\\\n\\\\ \n\\textbf{user}: We're checking in on June 28, 2025 and checking out on July 10, 2025.\n\\\\\n\\\\\n\\textbf{assistant}: Are you interested in any specific attractions in Portland?\n\\\\\n\\\\ \n\\textbf{user}: Yes, we want to visit Pittock Mansion, which is a Social attraction.\n\\\\\n\\\\\n\\textbf{assistant}: That sounds like a great choice! I can help you find a hotel near Pittock Mansion. What kind of amenities are you look for in the hotel?\n\\\\\n\\\\ \n\\textbf{user}: We need a hotel with a gym and wifi.\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 8. Sample conversation for flight-hotel-attraction,breakable]\n\\textbf{assistant}: Hello, I'd be happy to help you plan your trip. What's on your mind?\n\\\\\n\\\\\n\\textbf{user}: I'm thinking of going to Las Vegas for my birthday and I need a business flight from Tucson.\n\\\\\n\\\\\n\\textbf{assistant}: Happy birthday in advance. When are you thinking of traveling?\n\\\\\n\\\\\n\\textbf{user}: We're looking at May 19, 2025 to May 27, 2025.\n\\\\\n\\\\\n\\textbf{assistant}: That's a great time. How many people are traveling?\n\\\\\n\\\\ \n\\textbf{user}: Just 2 of us.\n\\\\\n\\\\\n\\textbf{assistant}: Lovely. For your stay, what kind of hotel are you envisioning?\n\\\\\n\\\\ \n\\textbf{user}: A 2 star hotel with a spa and room service would be perfect. And we'd love to stay near Fountains of Bellagio with a beautiful view.\n\\\\\n\\\\\n\\textbf{assistant}: That sounds like a great choice! I can help you find a hotel near Pittock Mansion. What kind of amenities are you look for in the hotel?\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[colback=gray!10,colframe=black,title=Box 9. Sample conversation for flight-hotel-restaurant,breakable]\n\\textbf{assistant}: Welcome to our travel assistant. How can I help you today?\n\\\\\n\\\\\n\\textbf{user}: I'm looking to travel from Tucson to St. Louis for a business trip.\n\\\\\n\\\\\n\\textbf{assistant}: What are your preferred travel dates?\n\\\\\n\\\\\n\\textbf{user}: I'd like to fly out on May 18, 2025 and come back on June 1, 2025\n\\\\\n\\\\\n\\textbf{assistant}: What class would you like to fly in?\n\\\\\n\\\\ \n\\textbf{user}: I prefer first.\n\\\\\n\\\\\n\\textbf{assistant}: Great, I can look into that. Where would you like to stay in St. Louis?\n\\\\\n\\\\ \n\\textbf{user}: I'd like a hotel in Downtown St. Louis with a 3 star rating.\n\\\\\n\\\\\n\\textbf{assistant}: And what kind of restaurant are you looking for?\n\\\\\n\\\\ \n\\textbf{user}: I'd like a restaurant in Downtown St. Louis with a rating of at least 3.5.\n\\end{tcolorbox}\n\n% \\section{Appendix / supplemental material}\n\n% \\section{System Prompt for Generating Planner Code}\n% \\label{appendix:prompt-design-system-planner}\n\n\\section{System Prompt Design for Single-Domain Template Generation}\n\\label{appendix:prompt-design-user-planner}\n\nThis section details the unified system prompt and its domain-specific customizations used for generating diverse, realistic multi-turn conversations for four domains: \\textbf{Flights, Hotels, Attractions, and Restaurants}.\n\n\\subsection{Unified Prompt Instructions (Common Across Domains)}\n\nThe following design principles apply across all domains to ensure consistency, diversity, and realism in the generated templates:\n\n\\begin{itemize}[leftmargin=1.5em]\n \\item \\textbf{Conversation Format:}\n \\begin{itemize}\n \\item Each template contains 6–8 dialogue turns (3–4 exchanges).\n \\item Each template starts with an \\texttt{assistant} turn and ends with a \\texttt{user} turn.\n \\item Turns alternate between \\texttt{assistant:} and \\texttt{user:}.\n \\end{itemize}\n\n \\item \\textbf{Placeholder Handling:}\n \\begin{itemize}\n \\item Use numbered placeholders like \\texttt{<CITY\\_1>}, \\texttt{<PRICE\\_2>}.\n \\item Numbering resets at the start of each new template.\n \\end{itemize}\n\n \\item \\textbf{Assistant Behavior Diversity:}\n \\begin{itemize}\n \\item Vary personality: formal/informal, concise/verbose.\n \\item Ask both open-ended and specific questions.\n \\item Do not assume user intent or provide options in the first message.\n \\item Correct misunderstandings if needed.\n \\end{itemize}\n\n \\item \\textbf{User Behavior Diversity:}\n \\begin{itemize}\n \\item Include verbose, terse, indecisive, and overly specific users.\n \\item Some users provide minimal context; others give excess information.\n \\item Include questions that revisit or skip steps.\n \\end{itemize}\n\n \\item \\textbf{Flow Diversity:}\n \\begin{itemize}\n \\item Avoid fixed dialogue patterns (e.g., greet $\\rightarrow$ date $\\rightarrow$ options).\n \\item Allow nonlinear flow: backtracking, parallel requests, etc.\n \\end{itemize}\n\n \\item \\textbf{Language Diversity:}\n \\begin{itemize}\n \\item Vary greetings, transitions, sentence structure, and phrasings.\n \\item No repeated phrasing across templates.\n \\end{itemize}\n\n \\item \\textbf{Output Requirements:}\n \\begin{itemize}\n \\item Output format is strict JSON with keys like \\texttt{\"template\\_1\"} through \\texttt{\"template\\_30\"}.\n \\item Each value is a newline-separated conversation string.\n \\item No preambles or postambles allowed.\n \\end{itemize}\n\\end{itemize}\n\n\\subsection{Domain-Specific Customization}\n\n\\begin{table}[!ht]\n\\centering\n\\small\n\\renewcommand{\\arraystretch}{1.3}\n\\begin{tabular}{|l|p{5.5cm}|p{7.5cm}|}\n\\hline\n\\textbf{Domain} & \\textbf{Placeholders Used} & \\textbf{Required Scenarios} \\\\\n\\hline\n\\textbf{Flight} & \n\\texttt{<CITY\\_x>}, \\texttt{<CLASS\\_x>}, \\texttt{<DEPARTURE\\_DATE\\_x>}, \\texttt{<DEPARTURE\\_TIME\\_x>}, \\texttt{<ARRIVAL\\_DATE\\_x>}, \\texttt{<ARRIVAL\\_TIME\\_x>}, \\texttt{<AIRLINE\\_x>}, \\texttt{<PRICE\\_x>}, \\texttt{<AIRPORT\\_x>}, \\texttt{<NUM\\_TRAVELERS\\_x>} & \nRound trip (with 2 departure dates), one-way, multi-city, strict arrival time, flexible dates, large group bookings, solo/business/family travel, weekend getaways, budget constraints, special occasions (e.g., birthdays) \\\\\n\\hline\n\n\\textbf{Hotel} & \n\\texttt{<CHECK\\_IN\\_DATE\\_x>}, \\texttt{<CHECK\\_OUT\\_DATE\\_x>}, \\texttt{<CITY\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>}, \\texttt{<STAR\\_x>}, \\texttt{<RATING\\_x>}, \\texttt{<PRICE\\_x>}, \\texttt{<NUM\\_ROOMS\\_x>}, \\texttt{<NUM\\_TRAVELERS\\_x>} & \nMulti-city trips, multiple hotels in one city, specific neighborhoods, special occasions, last-minute reservations, business vs. leisure, extended stays, view/accessibility/pet-friendly requests, family and group accommodations \\\\\n\\hline\n\n\\textbf{Attraction} & \n\\texttt{<ATTRACTION\\_TYPE\\_x>}, \\texttt{<CITY\\_x>}, \\texttt{<STATE\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>} & \nMulti-type attraction queries, across cities/states, neighborhood-specific exploration, curiosity about state-level offerings. Assistant must ask open-ended questions and only mention placeholders if user provides them. \\\\\n\\hline\n\n\\textbf{Restaurant} & \n\\texttt{<RESTAURANT\\_RATING\\_x>}, \\texttt{<RESTAURANT\\_PRICE\\_x>}, \\texttt{<RESTAURANT\\_CUISINE\\_x>}, \\texttt{<CITY\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>} & \nMulti-city dining, cuisine preferences, dietary restrictions (e.g., nut-free, vegan, halal), budget vs. premium, special occasion dining, rating-focused or casual vs. upscale preferences \\\\\n\\hline\n\\end{tabular}\n\\vspace{1mm}\n\\caption{Domain-specific customization for template generation. Each domain builds on the shared prompt instructions with unique placeholders and required conversation scenarios.}\n\\label{tab:domain-customization}\n\\end{table}\n\\section{System Prompt Design for Multi-Domain Template Generation}\n\\label{appendix:multi-domain-prompt-design}\n\nThis section outlines the system prompt instructions used for generating multi-turn conversations that span multiple domains. These prompts are tailored to create realistic, nonlinear interactions involving combinations of Flights, Hotels, Attractions, and Restaurants.\n\n\\subsection{Unified Prompt Instructions (Shared Across Multi-Domain Prompts)}\n\n\\begin{itemize}[leftmargin=1.5em]\n \\item \\textbf{Conversation Format:}\n \\begin{itemize}\n \\item Each template includes at least 8–10 dialogue turns (4–5 exchanges).\n \\item Each template begins with an \\texttt{assistant} turn and ends with a \\texttt{user} turn.\n \\item Turns alternate between \\texttt{assistant:} and \\texttt{user:}.\n \\end{itemize}\n\n \\item \\textbf{Placeholder Handling:}\n \\begin{itemize}\n \\item Use only predefined placeholders (e.g., \\texttt{<CITY\\_1>}, \\texttt{<DEPARTURE\\_DATE\\_1>}).\n \\item Numbering restarts from 1 in every template.\n \\item Assistant must never mention a placeholder until the user provides it.\n \\end{itemize}\n\n \\item \\textbf{Assistant Behavior:}\n \\begin{itemize}\n \\item Vary personality (formal, informal), verbosity, and strategies (direct vs. open-ended questions).\n \\item Must not assume user intent or combine domain-specific questions unless user initiates.\n \\item Must correct misunderstandings and adapt to user behavior.\n \\end{itemize}\n\n \\item \\textbf{User Behavior:}\n \\begin{itemize}\n \\item Include users who are indecisive, impatient, verbose, overly specific, or vague.\n \\item Users may change their mind, skip steps, or backtrack in conversation.\n \\end{itemize}\n\n \\item \\textbf{Conversation Flow:}\n \\begin{itemize}\n \\item Avoid rigid order (e.g., flight $\\rightarrow$ hotel $\\rightarrow$ attraction).\n \\item Encourage nonlinear scenarios: jumping between domains, multiple questions at once.\n \\end{itemize}\n\n \\item \\textbf{Language and Style:}\n \\begin{itemize}\n \\item Vary greetings, transitions, sentence structures, and terminology across templates.\n \\item Avoid repeated phrasings.\n \\end{itemize}\n\n \\item \\textbf{Output Requirements:}\n \\begin{itemize}\n \\item Format is strict JSON: \\texttt{\"template\\_1\"} through \\texttt{\"template\\_30\"}.\n \\item Each value is a newline-separated string of alternating assistant/user dialogue.\n \\item No preamble, postamble, or markdown allowed.\n \\end{itemize}\n\\end{itemize}\n\n\\subsection{Multi-Domain Scenario Requirements}\n\n\\begin{table}[!ht]\n\\centering\n\\small\n\\renewcommand{\\arraystretch}{1.2}\n\\begin{tabularx}{\\textwidth}{|l|X|X|}\n\\hline\n\\textbf{Domains} & \\textbf{Placeholders Used} & \\textbf{Required Scenarios} \\\\\n\\hline\n\n\\textbf{Flight + Hotel} & \n\\texttt{<CITY\\_x>}, \\texttt{<CLASS\\_x>}, \\texttt{<DEPARTURE\\_DATE\\_x>}, \\texttt{<CHECK\\_IN\\_DATE\\_x>}, \\texttt{<CHECK\\_OUT\\_DATE\\_x>}, \\texttt{<NUM\\_TRAVELERS\\_x>} & \nTrip planning involving both air travel and accommodation. Includes round-trip and one-way flights, hotel stays across one or more cities, budget and luxury travelers, group vs. solo travel, flexible dates, specific preferences like nonstop flights or hotels with amenities (e.g., pool, gym, pet-friendly). \\\\\n\\hline\n\n\\textbf{Flight + Hotel + Attraction} & \nAll flight, hotel, and attraction placeholders (e.g., \\texttt{<CITY\\_x>}, \\texttt{<CHECK\\_IN\\_DATE\\_x>}, \\texttt{<ATTRACTION\\_TYPE\\_x>}) & \nUser planning a full trip involving flights, hotel stays, and sightseeing. Must include: round-trip and one-way flights, multi-city stays, hotels near attractions, flexible schedules, user-provided attraction types or specific attraction names (only when linking to hotel proximity), and special constraints (e.g., group travel, business trips, anniversaries). Assistant must never use placeholder names before user introduces them. Includes amenity discussions and attraction-type grammar handling (e.g., cultural vs. \\texttt{<ATTRACTION\\_TYPE\\_1>} attraction). \\\\\n\\hline\n\n\\textbf{Flight + Hotel + Restaurant} & \nAll flight, hotel, and restaurant placeholders (e.g., \\texttt{<RESTAURANT\\_CUISINE\\_x>}, \\texttt{<RESTAURANT\\_PRICE\\_x>}) & \nEnd-to-end trip planning including flights, accommodation, and dining. Required scenarios include: dietary restrictions, cuisine-first or city-first planning, restaurant proximity to hotel, multiple hotels or restaurants in one city, round-trip and one-way flights, and amenities like pet-friendly or spa. Must feature diverse language, nonlinear flows, and varied user personas. Includes explicit handling of dietary needs (e.g., halal, nut-free, vegetarian), and placeholder logic as per prompt. \\\\\n\\hline\n\n\\textbf{Hotel + Attraction} & \n\\texttt{<CITY\\_x>}, \\texttt{<CHECK\\_IN\\_DATE\\_x>}, \\texttt{<ATTRACTION\\_TYPE\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>} & \nUser looking for accommodations and nearby attractions. Includes: specific neighborhoods, family-friendly vs. solo travel, themed vacations, extended stays, proximity to cultural or outdoor attractions, and cases where attraction type drives hotel location. \\\\\n\\hline\n\n\\textbf{Hotel + Restaurant} & \n\\texttt{<RESTAURANT\\_CUISINE\\_x>}, \\texttt{<HOTEL\\_PRICE\\_x>}, \\texttt{<CITY\\_x\\_NEIGHBORHOOD\\_y>} & \nCombines hotel booking with dining preferences. Includes cuisine-specific searches, budget dining vs. fine dining, dietary needs (gluten-free, halal), special events (anniversaries), restaurant proximity to hotel, and group size considerations. Templates vary in planning flow—some start with hotel, others with restaurants. \\\\\n\\hline\n\n\\end{tabularx}\n\\vspace{1mm}\n\\caption{Multi-domain combinations and scenario requirements. Each configuration builds on the unified instructions with additional placeholder logic and domain-specific complexity.}\n\\label{tab:multi-domain-customization}\n\\end{table}\n\n\\clearpage\n\\section{Example System Prompt: Flight Domain}\n\n\\begin{lstlisting}\nYour task is to generate diverse conversation templates for a flight finder chatbot.\n\nEach template should capture realistic, UNIQUE conversations between a user and an assistant about flight searches.\n\nPlaceholders to Use:\n- Departure city: <CITY_x>\n- Destination arrival city: <CITY_x>\n- Flight class: <CLASS_x>\n- Departure date: <DEPARTURE_DATE_x>\n- Departure time: <DEPARTURE_TIME_x>\n- Destination arrival date: <ARRIVAL_DATE_x>\n- Destination arrival time: <ARRIVAL_TIME_x>\n- Airline name: <AIRLINE_x>\n- Price: <PRICE_x>\n- Airport's name: <AIRPORT_x>\n- Number of travelers: <NUM_TRAVELERS_x>\n\nKey Requirements:\n1. Placeholder Numbering:\n - Use integers for ``x'' (e.g., <CITY_1>, <CITY_2>).\n - Reset numbering to 1 for each new template.\n\n2. Conversation Format & Structure:\n - 6-8 turns minimum per template (3-4 exchanges).\n - Format as alternating assistant: and user: lines.\n - Each template must start with an assistant turn and end with a user turn.\n - Vary conversation lengths-some should be shorter, some longer.\n\n3. Assistant Behavior Diversity:\n - Use distinctly different assistant personalities (formal, casual, verbose, concise).\n - Vary how information is requested (direct questions vs. open-ended).\n - Include templates where the assistant corrects misunderstandings.\n - NOTE: Assistant's first turn must be generic and not assume user intent (e.g., ``How can I help you?\").\n - NOTE: The assistant must not say it has found options for the user.\n\n4. User Behavior Diversity:\n - Create dramatically different user types (impatient, polite, verbose, terse).\n - Include users who provide minimal information (requiring follow-ups).\n - Include users who provide too much information.\n - Include complex, specific requests.\n - Include indecisive users who change their minds.\n\n5. Conversation Flow Diversity:\n - Avoid standard ``greeting -> dates -> preferences -> options'' structure.\n - Include nonlinear conversations (user circles back to earlier topics).\n - Include users asking multiple questions at once.\n - Include conversations skipping obvious steps.\n - Vary order in which info is elicited.\n\n6. Required Scenarios:\n - Multi-city trips\n - Round trip\n - One-way trip\n - Flexible travel dates\n - Users with strong preferences (airline, class, airport, etc.)\n - Non-stop flights only\n - Short layovers are okay\n - Rigid arrival time\n - Special occasions (e.g., anniversaries)\n - Large group bookings\n - Last-minute reservations\n - Business travel\n - Family vacations\n - Solo travelers\n - Budget constraints\n - Weekend getaways\n\n7. Round Trip Requirement:\n - Roundtrip flights must include 2 departure dates.\n\n8. Multiple Travelers:\n - Always include number of travelers via placeholder in multi-person scenarios.\n\n9. Linguistic Diversity:\n - Avoid repeating same greetings across templates.\n - Vary language used for dates, preferences, and constraints.\n - Use different phrasings for similar ideas.\n - Unique transitions between topics.\n - Varied sentence structures and response styles.\n\nImportant: Each template must be fundamentally different in structure, flow, language, and scenario.\n\\end{lstlisting}\n\n\\section{Example System Prompt: Flight-Hotel-Restaurant Domain}\n\n\\begin{lstlisting}\nYour task is to generate diverse conversation templates for a travel assistant chatbot.\n\nEach template should be a realistic and UNIQUE multi-turn interaction between a user and an assistant that includes:\n- Flight search\n- Hotel booking\n- Restaurant recommendations or reservations\n\nPlaceholders to Use:\n- Flight: <CITY_x>, <CLASS_x>, <DEPARTURE_DATE_x>, <DEPARTURE_TIME_x>, <ARRIVAL_DATE_x>, <ARRIVAL_TIME_x>, <AIRLINE_x>, <PRICE_x>, <AIRPORT_x>, <NUM_TRAVELERS_x>\n- Hotel: <HOTEL_x>, <CHECKIN_DATE_x>, <CHECKOUT_DATE_x>, <ROOM_TYPE_x>, <NUM_GUESTS_x>, <PRICE_x>\n- Restaurant: <RESTAURANT_x>, <CUISINE_x>, <RESERVATION_TIME_x>, <RESERVATION_DATE_x>, <PRICE_RANGE_x>, <LOCATION_x>, <NUM_PEOPLE_x>\n\nKey Requirements:\n1. Conversation must include all 3 components: flight, hotel, and restaurant.\n\n2. Placeholder Numbering:\n - Use integers for ``x\" (e.g., <CITY_1>, <CITY_2>).\n - Reset numbering to 1 for each new template.\n\n3. Conversation Format:\n - At least 8 turns (4 full exchanges).\n - Alternating assistant: and user: lines.\n - Assistant always starts the conversation and user always ends it.\n - Vary length and structure across templates.\n\n4. Assistant Behavior Diversity:\n - Include different tones: friendly, formal, efficient, humorous, inquisitive, etc.\n - Vary assistant strategies (confirming info early vs. late, etc.).\n - Assistant cannot confirm bookings or give specific results.\n - Must clarify ambiguous or missing information.\n\n5. User Behavior Diversity:\n - Mix of confident and indecisive users.\n - Include users who change minds mid-conversation.\n - Include users who ask multiple things at once.\n - Include low-information and high-information users.\n\n6. Conversation Flow Diversity:\n - Vary the sequence (flight -> hotel -> restaurant, or restaurant -> hotel -> flight, etc.).\n - Include users jumping between topics or circling back.\n - Include unexpected questions or constraints from users.\n\n7. Required Scenarios:\n - Honeymoon trip\n - Last-minute business travel\n - Budget backpacking vacation\n - Solo food tourism\n - Family summer vacation\n - Couple anniversary trip\n - Conference trip with team\n - Weekend getaway\n - Luxury experience\n - Specific date events (concerts, sports games, etc.)\n\n8. Linguistic Diversity:\n - Avoid repeating phrasing and structures across templates.\n - Vary tone and style significantly.\n - Mix concise and elaborate dialogues.\n\nImportant: Every template must feel distinct from all others in tone, language, structure, and scenario.\n\\end{lstlisting}\n\n\\section{Example System Prompt: Plan Generation Prompt}\n\\label{system-plan-generation-prompt}\n\\begin{lstlisting}\nYou are an expert AI travel planner and your responsibility is to generate Python code using APIs or Tools. \n\\end{lstlisting}\n\n\\section{Example User Prompt: Plan Generation Prompt}\n\\label{user-plan-generation-prompt}\n\\begin{lstlisting}\nYour task is to generate a Python code based on a conversation between the user and the assistant, where the last turn is from the user.\nThe code typically involves calling one or more tools (functions) to help the user in planning their travel request.\nIn the Python code, you need to use the following tools:\n# TOOL CONFIG\n<TOOL_CONFIG>\n# INSTRUCTIONS\n- Track content: Maintain the conversation state across turns and use all known information from earlier in the conversation.\n- As soon as the mandatory parameters (non-optional parameters) are all provided (refer to TOOL CONFIG to find mandatory parameters for each tool), generate the appropriate plan using Python code.\n- Do NOT modify entity values under any circumstances. Use them exactly as they appear in the conversation while populating attributes in the function during code generation.\nFor example, if the city is \"new york\" (lowercase), do not convert it to \"New York\" or \"NYC\".\n- Do not fill optional parameters unless they are explicitly provided in the conversation.\n- When generating seek_information, only mention mandatory parameters (non-optional parameters) that are missing. Never ask for optional parameters using seek_information. Refer to TOOL CONFIG to figure out what the mandatory parameters (non optional parameters) are and check CONVERSATION to know what parameters have been provided by the user. \nFor example, \"seek_information('<explain what mandatory parameters (non-optional parameters) are missing and must be gathered by the assistant>')\"\n- Only generate the code for the domain which the customer has mentioned in the conversation. For example, if user mentioned only about attractions, don't generate the code with restaurants search. Only if the user mentioned searching for restaurant anywhere in the conversation, then only search for restaurants.\n- If a tool result from a previous turn is still valid and relevant, use get_results_from_cache(key=\"<cache_key>\") to retrieve it. Use the cache summary to determine the most appropriate key to select from. If you have many keys in the cache for the same domain. Use the one which would be most relevant.\n- If you generate a tool call and its result could be reused later, save it with save_to_cache(\"<key>\",value). Ensure the cache key is unique and avoid naming collision with previously stored cache key name\n- If a result has already been stored in the cache for a conversation and no new result needs to be generated, do not regenerate the code. Instead, return the code as \"print(\"No planning needed\")\"\n# OUTPUT FORMAT\n- You need to generate the reasoning and the python code. The reasoning should clearly explain the process, steps and the reason behind the python plan that is going to be generated \nThe reasoning should be within the <REASONING> </REASONING> tags and the python code should be within the <CODE> </CODE> tags. Note while generating the python code, never have any markdown tags.\n# EXAMPLES\n<FEW_SHOT_EXAMPLES>\n# CONVERSATION\n<CONVERSATION>\n# CACHE\n<CACHE_FOR_CONVERSATION>\nGiven the provided conversation and cache summary, generate a Python code for the last user turn.\n\\end{lstlisting}\n\n\n\\section{Template: Plan Generation for Fine-Tuning}\n\\begin{lstlisting}\nYou are an expert AI travel planner and your responsibility is to generate Python code using APIs or Tools. \nYour task is to generate a Python code based on a conversation between the user and the assistant, where the last turn is from the user.\nThe code typically involves calling one or more tools (functions) to help the user in planning their travel request.\nIn the Python code, you need to use the following tools:\n# TOOL CONFIG\n<TOOL_CONFIG>\n# INSTRUCTIONS\n- Track content: Maintain the conversation state across turns and use all known information from earlier in the conversation.\n- As soon as the mandatory parameters (non-optional parameters) are all provided (refer to TOOL CONFIG to find mandatory parameters for each tool), generate the appropriate plan using Python code.\n- Do NOT modify entity values under any circumstances. Use them exactly as they appear in the conversation while populating attributes in the function during code generation.\n For example, if the city is \"new york\" (lowercase), do not convert it to \"New York\" or \"NYC\".\n- Do not fill optional parameters unless they are explicitly provided in the conversation.\n- When generating seek_information, only mention mandatory parameters (non-optional parameters) that are missing. Never ask for optional parameters using seek_information. Refer to TOOL CONFIG to figure out what the mandatory parameters (non optional parameters) are and check CONVERSATION to know what parameters have been provided by the user. \n For example, \"seek_information('<explain what mandatory parameters (non-optional parameters) are missing and must be gathered by the assistant>')\"\n- Only generate the code for the domain which the customer has mentioned in the conversation. For example, if user mentioned only about attractions, don't generate the code with restaurants search. Only if the user mentioned searching for restaurant anywhere in the conversation, then only search for restaurants.\n- If a tool result from a previous turn is still valid and relevant, use get_results_from_cache(key=\"<cache_key>\") to retrieve it. Use the cache summary to determine the most appropriate key to select from. If you have many keys in the cache for the same domain. Use the one which would be most relevant.\n- If you generate a tool call and its result could be reused later, save it with save_to_cache(\"<key>\",value). Ensure the cache key is unique and avoid naming collision with previously stored cache key name\n- If a result has already been stored in the cache for a conversation and no new result needs to be generated, do not regenerate the code. Instead, return the code as \"print(\"No planning needed\")\"\n# OUTPUT FORMAT\n- You need to generate only the python code. The python code should be within the <CODE> </CODE> tags. Note while generating the python code, never have any markdown tags.\n# CONVERSATION\n<CONVERSATION>\n# CACHE\n<CACHE_FOR_CONVERSATION>\nGiven the provided conversation and cache summary, generate a Python code for the last user turn.\n\\end{lstlisting}\n\n\\section{Script to replicate SFT} \\label{SFTScript}\n\\begin{lstlisting}\n>> git clone https://github.com/huggingface/trl.git\n>> cd trl\n>> git checkout v0.17.0 # We use the TRL version 0.17.0\n>> pip install -e .\n>> accelerate launch --config_file trl/examples/accelerate_configs/multi_gpu.yaml \\\n trl/scripts/sft.py \\\n --model_name_or_path <YOUR PATH TO A Meta-Llama-3.1-8B-Instruct LOCALLY> \\\n --dataset_name <TRAIN SET OF THE TOOL CALLING IN HUGGINGFACE DATASET FORMAT> \\\n --learning_rate 2.0e-5 \\\n --num_train_epochs 1 \\\n --packing \\\n --per_device_train_batch_size 1 \\\n --gradient_accumulation_steps 8 \\\n --gradient_checkpointing \\\n --logging_steps 25 \\\n --eval_strategy steps \\\n --eval_steps 100 \\\n --use_peft \\\n --lora_r 32 \\\n --lora_alpha 32 \\\n --lora_target_modules q_proj k_proj v_proj o_proj gate_proj up_proj down_proj \\\n --output_dir <SOME OUTPUT DIRECTORY>\\\n --report_to tensorboard \\\n --torch_dtype bfloat16\n\\end{lstlisting}\n\n\n\\end{document}"},"question":{"kind":"string","value":"For the tool call evaluation, what is the largest difference, across all metrics, between the best single-domain result and the best multi-domain result? And what is the metric?"},"answer":{"kind":"string","value":"8.48, Accuracy"},"plan":{"kind":"string","value":"SELECT all metrics under tool call evaluation\nLOOP for each metric\n COMPUTE max_single = max in single-domain\n COMPUTE max_multi = max in multi-domain\n COMPUTE difference = max_single − max_multi\nCOMPUTE target_metric = argmax metric over difference\n\n\nRETURN difference of target_metric, target_metric\n"}}},{"rowIdx":368,"cells":{"paper":{"kind":"string","value":"2511.05407"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t]\n","\\centering\n","\\scalebox{0.92}{\n","\\begin{tabular}{lcccccccccccc}\n","\\toprule\n","\\multirow{2}{*}{Models} & \\multicolumn{4}{c}{Minority} & \\multicolumn{4}{c}{Majority} & \\multicolumn{4}{c}{Minority+Majority} \\\\\n","\\cmidrule(lr){2-5} \\cmidrule(lr){6-9} \\cmidrule(lr){10-13}\n"," & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ &$F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ &$F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ \\\\\n","\\midrule\n","Llama-3-8B & 0.17 & 0.47 & 0.28 & 0.32 & 0.16 & 0.90 & 0.84 & 0.53 & 0.16 & 0.84 & 0.71 & 0.50 \\\\\n","\\quad +\\textbf{M\\textsuperscript{2}PC} & 0.68 & \\textbf{0.55} & 0.61 & 0.61 & 0.19 & 0.94 & \\textbf{0.89} & \\textbf{0.57} & 0.56 & 0.89 & 0.82 & 0.72 \\\\\n","\\midrule\n","Llama-3-8B-UCoT & 0.36 & 0.49 & 0.41 & 0.42 & 0.21 & 0.88 & 0.83 & 0.55 & 0.26 & 0.83 & 0.72 & 0.55 \\\\\n","\\quad +\\textbf{M\\textsuperscript{2}PC} & 0.73 & 0.18 & 0.56 & 0.46 & 0.00 & \\textbf{0.96} & 0.88 & 0.48 & 0.58 & 0.92 & 0.85 & 0.75 \\\\\n","\\midrule\n","Llama-3-8B-CoPeR & 0.29 & 0.53 & 0.37 & 0.41 & \\textbf{0.21} & 0.90 & 0.85 & 0.56 & 0.24 & 0.85 & 0.74 & 0.55 \\\\\n","\\quad +\\textbf{M\\textsuperscript{2}PC} & \\textbf{0.80} & 0.46 & \\textbf{0.70} & \\textbf{0.63} & 0.08 & 0.95 & 0.87 & 0.51 & \\textbf{0.60} & \\textbf{0.92} & \\textbf{0.86} & \\textbf{0.76} \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{\\textbf{Results of the proposed M\\textsuperscript{2}PC:} $F_1$ scores on the validation set across three model backbones, evaluated on minority, majority, and combined user groups. For each model, the reported M\\textsuperscript{2}PC results correspond to the best-performing EM iteration. \n","Llama‑3‑8B refers to the Llama‑3‑8B‑Instruct version.}\n","\\label{tab:em}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\scalebox{0.92}{\\n\",\n \"\\\\begin{tabular}{lcccccccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multirow{2}{*}{Models} & \\\\multicolumn{4}{c}{Minority} & \\\\multicolumn{4}{c}{Majority} & \\\\multicolumn{4}{c}{Minority+Majority} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-5} \\\\cmidrule(lr){6-9} \\\\cmidrule(lr){10-13}\\n\",\n \" & $F_1^{\\\\text{low}}$ & $F_1^{\\\\text{high}}$ &$F_1^{\\\\text{w}}$ & $F_1^{\\\\text{m}}$ & $F_1^{\\\\text{low}}$ & $F_1^{\\\\text{high}}$ & $F_1^{\\\\text{w}}$ & $F_1^{\\\\text{m}}$ &$F_1^{\\\\text{low}}$ & $F_1^{\\\\text{high}}$ & $F_1^{\\\\text{w}}$ & $F_1^{\\\\text{m}}$ \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Llama-3-8B & 0.17 & 0.47 & 0.28 & 0.32 & 0.16 & 0.90 & 0.84 & 0.53 & 0.16 & 0.84 & 0.71 & 0.50 \\\\\\\\\\n\",\n \"\\\\quad +\\\\textbf{M\\\\textsuperscript{2}PC} & 0.68 & \\\\textbf{0.55} & 0.61 & 0.61 & 0.19 & 0.94 & \\\\textbf{0.89} & \\\\textbf{0.57} & 0.56 & 0.89 & 0.82 & 0.72 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Llama-3-8B-UCoT & 0.36 & 0.49 & 0.41 & 0.42 & 0.21 & 0.88 & 0.83 & 0.55 & 0.26 & 0.83 & 0.72 & 0.55 \\\\\\\\\\n\",\n \"\\\\quad +\\\\textbf{M\\\\textsuperscript{2}PC} & 0.73 & 0.18 & 0.56 & 0.46 & 0.00 & \\\\textbf{0.96} & 0.88 & 0.48 & 0.58 & 0.92 & 0.85 & 0.75 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Llama-3-8B-CoPeR & 0.29 & 0.53 & 0.37 & 0.41 & \\\\textbf{0.21} & 0.90 & 0.85 & 0.56 & 0.24 & 0.85 & 0.74 & 0.55 \\\\\\\\\\n\",\n \"\\\\quad +\\\\textbf{M\\\\textsuperscript{2}PC} & \\\\textbf{0.80} & 0.46 & \\\\textbf{0.70} & \\\\textbf{0.63} & 0.08 & 0.95 & 0.87 & 0.51 & \\\\textbf{0.60} & \\\\textbf{0.92} & \\\\textbf{0.86} & \\\\textbf{0.76} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{\\\\textbf{Results of the proposed M\\\\textsuperscript{2}PC:} $F_1$ scores on the validation set across three model backbones, evaluated on minority, majority, and combined user groups. For each model, the reported M\\\\textsuperscript{2}PC results correspond to the best-performing EM iteration. \\n\",\n \"Llama‑3‑8B refers to the Llama‑3‑8B‑Instruct version.}\\n\",\n \"\\\\label{tab:em}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t]\n"," \\centering\n","\\includegraphics[width=\\linewidth]{figs/intro7.pdf}\n"," \\caption{\n"," \\textcolor{orange}{Majority} and \\textcolor{CBlue}{minority} users may assign different satisfaction ratings to system responses employing the same strategy due to varying individual intents and preferences. \n"," Additionally, users within the same group may exhibit similar preference patterns (e.g., cognition-oriented versus emotion-oriented strategies). This suggests that modeling both individual-specific and group-level preferences could be an effective approach for evaluating user feedback in dialogue systems.\n"," }\n"," \\label{fig:main}\n","\\end{figure}\n"],["\\begin{figure*}\n"," \\centering\n","\\includegraphics[width=\\textwidth]{figs/arch2.pdf}\n"," \\caption{The architecture of our proposed method for the user's satisfaction $y$ estimation, $x$ is the concatenation of context $c$ and \\hyperref[sec:UCOT_prompts]{UCoT prompt} $r_\\text{ucot}$.}\n"," \\label{fig:arch}\n","\\end{figure*}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\begin{subfigure}{\\linewidth}\n"," \\centering\n"," \\includegraphics[width=0.9\\linewidth]{figs/bar_major.pdf}\n"," \\label{fig:feedback_majority}\n"," \\end{subfigure}\n"," \\vspace{0.8em}\n"," \\begin{subfigure}{\\linewidth}\n"," \\centering\n"," \\includegraphics[width=0.9\\linewidth]{figs/bar_minor.pdf}\n"," \\label{fig:feedback_minority}\n"," \\end{subfigure}\n"," \\caption{Distribution of feedback scores for cognition‑ and emotion‑oriented supporter response strategies across majority and minority user groups from ESConv dataset.}\n"," \\label{fig:feedback_compare}\n","\\end{figure}\n"],["\\begin{table}[h]\n"," \\centering\n"," \\scalebox{0.91}{\n"," \\begin{tabular}{lcccc}\n"," \\toprule\n"," Models & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$\\\\\n"," \\midrule\n"," \\multicolumn{5}{l}{\\textit{Zero‑shot}}\\\\\n"," Llama‑3.2‑1B & 0.27 & 0.49 & 0.45 & 0.38 \\\\\n"," Llama‑3‑8B & 0.34 & 0.71 & 0.65 & 0.52 \\\\\n"," GPT4.1‑mini & \\textbf{0.40} & 0.67 & 0.62 & 0.53 \\\\\n"," \\midrule\n"," \\multicolumn{5}{l}{\\textit{\\textbf{UCoT}}}\\\\\n"," Llama‑3.2‑1B-UCoT & 0.28 & 0.40 & 0.38 & 0.34 \\\\\n"," Llama‑3‑8B-UCoT & 0.26 & 0.80 & 0.72 & 0.53 \\\\\n"," GPT4.1‑mini-UCoT & 0.38 & 0.57 & 0.54 & 0.47 \\\\\n"," \\midrule\n"," \\multicolumn{5}{l}{\\textit{SFT (with LoRA)}}\\\\\n"," Llama‑3.2‑1B & 0.28 & 0.76 & 0.67 & 0.52 \\\\\n"," Llama‑3.2‑1B-\\textbf{UCoT} & 0.18 & \\textbf{0.88} & 0.75 & 0.53 \\\\\n"," Llama‑3.2‑1B-\\textbf{CoPeR} & 0.27 & 0.85 & 0.74 & 0.56 \\\\\n"," Llama‑3‑8B & 0.24 & 0.82 & 0.71 & 0.53 \\\\\n"," Llama‑3‑8B-\\textbf{UCoT} & 0.27 & 0.86 & 0.75 & 0.56 \\\\\n"," Llama‑3‑8B-\\textbf{CoPeR} & 0.30 & 0.86 & \\textbf{0.76} & \\textbf{0.58} \\\\\n"," \\bottomrule\n"," \\end{tabular}}\n"," \\caption{\\textbf{Results of the proposed UCoT and CoPeR:} Comparison of baseline models and our proposed UCoT and CoPeR module. We report $F_1$ scores on low ($F_1^{\\text{low}}$) and high ($F_1^{\\text{high}}$) satisfaction classes, along with weighted ($F_1^{\\text{w}}$) and macro ($F_1^{\\text{m}}$) averages. \\textbf{Bold} in $F_1$ indicates the best performance. All Llama models refer to the instruction-tuned versions.}\n"," \\label{tab:sft}\n","\\end{table}\n"],["\\begin{table*}[t]\n","\\centering\n","\\scalebox{0.92}{\n","\\begin{tabular}{lcccccccccccc}\n","\\toprule\n","\\multirow{2}{*}{Models} & \\multicolumn{4}{c}{Minority} & \\multicolumn{4}{c}{Majority} & \\multicolumn{4}{c}{Minority+Majority} \\\\\n","\\cmidrule(lr){2-5} \\cmidrule(lr){6-9} \\cmidrule(lr){10-13}\n"," & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ &$F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ &$F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ \\\\\n","\\midrule\n","Llama-3-8B & 0.17 & 0.47 & 0.28 & 0.32 & 0.16 & 0.90 & 0.84 & 0.53 & 0.16 & 0.84 & 0.71 & 0.50 \\\\\n","\\quad +\\textbf{M\\textsuperscript{2}PC} & 0.68 & \\textbf{0.55} & 0.61 & 0.61 & 0.19 & 0.94 & \\textbf{0.89} & \\textbf{0.57} & 0.56 & 0.89 & 0.82 & 0.72 \\\\\n","\\midrule\n","Llama-3-8B-UCoT & 0.36 & 0.49 & 0.41 & 0.42 & 0.21 & 0.88 & 0.83 & 0.55 & 0.26 & 0.83 & 0.72 & 0.55 \\\\\n","\\quad +\\textbf{M\\textsuperscript{2}PC} & 0.73 & 0.18 & 0.56 & 0.46 & 0.00 & \\textbf{0.96} & 0.88 & 0.48 & 0.58 & 0.92 & 0.85 & 0.75 \\\\\n","\\midrule\n","Llama-3-8B-CoPeR & 0.29 & 0.53 & 0.37 & 0.41 & \\textbf{0.21} & 0.90 & 0.85 & 0.56 & 0.24 & 0.85 & 0.74 & 0.55 \\\\\n","\\quad +\\textbf{M\\textsuperscript{2}PC} & \\textbf{0.80} & 0.46 & \\textbf{0.70} & \\textbf{0.63} & 0.08 & 0.95 & 0.87 & 0.51 & \\textbf{0.60} & \\textbf{0.92} & \\textbf{0.86} & \\textbf{0.76} \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{\\textbf{Results of the proposed M\\textsuperscript{2}PC:} $F_1$ scores on the validation set across three model backbones, evaluated on minority, majority, and combined user groups. For each model, the reported M\\textsuperscript{2}PC results correspond to the best-performing EM iteration. \n","Llama‑3‑8B refers to the Llama‑3‑8B‑Instruct version.}\n","\\label{tab:em}\n","\\end{table*}\n"],["\\begin{table*}[t]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{lllllllllllll}\n","\\toprule\n","Models & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\n","\\midrule\n","\\multicolumn{11}{l}{Llama-3-8B+M\\textsuperscript{2}PC} \\\\\n","Maj. & \\textit{0.85(111)} & \\textit{0.68(105)} & \\textbf{0.89(67)} & \\textbf{0.84(60)} & \\textbf{0.91(55)} & \\textbf{0.91(38)} & \\textbf{0.96(38)} & \\textbf{0.92(31)} & \\textbf{0.95(27)} & \\textbf{0.79(21)} \\\\\n","Min. & \\textit{0.60(21)} & \\textit{0.71(21)} & \\textbf{0.68(10)} & \\textbf{0.77(9)} & 0.63(8) & 0.19(7) & \\textbf{0.84(6)} & \\textbf{0.91(6)} & 0.57(5) & \\textbf{1.00(5)} \\\\\n","\\midrule\n","\\multicolumn{11}{l}{Llama-3-8B-UCoT+M\\textsuperscript{2}PC} \\\\\n","Maj. & \\textit{0.68(109)} & \\textit{0.82(104)} & \\textbf{0.94(50)} & \\textbf{0.87(44)} & \\textbf{0.96(42)} & \\textbf{0.93(41)} & \\textbf{0.86(32)} & \\textbf{1.00(31)} & \\textbf{0.89(28)} & \\textbf{1.00(24)} \\\\\n","Min. & \\textit{0.62(29)} & \\textit{0.61(21)} & 0.60(11) & \\textbf{0.87(8)} & \\textbf{0.91(6)} & \\textbf{0.91(6)} & \\textbf{0.78(5)} & \\textbf{0.80(5)} & \\textbf{0.73(4)} & \\textbf{1.00(4)} \\\\\n","\\midrule\n","\\multicolumn{11}{l}{Llama-3-8B-CoPeR+M\\textsuperscript{2}PC} \\\\\n","Maj. & \\textit{0.71(134)} & \\textit{0.79(105)} & \\textbf{0.93(56)} & \\textbf{0.85(48)} & \\textbf{0.94(44)} & \\textbf{0.94(39)} & \\textbf{0.90(30)} & \\textbf{0.90(30)} & \\textbf{0.82(28)} & \\textbf{0.87(27)} \\\\\n","Min. & \\textit{0.70(22)} & \\textit{0.61(21)} & \\textbf{0.67(7)} & \\textbf{0.91(6)} & \\textbf{0.67(6)} & \\textbf{1.00(5)} & \\textbf{0.80(5)} & 0.34(5) & 0.64(4) & 0.33(4) \\\\\n","\\midrule\n","\\end{tabular}\n","}\n","\\end{table*}\n"],["\\begin{table*}[h]\n","\\centering\n","\\resizebox{\\textwidth}{!}{\n","\\begin{tabular}{lllllllllllll}\n","\\midrule\n","Models & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\\\\n","\\midrule\n","\\multicolumn{11}{l}{Llama-3-8B+M\\textsuperscript{2}PC} \\\\\n","Maj. & \\textbf{1.00(18)} & \\textbf{0.91(17)} & \\textbf{1.00(10)} & \\textbf{0.84(9)} & \\textbf{1.00(9)} & \\textbf{1.00(9)} & \\textbf{1.00(6)} & - & - & - \\\\\n","Min. & \\textbf{0.82(5)} & 0.63(5) & 0.00(4) & 0.64(4) & 0.50(4) & \\textbf{0.73(4)} & \\textbf{0.73(4)} & \\textbf{0.73(4)} & \\textbf{0.67(3)} & - \\\\\n","\\midrule\n","\\multicolumn{11}{l}{Llama-3-8B-UCoT+M\\textsuperscript{2}PC} \\\\\n","Maj. & \\textbf{0.88(24)} & \\textbf{0.87(22)} & \\textbf{0.90(15)} & \\textbf{1.00(14)} & \\textbf{1.00(13)} & \\textbf{1.00(12)} & \\textbf{1.00(9)} & \\textbf{1.00(8)} & \\textbf{1.00(5)} & \\textbf{1.00(3)} \\\\\n","Min. & 0.33(4) & \\textbf{1.00(4)} & 0.10(4) & 0.33(3) & 0.53(3) & 0.53(3) & \\textbf{0.67(2)} & \\textbf{0.67(2)} & 0.00(2) & 0.00(2) \\\\\n","\\midrule\n","\\multicolumn{11}{l}{Llama-3-8B-CoPeR+M\\textsuperscript{2}PC} \\\\\n","Maj. & \\textbf{0.91(22)} & \\textbf{0.94(20)} & \\textbf{0.90(19)} & \\textbf{0.96(14)} & \\textbf{1.00(9)} & \\textbf{1.00(8)} & \\textbf{1.00(8)} & \\textbf{1.00(7)} & \\textbf{1.00(4)} & - \\\\\n","Min. & \\textbf{1.00(4)} & 0.20(4) & \\textbf{0.67(3)} & 0.53(3) & 0.53(3) & \\textbf{0.67(3)} & \\textbf{1.00(3)} & \\textbf{0.67(2)} & \\textbf{1.00(2)} & \\textbf{1.00(2)} \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\caption{Weighted $F_1$ scores across $k \\in {1,\\ldots,20}$ for the majority (Maj.) and minority (Min.) user groups, shown in two parts for readability (top: $k=1$–$10$; bottom: $k=11$–$20$). Numbers in parentheses indicate the number of users in each subgroup, where subgroups ($k=1$–$20$) are ordered by their user counts. Bold values denote subgroups whose weighted $F_1$ exceeds the average of the two largest subgroups (shown in \\textit{italic}).}\n","\\label{tab:k_subgroups}\n","\\end{table*}\n"],["\\begin{table}[h]\n"," \\centering\n"," \\scalebox{0.95}{\n"," \\begin{tabular}{lcccc}\n"," \\toprule\n"," Models & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ \\\\\n"," \\midrule\n"," Llama‑3‑8B\n"," & 0.24 & 0.82 & 0.71 & 0.53 \\\\\n"," \\quad + PPO & 0.25 & 0.85 & 0.74 & 0.55 \\\\\n"," \\quad + \\textbf{PAda‑PPO} & 0.29 & 0.86 & 0.75 & 0.57 \\\\\n"," \\midrule\n"," Llama‑3‑8B-UCoT & 0.27 & 0.86 & 0.75 & 0.56 \\\\\n"," \\quad + PPO & 0.22 & 0.88 & 0.76 & 0.55 \\\\\n"," \\quad + \\textbf{PAda‑PPO} & \\textbf{0.36} & 0.86 & 0.77 & \\textbf{0.61} \\\\\n"," \\midrule\n"," Llama‑3‑8B-CoPeR & 0.30 & 0.86 & 0.76 & 0.58 \\\\\n"," \\quad + PPO & 0.34 & \\textbf{0.88} & \\textbf{0.78} & 0.61\\\\\n"," \\quad + \\textbf{PAda‑PPO} & 0.33 & 0.85 & 0.76 & 0.59 \\\\ \n"," \\bottomrule\n"," \\end{tabular}}\n"," \\caption{\\textbf{Results of the proposed PAda-PPO:} Comparison among SFT, PPO-based RL, and our proposed PAda-PPO method. Llama‑3‑8B refers to the Llama‑3‑8B‑Instruct version.}\n"," \\label{tab:adp_ppo}\n","\\end{table}\n"],["\\begin{table}[h]\n","\\begin{tabular}{@{}llrr@{}}\n","\\toprule\n","Group & Strategy & \\multicolumn{1}{c}{Low} & \\multicolumn{1}{c}{High} \\\\ \\midrule\n","\\multirow{2}{*}{Majority} & Cognition & 302 (0.09) & 3020 (0.91) \\\\\n"," & Emotion & 120 (0.06) & 1826 (0.94) \\\\\n","\\multirow{2}{*}{Minority} & Cognition & 542 (0.67) & 264 (0.33) \\\\\n"," & Emotion & 240 (0.56) & 192 (0.44) \\\\ \\bottomrule\n","\\end{tabular}\n","\\caption{Counts and proportion of groups by support strategy and satisfaction score}\n","\\label{tab:feedback_compare}\n","\\end{table}\n"],["\\begin{figure}[h]\n"," \\centering\n","\\includegraphics[width=\\linewidth]{figs/combined_f1_plots.pdf}\n"," \\caption{Results on the EM iterations during the Majority-Minority Preference-Aware Clustering stage.}\n"," \\label{fig:em_compare}\n","\\end{figure}\n"],["\\begin{figure*}\n"," \\centering\n","\\includegraphics[width=0.93\\textwidth]{figs/prompt_base.pdf}\n"," \\caption{Base prompt.}\n"," \\label{fig:base_prompt}\n","\\end{figure*}\n"],["\\begin{figure*}\n"," \\centering\n","\\includegraphics[width=0.93\\textwidth]{figs/prompt_ucot.pdf}\n"," \\caption{Prompt for User-specific Chain-of-Thought.}\n"," \\label{fig:prompt_cot}\n","\\end{figure*}\n"],["\\begin{figure*}\n"," \\centering\n","\\includegraphics[width=0.93\\textwidth]{figs/coper.pdf}\n"," \\caption{Prompt for User-specific Chains-of-Personalized-Reasoning synthesis.}\n"," \\label{fig:prompt_coper}\n","\\end{figure*}\n"],["\\begin{figure*}\n"," \\centering\n","\\includegraphics[width=0.93\\textwidth]{figs/cases.pdf}\n"," \\caption{Case Studies.}\n"," \\label{fig:cases}\n","\\end{figure*}\n"],["\\begin{table*}[h]\n"," \\centering\n"," \\scalebox{0.83}{\n"," \\begin{tabular}{@{}l ll\n"," rrrr\n"," rrrr\n"," rrrr@{}}\n"," \\toprule\n"," \\multirow{2}{*}{Iteration} & \\multirow{2}{*}{Users$_{\\text{minor}}$} & \\multirow{2}{*}{Users$_{\\text{major}}$}\n"," & \\multicolumn{4}{c}{Minority}\n"," & \\multicolumn{4}{c}{Majority}\n"," & \\multicolumn{4}{c}{Minority+Majority} \\\\\n"," \\cmidrule(lr){4-7}\\cmidrule(lr){8-11}\\cmidrule(lr){12-15}\n"," & & & $F^{\\text{low}}_1$ & $F^{\\text{high}}_1$ & $F^{\\text{w}}_1$ & $F^{\\text{m}}_1$\n"," & $F^{\\text{low}}_1$ & $F^{\\text{high}}_1$ & $F^{\\text{w}}_1$ & $F^{\\text{m}}_1$\n"," & $F^{\\text{low}}_1$ & $F^{\\text{high}}_1$ & $F^{\\text{w}}_1$ & $F^{\\text{m}}_1$ \\\\\n"," \\midrule\n","\n"," 0 & 10 & 10 & 0.29 & 0.53 & 0.37 & 0.41 & 0.15 & 0.91 & 0.85 & 0.53 & 0.22 & 0.85 & 0.73 & 0.54 \\\\\n"," \\rowcolor{paleGrayGreen} \n"," 1 & 10 & 10 & 0.73 & 0.46 & 0.63 & 0.60 & 0.06 & 0.94 & 0.87 & 0.50 & 0.56 & 0.90 & 0.84 & 0.73 \\\\\n"," 2 & 10 & 10 & 0.72 & 0.40 & 0.61 & 0.56 & 0.09 & 0.94 & 0.88 & 0.52 & 0.56 & 0.90 & 0.84 & 0.73 \\\\\n"," 3 & 9 & 11 & 0.72 & 0.37 & 0.60 & 0.54 & 0.11 & 0.94 & 0.87 & 0.52 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\n"," 4 & 8 & 12 & 0.70 & 0.26 & 0.56 & 0.48 & 0.08 & 0.94 & 0.85 & 0.51 & 0.50 & 0.90 & 0.83 & 0.70 \\\\\n"," 5 & 9 & 11 & 0.71 & 0.30 & 0.57 & 0.51 & 0.03 & 0.94 & 0.86 & 0.48 & 0.52 & 0.90 & 0.83 & 0.71 \\\\\n"," \\midrule\n","\n"," 0 & 20 & 20 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\n"," 1 & 18 & 22 & 0.75 & 0.46 & 0.66 & 0.60 & 0.09 & 0.95 & 0.88 & 0.52 & 0.56 & 0.91 & 0.85 & 0.74 \\\\\n"," \\rowcolor{paleGrayGreen} \n"," 2 & 17 & 23 & 0.80 & 0.46 & 0.70 & 0.63 & 0.08 & 0.95 & 0.87 & 0.51 & 0.60 & 0.92 & 0.86 & 0.76 \\\\\n"," 3 & 16 & 24 & 0.75 & 0.31 & 0.62 & 0.53 & 0.00 & 0.93 & 0.85 & 0.47 & 0.52 & 0.90 & 0.83 & 0.71 \\\\\n"," 4 & 15 & 25 & 0.79 & 0.38 & 0.67 & 0.58 & 0.09 & 0.94 & 0.86 & 0.52 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\n"," 5 & 17 & 23 & 0.72 & 0.36 & 0.60 & 0.54 & 0.07 & 0.94 & 0.86 & 0.50 & 0.51 & 0.90 & 0.83 & 0.71 \\\\\n"," \\midrule\n","\n"," 0 & 30 & 30 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\n"," \\rowcolor{paleGrayGreen} \n"," 1 & 27 & 33 & 0.73 & 0.40 & 0.63 & 0.57 & 0.12 & 0.95 & 0.88 & 0.53 & 0.56 & 0.91 & 0.85 & 0.74 \\\\\n"," 2 & 23 & 37 & 0.77 & 0.42 & 0.67 & 0.60 & 0.07 & 0.94 & 0.85 & 0.50 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\n"," 3 & 25 & 35 & 0.73 & 0.22 & 0.58 & 0.47 & 0.03 & 0.94 & 0.86 & 0.48 & 0.53 & 0.90 & 0.83 & 0.71 \\\\\n"," 4 & 25 & 35 & 0.73 & 0.29 & 0.60 & 0.51 & 0.03 & 0.94 & 0.86 & 0.49 & 0.54 & 0.91 & 0.84 & 0.72 \\\\\n"," 5 & 24 & 36 & 0.77 & 0.47 & 0.68 & 0.62 & 0.05 & 0.94 & 0.86 & 0.50 & 0.55 & 0.91 & 0.85 & 0.73 \\\\\n"," \\midrule\n","\n"," 0 & 40 & 40 & 0.29 & 0.53 & 0.37 & 0.41 & 0.15 & 0.91 & 0.85 & 0.53 & 0.22 & 0.85 & 0.73 & 0.54 \\\\\n"," \\rowcolor{paleGrayGreen} \n"," 1 & 34 & 46 & 0.78 & 0.39 & 0.67 & 0.59 & 0.10 & 0.94 & 0.87 & 0.52 & 0.59 & 0.91 & 0.85 & 0.75 \\\\\n"," 2 & 31 & 49 & 0.78 & 0.46 & 0.69 & 0.62 & 0.00 & 0.94 & 0.85 & 0.47 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\n"," 3 & 31 & 49 & 0.74 & 0.35 & 0.63 & 0.55 & 0.03 & 0.94 & 0.85 & 0.48 & 0.51 & 0.90 & 0.83 & 0.71 \\\\\n"," 4 & 33 & 47 & 0.76 & 0.42 & 0.66 & 0.59 & 0.03 & 0.94 & 0.86 & 0.48 & 0.54 & 0.91 & 0.84 & 0.72 \\\\\n"," 5 & 27 & 53 & 0.83 & 0.47 & 0.73 & 0.65 & 0.02 & 0.93 & 0.83 & 0.48 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\n"," \\midrule\n","\n"," 0 & 50 & 50 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\n"," 1 & 40 & 60 & 0.71 & 0.35 & 0.59 & 0.53 & 0.05 & 0.94 & 0.85 & 0.49 & 0.50 & 0.90 & 0.82 & 0.70 \\\\\n"," 2 & 43 & 57 & 0.73 & 0.47 & 0.64 & 0.60 & 0.08 & 0.94 & 0.87 & 0.51 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\n"," 3 & 37 & 63 & 0.83 & 0.47 & 0.73 & 0.65 & 0.11 & 0.93 & 0.85 & 0.52 & 0.58 & 0.91 & 0.85 & 0.75 \\\\\n"," \\rowcolor{paleGrayGreen}\n"," 4 & 42 & 58 & 0.77 & 0.36 & 0.63 & 0.57 & 0.06 & 0.94 & 0.87 & 0.50 & 0.59 & 0.91 & 0.85 & 0.75 \\\\\n"," 5 & 36 & 64 & 0.77 & 0.38 & 0.64 & 0.58 & 0.13 & 0.93 & 0.85 & 0.53 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\n"," \\bottomrule\n"," \\end{tabular}}\n"," \\caption{Results of the proposed \\textbf{Llama-3-8B-CoPeR + M\\textsuperscript{2}PC}, when initializing majority and minority users as 10, 20, 30, 40, and 50, respectively.}\n"," \\label{tab: users}\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \"\\\\includegraphics[width=\\\\linewidth]{figs/intro7.pdf}\\n\",\n \" \\\\caption{\\n\",\n \" \\\\textcolor{orange}{Majority} and \\\\textcolor{CBlue}{minority} users may assign different satisfaction ratings to system responses employing the same strategy due to varying individual intents and preferences. \\n\",\n \" Additionally, users within the same group may exhibit similar preference patterns (e.g., cognition-oriented versus emotion-oriented strategies). This suggests that modeling both individual-specific and group-level preferences could be an effective approach for evaluating user feedback in dialogue systems.\\n\",\n \" }\\n\",\n \" \\\\label{fig:main}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}\\n\",\n \" \\\\centering\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{figs/arch2.pdf}\\n\",\n \" \\\\caption{The architecture of our proposed method for the user's satisfaction $y$ estimation, $x$ is the concatenation of context $c$ and \\\\hyperref[sec:UCOT_prompts]{UCoT prompt} $r_\\\\text{ucot}$.}\\n\",\n \" \\\\label{fig:arch}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\begin{subfigure}{\\\\linewidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.9\\\\linewidth]{figs/bar_major.pdf}\\n\",\n \" \\\\label{fig:feedback_majority}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\\\vspace{0.8em}\\n\",\n \" \\\\begin{subfigure}{\\\\linewidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.9\\\\linewidth]{figs/bar_minor.pdf}\\n\",\n \" \\\\label{fig:feedback_minority}\\n\",\n \" \\\\end{subfigure}\\n\",\n \" \\\\caption{Distribution of feedback scores for cognition‑ and emotion‑oriented supporter response strategies across majority and minority user groups from ESConv dataset.}\\n\",\n \" \\\\label{fig:feedback_compare}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\scalebox{0.91}{\\n\",\n \" \\\\begin{tabular}{lcccc}\\n\",\n \" \\\\toprule\\n\",\n \" Models & $F_1^{\\\\text{low}}$ & $F_1^{\\\\text{high}}$ & $F_1^{\\\\text{w}}$ & $F_1^{\\\\text{m}}$\\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{5}{l}{\\\\textit{Zero‑shot}}\\\\\\\\\\n\",\n \" Llama‑3.2‑1B & 0.27 & 0.49 & 0.45 & 0.38 \\\\\\\\\\n\",\n \" Llama‑3‑8B & 0.34 & 0.71 & 0.65 & 0.52 \\\\\\\\\\n\",\n \" GPT4.1‑mini & \\\\textbf{0.40} & 0.67 & 0.62 & 0.53 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{5}{l}{\\\\textit{\\\\textbf{UCoT}}}\\\\\\\\\\n\",\n \" Llama‑3.2‑1B-UCoT & 0.28 & 0.40 & 0.38 & 0.34 \\\\\\\\\\n\",\n \" Llama‑3‑8B-UCoT & 0.26 & 0.80 & 0.72 & 0.53 \\\\\\\\\\n\",\n \" GPT4.1‑mini-UCoT & 0.38 & 0.57 & 0.54 & 0.47 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" \\\\multicolumn{5}{l}{\\\\textit{SFT (with LoRA)}}\\\\\\\\\\n\",\n \" Llama‑3.2‑1B & 0.28 & 0.76 & 0.67 & 0.52 \\\\\\\\\\n\",\n \" Llama‑3.2‑1B-\\\\textbf{UCoT} & 0.18 & \\\\textbf{0.88} & 0.75 & 0.53 \\\\\\\\\\n\",\n \" Llama‑3.2‑1B-\\\\textbf{CoPeR} & 0.27 & 0.85 & 0.74 & 0.56 \\\\\\\\\\n\",\n \" Llama‑3‑8B & 0.24 & 0.82 & 0.71 & 0.53 \\\\\\\\\\n\",\n \" Llama‑3‑8B-\\\\textbf{UCoT} & 0.27 & 0.86 & 0.75 & 0.56 \\\\\\\\\\n\",\n \" Llama‑3‑8B-\\\\textbf{CoPeR} & 0.30 & 0.86 & \\\\textbf{0.76} & \\\\textbf{0.58} \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}}\\n\",\n \" \\\\caption{\\\\textbf{Results of the proposed UCoT and CoPeR:} Comparison of baseline models and our proposed UCoT and CoPeR module. We report $F_1$ scores on low ($F_1^{\\\\text{low}}$) and high ($F_1^{\\\\text{high}}$) satisfaction classes, along with weighted ($F_1^{\\\\text{w}}$) and macro ($F_1^{\\\\text{m}}$) averages. \\\\textbf{Bold} in $F_1$ indicates the best performance. All Llama models refer to the instruction-tuned versions.}\\n\",\n \" \\\\label{tab:sft}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\scalebox{0.92}{\\n\",\n \"\\\\begin{tabular}{lcccccccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\multirow{2}{*}{Models} & \\\\multicolumn{4}{c}{Minority} & \\\\multicolumn{4}{c}{Majority} & \\\\multicolumn{4}{c}{Minority+Majority} \\\\\\\\\\n\",\n \"\\\\cmidrule(lr){2-5} \\\\cmidrule(lr){6-9} \\\\cmidrule(lr){10-13}\\n\",\n \" & $F_1^{\\\\text{low}}$ & $F_1^{\\\\text{high}}$ &$F_1^{\\\\text{w}}$ & $F_1^{\\\\text{m}}$ & $F_1^{\\\\text{low}}$ & $F_1^{\\\\text{high}}$ & $F_1^{\\\\text{w}}$ & $F_1^{\\\\text{m}}$ &$F_1^{\\\\text{low}}$ & $F_1^{\\\\text{high}}$ & $F_1^{\\\\text{w}}$ & $F_1^{\\\\text{m}}$ \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Llama-3-8B & 0.17 & 0.47 & 0.28 & 0.32 & 0.16 & 0.90 & 0.84 & 0.53 & 0.16 & 0.84 & 0.71 & 0.50 \\\\\\\\\\n\",\n \"\\\\quad +\\\\textbf{M\\\\textsuperscript{2}PC} & 0.68 & \\\\textbf{0.55} & 0.61 & 0.61 & 0.19 & 0.94 & \\\\textbf{0.89} & \\\\textbf{0.57} & 0.56 & 0.89 & 0.82 & 0.72 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Llama-3-8B-UCoT & 0.36 & 0.49 & 0.41 & 0.42 & 0.21 & 0.88 & 0.83 & 0.55 & 0.26 & 0.83 & 0.72 & 0.55 \\\\\\\\\\n\",\n \"\\\\quad +\\\\textbf{M\\\\textsuperscript{2}PC} & 0.73 & 0.18 & 0.56 & 0.46 & 0.00 & \\\\textbf{0.96} & 0.88 & 0.48 & 0.58 & 0.92 & 0.85 & 0.75 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Llama-3-8B-CoPeR & 0.29 & 0.53 & 0.37 & 0.41 & \\\\textbf{0.21} & 0.90 & 0.85 & 0.56 & 0.24 & 0.85 & 0.74 & 0.55 \\\\\\\\\\n\",\n \"\\\\quad +\\\\textbf{M\\\\textsuperscript{2}PC} & \\\\textbf{0.80} & 0.46 & \\\\textbf{0.70} & \\\\textbf{0.63} & 0.08 & 0.95 & 0.87 & 0.51 & \\\\textbf{0.60} & \\\\textbf{0.92} & \\\\textbf{0.86} & \\\\textbf{0.76} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{\\\\textbf{Results of the proposed M\\\\textsuperscript{2}PC:} $F_1$ scores on the validation set across three model backbones, evaluated on minority, majority, and combined user groups. For each model, the reported M\\\\textsuperscript{2}PC results correspond to the best-performing EM iteration. \\n\",\n \"Llama‑3‑8B refers to the Llama‑3‑8B‑Instruct version.}\\n\",\n \"\\\\label{tab:em}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{lllllllllllll}\\n\",\n \"\\\\toprule\\n\",\n \"Models & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{11}{l}{Llama-3-8B+M\\\\textsuperscript{2}PC} \\\\\\\\\\n\",\n \"Maj. & \\\\textit{0.85(111)} & \\\\textit{0.68(105)} & \\\\textbf{0.89(67)} & \\\\textbf{0.84(60)} & \\\\textbf{0.91(55)} & \\\\textbf{0.91(38)} & \\\\textbf{0.96(38)} & \\\\textbf{0.92(31)} & \\\\textbf{0.95(27)} & \\\\textbf{0.79(21)} \\\\\\\\\\n\",\n \"Min. & \\\\textit{0.60(21)} & \\\\textit{0.71(21)} & \\\\textbf{0.68(10)} & \\\\textbf{0.77(9)} & 0.63(8) & 0.19(7) & \\\\textbf{0.84(6)} & \\\\textbf{0.91(6)} & 0.57(5) & \\\\textbf{1.00(5)} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{11}{l}{Llama-3-8B-UCoT+M\\\\textsuperscript{2}PC} \\\\\\\\\\n\",\n \"Maj. & \\\\textit{0.68(109)} & \\\\textit{0.82(104)} & \\\\textbf{0.94(50)} & \\\\textbf{0.87(44)} & \\\\textbf{0.96(42)} & \\\\textbf{0.93(41)} & \\\\textbf{0.86(32)} & \\\\textbf{1.00(31)} & \\\\textbf{0.89(28)} & \\\\textbf{1.00(24)} \\\\\\\\\\n\",\n \"Min. & \\\\textit{0.62(29)} & \\\\textit{0.61(21)} & 0.60(11) & \\\\textbf{0.87(8)} & \\\\textbf{0.91(6)} & \\\\textbf{0.91(6)} & \\\\textbf{0.78(5)} & \\\\textbf{0.80(5)} & \\\\textbf{0.73(4)} & \\\\textbf{1.00(4)} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{11}{l}{Llama-3-8B-CoPeR+M\\\\textsuperscript{2}PC} \\\\\\\\\\n\",\n \"Maj. & \\\\textit{0.71(134)} & \\\\textit{0.79(105)} & \\\\textbf{0.93(56)} & \\\\textbf{0.85(48)} & \\\\textbf{0.94(44)} & \\\\textbf{0.94(39)} & \\\\textbf{0.90(30)} & \\\\textbf{0.90(30)} & \\\\textbf{0.82(28)} & \\\\textbf{0.87(27)} \\\\\\\\\\n\",\n \"Min. & \\\\textit{0.70(22)} & \\\\textit{0.61(21)} & \\\\textbf{0.67(7)} & \\\\textbf{0.91(6)} & \\\\textbf{0.67(6)} & \\\\textbf{1.00(5)} & \\\\textbf{0.80(5)} & 0.34(5) & 0.64(4) & 0.33(4) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \"\\\\centering\\n\",\n \"\\\\resizebox{\\\\textwidth}{!}{\\n\",\n \"\\\\begin{tabular}{lllllllllllll}\\n\",\n \"\\\\midrule\\n\",\n \"Models & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{11}{l}{Llama-3-8B+M\\\\textsuperscript{2}PC} \\\\\\\\\\n\",\n \"Maj. & \\\\textbf{1.00(18)} & \\\\textbf{0.91(17)} & \\\\textbf{1.00(10)} & \\\\textbf{0.84(9)} & \\\\textbf{1.00(9)} & \\\\textbf{1.00(9)} & \\\\textbf{1.00(6)} & - & - & - \\\\\\\\\\n\",\n \"Min. & \\\\textbf{0.82(5)} & 0.63(5) & 0.00(4) & 0.64(4) & 0.50(4) & \\\\textbf{0.73(4)} & \\\\textbf{0.73(4)} & \\\\textbf{0.73(4)} & \\\\textbf{0.67(3)} & - \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{11}{l}{Llama-3-8B-UCoT+M\\\\textsuperscript{2}PC} \\\\\\\\\\n\",\n \"Maj. & \\\\textbf{0.88(24)} & \\\\textbf{0.87(22)} & \\\\textbf{0.90(15)} & \\\\textbf{1.00(14)} & \\\\textbf{1.00(13)} & \\\\textbf{1.00(12)} & \\\\textbf{1.00(9)} & \\\\textbf{1.00(8)} & \\\\textbf{1.00(5)} & \\\\textbf{1.00(3)} \\\\\\\\\\n\",\n \"Min. & 0.33(4) & \\\\textbf{1.00(4)} & 0.10(4) & 0.33(3) & 0.53(3) & 0.53(3) & \\\\textbf{0.67(2)} & \\\\textbf{0.67(2)} & 0.00(2) & 0.00(2) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\multicolumn{11}{l}{Llama-3-8B-CoPeR+M\\\\textsuperscript{2}PC} \\\\\\\\\\n\",\n \"Maj. & \\\\textbf{0.91(22)} & \\\\textbf{0.94(20)} & \\\\textbf{0.90(19)} & \\\\textbf{0.96(14)} & \\\\textbf{1.00(9)} & \\\\textbf{1.00(8)} & \\\\textbf{1.00(8)} & \\\\textbf{1.00(7)} & \\\\textbf{1.00(4)} & - \\\\\\\\\\n\",\n \"Min. & \\\\textbf{1.00(4)} & 0.20(4) & \\\\textbf{0.67(3)} & 0.53(3) & 0.53(3) & \\\\textbf{0.67(3)} & \\\\textbf{1.00(3)} & \\\\textbf{0.67(2)} & \\\\textbf{1.00(2)} & \\\\textbf{1.00(2)} \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\caption{Weighted $F_1$ scores across $k \\\\in {1,\\\\ldots,20}$ for the majority (Maj.) and minority (Min.) user groups, shown in two parts for readability (top: $k=1$–$10$; bottom: $k=11$–$20$). Numbers in parentheses indicate the number of users in each subgroup, where subgroups ($k=1$–$20$) are ordered by their user counts. Bold values denote subgroups whose weighted $F_1$ exceeds the average of the two largest subgroups (shown in \\\\textit{italic}).}\\n\",\n \"\\\\label{tab:k_subgroups}\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\scalebox{0.95}{\\n\",\n \" \\\\begin{tabular}{lcccc}\\n\",\n \" \\\\toprule\\n\",\n \" Models & $F_1^{\\\\text{low}}$ & $F_1^{\\\\text{high}}$ & $F_1^{\\\\text{w}}$ & $F_1^{\\\\text{m}}$ \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Llama‑3‑8B\\n\",\n \" & 0.24 & 0.82 & 0.71 & 0.53 \\\\\\\\\\n\",\n \" \\\\quad + PPO & 0.25 & 0.85 & 0.74 & 0.55 \\\\\\\\\\n\",\n \" \\\\quad + \\\\textbf{PAda‑PPO} & 0.29 & 0.86 & 0.75 & 0.57 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Llama‑3‑8B-UCoT & 0.27 & 0.86 & 0.75 & 0.56 \\\\\\\\\\n\",\n \" \\\\quad + PPO & 0.22 & 0.88 & 0.76 & 0.55 \\\\\\\\\\n\",\n \" \\\\quad + \\\\textbf{PAda‑PPO} & \\\\textbf{0.36} & 0.86 & 0.77 & \\\\textbf{0.61} \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \" Llama‑3‑8B-CoPeR & 0.30 & 0.86 & 0.76 & 0.58 \\\\\\\\\\n\",\n \" \\\\quad + PPO & 0.34 & \\\\textbf{0.88} & \\\\textbf{0.78} & 0.61\\\\\\\\\\n\",\n \" \\\\quad + \\\\textbf{PAda‑PPO} & 0.33 & 0.85 & 0.76 & 0.59 \\\\\\\\ \\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}}\\n\",\n \" \\\\caption{\\\\textbf{Results of the proposed PAda-PPO:} Comparison among SFT, PPO-based RL, and our proposed PAda-PPO method. Llama‑3‑8B refers to the Llama‑3‑8B‑Instruct version.}\\n\",\n \" \\\\label{tab:adp_ppo}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[h]\\n\",\n \"\\\\begin{tabular}{@{}llrr@{}}\\n\",\n \"\\\\toprule\\n\",\n \"Group & Strategy & \\\\multicolumn{1}{c}{Low} & \\\\multicolumn{1}{c}{High} \\\\\\\\ \\\\midrule\\n\",\n \"\\\\multirow{2}{*}{Majority} & Cognition & 302 (0.09) & 3020 (0.91) \\\\\\\\\\n\",\n \" & Emotion & 120 (0.06) & 1826 (0.94) \\\\\\\\\\n\",\n \"\\\\multirow{2}{*}{Minority} & Cognition & 542 (0.67) & 264 (0.33) \\\\\\\\\\n\",\n \" & Emotion & 240 (0.56) & 192 (0.44) \\\\\\\\ \\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Counts and proportion of groups by support strategy and satisfaction score}\\n\",\n \"\\\\label{tab:feedback_compare}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[h]\\n\",\n \" \\\\centering\\n\",\n \"\\\\includegraphics[width=\\\\linewidth]{figs/combined_f1_plots.pdf}\\n\",\n \" \\\\caption{Results on the EM iterations during the Majority-Minority Preference-Aware Clustering stage.}\\n\",\n \" \\\\label{fig:em_compare}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}\\n\",\n \" \\\\centering\\n\",\n \"\\\\includegraphics[width=0.93\\\\textwidth]{figs/prompt_base.pdf}\\n\",\n \" \\\\caption{Base prompt.}\\n\",\n \" \\\\label{fig:base_prompt}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}\\n\",\n \" \\\\centering\\n\",\n \"\\\\includegraphics[width=0.93\\\\textwidth]{figs/prompt_ucot.pdf}\\n\",\n \" \\\\caption{Prompt for User-specific Chain-of-Thought.}\\n\",\n \" \\\\label{fig:prompt_cot}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}\\n\",\n \" \\\\centering\\n\",\n \"\\\\includegraphics[width=0.93\\\\textwidth]{figs/coper.pdf}\\n\",\n \" \\\\caption{Prompt for User-specific Chains-of-Personalized-Reasoning synthesis.}\\n\",\n \" \\\\label{fig:prompt_coper}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{figure*}\\n\",\n \" \\\\centering\\n\",\n \"\\\\includegraphics[width=0.93\\\\textwidth]{figs/cases.pdf}\\n\",\n \" \\\\caption{Case Studies.}\\n\",\n \" \\\\label{fig:cases}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[h]\\n\",\n \" \\\\centering\\n\",\n \" \\\\scalebox{0.83}{\\n\",\n \" \\\\begin{tabular}{@{}l ll\\n\",\n \" rrrr\\n\",\n \" rrrr\\n\",\n \" rrrr@{}}\\n\",\n \" \\\\toprule\\n\",\n \" \\\\multirow{2}{*}{Iteration} & \\\\multirow{2}{*}{Users$_{\\\\text{minor}}$} & \\\\multirow{2}{*}{Users$_{\\\\text{major}}$}\\n\",\n \" & \\\\multicolumn{4}{c}{Minority}\\n\",\n \" & \\\\multicolumn{4}{c}{Majority}\\n\",\n \" & \\\\multicolumn{4}{c}{Minority+Majority} \\\\\\\\\\n\",\n \" \\\\cmidrule(lr){4-7}\\\\cmidrule(lr){8-11}\\\\cmidrule(lr){12-15}\\n\",\n \" & & & $F^{\\\\text{low}}_1$ & $F^{\\\\text{high}}_1$ & $F^{\\\\text{w}}_1$ & $F^{\\\\text{m}}_1$\\n\",\n \" & $F^{\\\\text{low}}_1$ & $F^{\\\\text{high}}_1$ & $F^{\\\\text{w}}_1$ & $F^{\\\\text{m}}_1$\\n\",\n \" & $F^{\\\\text{low}}_1$ & $F^{\\\\text{high}}_1$ & $F^{\\\\text{w}}_1$ & $F^{\\\\text{m}}_1$ \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\n\",\n \" 0 & 10 & 10 & 0.29 & 0.53 & 0.37 & 0.41 & 0.15 & 0.91 & 0.85 & 0.53 & 0.22 & 0.85 & 0.73 & 0.54 \\\\\\\\\\n\",\n \" \\\\rowcolor{paleGrayGreen} \\n\",\n \" 1 & 10 & 10 & 0.73 & 0.46 & 0.63 & 0.60 & 0.06 & 0.94 & 0.87 & 0.50 & 0.56 & 0.90 & 0.84 & 0.73 \\\\\\\\\\n\",\n \" 2 & 10 & 10 & 0.72 & 0.40 & 0.61 & 0.56 & 0.09 & 0.94 & 0.88 & 0.52 & 0.56 & 0.90 & 0.84 & 0.73 \\\\\\\\\\n\",\n \" 3 & 9 & 11 & 0.72 & 0.37 & 0.60 & 0.54 & 0.11 & 0.94 & 0.87 & 0.52 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\\\\\\n\",\n \" 4 & 8 & 12 & 0.70 & 0.26 & 0.56 & 0.48 & 0.08 & 0.94 & 0.85 & 0.51 & 0.50 & 0.90 & 0.83 & 0.70 \\\\\\\\\\n\",\n \" 5 & 9 & 11 & 0.71 & 0.30 & 0.57 & 0.51 & 0.03 & 0.94 & 0.86 & 0.48 & 0.52 & 0.90 & 0.83 & 0.71 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\n\",\n \" 0 & 20 & 20 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\\\\\\n\",\n \" 1 & 18 & 22 & 0.75 & 0.46 & 0.66 & 0.60 & 0.09 & 0.95 & 0.88 & 0.52 & 0.56 & 0.91 & 0.85 & 0.74 \\\\\\\\\\n\",\n \" \\\\rowcolor{paleGrayGreen} \\n\",\n \" 2 & 17 & 23 & 0.80 & 0.46 & 0.70 & 0.63 & 0.08 & 0.95 & 0.87 & 0.51 & 0.60 & 0.92 & 0.86 & 0.76 \\\\\\\\\\n\",\n \" 3 & 16 & 24 & 0.75 & 0.31 & 0.62 & 0.53 & 0.00 & 0.93 & 0.85 & 0.47 & 0.52 & 0.90 & 0.83 & 0.71 \\\\\\\\\\n\",\n \" 4 & 15 & 25 & 0.79 & 0.38 & 0.67 & 0.58 & 0.09 & 0.94 & 0.86 & 0.52 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\\\\\\n\",\n \" 5 & 17 & 23 & 0.72 & 0.36 & 0.60 & 0.54 & 0.07 & 0.94 & 0.86 & 0.50 & 0.51 & 0.90 & 0.83 & 0.71 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\n\",\n \" 0 & 30 & 30 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\\\\\\n\",\n \" \\\\rowcolor{paleGrayGreen} \\n\",\n \" 1 & 27 & 33 & 0.73 & 0.40 & 0.63 & 0.57 & 0.12 & 0.95 & 0.88 & 0.53 & 0.56 & 0.91 & 0.85 & 0.74 \\\\\\\\\\n\",\n \" 2 & 23 & 37 & 0.77 & 0.42 & 0.67 & 0.60 & 0.07 & 0.94 & 0.85 & 0.50 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\\\\\\n\",\n \" 3 & 25 & 35 & 0.73 & 0.22 & 0.58 & 0.47 & 0.03 & 0.94 & 0.86 & 0.48 & 0.53 & 0.90 & 0.83 & 0.71 \\\\\\\\\\n\",\n \" 4 & 25 & 35 & 0.73 & 0.29 & 0.60 & 0.51 & 0.03 & 0.94 & 0.86 & 0.49 & 0.54 & 0.91 & 0.84 & 0.72 \\\\\\\\\\n\",\n \" 5 & 24 & 36 & 0.77 & 0.47 & 0.68 & 0.62 & 0.05 & 0.94 & 0.86 & 0.50 & 0.55 & 0.91 & 0.85 & 0.73 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\n\",\n \" 0 & 40 & 40 & 0.29 & 0.53 & 0.37 & 0.41 & 0.15 & 0.91 & 0.85 & 0.53 & 0.22 & 0.85 & 0.73 & 0.54 \\\\\\\\\\n\",\n \" \\\\rowcolor{paleGrayGreen} \\n\",\n \" 1 & 34 & 46 & 0.78 & 0.39 & 0.67 & 0.59 & 0.10 & 0.94 & 0.87 & 0.52 & 0.59 & 0.91 & 0.85 & 0.75 \\\\\\\\\\n\",\n \" 2 & 31 & 49 & 0.78 & 0.46 & 0.69 & 0.62 & 0.00 & 0.94 & 0.85 & 0.47 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\\\\\\n\",\n \" 3 & 31 & 49 & 0.74 & 0.35 & 0.63 & 0.55 & 0.03 & 0.94 & 0.85 & 0.48 & 0.51 & 0.90 & 0.83 & 0.71 \\\\\\\\\\n\",\n \" 4 & 33 & 47 & 0.76 & 0.42 & 0.66 & 0.59 & 0.03 & 0.94 & 0.86 & 0.48 & 0.54 & 0.91 & 0.84 & 0.72 \\\\\\\\\\n\",\n \" 5 & 27 & 53 & 0.83 & 0.47 & 0.73 & 0.65 & 0.02 & 0.93 & 0.83 & 0.48 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\\\\\\n\",\n \" \\\\midrule\\n\",\n \"\\n\",\n \" 0 & 50 & 50 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\\\\\\n\",\n \" 1 & 40 & 60 & 0.71 & 0.35 & 0.59 & 0.53 & 0.05 & 0.94 & 0.85 & 0.49 & 0.50 & 0.90 & 0.82 & 0.70 \\\\\\\\\\n\",\n \" 2 & 43 & 57 & 0.73 & 0.47 & 0.64 & 0.60 & 0.08 & 0.94 & 0.87 & 0.51 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\\\\\\n\",\n \" 3 & 37 & 63 & 0.83 & 0.47 & 0.73 & 0.65 & 0.11 & 0.93 & 0.85 & 0.52 & 0.58 & 0.91 & 0.85 & 0.75 \\\\\\\\\\n\",\n \" \\\\rowcolor{paleGrayGreen}\\n\",\n \" 4 & 42 & 58 & 0.77 & 0.36 & 0.63 & 0.57 & 0.06 & 0.94 & 0.87 & 0.50 & 0.59 & 0.91 & 0.85 & 0.75 \\\\\\\\\\n\",\n \" 5 & 36 & 64 & 0.77 & 0.38 & 0.64 & 0.58 & 0.13 & 0.93 & 0.85 & 0.53 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\\\\\\n\",\n \" \\\\bottomrule\\n\",\n \" \\\\end{tabular}}\\n\",\n \" \\\\caption{Results of the proposed \\\\textbf{Llama-3-8B-CoPeR + M\\\\textsuperscript{2}PC}, when initializing majority and minority users as 10, 20, 30, 40, and 50, respectively.}\\n\",\n \" \\\\label{tab: users}\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"% This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.\n\\pdfoutput=1\n% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.\n\n\\documentclass[11pt]{article}\n\n% Change \"review\" to \"final\" to generate the final (sometimes called camera-ready) version.\n% Change to \"preprint\" to generate a non-anonymous version with page numbers.\n\\usepackage[final]{acl}\n\n% Standard package includes\n\\usepackage{times}\n\\usepackage{latexsym}\n\\usepackage{url}\n\\usepackage{breakurl}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{multirow}\n\\definecolor{CBlue}{RGB}{9, 60, 146}\n\\usepackage{booktabs,multirow}\n\\usepackage[table]{xcolor}\n\\definecolor{lightrow}{gray}{0.93}\n\\newcommand{\\groupheader}[1]{%\n \\noalign{\\vskip -\\belowrulesep}% \n \\multicolumn{15}{@{}>{}l@{}}{\\textbf{#1}}\\\\[-\\aboverulesep]%\n}\n\n\\newcommand{\\hlrow}[1]{\\rowcolor{paleGrayGreen}[0pt][0pt] #1}\n\\definecolor{myLightBlue}{HTML}{E6F2FF}\n\\definecolor{myLightGreen}{HTML}{E8F5E9}\n\\definecolor{paleGrayGreen}{HTML}{E4EDE4}\n% For proper rendering and hyphenation of words containing Latin characters (including in bib files)\n\\usepackage[T1]{fontenc}\n\\usepackage{subcaption}\n\\usepackage{footnote}\n% For Vietnamese characters\n% \\usepackage[T5]{fontenc}\n% See https://www.latex-project.org/help/documentation/encguide.pdf for other character sets\n\n% This assumes your files are encoded as UTF8\n\\usepackage[utf8]{inputenc}\n\\usepackage{caption} % for \\ContinuedFloat\n\n% This is not strictly necessary, and may be commented out,\n% but it will improve the layout of the manuscript,\n% and will typically save some space.\n\\usepackage{microtype}\n\n% This is also not strictly necessary, and may be commented out.\n% However, it will improve the aesthetics of text in\n% the typewriter font.\n\\usepackage{inconsolata}\n\n%Including images in your LaTeX document requires adding\n%additional package(s)\n\\usepackage{graphicx}\n\\usepackage{booktabs}\n\\usepackage[dvipsnames]{xcolor}\n\n% If the title and author information does not fit in the area allocated, uncomment the following\n%\n%\\setlength\\titlebox{<dim>}\n%\n% and set <dim> to something 5cm or larger.\n\n% \\title{Minority-Aware Language Model Alignment via\\\\ Preference-Adaptive Optimization}\n% \\title {Minority-Aware Dialogue Personalization via\\\\ Preference-Adaptive Optimization}\n% \\title{Minority-Aware User Satisfaction Estimation for Dialogue Systems via Preference-Adaptive Optimization}\n% \\title{Minority-Aware Personalized Satisfaction Estimation for Dialogue Systems via Preference-Adaptive Reinforcement Learning}\n\\title{Minority-Aware Satisfaction Estimation in Dialogue Systems via Preference-Adaptive Reinforcement Learning}\n% \\thanks{\\textbf{This manuscript is currently under review. Please treat this as work-in-progress and do not circulate.}}}\n\n\n% Author information can be set in various styles:\n% For several authors from the same institution:\n% \\author{Author 1 \\and ... \\and Author n \\\\\n% Address line \\\\ ... \\\\ Address line}\n% if the names do not fit well on one line use\n% Author 1 \\\\ {\\bf Author 2} \\\\ ... \\\\ {\\bf Author n} \\\\\n% For authors from different institutions:\n% \\author{Author 1 \\\\ Address line \\\\ ... \\\\ Address line\n% \\And ... \\And\n% Author n \\\\ Address line \\\\ ... \\\\ Address line}\n% To start a separate ``row'' of authors use \\AND, as in\n% \\author{Author 1 \\\\ Address line \\\\ ... \\\\ Address line\n% \\AND\n% Author 2 \\\\ Address line \\\\ ... \\\\ Address line \\And\n% Author 3 \\\\ Address line \\\\ ... \\\\ Address line}\n\n% \\author{First Author \\\\\n% Affiliation / Address line 1 \\\\\n% Affiliation / Address line 2 \\\\\n% Affiliation / Address line 3 \\\\\n% \\texttt{email@domain} \\\\\\And\n% Second Author \\\\\n% Affiliation / Address line 1 \\\\\n% Affiliation / Address line 2 \\\\\n% Affiliation / Address line 3 \\\\\n% \\texttt{email@domain} \\\\}\n\n\\author{Yahui Fu, Zi Haur Pang, Tatsuya Kawahara \\\\ Graduate School of Informatics, Kyoto University, Japan\\\\ \\texttt{\\{fu,pang,kawahara\\}@sap.ist.i.kyoto-u.ac.jp}}\n\n\\begin{document}\n\\maketitle\n\n% \\begin{abstract}\n% % User satisfaction in dialogue systems is inherently subjective, therefore minority users may assign different satisfaction ratings than majority users for the same system response due to differing intents.\n\n% % Given the inherent subjectivity of user satisfaction in dialogue systems, minority users may assign satisfaction ratings that differ from those of majority users for the same system response, owing to differing intents. \n% Given the inherent subjectivity of user satisfaction in dialogue systems, minority users may assign different satisfaction ratings than majority users for identical system responses due to varying intents. \n% % Existing alignment methods in reinforcement learning typically rely on aggregated rewards and overlook this preference diversity. \n% Existing methods for aligning language models with diverse human preferences primarily aim to train a one-size-fits-all system that is less controversial, ignoring user adaptation. We propose a unified framework that models both individual-specific and group-level preferences for satisfaction estimation. We first introduce Chain-of-Personalized-Reasoning (\\textbf{CoPeR}) to capture individual preferences via interpretable chains. To learn group preferences, we propose an EM-based Majority-Minority Preference-Aware Clustering (\\textbf{M\\textsuperscript{2}PC}) module that discovers different groups without supervision. Finally, we integrate these components into a preference-adaptive reinforcement learning framework (\\textbf{PAda-PPO}) that jointly aligns with both individual and group preferences. Experiments on the Emotional Support Conversation dataset demonstrate improved satisfaction estimation across both majority and minority populations.\\footnote{We will release our code upon acceptance.}\n% \\end{abstract}\n\n% Given the inherent subjectivity of user satisfaction in dialogue systems, minority users may assign different satisfaction ratings than majority users for system responses due to varying intents and preferences. \n\n% User satisfaction in dialogue systems is inherently subjective, minority users may assign different satisfaction ratings than majority users for system responses employing the same strategy, due to diverse individual intents and preferences. Existing methods for aligning language models with human preferences primarily focus on training universal systems that minimize controversy while overlooking the need for user-specific adaptation. \n\n\\begin{abstract}\nUser satisfaction in dialogue systems is inherently subjective. When the same response strategy is applied across users, minority users may assign different satisfaction ratings than majority users due to variations in individual intents and preferences. However, existing alignment methods typically train one-size-fits-all models that aim for broad consensus, often overlooking minority perspectives and user-specific adaptation. We propose a unified framework that models both individual- and group-level preferences for user satisfaction estimation. First, we introduce Chain-of-Personalized-Reasoning (\\textbf{CoPeR}) to capture individual preferences through interpretable reasoning chains. Second, we propose an expectation--maximization--based Majority-Minority Preference-Aware Clustering (\\textbf{M\\textsuperscript{2}PC}) algorithm that discovers distinct user groups in an unsupervised manner to learn group-level preferences. Finally, we integrate these components into a preference-adaptive reinforcement learning framework (\\textbf{PAda-PPO}) that jointly optimizes alignment with both individual and group preferences. \nExperiments on the Emotional Support Conversation dataset demonstrate consistent improvements in user satisfaction estimation, particularly for underrepresented user groups.\\footnote{Our source code is publicly available at: \\url{https://github.com/fuyahuii/minority-aware-se}.}\n\n\n\n% Experiments on the Emotional Support Conversation dataset demonstrate improved user satisfaction estimation across different users.\n% both majority and minority populations.\n\n\\end{abstract}\n\n\n\\section{Introduction}\n% Large language models (LLMs) such as GPT‑4, Gemini, DeepSeek and Llama series already underpin everyday tools for writing, coding and search, with their behaviour typically steered post‑training by reinforcement learning from human feedback (RLHF), first popularised by InstructGPT \\cite{ouyang2022training}. \n% RLHF learns a single reward model from crowd‑sourced pairwise preferences, effectively averaging annotator votes, \n% Personalization is crucial for human-centric dialogue systems, adapt generation into individual preferences.\nPersonalized dialogue systems that adapt to individual user preferences are crucial for enhancing user satisfaction in human–AI interactions. Accordingly, accurately evaluating whether a dialogue system meets diverse user needs is essential.\n% Accordingly, evaluating whether a dialogue system meets user needs is essential. \n\\begin{figure}[t]\n \\centering\n\\includegraphics[width=\\linewidth]{figs/intro7.pdf}\n \\caption{\n \\textcolor{orange}{Majority} and \\textcolor{CBlue}{minority} users may assign different satisfaction ratings to system responses employing the same strategy due to varying individual intents and preferences. \n Additionally, users within the same group may exhibit similar preference patterns (e.g., cognition-oriented versus emotion-oriented strategies). This suggests that modeling both individual-specific and group-level preferences could be an effective approach for evaluating user feedback in dialogue systems.\n %\\textcolor{CBlue}{Minority users} may assign different satisfaction ratings than \\textcolor{orange}{majority users} for the same system response due to differing intents (individual preference). Besides, users in the same group (majority or minority) may share similar preference trend (eg. cognition-oriented or emotion-oriented), which make modeling both individual-specific and group-level preferences is a possible solving method when evaluating users' feedback in the emotional support conversations.\n }\n \\label{fig:main}\n\\end{figure}\nPrevious research has primarily evaluated dialogue systems using output-centric criteria such as informativeness, relevance, and empathy \\cite{bert-score,fu2023dual,xu2024multi}, as well as user-centric metrics such as satisfaction estimation \\cite{choi2019convSAT,see2021understanding,lin-etal-2024-interpretable}. However, satisfaction is inherently subjective: as illustrated in Figure~\\ref{fig:main}, users may assign divergent satisfaction ratings to the system response employing the same strategy, depending on their individual intents and preferences. \n\nReinforcement learning (RL) with a reward model has become a key approach for aligning language models with human preferences. However, existing reward models typically rely on aggregated human judgments \\cite{touvron2023llama} (e.g., majority voting or averaging), resulting in universal reward functions that overlook minority preferences and lack personalization. This induces preference collapse, where outputs maximize majority preferences while suppressing minority views \\cite{xiao2024algorithmic, yang2024llm, slocum2025diverse}. \n% Meta's alignment pipeline for Llama‑2, for instance, relies on majority voting and thus inherits the same bias \\cite{yang2024llm}. \nRecent methods tried to solve it by considering the diversity of human preferences into reward modeling \\cite{wang2023aligning, jang2023personalized,chakraborty2024maxmin}, but primarily aim to train a one-size-fits-all system that is less controversial. In contrast, we focus on user adaptation by modeling both individual-specific preferences and group-level trends to estimate satisfaction across both minority and majority populations. \n\nSpecifically, we introduce a User-specific Chain-of-Thought (\\textbf{UCoT}) prompting strategy and synthesize Chain-of-Personalized-Reasoning (\\textbf{CoPeR}) outputs, which capture individual user preferences through explicit reasoning, linking the seeker's intent, the supporter's strategy, and the resulting satisfaction. This enables the supervised fine-tuning (SFT) model to acquire interpretable and user-aligned reasoning capabilities. Since users' majority or minority status is unknown in real-world scenarios, predefined group supervision is impractical. To address this, we propose a Majority-Minority Preference-Aware Clustering (\\textbf{M\\textsuperscript{2}PC}) module, built upon the Expectation-Maximization (EM) algorithm \\cite{dempster1977maximum}, which routes users into majority or minority groups in an unsupervised manner by comparing model perplexities over their dialogues. Separate models are then trained to capture group-specific preferences. Finally, we integrate the individual-level SFT model and the group-specific models as the policy and reference models, respectively, within a Proximal Preference Optimization (PPO) \\cite{schulman2017proximal} framework. This results in our Preference-Adaptive Reinforcement Learning (\\textbf{PAda-PPO}) approach, which jointly optimizes for both individual and group-level preferences in user satisfaction estimation. \nOur main contributions are:\n\\begin{itemize}\n \\item To the best of our knowledge, we present the first framework that models both individual- and group-level preferences for satisfaction estimation, capturing user diversity by distinguishing majority and minority preferences. \n \\item We propose \\textbf{UCoT} prompting and \\textbf{CoPeR} synthesis, two CoT-based methods that infer individual satisfaction through explicit reasoning over user intent and system strategy. \n \\item We introduce \\textbf{M\\textsuperscript{2}PC}, an EM-based unsupervised module that clusters users into majority and minority groups by dialogue perplexity, capturing group-level preference trends.\n \\item We develop \\textbf{PAda-PPO}, a preference-adaptive reinforcement learning framework that integrates individual- and group-specific models to optimize satisfaction while preserving diverse user preferences.\n\\end{itemize}\n\n% Consequently, learning from human feedback is well-suited for training models in human-centric dialogue system. Currently, reinforcement learning (RL) with a reward model is the most popular method to align models with human preferences. \n% Existing reward models for LLMs use aggregated human judgments (e.g., majority voting or averaging), resulting in universal reward functions that overlook minority preferences and lack personalization.\n% and mounting evidence shows that this induces preference collapse, where outputs maximise majority preferences while suppressing minority views \\cite{xiao2024algorithmic, slocum2025diverse}. Meta's alignment pipeline for Llama‑2, for instance, relies on majority voting and thus inherits the same bias \\cite{yang2024llm}. \n\n% To take into account of minority preference, previous studies have either trains a Bayesian reward that keeps a posterior over annotator disagreement instead of point estimates, or fits a mixture of preference distributions with an Expectation Maximization (EM) loop and then maximises the minimum group reward, improving worst‑case alignment \\cite{wang2023aligning, chakraborty2024maxmin}. These studies, however, in the end are still trying to generate the same single response that able to fulfill most people needs, instead of the personalizated response that adapt to each and everyone needs, not matter they are from majority group, or minority group. \n\n% Evaluation practices share a parallel weakness. Academic datasets usually rely on indirect proxies—n‑gram overlap, embedding similarity or automatic empathy scores—rather than asking users whether the answer actually met their needs \\cite{xu2024multi}. Recent work shows that LLMs can predict user‑satisfaction labels more transparently than classical features, but these remain system‑centric estimators rather than signals elicited from the user \\cite{lin-etal-2024-interpretable}. \n% Furthermore, social‑identity research demonstrates that people who share a group affiliation also share semantic frames, implying that both individual and group context matter for satisfaction \\cite{vargas2025informational}. Taken together, current systems lack a mechanism that simultaneously respects each user's idiosyncratic tastes, while capturing group‑level regularities and measures satisfaction from the user's own perspective.\n\n% Specifically, we introduce a dual‑tier preference-based user satisfaction score evaluator. The user‑specific module \n% For the group‑oriented module, we proposed a majority-minority preference-aware clustering module which leverage EM algorithm \\cite{dempster1977maximum} to route users into two distinct groups based on the context semantics, and then training a separate model for each. We then propose the Preference-Adaptive Reinforcement Learning, a Proximal Preference Optimization (PPO) \\cite{schulman2017proximal} based framework that incorporates group-specific reference models following the majority–minority clustering to distill shared patterns, preventing data sparsity while avoiding preference collapse. \n% Through utlizting the user-specific module and group-orientated module, our proposed PPO can have a direct while better evaluate on user satisfaction during the interaction. Our main contributions are:\n% Finally, these group-specific models serve as reference models in a preference-adaptive reinforcement learning stage based on the PPO algorithm (PAda-PPO)\n\n\n\\section{Related Work}\n\\subsection{User Satisfaction Estimation}\n\nAccurately predicting user satisfaction is essential for evaluating and improving conversational systems. Prior research has focused on perspectives such as sentiment analysis \\cite{song-etal-2019-using}, context- and dynamics-aware modeling \\cite{choi2019convSAT, see2021understanding, deng-etal-2022-user,ye2023modeling}, and LLM-based frameworks that improve interpretability by inducing human-readable rubrics or dialogue-strategy features \\citep{lin-etal-2024-interpretable,kim-etal-2025-llm}.\nHowever, existing approaches often model all users jointly, which tends to suppress minority preferences. \n% Our approach jointly considers both majority and minority users to achieve more personalized and inclusive satisfaction estimation.\n% Differently, our approach leverages LLM-based reasoning to capture individual preferences and models majority or minority group-level trends, yielding more personalized and interpretable satisfaction estimation.\n\n\\subsection{Chain-of-Thought Prompting}\nChain-of-Thought (CoT) prompting has been widely used with LLMs to improve task performance by encouraging step-by-step reasoning \\cite{wei2022chain, chae2023dialogue, luong2024reft, xie2025leveraging}. For instance, \n% \\citet{chae2023dialogue} propose Dialogue CoT, which decomposes commonsense reasoning into intermediate steps by generating rationales as sequences of inferred knowledge for response generation. \n\\citet{zhang2024escot} introduce ESCoT, which augments emotional support dialogues with emotion- and strategy-focused CoTs to emulate human emotional reasoning. Differently, we leverage CoT prompting to elicit interpretable reasoning traces that explain how user preferences influence the satisfaction score.\n\n% One line of research on personalized chatbots focuses on conditioning generation on fixed persona profiles or integrating personality traits such as the Big Five into model training \\cite{zhang2018personalizing,fu2024styemp}.\n% Another direction explores post-hoc personalization or prompting-based approaches. \n% For instance, Personalized-RLHF attaches a lightweight user embedding to RLHF fine-tuning for per-user adaptation \\cite{li2024personalized}, while Personalized Soups independently trains specialist policies and then merges them post-hoc to avoid per-user RL runs \\cite{jang2023personalized}. Arithmetic-Control and similar multi-objective methods encode preferences as vectors in reward space, allowing on-the-fly style trade-offs \\cite{wang2024arithmetic}. \n\n\\begin{figure*}\n \\centering\n\\includegraphics[width=\\textwidth]{figs/arch2.pdf}\n \\caption{The architecture of our proposed method for the user's satisfaction $y$ estimation, $x$ is the concatenation of context $c$ and \\hyperref[sec:UCOT_prompts]{UCoT prompt} $r_\\text{ucot}$.}\n \\label{fig:arch}\n\\end{figure*}\n\n\n\\subsection{Aligning Language Models with Diverse Human Preferences}\n\nRecent work has incorporated preference diversity into reward modeling for RL-based alignment \\cite{jang2023personalized, wang2023aligning, li2024personalized, chakraborty2024maxmin, wang2024arithmetic, yang2024rewards, la2025fairness}. For example, \\citet{wang2023aligning} model rewards as a posterior over annotator opinions to capture disagreement, while \\citet{chakraborty2024maxmin} optimize for minority preferences via MaxMin-RLHF based on the Egalitarian principle. Other approaches, such as Personalized-RLHF \\cite{li2024personalized} and Personalized Soups \\cite{jang2023personalized}, adapt to diverse users by attaching user embeddings or merging specialist policy models. \n\nHowever, these methods either aim for a one-size-fits-all solution or maintain multiple policies for different groups. In contrast, we train a single policy model that adapts to users by jointly modeling individual and group-level preferences. In addition, prior work emphasizes reward modeling, RL training also depends on KL regularization with respect to a reference model, typically initialized from the SFT model. As the SFT model tends to overfit to majority behaviors, the reference model may inherit this bias, limiting its ability to guide the policy across diverse users. \n\nWe address this limitation from the source by enhancing preference awareness at both SFT and RL stages. We first model individual preferences via UCoT/ CoPeR during SFT, and then derive separate majority/minority reference models through M\\textsuperscript{2}PC clustering, enabling KL regularization to better reflect user diversity during RL.\n\n\n% \\subsection{Aligning Language Models To Diverse Human Preferences}\n% Recent methods have paid efforts to taking account the diversity of human preferences into reward modeling in reinforcement learning algorithms \\cite{jang2023personalized, wang2023aligning, li2024personalized, chakraborty2024maxmin, wang2024arithmetic, yang2024rewards, la2025fairness}. For example, \\citet{wang2023aligning} proposed a Bayesian formulation treats reward as a posterior over annotator opinions to capture disagreement more faithfully. \\citet{chakraborty2024maxmin} proposed MaxMin‑RLHF learns a mixture of preference distributions via EM and trains the policy against the minority based on the Egalitarian principle. \\citet {li2024personalized} proposed the Personalized-RLHF, which attaches a lightweight user embedding to RLHF fine-tuning for per-user adaptation. \\citet{jang2023personalized} proposed Personalized Soups which independently trains specialist policies for multiple preferences and model alignment via a post-hoc parameter merging. \n\n% However, they aim to either train a one-size-fits-all system that is less controversial to diverse humans, or train separate policy model for diverse human populations. In this work, we foucs on one policy model that adapt to user by modeling both individual-specific preferences and group-level trends.\n\n% In addition, they focus on reinforcement learning (RL) phrase to consider the diverse preference, however, reference model in RL is typically derived from the SFT stage, which tends to overfit to majority group behaviors while underperforming on minority preferences. As a result, a single reference model fails to reflect the diversity of human sub-populations and cannot effectively constraint policy learning across different user groups during reinforcement learning. Therefore, instead of reward modeling, we directly to solve this by build a diverse human preference aware reference model for RL.\n\n% Standard RLHF pipelines (e.g., InstructGPT) train one reward model on aggregated human rankings, which can trigger preference collapse and marginalize minority views \\cite{ouyang2022training, xiao2024algorithmic}. \n% Group Preference Optimization adds a small transformer module trained to steer outputs toward any demographic cohort with few-shot data \\cite{zhao2023group}, \n% while Rewards-in-Context turns alignment into a multi-objective prompting task \\cite{yang2024rewards}. \n% Fairness‑aware PPO variants introduce demographic‑parity penalties but still rely on a lone reference policy \\cite{la2025fairness}.\n% Yet all rely on a single reference policy and proxy metrics. Our method retains one reward model but uses EM to train two reference policies—majority and minority—and alternates PPO updates against both, with every update anchored by an explicit user-elicited satisfaction score.\n\n% One of the limitation of existing alignment methods lies in the assumption that human preferences can be captured by a single reference model. In practice, this reference model is typically derived from the SFT stage, which tends to overfit to majority group behaviors while underperforming on minority preferences due to group imbalance. As a result, a single reference model fails to reflect the diversity of human sub-populations and cannot effectively guide policy learning across different user groups during reinforcement learning. To address this, we propose the Preference-Adaptive Reinforcement Learning, a Proximal Preference Optimization (PPO) \\cite{schulman2017proximal} based framework that incorporates group-specific reference models following the majority–minority clustering.\n%%%TO DO: move to introduction, also it is needed to illustrate the correlation of different group and scoring, figure1, step 3\n\n\n\\section{Preliminary}\nWe conducted our experiments on the Emotional Support Conversation (ESConv) dataset \\cite{liu2021towards}. Throughout each conversation, help-seekers (users) provided feedback every two utterances received from the supporter, rating the helpfulness of these messages on a five-star scale. We denote this feedback score as ``satisfaction score.'' We categorized feedback scores of 3 or lower as ``low satisfaction'' and scores higher than 3 as ``high satisfaction.'' There is no clear, universally accepted rule for partitioning users, factors such as race, age, gender, and personality will create highly varied preferences \\cite{aroyo2023dices, chakraborty2024maxmin,fu2024styemp}. Therefore, we heuristically classified users whose proportion of high satisfaction scores exceeded 60\\% as belonging to a ``majority'' population, with the remainder designated as the ``minority.'' Consequently, 81.4\\% of conversations were identified as majority, while 18.6\\% fell into the minority category. \n\n\\section{Proposed Method}\nIn this work, we tackle user satisfaction prediction in dialogue, given a user's input and a supporter's response. As shown in Figure~\\ref{fig:arch}, our framework consists of four main steps.\n\nWe first introduce UCoT prompt and use GPT-4.1-mini\\footnote{\\href{https://platform.openai.com/docs/models/gpt-4.1-mini}{https://platform.openai.com/docs/models/gpt-4.1-mini}} for user-specific CoPeR synthesis, then fine-tune a base model $G(\\theta)$ on this reasoning to equip it with user-specific inference ability. Subsequently, we introduce M\\textsuperscript{2}PC algorithm to group users into two distinct clusters, training a separate model for each. Finally, these group-specific models serve as reference models in the proposed PAda-PPO framework.\n\n\\subsection{User-specific CoPeR Synthesis}\n\\subsubsection{UCoT Prompt}\n\\label{sec:UCOT_prompts}\n% In the post-conversation survey of the ESConv dataset, users rated their perceived empathy and relevance of the supporter's response, as well as their overall feedback score \\cite{liu2021towards}. We standardized the empathy and relevance scores using z-score normalization and computed a combined metric by summing the standardized values. Pearson correlation analysis revealed a significant association between this combined score and the user's overall feedback ($r=0.5868$, $p<0.05$), indicating that empathy and relevance are related to user satisfaction.\n\n% Drawing on prior work showing that accurate understanding of user intent, strategic response selection, and alignment with user needs are central to perceived empathy \\cite{fu2023reasoning, zhang2024escot}. Motivated by this finding, we design a User-specific Chain-of-Thought (\\textbf{UCoT}) prompt to model the underlying factors contributing to user satisfaction. By giving the context, we prompt the model through four structured reasoning steps: (1) infer the user's underlying intent from the dialogue context, (2) identify the supporter's main response strategy (e.g., Question, Reflection of Feelings), (3) evaluate whether the strategy aligns with the user's needs, (4) predict the user's feedback score from the perspectives of empathy and relevance. Details of the prompting format are provided in Appendix~\\ref{sec:prompts_example} (Figure~\\ref{fig:prompt_cot}).\n\nDrawing on findings that user satisfaction hinges on correctly identifying the user’s intent and deploying responses that appropriately match the intent and evolving needs \\cite{deng-etal-2022-user, fu2023reasoning, lin-etal-2024-interpretable}, we design a User-specific Chain-of-Thought (\\textbf{UCoT}) prompt to make this reasoning explicit for satisfaction estimation. Given a dialogue context, the model is guided to: (1) infer the user's underlying intent; (2) identify the supporter's primary response strategy (e.g., \\textit{Question}, \\textit{Reflection of Feelings}); (3) evaluate whether the strategy aligns with the user's need; and (4) predict the user's feedback score by considering factors such as empathy and relevance. Details of the prompt appear in Appendix~\\ref{sec:prompts_example} (Figure~\\ref{fig:prompt_cot}).\n\n\\subsubsection{CoPeR Synthesis}\n\n% \\begin{figure}\n% \\centering\n% \\includegraphics[width=0.49\\textwidth]{figs/coper.pdf}\n% \\caption{Comparison between majority-centered CoT and minority-aware CoPeR on the presence of reasoning path and feedback reward.} \n% \\label{fig:coper}\n% \\end{figure}\nTo train a model with the reasoning ability from steps (1)–(3) to correctly predict the user’s feedback score, we use GPT-4.1-mini to synthesize reasoning rationales conditioned on the user’s actual feedback score. Consequently, step (4) is to “explain the rationale behind the user’s feedback score in terms of emotional and practical relevance.” Further details are provided in Appendix \\ref{sec:prompts_example} (Figure \\ref{fig:prompt_coper}). This structured format enables more interpretable synthesis of user-centered reasoning behind feedback scores.\n\n\n\\subsection{Supervised Fine-Tuning}\nAfter obtaining the synthesized CoPeR output $r_{\\text{coper}}$, which comprises four components: $r_{\\text{intent}}$, $r_{\\text{strategy}}$, $r_{\\text{match}}$, and $r_{\\text{reason}}$ (as illustrated in Figure~\\ref{fig:arch}), along with the UCoT prompt $r_\\text{ucot}$, we fine-tune a base model on a dataset of input-target pairs formatted as $(c+r_\\text{ucot}, r_{\\text{coper}}+y)$. Formally, the output generation process can be decomposed into a sequence of next token prediction actions, denoting as $e = [a_1, a_2, \\dots, a_T, s, \\text{<eos>}]$. The training objective is defined as:\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{\\text{SFT}}(\\theta) \n= & - \\sum_{t=1}^{T} \\log G_\\theta(a_t \\mid c+r_\\text{ucot}, a_{<t}) \\\\\n & - \\log G_\\theta(s \\mid c+r_\\text{ucot}, a_{1:T}),\n\\end{aligned}\n\\end{equation}\nwhere $a_t$ is the token in the vocabulary, $s$ represents the satisfaction score, and $\\text{<eos>}$ indicates the end-of-sequence token.\nThe first term supervises the generation of user-specific reasoning ($r_{\\text{coper}}$), and the second term guides the model to accurately predict the satisfaction score ($s$) conditioned on the generated reasoning, and SFT stands for supervised fine-tuning. This warm-up phase equips the model with interpretable and user-aligned reasoning capabilities to generate a proper response. \n\n\\subsection{M\\textsuperscript{2}PC}\n\\label{sec:em}\nHuman preferences in dialogue vary due to factors such as socio-cultural background~\\cite{aroyo2023dices,chakraborty2024maxmin}, personality~\\cite{richendoller1994exploring}, and gender~\\cite{costa2014associations}. To model such diversity, we first examine preference differences between majority and minority users according to the supporter strategies, then apply an unsupervised EM-based clustering method to separate them.\n\n\\subsubsection{Preference Divergence Across Groups}\n\\label{subsec:user_pref}\nWe categorize supporter strategies in the ESConv dataset into two strategy types: Cognition-oriented, including \\textit{Question}, \\textit{Restatement or Paraphrasing}, \\textit{Providing Suggestions}, and \\textit{Information}; and Emotion-oriented, including \\textit{Reflection of Feelings}, \\textit{Self-disclosure}, and \\textit{Affirmation and Reassurance}. We then computed the score distributions (1–5) for each strategy within the majority and minority user groups (Figure~\\ref{fig:feedback_compare}).\n% and summarized each strategy's counts and proportions of low (1–3) and high (4–5) feedback scores in Table~\\ref{tab:feedback_compare}.\n\nAcross both majority and minority groups, emotion-oriented strategies are more likely to receive high feedback (0.94 > 0.91; 0.44 > 0.33), with the effect especially pronounced in the minority group. This preference divergence underscores the need for personalized modeling that accounts for group-specific preferences.\\footnote{Aggregated proportions reported in the text are obtained by summing the bars for scores 4 and 5 (e.g., 0.94 = 0.63 + 0.31 for emotion-oriented strategies in the majority group), further details are provided in Appendix~\\ref{sec:feedback_dis}.}\n\n% As shown in Figure~\\ref{fig:feedback_compare}, majority users exhibit similarly high satisfaction (scores 4 or 5) for both cognition- and emotion-oriented strategies. In contrast, minority users tend to assign higher scores to emotion-oriented strategies and lower scores to cognition-oriented ones. This preference divergence underscores the need for personalized modeling that accounts for group-specific preferences, also supports our hypothesis that the users can be clustered according to the contextual semantics of their inputs and the supporters' responses.\n\n% \\begin{figure}[t]\n% \\centering\n% \\begin{subfigure}{\\linewidth}\n% \\centering\n% \\includegraphics[width=0.8\\linewidth]{latex/figs/Feedback score distribution — Majority.pdf}\n% % \\caption{Majority}\n% \\label{fig:feedback_majority}\n% \\end{subfigure}\n% \\vspace{0.8em}\n% \\begin{subfigure}{\\linewidth}\n% \\centering\n% \\includegraphics[width=0.8\\linewidth]{latex/figs/Feedback score distribution — Minority.pdf}\n% % \\caption{Minority}\n% \\label{fig:feedback_minority}\n% \\end{subfigure}\n% \\caption{Distribution of feedback scores for cognition‑ and emotion‑oriented supporter response strategies across majority and minority user groups from ESConv dataset.}\n% \\label{fig:feedback_compare}\n% \\end{figure}\n\n\\begin{figure}[t]\n \\centering\n \\begin{subfigure}{\\linewidth}\n \\centering\n \\includegraphics[width=0.9\\linewidth]{figs/bar_major.pdf}\n % \\caption{Majority}\n \\label{fig:feedback_majority}\n \\end{subfigure}\n \\vspace{0.8em}\n \\begin{subfigure}{\\linewidth}\n \\centering\n \\includegraphics[width=0.9\\linewidth]{figs/bar_minor.pdf}\n % \\caption{Minority}\n \\label{fig:feedback_minority}\n \\end{subfigure}\n \\caption{Distribution of feedback scores for cognition‑ and emotion‑oriented supporter response strategies across majority and minority user groups from ESConv dataset.}\n \\label{fig:feedback_compare}\n\\end{figure}\n\n\n\n\\subsubsection{Diversity-Aware Clustering}\nWe adopt an EM strategy that divides users into majority and minority based on the perplexity of their dialogue data under different models.\nEach model is further fine-tuned on dialogues from the belonging cluster, separately.\nFormally, the algorithm proceeds as follows:\n\n\\noindent\\textbf{E-step (Expectation):} Given two cluster models at iteration $t$, denoted by $G(\\beta)_\\text{Major}^{(t)}$ and $G(\\beta)_\\text{Minor}^{(t)}$ (both initialized from the base model $G(\\theta)$ trained from the SFT stage), each user $i$ with dialogue set $D_i$ is assigned to the model with lower perplexity:\n\\begin{equation}\nl_i^{(t)} = \\arg\\min_{k \\in \\{\\text{Major}, \\text{Minor}\\}} \\text{PPL}(D_i; G(\\beta)_k^{(t)}),\n\\end{equation}\nwhere $l_i^{(t)}$ denotes the cluster assignment of user $i$ at the $t$-th EM iteration, and the perplexity is:\n\\begin{equation}\n\\text{PPL}(D_i;\\!G(\\beta))\\!=\\!\\exp\\!\\left(\\!-\\frac{1}{|D_i|}\\!\\sum_{w\\in D_i}\\!\\log\\!P_{G(\\beta)}\\!(w)\\!\\right)\n\\end{equation}\nThis step is to route users toward the model most closely aligned with their group preferences.\n\n\\noindent\\textbf{M-step (Maximization):} After cluster assignments are updated, we fine-tune each model $G(\\beta)_k$ on dialogues assigned to its respective cluster:\n\\begin{equation}\nG(\\beta)_k^{(t+1)} = \\arg\\min_{G(\\beta)_k^{(t)}} \\sum_{i: l_i^{(t)} = k} \\mathcal{L}(G(\\beta)_k^{(t)}; D_i),\n\\end{equation}\nwhere $\\mathcal{L}$ is the negative log-likelihood loss over the dialogue set $D_i$.\nThis EM process iteratively refines cluster assignments and model parameters, enabling the system to unsupervised discover latent user groups that reflect diverse preference patterns.\n\n% We perform these E-step and M-step iterations repeatedly for a fixed number of epochs (e.g., 10 epochs). At each epoch, we evaluate the models on a held-out validation set, routing validation users based on perplexity to measure cluster-specific performance. We save checkpoints separately for each cluster model based on distinct evaluation metrics: Cluster-0 prioritizes maximizing F1-score on the high-satisfaction class, whereas Cluster-1 prioritizes the low-satisfaction class.\n\n% Ultimately, this iterative clustering and model-training paradigm effectively captures distinct majority-minority preferences, thereby improving overall dialogue modeling effectiveness and personalization.\n\n\\subsection{PAda-PPO}\nLeveraging M\\textsuperscript{2}PC, each input within a batch is routed to either $G(\\beta)_\\text{Major}$ or $G(\\beta)_\\text{Minor}$ based on the model yielding lower perplexity, as shown in Figure~\\ref{fig:arch}. We employ PPO \\citep{schulman2017proximal} with a clipped objective algorithm for training. Following \\citet{luong2024reft}, the value model $V_{\\phi}$ is contructed by appending a linear value head on top of the last hidden states of the policy model $G(\\xi)$, which is initialized from the SFT model $G(\\theta)$. \n\n\\paragraph{Reward Modeling} Given a dataset consisting of \\text{(input, target)} pairs $(c +r_\\text{ucot}, r_{\\text{coper}}+y)$, and generated output as $e = [a_1, a_2, \\dots, a_T, s, \\texttt{<eos>}]$, the reward function is as follows:\n\\begin{equation}\nr_T = \\begin{cases}\n+1 & s=y,\\\\\n-1 & \\text{otherwise}.\n\\end{cases}\n\\end{equation}\nThe reward of 0 is given for the intermediate tokens ($r_t = 0$ for $t<=T$), such partial reward can help reduce the effect of learning from sparse reward \\cite{trott2019keeping}. \n\n% Throughout PPO training, the reference models $G(\\beta)_{\\text{Major}}$ and $G(\\beta)_{\\text{Minor}}$ remain fixed, guiding the policy model towards generating accurate and human-aligned responses tailored to each user cluster.\n\\paragraph{Diversity-aware KL Regularization} A divergence penalty was utilized to prevent the policy from diverging significantly from human-like reference behaviors in each group. At each timestep $t$, the Kullback-Leibler (KL) divergence \\cite{kullback1951information} between the current RL policy $G(\\xi)$ and the corresponding reference policy $G(\\beta)_m$ is computed as:\n\\begin{equation}\n\\mathrm{KL}_t = D_{\\mathrm{KL}}\\bigl(G(\\xi)(\\cdot \\mid s_t, m) \\parallel G(\\beta)_m(\\cdot \\mid s_t)\\bigr),\n\\label{eq:kl}\n\\end{equation}\nwhere $G(\\beta)_m$ corresponds to $G(\\beta)_\\text{Major}$ or $G(\\beta)_\\text{Minor}$ according to the perplexity routing, $m \\in \\{\\text{Major}, \\text{Minor}\\}$. $s_t$ comprises of all tokens in the \\text{input} and all tokens generated so far. In addition, following \\citet{zheng2023secrets,luong2024reft}, the total reward at each timestep combines the reward function score and KL penalty terms:\n\\begin{equation}\nr_t^{\\text{total}} = r_t - \\lambda_{\\text{KL}} \\cdot \\mathrm{KL}_t,\n\\end{equation}\nwhere $\\lambda_{\\text{KL}}$ controls penalty strength.\n\n\\paragraph{Optimization Objective} \nFollowing Generalized Advantage Estimation \\cite{schulman2015high}, we compute advantages $\\hat{A}_t$:\n\\begin{equation}\n\\begin{aligned}\n\\delta_t &= r_t^{\\text{total}} + \\gamma V_{\\phi_{\\text{old}}}(s_{t+1}) - V_{\\phi_{\\text{old}}}(s_t),\\\\\n\\hat{A}_t &= \\sum_{l=0}^{T-t}(\\gamma\\lambda)^l \\delta_{t+l},\n\\end{aligned}\n\\end{equation}\nwith discount factor $\\gamma \\in(0,1]$ and $\\lambda \\in(0,1]$. The value function $V_{\\phi}(s_t)$ is estimated by a value head jointly trained with the policy. $\\mathcal{L}_{\\text{value}}(\\phi)$ minimizes deviation between value estimate $V_{\\phi}(s_t)$ and return estimate $\\hat{R}_t = \\hat{A}_t + V_{\\phi_{\\text{old}}}(s_t)$:\n\\begin{equation}\n\\begin{aligned}\n&\\mathcal{L}_{\\text{value}}(\\phi)\n= \\frac{1}{2}\\,\\mathbb{E}_{t}\\!\\Bigl[\n\\max\\!\\Bigl(\n(V_{\\phi}(s_t)\\!-\\!\\hat{R}_t)^2,\\;\\\\\n&\\bigl(V_{\\phi_{\\text{old}}}(s_t)\\!+\\!\n\\operatorname{clip}\\!\\bigl(\nV_{\\phi}(s_t)\\!-\\!V_{\\phi_{\\text{old}}}(s_t),\\!-\\epsilon,\\!\\epsilon\n\\bigr)\\!-\\!\\hat{R}_t\\bigr)^2\n\\Bigr)\\!\\Bigr].\n\\end{aligned}\n\\end{equation}\nThe final policy objective is:\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{\\text{policy}}(\\xi) \\!=\\!\n& -\\mathbb{E}_{t}\\Big[\\min\\Big( \\rho_{t}(\\xi)\\hat{A}_{t}, \\nonumber \\\\\n& \\quad\\quad\\;\\;\\, \\mathrm{clip}\\left(\\rho_{t}(\\xi),\\, 1-\\epsilon,\\, 1+\\epsilon\\right)\\hat{A}_{t} \\Big)\\Big],\n\\end{aligned}\n\\end{equation}\nwhere the probability ratio $\\rho_t(\\xi)$ is:\n\\begin{equation}\n\\rho_t(\\xi) = \\frac{G(\\xi)(a_t\\mid s_t,m)}{G(\\xi_{\\text{old}})(a_t\\mid s_t,m)},\n\\end{equation}\nand $\\epsilon$ is a clipping parameter.\nThe combined PPO loss to minimize is:\n\\begin{equation}\n\\mathcal{L}_{\\text{PPO}}(\\xi,\\phi) = \\mathcal{L}_{\\text{policy}}(\\xi) + c_{\\text{VF}}\\cdot \\mathcal{L}_{\\text{value}}(\\phi),\n\\end{equation}\nwhere $c_{\\text{VF}}$ is the coefficient for the value objective. \n% \\begin{equation}\n% \\begin{aligned}\n% \\mathcal{L}_{\\text{value}}(\\phi)&=\n% \\frac{1}{2}\\,\\mathbb{E}_{t}\\!\\Bigl[\n% \\max\\bigl(\n% \\bigl(V_{\\phi}(s_{t})-\\hat{R}_{t}\\bigr)^{2},\\,\n% \\bigl(\\tilde{V}_{t}-\\hat{R}_{t}\\bigr)^{2}\n% \\bigr)\n% \\Bigr],\\\\\n% \\end{aligned}\\end{equation}\n% where $\\hat{R}_t$ and $\\tilde{V}_t$ is the estimate of return and clipped value prediction:\n% \\begin{equation}\n% \\begin{aligned}\n% \\hat{R}_t &= \\hat{A}_t + V_{\\phi}(s_t)\\\\\n% \\tilde{V}_{t} &= \n% V_{\\phi_{\\text{old}}}(s_{t}) +\n% \\text{clip}\\!\\bigl(\n% V_{\\phi}(s_{t})-V_{\\phi_{\\text{old}}}(s_{t}),\\,\n% -\\epsilon,\\,\\epsilon\n% \\bigr).\n% \\end{aligned}\n% \\end{equation}\n\n\\section{Experiments}\n\\subsection{Dataset}\nWe conducted our experiments on the ESConv dataset, which contains 1,300 conversations comprising 38,365 utterances between help-seekers (user) and supporters. The help-seeker provides a feedback score for every two dialogue turns exchanged with the supporter. Accordingly, we concatenate each two-turn as a single input and pair it with the corresponding feedback score as the output. Each input also includes the preceding contexts among the same conversation. We split the dataset into training, validation, and test sets using an 8:1:1 ratio at the conversation level, ensuring no conversation overlap among these subsets.\n\n\\subsection{Settings}\nAll models were fine-tuned using parameter-efficient Low-Rank Adaptation (LoRA) \\cite{hu2022lora} with 8-bit quantization. LoRA adapters were configured with a rank of $r=16$, scaling factor $\\alpha=16$, and a dropout rate of $0.1$. The base model weights were frozen, and only LoRA parameters were updated. We fixed the random seed to 42 and set the maximum input length to 1024. At inference time, we applied top-$p$ sampling with $p=0.85$, a temperature of $0.7$, and a maximum generation length of 256 tokens.\n\nDuring the SFT stage, we used a learning rate of $1\\times10^{-4}$, a batch size of 8, and trained for up to 15 epochs with an early stopping patience of 3.\nFor the M\\textsuperscript{2}PC stage, training was conducted for 10 EM iterations with a batch size of 2, gradient accumulation steps of 4, and a learning rate of $1\\times10^{-5}$. We set diverse user clusters as 20 each for the majority and minority groups for clustering initialization.\nBoth SFT and M\\textsuperscript{2}PC stages were trained on a single NVIDIA RTX A6000 GPU (49GB) using the AdamW optimizer \\cite{loshchilovdecoupled}.\n\nFor the PAda-PPO stage, training was performed on 4 NVIDIA RTX A6000 GPUs (49GB each) using DeepSpeed ZeRO Stage 2 \\cite{rasley2020deepspeed} and Hugging Face Accelerate \\cite{accelerate}. We used a batch size of 2, gradient accumulation of 2, a learning rate of $3\\times10^{-7}$, and trained for 5 epochs. Following \\citet{ziegler2019fine, luong2024reft}, we set PPO hyperparameters as follows: $\\lambda=1$, $\\gamma=0.95$, $c_{\\text{VF}}=0.1$, $\\epsilon=0.2$. And the KL penalty coefficient is set to 0.2.\n\n\\subsection{Comparative Models}\nWe organized our experiments into three stages: \\textit{zero-shot inference}, \\textit{UCoT inference}, and \\textit{supervised fine-tuning (SFT)} using LoRA.\n\n\\noindent\\textbf{Zero-shot}: we evaluated three backbone models with base prompt (Appendix~\\ref{sec:prompts_example}, Figure~\\ref{fig:base_prompt}): Llama‑3.2‑1B-Instruct\\footnote{\\href{https://huggingface.co/meta-llama/Llama-3.2-1B-Instruct}{https://huggingface.co/meta-llama/Llama-3.2-1B-Instruct}}, Llama-3-8B-Instruct\\footnote{\\href{https://huggingface.co/meta-llama/Meta-Llama-3-8B-Instruct}{https://huggingface.co/meta-llama/Meta-Llama-3-8B-Instruct}}, and GPT4.1‑mini, without training.\n\n\\noindent \\textbf{UCoT}: We augmented the input with UCoT prompts, without fine-tuning.\n% which guide the model to (1) infer the user's intent, (2) identify the supporter's strategy, (3) assess the alignment between the intent and strategy, and (4) predict the user's satisfaction from the perspectives of empathy and relevance. \n% and evaluated the corresponding variants: Llama‑3.2‑1B-Instruct-UCoT, Llama‑3‑8B-Instruct-UCoT, and GPT4.1‑mini-UCoT without fine-tuning.\n\n\\noindent\\textbf{SFT (LoRA)}: We fine-tuned Llama‑3.2‑1B-Instruct and Llama‑3‑8B-Instruct using LoRA adapters with both base and UCoT-augmented prompts.\n% , resulting in six variants: Llama‑3.2‑1B-Instruct, Llama‑3.2‑1B-Instruct-UCoT, Llama‑3.2‑1B-Instruct-CoPeR, Llama‑3‑8B-Instruct, Llama‑3‑8B-Instruct-UCoT, and Llama‑3‑8B-Instruct-CoPeR. \nWhile the model with UCoT or CoPeR module shares the same prompt, their training targets differ: the model with UCoT supervision uses only the final feedback score, whereas the model with CoPeR supervision additionally includes the synthesized step-by-step reasoning output ($r_{\\text{coper}}$).\n\n\\noindent\\textbf{Reinforcement Learning (RL)}: we further fine-tuned the SFT models using both standard PPO \\cite{schulman2017proximal} and our proposed PAda‑PPO. Specifically, we applied these methods to the following SFT variants: Llama‑3‑8B-Instruct, Llama‑3‑8B-Instruct-UCoT, and Llama‑3‑8B-Instruct-CoPeR. \n\n\\subsection{Evaluation Metrics}\nWe adopt four classification metrics: the $F_1$ score for each individual class (``low satisfaction'' and ``high satisfaction''), macro-averaged $F_1$, and weighted $F_1$.\nThe class-wise $F_1$ scores (denoted as $F_1^{\\text{low}}$ and $F_1^{\\text{high}}$ measure how well the model predicts each satisfaction label individually. The macro $F_1$ ($F_1^{\\text{m}}$) is computed by averaging the $F_1$ scores of both classes, giving equal weight to each regardless of class frequency. The weighted $F_1$ ($F_1^{\\text{w}}$) further accounts for label imbalance by weighting each class $F_1$ score by its support. \n% Together, these metrics allow us to assess overall model performance as well as its effectiveness in handling class imbalance.\n\n\\section{Results and Analysis}\n\n% \\begin{figure}\n% \\centering\n% \\includegraphics[width=0.49\\textwidth]{latex/figs/em_f1_cper_best.pdf}\n% \\caption{} \n% \\label{fig:coper}\n% \\end{figure}\n\n\\subsection{Evaluation of Synthesized Rationales by GPT-4.1-mini}\nWe evaluate the accuracy and quality of synthesized rationales by GPT-4.1-mini. Individual preference is inherently subjective, human evaluation may be unreliable: annotators cannot directly access the seeker’s real thoughts. \nWe assess the quality and accuracy of the synthesized rationales with two objective metrics:\n\n\\noindent (1) \\textbf{Supporter-strategy accuracy (7 classes)}: measures the alignment between the supporter strategy predicted in step 2 and the true label.\n\n\\noindent (2) \\textbf{Logical accuracy}: measures the consistency between reasoning steps (Steps~1–3) and the final judgment (Step~4). Step~3 infers whether the supporter’s strategy aligns with the seeker's intent based on predictions from Steps~1–2, while Step~4 provides the gold satisfaction score (1–5). We map “matched intent” to scores 4–5, ``partially matched'' to 2–3, and ``did not match'' to 1. A rationale is considered logically correct when this mapping holds.\nOn the training set, the synthesized rationales by GPT-4.1-mini achieve 63.44\\% supporter-strategy accuracy and 74.16\\% logical accuracy; on the validation set, 61.04\\% and 77.23\\%, respectively. Appendix~\\ref{sec:evaluation} presents additional case studies.\n\n\n\\begin{table}[h]\n \\centering\n \\scalebox{0.91}{\n \\begin{tabular}{lcccc}\n \\toprule\n Models & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$\\\\\n \\midrule\n \\multicolumn{5}{l}{\\textit{Zero‑shot}}\\\\\n Llama‑3.2‑1B & 0.27 & 0.49 & 0.45 & 0.38 \\\\\n Llama‑3‑8B & 0.34 & 0.71 & 0.65 & 0.52 \\\\\n GPT4.1‑mini & \\textbf{0.40} & 0.67 & 0.62 & 0.53 \\\\\n \\midrule\n \\multicolumn{5}{l}{\\textit{\\textbf{UCoT}}}\\\\\n Llama‑3.2‑1B-UCoT & 0.28 & 0.40 & 0.38 & 0.34 \\\\\n Llama‑3‑8B-UCoT & 0.26 & 0.80 & 0.72 & 0.53 \\\\\n GPT4.1‑mini-UCoT & 0.38 & 0.57 & 0.54 & 0.47 \\\\\n \\midrule\n \\multicolumn{5}{l}{\\textit{SFT (with LoRA)}}\\\\\n Llama‑3.2‑1B & 0.28 & 0.76 & 0.67 & 0.52 \\\\\n Llama‑3.2‑1B-\\textbf{UCoT} & 0.18 & \\textbf{0.88} & 0.75 & 0.53 \\\\\n Llama‑3.2‑1B-\\textbf{CoPeR} & 0.27 & 0.85 & 0.74 & 0.56 \\\\\n Llama‑3‑8B & 0.24 & 0.82 & 0.71 & 0.53 \\\\\n Llama‑3‑8B-\\textbf{UCoT} & 0.27 & 0.86 & 0.75 & 0.56 \\\\\n Llama‑3‑8B-\\textbf{CoPeR} & 0.30 & 0.86 & \\textbf{0.76} & \\textbf{0.58} \\\\\n \\bottomrule\n \\end{tabular}}\n \\caption{\\textbf{Results of the proposed UCoT and CoPeR:} Comparison of baseline models and our proposed UCoT and CoPeR module. We report $F_1$ scores on low ($F_1^{\\text{low}}$) and high ($F_1^{\\text{high}}$) satisfaction classes, along with weighted ($F_1^{\\text{w}}$) and macro ($F_1^{\\text{m}}$) averages. \\textbf{Bold} in $F_1$ indicates the best performance. All Llama models refer to the instruction-tuned versions.}\n \\label{tab:sft}\n\\end{table}\n\n\\begin{table*}[t]\n\\centering\n\\scalebox{0.92}{\n\\begin{tabular}{lcccccccccccc}\n\\toprule\n\\multirow{2}{*}{Models} & \\multicolumn{4}{c}{Minority} & \\multicolumn{4}{c}{Majority} & \\multicolumn{4}{c}{Minority+Majority} \\\\\n\\cmidrule(lr){2-5} \\cmidrule(lr){6-9} \\cmidrule(lr){10-13}\n & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ &$F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ &$F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ \\\\\n\\midrule\nLlama-3-8B & 0.17 & 0.47 & 0.28 & 0.32 & 0.16 & 0.90 & 0.84 & 0.53 & 0.16 & 0.84 & 0.71 & 0.50 \\\\\n\\quad +\\textbf{M\\textsuperscript{2}PC} & 0.68 & \\textbf{0.55} & 0.61 & 0.61 & 0.19 & 0.94 & \\textbf{0.89} & \\textbf{0.57} & 0.56 & 0.89 & 0.82 & 0.72 \\\\\n\\midrule\nLlama-3-8B-UCoT & 0.36 & 0.49 & 0.41 & 0.42 & 0.21 & 0.88 & 0.83 & 0.55 & 0.26 & 0.83 & 0.72 & 0.55 \\\\\n% \\quad +\\textbf{M\\textsuperscript{2}PC} & 0.72 & 0.30 & 0.58 & 0.51 & 0.00 & 0.95 & 0.87 & 0.48 & 0.57 & 0.91 & 0.85 & 0.74 \\\\\n\\quad +\\textbf{M\\textsuperscript{2}PC} & 0.73 & 0.18 & 0.56 & 0.46 & 0.00 & \\textbf{0.96} & 0.88 & 0.48 & 0.58 & 0.92 & 0.85 & 0.75 \\\\\n\\midrule\n% Llama-3-8B-CoPeR & 0.29 & 0.53 & 0.37 & 0.41 & \\textbf{0.21} & 0.90 & 0.85 & 0.51 & 0.20 & 0.86 & 0.74 & 0.55 \\\\\nLlama-3-8B-CoPeR & 0.29 & 0.53 & 0.37 & 0.41 & \\textbf{0.21} & 0.90 & 0.85 & 0.56 & 0.24 & 0.85 & 0.74 & 0.55 \\\\\n\\quad +\\textbf{M\\textsuperscript{2}PC} & \\textbf{0.80} & 0.46 & \\textbf{0.70} & \\textbf{0.63} & 0.08 & 0.95 & 0.87 & 0.51 & \\textbf{0.60} & \\textbf{0.92} & \\textbf{0.86} & \\textbf{0.76} \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\caption{\\textbf{Results of the proposed M\\textsuperscript{2}PC:} $F_1$ scores on the validation set across three model backbones, evaluated on minority, majority, and combined user groups. For each model, the reported M\\textsuperscript{2}PC results correspond to the best-performing EM iteration. \n% Parentheses indicate the number of distinct user clusters in the majority and minority groups.\nLlama‑3‑8B refers to the Llama‑3‑8B‑Instruct version.}\n\\label{tab:em}\n\\end{table*}\n\n\n\n\\subsection{Results of the Proposed UCoT and CoPeR}\nTable~\\ref{tab:sft} reports classification performance across three settings: \\textit{Zero-shot}, \\textit{UCoT}, and \\textit{SFT (with LoRA)}. Overall, supervised fine-tuning (SFT) consistently outperforms both the zero-shot and inference-only UCoT settings, emphasizing the importance of task-specific adaptation. Prompting with UCoT alone results in degraded performance compared to the zero-shot baseline, suggesting that, without a supervision, UCoT may overly constrain the model's reasoning process, failing to predict correctly.\n% These findings underscore the need for our proposed user-specific CoPeR synthesis, which explicitly supervised fine-training model to reason from both the user's and supporter's perspectives in relation to satisfaction outcomes.\nWithin the SFT setting, models fine-tuned with UCoT prompts consistently outperform their counterparts across both backbone architectures (Llama-3.2-1B-Instruct and Llama-3-8B-Instruct). Furthermore, our proposed CoPeR approach, which extends UCoT by additionally supervising the model to generate user-specific reasoning as output, achieves the highest performance in both weighted and macro $F_1$ scores. These results highlight the effectiveness of combining user-specific prompting with explicit supervision of personalized reasoning in enhancing the model's ability to predict user satisfaction from dialogue.\n\n\n\n% \\begin{table*}[t]\n% \\centering\n% \\caption{\\textbf{Results on the Proposed M\\textsuperscript{2}PC:} F\\textsubscript{1} scores on the validation set across three model backbones, evaluated on minority, majority, and combined user groups. For each model, the reported M\\textsuperscript{2}PC results correspond to the best-performing EM iteration.}\n% \\label{tab:em}\n% \\scalebox{0.95}{\n% \\begin{tabular}{lcccccccc}\n% \\toprule\n% \\multirow{2}{*}{Models} & \\multicolumn{2}{c}{Minority} & \\multicolumn{2}{c}{Majority} & \\multicolumn{4}{c}{Minority+Majority} \\\\\n% & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ \\\\\n% \\midrule\n% Llama-3-8B-Instruct & 0.171 & 0.470 & 0.156 & 0.902 & 0.163 & 0.841 & 0.713 & 0.502 \\\\\n% \\quad +\\textbf{M\\textsuperscript{2}PC} & 0.675 & \\textbf{0.551} & 0.189 & 0.942 & 0.563 & 0.885 & 0.824 & 0.724 \\\\\n% \\midrule\n% Llama-3-8B-Instruct-UCoT & 0.362 & 0.486 & \\textbf{0.211} & 0.882 & 0.261 & 0.829 & 0.722 & 0.545 \\\\\n% \\quad +\\textbf{M\\textsuperscript{2}PC} & 0.716 & 0.197 & 0.000 & \\textbf{0.956} & 0.567 & 0.914 & 0.848 & 0.740 \\\\\n% \\midrule\n% Llama-3-8B-Instruct-CoPeR & 0.286 & 0.530 & 0.207 & 0.903 & 0.199 & 0.858 & 0.735 & 0.547 \\\\\n% \\quad +\\textbf{M\\textsuperscript{2}PC} & \\textbf{0.802} & 0.464 & 0.083 & 0.945 & \\textbf{0.602} & \\textbf{0.919} & \\textbf{0.859} & \\textbf{0.761} \\\\\n% \\bottomrule\n% \\end{tabular}\n% }\n% \\end{table*}\n\n\\subsection{Results of the Proposed M\\textsuperscript{2}PC}\n\\subsubsection{Analysis of Majority and Minority}\nWe first evaluate the proposed method on the majority and minority groups to assess its group-level performance. Table~\\ref{tab:em} reports $F_1$ scores on the validation set across three model backbones: Llama-3-8B-Instruct, Llama-3-8B-Instruct-UCoT, and Llama-3-8B-Instruct-CoPeR, before and after applying our proposed M\\textsuperscript{2}PC method. Across all configurations, M\\textsuperscript{2}PC consistently improves overall performance, as measured by all four metrics on the combined minority and majority groups. For example, when applied to Llama-3-8B-Instruct-CoPeR, M\\textsuperscript{2}PC improves $F_1^{\\text{low}}$ from 0.24 to 0.60, $F_1^{\\text{high}}$ from 0.85 to 0.92, $F_1^{\\text{w}}$ from 0.74 to 0.86, and $F_1^{\\text{m}}$ from 0.55 to 0.76.\nFor the minority group, M\\textsuperscript{2}PC leads to significant improvements in low satisfaction prediction across all backbones. In the CoPeR setting, for example, $F_1^{\\text{low}}$ increases from 0.29 to 0.80, $F_1^{\\text{w}}$ from 0.37 to 0.70, and $F_1^{\\text{m}}$ from 0.41 to 0.63. For the majority group, M\\textsuperscript{2}PC consistently enhances high satisfaction prediction as well, for example, increasing from 0.90 to 0.95 in the CoPeR configuration. Although there is a modest decline in high satisfaction scores for the minority group and low satisfaction scores for the majority group, the overall performance improves, as reflected in higher weighted $F_1$ scores. The detailed results and trends across EM iterations can be seen in Appendix~\\ref{sec:em_iterations}.\n\nThese results highlight the effectiveness of modeling group-specific preferences through clustering. M\\textsuperscript{2}PC successfully adapts to diverse user satisfaction patterns by routing each user to the model most aligned with their latent preference semantics, enabling more accurate prediction across minority-majority groups. We further investigate the effect of different initializations of user clusters for majority and minority groups, with details provided in Appendix~\\ref{sec:ablation}.\n\n\\subsubsection{Analysis of Subgroups Within Majority and Minority}\nNext, we analyze finer-grained subgroups within the majority and minority groups. We applied the proposed M\\textsuperscript{2}PC method to cluster the validation set into majority and minority groups. Within each group, we extracted the last hidden states from the corresponding (majority or minority) model outputs and applied $k$-means++ \\cite{arthur2007k} to cluster users into 2-20 subgroups. We then used the silhouette score \\cite{rousseeuw1987silhouettes} to determine the optimal number of clusters ($k$) and computed the weighted $F_1$ for each cluster ($\\in k$). \n\nTable~\\ref{tab:k_subgroups} shows that our method captures most user subgroups, including smaller yet distinct clusters (in bold), suggesting that M\\textsuperscript{2}PC can generally adapt to diverse intra-group preferences. \n% Because the weighted F\\textsubscript{1} score is influenced by the model's overall performance level, setting an absolute criterion for subgroup consideration is unreliable. We therefore employ a relative comparison: \nSince weighted $F_1$ is affected by the model's overall performance, we adopt a relative criterion: if smaller subgroups outperform the two largest ones in weighted $F_1$ within either the majority or minority population, it indicates that the model capture diverse subgroup characteristics rather than overfitting to the more frequent patterns.\n\n\\begin{table*}[t]\n\\centering\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{lllllllllllll}\n\\toprule\nModels & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\n\\midrule\n\\multicolumn{11}{l}{Llama-3-8B+M\\textsuperscript{2}PC} \\\\\nMaj. & \\textit{0.85(111)} & \\textit{0.68(105)} & \\textbf{0.89(67)} & \\textbf{0.84(60)} & \\textbf{0.91(55)} & \\textbf{0.91(38)} & \\textbf{0.96(38)} & \\textbf{0.92(31)} & \\textbf{0.95(27)} & \\textbf{0.79(21)} \\\\\nMin. & \\textit{0.60(21)} & \\textit{0.71(21)} & \\textbf{0.68(10)} & \\textbf{0.77(9)} & 0.63(8) & 0.19(7) & \\textbf{0.84(6)} & \\textbf{0.91(6)} & 0.57(5) & \\textbf{1.00(5)} \\\\\n\\midrule\n\\multicolumn{11}{l}{Llama-3-8B-UCoT+M\\textsuperscript{2}PC} \\\\\nMaj. & \\textit{0.68(109)} & \\textit{0.82(104)} & \\textbf{0.94(50)} & \\textbf{0.87(44)} & \\textbf{0.96(42)} & \\textbf{0.93(41)} & \\textbf{0.86(32)} & \\textbf{1.00(31)} & \\textbf{0.89(28)} & \\textbf{1.00(24)} \\\\\n% Min. & 0.82(25) & 0.59(22) & 0.48(9) & 0.40(9) & 0.43(8) & \\textbf{0.71(7)} & 0.41(7) & 0.42(7) & \\textbf{0.85(7)} & \\textbf{1.00(6)} \\\\\nMin. & \\textit{0.62(29)} & \\textit{0.61(21)} & 0.60(11) & \\textbf{0.87(8)} & \\textbf{0.91(6)} & \\textbf{0.91(6)} & \\textbf{0.78(5)} & \\textbf{0.80(5)} & \\textbf{0.73(4)} & \\textbf{1.00(4)} \\\\\n\\midrule\n\\multicolumn{11}{l}{Llama-3-8B-CoPeR+M\\textsuperscript{2}PC} \\\\\nMaj. & \\textit{0.71(134)} & \\textit{0.79(105)} & \\textbf{0.93(56)} & \\textbf{0.85(48)} & \\textbf{0.94(44)} & \\textbf{0.94(39)} & \\textbf{0.90(30)} & \\textbf{0.90(30)} & \\textbf{0.82(28)} & \\textbf{0.87(27)} \\\\\nMin. & \\textit{0.70(22)} & \\textit{0.61(21)} & \\textbf{0.67(7)} & \\textbf{0.91(6)} & \\textbf{0.67(6)} & \\textbf{1.00(5)} & \\textbf{0.80(5)} & 0.34(5) & 0.64(4) & 0.33(4) \\\\\n\\midrule\n\\end{tabular}\n}\n% \\caption{Weighted F1 across $k$ subgroups ($k \\in {1,…,10}$) within the majority (Maj.) and minority (Min.) groups.}\n% \\label{tab:model_comparison_part1}\n\\end{table*}\n\n\\begin{table*}[h]\n\\centering\n\\resizebox{\\textwidth}{!}{\n\\begin{tabular}{lllllllllllll}\n\\midrule\nModels & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\\\\n\\midrule\n\\multicolumn{11}{l}{Llama-3-8B+M\\textsuperscript{2}PC} \\\\\nMaj. & \\textbf{1.00(18)} & \\textbf{0.91(17)} & \\textbf{1.00(10)} & \\textbf{0.84(9)} & \\textbf{1.00(9)} & \\textbf{1.00(9)} & \\textbf{1.00(6)} & - & - & - \\\\\nMin. & \\textbf{0.82(5)} & 0.63(5) & 0.00(4) & 0.64(4) & 0.50(4) & \\textbf{0.73(4)} & \\textbf{0.73(4)} & \\textbf{0.73(4)} & \\textbf{0.67(3)} & - \\\\\n\\midrule\n\\multicolumn{11}{l}{Llama-3-8B-UCoT+M\\textsuperscript{2}PC} \\\\\nMaj. & \\textbf{0.88(24)} & \\textbf{0.87(22)} & \\textbf{0.90(15)} & \\textbf{1.00(14)} & \\textbf{1.00(13)} & \\textbf{1.00(12)} & \\textbf{1.00(9)} & \\textbf{1.00(8)} & \\textbf{1.00(5)} & \\textbf{1.00(3)} \\\\\nMin. & 0.33(4) & \\textbf{1.00(4)} & 0.10(4) & 0.33(3) & 0.53(3) & 0.53(3) & \\textbf{0.67(2)} & \\textbf{0.67(2)} & 0.00(2) & 0.00(2) \\\\\n\\midrule\n\\multicolumn{11}{l}{Llama-3-8B-CoPeR+M\\textsuperscript{2}PC} \\\\\nMaj. & \\textbf{0.91(22)} & \\textbf{0.94(20)} & \\textbf{0.90(19)} & \\textbf{0.96(14)} & \\textbf{1.00(9)} & \\textbf{1.00(8)} & \\textbf{1.00(8)} & \\textbf{1.00(7)} & \\textbf{1.00(4)} & - \\\\\nMin. & \\textbf{1.00(4)} & 0.20(4) & \\textbf{0.67(3)} & 0.53(3) & 0.53(3) & \\textbf{0.67(3)} & \\textbf{1.00(3)} & \\textbf{0.67(2)} & \\textbf{1.00(2)} & \\textbf{1.00(2)} \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\caption{Weighted $F_1$ scores across $k \\in {1,\\ldots,20}$ for the majority (Maj.) and minority (Min.) user groups, shown in two parts for readability (top: $k=1$–$10$; bottom: $k=11$–$20$). Numbers in parentheses indicate the number of users in each subgroup, where subgroups ($k=1$–$20$) are ordered by their user counts. Bold values denote subgroups whose weighted $F_1$ exceeds the average of the two largest subgroups (shown in \\textit{italic}).}\n\\label{tab:k_subgroups}\n\\end{table*}\n\n\n\n\\begin{table}[h]\n \\centering\n \\scalebox{0.95}{\n \\begin{tabular}{lcccc}\n \\toprule\n Models & $F_1^{\\text{low}}$ & $F_1^{\\text{high}}$ & $F_1^{\\text{w}}$ & $F_1^{\\text{m}}$ \\\\\n \\midrule\n Llama‑3‑8B\n & 0.24 & 0.82 & 0.71 & 0.53 \\\\\n \\quad + PPO & 0.25 & 0.85 & 0.74 & 0.55 \\\\\n \\quad + \\textbf{PAda‑PPO} & 0.29 & 0.86 & 0.75 & 0.57 \\\\\n \\midrule\n Llama‑3‑8B-UCoT & 0.27 & 0.86 & 0.75 & 0.56 \\\\\n \\quad + PPO & 0.22 & 0.88 & 0.76 & 0.55 \\\\\n \\quad + \\textbf{PAda‑PPO} & \\textbf{0.36} & 0.86 & 0.77 & \\textbf{0.61} \\\\\n \\midrule\n Llama‑3‑8B-CoPeR & 0.30 & 0.86 & 0.76 & 0.58 \\\\\n \\quad + PPO & 0.34 & \\textbf{0.88} & \\textbf{0.78} & 0.61\\\\\n \\quad + \\textbf{PAda‑PPO} & 0.33 & 0.85 & 0.76 & 0.59 \\\\ \n \\bottomrule\n \\end{tabular}}\n \\caption{\\textbf{Results of the proposed PAda-PPO:} Comparison among SFT, PPO-based RL, and our proposed PAda-PPO method. Llama‑3‑8B refers to the Llama‑3‑8B‑Instruct version.}\n \\label{tab:adp_ppo}\n\\end{table}\n\n\n\\subsection{Results of the Proposed PAda-PPO}\nTable~\\ref{tab:adp_ppo} presents the performance of our proposed PAda-PPO algorithm applied to three model backbones: Llama‑3‑8B-Instruct (base), Llama‑3‑8B-Instruct-UCoT, and Llama‑3‑8B-Instruct-CoPeR. We compare three strategies: SFT, SFT followed by PPO, and SFT followed by PAda-PPO. Across both the base and UCoT-augmented backbones, PAda-PPO consistently outperforms SFT and PPO. For instance, with Llama‑3‑8B-Instruct-UCoT, PAda-PPO outperforms PPO on $F_1^{\\text{low}}$ from 0.22 to 0.36 and macro $F_1$ from 0.55 to 0.61, demonstrating its effectiveness in improving minority-class satisfaction prediction while maintaining strong performance on the majority class.\n\nHowever, on the Llama‑3‑8B-Instruct-CoPeR backbone, PAda-PPO performs slightly worse than PPO. We attribute this to the noise introduced by the GPT‑4.1‑mini synthesized CoPeR rationales. When the synthesized user-specific reasoning conflicts with the preference routing signals, it will lead to a higher KL divergence penalty (Equation~\\ref{eq:kl}), destabilizing training. Improving the quality of CoPeR synthesis will be done in future work.\n\n\n\\section{Conclusions and Future Work}\n% We have proposed to model both individual- and group-level preferences across majority and minority user populations for satisfaction estimation. To capture individual preferences, we introduce UCoT and CoPeR, which prompt and synthesizes interpretable reasoning chains. To learn group preferences, we propose an EM-based clustering module (M\\textsuperscript{2}PC) that identifies majority and minority groups without supervision. These components are integrated into a preference-adaptive reinforcement learning framework (PAda-PPO), enabling alignment with diverse user preferences. \nWe have introduced a unified framework for satisfaction estimation that simultaneously models individual- and group-level preferences among majority and minority user populations. We proposed UCoT and CoPeR to generate interpretable reasoning chains for capturing individual preferences, and developed M\\textsuperscript{2}PC, an unsupervised clustering module for identifying group-level preferences. These were integrated into PAda-PPO to align dialogue systems with diverse user preferences. Experiments on the ESConv dataset demonstrate improved satisfaction estimation across different user populations.\nIn future work, we will validate our proposed method on other LLMs, % such as Qwen\nand extend preference-adaptive reinforcement learning to additional RL algorithms. \n% including GRPO.\n\n\n\\section*{Limitations}\nA key limitation of our approach lies in the CoPeR supervision stage, where we rely on GPT‑4.1‑mini to generate reasoning chains as pseudo-ground truth. Given the inherently subjective nature of user satisfaction and context interpretation, it is challenging to synthesize rationales that accurately reflect the user's underlying intent. While this setup enables scalable training without manual annotation, the quality of the generated rationales may affect downstream fine-tuning and reinforcement learning. Inaccurate or overly generic reasoning can introduce noise into the learning process, hindering the model's ability to capture nuanced satisfaction patterns. \n% Future work could collecting real human data, including users’ own intents and explanations for their feedback scores, would be one of the best options, and we plan to pursue this as future work.\nFuture work could collect partial real human data, including users' own intents and explanations for their feedback scores, to enhance the reliability of reasoning supervision.\n\nAnother limitation is that M\\textsuperscript{2}PC does not model some subgroups of minority users well, as shown in Table~\\ref{tab:k_subgroups}. Future work is needed to better account for the nuanced preference patterns among these underrepresented subgroups.\n% Another limitation is the division of the subpopulations for majority and minority groups during M\\textsuperscript{2}PC. In this work, we divided 20 diverse user clusters for each majority and minority groups as the initialization, then \n\n\\section*{Acknowledgements}\nThis work was supported by JST Moonshot R\\&D Goal 1 Avatar Symbiotic Society Project (JPMJMS2011). \n\n% Bibliography entries for the entire Anthology, followed by custom entries\n%\\bibliography{anthology,custom}\n% Custom bibliography entries only\n\\bibliography{custom}\n% \\bibstyle{acl_natbib}\n\n\\appendix\n\n\\section{Prompts}\n\\label{sec:prompts_example}\n\nThe prompts used for base input, User-specific Chain-of-Thought, and for synthesizing User-specific Chains-of-Personalized-Reasoning are illustrated in Figure~\\ref{fig:base_prompt}, Figure~\\ref{fig:prompt_cot}, and Figure~\\ref{fig:prompt_coper} respectively.\n\n\n% \\begin{figure*}[t] \n% \\centering\n% \\begin{subfigure}{\\textwidth}\n% \\centering\n% \\includegraphics[width=0.9\\textwidth]{latex/figs/em_f1_base.pdf}\n% % \\caption{Base}\n% \\label{fig:em_base}\n% \\end{subfigure}\n% \\vspace{0.6em}\n% \\begin{subfigure}{\\textwidth}\n% \\centering\n% \\includegraphics[width=0.9\\textwidth]{latex/figs/em_f1_cot.pdf}\n% % \\caption{CoT}\n% \\label{fig:em_cot}\n% \\end{subfigure}\n% \\vspace{0.6em}\n% \\begin{subfigure}{\\textwidth}\n% \\centering\n% \\includegraphics[width=0.9\\textwidth]{latex/figs/em_f1_coper.pdf}\n% % \\caption{CoPeR}\n% \\label{fig:em_coper}\n% \\end{subfigure}\n% \\caption{Results on the EM iterations during the Majority-Minority Preference-Aware Clustering stage.}\n% \\label{fig:em_compare}\n% \\end{figure*}\n\n\\section{Analysis of Support Strategies and Feedback Scores}\n\\label{sec:feedback_dis}\nWe classify strategies into \\textbf{Cognition}-oriented (Question, Restatement or Paraphrasing, Providing Suggestions, Information) and \\textbf{Emotion}-oriented (Reflection of Feelings, Self-disclosure, Affirmation and Reassurance), and summarized each strategy's counts and proportions of low (1–3) and high (4–5) feedback scores in Table~\\ref{tab:feedback_compare}.\n% Table~\\ref{tab:counts} shows counts for each group; Table~\\ref{tab:proportion} shows the proportions receiving \\textbf{Low} (1–3) or \\textbf{High} (4–5) feedback scores. \n\nWe can see that for both majority and minority groups, emotion-oriented strategies are more likely to receive high feedback (0.94 > 0.91; 0.44 > 0.33), with the effect stronger in the minority group.\n\n\\begin{table}[h]\n\\begin{tabular}{@{}llrr@{}}\n\\toprule\nGroup & Strategy & \\multicolumn{1}{c}{Low} & \\multicolumn{1}{c}{High} \\\\ \\midrule\n\\multirow{2}{*}{Majority} & Cognition & 302 (0.09) & 3020 (0.91) \\\\\n & Emotion & 120 (0.06) & 1826 (0.94) \\\\\n\\multirow{2}{*}{Minority} & Cognition & 542 (0.67) & 264 (0.33) \\\\\n & Emotion & 240 (0.56) & 192 (0.44) \\\\ \\bottomrule\n\\end{tabular}\n% \\caption{Counts and proportion of feedback scores for cognition‑ and emotion‑oriented supporter response strategies across majority and minority user groups from ESConv dataset.}\n\\caption{Counts and proportion of groups by support strategy and satisfaction score}\n\\label{tab:feedback_compare}\n\\end{table}\n\n\n\\begin{figure}[h]\n \\centering\n\\includegraphics[width=\\linewidth]{figs/combined_f1_plots.pdf}\n \\caption{Results on the EM iterations during the Majority-Minority Preference-Aware Clustering stage.}\n \\label{fig:em_compare}\n\\end{figure}\n\n\n\\section{Evaluation of Synthesized Rationales}\n\\label{sec:evaluation}\n% We evaluate the accuracy and quality of synthesized rationales by GPT-4.1-mini. Individual preference is inherently subjective, human evaluation may be unreliable: annotators cannot directly access the seeker’s real thoughts. We therefore assess the quality and accuracy of the synthesized rationales with two objective metrics.\n\n% \\noindent (1) \\textbf{Supporter-strategy accuracy (7 classes)}: alignment between the supporter strategy predicted in Step 2 and the ground-truth label in the dataset.\n\n% \\noindent (2) \\textbf{Logical accuracy}: consistency between Step 1-3 and Step 4. Step 3 (“whether the support matched the seeker’s intent”) is reasoned from Step 1’s predicted seeker intent and Step 2’s predicted supporter strategy, while Step 4 provides the dataset’s gold satisfaction score (1-5). We define the mapping as: “matched intent” corresponds to scores 4–5; “partially matched” to 2–3; “did not match” to 1. A rationale is logically correct when this mapping holds.\n\n% On the training set, the synthesized rationales by GPT-4.1-mini achieve 63.44\\% supporter-strategy accuracy and 74.16\\% logical accuracy; on the validation set, 61.04\\% and 77.23\\%, respectively. \n\nFigure~\\ref{fig:cases} presents four case studies: \\textit{Low satisfaction} and \\textit{High satisfaction} examples under both correct and incorrect supporter-strategy and logical accuracies. \n\n\\section{Results on EM Iterations}\n\\label{sec:em_iterations}\n\nFigure~\\ref{fig:em_compare} presents the detailed results and trends across EM iterations during the Majority-Minority Preference-Aware Clustering stage.\n\n% \\begin{table}[ht]\n% \\centering\n% \\begin{tabular}{l l r r}\n% \\toprule\n% \\textbf{Group} & \\textbf{Strategy} & \\textbf{Low} & \\textbf{High} \\\\\n% \\midrule\n% Majority & Cognition & 302 & 3020 \\\\\n% Majority & Emotion & 120 & 1826 \\\\\n% Minority & Cognition & 542 & 264 \\\\\n% Minority & Emotion & 240 & 192 \\\\\n% \\bottomrule\n% \\end{tabular}\n% \\caption{Counts of Groups by Support Strategy and Satisfaction Score}\n% \\label{tab:counts}\n% \\end{table}\n\n% \\begin{table}[ht]\n% \\centering\n% \\begin{tabular}{l l r r}\n% \\toprule\n% \\textbf{Group} & \\textbf{Strategy} & \\textbf{Low} & \\textbf{High} \\\\\n% \\midrule\n% Majority & Cognition & 0.09 & 0.91 \\\\\n% Majority & Emotion & 0.06 & 0.94 \\\\\n% Minority & Cognition & 0.67 & 0.33 \\\\\n% Minority & Emotion & 0.56 & 0.44 \\\\\n% \\bottomrule\n% \\end{tabular}\n% \\caption{Proportion of Groups by Support Strategy and Satisfaction Score}\n% \\label{tab:proportion}\n% \\end{table}\n\n\n\n\\begin{figure*}\n \\centering\n\\includegraphics[width=0.93\\textwidth]{figs/prompt_base.pdf}\n \\caption{Base prompt.}\n \\label{fig:base_prompt}\n\\end{figure*}\n\n\n\\begin{figure*}\n \\centering\n\\includegraphics[width=0.93\\textwidth]{figs/prompt_ucot.pdf}\n \\caption{Prompt for User-specific Chain-of-Thought.}\n \\label{fig:prompt_cot}\n\\end{figure*}\n\n\\begin{figure*}\n \\centering\n\\includegraphics[width=0.93\\textwidth]{figs/coper.pdf}\n \\caption{Prompt for User-specific Chains-of-Personalized-Reasoning synthesis.}\n \\label{fig:prompt_coper}\n\\end{figure*}\n\n\n\\begin{figure*}\n \\centering\n\\includegraphics[width=0.93\\textwidth]{figs/cases.pdf}\n \\caption{Case Studies.}\n \\label{fig:cases}\n\\end{figure*}\n\n\n\n\\begin{table*}[h]\n \\centering\n % \\scriptsize\n \\scalebox{0.83}{\n \\begin{tabular}{@{}l ll\n rrrr\n rrrr\n rrrr@{}}\n \\toprule\n \\multirow{2}{*}{Iteration} & \\multirow{2}{*}{Users$_{\\text{minor}}$} & \\multirow{2}{*}{Users$_{\\text{major}}$}\n & \\multicolumn{4}{c}{Minority}\n & \\multicolumn{4}{c}{Majority}\n & \\multicolumn{4}{c}{Minority+Majority} \\\\\n \\cmidrule(lr){4-7}\\cmidrule(lr){8-11}\\cmidrule(lr){12-15}\n & & & $F^{\\text{low}}_1$ & $F^{\\text{high}}_1$ & $F^{\\text{w}}_1$ & $F^{\\text{m}}_1$\n & $F^{\\text{low}}_1$ & $F^{\\text{high}}_1$ & $F^{\\text{w}}_1$ & $F^{\\text{m}}_1$\n & $F^{\\text{low}}_1$ & $F^{\\text{high}}_1$ & $F^{\\text{w}}_1$ & $F^{\\text{m}}_1$ \\\\\n \\midrule\n\n % \\groupheader{Initializing Majority and Minority Groups as 10}\n 0 & 10 & 10 & 0.29 & 0.53 & 0.37 & 0.41 & 0.15 & 0.91 & 0.85 & 0.53 & 0.22 & 0.85 & 0.73 & 0.54 \\\\\n \\rowcolor{paleGrayGreen} \n 1 & 10 & 10 & 0.73 & 0.46 & 0.63 & 0.60 & 0.06 & 0.94 & 0.87 & 0.50 & 0.56 & 0.90 & 0.84 & 0.73 \\\\\n 2 & 10 & 10 & 0.72 & 0.40 & 0.61 & 0.56 & 0.09 & 0.94 & 0.88 & 0.52 & 0.56 & 0.90 & 0.84 & 0.73 \\\\\n 3 & 9 & 11 & 0.72 & 0.37 & 0.60 & 0.54 & 0.11 & 0.94 & 0.87 & 0.52 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\n 4 & 8 & 12 & 0.70 & 0.26 & 0.56 & 0.48 & 0.08 & 0.94 & 0.85 & 0.51 & 0.50 & 0.90 & 0.83 & 0.70 \\\\\n 5 & 9 & 11 & 0.71 & 0.30 & 0.57 & 0.51 & 0.03 & 0.94 & 0.86 & 0.48 & 0.52 & 0.90 & 0.83 & 0.71 \\\\\n % 6 & 8 & 12 & 0.75 & 0.36 & 0.62 & 0.55 & 0.11 & 0.94 & 0.85 & 0.53 & 0.54 & 0.91 & 0.84 & 0.72 \\\\\n % 7 & 7 & 13 & 0.76 & 0.35 & 0.63 & 0.55 & 0.02 & 0.93 & 0.83 & 0.48 & 0.49 & 0.90 & 0.82 & 0.69 \\\\\n % 8 & 8 & 12 & 0.76 & 0.27 & 0.60 & 0.51 & 0.11 & 0.93 & 0.85 & 0.52 & 0.54 & 0.90 & 0.83 & 0.72 \\\\\n % 9 & 7 & 13 & 0.76 & 0.42 & 0.65 & 0.59 & 0.04 & 0.93 & 0.83 & 0.48 & 0.48 & 0.90 & 0.82 & 0.69 \\\\\n % 10 & 7 & 13 & 0.73 & 0.38 & 0.62 & 0.55 & 0.06 & 0.93 & 0.83 & 0.50 & 0.46 & 0.90 & 0.82 & 0.68 \\\\\n \\midrule\n\n % \\groupheader{Initializing Majority and Minority Groups as 10}\n 0 & 20 & 20 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\n 1 & 18 & 22 & 0.75 & 0.46 & 0.66 & 0.60 & 0.09 & 0.95 & 0.88 & 0.52 & 0.56 & 0.91 & 0.85 & 0.74 \\\\\n \\rowcolor{paleGrayGreen} \n 2 & 17 & 23 & 0.80 & 0.46 & 0.70 & 0.63 & 0.08 & 0.95 & 0.87 & 0.51 & 0.60 & 0.92 & 0.86 & 0.76 \\\\\n 3 & 16 & 24 & 0.75 & 0.31 & 0.62 & 0.53 & 0.00 & 0.93 & 0.85 & 0.47 & 0.52 & 0.90 & 0.83 & 0.71 \\\\\n 4 & 15 & 25 & 0.79 & 0.38 & 0.67 & 0.58 & 0.09 & 0.94 & 0.86 & 0.52 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\n 5 & 17 & 23 & 0.72 & 0.36 & 0.60 & 0.54 & 0.07 & 0.94 & 0.86 & 0.50 & 0.51 & 0.90 & 0.83 & 0.71 \\\\\n % 6 & 17 & 23 & 0.73 & 0.24 & 0.58 & 0.49 & 0.07 & 0.94 & 0.86 & 0.51 & 0.54 & 0.90 & 0.83 & 0.72 \\\\\n % 7 & 12 & 28 & 0.75 & 0.29 & 0.61 & 0.52 & 0.08 & 0.92 & 0.82 & 0.50 & 0.46 & 0.90 & 0.82 & 0.68 \\\\\n % 8 & 11 & 29 & 0.75 & 0.28 & 0.62 & 0.51 & 0.09 & 0.92 & 0.82 & 0.51 & 0.44 & 0.90 & 0.81 & 0.67 \\\\\n % 9 & 13 & 27 & 0.79 & 0.42 & 0.69 & 0.61 & 0.07 & 0.93 & 0.84 & 0.50 & 0.51 & 0.91 & 0.83 & 0.71 \\\\\n % 10 & 11 & 29 & 0.75 & 0.38 & 0.65 & 0.56 & 0.06 & 0.92 & 0.82 & 0.49 & 0.43 & 0.90 & 0.82 & 0.67 \\\\\n \\midrule\n\n % \\groupheader{Initializing Majority and Minority Groups as 10}\n 0 & 30 & 30 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\n \\rowcolor{paleGrayGreen} \n 1 & 27 & 33 & 0.73 & 0.40 & 0.63 & 0.57 & 0.12 & 0.95 & 0.88 & 0.53 & 0.56 & 0.91 & 0.85 & 0.74 \\\\\n 2 & 23 & 37 & 0.77 & 0.42 & 0.67 & 0.60 & 0.07 & 0.94 & 0.85 & 0.50 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\n 3 & 25 & 35 & 0.73 & 0.22 & 0.58 & 0.47 & 0.03 & 0.94 & 0.86 & 0.48 & 0.53 & 0.90 & 0.83 & 0.71 \\\\\n 4 & 25 & 35 & 0.73 & 0.29 & 0.60 & 0.51 & 0.03 & 0.94 & 0.86 & 0.49 & 0.54 & 0.91 & 0.84 & 0.72 \\\\\n 5 & 24 & 36 & 0.77 & 0.47 & 0.68 & 0.62 & 0.05 & 0.94 & 0.86 & 0.50 & 0.55 & 0.91 & 0.85 & 0.73 \\\\\n % 6 & 22 & 38 & 0.78 & 0.40 & 0.66 & 0.59 & 0.07 & 0.93 & 0.85 & 0.50 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\n % 7 & 19 & 41 & 0.79 & 0.41 & 0.68 & 0.60 & 0.02 & 0.93 & 0.82 & 0.47 & 0.49 & 0.91 & 0.83 & 0.70 \\\\\n % 8 & 18 & 42 & 0.75 & 0.33 & 0.63 & 0.54 & 0.07 & 0.92 & 0.82 & 0.50 & 0.44 & 0.90 & 0.81 & 0.67 \\\\\n % 9 & 14 & 46 & 0.76 & 0.47 & 0.67 & 0.61 & 0.06 & 0.91 & 0.79 & 0.49 & 0.37 & 0.89 & 0.79 & 0.63 \\\\\n % 10 & 16 & 44 & 0.77 & 0.37 & 0.65 & 0.57 & 0.02 & 0.91 & 0.80 & 0.47 & 0.40 & 0.90 & 0.80 & 0.65 \\\\\n \\midrule\n\n % \\groupheader{Initializing Majority and Minority Groups as 10}\n 0 & 40 & 40 & 0.29 & 0.53 & 0.37 & 0.41 & 0.15 & 0.91 & 0.85 & 0.53 & 0.22 & 0.85 & 0.73 & 0.54 \\\\\n \\rowcolor{paleGrayGreen} \n 1 & 34 & 46 & 0.78 & 0.39 & 0.67 & 0.59 & 0.10 & 0.94 & 0.87 & 0.52 & 0.59 & 0.91 & 0.85 & 0.75 \\\\\n 2 & 31 & 49 & 0.78 & 0.46 & 0.69 & 0.62 & 0.00 & 0.94 & 0.85 & 0.47 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\n 3 & 31 & 49 & 0.74 & 0.35 & 0.63 & 0.55 & 0.03 & 0.94 & 0.85 & 0.48 & 0.51 & 0.90 & 0.83 & 0.71 \\\\\n 4 & 33 & 47 & 0.76 & 0.42 & 0.66 & 0.59 & 0.03 & 0.94 & 0.86 & 0.48 & 0.54 & 0.91 & 0.84 & 0.72 \\\\\n 5 & 27 & 53 & 0.83 & 0.47 & 0.73 & 0.65 & 0.02 & 0.93 & 0.83 & 0.48 & 0.53 & 0.91 & 0.84 & 0.72 \\\\\n % 6 & 32 & 48 & 0.76 & 0.27 & 0.63 & 0.52 & 0.00 & 0.94 & 0.85 & 0.47 & 0.54 & 0.91 & 0.84 & 0.72 \\\\\n % 7 & 31 & 49 & 0.72 & 0.32 & 0.61 & 0.52 & 0.12 & 0.94 & 0.86 & 0.53 & 0.52 & 0.91 & 0.83 & 0.71 \\\\\n % 8 & 29 & 51 & 0.74 & 0.33 & 0.63 & 0.54 & 0.02 & 0.93 & 0.84 & 0.48 & 0.49 & 0.90 & 0.82 & 0.69 \\\\\n % 9 & 26 & 54 & 0.86 & 0.56 & 0.78 & 0.71 & 0.09 & 0.93 & 0.84 & 0.51 & 0.56 & 0.92 & 0.85 & 0.74 \\\\\n % 10 & 23 & 57 & 0.80 & 0.26 & 0.66 & 0.53 & 0.06 & 0.93 & 0.82 & 0.49 & 0.49 & 0.91 & 0.83 & 0.70 \\\\\n \\midrule\n\n % \\groupheader{Initializing Majority and Minority Groups as 10}\n 0 & 50 & 50 & 0.29 & 0.53 & 0.37 & 0.41 & 0.11 & 0.91 & 0.85 & 0.51 & 0.20 & 0.86 & 0.73 & 0.53 \\\\\n 1 & 40 & 60 & 0.71 & 0.35 & 0.59 & 0.53 & 0.05 & 0.94 & 0.85 & 0.49 & 0.50 & 0.90 & 0.82 & 0.70 \\\\\n 2 & 43 & 57 & 0.73 & 0.47 & 0.64 & 0.60 & 0.08 & 0.94 & 0.87 & 0.51 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\n 3 & 37 & 63 & 0.83 & 0.47 & 0.73 & 0.65 & 0.11 & 0.93 & 0.85 & 0.52 & 0.58 & 0.91 & 0.85 & 0.75 \\\\\n \\rowcolor{paleGrayGreen}\n 4 & 42 & 58 & 0.77 & 0.36 & 0.63 & 0.57 & 0.06 & 0.94 & 0.87 & 0.50 & 0.59 & 0.91 & 0.85 & 0.75 \\\\\n 5 & 36 & 64 & 0.77 & 0.38 & 0.64 & 0.58 & 0.13 & 0.93 & 0.85 & 0.53 & 0.55 & 0.91 & 0.84 & 0.73 \\\\\n % 6 & 36 & 64 & 0.75 & 0.31 & 0.63 & 0.53 & 0.09 & 0.93 & 0.85 & 0.51 & 0.50 & 0.90 & 0.83 & 0.70 \\\\\n % 7 & 33 & 67 & 0.78 & 0.38 & 0.67 & 0.58 & 0.08 & 0.93 & 0.83 & 0.50 & 0.50 & 0.91 & 0.83 & 0.70 \\\\\n % 8 & 29 & 71 & 0.78 & 0.36 & 0.68 & 0.57 & 0.13 & 0.92 & 0.83 & 0.52 & 0.48 & 0.90 & 0.82 & 0.69 \\\\\n % 9 & 30 & 70 & 0.80 & 0.40 & 0.70 & 0.60 & 0.10 & 0.93 & 0.83 & 0.51 & 0.50 & 0.91 & 0.83 & 0.71 \\\\\n % 10 & 29 & 71 & 0.79 & 0.40 & 0.68 & 0.60 & 0.11 & 0.92 & 0.83 & 0.52 & 0.49 & 0.91 & 0.83 & 0.70 \\\\\n \\bottomrule\n \\end{tabular}}\n \\caption{Results of the proposed \\textbf{Llama-3-8B-CoPeR + M\\textsuperscript{2}PC}, when initializing majority and minority users as 10, 20, 30, 40, and 50, respectively.}\n \\label{tab: users}\n\\end{table*}\n\n\n\\section{Results on Different User Clusters}\n\\label{sec:ablation}\nFor training, we randomly selected from the majority group the same number of conversations as in the minority group, with each conversation representing a user. These users are evenly and randomly divided into 20 clusters per group. During M²PC training, each cluster (a batch of users) is reassigned to majority or minority groups based on perplexity in an unsupervised manner; therefore, no universally accepted partition rule is required. We believe this approach may help capture finer subpopulation preferences within each majority or minority group, as the routing perplexity is computed from the average perplexity of all users in each cluster/subpopulation.\nTable~\\ref{tab: users} presents the results of the proposed \\textbf{Llama-3-8B-CoPeR + M\\textsuperscript{2}PC} model when the numbers of majority and minority users are initialized to 10, 20, 30, 40, and 50, respectively. The best performance is obtained when both groups are initialized to 20, with which after the second iteration, the algorithm yields 23 distinct majority groups and 17 distinct minority groups, indicating that M\\textsuperscript{2}PC adaptively clusters users with similar preferences.\n\n\n% \\begin{table*}[h]\n% \\centering\n% \\resizebox{\\textwidth}{!}{\n% \\begin{tabular}{lllllllllllll}\n% \\midrule\n% Models & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\n% \\midrule\n% \\multicolumn{11}{l}{\\textit{Llama-3-8B+M2PC}} \\\\\n% Maj. & 0.85(111) & 0.68(105) & \\textbf{0.89(67)} & \\textbf{0.84(60)} & \\textbf{0.91(55)} & \\textbf{0.91(38)} & \\textbf{0.96(38)} & \\textbf{0.92(31)} & \\textbf{0.95(27)} & \\textbf{0.79(21)} \\\\\n% Min. & 0.60(21) & 0.71(21) & \\textbf{0.68(10)} & \\textbf{0.77(9)} & 0.63(8) & 0.19(7) & \\textbf{0.84(6)} & \\textbf{0.91(6)} & 0.57(5) & \\textbf{1.00(5)} \\\\\n% \\midrule\n% \\multicolumn{11}{l}{\\textit{Llama-3-8B-UCoT+M2PC}} \\\\\n% Maj. & 0.86(126) & 0.76(94) & \\textbf{0.97(58)} & \\textbf{1.00(44)} & \\textbf{0.92(26)} & \\textbf{1.00(26)} & \\textbf{1.00(26)} & \\textbf{0.88(25)} & \\textbf{0.82(24)} & \\textbf{0.94(24)} \\\\\n% Min. & 0.46(45) & 0.64(37) & 0.52(17) & \\textbf{0.55(11)} & 0.42(8) & \\textbf{0.87(7)} & \\textbf{0.76(7)} & 0.00(7) & \\textbf{0.67(6)} & 0.23(6) \\\\\n% \\midrule\n% \\multicolumn{11}{l}{\\textit{Llama-3-8B-CoPeR+M2PC}} \\\\\n% Maj. & 0.71(134) & 0.79(105) & \\textbf{0.93(56)} & \\textbf{0.85(48)} & \\textbf{0.94(44)} & \\textbf{0.94(39)} & \\textbf{0.90(30)} & \\textbf{0.90(30)} & \\textbf{0.82(28)} & \\textbf{0.87(27)} \\\\\n% Min. & 0.70(22) & 0.61(21) & \\textbf{0.67(7)} & \\textbf{0.91(6)} & \\textbf{0.67(6)} & \\textbf{1.00(5)} & \\textbf{0.80(5)} & 0.34(5) & 0.64(4) & 0.33(4) \\\\\n% \\midrule\n% \\end{tabular}\n% }\n% \\caption{Performance comparison across different models (Iterations 1-10)}\n% \\label{tab:model_comparison_part1}\n% \\end{table*}\n\n% \\begin{table*}[h]\n% \\centering\n% \\resizebox{\\textwidth}{!}{\n% \\begin{tabular}{lllllllllllll}\n% \\midrule\n% Models & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\\\\n% \\midrule\n% \\multicolumn{11}{l}{\\textit{Llama-3-8B+M2PC}} \\\\\n% Maj. & \\textbf{1.00(18)} & \\textbf{0.91(17)} & \\textbf{1.00(10)} & \\textbf{0.84(9)} & \\textbf{1.00(9)} & \\textbf{1.00(9)} & \\textbf{1.00(6)} & - & - & - \\\\\n% Min. & \\textbf{0.82(5)} & 0.63(5) & 0.00(4) & 0.64(4) & 0.50(4) & \\textbf{0.73(4)} & \\textbf{0.73(4)} & \\textbf{0.73(4)} & \\textbf{0.67(3)} & - \\\\\n% \\midrule\n% \\multicolumn{11}{l}{\\textit{Llama-3-8B-UCoT+M2PC}} \\\\\n% Maj. & \\textbf{0.93(20)} & \\textbf{0.85(20)} & \\textbf{1.00(18)} & \\textbf{1.00(16)} & \\textbf{1.00(14)} & 0.79(7) & \\textbf{1.00(6)} & \\textbf{1.00(5)} & - & - \\\\\n% Min. & \\textbf{0.63(5)} & \\textbf{1.00(4)} & 0.20(4) & \\textbf{0.73(4)} & \\textbf{0.67(4)} & 0.33(3) & \\textbf{0.67(3)} & \\textbf{0.80(3)} & 0.53(3) & \\textbf{1.00(3)} \\\\\n% \\midrule\n% \\multicolumn{11}{l}{\\textit{Llama-3-8B-CoPeR+M2PC}} \\\\\n% Maj. & \\textbf{0.91(22)} & \\textbf{0.94(20)} & \\textbf{0.90(19)} & \\textbf{0.96(14)} & \\textbf{1.00(9)} & \\textbf{1.00(8)} & \\textbf{1.00(8)} & \\textbf{1.00(7)} & \\textbf{1.00(4)} & - \\\\\n% Min. & \\textbf{1.00(4)} & 0.20(4) & \\textbf{0.67(3)} & 0.53(3) & 0.53(3) & \\textbf{0.67(3)} & \\textbf{1.00(3)} & \\textbf{0.67(2)} & \\textbf{1.00(2)} & \\textbf{1.00(2)} \\\\\n% \\midrule\n% \\end{tabular}\n% }\n% \\caption{Performance comparison across different models (Iterations 11-20)}\n% \\label{tab:model_comparison_part2}\n% \\end{table*}\n\n\n\n\n\n\\end{document}\n"},"question":{"kind":"string","value":"Upon all group-level evaluation setting, in F1 high satisfication metric, which model has the largest improvment to its M^2PC enhanced one?"},"answer":{"kind":"string","value":"Llama-3-8B"},"plan":{"kind":"string","value":"SELECT all models\nLOOP for each model\n SELECT all group-level evaluation settings\n LOOP for each group-level setting\n COMPUTE improvement = F1 high satisfaction score for M2PC-enhanced − F1 high satisfaction score for original model\nCOMPUTE target_model = argmax model over improvement\n\n\nRETURN target_model\n"}}},{"rowIdx":369,"cells":{"paper":{"kind":"string","value":"2511.11473"},"relevant_tables":{"kind":"list like","value":[["\\begin{table*}[t!]\n","\\caption{Evaluation on English (Libri, Candor, SpokenWoZ) and Mandarin (RAMC) testsets.}\n","\\vskip -0.1in\n","\\centering\n"," \\setlength{\\tabcolsep}{5.3pt}\n","{\\footnotesize\n","\\begin{tabular}{lcccccccc}\n","\\toprule\n","& \\multicolumn{4}{c}{Non-spatialized} & \\multicolumn{4}{c}{Spatialized} \\\\\n","\\cmidrule(r){2-5} \\cmidrule(l){6-9}\n","\\textbf{Metrics} & SISDRi($\\uparrow$) & Acc ($\\uparrow$) & CR ($\\downarrow$) & $\\Delta$PESQ($\\uparrow$) & SISDRi($\\uparrow$) & Acc($\\uparrow$) & CR($\\downarrow$) & $\\Delta$PESQ($\\uparrow$) \\\\\n","\\midrule\n","\\textbf{Baseline Model (SE)} &&&&&&&&\\\\\n","\\midrule\n","Synthetic Libri & -1.95 (1.94) & 26.8\\% & 26.3\\% & -0.16 (0.14) & -3.31 (2.23) & 10.5\\% & 27.7\\% & -0.13 (0.13)\\\\\n","Candor & -5.16 (3.19) & 13.5\\% & 24.4\\% & -0.29 (0.22) & -3.05 (2.84) & 18.8\\% & 21.7\\% & -0.16 (0.17)\\\\\n","SpokenWoz (OOD) & -5.05 (4.04) & 14.7\\% & 14.7\\% & -0.48 (0.33) & -3.45 (3.78) & 16.8\\% & 9.2\\% & -0.16 (0.21)\\\\\n","RAMC & -4.28 (6.01) & 13.6\\% & 27.9\\% & -0.32 (0.28) & -4.30 (3.37) & 6.8\\% & 19.9\\% & -0.17 (0.17)\\\\\n","\\midrule\n","\\textbf{Our Dual Models} &&&&&&\\\\\n","\\midrule\n","Synthetic Libri & 11.70 (4.56) & 96.3\\% & 1.4\\% & 1.11 (0.30) & 14.62 (6.05) & 96.8\\% & 0.8\\% & 0.63 (0.23) \\\\\n","Candor & 6.75 (4.29) & 87.0\\% & 2.7\\% & 0.64 (0.31) & 9.82 (3.77) & 93.9\\% & 1.1\\% & 0.56 (0.20)\\\\\n","SpokenWoz (OOD) & 7.27 (6.11) & 84.5\\% & 4.3\\% & 0.58 (0.44) &11.95 (6.22) & 92.1\\% & 1.5\\% & 0.52 (0.25) \\\\\n","RAMC & 6.50 (7.45) & 85.5\\% & 5.6\\% & 0.63 (0.41) & 8.05 (9.29) & 78.0\\% & 9.4\\% & 0.26 (0.40) \\\\\n","\\midrule\n","Libri (2spk) & 12.48 (4.28) & 98.4\\% & 0.6\\% & 1.14 (0.24) & 15.68 (5.46) & 99.2\\% & 0.2\\% & 0.65 (0.22) \\\\\n","Libri (3spk) & 12.03 (4.00) & 96.6\\% & 1.2\\% & 1.16 (0.25) & 14.29 (6.08) & 96.1\\% & 0.6\\% & 0.63 (0.21) \\\\\n","Libri (leaving) & 10.58 (5.10) & 94.1\\% & 2.5\\% & 1.03 (0.36) & 13.89 (6.42) & 95.7\\% & 1.5\\% & 0.60 (0.24)\\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:big_results}\n","\\vskip -0.15in\n","\\end{table*}\n"]],"string":"[\n [\n \"\\\\begin{table*}[t!]\\n\",\n \"\\\\caption{Evaluation on English (Libri, Candor, SpokenWoZ) and Mandarin (RAMC) testsets.}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \"\\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5.3pt}\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"& \\\\multicolumn{4}{c}{Non-spatialized} & \\\\multicolumn{4}{c}{Spatialized} \\\\\\\\\\n\",\n \"\\\\cmidrule(r){2-5} \\\\cmidrule(l){6-9}\\n\",\n \"\\\\textbf{Metrics} & SISDRi($\\\\uparrow$) & Acc ($\\\\uparrow$) & CR ($\\\\downarrow$) & $\\\\Delta$PESQ($\\\\uparrow$) & SISDRi($\\\\uparrow$) & Acc($\\\\uparrow$) & CR($\\\\downarrow$) & $\\\\Delta$PESQ($\\\\uparrow$) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Baseline Model (SE)} &&&&&&&&\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Synthetic Libri & -1.95 (1.94) & 26.8\\\\% & 26.3\\\\% & -0.16 (0.14) & -3.31 (2.23) & 10.5\\\\% & 27.7\\\\% & -0.13 (0.13)\\\\\\\\\\n\",\n \"Candor & -5.16 (3.19) & 13.5\\\\% & 24.4\\\\% & -0.29 (0.22) & -3.05 (2.84) & 18.8\\\\% & 21.7\\\\% & -0.16 (0.17)\\\\\\\\\\n\",\n \"SpokenWoz (OOD) & -5.05 (4.04) & 14.7\\\\% & 14.7\\\\% & -0.48 (0.33) & -3.45 (3.78) & 16.8\\\\% & 9.2\\\\% & -0.16 (0.21)\\\\\\\\\\n\",\n \"RAMC & -4.28 (6.01) & 13.6\\\\% & 27.9\\\\% & -0.32 (0.28) & -4.30 (3.37) & 6.8\\\\% & 19.9\\\\% & -0.17 (0.17)\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Our Dual Models} &&&&&&\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Synthetic Libri & 11.70 (4.56) & 96.3\\\\% & 1.4\\\\% & 1.11 (0.30) & 14.62 (6.05) & 96.8\\\\% & 0.8\\\\% & 0.63 (0.23) \\\\\\\\\\n\",\n \"Candor & 6.75 (4.29) & 87.0\\\\% & 2.7\\\\% & 0.64 (0.31) & 9.82 (3.77) & 93.9\\\\% & 1.1\\\\% & 0.56 (0.20)\\\\\\\\\\n\",\n \"SpokenWoz (OOD) & 7.27 (6.11) & 84.5\\\\% & 4.3\\\\% & 0.58 (0.44) &11.95 (6.22) & 92.1\\\\% & 1.5\\\\% & 0.52 (0.25) \\\\\\\\\\n\",\n \"RAMC & 6.50 (7.45) & 85.5\\\\% & 5.6\\\\% & 0.63 (0.41) & 8.05 (9.29) & 78.0\\\\% & 9.4\\\\% & 0.26 (0.40) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Libri (2spk) & 12.48 (4.28) & 98.4\\\\% & 0.6\\\\% & 1.14 (0.24) & 15.68 (5.46) & 99.2\\\\% & 0.2\\\\% & 0.65 (0.22) \\\\\\\\\\n\",\n \"Libri (3spk) & 12.03 (4.00) & 96.6\\\\% & 1.2\\\\% & 1.16 (0.25) & 14.29 (6.08) & 96.1\\\\% & 0.6\\\\% & 0.63 (0.21) \\\\\\\\\\n\",\n \"Libri (leaving) & 10.58 (5.10) & 94.1\\\\% & 2.5\\\\% & 1.03 (0.36) & 13.89 (6.42) & 95.7\\\\% & 1.5\\\\% & 0.60 (0.24)\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:big_results}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table*}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{figure}[t!]\n"," \\centering\n"," \\vskip -0.1in\n"," \\includegraphics[width=\\linewidth]{figs/teaser_figure.pdf}\n"," \\vskip -0.1in\n"," \\caption{In multi-conversation settings, our proactive hearing assistant uses conversational turn-taking dynamics to automatically infers the wearer's conversation partners and suppresses others in real-time. }\n"," \\vskip -0.15in\n"," \\label{fig:teaser}\n","\\end{figure}\n"],["\\begin{figure*}[t]\n"," \\centering\n"," \\includegraphics[width=1\\linewidth]{figs/diagram.pdf}\n"," \\vskip -0.14in\n"," \\caption{Overview of our model pipeline. A. The streaming beamformer extracts the wearer's self-speech from the binaural mixture. B. Dual-model architecture: the slow model runs every 1s ($T$) on the mixture and self-speech to produce a conversation embedding; the fast model runs every 12.5~ms ($\\tau$) on the current mixture and embedding from the previous 1s ($T$), to output the cleaned target conversation.\n"," }\n"," \\vskip -0.15in\n"," \\label{fig:pipeline}\n","\\end{figure*}\n"],["\\begin{table*}[t!]\n","\\caption{Evaluation on English (Libri, Candor, SpokenWoZ) and Mandarin (RAMC) testsets.}\n","\\vskip -0.1in\n","\\centering\n"," \\setlength{\\tabcolsep}{5.3pt}\n","{\\footnotesize\n","\\begin{tabular}{lcccccccc}\n","\\toprule\n","& \\multicolumn{4}{c}{Non-spatialized} & \\multicolumn{4}{c}{Spatialized} \\\\\n","\\cmidrule(r){2-5} \\cmidrule(l){6-9}\n","\\textbf{Metrics} & SISDRi($\\uparrow$) & Acc ($\\uparrow$) & CR ($\\downarrow$) & $\\Delta$PESQ($\\uparrow$) & SISDRi($\\uparrow$) & Acc($\\uparrow$) & CR($\\downarrow$) & $\\Delta$PESQ($\\uparrow$) \\\\\n","\\midrule\n","\\textbf{Baseline Model (SE)} &&&&&&&&\\\\\n","\\midrule\n","Synthetic Libri & -1.95 (1.94) & 26.8\\% & 26.3\\% & -0.16 (0.14) & -3.31 (2.23) & 10.5\\% & 27.7\\% & -0.13 (0.13)\\\\\n","Candor & -5.16 (3.19) & 13.5\\% & 24.4\\% & -0.29 (0.22) & -3.05 (2.84) & 18.8\\% & 21.7\\% & -0.16 (0.17)\\\\\n","SpokenWoz (OOD) & -5.05 (4.04) & 14.7\\% & 14.7\\% & -0.48 (0.33) & -3.45 (3.78) & 16.8\\% & 9.2\\% & -0.16 (0.21)\\\\\n","RAMC & -4.28 (6.01) & 13.6\\% & 27.9\\% & -0.32 (0.28) & -4.30 (3.37) & 6.8\\% & 19.9\\% & -0.17 (0.17)\\\\\n","\\midrule\n","\\textbf{Our Dual Models} &&&&&&\\\\\n","\\midrule\n","Synthetic Libri & 11.70 (4.56) & 96.3\\% & 1.4\\% & 1.11 (0.30) & 14.62 (6.05) & 96.8\\% & 0.8\\% & 0.63 (0.23) \\\\\n","Candor & 6.75 (4.29) & 87.0\\% & 2.7\\% & 0.64 (0.31) & 9.82 (3.77) & 93.9\\% & 1.1\\% & 0.56 (0.20)\\\\\n","SpokenWoz (OOD) & 7.27 (6.11) & 84.5\\% & 4.3\\% & 0.58 (0.44) &11.95 (6.22) & 92.1\\% & 1.5\\% & 0.52 (0.25) \\\\\n","RAMC & 6.50 (7.45) & 85.5\\% & 5.6\\% & 0.63 (0.41) & 8.05 (9.29) & 78.0\\% & 9.4\\% & 0.26 (0.40) \\\\\n","\\midrule\n","Libri (2spk) & 12.48 (4.28) & 98.4\\% & 0.6\\% & 1.14 (0.24) & 15.68 (5.46) & 99.2\\% & 0.2\\% & 0.65 (0.22) \\\\\n","Libri (3spk) & 12.03 (4.00) & 96.6\\% & 1.2\\% & 1.16 (0.25) & 14.29 (6.08) & 96.1\\% & 0.6\\% & 0.63 (0.21) \\\\\n","Libri (leaving) & 10.58 (5.10) & 94.1\\% & 2.5\\% & 1.03 (0.36) & 13.89 (6.42) & 95.7\\% & 1.5\\% & 0.60 (0.24)\\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:big_results}\n","\\vskip -0.15in\n","\\end{table*}\n"],["\\begin{table}[t!]\n","\\caption{SISDRi results for generalization.}\n","\\vskip -0.1in\n","\\centering\n"," \\setlength{\\tabcolsep}{5pt} % adjust column spacing\n","{\\footnotesize\n","\\begin{tabular}{lc}\n","\\toprule\n","\\textbf{Dataset} & SISDRi ($\\uparrow$) \\\\\n","\\midrule\n","Libri (2spk) & 12.48 (4.28) \\\\\n","Libri (3spk) & 12.03 (4.00) \\\\\n","Libri (4spk) & 11.94 (4.46) \\\\\n","Libri (5spk) & 11.85 (4.58) \\\\\n","\\midrule\n","RAMC & 6.50 (7.45) \\\\\n","Japanese (OOD) & 7.92 (5.19) \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:sisdr_datasets}\n","\\vskip -0.15in\n","\\end{table}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\vskip -0.1in\n"," \\includegraphics[width=0.6\\linewidth]{leaving_scatter.png}\n"," \\vskip -0.1in\n"," \\caption{Model enhances then suppresses speaker following shift from target to interfering conversation.}\n"," \\vskip -0.15in\n"," \\label{fig:leaving_scatter}\n","\\end{figure}\n"],["\\begin{table}[t!]\n","\\caption{Subjective evaluation results (5-point scale).}\n","\\vskip -0.1in\n","\\centering\n"," \\setlength{\\tabcolsep}{6pt} % adjust spacing as needed\n","{\\footnotesize\n","\\begin{tabular}{lcc}\n","\\toprule\n","\\textbf{Question} & \\textbf{Model Output} & \\textbf{Mixture} \\\\\n","\\midrule\n","Noise suppression & 4.29 (1.19) & 1.67 (1.04) \\\\\n","Comprehension & 4.35 (1.02) & 1.97 (0.93) \\\\\n","Effort & 4.45 (0.95) & 1.97 (0.96) \\\\\n","Overall MOS & 4.30 (1.14) & 1.88 (1.02) \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:user_study_table}\n","\\vskip -0.15in\n","\\end{table}\n"],["\\begin{table}[t!]\n","\\caption{Evaluation on real egocentric conversations.}\n","\\vskip -0.1in\n","\\centering\n"," \\setlength{\\tabcolsep}{5.3pt}\n","{\\footnotesize\n","\\begin{tabular}{lccc}\n","\\toprule\n","\\textbf{Metrics} & SISDRi($\\uparrow$) & Acc ($\\uparrow$) & CR ($\\downarrow$) \\\\\n","\\midrule\n","\\textbf{Number of speakers} & & &\\\\\n","\\midrule\n"," 2 speakers & 7.84 (6.79) & 85.0\\% & 1.1\\% \\\\\n"," 3 speakers & 6.00 (7.14) & 73.4\\% & 3.7\\% \\\\\n","\\midrule \n","\\textbf{Augmentation} & & & \\\\\n","\\midrule \n"," \\ding{55} & 5.49 (5.30) & 77.9\\% & 1.2\\% \\\\\n"," \\ding{51} & 7.22 (6.96) & 80.0\\% & 2.2\\% \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:hardware_result}\n","\\vskip -0.15in\n","\\end{table}\n"],["\\begin{table}[t!]\n","\\caption{Impact of perturbing the turn-taking in human conversations. (SD=standard deviation)}\n","\\vskip -0.1in\n","\\centering\n"," \\setlength{\\tabcolsep}{6pt} % adjust column spacing\n","{\\footnotesize\n","\\begin{tabular}{lc}\n","\\toprule\n","\\textbf{Perturbation SD} & \\textbf{SISDRi (dB)} \\\\ %& \\textbf{Overlap ratio (\\%)} \\\\\n","\\midrule\n","No perturbation & 6.75 \\\\ %& 13.32 \\\\\n","0.5s & 6.25 \\\\%& 14.67 \\\\\n","1s & 5.68 \\\\%& 15.55 \\\\\n","1.5s & 5.25 \\\\%& 16.14 \\\\\n","2s & 4.79 \\\\%& 16.56 \\\\\n","2.5s & 4.50 \\\\%& 16.94 \\\\\n","3s & 4.16 \\\\%& 17.30 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:perturbation}\n","\\vskip -0.15in\n","\\end{table}\n"],["\\begin{figure}[t!]\n"," \\centering\n"," \\includegraphics[width=0.65\\linewidth]{figs/Histogram.png}\n"," \\vskip -0.1in\n"," \\caption{SISDRi histogram on egocentric recordings.}\n"," \\vskip -0.15in\n"," \\label{fig:hist}\n","\\end{figure}\n"],["\\begin{table}[t!]\n","\\caption{When the conversation partners start speaking, how quickly does the model pick them up?}\n","\\vskip -0.1in\n"," \\setlength{\\tabcolsep}{3.8pt}\n","\\centering\n","{\\footnotesize\n","\\begin{tabular}{lccccc}\n","\\toprule\n","\\textbf{Chunk} & 0-2s & 2-4s & 4-6s & 6-8s & 8-10s \\\\\n","\\midrule\n","SISDRi (dB) & 4.77 & 8.04 & 8.17 & 8.69 & 9.16 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:pickup}\n","\\vskip -0.05in\n","\\end{table}\n"],["\\begin{table}[t!]\n","\\caption{Effects of turn-change gap between target conversation and interfering conversation.}\n","\\vskip -0.1in\n"," \\setlength{\\tabcolsep}{3.8pt}\n","\\centering\n","{\\footnotesize\n","\\begin{tabular}{lccccc}\n","\\toprule\n","\\textbf{Turn-change} & 0-1s & 1-2s & 2-4s & 4-6s & > 6s \\\\\n","\\textbf{Gap} & & & & & \\\\\n","\\midrule\n","Proportion & 11.3\\% & 12.2\\% & 20.7\\% & 15.5\\% & 40.3\\% \\\\\n","SISDRi (dB) & 4.98 & 8.03 & 7.80 & 8.22 & 8.46 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:collision}\n","\\vskip -0.15in\n","\\end{table}\n"],["\\begin{figure}[t!]\n"," \\centering\n"," \\includegraphics[width=0.75\\linewidth]{self_speech_absent.png}\n"," \\vskip -0.1in\n"," \\caption{Extended periods of wearer silence. The gray regions denote durations were the wearer was active.}\n"," \\vskip -0.15in\n"," \\label{fig:self_speech_absent}\n","\\end{figure}\n"],["\\begin{table}[t!]\n","\\caption{Beamformer evaluation on unseen real-world mixtures. DNSMOS BAK is the estimate of the ITU P.835 background noise quality using a neural net.}\n","\\vskip -0.1in\n","\\centering\n","{\\footnotesize\n","\\begin{tabular}{lccc}\n","\\toprule\n","\\textbf{Metrics} & SNR~(dB) & SI-SDR~(dB) & DNSMOS \\\\\n"," & & & BAK \\\\\n","\\midrule\n"," Mixture & -0.13 & -0.13 & 1.94 \\\\\n"," Beamformer & 8.36 & 7.78 & 3.96 \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:bf_eval}\n","\\vskip -0.15in\n","\\end{table}\n"],["\\begin{figure}[t!]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{figs/runtime.pdf}\n"," \\vskip -0.05in\n"," \\caption{Runtime of slow and fast model. A. The inference time of the fast model to process 12.5ms chunk on Orangpi 5B. B. The inference time of the slow model to process 1s chunk on Apple Silicon M2.}\n"," \\vskip -0.15in\n"," \\label{fig:runtime}\n","\\end{figure}\n"],["\\begin{figure}[t]\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{waveform_plot.png}\n"," \\vskip -0.1in\n"," \\caption{Visualized waveforms for conversation mixture, the beamformed self-speech, output of the model and the groundtruth target egocentric conversation.}\n"," \\label{fig:waveform}\n","\\end{figure}\n"],["\\begin{table}[t!]\n","\\caption{Statistics for our real egocentric conversation recordings. }\n","\\vskip -0.1in\n","\\centering\n","{\\footnotesize\n","\\begin{tabular}{lr}\n","\\toprule\n"," Statistic & Mean (STD)\\\\\n","\\midrule\n","Turn-change Frequency ($min^{-1}$) & 6.2 (4.6) \\\\\n","Turn Duration & 8.2s (8.8s) \\\\\n","Overlap Ratio & 1.3\\% (2.5\\%) \\\\\n","IPU Duration ($min^{-1}$) & 52.0s (3.54s) \\\\\n","FTO & 0.18s (1.38s) \\\\\n","\\bottomrule\n","\\end{tabular}\n","}\n","\\label{tab:realworldstats}\n","\\vskip -0.15in\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{figure}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\vskip -0.1in\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{figs/teaser_figure.pdf}\\n\",\n \" \\\\vskip -0.1in\\n\",\n \" \\\\caption{In multi-conversation settings, our proactive hearing assistant uses conversational turn-taking dynamics to automatically infers the wearer's conversation partners and suppresses others in real-time. }\\n\",\n \" \\\\vskip -0.15in\\n\",\n \" \\\\label{fig:teaser}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure*}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=1\\\\linewidth]{figs/diagram.pdf}\\n\",\n \" \\\\vskip -0.14in\\n\",\n \" \\\\caption{Overview of our model pipeline. A. The streaming beamformer extracts the wearer's self-speech from the binaural mixture. B. Dual-model architecture: the slow model runs every 1s ($T$) on the mixture and self-speech to produce a conversation embedding; the fast model runs every 12.5~ms ($\\\\tau$) on the current mixture and embedding from the previous 1s ($T$), to output the cleaned target conversation.\\n\",\n \" }\\n\",\n \" \\\\vskip -0.15in\\n\",\n \" \\\\label{fig:pipeline}\\n\",\n \"\\\\end{figure*}\\n\"\n ],\n [\n \"\\\\begin{table*}[t!]\\n\",\n \"\\\\caption{Evaluation on English (Libri, Candor, SpokenWoZ) and Mandarin (RAMC) testsets.}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \"\\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5.3pt}\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lcccccccc}\\n\",\n \"\\\\toprule\\n\",\n \"& \\\\multicolumn{4}{c}{Non-spatialized} & \\\\multicolumn{4}{c}{Spatialized} \\\\\\\\\\n\",\n \"\\\\cmidrule(r){2-5} \\\\cmidrule(l){6-9}\\n\",\n \"\\\\textbf{Metrics} & SISDRi($\\\\uparrow$) & Acc ($\\\\uparrow$) & CR ($\\\\downarrow$) & $\\\\Delta$PESQ($\\\\uparrow$) & SISDRi($\\\\uparrow$) & Acc($\\\\uparrow$) & CR($\\\\downarrow$) & $\\\\Delta$PESQ($\\\\uparrow$) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Baseline Model (SE)} &&&&&&&&\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Synthetic Libri & -1.95 (1.94) & 26.8\\\\% & 26.3\\\\% & -0.16 (0.14) & -3.31 (2.23) & 10.5\\\\% & 27.7\\\\% & -0.13 (0.13)\\\\\\\\\\n\",\n \"Candor & -5.16 (3.19) & 13.5\\\\% & 24.4\\\\% & -0.29 (0.22) & -3.05 (2.84) & 18.8\\\\% & 21.7\\\\% & -0.16 (0.17)\\\\\\\\\\n\",\n \"SpokenWoz (OOD) & -5.05 (4.04) & 14.7\\\\% & 14.7\\\\% & -0.48 (0.33) & -3.45 (3.78) & 16.8\\\\% & 9.2\\\\% & -0.16 (0.21)\\\\\\\\\\n\",\n \"RAMC & -4.28 (6.01) & 13.6\\\\% & 27.9\\\\% & -0.32 (0.28) & -4.30 (3.37) & 6.8\\\\% & 19.9\\\\% & -0.17 (0.17)\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Our Dual Models} &&&&&&\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Synthetic Libri & 11.70 (4.56) & 96.3\\\\% & 1.4\\\\% & 1.11 (0.30) & 14.62 (6.05) & 96.8\\\\% & 0.8\\\\% & 0.63 (0.23) \\\\\\\\\\n\",\n \"Candor & 6.75 (4.29) & 87.0\\\\% & 2.7\\\\% & 0.64 (0.31) & 9.82 (3.77) & 93.9\\\\% & 1.1\\\\% & 0.56 (0.20)\\\\\\\\\\n\",\n \"SpokenWoz (OOD) & 7.27 (6.11) & 84.5\\\\% & 4.3\\\\% & 0.58 (0.44) &11.95 (6.22) & 92.1\\\\% & 1.5\\\\% & 0.52 (0.25) \\\\\\\\\\n\",\n \"RAMC & 6.50 (7.45) & 85.5\\\\% & 5.6\\\\% & 0.63 (0.41) & 8.05 (9.29) & 78.0\\\\% & 9.4\\\\% & 0.26 (0.40) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Libri (2spk) & 12.48 (4.28) & 98.4\\\\% & 0.6\\\\% & 1.14 (0.24) & 15.68 (5.46) & 99.2\\\\% & 0.2\\\\% & 0.65 (0.22) \\\\\\\\\\n\",\n \"Libri (3spk) & 12.03 (4.00) & 96.6\\\\% & 1.2\\\\% & 1.16 (0.25) & 14.29 (6.08) & 96.1\\\\% & 0.6\\\\% & 0.63 (0.21) \\\\\\\\\\n\",\n \"Libri (leaving) & 10.58 (5.10) & 94.1\\\\% & 2.5\\\\% & 1.03 (0.36) & 13.89 (6.42) & 95.7\\\\% & 1.5\\\\% & 0.60 (0.24)\\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:big_results}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table*}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{SISDRi results for generalization.}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \"\\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5pt} % adjust column spacing\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Dataset} & SISDRi ($\\\\uparrow$) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Libri (2spk) & 12.48 (4.28) \\\\\\\\\\n\",\n \"Libri (3spk) & 12.03 (4.00) \\\\\\\\\\n\",\n \"Libri (4spk) & 11.94 (4.46) \\\\\\\\\\n\",\n \"Libri (5spk) & 11.85 (4.58) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"RAMC & 6.50 (7.45) \\\\\\\\\\n\",\n \"Japanese (OOD) & 7.92 (5.19) \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:sisdr_datasets}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\vskip -0.1in\\n\",\n \" \\\\includegraphics[width=0.6\\\\linewidth]{leaving_scatter.png}\\n\",\n \" \\\\vskip -0.1in\\n\",\n \" \\\\caption{Model enhances then suppresses speaker following shift from target to interfering conversation.}\\n\",\n \" \\\\vskip -0.15in\\n\",\n \" \\\\label{fig:leaving_scatter}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{Subjective evaluation results (5-point scale).}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \"\\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{6pt} % adjust spacing as needed\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lcc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Question} & \\\\textbf{Model Output} & \\\\textbf{Mixture} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Noise suppression & 4.29 (1.19) & 1.67 (1.04) \\\\\\\\\\n\",\n \"Comprehension & 4.35 (1.02) & 1.97 (0.93) \\\\\\\\\\n\",\n \"Effort & 4.45 (0.95) & 1.97 (0.96) \\\\\\\\\\n\",\n \"Overall MOS & 4.30 (1.14) & 1.88 (1.02) \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:user_study_table}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{Evaluation on real egocentric conversations.}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \"\\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{5.3pt}\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Metrics} & SISDRi($\\\\uparrow$) & Acc ($\\\\uparrow$) & CR ($\\\\downarrow$) \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"\\\\textbf{Number of speakers} & & &\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \" 2 speakers & 7.84 (6.79) & 85.0\\\\% & 1.1\\\\% \\\\\\\\\\n\",\n \" 3 speakers & 6.00 (7.14) & 73.4\\\\% & 3.7\\\\% \\\\\\\\\\n\",\n \"\\\\midrule \\n\",\n \"\\\\textbf{Augmentation} & & & \\\\\\\\\\n\",\n \"\\\\midrule \\n\",\n \" \\\\ding{55} & 5.49 (5.30) & 77.9\\\\% & 1.2\\\\% \\\\\\\\\\n\",\n \" \\\\ding{51} & 7.22 (6.96) & 80.0\\\\% & 2.2\\\\% \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:hardware_result}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{Impact of perturbing the turn-taking in human conversations. (SD=standard deviation)}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \"\\\\centering\\n\",\n \" \\\\setlength{\\\\tabcolsep}{6pt} % adjust column spacing\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Perturbation SD} & \\\\textbf{SISDRi (dB)} \\\\\\\\ %& \\\\textbf{Overlap ratio (\\\\%)} \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"No perturbation & 6.75 \\\\\\\\ %& 13.32 \\\\\\\\\\n\",\n \"0.5s & 6.25 \\\\\\\\%& 14.67 \\\\\\\\\\n\",\n \"1s & 5.68 \\\\\\\\%& 15.55 \\\\\\\\\\n\",\n \"1.5s & 5.25 \\\\\\\\%& 16.14 \\\\\\\\\\n\",\n \"2s & 4.79 \\\\\\\\%& 16.56 \\\\\\\\\\n\",\n \"2.5s & 4.50 \\\\\\\\%& 16.94 \\\\\\\\\\n\",\n \"3s & 4.16 \\\\\\\\%& 17.30 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:perturbation}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.65\\\\linewidth]{figs/Histogram.png}\\n\",\n \" \\\\vskip -0.1in\\n\",\n \" \\\\caption{SISDRi histogram on egocentric recordings.}\\n\",\n \" \\\\vskip -0.15in\\n\",\n \" \\\\label{fig:hist}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{When the conversation partners start speaking, how quickly does the model pick them up?}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \" \\\\setlength{\\\\tabcolsep}{3.8pt}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Chunk} & 0-2s & 2-4s & 4-6s & 6-8s & 8-10s \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"SISDRi (dB) & 4.77 & 8.04 & 8.17 & 8.69 & 9.16 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:pickup}\\n\",\n \"\\\\vskip -0.05in\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{Effects of turn-change gap between target conversation and interfering conversation.}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \" \\\\setlength{\\\\tabcolsep}{3.8pt}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lccccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Turn-change} & 0-1s & 1-2s & 2-4s & 4-6s & > 6s \\\\\\\\\\n\",\n \"\\\\textbf{Gap} & & & & & \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Proportion & 11.3\\\\% & 12.2\\\\% & 20.7\\\\% & 15.5\\\\% & 40.3\\\\% \\\\\\\\\\n\",\n \"SISDRi (dB) & 4.98 & 8.03 & 7.80 & 8.22 & 8.46 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:collision}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=0.75\\\\linewidth]{self_speech_absent.png}\\n\",\n \" \\\\vskip -0.1in\\n\",\n \" \\\\caption{Extended periods of wearer silence. The gray regions denote durations were the wearer was active.}\\n\",\n \" \\\\vskip -0.15in\\n\",\n \" \\\\label{fig:self_speech_absent}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{Beamformer evaluation on unseen real-world mixtures. DNSMOS BAK is the estimate of the ITU P.835 background noise quality using a neural net.}\\n\",\n \"\\\\vskip -0.1in\\n\",\n \"\\\\centering\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lccc}\\n\",\n \"\\\\toprule\\n\",\n \"\\\\textbf{Metrics} & SNR~(dB) & SI-SDR~(dB) & DNSMOS \\\\\\\\\\n\",\n \" & & & BAK \\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \" Mixture & -0.13 & -0.13 & 1.94 \\\\\\\\\\n\",\n \" Beamformer & 8.36 & 7.78 & 3.96 \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:bf_eval}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[t!]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{figs/runtime.pdf}\\n\",\n \" \\\\vskip -0.05in\\n\",\n \" \\\\caption{Runtime of slow and fast model. A. The inference time of the fast model to process 12.5ms chunk on Orangpi 5B. B. The inference time of the slow model to process 1s chunk on Apple Silicon M2.}\\n\",\n \" \\\\vskip -0.15in\\n\",\n \" \\\\label{fig:runtime}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[t]\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{waveform_plot.png}\\n\",\n \" \\\\vskip -0.1in\\n\",\n \" \\\\caption{Visualized waveforms for conversation mixture, the beamformed self-speech, output of the model and the groundtruth target egocentric conversation.}\\n\",\n \" \\\\label{fig:waveform}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[t!]\\n\",\n \"\\\\caption{Statistics for our real egocentric conversation recordings. }\\n\",\n \"\\\\vskip -0.1in\\n\",\n \"\\\\centering\\n\",\n \"{\\\\footnotesize\\n\",\n \"\\\\begin{tabular}{lr}\\n\",\n \"\\\\toprule\\n\",\n \" Statistic & Mean (STD)\\\\\\\\\\n\",\n \"\\\\midrule\\n\",\n \"Turn-change Frequency ($min^{-1}$) & 6.2 (4.6) \\\\\\\\\\n\",\n \"Turn Duration & 8.2s (8.8s) \\\\\\\\\\n\",\n \"Overlap Ratio & 1.3\\\\% (2.5\\\\%) \\\\\\\\\\n\",\n \"IPU Duration ($min^{-1}$) & 52.0s (3.54s) \\\\\\\\\\n\",\n \"FTO & 0.18s (1.38s) \\\\\\\\\\n\",\n \"\\\\bottomrule\\n\",\n \"\\\\end{tabular}\\n\",\n \"}\\n\",\n \"\\\\label{tab:realworldstats}\\n\",\n \"\\\\vskip -0.15in\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\n%% IMPORTANT NOTICE:\n%% \n%% For the copyright see the source file.\n%% \n%% Any modified versions of this file must be renamed\n%% with new filenames distinct from sample-sigconf-authordraft.tex.\n%% \n%% For distribution of the original source see the terms\n%% for copying and modification in the file samples.dtx.\n%% \n%% This generated file may be distributed as long as the\n%% original source files, as listed above, are part of the\n%% same distribution. (The sources need not necessarily be\n%% in the same archive or directory.)\n%%\n\\pdfoutput=1\n% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.\n\n\\documentclass[11pt]{article}\n\n% Change \"review\" to \"final\" to generate the final (sometimes called camera-ready) version.\n% Change to \"preprint\" to generate a non-anonymous version with page numbers.\n\\usepackage[final]{acl} \n%\\usepackage[preprint]{acl}\n\n% Standard package includes\n\\usepackage{times}\n\\usepackage{latexsym}\n\\usepackage{amssymb}% http://ctan.org/pkg/amssymb\n\\usepackage{pifont}% http://ctan.org/pkg/pifont\n\\newcommand{\\cmark}{\\ding{51}}%\n\\newcommand{\\xmark}{\\ding{55}}%\n% tables\n\\usepackage{booktabs}%\n\n% reverse order list\n\\usepackage{etaremune}\n\\usepackage[normalem]{ulem}\n\n% For proper rendering and hyphenation of words containing Latin characters (including in bib files)\n\\usepackage[T1]{fontenc}\n% For Vietnamese characters\n% \\usepackage[T5]{fontenc}\n% See https://www.latex-project.org/help/documentation/encguide.pdf for other character sets\n\n% This assumes your files are encoded as UTF8\n\\usepackage[utf8]{inputenc}\n\n% This is not strictly necessary, and may be commented out,\n% but it will improve the layout of the manuscript,\n% and will typically save some space.\n\\usepackage{microtype}\n\n% This is also not strictly necessary, and may be commented out.\n% However, it will improve the aesthetics of text in\n% the typewriter font.\n\\usepackage{inconsolata}\n\n%Including images in your LaTeX document requires adding\n%additional package(s)\n\\usepackage{graphicx}\n\n\\usepackage{enumitem}\n\n\\usepackage{tabu}\n\\usepackage{multirow}\n\\usepackage{booktabs}\n\\usepackage{arydshln}\n\\usepackage{xspace}\n\\usepackage{amsmath}\n%%\n\n\n% Additional packagaes by us that are not in the original source\n\\usepackage{soul} % for \\st\n\\usepackage{xcolor} % for colors\n\\setstcolor{red} % strike line color\n\n\n%% Submission ID.\n%% Use this when submitting an article to a sponsored event. You'll\n%% receive a unique submission ID from the organizers\n%% of the event, and this ID should be used as the parameter to this command.\n%%\\acmSubmissionID{123-A56-BU3}\n\n%%\n%% For managing citations, it is recommended to use bibliography\n%% files in BibTeX format.\n%%\n%% You can then either use BibTeX with the ACM-Reference-Format style,\n%% or BibLaTeX with the acmnumeric or acmauthoryear sytles, that include\n%% support for advanced citation of software artefact from the\n%% biblatex-software package, also separately available on CTAN.\n%%\n%% Look at the sample-*-biblatex.tex files for templates showcasing\n%% the biblatex styles.\n%%\n\n%%\n%% The majority of ACM publications use numbered citations and\n%% references. The command \\citestyle{authoryear} switches to the\n%% \"author year\" style.\n%%\n%% If you are preparing content for an event\n%% sponsored by ACM SIGGRAPH, you must use the \"author year\" style of\n%% citations and references.\n%% Uncommenting\n%% the next command will enable that style.\n%%\\citestyle{acmauthoryear}\n\n\n%%\n%% end of the preamble, start of the body of the document source.\n\\begin{document}\n\n\n\\author{\n Guilin Hu\\textsuperscript{*} \\quad\n Malek Itani\\textsuperscript{*} \\quad\n Tuochao Chen \\quad\n Shyamnath Gollakota \\\\\n \\textsuperscript{*}Co-primary student authors\\\\\n \\textsuperscript{1}Paul G. Allen School of Computer Science \\& Engineering, University of Washington \\\\\n \\texttt{\\{guilinhu,malek,tuochao,gshyam\\}@cs.washington.edu}\n}\n\n\n\n%%\n%% The \"title\" command has an optional parameter,\n%% allowing the author to define a \"short title\" to be used in page headers.\n\\title{Proactive Hearing Assistants that Isolate Egocentric Conversations}\n\n\n\n%\\title{{Conversation Filters: Hearables that Learn Who to Hear}}\n\n\n\n%\\title{{Conversation Filters: AI Hearables that Learn Who to Hear}}\n\n\n\n%-\\title{{Target Conversation Hearing: Learning Who to Hear on Hearables}}\n\n\n\n\\newcommand{\\squishlist}{%\n \\begin{itemize}[itemsep=1pt,parsep=2pt,topsep=3pt,partopsep=0pt,\n leftmargin=0em,itemindent=1em,labelwidth=1em,labelsep=0.5em]%\n}\n\\newcommand{\\squishend}{%\n \\end{itemize}%\n}\n\n\n%%\n%% By default, the full list of authors will be used in the page\n%% headers. Often, this list is too long, and will overlap\n%% other information printed in the page headers. This command allows\n%% the author to define a more concise list\n%% of authors' names for this purpose.\n\n%% This command processes the author and affiliation and title\n%% information and builds the first part of the formatted document.\n\n\n\\makeatletter\n\\renewcommand{\\sectionautorefname}{\\S\\@gobble}\n\\renewcommand{\\subsectionautorefname}{\\S\\@gobble}\n\\renewcommand{\\subsubsectionautorefname}{\\S\\@gobble}\n\\renewcommand{\\appendixautorefname}{Appendix \\@gobble}\n\\makeatother\n\n\n\n\\pagenumbering{gobble}\n\n\\newcommand{\\xref}[1]{\\S\\ref{#1}}\n\n\n\n\n\\maketitle\n\n\\begin{abstract}\n\n\nWe introduce proactive hearing assistants\\footnote{Our hearing assistants are `proactive' in that they infer and adapt to conversational engagement without user commands.} that automatically identify and separate the wearer's conversation partners, without requiring explicit prompts. Our system operates on egocentric binaural audio and uses the wearer’s self-speech as an anchor, leveraging turn-taking behavior and dialogue dynamics to infer conversational partners and suppress others. To enable real-time, on-device operation, we propose a dual-model architecture: a lightweight streaming model runs every 12.5~ms for low-latency extraction of the conversation partners, while a slower model runs less frequently to capture longer-range conversational dynamics. \nResults on real-world 2- and 3-speaker conversation test sets, collected with binaural egocentric hardware from 11 participants totaling 6.8 hours, show generalization in identifying and isolating conversational partners in multi-conversation settings. Our work marks a step toward hearing assistants that adapt proactively to conversational dynamics and engagement. More information can be found on our website: \\url{https://proactivehearing.cs.washington.edu/}\n\n\n\n%We introduce {\\it proactive hearing assistants} that automatically identify and separate conversations the wearer is actively engaged in, without any explicit input. The system processes egocentric binaural audio and uses self-speech as an anchor, leveraging turn-taking patterns to detect conversational partners and suppress others. To enable real-time, on-device operation, we propose a dual-model architecture: a lightweight model runs every 12.5ms for low-latency separation, guided by a slower contextual model that runs every few seconds and captures long-range conversational structure. Evaluations on both synthetic datasets and unseen real-world binaural recordings of 2-3 speaker conversations demonstrate strong performance in isolating relevant speakers, marking a step toward intelligent hearing assistants that adapt proactively to conversational dynamics.\n\n\n\n\n\n\\end{abstract}\n\n\\section{Introduction}\n\n\n\n\nHuman hearing is remarkably adaptable, yet fundamentally limited in crowded auditory environments. In such settings, isolating relevant voices, known as the cocktail party problem, becomes especially difficult. For individuals with hearing loss, distinguishing overlapping conversations can result in cognitive overload and listening fatigue~\\cite{hearingaidscocktail}.\n\n%Recent advances in hearing assistants, like augmented devices and hearing aids, use deep learning for {\\it manual} sound source selection, with spatial filtering or phone-based interfaces~\\cite{semantichearing,tsh}. However, these approaches struggle in multi-party conversations where speakers are spatially dispersed or involve more than two speakers, making manual enrollment impractical.\n\nExisting hearing assistants, like augmented devices, wireless earbuds and hearing aids, are ``reactive'' in that users manually prompt the devices to pick specific sound sources via spatial filtering or phone-based interfaces~\\cite{semantichearing,tsh}. However, these approaches struggle in multi-party conversations where speakers are spatially dispersed or involve more than two speakers, making manual enrollment impractical.\n\nWe propose an alternative: real-time proactive hearing assistants that automatically identify and enhance the voices involved in a conversation with the wearer, without explicit prompts. Our system processes egocentric binaural audio to dynamically track conversational partners and suppress others, adapting to engagement naturally and seamlessly, without explicit user commands or prompts.\n\n\n\\begin{figure}[t!]\n \\centering\n \\vskip -0.1in\n \\includegraphics[width=\\linewidth]{figs/teaser_figure.pdf}\n \\vskip -0.1in\n \\caption{In multi-conversation settings, our proactive hearing assistant uses conversational turn-taking dynamics to automatically infers the wearer's conversation partners and suppresses others in real-time. }\n \\vskip -0.15in\n \\label{fig:teaser}\n\\end{figure}\n\nThis task poses three key challenges:\n(1) identifying and separating conversational partners,\n(2) operating on-device in real-time with low latency, and\n(3) generalizing to real-world, egocentric, multi-party environments.\n\nOur approach builds on insights from core NLP tasks like turn-taking prediction, speaker diarization, and dialog modeling, to design a proactive hearing assistant. We make three key contributions:\n(1) an anchoring mechanism based on the wearer’s self-speech to track conversation partners,\n(2) a dual-model architecture that enables low-latency, real-time processing, and\n(3) a real-world end-to-end evaluation using egocentric binaural conversational recordings captured with wearable hardware.\n\n\nConcretely, we anchor the system on the wearer’s self-speech, extracted using a beamformer trained on egocentric audio. The assistant activates when the wearer speaks for a few seconds, signaling conversational intent. The assistant leverages turn-taking cues, such as alternating speech, low overlap, and temporal coordination, to identify conversational partners. These interactional patterns, well-studied in dialogue systems~\\cite{turntake2,frontiers,tce}, allow the proactive assistant to infer engagement in real time and selectively separate the voices of relevant speakers.\n\n\nTo meet real-time constraints, the system processes audio in short streaming chunks. However, as conversations unfold, the sequence length grows, increasing the memory demands of attention-based models. Since full self-attention scales quadratically with sequence length~\\cite{ainslie2020etcencodinglongstructured,10889061}, achieving both long-context awareness and low-latency performance requires a carefully designed architecture.\n\n\n\nTo balance real-time responsiveness and conversational context length, we use a dual-model architecture: A fast streaming model runs every 12.5~ms, extracting the target conversation in real time. A slower model runs once per second and provides periodic longer-term conversational embeddings, capturing conversation turn-taking and discourse structure without incurring full-attention memory.\n\n\n\n\nWe train on diverse speech and conversational English and Mandarin datasets, including Candor~\\cite{candor}, LibriTTS~\\cite{zen2019libritts} and RAMC~\\cite{ramc}, spatialized to emulate egocentric conditions. We evaluate our models on out-of-distribution SpokenWOZ~\\cite{si2023spokenwoz} and the Japanese Duplex Conversation Dataset \\cite{JapaneseDuplex2025}. We also collect real-world 2- and 3-speaker conversational testset using binaural egocentric hardware from 11 participants, totaling 6.8 hours.\n\nIn both out-of-distribution and real-world egocentric settings, our system accurately identifies conversational partners, with accuracies and confusion rates of 80-92\\% and 1.5-2.2\\% respectively. It also improves speech quality of the conversation partners by 7.22-11.95~dB (SISDRi), and operates in real time on embedded and mobile devices.\n\n\nThis work shows a path toward proactive hearing assistants that go beyond source separation to infer who the user wants to hear, adapting to conversation dynamics in a way that aligns closely with goals in dialogue systems, speech understanding, and human-AI interaction. It also offers future potential for adapting LLM agents to track spoken conversations in noisy, multi-party settings.\n\n\n\n\\section{Related work}\n\n\n\n\\noindent\\textbf{Conversational dynamics.} \nUnderstanding multi-party conversation structure has long been a focus in dialogue systems and speech processing. Prior work has explored speech recognition~\\cite{asr4conversation}, speaker diarization~\\cite{diarization4conversation}, and speech-driven question answering~\\cite{qa4conversation}, often under idealized conditions without interfering speakers. Dialogue-level sentiment analysis and discourse segmentation have also been explored in clean settings~\\cite{sa4conversation, sdu4conversation}.\n\nTurn-taking is a central feature of conversational dynamics~\\cite{frontiers}, and has been studied using corpus-based models~\\cite{turntake1, turntake2, turntake3} that identify patterns such as alternating speech, pauses, and backchannels. Recent approaches model turn-taking directly~\\cite{turn_model, turn_predict,nguyen-etal-2025-spirit}, including listener behavior prediction in dyadic settings~\\cite{9879511}.\n\n\nMost relevant to our task is Target Conversation Extraction (TCE)~\\cite{tce}, which uses turn-taking cues to extract a target conversation. Our work differs in three key aspects: (1) TCE operates offline and requires future context, making it unsuitable for real-time use; (2) it relies on explicit speaker embeddings, while we use self-speech extracted from egocentric binaural audio as a natural anchor; and (3) it uses monaural recordings, whereas we focus on realistic, spatialized egocentric audio from wearable devices.\n\n\n\n\n\n\n \n\\vskip 0.02in\\noindent{\\bf Audiovisual speech understanding.} Our work intersects with research in Active Speaker Detection (ASD) and Active Speaker Localization (ASL). ASD systems identify who is speaking using audio-visual correlations or facial features~\\cite{1544886}, while ASL focuses on spatial localization \\cite{8578556, 9879100, easycom}. Recent work in Selective Auditory Attention Localization extends this to inferring whom the user is attending to, using egocentric video and audio~\\cite{10203787, 10447323}.\n\nEfforts in egocentric video understanding have explored detecting social engagement~\\cite{6247805} and speaker attention~\\cite{ego4d}. For instance, the Ego4D benchmark includes a ``Talking to Me'' task focused on identifying who is addressing the camera wearer. However, these tasks typically stop at detection. In contrast, we go further: identifying, separating, and enhancing all speakers engaged with the wearer, in real time and on-device, under real-world constraints.\n\n\n\n\\vskip 0.02in\\noindent{\\bf Auditory attention decoding.} \n Research in this domain attempts to infer the target speaker by correlating brain activity (e.g., EEG or fNIRS) with competing audio streams~\\cite{aad1, Choudhari2024.02.05.579018,aad2}. While promising, these systems lack real-time deployment capabilities and require bulky or invasive hardware. Even with miniaturized in-ear EEG sensors~\\cite{cEEGrid,berkeleyearable}, challenges remain in noisy, real-world settings with multiple speakers~\\cite{separationeeg}. In contrast, our work explores an dialog-based approach that aligns better with practical hearing assistance, leveraging self-speech as an implicit signal of attention and engagement.\n\n\n\\vskip 0.02in\\noindent{\\bf Proactive assistants.} \n Prior work has explored proactive interaction in task planning~\\cite{zhang-etal-2024-ask}, user modeling~\\cite{lu2024proactiveagentshiftingllm}, and conversational guidance~\\cite{llamapie}. However, these systems focus on information-seeking or planning tasks, which are complementary to our task.\n\n\n\\vskip 0.02in\\noindent{\\bf Augmented hearing.} \nContemporary hearing systems support selection of target sound sources, e.g., a speaker or sound class, via spatial filtering or manual enrollment~\\cite{semantichearing, tsh,soundbubble,knowledgeboosting}. Apple’s Conversation Awareness mode~\\cite{apple-conversationawareness} reduces background volume upon detecting wearer speech, but does not perform speaker separation or conversational tracking. % extraction.\n\n%Our system is, to our knowledge, the first to support real-time, proactive speaker selection using conversational cues, to separate all relevant speakers in a multi-party conversation, enabling more natural interaction in noisy environments.\n\n\n\\section{Proactive Hearing Assistants}\n\n\n\\begin{figure*}[t]\n \\centering\n % \\vskip -0.1in\n \\includegraphics[width=1\\linewidth]{figs/diagram.pdf}\n \\vskip -0.14in\n \\caption{Overview of our model pipeline. A. The streaming beamformer extracts the wearer's self-speech from the binaural mixture. B. Dual-model architecture: the slow model runs every 1s ($T$) on the mixture and self-speech to produce a conversation embedding; the fast model runs every 12.5~ms ($\\tau$) on the current mixture and embedding from the previous 1s ($T$), to output the cleaned target conversation.\n }\n \\vskip -0.15in\n \\label{fig:pipeline}\n\\end{figure*}\n\n\n\n%We first formulate the problem of proactive hearing assistants (\\xref{sec:problem_formulation}), then describe the system architecture (\\xref{sec:modeling}) and training procedure (\\xref{sec:training}).\n\n\n\n\\subsection{Problem formulation}\n\\label{sec:problem_formulation}\n\nThe input egocentric audio stream can be decomposed into three components: the target conversation involving the wearer, interfering conversations, and background noise. \n%, \\emph{i.e.,} $m(t) = s^{conv}(t) + s^{inter}(t) + n(t)$. \n\n\n%The input is an egocentric audio stream, $m(t) \\in \\mathbf{R^{2}}$ which can be decomposed into three components: the target conversation involving the wearer, interfering conversations, and background noise, \\emph{i.e.,} $m(t) = s^{conv}(t) + s^{inter}(t) + n(t)$. \n\nThe target conversation consists of the wearer's self-speech and the speech of their conversational partners. Notably, in egocentric recordings, the wearer's own speech is typically louder than all other voices.\n\n\nOur goal is to identify and separate the wearer's conversation partners, which can be done by isolating the target conversation and suppressing model output during the wearer’s own speech, using on-device voice activity detection (e.g., as in AirPods~\\cite{apple-conversationawareness}). The system can then output the conversation partners' speech into the ear.\n\n\n\nThe system must handle dynamic conversational settings, where speakers may join or leave the conversation at any time, following natural turn-taking patterns. Real-world dialogue includes backchannels and overlaps, requiring the model to adapt as speakers shift between target and interfering conversations. For example, a speaker might begin as part of the target conversation (e.g., at a dinner table) but later engage in a separate, interfering conversation, requiring the system to adapt.\n\n\n\n\n\nOnce the conversation partners are extracted, their voices must be rendered to the wearer with minimal delay to preserve a natural conversational experience. Thus, the system must process audio in small chunks of 10–20~ms to maintain a latency below the perceptual threshold. Real-time operation requires each chunk to be processed faster than it is recorded. Because offloading to a phone or cloud introduces communication delays (10–30~ms over Bluetooth and 100–200~ms over the Internet), streaming processing must occur on-device on compute-limited embedded platforms.\n\nAn assumption we make is that the wearer is an active participant in the conversation. Thus, passive listening, such as eavesdropping, is a non-goal. \n\n\\subsection{Proactive assistant modeling}\\label{sec:modeling}\nFig.~\\ref{fig:pipeline} shows the full architecture, including all sub-networks and the data pipeline. The beamformer and the slow conversational embedding model operate on audio chunks of $T$ second length, while the fast streaming model runs on much shorter chunks of $\\tau$ seconds ($\\tau \\ll T$). The beamformer takes the egocentric binaural audio stream and isolates the wearer's own voice by beamforming toward their mouth. This self-speech, along with the monaural egocentric audio mixture, is inputted to the slow model, which generates an embedding every $T$ seconds. This embedding is then used by the fast streaming model to guide target conversation extraction for upcoming audio chunks. The fast model receives a single egocentric audio stream and the conversational embedding as input.\n\n\n\n\n\n\\subsubsection{Dual-model processing}\\label{sec:dual}\nConversations can occur continuously for very long durations. Thus, it is useful to utilize attention to effectively model and retain minutes-long contextual sequences of audio. However, with attention, it is challenging to meet the strict real-time requirements needed for proactive hearing assistants on hardware with tight processing capabilities. \n\nSpecifically, as conversation length increases, so does the number of chunks, leading to longer input sequences for the attention mechanism. This is problematic, as the memory requirements of full self-attention scale quadratically with sequence length~\\cite{ainslie2020etcencodinglongstructured,10889061}. Ideally, we want to maintain long-context awareness for accurate filtering while ensuring low memory usage and real-time performance. \n\nWe employ a dual-model pipeline. It incorporates a high-latency, attention-based network to model long sequences and extract a conversation embedding, and a low-latency, low-complexity LSTM-based network that integrates this conversation embedding to estimate the target conversation in small chunks. Since the fast model does not directly attend to historical context, its memory footprint is low. Further, because the large model processes fewer, longer chunks, it attends over fewer tokens for the same conversation duration, enabling it to efficiently capture extended context (details in~\\xref{sec:dualmodeldetails}).\n\nSeveral key design choices support real-time performance. First, the beamformed self-speech is not fed into the fast model, as doing so would introduce additional processing latency that would violate real-time constraints. Second, the slow embedding model processes audio $T$ seconds behind the fast stream. This decoupling allows these models to run remotely on say a smartphone. Further, it prevents their higher processing latency from affecting streaming performance, but introduces a tradeoff: larger $T$ values reduce the system’s responsiveness to conversational dynamics (see~\\xref{sec:ablation}). Third, both the fast and slow models use monaural rather than binaural audio as input. This reduces computational load on the fast model and ensures the models focus on conversational turn-taking and dynamics rather than spatial cues.\n\n\n\n\n\n\n\\subsection{Training strategy}\\label{sec:training}\n\n\nOur models must generalize to egocentric binaural conversations with 2–3 participants and handle dynamic scenarios where participants may leave the target conversation and join an interfering one. To jointly model conversation tracking and source separation, we require mixtures of a target egocentric conversation with a separate interfering conversation with no shared speakers. However, since the wearer's self-speech dominates in egocentric audio, we cannot simply mix two egocentric recordings. Instead, we need passive third-person binaural recordings to construct realistic mixtures.\n\nExisting egocentric datasets like EgoCom~\\cite{egocom} and EasyCom~\\cite{easycom} are unsuitable for this purpose: EgoCom features the same host in all recordings and both datasets lack third-person binaural recordings needed for mixture synthesis. \n\n\nInstead, we use non-egocentric datasets and spatialize them to simulate egocentric scenarios. We train on the Candor dataset~\\cite{candor}, which contains 850 hours of high-quality 2-speaker English conversations, and RAMC~\\cite{ramc}, which has 180 hours of 2-speaker Mandarin conversations. Both provide clean audio, speaker IDs, and timestamps. Large open-source datasets with 3-speaker conversations or complex dynamics (e.g., speakers switching conversations) are scarce.\n\n\n\\subsubsection{Synthetic dataset creation}\nTo address this, we adopt the time-preserving method from~\\cite{tce} and generate {five} synthetic datasets (see~\\xref{sec:datasetgen}):\n\\squishlist\n \\item {\\it Libri (2spk).} We align LibriTTS~\\cite{zen2019libritts} audio from two random English speakers with RAMC~\\cite{ramc} 2-spk timestamps, replacing the original Mandarin utterances.\n \n \\item {\\it Libri (3spk).} With RAMC timestamps, we randomly assign each turn to one of three LibriTTS speakers, creating a synthetic 3-spk conversation.\n \n \\item {\\it Libri (leaving).} A speaker active in the first 20 seconds of the 3-spk conversation leaves and reappears in the interfering conversation between 20–40 seconds, simulating speaker dynamics.\n\n \\item {\\it Libri (4spk) and (5spk) (Evaluation only).} {Two test-only datasets where RAMC test set timestamps are used to generate synthetic four- and five-speaker conversations by randomly assigning each turn to one of four or five LibriTTS speakers.}\n\n \n\\squishend\n\n\\subsubsection{Training procedure}\\label{sec:trainingrecipe}\n\n\nWe generate mixtures by combining a target conversation with an interfering conversation and noise. Each target conversation starts at least 5 seconds of the wearer’s self-speech, so the models can anchor to the wearer. Training proceeds in three stages.\n\n\n\n\n\n We pretrain on the training splits of the three synthetic datasets and Candor mixtures. The fast streaming model and the slow conversational embedding model are trained jointly, with a negative SNR loss computed on the fast model’s output to reconstruct the target conversation. The conversational embedding model receives ground-truth self-speech as input.\n\n\nIn the second stage, to simulate egocentric hearing, we spatialize the synthetic and Candor datasets (see~\\xref{sec:spatialize}). Ground-truth self-speech is replaced with the output of a pretrained beamformer, which serves as input to the slow model. Both models are trained jointly using the same loss function.\n\n\nTo address the distribution shift between Candor (Zoom-based, first-time interactions) and real-world, in-person conversations between familiar participants, in the final stage, we finetune the model by perturbing the amount of silence and overlap between speaker utterances (see~\\xref{sec:trainingdetails})). \n\n\n\\subsection{On-device real-time inference}\nThe fast streaming model runs on a low-power embedded device, while the slower conversational embedding model can operate remotely on device with more compute. \nTo meet real-time requirements, we run the fast streaming model on an embedded Orange Pi 5B and the slower conversational model on Apple M2 silicon, supported by commodity wearable devices. The fast model processes 12.5~ms audio chunks in 8.9~ms on average, while the slow model processes 1-second chunks in 41.3~ms. {In addition, we profiled memory usage for the slow and fast models. We run streaming inference of the slow and fast models for 100 runs. Then we measure the peak memory usage averaged over 100 runs. Peak memory is 591.47 MB (slow model) and 86.33 MB (fast model) during streaming inference.}\n \n\n\n\n\n\n\\section{Evaluation}\n\n\n%We first describe the evaluation metrics \\xref{sec:metrics}, and testsets \\xref{sec:testsets}, followed by detailed results \\xref{sec:results} and ablation studies \\xref{sec:ablation}.\n\n\\subsection{Metrics}\\label{sec:metrics}\n%To Evaluate the performance of our dual-model to extract the speech involving in the conversation. \n\nSince the beamformer already outputs self-speech and the proactive assistant aims to help the wearer hear conversational partners, we compute four metrics for the {\\it partners' speech} segments output by the models (see~\\xref{sec:beamformerdetails} for self-speech results).\n\n\n\\squishlist\n\\item {\\it SISDRi:} Scale-Invariant Signal-to-Distortion Ratio improvement (SISDRi) quantifies how much the target speech is enhanced relative to the noisy input. Higher values indicate better separation and preservation of the target speech.\n\n\\item {\\it $\\Delta$PESQ: } Perceptual Evaluation of Speech Quality (PESQ) estimates speech quality based on human auditory perception. $\\Delta$PESQ measures the perceptual improvement over the input mixture.\n%Perceptual Evaluation of Speech Quality (PESQ) is an ITU-T standard metric (P.862) that estimates speech quality by modeling human auditory perception. $\\Delta$ PESQ quantifies perceptual quality gain compared with the input mixture.\n\n\\item {\\it Accuracy (Acc):} Measures how often we correctly select the conversational partner at each conversation turn. A correct selection occurs when: (1) the conversational partner's SISDRi > 0, and (2) it exceeds all interfering speakers' SISDRi.\n\n\n%Accuracy (Acc) quantifies how often the model correctly selects the target speaker to enhance at the turn level. For each turn in conversation, it is considered to pick the target speaker correctly if: (1) the SISDRi of the target speaker is greater than 0, and (2) the SISDRi of the target speaker exceeds that of all interfering speakers.\n\n\\item {\\it Confusion Rate (CR):} How often we select an interfering speaker over the target. This occurs when: (1) the interfering speaker's SISDRi > 0, and (2) it exceeds the conversational partner's SISDRi.\n\n\\squishend\n\n% Please explain these..Emphasize sisdri, pesq is for other spekaer andnot self-speaker\n\n\n\n\\begin{table*}[t!]\n%\\vskip -0.07in\n\\caption{Evaluation on English (Libri, Candor, SpokenWoZ) and Mandarin (RAMC) testsets.}\n\\vskip -0.1in\n\\centering\n \\setlength{\\tabcolsep}{5.3pt}\n{\\footnotesize\n\\begin{tabular}{lcccccccc}\n\\toprule\n& \\multicolumn{4}{c}{Non-spatialized} & \\multicolumn{4}{c}{Spatialized} \\\\\n\\cmidrule(r){2-5} \\cmidrule(l){6-9}\n\\textbf{Metrics} & SISDRi($\\uparrow$) & Acc ($\\uparrow$) & CR ($\\downarrow$) & $\\Delta$PESQ($\\uparrow$) & SISDRi($\\uparrow$) & Acc($\\uparrow$) & CR($\\downarrow$) & $\\Delta$PESQ($\\uparrow$) \\\\\n\\midrule\n\\textbf{Baseline Model (SE)} &&&&&&&&\\\\\n\\midrule\nSynthetic Libri & -1.95 (1.94) & 26.8\\% & 26.3\\% & -0.16 (0.14) & -3.31 (2.23) & 10.5\\% & 27.7\\% & -0.13 (0.13)\\\\\nCandor & -5.16 (3.19) & 13.5\\% & 24.4\\% & -0.29 (0.22) & -3.05 (2.84) & 18.8\\% & 21.7\\% & -0.16 (0.17)\\\\\nSpokenWoz (OOD) & -5.05 (4.04) & 14.7\\% & 14.7\\% & -0.48 (0.33) & -3.45 (3.78) & 16.8\\% & 9.2\\% & -0.16 (0.21)\\\\\nRAMC & -4.28 (6.01) & 13.6\\% & 27.9\\% & -0.32 (0.28) & -4.30 (3.37) & 6.8\\% & 19.9\\% & -0.17 (0.17)\\\\\n\\midrule\n\\textbf{Our Dual Models} &&&&&&\\\\\n\\midrule\nSynthetic Libri & 11.70 (4.56) & 96.3\\% & 1.4\\% & 1.11 (0.30) & 14.62 (6.05) & 96.8\\% & 0.8\\% & 0.63 (0.23) \\\\\nCandor & 6.75 (4.29) & 87.0\\% & 2.7\\% & 0.64 (0.31) & 9.82 (3.77) & 93.9\\% & 1.1\\% & 0.56 (0.20)\\\\\nSpokenWoz (OOD) & 7.27 (6.11) & 84.5\\% & 4.3\\% & 0.58 (0.44) &11.95 (6.22) & 92.1\\% & 1.5\\% & 0.52 (0.25) \\\\\nRAMC & 6.50 (7.45) & 85.5\\% & 5.6\\% & 0.63 (0.41) & 8.05 (9.29) & 78.0\\% & 9.4\\% & 0.26 (0.40) \\\\\n\\midrule\nLibri (2spk) & 12.48 (4.28) & 98.4\\% & 0.6\\% & 1.14 (0.24) & 15.68 (5.46) & 99.2\\% & 0.2\\% & 0.65 (0.22) \\\\\nLibri (3spk) & 12.03 (4.00) & 96.6\\% & 1.2\\% & 1.16 (0.25) & 14.29 (6.08) & 96.1\\% & 0.6\\% & 0.63 (0.21) \\\\\nLibri (leaving) & 10.58 (5.10) & 94.1\\% & 2.5\\% & 1.03 (0.36) & 13.89 (6.42) & 95.7\\% & 1.5\\% & 0.60 (0.24)\\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:big_results}\n\\vskip -0.15in\n\\end{table*}\n\n% Japanese (OOD) & 7.92 (5.19) & -- & -- & -- & 10.26 (5.24) & -- & -- & -- \\\\ % Added row\n% Libri (4spk) & 11.94 (4.46) & -- & -- & -- & 11.82 (6.26) & -- & -- & -- \\\\ % Added row\n% Libri (5spk) & 11.85 (4.58) & -- & -- & -- & 10.87 (6.5) & -- & -- & -- \\\\ % Added row\n\n\n\\subsection{Testsets}\\label{sec:testsets}\nWe evaluate our models on several test sets: synthetic 2-speaker conversations (Libri 2spk), 3-speaker conversations (Libri 3spk), speaker-switching conversations (Libri leaving), and the Candor test set. There is no speaker {or turn-taking timestamp} overlap between the training, validation, and test sets, ensuring that the models have not seen the test conversations or speakers during training.\n\n% \\textcolor{red}{Additionally, we created synthetic 4- and 5-speaker conversations respectively (Libri 4spk and Libri 5spk) to serve only as test set. The two datasets are generated following the same process as Libri 2- and 3-speaker (see \\xref{sec:datasetgen}). } \n\nWe also assess generalization by testing the English-trained models on both the RAMC Mandarin test set, which contains no turn-taking timestamp data from training, {and the Japanese Duplex Conversation Dataset \\cite{JapaneseDuplex2025}. We also tested the model on Libri (4 spk) and Libri (5 spk), where the model was not trained on such a large number of speakers.} Finally, we evaluate on the out-of-distribution SpokenWOZ~\\cite{si2023spokenwoz} 2-speaker conversation dataset. Since SpokenWOZ contains relatively short utterances, we do not enforce the condition that the wearer speaks for at least 5 consecutive seconds at the beginning. Instead, we randomly select two recordings with disjoint speakers and designate the first speaker in the target conversation as the wearer. \n\n\n\n\\subsection{Results}\\label{sec:results}\nTable~\\ref{tab:big_results} shows evaluation results on several open-source conversational datasets. We use DeepFilterNet2~\\cite{schroter2022deepfilternet2}, a widely adopted speech enhancement model, as our baseline. In the non-spatialized setting, our dual-model consistently outperforms the baseline across all four metrics. On the synthetic Libri conversational dataset, the model achieves significant improvements in both SISDR and PESQ under various conditions, including 2-, 3-speaker and speaker-leaving scenarios. Additionally, our model achieves a high accuracy to pick the conversational partners and a very low confusion rate to pick the interfering speakers. In contrast, the baseline model enhances speech uniformly without distinguishing between target and interfering speakers. As it is not conversation-aware or capable of speech separation, it fails to deliver SISDR improvements.\n\n\n\nFig.~\\ref{fig:leaving_scatter} shows a scatterplot from the Libri (leaving) test set, where a speaker transitions from the target conversation to the interfering one. The plot depicts the SISDRi achieved by our dual-model for this speaker, both before and after leaving the target conversation. While part of the target conversation, the speaker receives a positive SISDRi, indicating successful enhancement. After switching to the interfering conversation, the SISDRi becomes negative, showing that the model correctly suppresses the speaker once they are no longer part of the conversational flow. This shows the model’s ability to adapt to dynamic, multi-party interactions.\n\n\\begin{table}[t!]\n\\caption{SISDRi results for generalization.}\n\\vskip -0.1in\n\\centering\n \\setlength{\\tabcolsep}{5pt} % adjust column spacing\n{\\footnotesize\n\\begin{tabular}{lc}\n\\toprule\n\\textbf{Dataset} & SISDRi ($\\uparrow$) \\\\\n\\midrule\nLibri (2spk) & 12.48 (4.28) \\\\\nLibri (3spk) & 12.03 (4.00) \\\\\nLibri (4spk) & 11.94 (4.46) \\\\\nLibri (5spk) & 11.85 (4.58) \\\\\n\\midrule\n% SpokenWoz (OOD) & 6.70 (6.11) \\\\\nRAMC & 6.50 (7.45) \\\\\nJapanese (OOD) & 7.92 (5.19) \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:sisdr_datasets}\n\\vskip -0.15in\n\\end{table}\n\n\n{To evaluate the model’s ability to generalize to conversations involving more than three speakers, we constructed Libri 4- and 5-speaker datasets, which were only used as test sets. As shown in Table \\ref{tab:sisdr_datasets}, although the model was not trained on conversations with such a number of speakers, it achieved performance comparable to that observed on the Libri 2- and 3-speaker datasets. This suggests the model generalizes well to conversations with previously unseen numbers of target speakers.}\n\n\n\\begin{figure}[t]\n \\centering\n \\vskip -0.1in\n \\includegraphics[width=0.6\\linewidth]{leaving_scatter.png}\n \\vskip -0.1in\n \\caption{Model enhances then suppresses speaker following shift from target to interfering conversation.}\n \\vskip -0.15in\n \\label{fig:leaving_scatter}\n\\end{figure}\n\n%. Our dual-model achieves 7.27 dB SISDRi, a 0.63 PESQ improvement, 84.5\\% speaker selection accuracy, and only a 4.3\\% confusion rate\n\nIn Table~\\ref{tab:big_results}, we further evaluate the model on SpokenWOZ, an out-of-distribution (OOD) English dataset, highlighting the generalization ability of both the model and training approach. {In addition, to assess the model’s ability to generalize across languages, we evaluate it on the Mandarin RAMC dataset and the Japanese Duplex Conversation Dataset \\cite{JapaneseDuplex2025}. As shown in Table \\ref{tab:sisdr_datasets}, our model reaches a 6.5 dB and a 7.92 dB SISDRi, respectively. This shows that even though our model is trained solely on English speakers, it can generalize to conversations in other languages, because it is primarily learning the turn-taking patterns. \n\nWe also evaluate our model on the noisy Libri (2-spk) test set, where WHAM! noise from its test split is added. The model achieves an SISDRi of 10.37 dB, demonstrating its ability to generalize to noisy conditions despite not being trained on such data. Further fine-tuning on noisy data for 35 epochs using the WHAM! training split yields an improved SISDRi of 11.84 dB.\n\n\n\nFinally, we evaluate all models on spatialized test sets that emulate egocentric conditions, as shown in Table~\\ref{tab:big_results}. In egocentric scenarios, speech from other speakers tends to have lower amplitude than the wearer’s self-speech due to physical distance. As a result, after spatializing the synthetic Libri conversational dataset, the average input SISDR for the conversation partners drops from 1 dB to –10 dB, and the average input PESQ decreases from 2.52 to 2.04.\nGiven this challenging setting, our model achieves a 14.62 dB improvement in SISDR and a 0.63 increase in PESQ, while maintaining high speaker selection accuracy (96.8\\%) and a low confusion rate (0.8\\%). We also observe similarly strong performance across other datasets including spatialized Candor and on the out-of-distribution spatialized SpokenWOZ testset. %These results show the effectiveness of our models in spatialized egocentric setups.\n\n% \\begin{table}[t!]\n% \\caption{User evaluation results (5-point scale).}\n% \\vskip -0.1in\n% \\centering\n% \\setlength{\\tabcolsep}{3.8pt} % tighten column spacing\n% {\\footnotesize\n% \\begin{tabular}{lcccc}\n% \\toprule\n% \\textbf{Question} & \\multicolumn{2}{c}{\\textbf{Model Output}} & \\multicolumn{2}{c}{\\textbf{Mixture}} \\\\\n% \\cmidrule(r){2-3} \\cmidrule(l){4-5}\n% & Avg. & SD & Avg. & SD \\\\\n% \\midrule\n% Noise Suppression & 4.29 & 1.19 & 1.67 & 1.04 \\\\\n% Conversation Comprehension & 4.35 & 1.02 & 1.97 & 0.93 \\\\\n% Effort & 4.45 & 0.95 & 1.97 & 0.96 \\\\\n% Overall MOS & 4.30 & 1.14 & 1.88 & 1.02 \\\\\n% \\bottomrule\n% \\end{tabular}\n% }\n% \\label{tab:user_study_table}\n% \\vskip -0.15in\n% \\end{table}\n\n\\begin{table}[t!]\n\\caption{Subjective evaluation results (5-point scale).}\n\\vskip -0.1in\n\\centering\n \\setlength{\\tabcolsep}{6pt} % adjust spacing as needed\n{\\footnotesize\n\\begin{tabular}{lcc}\n\\toprule\n\\textbf{Question} & \\textbf{Model Output} & \\textbf{Mixture} \\\\\n\\midrule\nNoise suppression & 4.29 (1.19) & 1.67 (1.04) \\\\\nComprehension & 4.35 (1.02) & 1.97 (0.93) \\\\\nEffort & 4.45 (0.95) & 1.97 (0.96) \\\\\nOverall MOS & 4.30 (1.14) & 1.88 (1.02) \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:user_study_table}\n\\vskip -0.15in\n\\end{table}\n\n\\subsection{Subjective human evaluation}\n\n{To evaluate the model from a user-centric perspective, we conducted a user study with 11 participants (8 males, 3 females, 1 non-binary) with an age range of 21-65. Each listened to six random conversations from the Candor dataset, experiencing both the original mixture and the model output in a random order. Following \\cite{10.1145/3613904.3642057}, we asked participants four 5-point scale questions about their experience in focusing on the target conversation (see \\xref{sec:user_study}). As shown in Table \\ref{tab:user_study_table}, the proposed system improves user-perceived quality across all four aspects, raising the overall mean opinion score from 1.88 to 4.30.}\n\n%We also evaluate these models on our spatalized testsets that emulate egocentric acoustic conditions in Table~\\ref{tab:big_results}. In egocentric settings, due to physical distance, the speech from other speakers tends to have lower amplitude than self-speech. This means that after spatializing the synthetic Libri conversational dataset, the average input SISDR for the other speakers drops from 1 dB to –10 dB, and the average input PESQ decreases from 2.52 to 2.04, because the amplitude of other speakers in conversation is lower than the self-speech. Despite this, our model achieves a 14.62 dB improvement in SISDR and a 0.63 increase in PESQ, while maintaining high speaker selection accuracy (96.8\\%) and a low confusion rate (0.8\\%).\n\n%We observe similar performance on other spatialized datasets showing that our dual-model remains effective in spatialized, egocentric setups.\n\n%On the spatialized CANDOR dataset, the model achieves a SISDRi of 9.82 dB and a $\\Delta$PESQ of 0.56. For the out-of-distribution spatialized SpokenWOZ dataset, the model achieves 11.95 dB SISDRi and a 0.52 PESQ improvement.\n\n\\subsection{Ablation studies}\\label{sec:ablation}\n%We conducted various ablation studies to validate our design choice for the models.\n\n\\noindent\\textit{Dual-model versus single model.} We compare our dual-model approach with a single fast streaming model that uses the self-speech and mixture audio as input. The single model achieves an SISDR improvement of only 1.45 dB for the conversation partners, much lower than the dual model's 12.48 dB. This shows that without the support of the slower conversation embedding model, the fast model alone, struggles to capture conversational dynamics effectively. \n\n%These configurations achieve Si-SDRi scores of XX, XXX, and XX~dB, respectively. As expected, the slow model achieves the highest performance due to its longer algorithmic latency (1 second), allowing it to leverage more context before producing output. However, this latency is unsuitable for real-time hearing assistance, which requires low-latency streaming. The remaining models operate on 12.5~ms chunks. The dual model achieves the best performance given our streaming constraints.\n\n\\vskip 0.02in\\noindent{\\it Update rate for conversational embeddings.} Since the fast streaming model relies on conversation embeddings generated by the slow model, we compare two embedding update intervals: 1 second and 4 seconds. We train the dual models on the {Libri 2-speaker training set for ten epochs each and evaluate them on the corresponding test set. Increasing the update interval from 1s to 4s leads to a drop of 1.22~dB in SISDRi. %, indicating that less frequent updates degrade performance.\n\n%from 4.14 dB to 2.92dB\n\n\n\\begin{table}[t!]\n%\\vskip -0.07in\n\\caption{Evaluation on real egocentric conversations.}\n\\vskip -0.1in\n\\centering\n \\setlength{\\tabcolsep}{5.3pt}\n{\\footnotesize\n\\begin{tabular}{lccc}\n\\toprule\n\\textbf{Metrics} & SISDRi($\\uparrow$) & Acc ($\\uparrow$) & CR ($\\downarrow$) \\\\\n\\midrule\n\\textbf{Number of speakers} & & &\\\\\n\\midrule\n 2 speakers & 7.84 (6.79) & 85.0\\% & 1.1\\% \\\\\n 3 speakers & 6.00 (7.14) & 73.4\\% & 3.7\\% \\\\\n\\midrule \n\\textbf{Augmentation} & & & \\\\\n\\midrule \n \\ding{55} & 5.49 (5.30) & 77.9\\% & 1.2\\% \\\\\n \\ding{51} & 7.22 (6.96) & 80.0\\% & 2.2\\% \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:hardware_result}\n\\vskip -0.15in\n\\end{table}\n\n\n\n\\vskip 0.02in\\noindent{\\it Speaker embedding versus self-speech.} Instead of anchoring conversation extraction on self-speech, we also explore using the wearer's speaker embedding~\\cite{variani2014deep}. Following~\\cite{tce}, we compute 256-dimensional d-vectors from clean wearer speech, and provide these as embeddings to the slow model. Using speaker embeddings reduces the SISDRi by 2.65~dB compared to self-speech, likely due to temporal variability in speech characteristics and lossy representation, which reduce embedding reliability.\n\n%from 13.6 dB to 10.95 dB\n\n\\vskip 0.02in\\noindent{\\it Beamforming versus self-speech}. \nTo study the impact of using the beamformer's self-speech output versus the ground truth self-speech from the conversation mixture, we use the model trained on spatialized data from stage 2 and evaluate it on Libri (2-spk) test set. The difference in SISDRi between the two modes was less than 0.38~dB.}\n\n\\begin{table}[t!]\n\\caption{Impact of perturbing the turn-taking in human conversations. (SD=standard deviation)}\n\\vskip -0.1in\n\\centering\n \\setlength{\\tabcolsep}{6pt} % adjust column spacing\n{\\footnotesize\n\\begin{tabular}{lc}\n\\toprule\n\\textbf{Perturbation SD} & \\textbf{SISDRi (dB)} \\\\ %& \\textbf{Overlap ratio (\\%)} \\\\\n\\midrule\nNo perturbation & 6.75 \\\\ %& 13.32 \\\\\n0.5s & 6.25 \\\\%& 14.67 \\\\\n1s & 5.68 \\\\%& 15.55 \\\\\n1.5s & 5.25 \\\\%& 16.14 \\\\\n2s & 4.79 \\\\%& 16.56 \\\\\n2.5s & 4.50 \\\\%& 16.94 \\\\\n3s & 4.16 \\\\%& 17.30 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:perturbation}\n\\vskip -0.15in\n\\end{table}\n\n\n\\vskip 0.02in\\noindent{\\it Impact of turn-taking disruption.} {We performed an ablation on the Candor test set to assess the impact of turn-taking pattern disruption. By perturbing inter-utterance silence durations with shifts sampled from a normal distribution with mean 0 and varying standard deviation (SD), we increasingly disrupted the natural turn-taking structure. Table. \\ref{tab:perturbation} shows that as SD and overlap ratio increases, performance gradually degrades, as this breaks the turn-taking structure that the model leverages to separate the targets.} % the target conversation.}\n\n\\vskip 0.02in\\noindent{\\it Context length.} {We trained models with different context lengths (full context, 10s, 5s, 1s) by masking the slow model’s self-attention to limit each token's access to past tokens on Libri 2spk training set. We then evaluated on the Libri 2spk testset. Compared to the model with full context access, SISDRi dropped by 2.12 dB, 4.06 dB, and 5.74 dB for context lengths of 10s, 5s, and 1s, respectively. This demonstrates that access to long-term context is a key factor for the system's performance.}\n\n\n\n\\section{Real-World Egocentric Recordings}\n\n\n\n%\\subsection{Dataset collection}\nWe recruited 11 participants (2 female, 9 male) with an age range of 21--39. The dataset comprises a total of 6.8 hours of binaural egocentric audio recordings, including seven two-speaker and five three-speaker conversations, each lasting approximately 10 minutes. The participants engaged in open-ended discussions in English, on topics such as food, hobbies, recent activities, research, workouts, and travel plans, with no constraints on subject matter. All recordings took place in an environment with typical background noise, including HVAC and ambient sounds. A summary of the conversation statistics is provided in Table~\\ref{tab:realworldstats}.\n\nAll sessions took place in the same acoustic environment so they can be mixed for creating mixtures. During recording, each speaker wore a pair of binaural microphones (Sonic Presence SP15C) and connected it to a smartphone to capture egocentric audio of the conversation. Further, in each conversation, a silent participant served as a listener by wearing the microphones and standing in the vicinity of the speakers. These passive recordings, which lack dominant self-speech, serve as representative samples of interfering conversations.\n\n\n\n\n\\begin{figure}[t!]\n \\centering\n \\includegraphics[width=0.65\\linewidth]{figs/Histogram.png}\n \\vskip -0.1in\n \\caption{SISDRi histogram on egocentric recordings.}\n \\vskip -0.15in\n \\label{fig:hist}\n\\end{figure}\n\n\n\\subsection{Data pre-processing}\n\nSince each conversation participant recorded their own egocentric audio, their self-speech appears with the highest amplitude in their recordings. Using these recordings alongside our beamformer network, we estimated the speech activity timestamps for each speaker. The authors manually verified these timestamps to ensure their quality.\n\nConversation mixtures were created by combining audio from a target speaker with that of a listener in a separate interfering conversation. To avoid amplifying noise, denoising (Sainburg et al., 2020; Sainburg, 2019) was applied only to the target audio, while interfering audio remained unprocessed to preserve realistic ambient noise. Speakers were not shared across the two conversations. Interfering conversations always involved two speakers, while target conversations had two or three. Each sample was constructed to begin with at least 3 seconds of self-speech, and none from a conversation partner. Input SNRs for the target conversation were uniformly sampled between –10 and 10 dB. We generated 200 conversation mixtures to serve as out-of-distribution test set for our model.\n\n\n\n\\begin{table}[t!]\n%\\vskip -0.07in\n\\caption{When the conversation partners start speaking, how quickly does the model pick them up?}\n\\vskip -0.1in\n \\setlength{\\tabcolsep}{3.8pt}\n\\centering\n{\\footnotesize\n\\begin{tabular}{lccccc}\n\\toprule\n\\textbf{Chunk} & 0-2s & 2-4s & 4-6s & 6-8s & 8-10s \\\\\n\\midrule\nSISDRi (dB) & 4.77 & 8.04 & 8.17 & 8.69 & 9.16 \\\\\n% \\midrule\n% \\textbf{Time (s)} & 10-12 & 12-14 & 14-16 & 16-18 & 18-20 \\\\\n% SISDRi (dB) & 8.50 & 8.60 & 8.84 & 9.10 & 8.95 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:pickup}\n\\vskip -0.05in\n\\end{table}\n\n\\begin{table}[t!]\n%\\vskip -0.07in\n\\caption{Effects of turn-change gap between target conversation and interfering conversation.}\n\\vskip -0.1in\n \\setlength{\\tabcolsep}{3.8pt}\n\\centering\n{\\footnotesize\n\\begin{tabular}{lccccc}\n\\toprule\n\\textbf{Turn-change} & 0-1s & 1-2s & 2-4s & 4-6s & > 6s \\\\\n\\textbf{Gap} & & & & & \\\\\n\\midrule\nProportion & 11.3\\% & 12.2\\% & 20.7\\% & 15.5\\% & 40.3\\% \\\\\nSISDRi (dB) & 4.98 & 8.03 & 7.80 & 8.22 & 8.46 \\\\\n% SISDRi & 4.98 (9.28) & 8.03 (6.29) & 7.80 (6.07) & 8.22 (7.05) & 8.46 (6.98) \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:collision}\n\\vskip -0.15in\n\\end{table}\n\n\n\\subsection{Real-world Results}\n\n\nTable~\\ref{tab:hardware_result} shows performance on real-world egocentric recordings with 2- and 3-speaker conversation mixtures. The performance drop with 3-speaker target conversations is because the three speakers turn-taking dynamic in our training data is all synthesized. Fine-tuning on real 3-speaker conversation datasets may further improve results. \n\nThese results show real-world generalization from simulated training data. Around 80\\% of conversations have a positive SISDRi (Fig.~\\ref{fig:hist}). These results also show the benefit of augmentation described in~\\xref{sec:trainingdetails}, which improves performance by 1.73 dB by creating a more diverse distribution of overlaps and silence in the training set. \n\n%better modeling the frequent overlaps typical in real-world conversations, unlike the more turn-based, remote interactions in the Candor training set. \n\n\n\n\n\n\n\n{\\it How quickly is a conversation partner picked up?} We investigate how fast the model enhances a conversation partner after they begin talking. Using a 2-second sliding window over each non-wearer turn in the real-world egocentric dataset, Table~\\ref{tab:pickup} shows the average SISDRi, averaged over all turns and samples in the real-world egocentric dataset. In the first 0–2 seconds, SISDRi is 4.77 dB, indicating initial adaptation. After 2 seconds, it exceeds 8 dB, showing the model quickly adapts to conversational partners within a turn.\n\n\n\n\n\n%Since our model is running in a streaming manner with very low latency, we investigate the following research question: \"When other speaker in the target conversation begins talking, how quickly does the model identify and enhance the correct speaker?\" To quantify it, we analyze each conversational turn of the non-wearer speaker by applying a 2-second sliding window (with a 2-second step size) to segment the entire turn into chunks. Table~\\ref{tab:pickup} reports the average SISDRi across different chunks, aggregated over all turns and samples in the real-world egocentric dataset. In the first 0–2 seconds of a new turn, the SISDRi is relatively low (4.77 dB), indicating the model is still adapting. However, after 2 seconds, the SISDRi rises above 8 dB. This indicates that our model can quickly adapt to conversational dynamics and begin effectively enhancing the correct speaker after approximately 2 seconds. \n\n\n\n\n\n\n\n{\\it How does turn-change collision impact performance?} We examine how overlapping turn transitions in target and interfering conversations affect performance. For each self-to-other turn change in the target conversation, we compute the time gap to the nearest turn change in the interference. A small gap indicates simultaneous speaker transitions. Table~\\ref{tab:pickup} shows that 11.3\\% of turns have gaps under 1 second, where SISDRi drops to 4.98 dB. This suggests that closely timed turn-changes can confuse the model. Future work could address this by incorporating conversation content. \n\n\n{\\it What happens with extended periods of wearer silence?} \n Fig.~\\ref{fig:self_speech_absent} shows a real-world example where the wearer did not speak for over 2 minutes. The purple curve indicates the SISDRi of the conversational partner in 30-second windows; grey areas show when the wearer was speaking. SISDRi stayed above 5~dB during intermittent speech but dropped below zero during prolonged silence, indicating the model failed. Performance recovered once the wearer resumed speaking, highlighting the model’s reliance on self-speech as an anchor.\n\n\n%\\textcolor{red}{We examined model performance during extended periods when the wearer remains silent. Fig \\ref{fig:self_speech_absent} shows an example in our real-world egocentric recording when the wearer did not speak for over 2 minutes. The purple curve represents the SI-SDRi of the other target speaker, computed over consecutive 30-second intervals. The grey area represents sections where the wearer was speaking. When the wearer spoke intermittently at the beginning, the SI-SDRi remained above 5 dB. However, once the wearer stopped speaking for over one minute, the SI-SDRi drops to negative as the model did not pick up any speaker in the conversation. Performance was gradually recovered when the wearer resumed speaking starting from approximately 315 seconds into the recording. This shows our model anchors on the wearer's self-speech to identify the other target speaker.}\n\n\n%Since our model relies on turn-taking dynamics to track the target conversation, we also examine what happens when a turn-change in the target conversation occurs close in time to a turn-change in an interfering conversation Specifically, for each turn transition from the self speaker to the other speaker in the target conversation, we identify the nearest turn-change event in the interfering conversation and compute the time gap between them — referred to as the turn-change gap. A smaller gap indicates that turn-taking events in both conversations occur close together in time. Table~\\ref{tab:pickup} shows the distribution of turn-change gaps and the corresponding SISDRi for each target turn. We find that 11.3\\% of turns have a turn-change gap of less than 1 second, and in these cases, the average SISDRi drops to 4.98 dB. This suggests that when turn-taking events in the target and interfering conversations occur too closely, the model may become confused to recognize the correct speaker, leading to degraded separation performance. In the future, this turn-change collision issue could potentially be mitigated by incorporating the textual information from the target conversation.\n\n\n\n\n\n%For these reasons, we run the fast streaming model on an embedded device, an Orange Pi 5B, and the slow model on an Apple M2 silicon. Both networks satisfy the real-time constraints on their respective hardware platforms, with the fast model taking 8.9~ms on average to run inference on a 12.5~ms audio chunk, and the slow model taking 41.3~ms on average for a 1 second chunk (Appendix~\\ref{sup:runtime}).\n\n\n\n\n\n\n\n\n\\begin{figure}[t!]\n \\centering\n \\includegraphics[width=0.75\\linewidth]{self_speech_absent.png}\n \\vskip -0.1in\n \\caption{Extended periods of wearer silence. The gray regions denote durations were the wearer was active.}\n \\vskip -0.15in\n \\label{fig:self_speech_absent}\n\\end{figure}\n\n\n\\section{Conclusion}\n\n We present the first real-time, proactive hearing assistant that automatically identifies the wearer’s conversational partners and suppresses unrelated speech, without requiring explicit user prompts. Our system runs on-device and generalizes to real-world egocentric recordings despite being trained only on synthetic data. By leveraging turn-taking cues to model conversational engagement, our approach connects speech separation with core dialogue modeling tasks. This work takes an important step towards proactive hearing assistants that interpret and adapt to conversation dynamics.\n\n \n\n\\section{Limitations and risks}\n\n{\\bf Limitations.} Our system is designed for scenarios in which the wearer is an active participant in a conversation, using self-speech as an anchor to identify conversational partners. It is not suited for passive listening, such as eavesdropping or passive consumption. %%In cases where the user's speech is infrequent or absent, the system may fail to maintain accurate tracking of conversational partners until additional self-speech is detected.\n\n\n\nThe current implementation prioritizes real-time, on-device performance and incorporates conversational turn-taking. While this design choice supports low-latency operation, it may limit the system's ability to disambiguate overlapping speakers, especially when multiple speakers begin speaking simultaneously. Incorporating lightweight content-aware models could be a direction for future work.\n\n\n%\\st{Our evaluation is limited to conversations involving 2–3 speakers. Extending the system to handle more complex multi-party interactions remains an open challenge. } Our evaluation on real-world egocentric data is limited to conversations involving 2–3 speakers. \\textcolor{red}{Although we were able to demonstrate the model generalizes to unseen number of speakers in the target conversation on our synthetic dataset, such generalization capability on real world audio remains unexplored. } \\st{Extending the system to handle more complex multi-party interactions remains an open challenge.}\n\n\nIn addition, while the model generalizes to real-world egocentric recordings without fine-tuning on such data, performance could likely benefit from supervised adaptation to real-world {acoustic and conversation} conditions.\n\n{Finally, although the model achieved cross-linguistic generalization in evaluations on English, Mandarin, and Japanese datasets}, cultural and linguistic differences in turn-taking behavior~\\cite{turntake2} suggest that further fine-tuning for language- or culture-specific dynamics may improve robustness.\n \n\n\n\\vskip 0.05in\\noindent{\\bf Ethical considerations. } \nProactive hearing assistants hold promise for improving communication access for individuals with hearing loss, particularly in dynamic and crowded settings. They may be especially valuable for older adults or users with limited dexterity, for whom manual control interfaces may be impractical.\n\n\nHowever, there are important risks. Incorrect speaker detection may suppress relevant voices or amplify unrelated ones. Such errors are particularly concerning in high-stakes or fast-moving conversational contexts. Improving this remains a key area for future work.\n\nAdditionally, if the assistant fails or behaves unpredictably, users should have a clear and intuitive means to override or adjust system behavior. One practical solution could be a physical control (e.g., a tactile button) to temporarily disable the assistant or reset its state. Addressing these through transparent design, user-centric controls, and robust real-world evaluation will be essential for safe and responsible deployment.\n\n\n\n%%\n%% The next two lines define the bibliography style to be used, and\n%% the bibliography file.\n%\\bibliographystyle{ACM-Reference-Format}\n% \\bibliographystyle{acl_natbib}\n\\bibliography{paper}\n\n\n\\appendix\n\n\\section{Dual Model architecture details}\\label{sec:dualmodeldetails}\n\nAs shown in Fig.~\\ref{fig:pipeline}, our architecture includes a fast streaming model and a slower conversation embedding model. The streaming model outputs audio with minimal latency, processing each chunk as it arrives. The slow model buffers $T$ seconds of audio to capture long-term conversational dynamics and generates a conversation embedding, which conditions the streaming model for the next $T$ seconds before being updated.\n\nThe conversation embedding model also takes the wearer's self-speech as input, estimated using a neural beamformer. While the beamformer adds some latency, it is negligible compared to $T$ and does not affect streaming model latency. The self-speech is concatenated with the noisy audio along the channel dimension and passed to the conversation embedding model.\n\n\nBoth the streaming and conversation embedding models are based on TF-GridNet~\\cite{tfgridnet} and operate on audio in the time-frequency (TF) domain. We first convert time-domain audio signal $x \\in \\mathbf{R}^{C \\times t}$, where $C$ is the number of channels and $t$ is the number of frames, using the short-time Fourier Transform (STFT) to obtain the TF-representation $X \\in \\mathbf{C}^{C \\times F \\times L}$, where $F$ is the number of frequency bins, and $L = \\frac{t}{\\tau}$ is the number of time steps after STFT. The real and imaginary components are concatenated along the channel dimension and the resulting tensor $X' \\in \\mathbf{R}^{2C \\times F \\times L}$ is provided as the input. \n\nThe conversation embedding model first maps $X'$ to a $D$-channel latent space using a $3\\times3$ 2D causal convolutional layer to get $Z_e \\in \\mathbf{R}^{D \\times F \\times L}$. Then, the input is processed by a stack of six extraction blocks, each of which consists of a local module and a global module. The local module processes audio information within a $T$ second chunk. It uses bidirectional LSTMs to 1) model the spectral information within the same time step, and 2) model the temporal information within the same frequency bin over exactly $T$ second chunks. This latter process requires that the model wait for $T$ seconds before it can process the sequence of chunks. The global module models relationships across sequences of $T$ second chunks. Specifically, we average pool the information from every $T$ seconds to reduce the temporal resolution and use self-attention on this pooled representation. To ensure causality, attention weights are masked using a lower-triangular matrix, allowing each time step to attend only to previous steps. We use 4 attention heads and absolute positional encoding. Following the global module, we replicate every time step in the pooled representation to retrieve a tensor with the original number of timesteps before pooling. After the last extraction block, we simulate the slow model's algorithmic latency by shifting the result backwards in time by $T$ seconds, inserting zeros at the beginning. This time-varying conversation embedding $E \\in \\mathbf{R}^{D \\times F \\times L }$ is returned and can be used to condition the streaming model.\n\nThe streaming model also maps $X'$ to a latent representation $Z_s \\in \\mathbf{R}^{D \\times F \\times L}$ using a $3\\times3$ 2D causal convolutional layer and processes the resulting tensor through six extraction blocks. The model is conditioned on the conversation embedding by multiplying it, element-wise, with the feature map between the first and second extraction blocks. The extraction block uses a bidirectional LSTM to model sequences of frequencies within the same time frame, but replaces the bidirectional temporal LSTM with a unidirectional LSTM to reduce latency and discards the global module entirely. After the last extraction block, we use a deconvolution layer to convert the data back to the TF-domain $Y'\\in \\mathbf{R}^{2C \\times T \\times F}$. Finally, we use an inverse STFT and overlap-add to reconstruct the output time-domain signal $x \\in \\mathbf{R}^{1 \\times T}$\n\n% Like the embedding model, it begins with an STFT using the same chunk size, look-back and lookahead. The resulting TF representation is passed through a \\(3 \\times 3\\) convolutional layer. Prior to the first extraction block, the model conditions on the embedding \\(\\mathbf{e}\\) by performing an element-wise multiplication with the input TF features.\n\nWe adopt the dual-window method for time–frequency transformation from~\\cite{low_latency_stft}. Using this framework, we use an STFT with a chunk size of 200 samples (12.5~ms) and a lookback and lookahead of 32 samples (2~ms). The output window size for the inverse STFT is 232 samples, i.e. we discard the first 32 samples of the inverse FFT output every STFT frame. We use rectangular synthesis and analysis windows. Both models use a latent dimension $D=32$, and an LSTM hidden dimension $H=32$. The local modules of the embedding module use unfolding to reduce the number of steps to process in the time and frequency sequences. This unfolding operation has a kernel size of 2 and a stride size of 2. The global modules project the tensor onto a smaller subspace with only 2 channels before applying self-attention.\n\n% Due to the quadratic memory complexity of self-attention with respect to sequence length, training on full 60-second sequences is computationally expensive \\textcolor{red}{but now there's no attention in the streaming model, what's a good reason for training on 10s audio}. Therefore, during training, we randomly sample 10-second segments from the full input. The corresponding 10-second slice of the conversation embedding \\(\\mathbf{e}\\) is extracted and provided to the streaming model. The loss is then computed only on the 10-second predicted output.\nThe conversation embedding model has 986K parameters and the streaming model has 491K parameters.\n\n\\section{Beamformer model details}\\label{sec:beamformerdetails}\n\nOur beamformer model follows the architecture in~\\cite{soundbubble}, excluding the frequency compression modules. To minimize algorithmic latency, we once again use the dual-window method for time–frequency transformation from~\\cite{low_latency_stft}. We use a chunk size of 96 samples (6~ms), with a lookback of 96 samples (4~ms) and a lookahead of 64 samples (6~ms). The encoder consists of 3×3 2D causal convolution layers, producing a 32-dimensional latent representation. The model then processes the input with 6 GridNet blocks and LSTMs with a hidden dimension of 32. The inverse DFT uses a 160-sample output window, discarding the first 96 samples during overlap-add. The network outputs two channels, which are averaged to produce the final single-channel beamformer output.\n\n\n%We use a chunk size of 96 samples (6~ms), a lookback of 96 samples (4~ms), and a lookahead of 64 samples (6~ms). The network uses 3$\\times$3 convolution layers for the encoder, an latent dimension of 32 after the encoder, 6 repetitions of GridNet blocks, and an LSTM hidden dimension of 32. The inverse DFT uses an output window size of 160 samples. The network outputs two channels, and we average them to obtain then final, single-channel beamformer output.\n\n\n\n\\subsection{Beamformer datasets }\\label{sec:beamformerdatasets}\n\n\n\nThe beamformer is a neural network designed to extract the user's self-speech in the presence of surrounding speech and noise. It takes binaural audio recorded from a headset worn by the user as input. Because the network relies on spatial cues, such as inter-channel phase and level differences, it is especially sensitive to spatial features that are difficult to model accurately in simulated environments.\n\nTo address this, we first pretrain the beamformer on a large dataset of synthetically generated binaural recordings, then finetune it on a smaller set of real-world binaural recordings. The final model is a lightweight beamformer with 174K parameters that generalizes well to real-world acoustic conditions, making it well-suited for use as a self-speech extractor for our real-time hearing assistant.\n\n\n%The beamformer is a neural network that is tasked with extracting the user's self-speech in the presence of interfering speech and noise sources around the user. The input to the network is a binaural audio signal recorded by a headset worn by the user. We seek to train a beamformer that generalizes to real world multipath. However, since this network operates on binaural audio, it is particularly sensitive to spatial features such as inter-channel phase and level differences, which are tricky to capture accurately with spatial acoustic simulators. To alleviate this problem, we first pretrain our network on a large dataset of synthetically generated binaural recordings, and then finetune on a smaller dataset of binaural audio collected in the real world. The resulting network is a lightweight beamformer with 174~K parameters that generalizes well to the real world, making it suitable to use as a self-speech extractor to the proposed conversation extraction system.\n\nTo train the beamformer on synthetic data, we create a dataset of 5-second audio mixtures. Each mixture includes speech from a user wearing a binaural headset and 1 to 5 interfering speakers, sampled with equal probability. All speech signals are drawn from LibriSpeech. If an audio clip exceeds 5 seconds, we randomly crop a 5-second segment; if it is shorter, we pad it with a random duration of silence. Simulated egocentric binaural signals are generated using the method described in~\\xref{sec:spatialize}, and these signals are summed to form the final mixture. Interfering signals are scaled so that the mixture’s SNR is uniformly distributed between -5 and 20dB. Training and validation audio are sampled from LibriSpeech’s \\verb+train-clean-360+ and \\verb+dev-clean+ splits, respectively. The final synthetic dataset contains 20K training mixtures and 1K val mixtures.\n\n\n%We obtain simulated egocentric binaural signals using the process described in~\\ref{sec:spatialize}, and sum the signals together to obtain the mixture. We scale the interfering signals so that the SNR of the mixtures is uniformly distributed in $[-5, 20]$. The audio for the train and validation splits is sampled from LibriSpeech's \\verb+train-clean-360+ and \\verb+dev-clean+ splits respectively. This synthetic dataset consisted of 20K training mixtures and 1k validation mixtures.\n\nWe further train the beamformer using real-world data. For this, we collected 3 hours of self-speech from 9 participants across 15 different rooms, along with 4 hours of interfering speech from 4 participants in 3 rooms. To generate training examples, we create 5-second binaural mixtures by combining a 5-second self-speech clip with 0 to 5 interfering speech clips of the same length. Each 5-second clip is formed by extracting 2–5 seconds of active speech from a speaker and padding it with a random amount of silence.\n\nAll audio clips are scaled so that their power (in dBFS) follows a normal distribution with a mean of -25 and a standard deviation of 5. Additionally, we include a 5-second binaural noise clip from the binaural WHAM! dataset. The WHAM! noise is randomly scaled by a factor in $[0,1]$ before being added to the mixture. Noise clips for training and validation are drawn from the \\verb+tr+ and \\verb+cv+ splits of the WHAM! dataset, respectively. The final mixture is obtained by summing the self-speech, interfering speech, and noise. Interfering speech and noise are scaled to produce an overall SNR uniformly distributed in $[-5,20]$~dB. These real-world mixtures are generated on the fly during training, and we use 1,000 mixtures for validation.\n\n% 315\n% 403\n% 422\n% 306\n% 324\n% 503\n% 305\n% 314\n% 303\n% hallway\n% evacuation stairs\n% 322\n% 318\n% Habib room\n% Noe room\n\n\\subsection{Beamformer training }\\label{sec:beamformertrainingdetails}\n\nThe beamformer is trained in two stages: (1) on synthetic data, and (2) fine-tuned on real-world recordings. In both stages, we use a batch size of 8, apply gradient clipping with a max norm of 0.1, and optimize using AdamW \\cite{adamw} with a weight decay of 0.01.\n\n\nThe synthetic data training stage is trained for 200 epochs on negative SNR Loss. We vary the learning rate based on a schedule. For the first 10 epochs, we linearly increase the learning rate from 0.0001 to 0.001. Then, we maintain this learning rate for 140 epochs. Finally, we further train for 50 epochs, halving the learning rate every 15 epochs.\n\nThe real world data fine-tuning stage occurs over 300 epochs, with each epoch defined as 20K iterations. Here, we use the following composite loss function: $L(\\hat{x}, x) = 10 ||x-\\hat{x}||_1 + L_{MR}(\\hat{x}, x)$, where $x$ is the target signal, $\\hat{x}$ is the beamformer output signal, $||\\cdot||_1$ is the L1-norm, and $L_{MR}$ is the multiresolution STFT loss. The multiresolution STFT loss uses a weight of 1 for the spectral convergence loss term, a weight of 1 for the log magnitude loss term, a weight of 4 for the linear magnitude loss term. It also uses Hanning windows with FFT sizes $[1024, 2048, 512]$, hop sizes $[120, 240, 50]$, and window lengths $[600,1200,240]$. The learning rate is initially 0.001 and we halve it if the loss function does not improve after 8 epochs.\n\n\\subsection{Beamformer real-world evaluation}\\label{sec:beamformereval}\nWe evaluate the beamformer on real world recorded data from 6 unseen human participants in 3 unseen rooms. We group participants in pairs, and record data for every pair of participants in a different room. Each participant wears a microphone around each ear to record a binaural recording. The pair of participants take turns speaking for 8-10 minutes, with both participants recording audio the entire time. We process the recordings to slice out sections of self-speech recordings (same recorder and speaker) and interfering speech recordings (different recorder and speaker). Then, we create 100 5-second mixtures per speaker by combining a 5-second crop of self-speech and with a 5-second crop of interfering speech recorded by the same participant. We scale the power of each segment in a similar fashion as described in \\xref{sec:beamformerdatasets}, and then further scale the interfering speech so the scaled SNR is now uniformly sampled from $[-5, 5]$~dB. We report the results on this out-of-distribution beamformer dataset in Table~\\ref{tab:bf_eval}, clearly showing significant noise reduction and self-speech extraction.\n\n\\begin{table}[t!]\n%\\vskip -0.07in\n\\caption{Beamformer evaluation on unseen real-world mixtures. DNSMOS BAK is the estimate of the ITU P.835 background noise quality using a neural net.}\n\\vskip -0.1in\n\\centering\n{\\footnotesize\n\\begin{tabular}{lccc}\n\\toprule\n\\textbf{Metrics} & SNR~(dB) & SI-SDR~(dB) & DNSMOS \\\\\n & & & BAK \\\\\n\\midrule\n Mixture & -0.13 & -0.13 & 1.94 \\\\\n Beamformer & 8.36 & 7.78 & 3.96 \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:bf_eval}\n\\vskip -0.15in\n\\end{table}\n\n\n\n\\section{Datasets}\nWe detail the dataset generation and spatialization process. With the exception of the Libri (leaving) dataset, the interference conversation in all datasets is always composed of exactly 2 speakers, with the target and interference conversations never sharing a common speaker.\n\n% For the Candor dataset, we ensured no speaker appeared in more than one split. \n\n\\subsection{Dataset Generation}\\label{sec:datasetgen}\n\\textbf{Libri}. This is a combination of 5 datasets -- Libri (2 spk), Libri (3 spk), {Libri (4 spk), Libri (5 spk), and} Libri (leaving) -- each of which consists of 60-second conversation mixtures between a target conversation and an interference conversation. These conversations are synthesized by populating speaker timestamps from one conversation dataset (RAMC~\\cite{ramc}), with audio from another dataset LibriTTS~\\cite{zen2019libritts}. Libri has 16,000 training samples, 2,600 validation samples, and {1000} test samples. Among the 1000 test samples, there are 200 samples for Libri (2 spk), 200 samples for Libri (3 spk), 200 samples for Libri (4 spk), 200 samples for Libri (5 spk), and 200 samples for Libri (leaving). The input SNR for the target conversation is sampled uniformly from –10 to 10 dB.\n\n\\textit{Libri (2 spk)}. The target conversations in this dataset have exactly 2 speakers. Since our model relies on self-speech to identify other speakers in the target conversation, we initially populate the timestamps with the self-speaker's audio for a minimum total duration of 5 seconds. Subsequently, for every remaining timestamp, we randomly populate it with speech from either the self speaker or the conversation partner. To prevent one speaker from dominating the conversation, we ensure the other target speaker meets a minimum utterance duration of 5 seconds. \n\n\\vskip 0.02in\\noindent\\textit{Libri (3 spk)}. The target conversations in this dataset have exactly 3 speakers. Similar to the generation procedure for Libri (2 spk), we begin by ensuring the self-speaker speaks for the first 5 seconds. For all subsequent utterances, we randomly pick one speaker from the target conversation and insert their corresponding Libri audio into the utterance. Finally, we verify that each of the two conversation partners has at least one utterance exceeding 5 seconds in duration. The interference conversation in this mixture has 2 speakers.\n\n\\vskip 0.02in\\noindent\\textit{Libri (4 spk) and Libri (5 spk) (Evaluation only)}. {The target conversations in these two datasets contain exactly four and five speakers, respectively. The generation procedure is the same as in Libri (2 spk) and Libri (3 spk), except that for each utterance, we populate the audio with a randomly sampled speaker from a pool of 4 or 5 speakers. We ensure that the self-speaker speaks for the first 5 seconds, and that every other speaker has at least one utterance longer than 5 seconds to ensure their participation in the conversation.}\n\n\\vskip 0.02in\\noindent\\textit{Libri (leaving)}. Since human conversations are highly dynamic, our model must adapt to both preserve target speakers and suppress them when they leave the conversation and join the interference. To model this behavior, we generate a dataset that initially consists of a 3-speaker target conversation and a 2-speaker interference, which then transitions into a 2-speaker target conversation and a 3-speaker interference. We first ensure the self speaker speaks consecutively for at least 5 seconds at the start of the conversation. %Additionally, at least one other target speaker must have a 5-second consecutive utterance within the first 40 seconds.\n\nThen, one of the two conversation partners is chosen at random to leave the target conversation and join the interference conversation. Specifically, we randomly select a timestamp from the interference conversation that starts after that chosen timestamp for the conversation partner and before the 40 second mark to use for their first utterance in the interference conversation. We also require the leaving speaker to have a consecutive 5-second utterance in the interference conversation to confirm their presence. After this transition, the target conversation becomes a two-speaker conversation, and the interference becomes a three-speaker conversation.\n\n\n\\vskip 0.02in\\noindent\\textbf{Candor}. {This is a dataset consisting of 60-second conversation mixtures between a target and interference conversation from Candor. Since Candor dataset does not provide predefined splits, we created our own own by assigning 80\\% of speakers to training, 10\\% to validation, and 10\\% to testing. Thus, we ensure there are no overlapping speakers across splits. When generating conversation mixture, we randomly select two recordings from the same split and ensure that they do not share any speakers. For the target conversation, we extract the 60-second segment where the self-speaker speaks continuously for at least 5 seconds at the beginning. In total, we generate 7000 training samples, 900 validation samples and 500 testing samples. Similar to the Libri datasets, the input SNR for the target conversation is sampled uniformly from –10 to 10~dB.}\n\n\n%\\vskip 0.02in\\noindent\\textbf{Testsets.} For each test set, we create XXX mixtures, where the interfering 2-speaker conversation is drawn from the same test set, with no overlapping speakers. The input SNR for the target conversation is sampled uniformly from –10 to 10~dB.\n\n\n\\subsection{Dataset Spatialization}\\label{sec:spatialize}\n\nWe generate synthetic egocentric audio using PyRoomAcoustics, an open-source room acoustics simulator widely used in audio research. The simulator produces left- and right-channel room impulse responses (RIRs) from each speaker, including the wearer, to microphones placed at the wearer’s ears.\n\nRooms have dimensions sampled uniformly: length and width from $[5, 10]$~m, and height from $[3, 4]$~m. The user is positioned at a distance uniformly sampled from $[0, 1]$m from the room center; other speakers are placed at distances from $[0.5, 1.5]$m. Person heights are sampled from $\\mathcal{N}(175\\text{cm}, 7\\text{cm})$.\n\nMicrophones are placed near the user’s ears, offset laterally from the head center by half the head width, sampled from $\\mathcal{N}(15~\\text{cm}, 2~\\text{cm})$. Audio sources are placed near each speaker’s mouth: vertically offset along the negative z-axis by $\\mathcal{N}(18~\\text{cm}, 2~\\text{cm})$, and horizontally offset from their center by $\\mathcal{N}(10.75~\\text{cm}, 2~\\text{cm})$.\n\nRoom reverberation time (RT60) is sampled uniformly from $[0.15, 1]$~s, capturing a range of acoustic environments.\n\n\n\n\n%We place a pair of microphones near the ears of the user, at an offset from the user's position by half the human head width, which is sampled from $\\mathcal{N}(15~cm, 2~cm)$. We place audio sources near the mouths of each person, at an offset along the negative z-axis from that person's height sampled from $\\mathcal{N}(18~cm, 2~cm)$, and an offset from the center of the person's position sampled from $\\mathcal{N}(10.75~cm, 2~cm)$. The RT60 reverberation time, which is the time it takes for energy to decay in the room by 60~dB, is sampled uniformly from the range $[0.15, 1]~s$.\n\n\\section{Training details}\\label{sec:trainingdetails}\nIn the first stage, we pretrain on 2K Libri (2spk) mixtures, 7K Libri (3spk) mixtures, 7K Libri (leaving) mixtures, and 7K Candor mixtures. The fast streaming model and the slow conversation embedding model are trained jointly without any pre-training. The two models were jointly trained for 120 epochs, with an initial learning rate of 0.002, AdamW optimizer with a weight decay of 0.01, and clip gradient norms to 1. We halve the learning rate if the loss does not decrease after 8 epochs. We use the negative SNR loss function and a batch size of 16 on 8 L40s.\n\n{In the second stage, we jointly train the two models on the spatialized dataset (procedure outlined in Appendix~\\ref{sec:spatialize}). The slow model is initialized with the pretrained weights from Stage 1, while the fast model is initialized from scratch. The models are jointly trained for 50 epochs with a with an initial learning rate of 0.002, AdamW optimizer with a weight decay of 0.01, and clip gradient norms to 1. We halve the learning rate if the loss does not decrease after 4 epochs. We use the negative SNR loss function and a batch size of 16 on 8 L40s.}\n\nIn the final stage, we augment our datasets by changing the duration of silence between every successive conversation partner utterance by a random amount sampled from $\\mathcal{N}(0, 0.5~s)$. To preserve the order of utterances from the same speaker, we clip all silent durations to at least 1 sample. Finally, to retain the same overall duration of silence in the clip, we then normalize the length of each silent duration by sum of all silent duration in the audio clip. As a result, the speaker utterances occur at slightly different (and random) times, often overlapping with the user's speech. Here, we use the AdamW optimizer with a weight decay of 0.01, clip gradient norms to 1, and an initial learning rate of 0.0005. We halve the learning rate if the loss does not decrease after 8 epochs. This stage was trained for 42 epochs with a batch size of 4 on 2 A100 GPUs and the negative SNR loss function.\n\n\n\n\n\\begin{figure}[t!]\n \\centering\n \\includegraphics[width=\\linewidth]{figs/runtime.pdf}\n \\vskip -0.05in\n \\caption{Runtime of slow and fast model. A. The inference time of the fast model to process 12.5ms chunk on Orangpi 5B. B. The inference time of the slow model to process 1s chunk on Apple Silicon M2.}\n \\vskip -0.15in\n \\label{fig:runtime}\n\\end{figure}\n\n\n\\section{Runtime analysis}\\label{sup:runtime}\n\nFig.~\\ref{fig:runtime} reports CDF plots for the inference time of both the fast and slow models on the OrangePi 5B and Apple M2 silicon, respectively. % for the slow model.\n\n%\\textcolor{red}{\\textbf{Need to double check reasoning here} Since the fast streaming model operates chunk-wise where each chunk is 12.5 ms (see Appendix~\\ref{sec:dualmodeldetails}), this results in long sequence length that makes it computationally expensive to train due to the LSTM operating over the sequence dimension. To make training feasible, we randomly slice a 10-second mixture audio from the 60-second input before the audio is passed as input into the streaming model. The corresponding conversation embedding is also segmented by time and provided as a second input. The audio input for the conversational embedding model remains unchanged.}\n\n\\section{Conversation waveform examples}\\label{sec:waveform}\n{Fig. \\ref{fig:waveform} shows an example from the spatialized Libri (2 spk) dataset. The mixture audio contains both the target and interference conversations. The beamformed self-speech is generated by applying our beamformer to this mixture. Due to spatialization, the self-speech is emitted closer to the wearer's ears, resulting in a higher amplitude compared to the other target speaker. However, our model was able to capture the low-amplitude speech of the other speaker. }\n\n\n\\section{Details of Ablation studies}\\label{seC:ablationdetails}\n\n\\textit{Dual-model versus single model}. The fast only streaming model is trained on the same dataset as our dual model from stage 1, with a learning rate of 0.002, AdamW optimizer, a negative SNR loss function, and a batch size of 16 on 8 L40s. After training, we evaluate the model on the Libri 2-speaker testing dataset. \n\n% Since the fast streaming model processes audio with a chunk size of 12.5ms, this results in long sequence length in the self attention. Since the memory requirement of full self-attention increases quadratically with sequence length, we randomly slice a 10-second section of audio from the 60-second audio input \\textcolor{red}{during training to reduce memory usage}. This is applied when training the fast-only and dual-model configurations. The loss is computed on the 10-second section. For the dual-model, we used the model we trained during stage 1. We trained a total of \\textcolor{red}{120} epochs with a learning rate of 0.002, AdamW optimizer \\cite{loshchilov2017decoupled}, a negative SNR loss function \\cite{ma2011snr}, and a batch size of 16 on 8 L40s. \n\n\\noindent\\textit{Conversation embedding update rate}. The two dual-models are trained from scratch for 10 epochs using a learning rate of 0.001, the AdamW optimizer, a negative SNR loss, and a batch size of 8 on 8 RTX 6000 GPUs. After 10 epochs, the models show a consistent trend where the 1-second update rate outperforms the 4-second rate. Evaluation was conducted on 200 Libri 2-speaker test samples.\n\n\n\\begin{figure}[t]\n \\centering\n % \\vskip -0.1in\n \\includegraphics[width=\\linewidth]{waveform_plot.png}\n \\vskip -0.1in\n \\caption{Visualized waveforms for conversation mixture, the beamformed self-speech, output of the model and the groundtruth target egocentric conversation.}\n %\\vskip -0.15in\n \\label{fig:waveform}\n\\end{figure}\n\n\n\\noindent\\textit{Speaker embedding versus self-speech}. We trained two slow models on the {Libri 2-speaker} training dataset. One model uses speaker embeddings and the other uses self-speech. Both models were trained for 100 epochs with a learning rate of 0.001, the AdamW optimizer, a negative SNR loss on 4 L40s. Evaluation was performed on 200 {Libri 2 speaker} test samples. \n\n\\noindent\\textit{Beamforming versus groundtruth self-speech}. For this ablation study, we used the model trained in stage 2 and evaluated it on 200 spatialized Libri 2-speaker test samples. During evaluation, the model was conditioned on either the original self-speech audio present in the mixture or the self-speech audio output by our beamformer.\n\n\\noindent\\textit{Impact of turn-taking disruption} {We changed the duration of silence between two consecutive utterances from every speaker by sampling a duration shift from a normal distribution with mean 0 and a standard deviation parameter SD. This duration shift is added to the original silence duration and clipped to preserve the order of the utterances. The lengths of the new silent sections are normalized so that the overall silence duration remains the same. With this perturbation technique, the parameter SD controls the extent to which the turn-taking dynamics are changed. Larger values of the standard deviation correspond to larger distortions of the original turn-taking structure. This process maintains the overall speech content but disrupts the natural temporal flow of the conversation. We then evaluate the performance of our model trained in stage 1 on our Candor test set with different perturbations.\n}\n\n\\noindent\\textit{Context length.} {We trained 4 dual models with different context length configurations (1s, 5s, 10s, full context) for 20 epochs with a learning rate of 0.001, AdamW optimizer and negative SNR loss. We train the models on Libri 2-speaker training set and evaluate them on 200 Libri 2 speaker test samples.}\n\n\n\n\\begin{table}[t!]\n%\\vskip -0.07in\n\\caption{Statistics for our real egocentric conversation recordings. }\n\\vskip -0.1in\n% \\begin{table*}[!t]\n\\centering\n{\\footnotesize\n\\begin{tabular}{lr}\n\\toprule\n Statistic & Mean (STD)\\\\\n\\midrule\nTurn-change Frequency ($min^{-1}$) & 6.2 (4.6) \\\\\nTurn Duration & 8.2s (8.8s) \\\\\nOverlap Ratio & 1.3\\% (2.5\\%) \\\\\nIPU Duration ($min^{-1}$) & 52.0s (3.54s) \\\\\nFTO & 0.18s (1.38s) \\\\\n\\bottomrule\n\\end{tabular}\n}\n\\label{tab:realworldstats}\n% \\end{table*}\n\\vskip -0.15in\n\\end{table}\n\n\\section{{User Study Design}}\\label{sec:user_study}\n{We ask each participant the following four questions after they listen to both the original audio mixture and our model's output. Each question used a 5-point scale.}\n\n\\begin{enumerate}[label=(\\arabic*), leftmargin=*, itemsep=0pt, topsep=0pt]\n \\item \\textbf{Noise Suppression}: How INTRUSIVE/NOTICEABLE were the INTERFERING SPEAKERS? 5 - Not noticeable; 4 - Slightly noticeable; 3 - Noticeable, but not intrusive; 2 - Somewhat intrusive; 1- Very intrusive\n\n \\item \\textbf{Conversation Comprehension}: How EASY was it to understand the target conversation in this audio sample? 5 - Very easy; 4 - Easy; 3 - Neutral or Neither easy nor hard; 2 - Hard; 1 - Very hard\n\n \\item \\textbf{Effort}: How much EFFORT did it take to focus on the target conversation in this audio sample? 5 - Very little effort; 4 - Little effort; 3 - Moderate effort; 2 - High effort; 1 - Very high effort\n\n \\item \\textbf{Overall MOS}: If the goal is to focus on this target conversation, how was your OVERALL experience? 5 - Excellent; 4 - Good; 3 - Fair; 2 - Poor; 1 - Bad\n\\end{enumerate}\n\n\\section{Egocentric evaluation participants}\nThe study was approved by our institution's IRB. All participants provided informed consent and were recruited from our institution and nearby areas. They were offered a \\$15 compensation. %Participants ranged from XXX to XXX years old, with XX\\% identifying as female and the rest as male.\n\n\n\n\\section{Real-egocentric conversation analysis}\n\nWe compute several conversational statistics from our collected real-world egocentric recordings:\n\\squishlist\n\\item {\\it Turn-Change Frequency.} The number of speaker turn changes per minute.\n\n \\item {\\it Turn Duration.} The length of each individual speaking turn.\n\n \\item {\\it Overlap Ratio.} The proportion of time during which multiple speakers talk simultaneously.\n\n \\item {\\it Interpausal Unit (IPU) Duration.} A continuous stretch of speech from a single speaker, bounded by silences longer than 200 ms on both sides, as detected by a voice activity detector.\n\n \\item {\\it Floor-Transfer Offset (FTO).} The time gap between the end of one speaker’s turn and the start of the next, which is a combination of overlaps and gaps. Negative values indicate overlapping speech, while positive values indicate gaps between turns.\n\n\\squishend\n\n\n\n\n \n%We compute the several conversational statistic of our collected Real-egocentric conversation: (1) Turn-change Frequency: the frequency of turn-change events happen per minutes (2) Turn Duration: the duration of each turn (3) Overlap Ratio: it measures the overlap among speakers in the conversations (4) Pausal Units (IPUs) Duration: it is defined as the continuous stretch of speech in one speaker’s channel, delimited by a VAD silence of more than 200 ms on both side. (5) Floor-Transfer Offset (FTO): FTO is the duration of between turn-transitions, which is a combination of overlaps and gaps – negative FTOs represent overlaps and positive FTOs represent gaps.\n\n\n\n\\end{document}\n\\endinput\n%%\n%% End of file `sample-sigconf-authordraft.tex'.\n"},"question":{"kind":"string","value":"Considering only English testsets, find the testset where switching from the Baseline Model to its Dual counterpart yields the largest reduction in non-spatialized CR. Relative to the baseline of the identified testset, which Libri variant has the greatest combined improvement in non-spatialized SISDRi and ΔPESQ, and what is the value?"},"answer":{"kind":"string","value":"Libri (2spk), 15.73"},"plan":{"kind":"string","value":"SELECT all table cell values except headers\nCOMPUTE distinct value, count of that value\nCOMPUTE value with minimum count\nSELECT framework where any value is that value\nRETURN framework, value\n"}}},{"rowIdx":370,"cells":{"paper":{"kind":"string","value":"2508.20729"},"relevant_tables":{"kind":"list like","value":[["\\begin{table}\n","\\begin{center}\n","\\def~{\\hphantom{0}}\n","\\begin{tabular}{c|c|c|c|c|c|c}\n","\\cline{1-7}\n","&Reasoning&Expansion&Debugging&Refinement&\\makecell{Review}&\\makecell{Single/Multiple\\\\ LLMs} \\\\ \\cline{1-7}\n","\\makecell{Non-reasoning\\\\ LLMs}&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&Single \\\\ \\cline{1-7}\n","\n","\\makecell{Reasoning\\\\ LLMs}&$\\usym{1F5F8}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&Single \\\\ \\cline{1-7}\n","\n","\\makecell{CodePDE\\\\ Agent}&$\\usym{1F5F8}$&$\\usym{2613}$&$\\usym{1F5F8}$&\\makecell{based on \\\\posterior error} &$\\usym{2613}$&Single \\\\ \\cline{1-7}\n","\n","\\multirow{2}{*}{\\makecell{PINNsAgent}}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{Single} \\\\ \n","&&&&&& \\\\ \\cline{1-7}\n","\n","\\multirow{2}{*}{\\makecell{Madaan's\\\\ Agent}}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{Single} \\\\ \n","&&&&&& \\\\ \\cline{1-7}\n","\n","\\multirow{2}{*}{\\makecell{Our Agent}}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{Multiple} \\\\ \n","&&&&&& \\\\ \\cline{1-7}\n","\\end{tabular}\n","\\caption{Comparison among existing LLM-based agent frameworks for scientific computing and the one we proposed.}\n","\\label{tab:agents_compare}\n","\\end{center}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{table}\\n\",\n \"\\\\begin{center}\\n\",\n \"\\\\def~{\\\\hphantom{0}}\\n\",\n \"\\\\begin{tabular}{c|c|c|c|c|c|c}\\n\",\n \"\\\\cline{1-7}\\n\",\n \"&Reasoning&Expansion&Debugging&Refinement&\\\\makecell{Review}&\\\\makecell{Single/Multiple\\\\\\\\ LLMs} \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\\\makecell{Non-reasoning\\\\\\\\ LLMs}&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&Single \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\makecell{Reasoning\\\\\\\\ LLMs}&$\\\\usym{1F5F8}$&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&Single \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\makecell{CodePDE\\\\\\\\ Agent}&$\\\\usym{1F5F8}$&$\\\\usym{2613}$&$\\\\usym{1F5F8}$&\\\\makecell{based on \\\\\\\\posterior error} &$\\\\usym{2613}$&Single \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\multirow{2}{*}{\\\\makecell{PINNsAgent}}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{Single} \\\\\\\\ \\n\",\n \"&&&&&& \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\multirow{2}{*}{\\\\makecell{Madaan's\\\\\\\\ Agent}}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{Single} \\\\\\\\ \\n\",\n \"&&&&&& \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\multirow{2}{*}{\\\\makecell{Our Agent}}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{Multiple} \\\\\\\\ \\n\",\n \"&&&&&& \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Comparison among existing LLM-based agent frameworks for scientific computing and the one we proposed.}\\n\",\n \"\\\\label{tab:agents_compare}\\n\",\n \"\\\\end{center}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"tables":{"kind":"list like","value":[["\\begin{table}\n","\\begin{center}\n","\\def~{\\hphantom{0}}\n","\\begin{tabular}{c|c|c|c|c|c|c}\n","\\cline{1-7}\n","&Reasoning&Expansion&Debugging&Refinement&\\makecell{Review}&\\makecell{Single/Multiple\\\\ LLMs} \\\\ \\cline{1-7}\n","\\makecell{Non-reasoning\\\\ LLMs}&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&Single \\\\ \\cline{1-7}\n","\n","\\makecell{Reasoning\\\\ LLMs}&$\\usym{1F5F8}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&Single \\\\ \\cline{1-7}\n","\n","\\makecell{CodePDE\\\\ Agent}&$\\usym{1F5F8}$&$\\usym{2613}$&$\\usym{1F5F8}$&\\makecell{based on \\\\posterior error} &$\\usym{2613}$&Single \\\\ \\cline{1-7}\n","\n","\\multirow{2}{*}{\\makecell{PINNsAgent}}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{Single} \\\\ \n","&&&&&& \\\\ \\cline{1-7}\n","\n","\\multirow{2}{*}{\\makecell{Madaan's\\\\ Agent}}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{Single} \\\\ \n","&&&&&& \\\\ \\cline{1-7}\n","\n","\\multirow{2}{*}{\\makecell{Our Agent}}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{Multiple} \\\\ \n","&&&&&& \\\\ \\cline{1-7}\n","\\end{tabular}\n","\\caption{Comparison among existing LLM-based agent frameworks for scientific computing and the one we proposed.}\n","\\label{tab:agents_compare}\n","\\end{center}\n","\\end{table}\n"],["\\begin{figure}\n","\\centering{\\includegraphics[width=\\textwidth]{Figs/schematic_Agent_Ver2.png}}\n","\\caption{Schematic of the agent framework.}\n","\\label{Fig_schematic_agent}\n","\\end{figure}\n"],["\\begin{table}\n","\\begin{center}\n","\\def~{\\hphantom{0}}\n","\\begin{tabular}{|c|c|c|}\n","\\cline{1-3}\n","\\multirow{2}{*}{PDE systems}&\\multirow{2}{*}{Challenges}&\\multirow{2}{*}{Reference solutions}\\\\\n","& & \\\\\n","\\cline{1-3}\n","\n","\\makecell{\\textbf{Burgers euqation}\\\\ $\\frac{\\partial u}{\\partial t}+u u_x-\\nu u_{xx}=0$} & \\makecell{\\textbf{Nonlinear,Unsteady \\checkmark}\\\\Accurately resolve\\\\ oscillations and capture\\\\ shock waves}&\n","\\begin{minipage}{0.25\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/burgers_reference_.pdf}\n"," \\end{minipage}\\\\\n","\\cline{1-3}\n","\n","\\makecell{\\textbf{Sod Shock Tube}\\\\ \n","$\\begin{cases}\n","\\frac{\\partial \\rho}{\\partial t} + \\frac{\\partial (\\rho u)}{\\partial x} = 0\\\\\n","\\frac{\\partial (\\rho u)}{\\partial t} + \\frac{\\partial (\\rho u^2 + p)}{\\partial x} = 0\\\\\n","\\frac{\\partial (\\rho E)}{\\partial t} + \\frac{\\partial (\\rho E u + p u)}{\\partial x} = 0\n","\\end{cases}$}&\\makecell{\\textbf{Unsteady \\checkmark} \\\\Precisely capture\\\\ time-dependent positions\\\\ and strengths of\\\\ multiple wave systems}&\n","\\begin{minipage}{0.23\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/SodShock_reference_2d.pdf}\n"," \\end{minipage}\\\\\n","\\cline{1-3}\n","\n","\\makecell{\\textbf{Poisson equation}\\\\ $\\Delta u = 0$}&\\makecell{\\textbf{Complex Geometry \\checkmark}\\\\ Precise discretization of \\\\curvilinear circular holes \\\\and rectangular edges}&\n","\\begin{minipage}{0.25\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/Poisson_reference_.pdf}\n"," \\end{minipage}\\\\\n","\\cline{1-3}\n"," \n","\\makecell{\\textbf{Helmholtz equation}\\\\ $-\\Delta u + k^2 u = f$}&\\makecell{\\textbf{Complex Geometry \\checkmark}\\\\ Proper discretization of\\\\ complex boundaries\\\\ and handling of\\\\ high-frequency oscillation} &\n","\\begin{minipage}{0.25\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/Helmholtz_reference_.pdf}\n"," \\end{minipage}\\\\\n","\\cline{1-3}\n"," \n","\\makecell{\\textbf{Lid-Driven Cavity}\\\\ $\\begin{cases}\n","\\nabla \\cdot \\textbf{u} = 0 \\\\\n","\\textbf{u} \\cdot \\nabla \\textbf{u} + \\nabla p = \\frac{1}{\\mathrm{Re}} \\Delta \\textbf{u} \\\\\n","\\end{cases}$}&\\makecell{\\textbf{Nonlinear \\checkmark}\\\\ Complex flow details and\\\\ velocity-pressure coupling} &\n","\\begin{minipage}{0.25\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/LidDriven_reference_.pdf}\n"," \\end{minipage}\\\\\n"," \\cline{1-3}\n"," \n","\\makecell{\\textbf{Unsteady NS equation}\\\\ $\\begin{cases}\n","\\nabla \\cdot \\textbf{u} = 0 \\\\\n","\\frac{\\partial \\mathbf{u}}{\\partial t} + \\mathbf{u} \\cdot \\nabla \\textbf{u} + \\nabla p - \\frac{1}{\\mathrm{Re}} \\Delta \\textbf{u} = \\mathbf{f}\\\\\n","\\end{cases}$}&\\makecell{\\textbf{Nonlinear,Unsteady \\checkmark}\\\\ Temporal evolution and\\\\ velocity-pressure coupling} &\n","\\begin{minipage}{0.25\\textwidth}\n"," \\centering\n"," \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/LongTimeNS_reference_.pdf}\n"," \\end{minipage}\\\\\n"," \\cline{1-3}\n","\n","\\end{tabular}\n","\\caption{Summary of various equations in PDEbench.}\n","\\label{tab:Pdebench}\n","\\end{center}\n","\\end{table}\n"],["\\begin{table}\n","\\begin{center}\n","\\renewcommand{\\arraystretch}{1.2}\n","\\setlength{\\tabcolsep}{2.5pt}\n","\\begin{tabular}{c|ccc|ccc|ccc}\n","\\cline{1-10}\n","\\multirow{2}{*}{Programmer} & \\multicolumn{3}{c|}{Gpt-4.1-mini} & \\multicolumn{3}{c|}{Gemini-2.5-flash} & \\multicolumn{3}{c}{Deepseek-R1} \\\\ \\cline{2-10}\n","& ans-0& rev-1& rev-2&ans-0& rev-1& rev-2&ans-0& rev-1& rev-2 \\\\ \\cline{1-10}\n","Burgers &5.8e-02&2.5e-02&\\underline{\\textbf{2.3e-02}}&4.1e-02&3.5e-02&\\underline{3.1e-02}&7.0e-02&4.1e-02&\\underline{3.0e-02} \\\\\n","Sod Shock &1.3e-01&\\underline{6.0e-02}&6.1e-02&6.4e-02&\\underline{6.4e-02}&7.0e-02&1.7e-01&\\underline{\\textbf{4.4e-02}}&4.6e-02 \\\\\n","Poisson &4.4e-02&2.6e-02&\\underline{1.9e-02}&3.5e-02&2.4e-02&\\underline{\\textbf{1.5e-02}}&4.1e-02&2.6e-02&\\underline{1.5e-02} \\\\\n","Helmholtz &4.9e-02&4.5e-02&\\underline{3.7e-02}&3.4e-02&3.2e-02&\\underline{\\textbf{2.6e-02}}&4.5e-02&3.5e-02&\\underline{2.8e-02} \\\\\n","Lid-Driven &4.2e-01&1.4e-01&\\underline{\\textbf{5.7e-02}}&2.7e-01&2.3e-01&\\underline{9.9e-02}&3.0e-01&2.6e-01&\\underline{1.8e-01} \\\\\n","Unsteady NS &2.9e-01&2.3e-01&\\underline{1.9e-01}&2.1e-02&2.1e-02&\\underline{2.1e-02}&2.4e-01&9.0e-02&\\underline{\\textbf{2.0e-02}} \\\\ \\cline{1-10}\n","\\end{tabular}\n","\\caption{The summary of average $L^2$ relative error across all cases in PDEbench, where underlined entries denote each Programmer’s minimum errors at different response stages, and bold entries indicate the overall minimum errors among all Programmers.}\n","\\label{tab:pdebench_overall_average_rel_error}\n","\\end{center}\n","\\end{table}\n"],["\\begin{figure}[htbp]\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/All_average_Execution_Success_Rate.pdf}}\n","\\end{subfigure}\n"," \\caption{The overall average execution success rate of numerical algorithms employed by Programmers across all equations in the PDEbench.}\n","\\label{fig:All_average_exe_rate}\n","\\end{figure}\n"],["\\begin{figure}[htbp]\n"," \\centering\n","\\begin{subfigure}[b]{0.9\\textwidth}\n","\\centering\n","{\\includegraphics[width = \\textwidth]{Figs/PDE_all_Average/All_average_Box_Legend.pdf}}\n","\\end{subfigure} \n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/All_average_Error_Box.pdf}}\n","\\end{subfigure}\n"," \\caption{Boxplot of the average $L^2$ relative errors for all equations in the PDEbench. The \\textbf{annotated numbers} in the figure denote the average of relative errors.}\n","\\label{fig:All_average_error_box}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n","\\begin{subfigure}[b]{0.95\\textwidth}\n"," \\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Best_unsteadyNS_contours.pdf}}\n","\\end{subfigure}\n","\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n","\\label{fig:Unsteady_NS_Best_3LLMs}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n","\\begin{subfigure}[b]{0.95\\textwidth}\n"," \\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/R1_unsteadyNS_contours.pdf}}\n","\\end{subfigure}\n","\\caption{The runtime outputs of the executable code provided by Programmer Deepseek-R1 in the initial response (answer-0), together with those in the Reviewer's first (review-1) and second (review-2) interventions, respectively.}\n","\\label{fig:Unsteady_NS_R1_improvement}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.65\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/cond_traditionMethods.pdf}}\n","\\end{subfigure}\n"," \\caption{Schematic diagram of (a) variation of the 2-norm condition number with matrix dimension; (b) $L^\\infty$ error obtained by direct solution using the naive methods.}\n","\\label{fig:hil_naive_cond}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.8\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hilbert_Complete_Rate_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hilbert_Complete_Rate.pdf}}\n","\\end{subfigure}\n"," \\caption{Proportional distribution of executable code provided by Programmers across three different completion statuses.}\n","\\label{fig:hil_complete_rate}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.65\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/legend_HilbMat_methodsDist_3status.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/HilbMat_methodsDist_3status.pdf}}\n","\\end{subfigure}\n"," \\caption{Proportional distribution of completion status for various methods at different response stages. A single dark-colored patch represents SVD method results consistently below the threshold. The color patches corresponding to other methods are divided into three segments, with colors darkening gradually to indicate the following respectively: results contain NaN, exceed $L^{\\infty}$ threshold and below $L^{\\infty}$ threshold.}\n","\\label{fig:hil_methodDist_3status}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","\\includegraphics[width=\\textwidth]{Figs/dimensional_analysis/dimension_Success_Rate_legend.pdf}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","\\includegraphics[width=\\textwidth]{Figs/dimensional_analysis/Dimensional_Success_Rate.pdf}\n","\\end{subfigure}\n","\\caption{The success rate of Programmers' search algorithms in identifying dominant dimensionless quantities Ke.}\n","\\label{fig:dimension_success_rate}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.9\\textwidth}\n","\\centering\n","\\includegraphics[width=\\textwidth]{Figs/dimensional_analysis/scaling_keyhole.pdf}\n","\\end{subfigure}\n","\\caption{Fitting curve of the dimensionless number $\\Pi$ as a function of e* derived by all programmers in final response (review-2).}\n","\\label{fig:keyhole_scale}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Burgers/Burgers_Execution_Success_Rate.pdf}}\n","\\end{subfigure}\n"," \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Burgers equation.}\n","\\label{fig:Burgers_exe_rate}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Burgers/Burgers_Error_Box.pdf}}\n","\\end{subfigure}\n"," \\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n","\\label{fig:Burgers_error_box}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n","\\begin{subfigure}[b]{0.95\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Burgers_contours.pdf}}\n","\\end{subfigure}\n"," \\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n"," \\label{fig:Burgers_best_3LLMsl}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering{\\includegraphics[width=0.35\\textwidth]{Figs/Sod_sb_schem.pdf}}\n","\\caption{Schematic of the Sod shock tube with initial conditions at $t=0$}\n","\\label{Fig_schematic_sod_sb}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/SodShock_Execution_Success_Rate.pdf}}\n","\\end{subfigure}\n"," \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Sod shock tube problem.}\n","\\label{fig:Sod_exe_rate}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/Sod_Space_method_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/Sod_Space_method_protion.pdf}}\n","\\end{subfigure}\n"," \\caption{Proportional distribution of the spatial reconstruction schemes employed by Programmers. All Programmers selected the Harten–Lax–vanLeer–Contact (HLLC) Riemann solver during the sampling process.}\n","\\label{fig:Sod_space_method}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/Sod_Time_method_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/Sod_Time_method_protion.pdf}}\n","\\end{subfigure}\n"," \\caption{Proportional distribution of the time integration methods employed by Programmers.}\n","\\label{fig:Sod_time_method}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_u.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_p.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_Rho.pdf}}\n","\\end{subfigure}\n"," \\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers. (a) velocity $u$, (b) pressure $p$, (c) density $\\rho$.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n","\\label{fig:Sod_error_box}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_u.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_rho.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_p.pdf}}\n","\\end{subfigure}\n"," \\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n","\\label{fig:Sod_3LMMs_best_plots}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Poisson_/Poisson_Execution_Success_Rate.pdf}}\n","\\end{subfigure}\n"," \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Poisson equation.}\n","\\label{fig:Poisson_exe_rate}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Poisson_/Poisson_Error_Box.pdf}}\n","\\end{subfigure}\n"," \\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n","\\label{fig:Poisson_error_box}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.95\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Poisson_contours.pdf}}\n","\\end{subfigure}\n","\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n","\\label{fig:Poisson_best_3LLMsl}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Helmholtz/Helmholtz_Execution_Success_Rate.pdf}}\n","\\end{subfigure}\n"," \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Helmholtz equation.}\n","\\label{fig:Helmholtz_exe_rate}\n","\\end{figure}\n"],["\\begin{figure}\n"," \\centering\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Helmholtz/Helmholtz_Error_Box.pdf}}\n","\\end{subfigure}\n"," \\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n","\\label{fig:Helmholtz_error_box}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.95\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Helmholtz_contours.pdf}}\n","\\end{subfigure}\n","\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n","\\label{fig:Helmholtz_best_3LLMsl}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Lid_cavity/Cavity_NS_Execution_Success_Rate.pdf}}\n","\\end{subfigure}\n"," \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Lid-driven flow.}\n","\\label{fig:Lid-cavity-ExeSucess}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Lid_cavity/Cavity_NS_Error_Box.pdf}}\n","\\end{subfigure}\n","\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n","\\label{fig:Lid-cavity-boxError}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.95\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Lid_driven_contours.pdf}}\n","\\end{subfigure}\n","\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n","\\label{fig:Lid_driven_best_3LLMsl}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.6\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Execution_Success_Rate.pdf}}\n","\\end{subfigure}\n","\\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the unsteady NS equation.}\n","\\label{fig:LT_NS_sucessRate}\n","\\end{figure}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Error_Box.pdf}}\n","\\end{subfigure}\n","\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n","\\label{fig:LT_NS_boxError}\n","\\end{figure}\n"],["\\begin{table}[h]\n","\\begin{center}\n","\\renewcommand{\\arraystretch}{1.2}\n","\\begin{tabular}{c|ccc|c}\n","\\cline{1-5}\n","Programmer & Gpt-4.1-mini & Gemini-2.5-flash & Deepseek-R1 & Quantity\\\\ \\cline{1-5}\n","Burgers & $1.98\\times10^{-2}$ & $\\mathbf{1.82\\times10^{-2}}$ & $1.85\\times10^{-2}$ & $u(x,t)$\\\\\n","Sod Shock & $3.60\\times10^{-2}$ & $5.81\\times10^{-2}$ & $\\mathbf{2.31\\times10^{-2}}$ & $u(x,t)$\\\\\n","Poisson & $9.90\\times10^{-3}$ & $1.18\\times10^{-2}$ & $\\mathbf{7.15\\times10^{-3}}$ & $u(x,y)$\\\\\n","Helmholtz & $2.30\\times10^{-2}$ & $2.09\\times10^{-2}$ & $\\mathbf{1.47\\times10^{-2}}$ & $u(x,y)$\\\\\n","Lid-Driven & $\\mathbf{2.74\\times10^{-3}}$ & $6.55\\times10^{-3}$ & $8.77\\times10^{-3}$ & $\\|\\vec{u}\\|$\\\\\n","Unsteady NS & $1.89\\times10^{-2}$ & $1.83\\times10^{-2}$ & $\\mathbf{1.81\\times10^{-2}}$ & $u(x,y)$ \\\\ \\cline{1-5}\n","\\end{tabular}\n","\\caption{The summary of $L^2$ relative error for the final refined runtime outputs after two rounds of Reviewer intervention (review-2) across all cases in PDEbench.}\n","\\label{tab:pdebench_overall_best_rel_error}\n","\\end{center}\n","\\end{table}\n"],["\\begin{figure}\n","\\centering\n","\\begin{subfigure}[b]{0.8\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hilbert_diffStage_legend.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-NaN_protion.pdf.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-overThrehold_protion.pdf}}\n","\\end{subfigure}\n","\\begin{subfigure}[b]{0.85\\textwidth}\n","\\centering\n","{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-belowThrehold_protion.pdf}}\n","\\end{subfigure}\n","\\caption{Proportional distribution of specific numerical methods employed by Programmers across three completion statuses, serving as a detailed elaboration to the solution success rate. (a) Results Contain NaN; (b) Over $L^\\infty$ threshold; (c) Below $L^\\infty$ threshold.}\n","\\label{fig:Hil_diff_stage_proportion}\n","\\end{figure}\n"],["\\begin{table}\n","\\begin{center}\n","\\renewcommand{\\arraystretch}{1.2}\n","\\begin{tabular}{c|c|ccccc}\n","\\cline{1-7}\n","\\multirow{2}{*}{Programmer} & \\multirow{2}{*}{Methods} & \\multicolumn{5}{c}{$L^\\infty$ error w.r.t. matrix size $n$} \\\\ \\cline{3-7}\n","& & 5&10&15&20&25\\\\ \\cline{1-7}\n","\\multirow{5}{*}{\\makecell{Gpt-4.1-mini}} & Chol-Reg & 3.08e-04&6.81e-04&9.66e-04&1.36e-03&1.36e-03\\\\\n","& LU-Reg & 3.15e-04&8.77e-04&8.92e-04&1.38e-03&1.37e-03\\\\\n","& QR-Reg & 3.20e-04&9.90e-04&1.18e-03&1.31e-03&1.62e-03\\\\\n","& Pre-CG & \\textbf{9.80e-12}&8.79e-05&7.16e-05&\\textbf{4.32e-05}&\\textbf{9.96e-05}\\\\\n","& SVD & 1.46e-11&7.32e-04&3.91e-03&7.81e-03&7.32e-04\\\\ \\cline{1-7}\n","\\multirow{4}{*}{\\makecell{Gemini-2.5-flash}} & Chol-Reg & 8.64e-04&1.12e-03&1.45e-03&1.61e-03&1.73e-03 \\\\\n","& CG & 4.49e-04&9.34e-04&4.85e-04&6.60e-04&4.23e-04\\\\\n","& Pre-CG & 8.44e-04&5.57e-04&5.19e-04&7.50e-04&7.41e-04\\\\\n","& SVD & 7.13e-04&4.76e-04&5.36e-04&5.02e-04&6.30e-04 \\\\ \\cline{1-7}\n","\\multirow{5}{*}{\\makecell{Deepseek-R1}} &Chol-Reg & 1.11e-09&\\textbf{3.84e-05}&\\textbf{5.05e-05}&1.45e-04&2.68e-04\\\\\n","& LU-Reg & 1.11e-09&8.61e-05&1.81e-04&1.51e-04&2.01e-04\\\\\n","& QR-Reg & 3.80e-03&6.07e-04&1.01e-03&1.10e-03&1.31e-03\\\\\n","& CG & 5.42e-11&5.99e-04&3.93e-04&2.09e-04&4.30e-04\\\\\n","& Pre-CG & \\textbf{9.80e-12}&6.01e-04&3.95e-04&2.08e-04&4.32e-04\\\\ \\cline{1-7}\n","\\end{tabular}\n","\\caption{The summary of $L^\\infty$ errors in solving linear systems with Hilbert matrices via various methods provided by each Programmer in the final response (review-2).}\n","\\label{tab:hil_Linf_error}\n","\\end{center}\n","\\end{table}\n"]],"string":"[\n [\n \"\\\\begin{table}\\n\",\n \"\\\\begin{center}\\n\",\n \"\\\\def~{\\\\hphantom{0}}\\n\",\n \"\\\\begin{tabular}{c|c|c|c|c|c|c}\\n\",\n \"\\\\cline{1-7}\\n\",\n \"&Reasoning&Expansion&Debugging&Refinement&\\\\makecell{Review}&\\\\makecell{Single/Multiple\\\\\\\\ LLMs} \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\\\makecell{Non-reasoning\\\\\\\\ LLMs}&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&Single \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\makecell{Reasoning\\\\\\\\ LLMs}&$\\\\usym{1F5F8}$&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&$\\\\usym{2613}$&Single \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\makecell{CodePDE\\\\\\\\ Agent}&$\\\\usym{1F5F8}$&$\\\\usym{2613}$&$\\\\usym{1F5F8}$&\\\\makecell{based on \\\\\\\\posterior error} &$\\\\usym{2613}$&Single \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\multirow{2}{*}{\\\\makecell{PINNsAgent}}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{Single} \\\\\\\\ \\n\",\n \"&&&&&& \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\multirow{2}{*}{\\\\makecell{Madaan's\\\\\\\\ Agent}}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{2613}$}&\\\\multirow{2}{*}{Single} \\\\\\\\ \\n\",\n \"&&&&&& \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\n\",\n \"\\\\multirow{2}{*}{\\\\makecell{Our Agent}}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{$\\\\usym{1F5F8}$}&\\\\multirow{2}{*}{Multiple} \\\\\\\\ \\n\",\n \"&&&&&& \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Comparison among existing LLM-based agent frameworks for scientific computing and the one we proposed.}\\n\",\n \"\\\\label{tab:agents_compare}\\n\",\n \"\\\\end{center}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering{\\\\includegraphics[width=\\\\textwidth]{Figs/schematic_Agent_Ver2.png}}\\n\",\n \"\\\\caption{Schematic of the agent framework.}\\n\",\n \"\\\\label{Fig_schematic_agent}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}\\n\",\n \"\\\\begin{center}\\n\",\n \"\\\\def~{\\\\hphantom{0}}\\n\",\n \"\\\\begin{tabular}{|c|c|c|}\\n\",\n \"\\\\cline{1-3}\\n\",\n \"\\\\multirow{2}{*}{PDE systems}&\\\\multirow{2}{*}{Challenges}&\\\\multirow{2}{*}{Reference solutions}\\\\\\\\\\n\",\n \"& & \\\\\\\\\\n\",\n \"\\\\cline{1-3}\\n\",\n \"\\n\",\n \"\\\\makecell{\\\\textbf{Burgers euqation}\\\\\\\\ $\\\\frac{\\\\partial u}{\\\\partial t}+u u_x-\\\\nu u_{xx}=0$} & \\\\makecell{\\\\textbf{Nonlinear,Unsteady \\\\checkmark}\\\\\\\\Accurately resolve\\\\\\\\ oscillations and capture\\\\\\\\ shock waves}&\\n\",\n \"\\\\begin{minipage}{0.25\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figs/Reference_table_summary/burgers_reference_.pdf}\\n\",\n \" \\\\end{minipage}\\\\\\\\\\n\",\n \"\\\\cline{1-3}\\n\",\n \"\\n\",\n \"\\\\makecell{\\\\textbf{Sod Shock Tube}\\\\\\\\ \\n\",\n \"$\\\\begin{cases}\\n\",\n \"\\\\frac{\\\\partial \\\\rho}{\\\\partial t} + \\\\frac{\\\\partial (\\\\rho u)}{\\\\partial x} = 0\\\\\\\\\\n\",\n \"\\\\frac{\\\\partial (\\\\rho u)}{\\\\partial t} + \\\\frac{\\\\partial (\\\\rho u^2 + p)}{\\\\partial x} = 0\\\\\\\\\\n\",\n \"\\\\frac{\\\\partial (\\\\rho E)}{\\\\partial t} + \\\\frac{\\\\partial (\\\\rho E u + p u)}{\\\\partial x} = 0\\n\",\n \"\\\\end{cases}$}&\\\\makecell{\\\\textbf{Unsteady \\\\checkmark} \\\\\\\\Precisely capture\\\\\\\\ time-dependent positions\\\\\\\\ and strengths of\\\\\\\\ multiple wave systems}&\\n\",\n \"\\\\begin{minipage}{0.23\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figs/Reference_table_summary/SodShock_reference_2d.pdf}\\n\",\n \" \\\\end{minipage}\\\\\\\\\\n\",\n \"\\\\cline{1-3}\\n\",\n \"\\n\",\n \"\\\\makecell{\\\\textbf{Poisson equation}\\\\\\\\ $\\\\Delta u = 0$}&\\\\makecell{\\\\textbf{Complex Geometry \\\\checkmark}\\\\\\\\ Precise discretization of \\\\\\\\curvilinear circular holes \\\\\\\\and rectangular edges}&\\n\",\n \"\\\\begin{minipage}{0.25\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figs/Reference_table_summary/Poisson_reference_.pdf}\\n\",\n \" \\\\end{minipage}\\\\\\\\\\n\",\n \"\\\\cline{1-3}\\n\",\n \" \\n\",\n \"\\\\makecell{\\\\textbf{Helmholtz equation}\\\\\\\\ $-\\\\Delta u + k^2 u = f$}&\\\\makecell{\\\\textbf{Complex Geometry \\\\checkmark}\\\\\\\\ Proper discretization of\\\\\\\\ complex boundaries\\\\\\\\ and handling of\\\\\\\\ high-frequency oscillation} &\\n\",\n \"\\\\begin{minipage}{0.25\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figs/Reference_table_summary/Helmholtz_reference_.pdf}\\n\",\n \" \\\\end{minipage}\\\\\\\\\\n\",\n \"\\\\cline{1-3}\\n\",\n \" \\n\",\n \"\\\\makecell{\\\\textbf{Lid-Driven Cavity}\\\\\\\\ $\\\\begin{cases}\\n\",\n \"\\\\nabla \\\\cdot \\\\textbf{u} = 0 \\\\\\\\\\n\",\n \"\\\\textbf{u} \\\\cdot \\\\nabla \\\\textbf{u} + \\\\nabla p = \\\\frac{1}{\\\\mathrm{Re}} \\\\Delta \\\\textbf{u} \\\\\\\\\\n\",\n \"\\\\end{cases}$}&\\\\makecell{\\\\textbf{Nonlinear \\\\checkmark}\\\\\\\\ Complex flow details and\\\\\\\\ velocity-pressure coupling} &\\n\",\n \"\\\\begin{minipage}{0.25\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figs/Reference_table_summary/LidDriven_reference_.pdf}\\n\",\n \" \\\\end{minipage}\\\\\\\\\\n\",\n \" \\\\cline{1-3}\\n\",\n \" \\n\",\n \"\\\\makecell{\\\\textbf{Unsteady NS equation}\\\\\\\\ $\\\\begin{cases}\\n\",\n \"\\\\nabla \\\\cdot \\\\textbf{u} = 0 \\\\\\\\\\n\",\n \"\\\\frac{\\\\partial \\\\mathbf{u}}{\\\\partial t} + \\\\mathbf{u} \\\\cdot \\\\nabla \\\\textbf{u} + \\\\nabla p - \\\\frac{1}{\\\\mathrm{Re}} \\\\Delta \\\\textbf{u} = \\\\mathbf{f}\\\\\\\\\\n\",\n \"\\\\end{cases}$}&\\\\makecell{\\\\textbf{Nonlinear,Unsteady \\\\checkmark}\\\\\\\\ Temporal evolution and\\\\\\\\ velocity-pressure coupling} &\\n\",\n \"\\\\begin{minipage}{0.25\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \" \\\\includegraphics[width=\\\\linewidth]{Figs/Reference_table_summary/LongTimeNS_reference_.pdf}\\n\",\n \" \\\\end{minipage}\\\\\\\\\\n\",\n \" \\\\cline{1-3}\\n\",\n \"\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{Summary of various equations in PDEbench.}\\n\",\n \"\\\\label{tab:Pdebench}\\n\",\n \"\\\\end{center}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{table}\\n\",\n \"\\\\begin{center}\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.2}\\n\",\n \"\\\\setlength{\\\\tabcolsep}{2.5pt}\\n\",\n \"\\\\begin{tabular}{c|ccc|ccc|ccc}\\n\",\n \"\\\\cline{1-10}\\n\",\n \"\\\\multirow{2}{*}{Programmer} & \\\\multicolumn{3}{c|}{Gpt-4.1-mini} & \\\\multicolumn{3}{c|}{Gemini-2.5-flash} & \\\\multicolumn{3}{c}{Deepseek-R1} \\\\\\\\ \\\\cline{2-10}\\n\",\n \"& ans-0& rev-1& rev-2&ans-0& rev-1& rev-2&ans-0& rev-1& rev-2 \\\\\\\\ \\\\cline{1-10}\\n\",\n \"Burgers &5.8e-02&2.5e-02&\\\\underline{\\\\textbf{2.3e-02}}&4.1e-02&3.5e-02&\\\\underline{3.1e-02}&7.0e-02&4.1e-02&\\\\underline{3.0e-02} \\\\\\\\\\n\",\n \"Sod Shock &1.3e-01&\\\\underline{6.0e-02}&6.1e-02&6.4e-02&\\\\underline{6.4e-02}&7.0e-02&1.7e-01&\\\\underline{\\\\textbf{4.4e-02}}&4.6e-02 \\\\\\\\\\n\",\n \"Poisson &4.4e-02&2.6e-02&\\\\underline{1.9e-02}&3.5e-02&2.4e-02&\\\\underline{\\\\textbf{1.5e-02}}&4.1e-02&2.6e-02&\\\\underline{1.5e-02} \\\\\\\\\\n\",\n \"Helmholtz &4.9e-02&4.5e-02&\\\\underline{3.7e-02}&3.4e-02&3.2e-02&\\\\underline{\\\\textbf{2.6e-02}}&4.5e-02&3.5e-02&\\\\underline{2.8e-02} \\\\\\\\\\n\",\n \"Lid-Driven &4.2e-01&1.4e-01&\\\\underline{\\\\textbf{5.7e-02}}&2.7e-01&2.3e-01&\\\\underline{9.9e-02}&3.0e-01&2.6e-01&\\\\underline{1.8e-01} \\\\\\\\\\n\",\n \"Unsteady NS &2.9e-01&2.3e-01&\\\\underline{1.9e-01}&2.1e-02&2.1e-02&\\\\underline{2.1e-02}&2.4e-01&9.0e-02&\\\\underline{\\\\textbf{2.0e-02}} \\\\\\\\ \\\\cline{1-10}\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{The summary of average $L^2$ relative error across all cases in PDEbench, where underlined entries denote each Programmer’s minimum errors at different response stages, and bold entries indicate the overall minimum errors among all Programmers.}\\n\",\n \"\\\\label{tab:pdebench_overall_average_rel_error}\\n\",\n \"\\\\end{center}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/All_average_Execution_Success_Rate.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{The overall average execution success rate of numerical algorithms employed by Programmers across all equations in the PDEbench.}\\n\",\n \"\\\\label{fig:All_average_exe_rate}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}[htbp]\\n\",\n \" \\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.9\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width = \\\\textwidth]{Figs/PDE_all_Average/All_average_Box_Legend.pdf}}\\n\",\n \"\\\\end{subfigure} \\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/All_average_Error_Box.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Boxplot of the average $L^2$ relative errors for all equations in the PDEbench. The \\\\textbf{annotated numbers} in the figure denote the average of relative errors.}\\n\",\n \"\\\\label{fig:All_average_error_box}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.95\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/3LLMs_Best_unsteadyNS_contours.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\\n\",\n \"\\\\label{fig:Unsteady_NS_Best_3LLMs}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.95\\\\textwidth}\\n\",\n \" \\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/R1_unsteadyNS_contours.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{The runtime outputs of the executable code provided by Programmer Deepseek-R1 in the initial response (answer-0), together with those in the Reviewer's first (review-1) and second (review-2) interventions, respectively.}\\n\",\n \"\\\\label{fig:Unsteady_NS_R1_improvement}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.65\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/cond_traditionMethods.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Schematic diagram of (a) variation of the 2-norm condition number with matrix dimension; (b) $L^\\\\infty$ error obtained by direct solution using the naive methods.}\\n\",\n \"\\\\label{fig:hil_naive_cond}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.8\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/Hilbert_Complete_Rate_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/Hilbert_Complete_Rate.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Proportional distribution of executable code provided by Programmers across three different completion statuses.}\\n\",\n \"\\\\label{fig:hil_complete_rate}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.65\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/legend_HilbMat_methodsDist_3status.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/HilbMat_methodsDist_3status.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Proportional distribution of completion status for various methods at different response stages. A single dark-colored patch represents SVD method results consistently below the threshold. The color patches corresponding to other methods are divided into three segments, with colors darkening gradually to indicate the following respectively: results contain NaN, exceed $L^{\\\\infty}$ threshold and below $L^{\\\\infty}$ threshold.}\\n\",\n \"\\\\label{fig:hil_methodDist_3status}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{Figs/dimensional_analysis/dimension_Success_Rate_legend.pdf}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{Figs/dimensional_analysis/Dimensional_Success_Rate.pdf}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{The success rate of Programmers' search algorithms in identifying dominant dimensionless quantities Ke.}\\n\",\n \"\\\\label{fig:dimension_success_rate}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.9\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"\\\\includegraphics[width=\\\\textwidth]{Figs/dimensional_analysis/scaling_keyhole.pdf}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{Fitting curve of the dimensionless number $\\\\Pi$ as a function of e* derived by all programmers in final response (review-2).}\\n\",\n \"\\\\label{fig:keyhole_scale}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Burgers/Burgers_Execution_Success_Rate.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Burgers equation.}\\n\",\n \"\\\\label{fig:Burgers_exe_rate}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Burgers/Burgers_Error_Box.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\\\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\\n\",\n \"\\\\label{fig:Burgers_error_box}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.95\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/3LLMs_Burgers_contours.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\\n\",\n \" \\\\label{fig:Burgers_best_3LLMsl}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering{\\\\includegraphics[width=0.35\\\\textwidth]{Figs/Sod_sb_schem.pdf}}\\n\",\n \"\\\\caption{Schematic of the Sod shock tube with initial conditions at $t=0$}\\n\",\n \"\\\\label{Fig_schematic_sod_sb}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Sod_shock/SodShock_Execution_Success_Rate.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Sod shock tube problem.}\\n\",\n \"\\\\label{fig:Sod_exe_rate}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Sod_shock/Sod_Space_method_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Sod_shock/Sod_Space_method_protion.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Proportional distribution of the spatial reconstruction schemes employed by Programmers. All Programmers selected the Harten–Lax–vanLeer–Contact (HLLC) Riemann solver during the sampling process.}\\n\",\n \"\\\\label{fig:Sod_space_method}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Sod_shock/Sod_Time_method_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Sod_shock/Sod_Time_method_protion.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Proportional distribution of the time integration methods employed by Programmers.}\\n\",\n \"\\\\label{fig:Sod_time_method}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_u.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_p.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_Rho.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers. (a) velocity $u$, (b) pressure $p$, (c) density $\\\\rho$.The \\\\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\\n\",\n \"\\\\label{fig:Sod_error_box}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_u.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_rho.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_p.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\\n\",\n \"\\\\label{fig:Sod_3LMMs_best_plots}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Poisson_/Poisson_Execution_Success_Rate.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Poisson equation.}\\n\",\n \"\\\\label{fig:Poisson_exe_rate}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Poisson_/Poisson_Error_Box.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\\\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\\n\",\n \"\\\\label{fig:Poisson_error_box}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.95\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/3LLMs_Poisson_contours.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\\n\",\n \"\\\\label{fig:Poisson_best_3LLMsl}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Helmholtz/Helmholtz_Execution_Success_Rate.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Helmholtz equation.}\\n\",\n \"\\\\label{fig:Helmholtz_exe_rate}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \" \\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Helmholtz/Helmholtz_Error_Box.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\\\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\\n\",\n \"\\\\label{fig:Helmholtz_error_box}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.95\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/3LLMs_Helmholtz_contours.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\\n\",\n \"\\\\label{fig:Helmholtz_best_3LLMsl}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Lid_cavity/Cavity_NS_Execution_Success_Rate.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \" \\\\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Lid-driven flow.}\\n\",\n \"\\\\label{fig:Lid-cavity-ExeSucess}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Lid_cavity/Cavity_NS_Error_Box.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\\\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\\n\",\n \"\\\\label{fig:Lid-cavity-boxError}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.95\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/PDE_all_Average/3LLMs_Lid_driven_contours.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\\n\",\n \"\\\\label{fig:Lid_driven_best_3LLMsl}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.6\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Execution_Success_Rate.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the unsteady NS equation.}\\n\",\n \"\\\\label{fig:LT_NS_sucessRate}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/LT_NS/LT_NS_Error_Box.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\\\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\\n\",\n \"\\\\label{fig:LT_NS_boxError}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}[h]\\n\",\n \"\\\\begin{center}\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.2}\\n\",\n \"\\\\begin{tabular}{c|ccc|c}\\n\",\n \"\\\\cline{1-5}\\n\",\n \"Programmer & Gpt-4.1-mini & Gemini-2.5-flash & Deepseek-R1 & Quantity\\\\\\\\ \\\\cline{1-5}\\n\",\n \"Burgers & $1.98\\\\times10^{-2}$ & $\\\\mathbf{1.82\\\\times10^{-2}}$ & $1.85\\\\times10^{-2}$ & $u(x,t)$\\\\\\\\\\n\",\n \"Sod Shock & $3.60\\\\times10^{-2}$ & $5.81\\\\times10^{-2}$ & $\\\\mathbf{2.31\\\\times10^{-2}}$ & $u(x,t)$\\\\\\\\\\n\",\n \"Poisson & $9.90\\\\times10^{-3}$ & $1.18\\\\times10^{-2}$ & $\\\\mathbf{7.15\\\\times10^{-3}}$ & $u(x,y)$\\\\\\\\\\n\",\n \"Helmholtz & $2.30\\\\times10^{-2}$ & $2.09\\\\times10^{-2}$ & $\\\\mathbf{1.47\\\\times10^{-2}}$ & $u(x,y)$\\\\\\\\\\n\",\n \"Lid-Driven & $\\\\mathbf{2.74\\\\times10^{-3}}$ & $6.55\\\\times10^{-3}$ & $8.77\\\\times10^{-3}$ & $\\\\|\\\\vec{u}\\\\|$\\\\\\\\\\n\",\n \"Unsteady NS & $1.89\\\\times10^{-2}$ & $1.83\\\\times10^{-2}$ & $\\\\mathbf{1.81\\\\times10^{-2}}$ & $u(x,y)$ \\\\\\\\ \\\\cline{1-5}\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{The summary of $L^2$ relative error for the final refined runtime outputs after two rounds of Reviewer intervention (review-2) across all cases in PDEbench.}\\n\",\n \"\\\\label{tab:pdebench_overall_best_rel_error}\\n\",\n \"\\\\end{center}\\n\",\n \"\\\\end{table}\\n\"\n ],\n [\n \"\\\\begin{figure}\\n\",\n \"\\\\centering\\n\",\n \"\\\\begin{subfigure}[b]{0.8\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/Hilbert_diffStage_legend.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-NaN_protion.pdf.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-overThrehold_protion.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\begin{subfigure}[b]{0.85\\\\textwidth}\\n\",\n \"\\\\centering\\n\",\n \"{\\\\includegraphics[width=\\\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-belowThrehold_protion.pdf}}\\n\",\n \"\\\\end{subfigure}\\n\",\n \"\\\\caption{Proportional distribution of specific numerical methods employed by Programmers across three completion statuses, serving as a detailed elaboration to the solution success rate. (a) Results Contain NaN; (b) Over $L^\\\\infty$ threshold; (c) Below $L^\\\\infty$ threshold.}\\n\",\n \"\\\\label{fig:Hil_diff_stage_proportion}\\n\",\n \"\\\\end{figure}\\n\"\n ],\n [\n \"\\\\begin{table}\\n\",\n \"\\\\begin{center}\\n\",\n \"\\\\renewcommand{\\\\arraystretch}{1.2}\\n\",\n \"\\\\begin{tabular}{c|c|ccccc}\\n\",\n \"\\\\cline{1-7}\\n\",\n \"\\\\multirow{2}{*}{Programmer} & \\\\multirow{2}{*}{Methods} & \\\\multicolumn{5}{c}{$L^\\\\infty$ error w.r.t. matrix size $n$} \\\\\\\\ \\\\cline{3-7}\\n\",\n \"& & 5&10&15&20&25\\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\\\multirow{5}{*}{\\\\makecell{Gpt-4.1-mini}} & Chol-Reg & 3.08e-04&6.81e-04&9.66e-04&1.36e-03&1.36e-03\\\\\\\\\\n\",\n \"& LU-Reg & 3.15e-04&8.77e-04&8.92e-04&1.38e-03&1.37e-03\\\\\\\\\\n\",\n \"& QR-Reg & 3.20e-04&9.90e-04&1.18e-03&1.31e-03&1.62e-03\\\\\\\\\\n\",\n \"& Pre-CG & \\\\textbf{9.80e-12}&8.79e-05&7.16e-05&\\\\textbf{4.32e-05}&\\\\textbf{9.96e-05}\\\\\\\\\\n\",\n \"& SVD & 1.46e-11&7.32e-04&3.91e-03&7.81e-03&7.32e-04\\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\\\multirow{4}{*}{\\\\makecell{Gemini-2.5-flash}} & Chol-Reg & 8.64e-04&1.12e-03&1.45e-03&1.61e-03&1.73e-03 \\\\\\\\\\n\",\n \"& CG & 4.49e-04&9.34e-04&4.85e-04&6.60e-04&4.23e-04\\\\\\\\\\n\",\n \"& Pre-CG & 8.44e-04&5.57e-04&5.19e-04&7.50e-04&7.41e-04\\\\\\\\\\n\",\n \"& SVD & 7.13e-04&4.76e-04&5.36e-04&5.02e-04&6.30e-04 \\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\\\multirow{5}{*}{\\\\makecell{Deepseek-R1}} &Chol-Reg & 1.11e-09&\\\\textbf{3.84e-05}&\\\\textbf{5.05e-05}&1.45e-04&2.68e-04\\\\\\\\\\n\",\n \"& LU-Reg & 1.11e-09&8.61e-05&1.81e-04&1.51e-04&2.01e-04\\\\\\\\\\n\",\n \"& QR-Reg & 3.80e-03&6.07e-04&1.01e-03&1.10e-03&1.31e-03\\\\\\\\\\n\",\n \"& CG & 5.42e-11&5.99e-04&3.93e-04&2.09e-04&4.30e-04\\\\\\\\\\n\",\n \"& Pre-CG & \\\\textbf{9.80e-12}&6.01e-04&3.95e-04&2.08e-04&4.32e-04\\\\\\\\ \\\\cline{1-7}\\n\",\n \"\\\\end{tabular}\\n\",\n \"\\\\caption{The summary of $L^\\\\infty$ errors in solving linear systems with Hilbert matrices via various methods provided by each Programmer in the final response (review-2).}\\n\",\n \"\\\\label{tab:hil_Linf_error}\\n\",\n \"\\\\end{center}\\n\",\n \"\\\\end{table}\\n\"\n ]\n]","isConversational":false},"fulltext":{"kind":"string","value":"\\documentclass{article}\n\n\n\n\\usepackage{arxiv}\n\n\\usepackage[utf8]{inputenc} % allow utf-8 input\n\\usepackage[T1]{fontenc} % use 8-bit T1 fonts\n\\usepackage{hyperref} % hyperlinks\n\\usepackage{url} % simple URL typesetting\n\\usepackage{booktabs} % professional-quality tables\n\\usepackage{amsfonts} % blackboard math symbols\n\\usepackage{nicefrac} % compact symbols for 1/2, etc.\n\\usepackage{microtype} % microtypography\n\\usepackage{lipsum}\t\t% Can be removed after putting your text content\n\\usepackage{graphicx}\n\\usepackage{natbib}\n\\usepackage{doi}\n\n\n\\usepackage[dvipsnames, svgnames, x11names]{xcolor}\n\\usepackage{todonotes}\n\\usepackage{epstopdf, epsfig}\n\\usepackage{amsmath}\n\\usepackage{verbatim}\n\\usepackage[hang,splitrule,symbol]{footmisc}\n\\usepackage{amssymb}\n\\usepackage{multirow}\n\\usepackage{lineno}\n\\usepackage{mathrsfs}\n\\usepackage{graphicx}\n\\usepackage{adjustbox}\n\\usepackage{subcaption}\n\\usepackage{makecell}\n\\usepackage{array}\n\\usepackage{utfsym}\n\\usepackage{algorithm}\n\\usepackage{algpseudocode}\n\\usepackage{algorithmicx}\n\\usepackage{enumerate}\n\\usepackage{bigints}\n\\newcommand{\\integral}[2]{\\int\\limits_{#1}^{#2}}\n\\newtheorem{lemma}{Lemma}\n\\newtheorem{corollary}{Corollary}\n\\usepackage{xspace}\n\\usepackage{tcolorbox}\n\\usepackage{xcolor}\n\\usepackage{lipsum}\n\\usepackage{listings}\n\n\n\\title{$\\text{Re}^4$: Scientific Computing Agent with Rewriting, Resolution, Review and Revision} \n\n%\\date{September 9, 1985}\t% Here you can change the date presented in the paper title\n% \\date{} \t\t\t\t\t% Or removing it\n\n% \n% \\author{\n% Ao Cheng\\aff{1,2},\n% % Long Wang\\aff{1,2},\n% Lei Zhang\\aff{1,2,\\corresp{\\email{zhanglei@imech.ac.cn}}},\n% \\and Guo-wei He\\aff{1,2,\\corresp{\\email{hgw@lnm.imech.ac.cn}}}}\n% \\affiliation{\\aff{1}The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China\n% \\aff{2}School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China}\n\\author%\n{Ao Cheng$^{1,2}$, Lei Zhang$^{1,2,}$\\thanks{Corresponding author: zhanglei@imech.ac.cn} and Guowei He$^{1,2,}$\\thanks{Corresponding author: hgw@lnm.imech.ac.cn} \\\\\n$^{1}$The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics,\\\\ Chinese Academy of Sciences, Beijing 100190, China \\\\\n$^{2}$School of Engineering Sciences,\\\\\nUniversity of Chinese Academy of Sciences, Beijing 100049, China \\\\\n}\n\n% \\author{ {Ao Cheng}\\thanks{.} \\\\\n% \tDepartment of Computer Science\\\\\n% \tCranberry-Lemon University\\\\\n% \tPittsburgh, PA 15213 \\\\\n% \t\\texttt{hippo@cs.cranberry-lemon.edu} \\\\\n% \t%% examples of more authors\n% \t\\And\n% \t{Lei Zhang} \\\\\n% \tDepartment of Electrical Engineering\\\\\n% \tMount-Sheikh University\\\\\n% \tSanta Narimana, Levand \\\\\n% \t\\texttt{\\email{zhanglei@imech.ac.cn}} \\\\\n% \t%% \\AND\n% \t%% Coauthor \\\\\n% \t%% Affiliation \\\\\n% \t%% Address \\\\\n% \t%% \\texttt{email} \\\\\n% \t%% \\And\n% \t%% Coauthor \\\\\n% \t%% Affiliation \\\\\n% \t%% Address \\\\\n% \t%% \\texttt{email} \\\\\n% \t%% \\And\n% \t%% Coauthor \\\\\n% \t%% Affiliation \\\\\n% \t%% Address \\\\\n% \t%% \\texttt{email} \\\\\n% }\n\n% Uncomment to remove the date\n\\date{}\n\n% Uncomment to override the `A preprint' in the header\n%\\renewcommand{\\headeright}{Technical Report}\n\\renewcommand{\\undertitle}{}\n\\renewcommand{\\shorttitle}{$\\text{Re}^4$: agent framework for scientific computing}\n\n%%% Add PDF metadata to help others organize their library\n%%% Once the PDF is generated, you can check the metadata with\n%%% $ pdfinfo template.pdf\n% \\hypersetup{\n% pdftitle={A template for the arxiv style},\n% pdfsubject={q-bio.NC, q-bio.QM},\n% pdfauthor={David S.~Hippocampus, Elias D.~Striatum},\n% pdfkeywords={First keyword, Second keyword, More},\n% }\n\n\\begin{document}\n\\maketitle\n\n\\begin{abstract}\nLarge language models (LLMs) serve as an active and promising field of generative artificial intelligence and have demonstrated abilities to perform complex tasks in multiple domains, including mathematical and scientific reasoning. In this work, we construct a novel agent framework for solving representative problems in scientific computing. The proposed agent, incorporating a \"rewriting-resolution-review-revision\" logical chain via three reasoning LLMs (functioning as the Consultant, Reviewer, and Programmer, respectively), is integrated in a collaborative and interactive manner. The Consultant module endows the agent with knowledge transfer capabilities to link problems to professional domain insights, thereby rewriting problem descriptions through text augmentation. The Programmer module is responsible for generating and executing well-structured code to deliver the problem resolution. The Reviewer module equips the agent with the capacity for self-debugging and self-refinement through interactive feedback with code runtime outputs. By leveraging the end-to-end review mechanism, the executable code provided by the Programmer attains the iterative revision. A comprehensive evaluation is conducted on the performance of the proposed agent framework in solving PDEs, ill-conditioned linear systems, and data-driven physical analysis problems. \nCompared to single-model, this collaborative framework significantly improves the bug-free code generation rate and reduces the occurrence of non-physical solutions, thereby establishing a highly reliable framework for autonomous code generation based on natural language descriptions. The review mechanism improved the average execution success (bug-free code and non-NaN solutions) rate of the latest reasoning models, DeepSeek R1, from $59\\%$ to $82\\%$, while ChatGPT 4.1-mini improved from $66\\%$ to $87\\%$ and Gemini-2.5 improved from $60\\%$ to $84\\%$.\nIn summary, our agent framework establishes automatic code generation and review as a promising scientific computing paradigm. \n\\end{abstract}\n\n% keywords can be removed\n% \\keywords{First keyword \\and Second keyword \\and More}\n\n\n\\section{Introduction}\\label{sec:Introduction}\nScientific computing, as a cornerstone of modern science and engineering, enables the modeling, simulation, and analysis of complex physical phenomena, including fluid dynamics~\\citep{brunton2020machine}, computational mechanics~\\citep{zhang2022hidenn}, electromagnetism~\\citep{oskooi2010meep}, material science~\\citep{ramprasad2017machine} and quantum computing~\\citep{meng2023quantum}. However, solving scientific computing problems typically requires profound domain expertise, sophisticated algorithm design, and rigorous code implementation.\n% Traditional approaches often face challenges such as: (a) Complexity in algorithm design: Selecting appropriate methods for specific problems demands the mastery and application of extensive domain-specific knowledge; (b) Debugging and refinement hurdles: Carelessness in details or insufficient understanding of the inherent nature of problems can easily result in poor performance of the solving algorithms. \nIn recent years, large language models (LLMs)~\\citep{zhao2023survey} with advanced reasoning capabilities have emerged as transformative and low-barrier tools in scientific computing: automatically generating code based on a small amount of vague natural language descriptions. Implementing a natural-language-based solving paradigm faces two major challenges: (1) how to autonomously select and implement appropriate methods for specific problems; and (2) how to generate bug-free code. The first challenge demands the mastery and application of extensive domain-specific knowledge, necessitating that the LLMs complete the entire reasoning chain—from determining the type of equation (e.g., elliptic, parabolic, hyperbolic) to selecting the appropriate numerical method—without human intervention. The second challenge is a critical prerequisite for achieving autonomous scientific computing, requiring the model to translate vague natural language into precise code language.\n\nSince the advent of LLMs like ChatGPT~\\citep{achiam2023gpt}, researchers have begun to explore generating code through natural language descriptions~\\citep{chen2021evaluating,wang2023codet5+,roziere2023code}. Early models heavily relied on meticulous prompt engineering~\\citep{wei2022chain,kojima2022large}, requiring manual specification of numerical methods and model parameters, often resulting in logical and syntactical errors. At that stage, LLMs essentially functioned merely as code generation tools, providing rough program templates based on detailed customization from researchers, with low autonomy and necessitating extensive modification and debugging by users\\citep{jiang2024survey}. Recently, the excellent reasoning capabilities of reasoning LLMs have shown promise in addressing autonomy issues. Studies by Jiang et al. \\citep{jiang2025deepseek} and Wang et al. \\citep{wang2025eval} have tested the capabilities of these reasoning models in scientific computing, indicating that they generally outperform non-reasoning models. However, it was found that even when addressing classical problems with established solutions, the code generated by reasoning models frequently contained errors requiring human correction. Furthermore, in tests conducted by Wang et al., reasoning models such as DeepSeek R1~\\citep{guo2025deepseek} and OpenAI's o3-mini-high~\\citep{openai_o3_mini_2025} proved ineffective in solving challenging problems like the Hilbert linear algebra problem, with DeepSeek R1 proposing potential strategies during thinking but failing to implement them. In addition to low bug-free rates in code generation, reasoning models currently face issues such as strong randomness in the selection of numerical methods, unstable output results, and reasoning hallucinations. These factors can lead to the selection of suboptimal numerical schemes, thereby significantly affecting the reliability of LLMs in scientific computing.\n\nThe agent framework based on LLMs provides the capability to interact with external systems. Prompt-engineering-based interactive feedback enables self-refinement without the need for extra training. Madaan et al.~\\citep{madaan2023self} leveraged a single non-reasoning LLM to generate an initial output, provided self-feedback, and iteratively optimized subsequent outputs using historical feedback and prior iterative outputs. Such a self-feedback framework, by simulating the iterative process of \"draft-reflection-revision\" of humans, significantly improves the quality of outputs compared with the traditional one-step generation approach. By encoding Standardized Operating Procedures (SOPs) into prompt sequences, the multi-agent collaboration framework MetaGPT~\\citep{hong2023metagpt} empowered LLMs to simulate human professional roles, delivered structured outputs, and collaborated in an assembly-line manner, thereby reducing errors and boosting task efficiency. By assigning unique roles to multiple LLMs, the ChatEval framework constructed a multi-agent referee team that enhanced text evaluation accuracy through collaborative debate, and experimental results underscore the strengths of multi-agent collaboration~\\citep{chan2023chateval}. In the field of scientific computing, such as computational fluid dynamics, an LLM-driven framework enabled end-to-end output from natural language input to user-interactive wall-bounded turbulence modeling problems~\\citep{yang2025large}. Xu et al.~\\citep{xu2025cfdagent} proposed a zero-shot, natural language-driven multi-agent system called CFDagent, which, coordinated by LLMs, completes the end-to-end process from natural language prompts to fully automated computational fluid dynamics (CFD) simulations. For PDE solving, the PINNsAgent~\\citep{wuwu2025pinnsagent}, which integrates physics-informed knowledge replay and memory tree reasoning strategies, serves as an LLM-based surrogate framework to automatically construct and optimize PINNs architectures, effectively bridging the gap between domain-specific knowledge and deep learning expertise. The task-specific-tuning-free framework CodePDE was validated on a range of representative PDE problems by enabling LLMs to perform iterative debugging~\\citep{li2025codepde}. The best solutions achieved by this framework on multiple PDE problems reach or exceed human levels, indicating the potential of LLM-based agents in solving PDEs. However, existing applications of LLMs in scientific computing often lack a structured framework to ensure the designed algorithms adaptable to diverse tasks and code refinement through feedback that interacts with runtime results.\n\n\\begin{table}\n\\begin{center}\n\\def~{\\hphantom{0}}\n\\begin{tabular}{c|c|c|c|c|c|c}\n\\cline{1-7}\n&Reasoning&Expansion&Debugging&Refinement&\\makecell{Review}&\\makecell{Single/Multiple\\\\ LLMs} \\\\ \\cline{1-7}\n\\makecell{Non-reasoning\\\\ LLMs}&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&Single \\\\ \\cline{1-7}\n\n\\makecell{Reasoning\\\\ LLMs}&$\\usym{1F5F8}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&$\\usym{2613}$&Single \\\\ \\cline{1-7}\n\n\\makecell{CodePDE\\\\ Agent}&$\\usym{1F5F8}$&$\\usym{2613}$&$\\usym{1F5F8}$&\\makecell{based on \\\\posterior error} &$\\usym{2613}$&Single \\\\ \\cline{1-7}\n\n\\multirow{2}{*}{\\makecell{PINNsAgent}}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{Single} \\\\ \n&&&&&& \\\\ \\cline{1-7}\n\n\\multirow{2}{*}{\\makecell{Madaan's\\\\ Agent}}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{2613}$}&\\multirow{2}{*}{Single} \\\\ \n&&&&&& \\\\ \\cline{1-7}\n\n\\multirow{2}{*}{\\makecell{Our Agent}}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{$\\usym{1F5F8}$}&\\multirow{2}{*}{Multiple} \\\\ \n&&&&&& \\\\ \\cline{1-7}\n\\end{tabular}\n\\caption{Comparison among existing LLM-based agent frameworks for scientific computing and the one we proposed.}\n\\label{tab:agents_compare}\n\\end{center}\n\\end{table}\n\nTo address the autonomy and reliability issues encountered by LLMs in achieving solutions autonomously, while leveraging the merits of multi-step multi-agent collaboration, we propose a novel agent framework for scientific computing that integrates three collaborative modules: Consultant, Reviewer, and Programmer, to automate the end-to-end process of problem solving.\n% This framework is designed to: (a) Adaptively link scientific computing tasks to corresponding domain knowledge; (b) Enable self-debugging and self-refinement via iterative feedback loops.\nThis framework is designed to incorporate: \n\n$\\bullet$ \\textbf{Rewriting}. By expanding the task background through adaptive integration of domain knowledge and providing algorithmic strategies, LLMs' understanding of specific scientific computing problems is deepened. \n\n$\\bullet$ \\textbf{Resolution}. In the initial response, Python code are generated leveraging the augmented task text and run in the terminal, while capturing the runtime output text for subsequent refinement. \n\n$\\bullet$ \\textbf{Review}. As an independent third party, an independent LLM evaluates the solution quality of the designed algorithm, with suggestions for the code's implementation details, thereby endowing the agent with the traits of self-debugging and self-refinement. \n\n$\\bullet$ \\textbf{Revision}. In the revision loop, the executable code are comprehensively enhanced in execution/solving success rate, readability, modularity, and solution accuracy through feedback-driven refinement. \n\nWe quantitatively assess the performance of both the agent with and without the Reviewer module in autonomously solving PDEs, challenging Hilbert systems and conducting data-driven physical analysis. This assessment encompasses various dimensions, including bug-free rate, occurrence of non-physical solutions, high-precision solution generation rate (with errors below a certain threshold), and solution accuracy. Through multi-model cross-validation and the implementation of self-debugging, the review mechanism improved the average execution success (bug-free code and non-NaN solutions) rate of the latest reasoning models: DeepSeek R1 improved from $59\\%$ to $82\\%$, ChatGPT 4.1-mini improved from $66\\%$ to $87\\%$ and Gemini-2.5 improved from $60\\%$ to $84\\%$. Additionally, this framework significantly increased the probability of selecting high-precision methods, resulting in a noticeable improvement in average solution accuracy compared to single models. This agent framework demonstrates generality and versatility; we have extended it to data-driven analyses of governing physical relationships, and results indicate its capacity to consistently produce correct analytical outcomes.\n\nA detailed comparison of current LLM-based agents' capabilities is presented in Table~\\ref{tab:agents_compare}. Our contributions are as follows:\n\n(1) We introduce, for the first time, an agent framework for scientific computing that incorporates a \"rewriting-resolution-review-revision\" logical chain, significantly improving the bug-free code generation rate and reducing the occurrence of non-physical solutions, thereby establishing a highly reliable framework for autonomous code generation based on natural language descriptions.\n\n(2) We present, for the first time, a multi-LLMs collaborative framework for scientific computing that outperforms single models across all performance metrics.\n\n(3) We apply the agent framework to the analysis of governing physical mechanisms, validating its generality and versatility.\n\n\nThe rest of the paper is organized as follows: the construction of the agent framework is introduced in Section~\\ref{sec:Methodology}; the comprehensive validation on different scientific computing problems is presented in Section~\\ref{sec:Experiments}; and the conclusions are drawn in Section~\\ref{sec:Conclusion}.\n\n\\section{Methodology}\\label{sec:Methodology}\n\n\\begin{figure}\n\\centering{\\includegraphics[width=\\textwidth]{Figs/schematic_Agent_Ver2.png}}\n\\caption{Schematic of the agent framework.}\n\\label{Fig_schematic_agent}\n\\end{figure}\nIn this section, the overall framework of the agent and the specific responsibility of each module will be detailed. Specifically, the collaboration of multiple large language models (LLMs), as depicted in Fig.~\\ref{Fig_schematic_agent}, encompasses three main modules:\n\\begin{enumerate}[(i) ]\n\\item \\textbf{Consultant module.} This module elaborates the problem background and provides the candidate algorithms. One LLM governs this module, where the input is the natural language description of problems (e.g., PDE), and the output is a report that expands the contextual background of the original problem and suggests various algorithmic strategies, thereby deepening the understanding of specific task through text augmentation.\n\n\\item \\textbf{Programmer module.} The LLM in this module determines the algorithm based on the analysis from the Consultant module, generates Python code, and enables terminal execution. In this module, the input configuration to LLM varies by operational phase: during the initial answering, the LLM ingests the Consultant's augmented context, whereas during revision loop, the input transitions to feedback from the following Reviewer module. The LLM performs algorithm framework selection, structured Python code generation, and terminal execution on the Python compiler to validate solution efficacy.\n\n\\item \\textbf{Reviewer module.} This module assesses algorithms and results from the Programmer module, assisting in debugging and refining the code. Governed by an LLM independent of the Programmer module, it processes inputs comprising the Consultant's augmented context, the Programmer's code, and the outputs of the compiler including warnings, errors and solutions. Its primary output objectives include: \\textbf{$(a)$} conducting a comprehensive evaluation of the Programmer's algorithmic implementation; \\textbf{$(b)$} debugging code if errors or warnings arise due to bugs; \\textbf{$(c)$} refining selections of algorithms, parameter settings and code implementations to enhance overall performance. The Programmer module and Reviewer module form a feedback loop, enabling the agent's self-debugging and self-refinement.\n\n\\end{enumerate}\n\nBeyond a single-LLM loop, the proposed agent supports a collaborative framework of multiple LLMs, allowing distinct LLMs to operate in different modules.\n\nGiven the great potential of reasoning LLMs\\citep{wang2025eval,jiang2025deepseek}, we primarily evaluate the agent's performance of \\textbf{Gpt-4.1-mini-2025-04-14}~\\citep{gpt4p1_mini_050414}, \\textbf{Gemini-2.5-flash-preview-05-20}~\\citep{gemini_2.5flash_preview-0520}, and \\textbf{Deepseek-R1-250528}~\\citep{deepseek_r1_20250528} \\textbf{as Programmers} in the domain of scientific computing. \n\nDue to the token limits for context windows and maximum output lengths in LLM conversations, we prefer designating Gpt-4.1-mini-2025-04-14 as both Consultant and Reviewer, leveraging its exceptional long-text comprehension and high-response efficiency. Specifically, scenarios involving relatively long prompt content (over 4500 tokens), such as when Consultant inputs include necessary attachments (e.g., the .csv dataset files for dimensional analysis) or Reviewer inputs combine Consultant’s augmented contexts with Programmer’s code execution outputs, may compromise the LLM's ability to generate valid responses.\n\nTo overcome LLM context window limitations, our strategy is to truncate the content printed by the Programmer's code—for example, iterative error messages from time-stepping in numerical methods. Otherwise, if Deepseek-R1 receives such long and redundant prompts, it would likely fail to generate valid outputs.\n\n% In other words, within our agent framework, both the \\textbf{Consultant and Reviewer} should have sufficient context windows, with the generated content maintaining a moderate length (approximately 1500–2500 tokens). Unlike \\textbf{Gemini-2.5-flash-preview}, which tends to generate detailed yet overly verbose content, \\textbf{Gpt-4.1-mini} stands out as the most suitable choice due to its high-response efficiency comparable to Gemini, 1-million-token context handling capability, and tremendous multimodal potential.\n\nThe key innovation of the proposed agent lies in its collaborative framework of multiple LLMs, structured based on the thought chain of \"rewriting-resolution-review-revision\":\n\\begin{enumerate}[(i) ]\n \\item Leveraging the Consultant module to enable the agent to \\textbf{link problems to specific domain knowledge}, fostering deeper understanding and well-designed solutions through text augmentation;\n \\item Introducing the Reviewer module, which generates detailed feedback through the agent's interaction with code execution outputs, endowing the agent with \\textbf{self-debugging and self-refinement capabilities}.\n\\end{enumerate}\n\n\\section{Experiments}\\label{sec:Experiments}\n\n\\textbf{Tasks.} In this section, we conduct a comprehensive performance evaluation of the proposed agent architecture across diverse specialized scenarios in scientific computing, with explicit focus on PDE benchmarks (including six specific equations), ill-conditioned Hilbert linear systems, and data-driven physical analysis based on dimensional analysis. In the first two tasks, the agent is required to solve given PDEs or linear algebraic systems. In the last task, the agent autonomously analyzes the dominant dimensionless quantities from an infinite set of possibilities based on available experimental data.\n\n\\textbf{Models.} We evaluate the newest and most popular LLMs as the Programmer, including Gpt-4.1-mini-2025-04-14, Gemini-2.5-flash-preview-05-20, and Deepseek-R1-250528.\n\n\\textbf{Metrics.} The capabilities of generating high-quality code and solutions, compared to the original LLM without feedback from the Reviewer module, are measured by:\n\n$\\bullet$ \\textbf{Code execution success rate.} The percentage of generating bug-free code and providing non-NaN solutions. This metric indicates the reliability of the code generation.\n\n$\\bullet$ \\textbf{Solving success rate.} The percentage of errors below a specified threshold, particularly in the task of solving ill-conditioned Hilbert linear systems. For the data-driven physical analysis task, this refers to the percentage of successfully identifying dominant dimensionless quantities.\n\n$\\bullet$ \\textbf{Accuracy.} The $L^2$-norm or $L^\\infty$-norm relative error.\n\n\n% From a statistical perspective, we demonstrate the capabilities of agent self-debugging and self-refinement by performing multiple samplings on the iterative problem-solving results to evaluate the performance of different state-of-the-art LLMs (such as \\textbf{Gpt-4.1-mini-2025-04-14, Gemini-2.5-flash-preview-05-20, and Deepseek-R1-250528}) in their roles as programmers across two critical dimensions: $(a)$ Improvement in code execution success rate; $(b)$ Enhancement in comprehensive performance of generated numerical algorithm.\n\n\\subsection{Partial Differential Equation benchmark}\\label{subsec: PDE bench}\nIn this subsection, we assess the performance of the proposed agent framework in designing algorithms to solve a set of PDE problems that represent a wide range of challenges. The reference PDE benchmark consists of three categories: \\textbf{discontinuous problems} (Burgers equation and Sod shock tube), \\textbf{elliptic equations} (Poisson equation and Helmholtz equation), and \\textbf{Navier-Stokes equations} (both steady and unsteady).\n\n% \\subsubsection{Overall performance on PDEbench}\nIt should be noted that the PDEs selected for this paper encompass a diverse range of mathematical properties. This ensures that the benchmarks do not favor a specific type of PDE. The curated set of PDE problems introduces several fundamental challenges, outlined as follows:\n\\begin{itemize}\n \\item \\textbf{Nonlinear Behavior:} When PDEs exhibit nonlinearity, minor deviations in initial conditions can lead to significant divergence in results.\n \\item \\textbf{Complex geometry:} Irregular geometries directly pose challenges for the agent in accurately representing boundary behaviors.\n \\item \\textbf{Unsteady Evolution:} The solutions of some PDEs change dynamically over time, requiring algorithms to accurately handle time-varying processes and robustly capture transient phenomena.\n\\end{itemize}\n\nTable~\\ref{tab:Pdebench} provides a detailed overview of various PDEs, the challenges, and reference solutions. The reference datasets are collected from the benchmark of \\citet{zhongkai2024pinnacle}. More details of the PDEs and the evaluation results can be found in Appendix~\\ref{app:pdebench_details}.\n\n\\begin{table}\n\\begin{center}\n\\def~{\\hphantom{0}}\n\\begin{tabular}{|c|c|c|}\n\\cline{1-3}\n\\multirow{2}{*}{PDE systems}&\\multirow{2}{*}{Challenges}&\\multirow{2}{*}{Reference solutions}\\\\\n& & \\\\\n\\cline{1-3}\n\n\\makecell{\\textbf{Burgers euqation}\\\\ $\\frac{\\partial u}{\\partial t}+u u_x-\\nu u_{xx}=0$} & \\makecell{\\textbf{Nonlinear,Unsteady \\checkmark}\\\\Accurately resolve\\\\ oscillations and capture\\\\ shock waves}&\n\\begin{minipage}{0.25\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/burgers_reference_.pdf}\n \\end{minipage}\\\\\n\\cline{1-3}\n\n\\makecell{\\textbf{Sod Shock Tube}\\\\ \n$\\begin{cases}\n\\frac{\\partial \\rho}{\\partial t} + \\frac{\\partial (\\rho u)}{\\partial x} = 0\\\\\n\\frac{\\partial (\\rho u)}{\\partial t} + \\frac{\\partial (\\rho u^2 + p)}{\\partial x} = 0\\\\\n\\frac{\\partial (\\rho E)}{\\partial t} + \\frac{\\partial (\\rho E u + p u)}{\\partial x} = 0\n\\end{cases}$}&\\makecell{\\textbf{Unsteady \\checkmark} \\\\Precisely capture\\\\ time-dependent positions\\\\ and strengths of\\\\ multiple wave systems}&\n\\begin{minipage}{0.23\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/SodShock_reference_2d.pdf}\n \\end{minipage}\\\\\n\\cline{1-3}\n\n\\makecell{\\textbf{Poisson equation}\\\\ $\\Delta u = 0$}&\\makecell{\\textbf{Complex Geometry \\checkmark}\\\\ Precise discretization of \\\\curvilinear circular holes \\\\and rectangular edges}&\n\\begin{minipage}{0.25\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/Poisson_reference_.pdf}\n \\end{minipage}\\\\\n\\cline{1-3}\n \n\\makecell{\\textbf{Helmholtz equation}\\\\ $-\\Delta u + k^2 u = f$}&\\makecell{\\textbf{Complex Geometry \\checkmark}\\\\ Proper discretization of\\\\ complex boundaries\\\\ and handling of\\\\ high-frequency oscillation} &\n\\begin{minipage}{0.25\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/Helmholtz_reference_.pdf}\n \\end{minipage}\\\\\n\\cline{1-3}\n \n\\makecell{\\textbf{Lid-Driven Cavity}\\\\ $\\begin{cases}\n\\nabla \\cdot \\textbf{u} = 0 \\\\\n\\textbf{u} \\cdot \\nabla \\textbf{u} + \\nabla p = \\frac{1}{\\mathrm{Re}} \\Delta \\textbf{u} \\\\\n\\end{cases}$}&\\makecell{\\textbf{Nonlinear \\checkmark}\\\\ Complex flow details and\\\\ velocity-pressure coupling} &\n\\begin{minipage}{0.25\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/LidDriven_reference_.pdf}\n \\end{minipage}\\\\\n \\cline{1-3}\n \n\\makecell{\\textbf{Unsteady NS equation}\\\\ $\\begin{cases}\n\\nabla \\cdot \\textbf{u} = 0 \\\\\n\\frac{\\partial \\mathbf{u}}{\\partial t} + \\mathbf{u} \\cdot \\nabla \\textbf{u} + \\nabla p - \\frac{1}{\\mathrm{Re}} \\Delta \\textbf{u} = \\mathbf{f}\\\\\n\\end{cases}$}&\\makecell{\\textbf{Nonlinear,Unsteady \\checkmark}\\\\ Temporal evolution and\\\\ velocity-pressure coupling} &\n\\begin{minipage}{0.25\\textwidth}\n \\centering\n \\includegraphics[width=\\linewidth]{Figs/Reference_table_summary/LongTimeNS_reference_.pdf}\n \\end{minipage}\\\\\n \\cline{1-3}\n\n\\end{tabular}\n\\caption{Summary of various equations in PDEbench.}\n\\label{tab:Pdebench}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\begin{center}\n\\renewcommand{\\arraystretch}{1.2}\n\\setlength{\\tabcolsep}{2.5pt}\n\\begin{tabular}{c|ccc|ccc|ccc}\n\\cline{1-10}\n\\multirow{2}{*}{Programmer} & \\multicolumn{3}{c|}{Gpt-4.1-mini} & \\multicolumn{3}{c|}{Gemini-2.5-flash} & \\multicolumn{3}{c}{Deepseek-R1} \\\\ \\cline{2-10}\n& ans-0& rev-1& rev-2&ans-0& rev-1& rev-2&ans-0& rev-1& rev-2 \\\\ \\cline{1-10}\n% Burgers &$\\scriptscriptstyle 5.8\\times10^{-2}$&$\\scriptscriptstyle 2.5\\times10^{-2}$&$\\scriptscriptstyle 2.3\\times10^{-2}$&$\\scriptscriptstyle 4.1\\times10^{-2}$&$\\scriptscriptstyle 3.5\\times10^{-2}$&$\\scriptscriptstyle 3.1\\times10^{-2}$&$\\scriptscriptstyle 7.0\\times10^{-2}$&$\\scriptscriptstyle 4.1\\times10^{-2}$&$\\scriptscriptstyle 3.0\\times10^{-2}$ \\\\\nBurgers &5.8e-02&2.5e-02&\\underline{\\textbf{2.3e-02}}&4.1e-02&3.5e-02&\\underline{3.1e-02}&7.0e-02&4.1e-02&\\underline{3.0e-02} \\\\\nSod Shock &1.3e-01&\\underline{6.0e-02}&6.1e-02&6.4e-02&\\underline{6.4e-02}&7.0e-02&1.7e-01&\\underline{\\textbf{4.4e-02}}&4.6e-02 \\\\\nPoisson &4.4e-02&2.6e-02&\\underline{1.9e-02}&3.5e-02&2.4e-02&\\underline{\\textbf{1.5e-02}}&4.1e-02&2.6e-02&\\underline{1.5e-02} \\\\\nHelmholtz &4.9e-02&4.5e-02&\\underline{3.7e-02}&3.4e-02&3.2e-02&\\underline{\\textbf{2.6e-02}}&4.5e-02&3.5e-02&\\underline{2.8e-02} \\\\\nLid-Driven &4.2e-01&1.4e-01&\\underline{\\textbf{5.7e-02}}&2.7e-01&2.3e-01&\\underline{9.9e-02}&3.0e-01&2.6e-01&\\underline{1.8e-01} \\\\\nUnsteady NS &2.9e-01&2.3e-01&\\underline{1.9e-01}&2.1e-02&2.1e-02&\\underline{2.1e-02}&2.4e-01&9.0e-02&\\underline{\\textbf{2.0e-02}} \\\\ \\cline{1-10}\n\\end{tabular}\n\\caption{The summary of average $L^2$ relative error across all cases in PDEbench, where underlined entries denote each Programmer’s minimum errors at different response stages, and bold entries indicate the overall minimum errors among all Programmers.}\n\\label{tab:pdebench_overall_average_rel_error}\n\\end{center}\n\\end{table}\n\nTo evaluate the deviation between the agent's answers and reference solutions, we adopt the relative $L^2$ error metric to rigorously quantify the global fidelity of the solutions, defined as follows:\n\\begin{equation}\nerror = \\sqrt{\\frac{\\sum_{i=1}^n (y_i' - y_i)^2}{\\sum_{i=1}^n (y_i)^2}}\n\\label{equ:rel2_err}\n\\end{equation}\nwhere $\\boldsymbol{y} = (y_i)_{i=1}^n$ is the ground truth and $\\boldsymbol{y'} = (y_i')_{i=1}^n$ is the calculated results, and $n$ is the reference solution’s grid point count.\n\n\\begin{figure}[htbp]\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/All_average_Execution_Success_Rate.pdf}}\n\\end{subfigure}\n \\caption{The overall average execution success rate of numerical algorithms employed by Programmers across all equations in the PDEbench.}\n\\label{fig:All_average_exe_rate}\n\\end{figure}\n\n\\begin{figure}[htbp]\n \\centering\n\\begin{subfigure}[b]{0.9\\textwidth}\n\\centering\n{\\includegraphics[width = \\textwidth]{Figs/PDE_all_Average/All_average_Box_Legend.pdf}}\n\\end{subfigure} \n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/All_average_Error_Box.pdf}}\n\\end{subfigure}\n \\caption{Boxplot of the average $L^2$ relative errors for all equations in the PDEbench. The \\textbf{annotated numbers} in the figure denote the average of relative errors.}\n\\label{fig:All_average_error_box}\n\\end{figure}\n\nThe overall average execution success rate of the code generated by the agent framework across all PDE problems is presented in Figure~\\ref{fig:All_average_exe_rate}, from which it can be intuitively seen that with the involvement of Reviewer, the Programmers effectively perform self-debugging and self-refinement, leading to up to $24\\%$ improvement in code execution success rate on average.\n\nAfter multiple samplings of Programmers' answers for different PDE equations, the average $L^2$-norm relative errors are displayed in Table~\\ref{tab:pdebench_overall_average_rel_error} and as a boxplot in Figure~\\ref{fig:All_average_error_box}. The boxes represent the interquartile range between the first and third quartiles, while the horizontal line in each box indicates the median. Additional error bars (or whiskers) depict the upper and lower limit values. As can be seen from Table~\\ref{tab:pdebench_overall_average_rel_error}, except for the Sod shock tube, the minimum errors of all other cases appear in the Reviewer's second interventions (review-2). Additionally, observations from the boxplot indicate that with the Reviewer's guidance, the mean, median, and error distribution of the average relative error all show an overall improvement. From the best-of-$n$ sample perspective, Table~\\ref{tab:pdebench_overall_best_rel_error} presents the relative errors of the final runtime outputs from each Programmer against the reference solutions. Both of the above two metrics confirm that with the Reviewer's successive interventions, the solvers developed by Programmers for various PDE equations exhibit improvements in code quality and accuracy.\n\n\\begin{figure}\n \\centering\n\\begin{subfigure}[b]{0.95\\textwidth}\n \\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Best_unsteadyNS_contours.pdf}}\n\\end{subfigure}\n\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n\\label{fig:Unsteady_NS_Best_3LLMs}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n\\begin{subfigure}[b]{0.95\\textwidth}\n \\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/R1_unsteadyNS_contours.pdf}}\n\\end{subfigure}\n\\caption{The runtime outputs of the executable code provided by Programmer Deepseek-R1 in the initial response (answer-0), together with those in the Reviewer's first (review-1) and second (review-2) interventions, respectively.}\n\\label{fig:Unsteady_NS_R1_improvement}\n\\end{figure}\n\n% \\subsubsection{A specific case in PDEbench}\n\\textbf{Evaluations on the long-time evolved unsteady NS equation.} The long-time evolved unsteady NS equation is selected to specifically illustrate the excellent performance of our agent framework. The prompt template for this case, the statistically determined code execution success rate, and the relative $L^2$ error obtained through multiple samplings are all presented in Appendix~\\ref{subapp:pde_Unsteady_NS}. The reason for choosing the unsteady NS equation stems from the fact that its difficulties arise in multiple aspects:\n\\begin{enumerate}[(i) ]\n \\item The equations are a coupled system of PDEs, including the momentum equation and the continuity equation, which require simultaneous solution of the velocity $(u, v)$ and pressure $(p)$~\\citep{chorin1967numerical}.\n \\item The equations are unsteady in time, necessitating the handling of time-varying source terms and left inlet velocity boundary conditions, both of which are time-dependent, as well as the consideration of time integration stability.\n \\item The solution process typically employs the GMRES iterative method~\\citep{saad1986gmres} for the pressure Poisson equation, presenting numerical challenges from the ill-conditioned discrete linear system and the computational cost of achieving convergence, both of which arise from the global continuity constraint in incompressible NS simulations.\n\\end{enumerate}\n\nDeveloping numerical algorithms involves discretizing governing equations, properly handling boundary conditions, and implementing iterative solution schemes. Addressing these requirements necessitates robust expertise in numerical methods and programming, while agents must balance accuracy, stability, and computational efficiency during the solution process. These considerations fully highlight the complexities and challenges inherent in solving this unsteady NS equation.\n\nNotably, as depicted in Figure~\\ref{fig:LT_NS_sucessRate}-\\ref{fig:LT_NS_boxError}, the Reviewer's intervention has resulted in up to a $40\\%$ surge in the success rate of code execution following self-debugging. Meanwhile, the relative error shows a noticeable reduction after iterative self-refinement, illustrating how step-by-step improvements enhance code quality. \n\nSpecifically, for Gemini, the relative error in streamwise velocity from its execution results remains minimal, whether in the minority of executable code provided in the initial response or the majority of executable code after Reviewer interventions. In contrast, GPT demonstrates a weaker overall improvement in the relative error, while R1 achieves the most significant decrease, highlighting the agent's superior performance in iterative self-refinement. As evidence, the contour plots and their corresponding relative errors are visualized in Figure~\\ref{fig:Unsteady_NS_Best_3LLMs}, which depicts the best runtime outputs from each Programmer after two rounds of Reviewer guidance.\n\nTo provide a more comprehensive demonstration of Programmer R1’s code quality improvement, Figure~\\ref{fig:Unsteady_NS_R1_improvement} illustrates the contours of streamwise velocity $u$, normal velocity $v$, and pressure $p$ in the flow field generated by Deepseek-R1 after successive guidance from the Reviewer. The results generated during the initial run show larger deviations from the reference across all three physical quantities.\n\n% With successive interventions by the Reviewer, the runtime outputs exhibit progressively closer matches to the reference due to Deepseek-R1’s enhancement of boundary condition discretization accuracy and implementation of preconditioner strategies for Poisson solver. To ensure conciseness in the main text, the detailed runtime outputs for other cases in Pdebench are presented in Appendix~\\ref{subapp:pde_burgers}-\\ref{subapp:pde_Lid-Driven}.\n\n\\subsection{Hilbert linear algebraic systems}\\label{subsec: Hilbert mat}\nIn this subsection, we assess the performance of the proposed agent framework in solving the Hilbert linear algebraic system~\\citep{kress1998ill}. Specifically, we vary the dimensions of the Hilbert matrix by taking \\(n = 5,10,\\dots,25\\) and compute the $L^\\infty$ error between numerical solutions and the exact solution $x^*=(1,1,\\cdots,1)^\\mathrm{T}$ for each value of $n$. The specific linear algebraic system with Hilbert matrix is given by:\n\\begin{equation}\n\\label{Hilbert_equation}\n\\Large\n\\mathbf{b} = H_n \\mathbf{x^*} = \\begin{bmatrix}\n1 & \\frac{1}{2} & \\cdots & \\frac{1}{n} \\\\\n\\frac{1}{2} & \\frac{1}{3} & \\cdots & \\frac{1}{n+1} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\n\\frac{1}{n} & \\frac{1}{n+1} & \\cdots & \\frac{1}{2n-1}\n\\end{bmatrix}\n\\normalsize\n\\begin{bmatrix}\n1\\\\\n1\\\\\n\\vdots\\\\\n1\n\\end{bmatrix}\n\\end{equation}\nwhere \\( H_n \\) is a \\( n \\times n \\) Hilbert matrix with elements \\( h_{i,j} = \\frac{1}{i+j-1} \\), and the vector \\( \\mathbf{b} \\) is obtained by substituting the exact solution \\( \\mathbf{x}^* = (1, 1, \\dots, 1)^{\\top} \\) into \\( H_n \\mathbf{x}^*\\). Hilbert matrix serves as a prototypical example of ill-conditioned matrices, whose 2-condition number $\\kappa_2(H_n)$ grows exponentially with the dimension $n$, as shown in Figure~\\ref{fig:hil_naive_cond}.\n\nThe extremely high condition number renders naive methods ineffective, that is, even minor perturbations in input data could lead to drastic errors in the computed solution, thereby posing significant challenges for solving this ill-conditioned matrix. The following template is adopted as the problem description prompt for input into the agent framework:\n\\begin{tcolorbox}[\n title={Problem Description Prompt: Hilbert Matrix},\n coltitle = blue,\n colback=white, \n colbacktitle=GreenYellow!10, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\nImplement \\textbf{various appropriate methods from scratch} to solve the system of linear algebra equations \\( H_{n}\\mathbf{x} = \\mathbf{b} \\) accurately and efficiently, where \\( H_{n} \\) is an \\( n \\times n \\) matrix defined by \\( h_{ij} = 1/(i+j-1) \\), and the vector \\(\\mathbf{b}\\) is taken to ensure that the system admits an exact solution \\( \\mathbf{x^*} = (x_{i})_{n \\times 1} = (1)_{n \\times 1} \\).\\\\\nPlease primarily use \\texttt{numpy}, \\texttt{scipy}, and \\texttt{matplotlib} libraries.\\\\\nCompare the \\( L_{\\infty} \\) error of the numerical results with the exact solution for \\( n = 5, 10, 15, 20, 25 \\).\n\\end{tcolorbox}\n\nTo prevent the agent from cheating by using numpy.linalg.solve or scipy.linalg.solve, while also avoiding unfair performance evaluations caused by certain methods' inherent lack of adaptability when addressing ill-conditioned matrices, we explicitly required the agent in the problem description prompt to \\textbf{implement various appropriate methods from scratch}.\n\nBy statistically analyzing the results of the agent framework solving this problem eight times independently, we categorize the completion status of executable code into three types: \\textbf{results contain NaN, exceed $L^\\infty$ threshold, and below $L^\\infty$ threshold}, with the threshold set to $10^{-2}$.\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.65\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/cond_traditionMethods.pdf}}\n\\end{subfigure}\n \\caption{Schematic diagram of (a) variation of the 2-norm condition number with matrix dimension; (b) $L^\\infty$ error obtained by direct solution using the naive methods.}\n\\label{fig:hil_naive_cond}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.8\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hilbert_Complete_Rate_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hilbert_Complete_Rate.pdf}}\n\\end{subfigure}\n \\caption{Proportional distribution of executable code provided by Programmers across three different completion statuses.}\n\\label{fig:hil_complete_rate}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.65\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/legend_HilbMat_methodsDist_3status.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/HilbMat_methodsDist_3status.pdf}}\n\\end{subfigure}\n \\caption{Proportional distribution of completion status for various methods at different response stages. A single dark-colored patch represents SVD method results consistently below the threshold. The color patches corresponding to other methods are divided into three segments, with colors darkening gradually to indicate the following respectively: results contain NaN, exceed $L^{\\infty}$ threshold and below $L^{\\infty}$ threshold.}\n\\label{fig:hil_methodDist_3status}\n\\end{figure}\n\n% \\begin{table}\n% \\begin{center}\n% \\def~{\\hphantom{0}}\n% \\begin{tabular}{|c|c|c|c|}\n% \\cline{1-4}\n% Methods &Stability&\\makecell{Adaptability\\\\ for large $n$} &Notes\\\\ \\cline{1-4}\n% \\makecell{LU w/ Partial Pivoting}&Moderate&bad&Easy to implement \\\\\\cline{1-4}\n% \\makecell{Cholesky Decomposition}&Moderate&Moderate&Exploits symmetry \\\\\\cline{1-4}\n% QR Decomposition&High&Moderate&Complex to implement \\\\\\cline{1-4}\n% Conjugate Gradient&High&Good&Suitable for large $n$ \\\\\\cline{1-4}\n% Tikhonov Regularization&High&Good&Balance accuracy/stability\\\\\\cline{1-4}\n% High-Precision Arithmetic&High&Good&Computationally expensive\\\\ \\cline{1-4}\n% \\end{tabular}\n% \\caption{Various alternative methods provided by Consultant.}\n% \\label{tab:Hilbert_consultant_}\n% \\end{center}\n% \\end{table}\n\nAs shown in Figure~\\ref{fig:hil_complete_rate}, Gpt-4.1-mini failed to provide any solution with errors below the threshold in its initial response, i.e., the original solving success rate is zero. However, with the guidance of the Reviewer, all three Programmers provided more numerically precise and stable algorithms. Specifically, in terms of the enhancement in solving success rate driven by review mechanism, GPT-4.1-mini improved from $0\\%$ to $57\\%$, while Gemini-2.5-flash improved from $32\\%$ to $43\\%$ and Deepseek-R1 improved from $11\\%$ to $46\\%$. Figure~\\ref{fig:hil_methodDist_3status} presents the percentage contribution of various methods to the solution success rate, with Cholesky and Conjugate Gradient accounting for the major share. The marked increase in the darkest color patch (below $L^{\\infty}$ threshold) fully demonstrates the refined stability and accuracy of solution schemes with the Reviewer's suggestions.\n\nTo more intuitively illustrate the adaptability of various approaches underlying the success rate in solving Hilbert ill-conditioned matrices, Figure~\\ref{fig:Hil_diff_stage_proportion} presents the proportional distribution of specific methods across three completion statuses. The improvement observed from the above statistical perspective stems from the Reviewer pointing out that regularization techniques (e.g., Tikhonov regularization~\\citep{golub1999tikhonov}) or iterative methods (e.g., conjugate gradient~\\citep{hestenes1952methods}) should be adopted to stably and accurately solve Hilbert matrices. At a more essential level, the reason is that the agent framework recognizes that ill-conditioning restricts the effectiveness of naive algorithms, thus necessitating sophisticated enhancements.\n\nTable~\\ref{tab:hil_Linf_error} summarizes the results of various approaches provided by each Programmer after 2 rounds of Reviewer intervention. From the best-of-$n$ sample perspective, the superior performance of the agent framework's self-refinement mechanism in solving ill-conditioned matrix problems is amply demonstrated.\n\n\\subsection{Data-driven physical analysis based on dimensional analysis}\\label{subsec: Dimensional anal}\nIn this subsection, we assess the performance of the proposed agent framework in the data-driven physical analysis based on the dimensional analysis. The background of the specific problem we selected is as follows:\n\nDuring laser-metal interaction, a vapor-filled depression (i.e., keyhole) typically forms in the molten metal pool. Induced by vaporization-driven recoil pressure, its dynamics are inherently complex due to multi-physical dependencies. Quantifying this phenomenon is critical, as it directly influences energy absorption and defect formation in diverse industrial applications.\n\nBy leveraging \\text{X-ray} pulses, images of the keyhole region within metals can be captured at micrometer-level spatial resolution. The keyhole depth $e$, measurable from these X-ray images, is contingent on diverse materials and process parameters, including effective laser power ($\\eta_p$), laser scan speed ($V_s$), and laser beam radius ($r_0$).\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n\\includegraphics[width=\\textwidth]{Figs/dimensional_analysis/dimension_Success_Rate_legend.pdf}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n\\includegraphics[width=\\textwidth]{Figs/dimensional_analysis/Dimensional_Success_Rate.pdf}\n\\end{subfigure}\n\\caption{The success rate of Programmers' search algorithms in identifying dominant dimensionless quantities Ke.}\n\\label{fig:dimension_success_rate}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.9\\textwidth}\n\\centering\n\\includegraphics[width=\\textwidth]{Figs/dimensional_analysis/scaling_keyhole.pdf}\n\\end{subfigure}\n\\caption{Fitting curve of the dimensionless number $\\Pi$ as a function of e* derived by all programmers in final response (review-2).}\n\\label{fig:keyhole_scale}\n\\end{figure}\n\nA dataset of keyhole X-ray images was collated from the work of \\citet{zhao2019bulk} and \\citet{gan2021universal}, encompassing 90 experiments across three materials (titanium alloy Ti6Al4V, aluminium alloy Al6061, and stainless steel SS316) under varied process conditions. And materials are characterized by thermal diffusivity ($\\alpha$), density ($\\rho$), heat capacity ($C_p$), and the temperature difference ($T_l-T_0$) between melting and ambient temperatures. Thus, the causal relationship is formalized as:\n\\begin{equation}\ne^* = f(\\eta_p,V_s,r_0,\\alpha,\\rho, C_p, T_l-T_0)\n\\label{equ:Keyhole_}\n\\end{equation}\nWhere the output variable is normalized as the keyhole aspect ratio $e^*=\\frac{e}{r_0}$, a dimensionless parameter widely used to characterize keyhole features~\\citep{fabbro2018analysis}. The aim is to search the dimensionless parameter space based on the $R^2$ criterion for dominant dimensionless numbers in keyhole dynamics, with the following template adopted as the problem description prompt for input into the agent framework:\n\n\\begin{tcolorbox}[\n title={Problem Description Prompt: Keyhole Dimensional Analysis},\n coltitle = blue,\n colback=white, \n colbacktitle=GreenYellow!10, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\nPlease read the CSV data file and consider the data in columns 3, 4, 5, 6, 7, 8 and 11. These columns correspond to seven physical quantities respectively: the effective laser power ($\\eta P$), the laser scan speed ($V_s$), the laser beam radius ($r_0$), the thermal diffusivity ($\\alpha$), the material density ($\\rho$), the heat capacity ($C_p$), and the difference between melting and ambient temperatures ($T_l - T_0$).\\\\\\\\\n\\text{The File path:} \\texttt{/home/Username/dataset\\_keyhole.csv} \\\\\nSome sample data from the CSV file is as follows:\\\\\n\\scriptsize\n\\begin{verbatim}\ncase source etaP Vs r0 alpha rho Cp Tv-T0 Lv Tl-T0 Lm e Ke e*\nkeyhole Mat1 45.62 0.4 4.8e-5 1e-5 3920 830 3267 9.25e+6 1630 2.86e+5 3.3e-5 4.127 0.695\n\n\\end{verbatim}\n\\normalsize \nBased on dimensional analysis and using the data of these physical quantities in the file, please identify the optimal dimensionless quantity formed by combining these parameters, which exhibits the highest coefficient of determination ($R^2$) and thus dominates the variation in the keyhole aspect ratio $e^*$ (data in the last column).\\\\\n\nPlease implement an appropriate method from scratch to solve this problem, primarily using these libraries \\texttt{(numpy, scipy, sklearn, pandas, matplotlib, and pytorch)}.\\\\\n\nEnsure that the resulting dimensionless exponents are normalized by $V_s$ and that the exponents of physical quantities be integers or rational fractions with absolute values not exceeding 3.\n\\end{tcolorbox}\n\nAs established in the work of \\citet{xie2022data}, for the present dimensional analysis problem, the dominant dimensionless number emerging from keyhole dynamics is\n\\begin{equation}\n\\Pi = \\frac{\\eta P}{(T_l - T_0)\\rho C_p \\sqrt{\\alpha V_s r_0^3}}\n\\label{equ:Ke_dimensionless} \n\\end{equation}\nThis dimensionless number exhibits a form identical to the newly discovered keyhole number Ke~\\citep{gan2021universal} (also referred to as normalized enthalpy~\\citep{ye2019energy}), which can be derived from heat transfer theory. Therefore, we adopt the dimensionless number Ke as the metric to evaluate the success rate of the executable code provided by the agent framework. At the end of the above-mentioned prompt template, we propose constraints on dimensionless exponents which are mainly derived from the following physical insights:\n\\begin{enumerate}[(i) ]\n \\item To avoid identifying equivalent dimensionless numbers with different powers and reduce the computational cost, we select the laser scan speed $V_s$ for normalizing the exponents.\n \\item The exponents of dimensionless numbers tend to be rational numbers to maintain dimensional invariance~\\citep{xie2022data}, with a preference for small rational powers such as -1, 1, or 2, etc.\n \\item The typical range of the exponents for dimensionless numbers is limited, with the absolute value of coefficients in most dimensionless numbers and scaling laws being less than 4~\\citep{barenblatt2003scaling}.\n\\end{enumerate}\n\nIn contrast to the crude generation of dimensionless quantities directly via Buckingham's $\\Pi$ theorem, the Programmers consistently adopt grid search and linear regression methods. The specific differences in the implementation of executable code stem from the compatibility between dimensional homogeneity and exponent constraints, as well as the robustness of data extraction.\n\nThe solving success rate, obtained by statistically analyzing the agent's results from multiple attempts to solve this problem, is shown in Figure~\\ref{fig:dimension_success_rate}. Statistically, it can be intuitively observed that as the response stage advances, the success rate of discovering the dimensionless number Ke increases by up to $50\\%$. This improvement arises because, with the involvement of Reviewer, the Programmers revised the implementation details of exponent constraints and ensured strict compliance with dimensional homogeneity.\n\nSpecifically, deficiencies in the implementation logic of the triple exponent constraints could undermine dimensional homogeneity, leading to search results with high coefficients of determination ($R^2$) but physically meaningless; on a more essential level, the agent framework realized that $R^2$ can only measure the goodness of fit for curves but is insufficient to guarantee the dimensional homogeneity of dimensionless numbers.\n\nThe fitting curve of the dimensionless number Ke as a function of the keyhole aspect ratio e* is shown in Figure~\\ref{fig:keyhole_scale}. The high $R^2$ value calculated on a log-log scale further validates the excellent performance of the agent framework in fully solving dimensional analysis problems.\n\n\\section{Conclusions}\\label{sec:Conclusion}\n\nIn this work, we introduced a reliable agent framework for autonomous code generation in scientific computing without domain-specific training. We quantitatively assess its performance in solving PDEs, challenging ill-conditioned linear algebra systems, and conducting data-driven physical analysis. By solving various problems with distinctly different backgrounds, the agent's capability to analyze problems and link them to specific domains through knowledge transfer is fully demonstrated; from both statistical and sampling results perspectives, the agent's ability to progressively perform self-debugging and self-refinement through interaction with runtime outputs is reflected. Therefore, with guidance from the Consultant and feedback from the Reviewer, the algorithms designed by the Programmers achieved significant improvements in performance and robustness, as measured by code execution success rates, solving success rates, and overall accuracy.\n\nThis agent framework provides a collaborative platform for multiple LLMs, overcoming the reasoning limitations of single models. The core modules, Consultant, Programmer, and Reviewer, support heterogeneous model combinations (such as ChatGPT, DeepSeek, and Gemini), and the Reviewer module allows for parallel evaluation by multiple models. Multi-model collaboration can mitigate hallucination issues arising from design flaws in a single model. For instance, in solving the SOD shock tube problem, Gemini 2.5-flash consistently \"stubbornly\" selected the forward Euler scheme; however, after review by ChatGPT 4.1-mini, it shifted toward selecting high-precision time schemes.\n\nLooking ahead, there are several promising directions for enhancing the capabilities of the current agent. The Reviewer module's assessment of code design is based on general and abstract principles for scientific computing, highlighting the need for a more comprehensive, detailed, and quantifiable evaluation system. Additionally, the LLMs in the Reviewer module may encounter token limitations when handling long contexts (such as review comments combined with runtime logs), necessitating the development of information distillation algorithms or adaptations for long-context models. Furthermore, we observed that LLMs generate code with version lag issues (e.g., outdated Python syntax), indicating a need to update and optimize the LLMs themselves or integrate them with domain knowledge bases. As LLMs' reasoning capabilities continue to evolve, the performance of this agent framework is expected to improve further.\n\nIn summary, the agent framework we proposed establishes automatic code generation and review as a promising paradigm in the field of scientific computing, thereby offering a new perspective for physically interpretable and clearly reasoning-grounded algorithm design. \n\n\\section*{Acknowledgements}\nThis work was supported by the National Natural Science Foundation of China (NSFC) Excellence Research Group Program for ``Multiscale Problems in Nonlinear Mechanics'' (No. 12588201). L. Zhang was also supported by the National Natural Science Foundation of China (NSFC) under Grant No. 12202451. The authors would like to thank Zhaobin Li for his suggestions on early topic selection for this paper.\n\n\\section*{Declaration of Interests}\nThe authors report that they have no conflict of interest.\n\n\\appendix\n\\section{\\label{app:prompt_for_agent} Detailed construction of agent prompt}\n% The Consultant model prompt\n\\begin{tcolorbox}[\n title={Consultant model prompt}, \n colback=white, \n colbacktitle=black!60, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\n\\textbf{[Code Expert]} You are a code expert specializing in scientific computing and numerical methods. \n\\begin{enumerate}[(i) ]\n \\item Provide deep technical insights into algorithm implementation, code optimization, and numerical solution strategies.\n \\item Use programming-specific terminology to analyze code structures, identify bugs, and offer advanced coding solutions.\n\\end{enumerate}\n\n\\begin{tcolorbox}[\n colback=gray!10, % 代码块背景色\n colframe=black!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{red!80}{\\textbf{[Task]}}\\\\\nExpand the context of a scientific problem and provide a variety of solution options.\\\\\n\\textcolor{red!80}{\\textbf{[Goal]}}\\\\\nFor specific problems, expand the problem background while maintaining the original meaning and carefully analyze the problems, then provide multiple detailed solution algorithms.\n\n\\begin{tcolorbox}[\n colback=GreenYellow!10, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{blue!80}{\\textbf{[Original Specific Problem]}}\\\\\n$<Problem\\; Description>$\n\n\\end{tcolorbox}\n\n\\textcolor{Melon!95}{\\textbf{[Output Requirement]}}\\\\\nProvide a robust context of the problem, maintaining the same main context, and offer multiple detailed solution plans.\n\\begin{enumerate}[(i) ]\n \\item Expand the original problem's context as much as possible based on its simple outline.\n \\item Please provide a variety of detailed solution plans, with the requirement that each plan is thorough and specific.\n\\end{enumerate}\n\\end{tcolorbox}\n\\end{tcolorbox}\n\n% THE Programmer LLM--first time answer\n\\clearpage\n\\begin{tcolorbox}[\n title={Programmer model prompt (initial answer)}, \n colback=white, \n colbacktitle=black!60, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\n\\textbf{[Code Expert]} You are a code expert specializing in scientific computing and numerical methods. \n\\begin{enumerate}[(i) ]\n \\item Provide deep technical insights into algorithm implementation, code optimization, and numerical solution strategies.\n \\item Use programming-specific terminology to analyze code structures, identify bugs, and offer advanced coding solutions.\n\\end{enumerate}\n\n\\begin{tcolorbox}[\n colback=gray!10, % 代码块背景色\n colframe=black!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{red!80}{\\textbf{[Task]}}\\\\\nFor the specific problem, select an appropriate solving algorithm and generate Python code to complete the problem-solving process.\\\\\n\\textcolor{red!80}{\\textbf{[Goal]}}\\\\\nGenerate structured Python code by first leveraging your understanding based on the detailed descriptions of the specific problem and its solving algorithm.\n\n\\begin{tcolorbox}[\n colback=GreenYellow!10, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{blue!80}{\\textbf{[Original Specific Problem]}}\\\\\n$<Problem\\; Description>$\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[\n colback=SeaGreen!10, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{magenta!80}{\\textbf{[Consultant's expansion]}}\\\\\n$<Complete\\;description\\;of\\;the\\;problem>$\\\\\n$<Descriptions\\;of\\;Multiple\\;solution\\;plans>$\n\\end{tcolorbox}\n\n\\textcolor{Melon!95}{\\textbf{[Output Requirement]}}\\\\\nBased on the specific description of the problem and solving algorithms, select an appropriate framework to accomplish the problem-solving.\\\\\n\\textbf{\\textcolor{Melon}{Ensure the code includes:}}\n\\begin{enumerate}[(i) ]\n \\item Ensure only use \\# for annotations to explain each section of the code.\n \\item Technical explanation for the solving algorithm.\n \\item Implement detailed result printing within the code architecture.\n\\end{enumerate}\n\\textbf{\\textcolor{Melon}{The output code should be enclosed with $\\textit{```}$ as follows:}}\n\\begin{tcolorbox}[\n colback=gray!5, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\scriptsize\n\\begin{verbatim}\n# Technical explanation content\n\n```python:\n\n#Hints:\n#Properly handle the dimensions, indexing, and related operations of arrays or tensors.\n#Provide a bug-free and well-structured code for reproductibility.\n'''\n\n# Optimized explanation content\n\\end{verbatim}\n\\normalsize \n\\end{tcolorbox}\n\\end{tcolorbox}\n\\end{tcolorbox}\n\n% THE Reviewer LLM\n\\clearpage\n\\begin{tcolorbox}[\n title={Reviewer model prompt}, \n colback=white, \n colbacktitle=black!60, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\n\\textbf{[Code Expert]} You are a code expert specializing in scientific computing and numerical methods. \n\\begin{enumerate}[(i) ]\n \\item Provide deep technical insights into algorithm implementation, code optimization, and numerical solution strategies.\n \\item Use programming-specific terminology to analyze code structures, identify bugs, and offer advanced coding solutions.\n\\end{enumerate}\n\n\\begin{tcolorbox}[\n colback=gray!10, % 代码块背景色\n colframe=black!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{red!80}{\\textbf{[Task]}}\\\\\nReview the answer provided by the programmer to the specific problem and provide feedback.\\\\\n\\textcolor{red!80}{\\textbf{[Goal]}}\\\\\nPlease conduct a detailed review according to the complete description of a scientific problem and analyze the results output by the programmer's code.\n\n\\begin{tcolorbox}[\n colback=GreenYellow!10, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{blue!80}{\\textbf{[Original Specific Problem]}}\\\\\n$<Problem\\; Description>$\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[\n colback=SeaGreen!10, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{magenta!80}{\\textbf{[Consultant's expansion]}}\\\\\n$<Complete\\;description\\;of\\;the\\;problem>$\\\\\n$<Descriptions\\;of\\;Multiple\\;solution\\;plans>$\\\\\n\\\\\n\\textcolor{magenta!80}{\\textbf{[Programmer's solution]}}\\\\\n$<Code\\; and\\;Executing\\;Results>$\n\\end{tcolorbox}\n\n\n\\textcolor{Melon!95}{\\textbf{[Output Requirement]} }\\\\\nBased on the detailed analysis of the problem and the Programmer's solution, analyze the results output by the code and provide detailed feedback, guide the programmer in further deepening his understanding of the problem and solving it with greater perfection. \\textbf{\\textcolor{Melon}{Ensure your feedback includes:}}\n\\begin{enumerate}[(i) ]\n \\item Determine whether the programmer has perfectly solved the problem and whether the most appropriate algorithm has been used.\n \\item Assist the programmer in checking and refining runtime errors and warnings in the code.\n \\item Provide suggestions for optimizing the code, including but not limited to algorithm optimization, code structure optimization, and handling of potential errors in the code.\n \\item Your feedback includes posteriori issue identification based on programmer's results, and may also include a priori analysis based on your understanding of the specific problem.\n\\end{enumerate}\n\\end{tcolorbox}\n\\end{tcolorbox}\n\n% THE Programmer LLM --in revise loop\n\\clearpage\n\\begin{tcolorbox}[\n title={Programmer model prompt (in revise loop)}, \n colback=white, \n colbacktitle=black!60, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\n\\textbf{[Code Expert]} You are a code expert specializing in scientific computing and numerical methods. \n\\begin{enumerate}[(i) ]\n \\item Provide deep technical insights into algorithm implementation, code optimization, and numerical solution strategies.\n \\item Use programming-specific terminology to analyze code structures, identify bugs, and offer advanced coding solutions.\n\\end{enumerate}\n\n\\begin{tcolorbox}[\n colback=gray!10, % 代码块背景色\n colframe=black!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{red!80}{\\textbf{[Task]}}\\\\\nFor the specific problem, select an appropriate solving algorithm and generate Python code to complete the problem-solving process.\\\\\n\\textcolor{red!80}{\\textbf{[Goal]}}\\\\\nGenerate structured Python code by first leveraging your understanding based on the detailed descriptions of the specific problem and its solving algorithm.\\\\\n\\textcolor{red!90}{Then fully incorporating feedback from the reviewer model}\n\n\\begin{tcolorbox}[\n colback=GreenYellow!10, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{blue!80}{\\textbf{[Original Specific Problem]}}\\\\\n$<Problem\\; Description>$\n\\end{tcolorbox}\n\n\\begin{tcolorbox}[\n colback=SeaGreen!10, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\textcolor{magenta!80}{\\textbf{[Programmer's previous solution]}}\\\\\n$<Code\\; and\\;Executing\\;Results>$\\\\\n\\\\\n\\textcolor{magenta!80}{\\textbf{[Reviewer's Feedback]}}\\\\\n$<Advice\\;to\\;Algorithm\\;and\\;Debug>$\n\\end{tcolorbox}\n\n\\textcolor{Melon!95}{\\textbf{[Output Requirement]}}\\\\\nGenerate refined Python code by rationally incorporating feedback from the reviewer model, based on your comprehensive understanding of the specific problem and its solving algorithms.\\\\\n\\textbf{\\textcolor{Melon}{Ensure the code includes:}}\n\\begin{enumerate}[(i) ]\n \\item Ensure only use \\# for annotations to explain each section of the code.\n \\item Technical explanation for the solving algorithm.\n \\item Implement detailed result printing within the code architecture.\n \\item Explain the specific parts of the code that have been optimized.\n\\end{enumerate}\n\\textbf{\\textcolor{Melon}{The output code should be enclosed with $\\textit{```}$ as follows:}}\n\\begin{tcolorbox}[\n colback=gray!5, % 代码块背景色\n colframe=gray!30, % 代码块边框色\n boxrule=0.5pt, % 边框粗细\n arc=2pt, % 圆角\n width=\\linewidth,\n boxsep=4pt,\n left=5pt, right=5pt, top=3pt, bottom=3pt\n]\n\\scriptsize\n\\begin{verbatim}\n# Technical explanation content\n\n```python:\n\n#Hints:\n#Properly handle the dimensions, indexing, and related operations of arrays or tensors.\n#Provide a bug-free and well-structured code for reproductibility.\n'''\n\n# Optimized explanation content\n\\end{verbatim}\n\\normalsize \n\\end{tcolorbox}\n\n\\end{tcolorbox}\n\\end{tcolorbox}\n\n\\clearpage\n\\section{\\label{app:pdebench_details} Detailed description of PDEs}\n\\subsection{\\label{subapp:pde_burgers}Burgers equation}\nThe Burgers equation is a prototypical PDE that couples a nonlinear convective term and a viscous diffusion term~\\citep{benton1972table}. When the viscosity coefficient $\\nu$ is small, the nonlinear convective term dominates, causing the initially smooth velocity profile to gradually form discontinuous abrupt changes (i.e., shock waves).\n\nThe specific equations and initial/boundary conditions are detailed in the following template of the problem description prompt for input into the agent framework:\n\\begin{tcolorbox}[\n title={Problem Description Prompt: Burgers Equation},\n coltitle = blue,\n colback=white, \n colbacktitle=GreenYellow!10, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\nThe PDE of 1-D Burgers equation is given by:\\\\\n\\[\\frac{\\partial u}{\\partial t} + u u_x - \\nu u_{xx} = 0, (x,t) \\in \\Omega\\]\\\\\nwhere the domain is defined as $(x,y)\\in \\Omega = [-1,1]\\times [0,1]$, the the parameter is $\\nu=\\frac{0.01}{\\pi}$. The initial and boundary conditions are:\\\\\n\\[\\begin{cases}\nu(x,0)= -sin(\\pi x)\\\\\nu(-1,t)=u(1,t)=0\n\\end{cases}\\]\nPlease primarily use these libraries (\\texttt{numpy, scipy, matplotlib}) to implement an appropriate method from scratch to solve this problem.\\\\\nPlot the contour of \\(u(x,t)\\) in one figure.\n\\end{tcolorbox}\n\nThe statistical results of each programmer repeatedly answering the problem within the proposed agent framework are shown in Figures~\\ref{fig:Burgers_exe_rate}-\\ref{fig:Burgers_best_3LLMsl}, including the code execution success rate and the relative error boxplot, both from a statistical perspective, as well as the optimal runtime outputs in the final response (review-2) from the best-of-$n$ sample perspective.\n\n\\clearpage\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Burgers/Burgers_Execution_Success_Rate.pdf}}\n\\end{subfigure}\n \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Burgers equation.}\n\\label{fig:Burgers_exe_rate}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Burgers/Burgers_Error_Box.pdf}}\n\\end{subfigure}\n \\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n\\label{fig:Burgers_error_box}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n\\begin{subfigure}[b]{0.95\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Burgers_contours.pdf}}\n\\end{subfigure}\n \\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n \\label{fig:Burgers_best_3LLMsl}\n\\end{figure}\n\n\\clearpage\n\\subsection{\\label{subapp:Sod_Shock}Sod shock tube}\nThe Sod shock tube problem~\\citep{sod1978survey} is a classic one-dimensional PDE system as depicted in Figure~\\ref{Fig_schematic_sod_sb}. The governing equations for this problem are the Euler equations simplified from the compressible NS equations, used to describe the wave systems in inviscid compressible flows.\n\nAt the initial time $t=0$, the left domain of the diaphragm is occupied by high-pressure gas, while the right domain contains low-pressure gas. Upon removal of the diaphragm at $t>0$, the high-pressure gas undergoes rapid expansion into the low-pressure region on the right, generating three distinct wave systems.\n\n\\begin{enumerate}[(i) ]\n \\item a left-traveling rarefaction wave where pressure and density exhibit continuous variation across the wave front, with velocity gradually increasing to its peak.\n \\item a right-traveling shock wave where pressure and density sharply increase across the shock wave front while velocity decreases abruptly.\n \\item a contact between the two waves, where pressure and velocity remain continuous across the discontinuity surface, but density experiences an abrupt jump.\n\\end{enumerate}\n\nThe specific equations and initial/boundary conditions are detailed in the following template of the problem description prompt for input into the agent framework:\n\\begin{tcolorbox}[\n title={Problem Description Prompt: Sod Shock Tube},\n coltitle = blue,\n colback=white, \n colbacktitle=GreenYellow!10, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\nThe PDEs of 1-D Euler equations are given by:\n\\[\\begin{cases}\n\\vspace{2mm}\n\\frac{\\partial \\rho}{\\partial t} + \\frac{\\partial (\\rho u)}{\\partial x} = 0,\\\\\n\\vspace{2mm}\n\\frac{\\partial (\\rho u)}{\\partial t} + \\frac{\\partial (\\rho u^2 + p)}{\\partial x} = 0, \\\\\n\\frac{\\partial (\\rho E)}{\\partial t} + \\frac{\\partial (\\rho E u + p u)}{\\partial x} = 0,\n\\end{cases}\\]\nwhere the total energy \\(E = \\frac{1}{2} u^2 + \\frac{p}{(\\gamma - 1)\\rho}\\) and the adiabatic index \\(\\gamma = 1.4\\).\\\\\nAt \\(t = 0\\), the initial conditions in the interval \\(x \\in [0,1]\\) are:\n\\[(\\rho, u, p) = \n\\begin{cases}\n(1.0, 0.0, 1.0), & 0 < x \\leq 0.5, \\\\\n(0.125, 0.0, 0.1), & 0.5 \\leq x < 1.\n\\end{cases}\\]\nPlease primarily use these libraries (\\texttt{numpy, scipy, matplotlib}) to implement an appropriate method from scratch to solve this problem.\\\\\nPlot the density \\(\\rho\\), velocity \\(u\\), and pressure \\(p\\) at \\(t = 0.2\\) in one figure.\n\\end{tcolorbox}\n\nIn Figure~\\ref{fig:Sod_exe_rate}, the code execution success rates of \\textbf{Gpt-4.1-mini} and \\textbf{Gemini-2.5-flash} as Programmers each exhibit a decline during the review-1 stage, followed by a subsequent recovery. To explain this trend, additional statistics on the proportions of numerical methods employed by each Programmer across different response stages were compiled, as presented in Figures~\\ref{fig:Sod_space_method}-\\ref{fig:Sod_time_method}. Results indicate that with Reviewer intervention, the proportional distribution of spatiotemporally high-order schemes increased significantly, which improved the accuracy but also elevated the risk of introducing bugs or NaN values in specific code implementations due to the inherent complexity of these schemes.\n\nThe boxplot of relative errors and the 1D physical quantity plots compiled from runtime outputs are presented in Figure~\\ref{fig:Sod_error_box} and ~\\ref{fig:Sod_3LMMs_best_plots}, respectively. From both statistical and best-of-$n$ sample perspectives, the agent framework demonstrates excellent performance in solving this problem.\n\n\\clearpage\n\\begin{figure}\n\\centering{\\includegraphics[width=0.35\\textwidth]{Figs/Sod_sb_schem.pdf}}\n\\caption{Schematic of the Sod shock tube with initial conditions at $t=0$}\n\\label{Fig_schematic_sod_sb}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/SodShock_Execution_Success_Rate.pdf}}\n\\end{subfigure}\n \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Sod shock tube problem.}\n\\label{fig:Sod_exe_rate}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/Sod_Space_method_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/Sod_Space_method_protion.pdf}}\n\\end{subfigure}\n \\caption{Proportional distribution of the spatial reconstruction schemes employed by Programmers. All Programmers selected the Harten–Lax–vanLeer–Contact (HLLC) Riemann solver during the sampling process.}\n\\label{fig:Sod_space_method}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/Sod_Time_method_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/Sod_Time_method_protion.pdf}}\n\\end{subfigure}\n \\caption{Proportional distribution of the time integration methods employed by Programmers.}\n\\label{fig:Sod_time_method}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_u.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_p.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Sod_shock/SodShock_Error_Box_Rho.pdf}}\n\\end{subfigure}\n \\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers. (a) velocity $u$, (b) pressure $p$, (c) density $\\rho$.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n\\label{fig:Sod_error_box}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_u.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_rho.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_SodShock_contours_p.pdf}}\n\\end{subfigure}\n \\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n\\label{fig:Sod_3LMMs_best_plots}\n\\end{figure}\n\n\\clearpage\n\\subsection{\\label{subapp:pde_Poisson}Poisson equation}\nThe Poisson equation~\\citep{strauss2007partial}, as a typical elliptic partial differential equation, the uniqueness of its solution is completely determined by the boundary conditions. In this case, the solution domain is a multiply connected domain formed by a rectangle with four symmetric circular holes excavated. This complex configuration composed of a regular outer boundary and an irregular inner boundary poses challenges to numerical methods.\n\nThe specific equations and initial/boundary conditions are detailed in the following template of the problem description prompt for input into the agent framework:\n\n\\begin{tcolorbox}[\n title={Problem Description Prompt: Poisson Equation},\n coltitle = blue,\n colback=white, \n colbacktitle=GreenYellow!10, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\nThe PDE of 2-D Poisson equation is given by:\n\\[\\Delta u = 0, (x,y) \\in \\Omega\\]\nThe domain is a rectangle minus several circles \\(\\Omega = \\Omega_{\\text{rec}} \\setminus \\Omega_{\\text{circle}}\\), where \\(\\Omega_{\\text{rec}} = [-0.5, 0.5]^2\\) is the rectangle, and the circles \\(\\Omega_{\\text{circle}} = \\bigcup_{i = 1}^{4} R_i\\) are defined as:\n\\[\\begin{cases}\nR_1 = \\left\\{ (x,y) : (x - 0.3)^2 + (y - 0.3)^2 \\leq 0.1^2 \\right\\} \\\\\nR_2 = \\left\\{ (x,y) : (x + 0.3)^2 + (y - 0.3)^2 \\leq 0.1^2 \\right\\} \\\\\nR_3 = \\left\\{ (x,y) : (x - 0.3)^2 + (y + 0.3)^2 \\leq 0.1^2 \\right\\} \\\\\nR_4 = \\left\\{ (x,y) : (x + 0.3)^2 + (y + 0.3)^2 \\leq 0.1^2 \\right\\} \\\\\n\\end{cases}\\]\nThe boundary conditions are:\n\\[\\begin{cases}\nu = 0,\\, x \\in \\partial \\Omega_{\\text{circle}} \\\\\nu = 1,\\, x \\in \\partial \\Omega_{\\text{rec}} \\\\\n\\end{cases}\\]\nPlease primarily use these libraries (\\texttt{numpy, scipy, matplotlib}) to implement an appropriate method from scratch to solve this problem.\\\\\nPlot the contour of \\(u(x,y)\\) in one figure, and mark the circles in the plot.\n\\end{tcolorbox}\n\nThe statistical results of each programmer repeatedly answering the problem within the proposed agent framework are shown in Figures~\\ref{fig:Poisson_exe_rate}-\\ref{fig:Poisson_best_3LLMsl} including the code execution success rate and relative error boxplot from a statistical perspective, as well as the optimal runtime outputs in the final response (review-2) from the best-of-n sample perspective.\n\n\\clearpage\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Poisson_/Poisson_Execution_Success_Rate.pdf}}\n\\end{subfigure}\n \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Poisson equation.}\n\\label{fig:Poisson_exe_rate}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Poisson_/Poisson_Error_Box.pdf}}\n\\end{subfigure}\n \\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n\\label{fig:Poisson_error_box}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.95\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Poisson_contours.pdf}}\n\\end{subfigure}\n\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n\\label{fig:Poisson_best_3LLMsl}\n\\end{figure}\n\n\\clearpage\n\\subsection{\\label{subapp:pde_Helmholtz}Helmholtz equation}\n\nThe Helmholtz equation~\\citep{strauss2007partial}, a time-independent form of the wave equation, often emerges in spatiotemporal PDE studies. Derived via separation of variables to simplify analysis, it captures steady-state wave behaviors. As a typical elliptic PDE, the uniqueness of its solution is jointly determined by the boundary conditions and the wave number $k$. In this case, the solution domain is a simple rectangular region with four circular holes excavated, forming a multiply-connected domain.\n\nThe specific equations and initial/boundary conditions are detailed in the following template of the problem description prompt for input into the agent framework:\n\n\\begin{tcolorbox}[\n title={Problem Description Prompt: Helmholtz Equation},\n coltitle = blue,\n colback=white, \n colbacktitle=GreenYellow!10, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\nThe PDE of 2-D Helmholtz equation is given by:\n\\[-\\Delta u + k^2u = f(x,y), (x,y) \\in \\Omega\\]\nThe function f(x) is defined as:\n\\[f(x)=A\\cdot\\left(\\sum_{i}\\mu_{i}^{2}+x_{i}^{2}\\right)\\sin(\\mu_{1}\\pi x_{1})\\sin(\\mu_{2}\\pi x_{2})\\]\nThe parameter values are:\n\\[\\mu_1 = 1,\\quad \\mu_2 = 4,\\quad k = 8,\\quad A = 10\\]\nThe domain is a rectangle minus several circles \\(\\Omega = \\Omega_{\\text{rec}} \\setminus \\Omega_{\\text{circle}}\\), where \\(\\Omega_{\\text{rec}} = [-1, 1]^2\\) is the rectangle, and the circles \\(\\Omega_{\\text{circle}} = \\bigcup_{i = 1}^{4} R_i\\) are defined as:\n\\[\\begin{cases}\nR_{1}=\\left\\{(x,y):(x - 0.5)^{2}+(y - 0.5)^{2}\\leq0.2^{2}\\right\\}\\\\\nR_{2}=\\left\\{(x,y):(x - 0.4)^{2}+(y + 0.4)^{2}\\leq0.4^{2}\\right\\}\\\\\nR_{3}=\\left\\{(x,y):(x + 0.2)^{2}+(y + 0.7)^{2}\\leq0.1^{2}\\right\\}\\\\\nR_{4}=\\left\\{(x,y):(x + 0.6)^{2}+(y - 0.5)^{2}\\leq0.3^{2}\\right\\}\\\\\n\\end{cases}\\]\nThe boundary conditions are:\n\\[\\begin{cases}\nu = 0.2, & x\\in\\partial\\Omega_{\\text{rec}}\\\\\nu = 1, & x\\in\\partial\\Omega_{\\text{circle}}\n\\end{cases}\\]\nPlease primarily use these libraries (\\texttt{numpy, scipy, matplotlib}) to implement an appropriate method from scratch to solve this problem.\\\\\nPlot the contour of \\(u(x,y)\\) in one figure, and mark the circles in the plot.\n\\end{tcolorbox}\n\nThe statistical results of each programmer repeatedly answering the problem within the proposed agent framework are shown in Figures~\\ref{fig:Helmholtz_exe_rate}-\\ref{fig:Helmholtz_best_3LLMsl} including the code execution success rate and relative error boxplot from a statistical perspective, as well as the optimal runtime outputs in the final response (review-2) from the best-of-n sample perspective.\n\n\\clearpage\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Helmholtz/Helmholtz_Execution_Success_Rate.pdf}}\n\\end{subfigure}\n \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Helmholtz equation.}\n\\label{fig:Helmholtz_exe_rate}\n\\end{figure}\n\n\\begin{figure}\n \\centering\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Helmholtz/Helmholtz_Error_Box.pdf}}\n\\end{subfigure}\n \\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n\\label{fig:Helmholtz_error_box}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.95\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Helmholtz_contours.pdf}}\n\\end{subfigure}\n\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n\\label{fig:Helmholtz_best_3LLMsl}\n\\end{figure}\n\n\\clearpage\n\\subsection{\\label{subapp:pde_Lid-Driven}Lid-driven Cavity}\nLid-driven cavity flow~\\citep{ghia1982high} refers to a flow phenomenon in which a specified velocity is imposed on the top boundary of a closed cavity, whereas the other boundaries remain stationary. The governing equations are the incompressible steady NS equations, which describe the motion of the fluid inside the cavity under the influence of viscosity.\n\nSince the divergence-free continuity equation does not explicitly contain pressure while the momentum equations rely on pressure gradients, the pressure and velocity fields cannot be solved independently, thus requiring special algorithms to handle the pressure-velocity coupling.\n\nMeanwhile, the nonlinear convection terms lead to numerical issues such as iterative divergence or slow convergence. The above two inherent properties of the governing equations both pose significant challenges for robust numerical solutions.\n\nThe specific equations and initial/boundary conditions are detailed in the following template of the problem description prompt for input into the agent framework:\n\\begin{tcolorbox}[\n title={Problem Description Prompt: Lid-driven flow},\n coltitle = blue,\n colback=white, \n colbacktitle=GreenYellow!10, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\nThe governing PDEs for 2D steady incompressible NS equations are given by:\n\\[\\begin{cases}\nu \\frac{\\partial u}{\\partial x} + v \\frac{\\partial u}{\\partial y} + \\frac{\\partial p}{\\partial x} - \\frac{1}{\\mathrm{Re}} \\left( \\frac{\\partial^2 u}{\\partial x^2} + \\frac{\\partial^2 u}{\\partial y^2} \\right) = 0, (x,y) \\in \\Omega,\\\\\nu \\frac{\\partial v}{\\partial x} + v \\frac{\\partial v}{\\partial y} + \\frac{\\partial p}{\\partial y} - \\frac{1}{\\mathrm{Re}} \\left( \\frac{\\partial^2 v}{\\partial x^2} + \\frac{\\partial^2 v}{\\partial y^2} \\right) = 0, (x,y) \\in \\Omega,\\\\\n\\frac{\\partial u}{\\partial x} + \\frac{\\partial v}{\\partial y} = 0, (x,y) \\in \\Omega,\\\\\n\\end{cases}\\]\nThe Reynolds number Re = 100. The domain is \\(\\Omega = ([0, 2]^2\\), and the top boundary is \\(\\Gamma_1\\), the left, right and bottom boundary is \\(\\Gamma_2\\). The boundary conditions are:\n\\[\\begin{cases}\n(u,v) = (\\alpha(x(1-x)), 0), (x,y) \\in \\Gamma_1\\\\\n(u,v) = (0,0), (x,y) \\in \\Gamma_2\\\\\n\\text{Reference pressure: } p(x=0,y=0) = 0\\\\\n\\text{Zero normal pressure gradient: } \\frac{\\partial p}{\\partial n} = 0, (x,y) \\in \\partial\\Omega\n\\end{cases}\\]\nwhere \\(\\alpha\\) is 2. Please primarily use these libraries (\\texttt{numpy, scipy, matplotlib}) to implement an appropriate method from scratch to solve this problem.\\\\\nPlot the contour of the velocity magnitude with the streamlines, velocity \\(u\\), \\(v\\) and pressure \\(p\\) in four figures, respectively.\n\\end{tcolorbox}\n\n\n\\clearpage\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Lid_cavity/Cavity_NS_Execution_Success_Rate.pdf}}\n\\end{subfigure}\n \\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the Lid-driven flow.}\n\\label{fig:Lid-cavity-ExeSucess}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Lid_cavity/Cavity_NS_Error_Box.pdf}}\n\\end{subfigure}\n\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n\\label{fig:Lid-cavity-boxError}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.95\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/PDE_all_Average/3LLMs_Lid_driven_contours.pdf}}\n\\end{subfigure}\n\\caption{The best runtime outputs of the executable code provided by each Programmer in the final response (review-2).}\n\\label{fig:Lid_driven_best_3LLMsl}\n\\end{figure}\n\n\n\\clearpage\n\\subsection{\\label{subapp:pde_Unsteady_NS}Unsteady NS equation}\nThe specific equations and initial/boundary conditions are detailed in the following template of the problem description prompt for input into the agent framework:\n\\begin{tcolorbox}[\n title={Problem Description Prompt: Unsteady Incompressible NS equation},\n coltitle = blue,\n colback=white, \n colbacktitle=GreenYellow!10, \n colframe=gray!50, \n fonttitle=\\bfseries, % 标题字体加粗\n width=\\linewidth, % 宽度占满行\n boxsep=6pt, % 内边距（调整内容与边框距离）\n top=3pt, bottom=3pt, left=3pt, right=3pt % 四边边距\n]\nThe governing PDEs for 2D unsteady incompressible NS equations are given by:\n\\[\\begin{cases}\n\\frac{\\partial u }{\\partial t} + u \\frac{\\partial u}{\\partial x} + v \\frac{\\partial u}{\\partial y} + \\frac{\\partial p}{\\partial x} - \\frac{1}{\\mathrm{Re}} \\left( \\frac{\\partial^2 u}{\\partial x^2} + \\frac{\\partial^2 u}{\\partial y^2} \\right) = f_x, (x,y) \\in \\Omega,\\\\\n\\frac{\\partial v }{\\partial t} + u \\frac{\\partial v}{\\partial x} + v \\frac{\\partial v}{\\partial y} + \\frac{\\partial p}{\\partial y} - \\frac{1}{\\mathrm{Re}} \\left( \\frac{\\partial^2 v}{\\partial x^2} + \\frac{\\partial^2 v}{\\partial y^2} \\right) = f_y, (x,y) \\in \\Omega,\\\\\n\\frac{\\partial u}{\\partial x} + \\frac{\\partial v}{\\partial y} = 0, (x,y) \\in \\Omega,\\\\\n\\end{cases}\\]\nThe Reynolds number Re = 100. The domain is \\(\\Omega \\times T = ([0, 2] \\times [0, 1]) \\times [0, 0.5]\\), and the forcing term \\(f(x, y, t)\\) can be given as:\n\\[f(x, y, t) = (0, -\\sin(\\pi x) \\sin(\\pi y) \\sin(\\pi t)).\\]\nThe boundary conditions are specified as follows:\\\\\nNo-slip condition on the top and bottom walls \\(\\Gamma_1\\):\n\\[(u, v) = (0, 0), (x, y) \\in \\Gamma_1.\\]\nInlet condition at the left boundary \\(\\Gamma_2\\):\n\\[\\begin{cases}\nu(0, y, t) = \\sin(\\pi y) \\left(\\sin(\\pi t) + \\sin(3\\pi t) + \\sin(5\\pi t) \\right)\\\\\nv(0, y, t) = 0\n\\end{cases}\\]\nOutlet condition at the right boundary \\(\\Gamma_3\\):\n\\[\\begin{cases}\n\\frac{\\partial u}{\\partial x} = \\frac{\\partial v}{\\partial x} = 0\\\\\np(2, y, t) = 0\n\\end{cases}\\]\nThe initial condition in the domain is:\n\\[u(x, y, 0) = v(x, y, 0) = 0, (x,y) \\in \\Omega\\]\nPlease primarily use these libraries (\\texttt{numpy, scipy, matplotlib}) to implement an appropriate method from scratch to solve this problem.\\\\\nSolve the Poisson equation using GMRES iteration methods.\\\\\nPlot the contour of the velocity \\(u\\), \\(v\\) and pressure \\(p\\) at timestep t = 0.5 in three figures, respectively.\n\\end{tcolorbox}\n\nThe statistical results of each programmer repeatedly answering the problem within the proposed agent framework are shown in Figure~\\ref{fig:LT_NS_sucessRate} and \\ref{fig:LT_NS_boxError} including the code execution success rate and streamwise velocity relative error boxplot from the statistical perspective.\n\n\\clearpage\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.6\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Exe_Success_Rate_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Execution_Success_Rate.pdf}}\n\\end{subfigure}\n\\caption{Execution success rate of the numerical algorithms employed by Programmers to solve the unsteady NS equation.}\n\\label{fig:LT_NS_sucessRate}\n\\end{figure}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/LT_NS/LT_NS_Error_Box.pdf}}\n\\end{subfigure}\n\\caption{Boxplot of Relative $L^2$ error for successful solutions by Programmers.The \\textbf{annotated numbers} in the figure indicate the mean relative $L^2$ errors.}\n\\label{fig:LT_NS_boxError}\n\\end{figure}\n\n\\clearpage\n\\section{Relative errors from the best-of-n sample perspective}\n\n\\subsection{Partial differential equation benchmark}\n\n\\begin{table}[h]\n\\begin{center}\n\\renewcommand{\\arraystretch}{1.2}\n\\begin{tabular}{c|ccc|c}\n\\cline{1-5}\nProgrammer & Gpt-4.1-mini & Gemini-2.5-flash & Deepseek-R1 & Quantity\\\\ \\cline{1-5}\nBurgers & $1.98\\times10^{-2}$ & $\\mathbf{1.82\\times10^{-2}}$ & $1.85\\times10^{-2}$ & $u(x,t)$\\\\\nSod Shock & $3.60\\times10^{-2}$ & $5.81\\times10^{-2}$ & $\\mathbf{2.31\\times10^{-2}}$ & $u(x,t)$\\\\\nPoisson & $9.90\\times10^{-3}$ & $1.18\\times10^{-2}$ & $\\mathbf{7.15\\times10^{-3}}$ & $u(x,y)$\\\\\nHelmholtz & $2.30\\times10^{-2}$ & $2.09\\times10^{-2}$ & $\\mathbf{1.47\\times10^{-2}}$ & $u(x,y)$\\\\\nLid-Driven & $\\mathbf{2.74\\times10^{-3}}$ & $6.55\\times10^{-3}$ & $8.77\\times10^{-3}$ & $\\|\\vec{u}\\|$\\\\\nUnsteady NS & $1.89\\times10^{-2}$ & $1.83\\times10^{-2}$ & $\\mathbf{1.81\\times10^{-2}}$ & $u(x,y)$ \\\\ \\cline{1-5}\n\\end{tabular}\n\\caption{The summary of $L^2$ relative error for the final refined runtime outputs after two rounds of Reviewer intervention (review-2) across all cases in PDEbench.}\n\\label{tab:pdebench_overall_best_rel_error}\n\\end{center}\n\\end{table}\n\nTable~\\ref{tab:pdebench_overall_best_rel_error} summarizes the relative errors of each programmer's optimal runtime outputs in the final response (review-2) against the reference solutions, with the reference physical quantities for comparison in the last column.\n\n\n\n\\subsection{Hilbert linear algebraic systems}\n\n\\begin{figure}\n\\centering\n\\begin{subfigure}[b]{0.8\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hilbert_diffStage_legend.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-NaN_protion.pdf.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-overThrehold_protion.pdf}}\n\\end{subfigure}\n\\begin{subfigure}[b]{0.85\\textwidth}\n\\centering\n{\\includegraphics[width=\\textwidth]{Figs/Hilbert_Matrix/Hil_rate-belowThrehold_protion.pdf}}\n\\end{subfigure}\n\\caption{Proportional distribution of specific numerical methods employed by Programmers across three completion statuses, serving as a detailed elaboration to the solution success rate. (a) Results Contain NaN; (b) Over $L^\\infty$ threshold; (c) Below $L^\\infty$ threshold.}\n\\label{fig:Hil_diff_stage_proportion}\n\\end{figure}\n\n\\begin{table}\n\\begin{center}\n\\renewcommand{\\arraystretch}{1.2}\n\\begin{tabular}{c|c|ccccc}\n\\cline{1-7}\n\\multirow{2}{*}{Programmer} & \\multirow{2}{*}{Methods} & \\multicolumn{5}{c}{$L^\\infty$ error w.r.t. matrix size $n$} \\\\ \\cline{3-7}\n& & 5&10&15&20&25\\\\ \\cline{1-7}\n\\multirow{5}{*}{\\makecell{Gpt-4.1-mini}} & Chol-Reg & 3.08e-04&6.81e-04&9.66e-04&1.36e-03&1.36e-03\\\\\n% \\\\Answer-0 20\\\\Review-1 30\\\\Review-2 35\n& LU-Reg & 3.15e-04&8.77e-04&8.92e-04&1.38e-03&1.37e-03\\\\\n& QR-Reg & 3.20e-04&9.90e-04&1.18e-03&1.31e-03&1.62e-03\\\\\n& Pre-CG & \\textbf{9.80e-12}&8.79e-05&7.16e-05&\\textbf{4.32e-05}&\\textbf{9.96e-05}\\\\\n& SVD & 1.46e-11&7.32e-04&3.91e-03&7.81e-03&7.32e-04\\\\ \\cline{1-7}\n\\multirow{4}{*}{\\makecell{Gemini-2.5-flash}} & Chol-Reg & 8.64e-04&1.12e-03&1.45e-03&1.61e-03&1.73e-03 \\\\\n% \\\\Answer-0 28\\\\Review-1 34\\\\Review-2 35\n% & Chol-Iter &3.26e-03&3.08e-03&2.99e-03&3.86e-03&4.01e-03\\\\ \\cline{2-7}\n& CG & 4.49e-04&9.34e-04&4.85e-04&6.60e-04&4.23e-04\\\\\n& Pre-CG & 8.44e-04&5.57e-04&5.19e-04&7.50e-04&7.41e-04\\\\\n& SVD & 7.13e-04&4.76e-04&5.36e-04&5.02e-04&6.30e-04 \\\\ \\cline{1-7}\n\\multirow{5}{*}{\\makecell{Deepseek-R1}} &Chol-Reg & 1.11e-09&\\textbf{3.84e-05}&\\textbf{5.05e-05}&1.45e-04&2.68e-04\\\\\n% \\\\Answer-0 27\\\\Review-1 35\\\\Review-2 46\n& LU-Reg & 1.11e-09&8.61e-05&1.81e-04&1.51e-04&2.01e-04\\\\\n& QR-Reg & 3.80e-03&6.07e-04&1.01e-03&1.10e-03&1.31e-03\\\\\n& CG & 5.42e-11&5.99e-04&3.93e-04&2.09e-04&4.30e-04\\\\\n& Pre-CG & \\textbf{9.80e-12}&6.01e-04&3.95e-04&2.08e-04&4.32e-04\\\\ \\cline{1-7}\n\\end{tabular}\n\\caption{The summary of $L^\\infty$ errors in solving linear systems with Hilbert matrices via various methods provided by each Programmer in the final response (review-2).}\n\\label{tab:hil_Linf_error}\n\\end{center}\n\\end{table}\n\nFigure~\\ref{fig:Hil_diff_stage_proportion}, serving as the supplement and underpinning for subsequent sampling, presents the proportions of different methods across the three completion statuses of executable code. It provides a more detailed illustration of the adaptability that regularization techniques and iterative methods outperform naive approaches in solving ill-conditioned matrices.\n\nTable~\\ref{tab:hil_Linf_error} summarizes the relative errors of the various methods provided by each programmer in the final response (review-2). The significant order-of-magnitude reduction in relative errors of the various methods compared to the naive methods in Figure~\\ref{fig:hil_naive_cond} fully demonstrates the generalizability of the agent framework.\n\n\\clearpage\n\n\\bibliographystyle{unsrtnat}\n% Note the spaces between the initials\n\\bibliography{references}\n\n\\end{document}\n"},"question":{"kind":"string","value":"What is the minimum mode value in the given table (apart from the row heads and column heads) and for what LLM agent framework it is?"},"answer":{"kind":"string","value":"CodePDE Agent : based on posterior error,Our Agent: Multiple"},"plan":{"kind":"null"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":3,"numItemsPerPage":100,"numTotalItems":371,"offset":300,"length":100}},"jwt":"eyJhbGciOiJFZERTQSIsImtpZCI6IjVHZDBvd0g5MTM2eDZjc1FvbE1zcktNWUZoRVFoUm5PVVVybEpjOUhaUEEifQ.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc4NTcwMzcwMCwianRpIjoiMjlhYzc0ZWItNjVjMS00M2ZlLWI1OWQtMzBiM2VhODc1NjI3Iiwic3ViIjoiL2RhdGFzZXRzL2podS1jbHNwL1NjaVRhUkMiLCJleHAiOjE3ODU3MDczMDAsImlzcyI6Imh0dHBzOi8vaHVnZ2luZ2ZhY2UuY28ifQ.6DNUT4kDsVoLhqZ7e3k4UJZNF1mpCBG1kXSSWkwW6V8cXEwEhJYKFIbhAe7nUyFI5PvWHwjmXsKWf592dHNzBQ","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"test","numRows":371,"numBytesParquet":13748575}]},"discussionsStats":{"closed":0,"open":1,"total":1},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">
paper stringlengths 10 10 | relevant_tables listlengths 1 3 | tables listlengths 3 55 | fulltext stringlengths 27.1k 359k | question stringlengths 36 601 | answer stringlengths 1 126 | plan stringlengths 76 1.47k ⌀ |
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2509.05208 | [
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\documentclass[11pt]{article}
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\synctex=-1
\usepackage{fix-cm}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\usepackage{b... | Which domain has the highest average object score across all models and how much higher is it when compared to that of the model with the third highest average object score? | DINO, 0.3093 | SELECT all domains
LOOP for each domain
COMPUTE domain_avg = average of obj scores of this domain across all models
COMPUTE rank_domains = rank domains by domain_avg descending
COMPUTE best_domain = domain at rank 1
COMPUTE best_domain_avg = domain_avg of best_domain
SELECT all models
LOOP for each model
COMP... |
2509.05208 | [
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\documentclass[11pt]{article}
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\usepackage{bm}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\usepackage{b... | What is the average of the difference between the average object scores of all open sourced and all closed source models across all domains? | 0.0433 | SELECT all closed-source models
COMPUTE closed_avg = average of obj scores for closed-source models across all domains
SELECT all open-source models
COMPUTE open_avg = average of obj scores for open-source models across all domains
COMPUTE result = closed_avg − open_avg
RETURN result
|
2509.05075 | [
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"\t\t\t\t\tMethod & Metric & R0 & R1 & R2 & OFF0 & OFF1 & OFF2 & OFF3 & OFF4 \\\\\n",
"\t\t\t\t\t\\hline\n",
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... | \documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left)... | What is the best method when measured on average PSNR across all datasets? And how much better is it compared to the next best model? | GeoSplat, w/ Manifold-based Priors, 0.02 | SELECT all methods
LOOP for each method
COMPUTE avg_psnr = average of psnr scores across datasets
COMPUTE rank_methods = rank methods by avg_psnr descending
COMPUTE best_method = method at rank 1
COMPUTE second_best_method = method at rank 2
COMPUTE difference = avg_psnr of best_method − avg_psnr of second_best_m... |
2509.05075 | [
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"\t\t\\begin{table*}[t]\n",
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"\t\t\t\t\t\\hline\n",
"\t\t\t\t\tMethod & Metric & R0 & R1 & R2 & OFF0 & OFF1 & OFF2 & OFF3 & OFF4 \\\\\n",
"\t\t\t\t\t\\hline\n",
... | [
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"\t\t\\begin{table*}[t]\n",
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... | \documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left)... | Which is the third best dataset in terms of average across all SSIM scores and what is its differnce from the score of the fifth best dataset in terms of LPIPS score? | OFF4, 0.8663 | SELECT all datasets
LOOP for each dataset
COMPUTE avg_ssim = average of ssim scores across methods for this dataset
COMPUTE rank_ssim = rank datasets by avg_ssim descending
COMPUTE third_best_dataset = dataset at rank 3 in rank_ssim
SELECT all datasets
LOOP for each dataset
COMPUTE avg_lpips = average of lpip... |
2505.12415 | [
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"\\caption{In \\ourmethod{}, we adopt the Col \\& Row-based Table Region for its structured definition. Compared to the cell-based Table Region, it not only saves input tokens but also preserves the sub-tabl... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
% \PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2025
% ready for submission
\usepackage[preprint]{neurips_2025}
% to compile a preprint version, e.g., for submission to arXiv, add add the
% [preprint] optio... | Among base families appearing in both the general-purpose and same-base blocks, take from their Table-R1 row the average of the two middle values for DP, TCoT, SCoT, and PoT. From the general-purpose side of that base, use the model with the best overall score and take the smaller of the WikiTQ and WikiSQL scores. Whic... | DS-Coder, -5.57 | SELECT base families that appear in both the general-purpose block and the same-base block
LOOP for each base family
SELECT the table-r1 row for this base family in the same-base block
COMPUTE ordered_list = sort of {dp, tcot, scot, pot}
COMPUTE middle_avg = average of ordered_list rank 2 and rank 3
S... |
2505.12415 | [
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"\\hline\n",
"\\specialrule{0em}{1pt}{0pt}\n",
"\\raisebox{-2pt}[0pt][0pt]{\\multirow{2}{*} {Model}}& \n",
"\\raisebox{-2pt}[0pt][0pt]{\\multiro... | [
[
"\\begin{figure*}[tp]\n",
"\\centerline{\\includegraphics[width=\\columnwidth]{intro.pdf}}\n",
"\\caption{In \\ourmethod{}, we adopt the Col \\& Row-based Table Region for its structured definition. Compared to the cell-based Table Region, it not only saves input tokens but also preserves the sub-tabl... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
% \PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2025
% ready for submission
\usepackage[preprint]{neurips_2025}
% to compile a preprint version, e.g., for submission to arXiv, add add the
% [preprint] optio... | In the same-base block, keep bases where the DP vs. PoT ordering flips from TableLLM to w/ RE-SFT. For each, compute the sum of TCoT and WikiTQ from Table-R1 and subtract from that the maximum of WikiSQL of TableLLM and RE-SFT. Which base gives the largest result, and how much does its difference between PoT and DP cha... | CodeQwen (7B), +19.53 | SELECT all base groups in the same-base block
LOOP for each base group
COMPUTE tablellm_order = sign tablellm dp − tablellm pot
COMPUTE resft_order = sign resft dp − resft pot
IF tablellm_order != resft_order
COMPUTE r1_sum = table-r1 tcot + table-r1 wikitq
COMPUTE max_wikisql = max of table... |
2505.07858 | [
[
"\\begin{table}[t]\n",
" \\caption{Acceptance rates on various datasets for different models and methods ($T=0$ vs. $T=1$). The Medusa/EAGLE/EAGLE2 results are cited from their papers. See EAGLE3 in Appendix~\\ref{app:eagle3}}\n",
" \\label{table:results_restructured}\n",
" \\centering\n",
... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\begin{subfigure}[b]{0.32\\textwidth}\n",
" \\centering\n",
" \\includegraphics[width=\\linewidth]{f1a.pdf}\n",
" \\label{fig:scaling_pretrain_tokens}\n",
" \\end{subfigure}\\hfill\n",
" \\begin{subfigure}[b]{0.32\\textwidth... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
% \PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2025
% ready for submission
% \usepackage{neurips_2025}
% to compile a preprint version, e.g., for submission to arXiv, add the
% [preprint] option:
\usepacka... | Consider only the Scylla rows, which base has Mean at T=0 is at least 5.6 yet the Mean changes by less than 0.1 when moving to T=1? For that, add together how much GSM8K and NQ changes from T=0 to T=1. What is the number? | LC70B, -0.05 | SELECT scylla rows
SELECT candidate base where mean t0 >= 5.6 AND absolute(mean t0 − mean t1) < 0.1
COMPUTE gsm8k_change = gsm8k t1 − gsm8k t0
COMPUTE nq_change = nq t1 − nq t0
COMPUTE result = gsm8k_change + nq_change
RETURN candidate base, result
|
2504.15077 | [
[
"\\begin{table}[htbp]\n",
" \\centering\n",
" \\caption{Performance comparison of open-source and proprietary models on the Bird Dev dataset for the Text2SQL task.\n",
" All models were evaluated with a temperature setting of 0.7 and a top\\_p value of 0.95.\n",
" \\texttt{... | [
[
"\\begin{figure*}[htbp]\n",
" \\centering\n",
" \\begin{tcolorbox}[title=Prompt Synthetic data annotation, promptstyle]\n",
" \\lstset{\n",
" basicstyle=\\normalfont\\sffamily\\footnotesize,\n",
" breaklines=true,\n",
" frame=none,\n",
... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
% \PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2024
% ready for submission
\usepackage[nonatbib,preprint]{neurips_2025}
\usepackage[numbers]{natbib}
% to compile a preprint version, e.g., for submission to... | Consider the Llama Turbo models and the Qwen2.5-Coder bases that also appear as Think2SQL. Keep a base size only if its Reasoning flag differs from its Think2SQL counterpart. For the base with the larger Think2SQL gain (mean improvement over Simple, Medium, Challenging), subtract the largest Simple to Challenging drop ... | −0.141, Qwen2.5-Coder-3B/Think2SQL-3B | SELECT qwen2.5-coder base models that have a think2sql counterpart at the same size
SELECT size-matched base/think2sql pairs where reasoning flag of base != reasoning flag of think2sql
LOOP for each kept pair
COMPUTE d_simple = think2sql simple − base simple
COMPUTE d_medium = think2sql medium − base medium
... |
2504.09809 | [
[
"\\begin{table*}[t]\n",
"\\setlength{\\tabcolsep}{2.5pt} % Reduce column spacing (default is 6pt)\n",
"\\resizebox{\\textwidth}{!}{\n",
"\\scriptsize\n",
"\\centering\n",
"\\begin{tabular}{ccccccccccl}\n",
" \\hline\n",
"Visualization & Task & P1 (See + Recall) & P2 (See + No Re... | [
[
"\\begin{figure}[t]\n",
"\\centering \n",
" \\includegraphics[width=0.9\\linewidth]{images/visualization-literacy-example.pdf}\n",
" \\caption{An example from the VLAT dataset where the highlighted text \"oil price in 2015\" provides context for MLLM that can trigger factual recall, allowi... | % $Id: template.tex 11 2007-04-03 22:25:53Z jpeltier $
\documentclass{vgtc} % final (conference style)
%\documentclass[review,journal]{vgtc} % review
%\documentclass[widereview]{vgtc} % wide-spaced review
%\documentclass[preprint]{vgtc} % preprint
%\do... | Consider visualizations with at least one row where C1 is checked and C1 and C3 are not; for each, take the largest difference between P1 and P4 among its "retrieve value" rows minus the smallest difference between P1 and P4 among its "make comparison" rows. Which visualization gives the maximum result, and what is it? | Stacked Bar Chart (3), 0.96 | SELECT visualizations where exists a row with c1 == ✓ AND c3 != ✓
LOOP for each visualization
SELECT rows where task contains "retrieve value"
COMPUTE retrieve_max = maximum over p1, p2, p3, p4
SELECT rows where task contains "make comparison"
COMPUTE comparison_min = minimum over p1, p2, p3, p4
... |
2504.09809 | [
[
"\\begin{table*}[t]\n",
"\\setlength{\\tabcolsep}{2.5pt} % Reduce column spacing (default is 6pt)\n",
"\\resizebox{\\textwidth}{!}{\n",
"\\scriptsize\n",
"\\centering\n",
"\\begin{tabular}{ccccccccccl}\n",
" \\hline\n",
"Visualization & Task & P1 (See + Recall) & P2 (See + No Re... | [
[
"\\begin{figure}[t]\n",
"\\centering \n",
" \\includegraphics[width=0.9\\linewidth]{images/visualization-literacy-example.pdf}\n",
" \\caption{An example from the VLAT dataset where the highlighted text \"oil price in 2015\" provides context for MLLM that can trigger factual recall, allowi... | % $Id: template.tex 11 2007-04-03 22:25:53Z jpeltier $
\documentclass{vgtc} % final (conference style)
%\documentclass[review,journal]{vgtc} % review
%\documentclass[widereview]{vgtc} % wide-spaced review
%\documentclass[preprint]{vgtc} % preprint
%\do... | For the visualization that includes "identify hierarchical structure", pool the P1-P4 cells from task rows with exactly one checkmark among C1-C3 and take the midpoint of the 4th and 5th smallest values, substract the mean of P1 to P4 from task row with no checkmark, then add the smallest P among rows whose task name c... | 0.435 | SELECT rows where task == "identify hierarchical structure"
SELECT rows where count of ✓ across c1, c2, c3 == 1
COMPUTE sorted_values = rank p values from these rows in increasing order
COMPUTE s1 = average of sorted_values at rank 4 and rank 5
SELECT rows where count of ✓ across c1, c2, c3 == 0
COMPUTE s2 = averag... |
2504.07089 | [
[
"\\begin{table}[t]\n",
"\\caption{Performance comparison on various visual benchmarks between our \\textsc{OmniCaptioner}-inserted LLMs and previous SOTA MLLMs. \\textbf{We would like to emphasize} that by utilizing \\textsc{OmniCaptioner}, LLMs can function as MLLMs without requiring additional training.... | [
[
"\\begin{figure}[h]\n",
"\\vspace{-10pt}\n",
" \\centering\n",
" \\includegraphics[width=\\linewidth]{Figures/Fig1_omnicaptioner_2.pdf}\n",
" \\vspace{-18pt}\\caption{\\textsc{\\textbf{OmniCaptioner}}: the top section demonstrates its capability to process diverse visual domains. The ... | \documentclass{article}
\usepackage[preprint]{colm2025_conference}
\usepackage{microtype}
\usepackage[utf8]{inputenc} % allow utf-8 input
\usepackage[T1]{fontenc} % use 8-bit T1 fonts
% \usepackage{hyperref} % hyperlinks
\definecolor{green}{RGB}{0,150,10}
\definecolor{blue}{RGB}{0,148,181}
\definecolor{orange... | For each parameter block where at least one non-OmniCaptioner baseline model and at least one OmniCaptioner model is evaluated on the Olympiad benchmark, take the smallest score difference between OmniCaptioner and best baseline model among the MathVision, MathVerse, and Olympiad benchmarks and sum these block-wise min... | 5 | SELECT parameter blocks where both baseline and omnicaptioner models have olympiad scores
LOOP for each block
COMPUTE omni_best_mathvision = max mathvision over omnicaptioner models
COMPUTE base_best_mathvision = max mathvision over baseline models
COMPUTE diff_mathvision = omni_best_mathvision − base_best_... |
2504.01346 | [
[
"\\begin{table*}[t]\n",
" \\centering\n",
" \\resizebox{\\textwidth}{!}{\n",
" \\begin{tabular}{l|l|cccccc|cccccc|cccccc}\n",
" \\toprule\n",
"\n",
"\n",
" \\multirow{3}{*}{\\textbf{Category}} & \\multirow{3}{*}{\\textbf{Methods}} & \\multicolumn{6}{c|}{\\textbf{TFV}} & ... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=0.5\\textwidth]{figures/cross-table-rag.png}\n",
" \\caption{A Real-World Example of Information Retrieval for Cross-Table Question Answering. Given a user query, relevant information is retrieved and integrated (into LLM... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | Using the main result table, compute the sum across tasks of the differences between the bolded and the underlined recall at 50 score. Then, with additional data from the table with experimental results on downstream performance, take LLMs whose Multi-hop F1@50 is larger than the GTR’s Recall at 10 minus 30, compute th... | 48.3 | SELECT tasks in the main result table that report recall@50
LOOP for each task
COMPUTE gap = bold recall@50 − underlined recall@50
COMPUTE sum_gap = sum of all gap
COMPUTE threshold = gtr recall@10 under multi-hop tqa in the main result table − 30
SELECT llms in the downstream experimental results table where m... |
2504.01346 | [
[
"\\begin{table*}[!th]\n",
" \\centering\n",
" \\resizebox{\\linewidth}{!}{\n",
" \\begin{tabular}{*{1}{l}|*{3}c|*{6}c|*{6}c|c}\n",
" \\toprule\n",
" \\multirow{2}{*}{\\textbf{Models}} & \\multicolumn{3}{c|}{\\textbf{TFV}} & \\multicolumn{6}{c|}{\\textbf{Single-hop TQA}} & \\mult... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=0.5\\textwidth]{figures/cross-table-rag.png}\n",
" \\caption{A Real-World Example of Information Retrieval for Cross-Table Question Answering. Given a user query, relevant information is retrieved and integrated (into LLM... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | For models whose Multi-hop TQA EM@50 score in the main result table is at least as close to the variant using the TAPAS method as to the variant using the Tabel-E5 method (ties included), take the median listed improvement from the main result table. Then, over the same subset, compute the mean of the single-hop TQA F1... | 6.3 | SELECT models that appear in the main result table and in both baseline-variant tables
LOOP for each selected model
COMPUTE dist_tapas = absolute(main multi-hop tqa em@50 − tapas-variant multi-hop tqa em@50)
COMPUTE dist_e5 = absolute(main multi-hop tqa em@50 − table-e5-variant multi-hop tqa em@50)
IF dist_... |
2504.01346 | [
[
"\\begin{table*}[t]\n",
" \\centering\n",
" \\resizebox{\\textwidth}{!}{\n",
" \\begin{tabular}{l|l|cccccc|cccccc|cccccc}\n",
" \\toprule\n",
"\n",
"\n",
" \\multirow{3}{*}{\\textbf{Category}} & \\multirow{3}{*}{\\textbf{Methods}} & \\multicolumn{6}{c|}{\\textbf{TFV}} & ... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=0.5\\textwidth]{figures/cross-table-rag.png}\n",
" \\caption{A Real-World Example of Information Retrieval for Cross-Table Question Answering. Given a user query, relevant information is retrieved and integrated (into LLM... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | When switching the LLM baseline from Table-E5 to TAPAS, which model gains the most in TFV EM@50? For that model, take its TFV EM@50 gain minus its single-hop TQA F1@50 change, then subtract from it the difference between the bolded and underlined multi-hop TQA Recall@50 score from the main results table. What is the re... | Phi-3.5-mini, -0.4 | SELECT models appearing in both Table-E5 and TAPAS baselines
LOOP for each model
COMPUTE gain_TFV = TFV EM@50 (TAPAS) − TFV EM@50 (Table-E5)
COMPUTE BestModel = argmax gain_TFV
SELECT BestModel
COMPUTE GAIN = TFV EM@50 (TAPAS) − TFV EM@50 (Table-E5)
COMPUTE CHANGE = Single-hop TQA F1@50 (TAPAS) − Single-hop TQA F... |
2504.03598 | [
[
"\\begin{table}\n",
"\\centering\n",
"\n",
"\\begin{adjustbox}{max width=\\linewidth}\n",
"\\begin{tabular}{lcccccccccccc|cccccccccccc}\n",
"& \\multicolumn{12}{c}{$k=10$} & \\multicolumn{12}{c}{$k=100$}\\\\\n",
"\\cmidrule(lr){2-13} \\cmidrule(lr){14-25}\n",
"& \\multicolumn{2}{c}... | [
[
"\\begin{figure}\n",
"\\centering\n",
"\\includegraphics[width=0.75\\linewidth, trim=0cm 2cm 0cm 0cm, clip]{figures/diagram.pdf}\n",
"\\caption{\\sys{} leverages LLMs \\textit{offline} to enrich each object, creating multiple semantically-enhanced indices. During online retrieval, it computes obje... | \documentclass{article} % For LaTeX2e
\usepackage[preprint]{colm2025_conference}
\usepackage{microtype}
\usepackage{hyperref}
\usepackage{url}
\usepackage{booktabs}
\usepackage{lineno}
\definecolor{darkblue}{rgb}{0, 0, 0.5}
\hypersetup{colorlinks=true, citecolor=darkblue, linkcolor=darkblue, urlcolor=darkblue}
\use... | Among the BM25+X variants in the Original question block, which one gains the most in average recall growth for k=10 and k=100 when using EnrichIndex compared to not using it? For that method, subtract its Coding NDCG at k=10 with EnrichIndex from its StackEx. Recall at k=100 without EnrichIndex. What is the result? | BM25+Snow, 37.4 | SELECT all "BM25+X" methods and their EnrichIndex variants in the original question block
LOOP for each method
COMPUTE gain = (avg recall k=100 with EnrichIndex - avg recall k=10 with EnrichIndex) - (avg recall k=100 without EnrichIndex - avg recall k=10 without EnrichIndex)
COMPUTE best_method = argmax method over... |
2504.03598 | [
[
"\\begin{table}[H]\n",
"\\centering\n",
"\n",
"\\begin{adjustbox}{max width=\\linewidth}\n",
"\\begin{tabular}{lcccccccc|cccccccc}\n",
"& \\multicolumn{8}{c}{$k=10$} & \\multicolumn{8}{c}{$k=100$}\\\\\n",
"\\cmidrule(lr){2-9} \\cmidrule(lr){10-17}\n",
"& \\multicolumn{2}{c}{StackEx... | [
[
"\\begin{figure}\n",
"\\centering\n",
"\\includegraphics[width=0.75\\linewidth, trim=0cm 2cm 0cm 0cm, clip]{figures/diagram.pdf}\n",
"\\caption{\\sys{} leverages LLMs \\textit{offline} to enrich each object, creating multiple semantically-enhanced indices. During online retrieval, it computes obje... | \documentclass{article} % For LaTeX2e
\usepackage[preprint]{colm2025_conference}
\usepackage{microtype}
\usepackage{hyperref}
\usepackage{url}
\usepackage{booktabs}
\usepackage{lineno}
\definecolor{darkblue}{rgb}{0, 0, 0.5}
\hypersetup{colorlinks=true, citecolor=darkblue, linkcolor=darkblue, urlcolor=darkblue}
\use... | Among the "Average" rows, compare the Recall at k=100 for Original setting without EnrichIndex against the NDCG at the same k for GPT-4 expanded queries with EnrichIndex; from this difference, remove the gap between GPT-4 Recall without EnrichIndex and the Original NDCG at k=10 with EnrichIndex. What is the result? | 0.4 | SELECT the "Average" rows from both blocks
COMPUTE d1 = recall at k=100 in original question without EnrichIndex - ndcg at k=100 in GPT-4 generated expanded query with EnrichIndex
COMPUTE d2 = recall at k=100 in GPT-4 generated expanded query without EnrichIndex - ndcg at k=10 in original question with EnrichIndex
COMP... |
2504.03598 | [
[
"\\begin{table}[H]\n",
"\\centering\n",
"\n",
"\\begin{adjustbox}{max width=\\linewidth}\n",
"\\begin{tabular}{lcccccccc|cccccccc}\n",
"& \\multicolumn{8}{c}{$k=10$} & \\multicolumn{8}{c}{$k=100$}\\\\\n",
"\\cmidrule(lr){2-9} \\cmidrule(lr){10-17}\n",
"& \\multicolumn{2}{c}{StackEx... | [
[
"\\begin{figure}\n",
"\\centering\n",
"\\includegraphics[width=0.75\\linewidth, trim=0cm 2cm 0cm 0cm, clip]{figures/diagram.pdf}\n",
"\\caption{\\sys{} leverages LLMs \\textit{offline} to enrich each object, creating multiple semantically-enhanced indices. During online retrieval, it computes obje... | \documentclass{article} % For LaTeX2e
\usepackage[preprint]{colm2025_conference}
\usepackage{microtype}
\usepackage{hyperref}
\usepackage{url}
\usepackage{booktabs}
\usepackage{lineno}
\definecolor{darkblue}{rgb}{0, 0, 0.5}
\hypersetup{colorlinks=true, citecolor=darkblue, linkcolor=darkblue, urlcolor=darkblue}
\use... | Among the BM25+X variants that appear in both tables, which gains most in the difference between average recall and average NDCG when EnrichIndex is applied on the Bright dataset (GPT-4, k=100)? For that method, applied to GPT-4o-mini on the table retrieval datasets, compute the rise in average NDCG score from k=10 to ... | BM25+GTE, -3.5 | SELECT all bm25+X method families that appear in both tables
LOOP for each bm25+X family
SELECT gpt-4, k=100, avg recall and avg ndcg for each bm25+X family under the original-query rows
SELECT gpt-4, k=100, avg recall and avg ndcg for each bm25+X family under the enrichindex rows
COMPUTE base_gap = avg_r... |
2509.09583 | [
[
"\\begin{table*}\n",
"\\renewcommand{\\arraystretch}{1.2}\n",
"\\centering\n",
"\\caption{Model Performance by Trait (Accuracy and F1 Score). \n",
"Traits: O = Openness, E = Extroversion, A = Agreeableness, C = Conscientiousness, N = Neuroticism.}\n",
"\\label{tab:model_performance}\n",
... | [
[
"\\begin{table}[H]\n",
"\\renewcommand{\\arraystretch}{1.2}\n",
"\\centering\n",
"\\caption{Descriptive Statistics for Big Five Personality Traits. Trait abbreviations: O = Openness, C = Conscientiousness, E = Extroversion, A = Agreeableness, N = Neuroticism.}\n",
"\\label{tab:trait_stats}\n",... | % This is an example file showing how to use the 'edm_article.cls' LaTeX2e document class file for Conference Proceedings submissions.
% Based originally on ACM conference template SIGPROC-SP.TEX - VERSION 3.1 and V3.2SP of ACM_PROC_ARTICLE-SP.CLS
% ----------------------------------------------------------------------... | In which trait does GPT-4o Mini achieve the highest accuracy? Is its accuracy the best for all models? If so, what is the average F1 score in that trait? If not, compute the change rates for accuracy and F1 score for that trait to the trait that has the lowest accuracy for GPT-4o Mini. Is the change rate for the F1 sc... | Trait O (Openness), not the highest, accuracy decrease 41.462%;F1 score decrease 98.05%, No | SELECT gpt-4o mini accuracy for all traits
COMPUTE best_trait = argmax trait over gpt-4o mini accuracy
COMPUTE worst_trait = argmin trait over gpt-4o mini accuracy
COMPUTE best_is_global = yes
SELECT all models
LOOP for each model
IF accuracy of model for best_trait > accuracy of gpt-4o mini for best_trait
... |
2509.09583 | [
[
"\\begin{table*}\n",
"\\renewcommand{\\arraystretch}{1.2}\n",
"\\centering\n",
"\\caption{Model Performance by Trait (Accuracy and F1 Score). \n",
"Traits: O = Openness, E = Extroversion, A = Agreeableness, C = Conscientiousness, N = Neuroticism.}\n",
"\\label{tab:model_performance}\n",
... | [
[
"\\begin{table}[H]\n",
"\\renewcommand{\\arraystretch}{1.2}\n",
"\\centering\n",
"\\caption{Descriptive Statistics for Big Five Personality Traits. Trait abbreviations: O = Openness, C = Conscientiousness, E = Extroversion, A = Agreeableness, N = Neuroticism.}\n",
"\\label{tab:trait_stats}\n",... | % This is an example file showing how to use the 'edm_article.cls' LaTeX2e document class file for Conference Proceedings submissions.
% Based originally on ACM conference template SIGPROC-SP.TEX - VERSION 3.1 and V3.2SP of ACM_PROC_ARTICLE-SP.CLS
% ----------------------------------------------------------------------... | Find the median and mean for accuracy and F1 score across all traits and all models. | Acc_mean:64.7,acc_median:59.44;f1_mean:66.73, f1_median: 72.22 | SELECT all models
LOOP for each model
SELECT all traits
LOOP for each trait
COMPUTE add accuracy value of model, trait to accuracy_list
COMPUTE add f1 value of model, trait to f1_list
COMPUTE median_accuracy = median of accuracy_list
COMPUTE mean_accuracy = mean of accuracy_list
COMPUTE median... |
2504.06560 | [
[
"\\begin{table*}[!h]\n",
"\n",
"\\centering\n",
"\\caption{Performance results on Cropped Tables of mainstream text-LLMs, TableLLM, MLLMs, and foundation models fine-tuned on our synthetic data. The best results are highlighted in \\textbf{bold}, and \\textit{+ ours} denotes models further fine-tu... | [
[
"\\begin{figure}\n",
" \\begin{center}\n",
" \\includegraphics[width=\\textwidth]{images/benchmark_comparison.pdf}\n",
" \\end{center} \n",
" \\caption{Comparison of previous long-context benchmarks, tabular benchmarks and the proposed NIAT benchmark. Existing long-context benc... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
%
% before loading neurips_2025
% ready for submission
\PassOptionsToPackage{numbers, compress}{natbib}
% \usepackage{neurips_2025}
% \usepackage[nonatbib]{neurips_2025}
\usepackage[preprint]{neurips_2025}
% to compile a preprint ve... | Among the models fine-tuned on synthetic data, pair each with its base variant and sum the 8-column and 20-column gains over that base, which row gives the larger total? And if you then subtract its 32-column value from the maximum 16-column entry in the Thinker LLM and Coder LLM block, what is the result? | Qwen2.5-7B-Instruct + ours, 53.75 | SELECT all models with + ours
LOOP for each selected model
COMPUTE gain_8 = column 8 model - column 8 base
COMPUTE gain_20 = column 20 model - column 20 base
COMPUTE total_gain = gain_8 + gain_20
COMPUTE m1 = argmax model over total_gain
COMPUTE max_16 = max of column 16 values in the thinker llm and code... |
2503.16856 | [
[
"\\begin{table*}[t!]\n",
"\\setlength{\\tabcolsep}{2.8pt}\n",
"\\small\n",
"\\begin{center}\n",
"\\begin{tabular}{lccccccccccccc}\n",
"\\toprule\n",
"\\textbf{Model} & \\textbf{Date} & \\textbf{\\#Param} & \\textbf{Overall} & \\textbf{FIC} & \\textbf{MF} & \\textbf{FTA} & \\textbf{FTE}... | [
[
"\\begin{table*}[t]\n",
"\\setlength{\\tabcolsep}{3.5pt}\n",
"\\centering\n",
"\\small\n",
"\\vspace{2ex}\n",
"\\begin{tabular}{l|c|ccccccccc}\n",
"\\toprule\n",
"\\textbf{Benchmarks} & \\textbf{Avg. Pages} & \\textbf{Cross-Page} & \\textbf{Text} & \\textbf{Chart} & \\textbf{Table... | % ICCV 2025 Paper Template
\PassOptionsToPackage{dvipsnames}{xcolor}
\documentclass[10pt,twocolumn,letterpaper]{article}
\pdfoutput=1
\usepackage[margin=1in]{geometry}
\usepackage[many]{tcolorbox}
\usepackage{graphicx}
\usepackage{caption}
\usepackage{multicol}
\usepackage{amsmath}
\usepackage{mathptmx}
\usepackag... | Considering the open-source models whose names contains “2.5” and that appear at two parameter scales, which family has the largest value of the increase in Overall from the smaller to the larger variant minus the simultaneous increase in the average of TAC and MT? Additionally, what is its difference between FF of the... | Qwen2.5-VL, 13.46 | SELECT open-source models whose names contain 2.5 and that have two parameter scales
LOOP for each model family
COMPUTE overall_increase = overall for the larger variant - overall for the smaller variant
COMPUTE avg_small = average of tac and mt for the smaller variant
COMPUTE avg_large = average of tac and... |
2502.17315 | [
[
"\\begin{table*}[t]\n",
"\\centering\n",
"\\small\n",
"\\begin{tabular}{l|c|ccccc|cc} \n",
"\\hline\n",
"\\multirow{3}{*}{\\textbf{Method}} & \\multirow{3}{*}{\\textbf{Parameters}} & \\multicolumn{5}{c|}{\\textbf{Question Answering}} & \\multicolumn{2}{c}{\\textbf{Fact Verification}} \\\\ ... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=0.95\\linewidth]{image/hippo_example.pdf}\n",
" \\caption{Illustration of the Effectiveness of Text-Based and Image-Based Table Representations in Question Answering. We present the answers generated by the MLLM (\\includ... | \pdfoutput=1
\documentclass[11pt]{article}
\usepackage[]{acl}
\usepackage{times}
\usepackage{latexsym}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{microtype}
\usepackage{inconsolata}
\usepackage{graphicx}
\usepackage{natbib}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{multirow}
\usepacka... | Considering only the models that appear in both "MLLM (Image)" and "MLLM (Image&Text)" with the same parameter size, which model has the largest value of the difference between the gain from Image to Image&Text in the average of WTQ, HiTab, and TAT-QA on the one hand and the gain in the average of TabFact and InfoTabs ... | Table-LLAVA 13B, 24.85 | SELECT models that appear in both mllm (image) and mllm (image & text) with the same parameter size
LOOP for each model
COMPUTE avg_qa_image = average of wtq, hitab, and tat-qa in mllm (image)
COMPUTE avg_qa_it = average of wtq, hitab, and tat-qa in mllm (image & text)
COMPUTE gain_qa = avg_qa_it - avg_qa_i... |
2502.17253 | [
[
"\\begin{table*}[ht]\n",
"\\centering\n",
"\\tiny\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\\begin{tabular}{l|l|ccccccccccc|c}\n",
" \\toprule\n",
" \\textbf{Model} & \\textbf{Method} & \\textbf{bn} & \\textbf{de} & \\textbf{en} & \\textbf{es} & \\textbf{fr} &... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=1.\\linewidth]{fig/intro.pdf}\n",
" \\vspace{-0.5em}\n",
" \\caption{\n",
" Comparison of the English and Chinese examples in \\ourdataset.\n",
" Entities with the same color annotation represent corr... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | Which model maximizes the difference in the F1 score and exact match score improvements between the proposed method over En-PoT? And what is that model's mean F1 score difference between the En-PoT and En-CoT method minus the same comparison in exact match for Bengali, English, and Chinese? | gpt-4o, -6.37 | SELECT all models
LOOP for each model
COMPUTE em_improvement = average(exact match value of method ours - exact match value of en-pot) over all languages
COMPUTE f1_improvement = average(f1 of ours - f1 of en-pot) over all languages
COMPUTE gap_improvement = f1_improvement - em_improvement
COMPUTE m1 = argm... |
2502.13923 | [
[
"\\begin{table}[h]\n",
"\\centering\n",
"\\caption{\\textbf{Performance of Qwen2.5-VL and State-of-the-art.}}\n",
"\\label{tab:sota_results}\n",
"\\setlength{\\tabcolsep}{3.0pt}\n",
"\\scalebox{0.63}{\n",
"\\begin{tabular}{@{}lcccccccc@{}}\n",
"\\toprule\n",
"\\textbf{Datasets}... | [
[
"\\begin{figure*}[ht]\n",
"\\centering\n",
"\\includegraphics[width= 1\\linewidth]{figures/head.jpg}\n",
"\\end{figure*}\n"
],
[
"\\begin{figure*}[t]\n",
"\\centering\n",
"\\includegraphics[width= 1\\linewidth]{figures/qwen2.5vl_arc.jpeg}\n",
" \\caption{The Qwen2.5-VL framew... | \documentclass{article} % For LaTeX2e
\usepackage{colm2024_conference}
\usepackage{booktabs}
\usepackage{graphicx}
\usepackage{enumitem}
\usepackage{wrapfig}
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{natbib}
\usepackage{makecell}
\usepackage{booktabs}
\usepackage{array}
\usepackage{amsmath}
\usepac... | Consider only datasets citing Chen et al. (2024d). For each block, which block has the largest average across the gaps between Qwen2.5-VL 72B and Qwen2-VL 72B over rows with both values? Within that block, which dataset maximizes the sum of the difference between Qwen2.5-VL 72B and GPT-4o 0513 as well as the difference... | Math; MathVerse_mini, 3.3 | SELECT all blocks
LOOP for each block
SELECT rows citing chen et al. (2024d) where both qwen2.5-vl 72b and qwen2-vl 72b are present
LOOP for each row
COMPUTE gap = qwen2.5-vl 72b - qwen2-vl 72b
COMPUTE avg_gap = average of gap over selected rows
COMPUTE target_block = argmax block block over avg_gap... |
2502.12911 | [
[
"\\begin{table*}[t]\n",
" \\caption{The SQL generation performance of enhanced text-to-SQL models using KaSLA, which features 1.6 B parameters combining DeepSeek-coder-1.3B and RoBERTa-Large, is evaluated in terms of Execution Accuracy (EX) (\\%) and Valid Efficiency Score (VES) (\\%) on the BIRD-dev an... | [
[
"\\begin{figure}[!t]\n",
"\t\\centering\n",
" \\includegraphics[width=1.0\\linewidth]{fig/impact_of_schema-linking_in_text-to-SQL.pdf}\n",
" \\caption{Performance comparison of different schema linking methods on the BIRD-dev dataset, using CodeS-15B as the SQL generation model.} \n... | \documentclass[conference]{IEEEtran}
\IEEEoverridecommandlockouts
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left)}}
\newcommand{\figcenter}{{\em (Center)}}
\newcommand{\figright}{{\em (Right)}}
\newc... | Among +KaSLA rows where the gray-box gain on BIRD-EX exceeds that on Spider-VES while the gain on BIRD-VES is smaller than that on Spider-EX, which method qualifies, and what is the value of the difference between the change from Spider-EX Total without to with KaSLA and the change from Spider-VES Total without KaSLA t... | RSL-SQL + KaSLA, 42.27 | SELECT all +kasla rows
LOOP for each row
COMPUTE cond1 = gray-box gain on bird ex total - gray-box gain on spider ves total
COMPUTE cond2 = gray-box gain on bird ves total - gray-box gain on spider ex total
IF cond1 > 0 AND cond2 < 0
COMPUTE m1 = method name of this row
SELECT m1
COMPUTE delta_s... |
2509.14233 | [
[
"\\begin{table}[t]\n",
" \\scriptsize\n",
" \\centering \n",
" \\caption{\\textbf{Pretraining Evaluation:} Performance (\\%) of \\apertus{} models on \\textit{general language understanding} tasks compared to other pretrained models. The arrows (↑,↓) show the desired direction for eac... | [
[
"\\begin{table}[h]\n",
"\\centering\n",
"\\caption{\\textbf{\\modelname Model Architecture Overview.} We adapt our custom \\modelname architecture with the xIELU activation function~\\citep{huang2025derivingactivationfunctionsusing} across two scales, 8B and 70B. Both models support long contexts up t... | \documentclass{article} % For LaTeX2e
\usepackage{iclr2025_conference,times}
\usepackage{xspace}
\usepackage{mathpazo}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of... | Among open weight models where ARC exceeds WinoGrande and BLEND is above 80, which model maximizes the difference between PIQA and HellaSwag, and what is the value of sum of the scores Global-MMLU, BLEND, and XNLI minus the sum of the scores for INCLUDE V1, Cultural-Bench and ARC for that model? | Qwen3-32B, −21.7 | SELECT open-weight models where arc > winogrande and blend > 80
LOOP for each model
COMPUTE gap = piqa - hellaswag
COMPUTE model1 = argmax model over gap
SELECT model1
COMPUTE s1 = global-mmlu + blend + xnli
COMPUTE s2 = include v1 + cultural-bench + arc
COMPUTE result = s1 - s2
RETURN model1, result
|
2509.14233 | [
[
"\\begin{table}[t]\n",
" \\scriptsize\n",
" \\centering \n",
" \\caption{\\textbf{Pretraining Evaluation:} Performance (\\%) of \\apertus{} models on \\textit{factual knowledge acquisition} tasks compared to other pretrained models. The arrows (↑,↓) show the desired direction for each ben... | [
[
"\\begin{table}[h]\n",
"\\centering\n",
"\\caption{\\textbf{\\modelname Model Architecture Overview.} We adapt our custom \\modelname architecture with the xIELU activation function~\\citep{huang2025derivingactivationfunctionsusing} across two scales, 8B and 70B. Both models support long contexts up t... | \documentclass{article} % For LaTeX2e
\usepackage{iclr2025_conference,times}
\usepackage{xspace}
\usepackage{mathpazo}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of... | Consider models with the same size present in both tables. Compute the difference between GSM8K and MGSM from the post-training evaluation, subtract the difference between HumanEval Pass@10 and MBPP Pass@1 also from the post-training evaluation, and then subtract the absolute gap between MMLU and Global-MMLU from the p... | Qwen3-32B, 9 | SELECT models that appear in both tables at the same size
LOOP for each model
COMPUTE d1 = gsm8k - mgsm
COMPUTE d2 = humaneval pass@10 - mbpp pass@1
COMPUTE d3 = absolute of mmlu - global-mmlu
COMPUTE d4 = blend - switzerlandqa
COMPUTE result = (d1 - d2) - (d3 - d4) + (post-training avg - pretrainin... |
2509.14034 | [
[
"\\begin{table*}[!htbp]\n",
" \\centering\n",
" \\resizebox{\\textwidth}{!}{\n",
" \\begin{tabular}{ll|ccc|ccc}\n",
" \\toprule\n",
" \\textbf{Dataset} & \\textbf{Setting} \n",
" & \\multicolumn{3}{c|}{\\textbf{4o-mini + LLaMA}} \n",
" & \\multicolumn{3}{c}... | [
[
"\\begin{figure}[t]\n",
" \\includegraphics[width=\\columnwidth]{Figure/proportion.pdf}\n",
" \\caption{Debate outcomes in the initial round when only one LLM is initially correct. “Correct” indicates convergence to the right answer, “Incorrect” to the wrong one, and “Disagree” means no consensus. D... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Custom packages
\usepackage{amsmath}
\usepackage[ruled,vlined]{algorithm2e}
\usep... | For each dataset and model pair, discard the worst-performing setting(s) defined by the caption, and pick the one with the smallest absolute gap between the WR of Round 0 and 1 scores. Then compute accuracy minus WR of Round 0 score and sum over the 4 datasets. Which model pair has the largest sum, and by how much? | 4o-mini + LLaMA, 0.058 | SELECT both model pairs
LOOP for each model pair
SELECT all datasets
LOOP for each dataset
SELECT all settings excluding worst-performing setting(s)
LOOP for each setting
COMPUTE gap = absolute(wr of round 0 - wr of round 1)
COMPUTE chosen_setting = argmin setting over gap
... |
2509.14008 | [
[
"\\begin{table}[t]\n",
"\\centering\n",
"\\renewcommand{\\arraystretch}{1.2}\n",
"\\begingroup\n",
"\\setlength{\\tabcolsep}{5.5pt}\n",
"\\newcommand{\\best}[1]{\\textbf{#1}}\n",
"\\newcommand{\\secondbest}[1]{\\underline{#1}}\n",
"\\newcommand{\\NA}{\\textemdash}\n",
"\n",
... | [
[
"\\begin{figure}[h!]\n",
" \\centering \\includegraphics[width=0.6\\linewidth]{halalogo.png}\n",
" \\label{fig:placeholder}\n",
"\\end{figure}\n"
],
[
"\\begin{table}[H]\n",
"\\centering\n",
"\\begin{tabular}{@{}r@{\\hspace{2pt}}l@{}}\n",
"\\huggingface & \\textbf{Mode... | \documentclass{article}
\PassOptionsToPackage{numbers, compress}{natbib}
\usepackage[preprint]{neurips_2025}
\usepackage[T1]{fontenc}
\usepackage{xcolor}
\usepackage{graphicx}
\usepackage{xspace}
\usepackage{url}
\definecolor{linkColor}{rgb}{0.2,0.4,0.6}
\definecolor{abstractbg}{gray}{0.95}
\definecolor{darkgreen}{rg... | For each size bucket, take the model whose Average score is underlined and compute the difference between its AlGhafa score and its AraTrust score. Sum these differences across the size buckets. Then subtract the difference in ArbMMLU-HT scores between the models with bolded Average scores in Small and Nano. What is th... | -47.9; underlined: Qwen3-1.7B-Base (Nano) and QCRI/Fanar-9-9B-Instruct (Small), bold: HALA-1.2B (Nano) and HALA-9B (Small) | SELECT model1 = model in Nano (≤2B) size bucket whose Average is underlined
COMPUTE nano_diff = AlGhafa − AraTrust of model 1
SELECT model2 =model in Small (7B–9B) size bucket whose Average is underlined
COMPUTE small_diff = AlGhafa − AraTrust
COMPUTE sum_underline = nano_diff + small_diff
SELECT model3 = model in Na... |
2509.14031 | [
[
"\\begin{table*}[p]\n",
" \\centering\n",
" \\small\n",
" \\begin{tabular}{lrrrrrrrrrr}\n",
" \\hline\n",
" \\textbf{Model} & \\textbf{En-De} & \\textbf{En-Es} & \\textbf{En-Fr} & \\textbf{En-Pl} & \\textbf{En-Ru} & \\textbf{De-En} & \\textbf{Es-En} & \\textbf{Fr-En} & \\tex... | [
[
"\\begin{figure}\n",
" \\centering\n",
" \\includegraphics[width=0.85\\linewidth]{images/data_composition_gender.png}\n",
" \\caption{Composition of the English-to-German training datasets with the Gender phenomenon in Pure IWSLT and IWSLT+OpenSubtitles settings. Annotations are based on ... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | For each shared language pair in the two tables, compute the difference between average gender scores and average formality scores. Consider only language pairs where a different linguistic aspect scores higher between the two tables. Which language pair shows the largest absolute change in this difference, and what is... | En-Ru, 0.387 | SELECT shared language pairs in both tables
LOOP for each shared language pair
COMPUTE avg_gender_nllb = average of gender BLEU values in the nllb-200 600m table
COMPUTE avg_formality_nllb = average of formality BLEU values in the nllb-200 600m table
COMPUTE diff_nllb = avg_gender_nllb - avg_formality_nllb... |
2509.14031 | [
[
"\\begin{table*}[p]\n",
" \\centering\n",
" \\small\n",
" \\begin{tabular}{lrrrrrrrrrr}\n",
" \\hline\n",
" \\textbf{Model} & \\textbf{En-De} & \\textbf{En-Es} & \\textbf{En-Fr} & \\textbf{En-Pl} & \\textbf{En-Ru} & \\textbf{De-En} & \\textbf{Es-En} & \\textbf{Fr-En} & \\tex... | [
[
"\\begin{figure}\n",
" \\centering\n",
" \\includegraphics[width=0.85\\linewidth]{images/data_composition_gender.png}\n",
" \\caption{Composition of the English-to-German training datasets with the Gender phenomenon in Pure IWSLT and IWSLT+OpenSubtitles settings. Annotations are based on ... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | Considering only the cases where the training language pair is the same as the evaluation language pair and where the formality COMET score is larger than gender COMET score, compute the difference between gender and formality BLEU scores. Which language pair has the largest absolute difference? For that language pair,... | En-Fr, -0.12 | SELECT all diagonal language pairs for gender and formality in bleu and comet scores
LOOP for each diagonal language pair
COMPUTE comet_diff = formality comet - gender comet\
IF comet_diff > 0
COMPUTE bleu_diff = absolute(gender bleu - formality bleu)
COMPUTE target_pair = argmax language pair over bleu... |
2509.05075 | [
[
"\t\t\\begin{table*}[t]\n",
"\t\t\\centering\n",
"\t\t\\scalebox{0.8}{\\setlength{\\tabcolsep}{0.85mm}{\n",
"\t\t\t\t\\begin{tabular}{c|c|cccccccc}\n",
"\t\t\t\t\t\\hline\n",
"\t\t\t\t\tMethod & Metric & R0 & R1 & R2 & OFF0 & OFF1 & OFF2 & OFF3 & OFF4 \\\\\n",
"\t\t\t\t\t\\hline\n",
... | [
[
"\t\t\\begin{table*}[t]\n",
"\t\t\\centering\n",
"\t\t\\scalebox{0.8}{\\setlength{\\tabcolsep}{0.85mm}{\n",
"\t\t\t\t\\begin{tabular}{c|c|cccccccc}\n",
"\t\t\t\t\t\\hline\n",
"\t\t\t\t\tMethod & Metric & R0 & R1 & R2 & OFF0 & OFF1 & OFF2 & OFF3 & OFF4 \\\\\n",
"\t\t\t\t\t\\hline\n",
... | \documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left)... | What is the absolute difference between the multiplication of average PSNR value for R0 and average SSIM value for R2 and the sum of the average LPIPS value for OFF2 and the PSNR value for OFF1? | 8.6918 | SELECT all PSNR values under R0
COMPUTE avg_psnr_r0 = average of selected values
SELECT all SSIM values under R2
COMPUTE avg_ssim_r2 = average of selected values
COMPUTE product = avg_psnr_r0 * avg_ssim_r2
SELECT all LPIPS values under OFF2
COMPUTE avg_lpips_off2 = average of selected values
SELECT all PSNR val... |
2509.19212 | [
[
"\\begin{table*}[t!]\n",
"\\centering\n",
"\\scalebox{0.65}{\n",
"\\begin{tabular}{l|ccc|ccc|c|cccc}\n",
"\\toprule\n",
"\\multirow{2}{*}{\\textbf{Models}} \n",
"& \\multicolumn{7}{c|}{\\textbf{MSSBench (Accuracy) ($\\uparrow$)}} \n",
"& \\multicolumn{4}{c}{\\textbf{MOSSBench (Reje... | [
[
"\\begin{figure}[ht]\n",
" \\centering\n",
" \\vspace{-1.2ex}\n",
" \\includegraphics[width=0.85\\textwidth]{Figure/intro_2.pdf} \n",
" \\caption{Illustration of multimodal situational safety. The model must judge the safety of a user’s query based on the accompanying visual ... | \documentclass{article} % For LaTeX2e
% \usepackage{iclr2026_conference,times}
\usepackage{iclr2025_conference}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
% \input{math_commands.tex}
\usepackage{arxiv}
\usepackage{hyperref}
\usepackage{url}
\usepackage{enumitem}
\usepackage{float}
\... | For each model, check if the base method average embedding score or average chat score is higher. Considering only method variants where this relationship flips, pick the one with the highest overall average, add up all the differences between the overall average and the MOSSBench average for all of the models, then su... | 16.53; LLaVA-1.6-7B+Ours, Qwen-VL-7B-Instruct+Paraphrase, InstructionBlip-7B+Self-Remind, Idefics-9B-Instruct+Ours | SELECT all model blocks
LOOP for each model block
COMPUTE base_diff = base avg emb - base avg chat
SELECT all non-base method rows
LOOP for each method row
COMPUTE method_diff = method row avg emb - method row avg chat
IF base_diff and method_diff have different signs
COMPUTE add... |
2509.21310 | [
[
"\\begin{table}\n",
" \\caption{Performance of embedding models and classical similarity metrics on the SAGE benchmark across five evaluation categories. Scores are normalized to [0,1]. The overall score is the unweighted mean across categories.}\n",
" \\label{tab:sage-results-updated-retrieval}\n",... | [
[
"\\begin{table}\n",
" \\caption{Performance of embedding models and classical similarity metrics on the SAGE benchmark across five evaluation categories. Scores are normalized to [0,1]. The overall score is the unweighted mean across categories.}\n",
" \\label{tab:sage-results-updated-retrieval}\n",... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
\PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2025
% The authors should use one of these tracks.
% Before accepting by the NeurIPS conference, select one of the options below.
% 0. "default" for submission
% \... | Calculate the average score across the three robustness subtasks for each embedding model. Then, for each model, compare this average to its overall robustness score on the SAGE benchmark. Which single model (or models, in case of a tie) is closest to its overall SAGE robustness score? | text-embedding-3-large and voyage-3-large | SELECT all embedding models
LOOP for each model
SELECT robustness metric columns in robustness scores table
COMPUTE robustness_mean = average of robustness scores
SELECT robustness scores in main benchmark table
COMPUTE consistency = abs(robustness_mean - robustness score in main benchmark table)
COMPU... |
2509.21310 | [
[
"\\begin{table}\n",
" \\caption{Performance of embedding models and classical similarity metrics on the SAGE benchmark across five evaluation categories. Scores are normalized to [0,1]. The overall score is the unweighted mean across categories.}\n",
" \\label{tab:sage-results-updated-retrieval}\n",... | [
[
"\\begin{table}\n",
" \\caption{Performance of embedding models and classical similarity metrics on the SAGE benchmark across five evaluation categories. Scores are normalized to [0,1]. The overall score is the unweighted mean across categories.}\n",
" \\label{tab:sage-results-updated-retrieval}\n",... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
\PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2025
% The authors should use one of these tracks.
% Before accepting by the NeurIPS conference, select one of the options below.
% 0. "default" for submission
% \... | For each embedding model, compute the mean insertion perturbation score and the mean removal perturbation score. Average these two means to obtain a Sensitivity composite. Then, compare this composite to the model’s overall Sensitivity score on the SAGE benchmark. Which single model diverges the most in absolute value?... | embed-v4.0 (+0.000583) and voyage-3-large (−0.000583) | SELECT all embedding models
LOOP for each model
SELECT insertion dataset columns in insertion scores table
COMPUTE insertion_mean = average of insertion scores
SELECT removal dataset columns in removal scores table
COMPUTE removal_mean = average of removal scores
COMPUTE sensitivity_composite = aver... |
2509.22558 | [
[
"\\begin{table*}[t]\n",
" \\footnotesize\n",
" \\centering\n",
" \\caption{Performance comparison of \\model{} under different inference scaling strategies.\n",
" }\n",
" \\label{table:inference scaling}\n",
" \\setlength{\\tabcolsep}{2pt}\n",
" \\vskip 0.15in... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=1\\linewidth]{figs/temp0924open008_black.png}\n",
" \\vspace{-15pt}\n",
" \\caption{The illustration of (a) the credit assignment problem of outcome reward and (b) the myopic issue of discriminative process supervi... | \documentclass{article}
\usepackage{iclr2026_conference,times}
\usepackage{url}
\iclrfinalcopy % 录用后打开；投稿/评审阶段保持注释
%% ---------------------------------------------------------------
%% PACKAGE SETUP
%% ---------------------------------------------------------------
\usepackage{microtype}
\usepack... | Among the strategies that use StepORLM as the policy model, which strategy achieves the second-largest improvement in macro-average score compared to the base StepORLM, and what is the value of this improvement? | Solver Exec, 3.1 | SELECT all strategies under StepORLM as policy model excluding base StepORLM
LOOP for each strategy
COMPUTE improvement = strategy Avg. - base StepORLM Avg.
COMPUTE rank strategy by improvement descending
COMPUTE target_strategy = strategy of rank 2
RETURN target_strategy
|
2509.22558 | [
[
"\\begin{table*}[t]\n",
" \\footnotesize\n",
" \\centering\n",
" \\caption{Ablation study of \\model{} on Pass@1 accuracy (\\%).\n",
" The best results are given in \\textbf{bold}, and the second-best values are \\underline{underlined}.}\n",
" \\label{table:ablation}\n",
... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=1\\linewidth]{figs/temp0924open008_black.png}\n",
" \\vspace{-15pt}\n",
" \\caption{The illustration of (a) the credit assignment problem of outcome reward and (b) the myopic issue of discriminative process supervi... | \documentclass{article}
\usepackage{iclr2026_conference,times}
\usepackage{url}
\iclrfinalcopy % 录用后打开；投稿/评审阶段保持注释
%% ---------------------------------------------------------------
%% PACKAGE SETUP
%% ---------------------------------------------------------------
\usepackage{microtype}
\usepack... | Which component has the highest criticality score, defined as the Euclidean norm of its 7-dimensional drop vector pointing from the base to the ablation, and what is that score? | SFT, 48.81 | SELECT all rows excluding StepORLM
LOOP for each row
SELECT all metrics except Avg.
LOOP for each metric
COMPUTE drop = StepORLM value - ablated component value
COMPUTE sq = drop * drop
COMPUTE sum_sq = sum of sq
COMPUTE criticality_score = sqrt(sum_sq)
COMPUTE target_component = argmax ... |
2509.14031 | [
[
"\\begin{table*}[p]\n",
" \\centering\n",
" \\small\n",
" \\begin{tabular}{lrrrrrrrrrr}\n",
" \\hline\n",
" \\textbf{Model} & \\textbf{En-De} & \\textbf{En-Es} & \\textbf{En-Fr} & \\textbf{En-Pl} & \\textbf{En-Ru} & \\textbf{De-En} & \\textbf{Es-En} & \\textbf{Fr-En} & \\tex... | [
[
"\\begin{figure}\n",
" \\centering\n",
" \\includegraphics[width=0.85\\linewidth]{images/data_composition_gender.png}\n",
" \\caption{Composition of the English-to-German training datasets with the Gender phenomenon in Pure IWSLT and IWSLT+OpenSubtitles settings. Annotations are based on ... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | Considering only the setting where training and testing is done on the same language pair for the Gender, Formality, and Auxiliary annotation types, which pair has a different type performing best for BLEU and COMET, and what is the BLEU margin between those language pairs? When testing in the reverse translation direc... | En–De, 0.2, 0.0102 | SELECT diagonal language pairs
LOOP for each diagonal language pair
COMPUTE BLEU-best = argmax type over Gender, Formality, Auxiliary BLEU scores
COMPUTE COMET-best = argmax type over Gender, Formality, Auxiliary COMET sores
IF BLEU-best != COMET-best
COMPUTE BLEU_margin = BLEU score of BLEU-best −... |
2509.22651 | [
[
"\\begin{table}[t]\n",
"\\vspace{-0.1mm}\n",
"\\caption{Models' scores on \\fulldatasetname. Listening Tasks: GEN: General, MUS: Music, SND: Sound, SPH: Speech. Speaking Tasks: AST: Assistant, EMO: Emotion, IF: Instruction Following, MR: Multi-Round, RSN: Reasoning, RBT: Robustness, RLP: Roleplay, SFT... | [
[
"\\begin{figure}[h]\n",
"\\begin{center}\n",
" \\vspace{-2mm}\n",
" \\begin{minipage}{0.505\\textwidth}\n",
" \\centering\n",
" \\vspace{-2.2mm}\n",
" \\includegraphics[width=1\\linewidth]{figures/radar_models.pdf}\n",
" \\vspace{-3mm}\n",
" \\c... |
\documentclass{article} % For LaTeX2e
\usepackage{conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left)}}
\newc... | In speaking tasks, for each task where the Δ row shows GPT-4o-Audio scoring below the best open-source model, take the winning open-source model’s larger value between GEN and SPH scores and subtract its MDS score (treat blanks as 0). Sum these results. What is the total, and which models contribute? | 37.6, MiniCPM-o-2_6 and Freeze-Omni | SELECT speaking tasks where "Δ Best Open-source Model" value < 0
LOOP for each speaking task
COMPUTE winner_model = argmax model over overall score on this speaking task
COMPUTE higher_listen = max of winner_model gen score and winner_model sph score
COMPUTE contribution = higher_listen - winner_model mds s... |
2509.22651 | [
[
"\\begin{table}[t]\n",
"\\vspace{-0.1mm}\n",
"\\caption{Models' scores on \\fulldatasetname. Listening Tasks: GEN: General, MUS: Music, SND: Sound, SPH: Speech. Speaking Tasks: AST: Assistant, EMO: Emotion, IF: Instruction Following, MR: Multi-Round, RSN: Reasoning, RBT: Robustness, RLP: Roleplay, SFT... | [
[
"\\begin{figure}[h]\n",
"\\begin{center}\n",
" \\vspace{-2mm}\n",
" \\begin{minipage}{0.505\\textwidth}\n",
" \\centering\n",
" \\vspace{-2.2mm}\n",
" \\includegraphics[width=1\\linewidth]{figures/radar_models.pdf}\n",
" \\vspace{-3mm}\n",
" \\c... |
\documentclass{article} % For LaTeX2e
\usepackage{conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left)}}
\newc... | For a listening task where GPT-4o-Audio trails open-source models more in overall than in content scoring, take the medium-scale open-source model with the highest overall score and compute the sum of its content score minus the mean of its other listening overall scores and its SFT content–overall gap. What model and ... | Step-Audio-2-mini, 37.43 | SELECT listening task columns in overall score table
LOOP for each listening task
COMPUTE delta_overall = absolute("Δ Best Open-source Model" value in overall score table)
COMPUTE delta_content = absolute("Δ Best Open-source Model" value in content score table)
IF "Δ Best Open-source Model" value in overall... |
2509.22651 | [
[
"\\begin{table}[t]\n",
"\\caption{Models' content scores on \\fulldatasetname. Listening Tasks: GEN: General, MUS: Music, SND: Sound, SPH: Speech. Speaking Tasks: AST: Assistant, EMO: Emotion, IF: Instruction Following, MR: Multi-Round, RSN: Reasoning, RBT: Robustness, RLP: Roleplay, SFT: Safety. Viewing ... | [
[
"\\begin{figure}[h]\n",
"\\begin{center}\n",
" \\vspace{-2mm}\n",
" \\begin{minipage}{0.505\\textwidth}\n",
" \\centering\n",
" \\vspace{-2.2mm}\n",
" \\includegraphics[width=1\\linewidth]{figures/radar_models.pdf}\n",
" \\vspace{-3mm}\n",
" \\c... |
\documentclass{article} % For LaTeX2e
\usepackage{conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left)}}
\newc... | For listening tasks, find the task where GPT-4o-Audio trails the best open-source model by the smallest margin on content scores. From medium-scale models, take the leader on that task, and compute its consistency score on that task minus the mean of its other three listening content scores, then add its consistency sc... | Step-Audio-2-mini, 47.9 | SELECT listening task columns in content score table
LOOP for each listening task
IF "Δ Best Open-source Model" value < 0
COMPUTE add listening task to listening_list
SELECT listening_list
COMPUTE target_listening_task = argmax listening task over "Δ Best Open-source Model" value
SELECT medium-scale open... |
2510.01146 | [
[
"\\begin{table*}[!t]\n",
"\\centering\n",
"\\caption{Overall results of $\\modelname$ compared to other baselines when prompted with English and think on English (when applicable for reasoning models) on pairwise evaluation benchmarks. \\textbf{Bolded} and \\underline{underlined} indicate the best-per... | [
[
"\\begin{figure*}[!th]\n",
" \\centering\n",
" \\includegraphics[width=.98\\textwidth]{images/example.png}\n",
" \\caption{The $\\modelname$ model supports multilingual input and enables reasoning outputs to be tailored to user preferences. $\\modelname$ can process information, perform r... |
\documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left... | For all models are there any cases where the actual accuracy across the 4 datasets is different from the accuracy calculated by the authors? If yes, tell me how many such cases are there. | 4 | SELECT all models
LOOP for each model
COMPUTE = average of all 4 datasets
IF computed_avg != Avg. Acc.
COMPUTE add model to mismatch_models
COMPUTE mismatch_count = number of models in mismatch_models
RETURN mismatch_count
|
2510.01146 | [
[
"\\begin{table*}[!t]\n",
"\\centering\n",
"\\caption{Overall results of $\\modelname$ compared to other baselines when prompted with English and think on English (when applicable for reasoning models) on pairwise evaluation benchmarks. \\textbf{Bolded} and \\underline{underlined} indicate the best-per... | [
[
"\\begin{figure*}[!th]\n",
" \\centering\n",
" \\includegraphics[width=.98\\textwidth]{images/example.png}\n",
" \\caption{The $\\modelname$ model supports multilingual input and enables reasoning outputs to be tailored to user preferences. $\\modelname$ can process information, perform r... |
\documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left... | What is the difference between the sum of all m-RewardBench scores and the sum of all MM-Eval scores for the cases in which the calculated average across all 4 datasets does not match the printed accuracy? | 23.07 | SELECT all models
LOOP for each model
COMPUTE computed_avg = average of all 4 datasets
IF computed_avg != Avg. Acc.
COMPUTE add this model to mismatch_models
COMPUTE sum_reward = sum of m-RewardBench scores for all models in mismatch_models
COMPUTE sum_mmeval = sum of MM-Eval scores for all models in ... |
2510.01146 | [
[
"\\begin{table*}[!t]\n",
"\\centering\n",
"\\caption{Overall results of $\\modelname$ compared to other baselines when prompted with English and think on English (when applicable for reasoning models) on pairwise evaluation benchmarks. \\textbf{Bolded} and \\underline{underlined} indicate the best-per... | [
[
"\\begin{figure*}[!th]\n",
" \\centering\n",
" \\includegraphics[width=.98\\textwidth]{images/example.png}\n",
" \\caption{The $\\modelname$ model supports multilingual input and enables reasoning outputs to be tailored to user preferences. $\\modelname$ can process information, perform r... |
\documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left... | What is the difference between the sum of dataset-wise averages of those datasets that have more than 5 languages and those with less than 5 languages? | 8.64 | SELECT all datasets with language count > 5
LOOP for each dataset
COMPUTE avg_more = average(all model accuracies)
COMPUTE sum_more = sum(avg_more values)
SELECT all datasets with language count < 5
LOOP for each dataset
COMPUTE avg_less = average(all model accuracies)
COMPUTE sum_less = sum(avg_less values)
... |
2510.01172 | [
[
"\\begin{table*}[t]\n",
"\\centering\n",
"\\caption{Comparison of \\METHODNAME{} with existing methods on sequential editing. \n",
"\\emph{Eff.}, \\emph{Gen.}, \\emph{Spe.}, \\emph{Flu.} and \\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \n",
... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\vspace{-8mm}\n",
" \\includegraphics[width=0.98\\textwidth]{Figures/sphere_sparse.png} \n",
" \\caption{\n",
" (a) A weight matrix is viewed as a set of neurons (\\textcolor{red}{red dots}) on a hypersphere. \n",
" (b) Cur... |
\documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{graphicx} % for \rotatebox
\usepackage{ma... | For each model (excluding pre-edited), take the second-best method on Counterfact Specificity. Pick the one whose ZSRE Generalization differs most from its base pre-edited value, and find the difference between the sum of ZSRE and Counterfact Efficacy and the larger of their Specificity scores. Which pair is chosen, an... | Qwen2.5-7B + SPHERE, 103.45 | SELECT all models
LOOP for each model
COMPUTE rank method rows by counterfact spe descending
COMPUTE second_best_method = the method row at rank 2
COMPUTE gen_diff = absolute(zsre gen of second_best_method − zsre gen of the pre-edited)
COMPUTE chosen_pair = argmax model and its second_best_method over gen_d... |
2508.10776 | [
[
"\\begin{table*}[htbp]\n",
"\\centering\n",
"\\caption{Average annualized volatility in each portfolio. All models use $\\delta_{\\text{in}}=21$ days for estimation. Historical: historical covariances with lookback $\\delta_{in}$; EW: Equal-weighted portfolio; LW-D: Ledoit-Wolf shrinkage estimator wit... | [
[
"\\begin{figure*}[htbp]\n",
" \\centering\n",
" \\includegraphics[width=\\textwidth]{Figure/overview.pdf}\n",
" \\caption{DFL framework for GMVP construction. Historical returns of N assets are processed by DLinear to predict covariance matrix $\\Sigma$. The GMVP optimization layer comput... | \documentclass[sigconf,nonacm]{acmart} %authordraft, review,
\usepackage{framed}
\usepackage{amsthm}
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{pifont}
\usepackage{etoolbox}
\usepackage[ruled,vlined]{algorithm2e}
\usepackage{float} % H 옵션 사용 가능
\usepackage{placeins} % \FloatBarrier 명령어 사용
\newtheor... | On average which method varies more from its mean across all setups, PFL or DFL? And what is the difference? | DFL, 0.0005 | COMPUTE pfl_mean = average of pfl volatility values over all setups
COMPUTE pfl_total_abs_dev = 0
SELECT all setups
LOOP for each setup
COMPUTE abs_dev = absolute(setup pfl volatility − pfl_mean)
COMPUTE pfl_total_abs_dev += abs_dev
COMPUTE pfl_avg_abs_dev = average of all pfl_total_abs_dev
COMPUTE dfl_mean =... |
2510.03232 | [
[
"\\begin{table*}[t!]\n",
" \\centering\n",
" \\caption{Quantitative results of different learning strategies on the Kvasir-VQA dataset. All scores are reported in percentage (\\%) of VQA accuracy. Only 1\\% data are labeled during training and we use NVILA-Lite-2B as the MLLM backbone.}\n",
... | [
[
"\\begin{figure*}[!t]\n",
" \\centering\n",
" \\includegraphics[width=\\linewidth]{model1fig.pdf}\n",
" \\caption{Overview of the proposed two-stage \\nameshort~framework for OOD VQA adaptation. In \\namestagea, the QA Generator is trained using a small set of labeled question-answer pairs and ... | %File: anonymous-submission-latex-2026.tex
\documentclass[letterpaper]{article} % DO NOT CHANGE THIS
\usepackage[draft]{aaai2026} % DO NOT CHANGE THIS
\usepackage{times} % DO NOT CHANGE THIS
\usepackage{helvet} % DO NOT CHANGE THIS
\usepackage{courier} % DO NOT CHANGE THIS
\usepackage[hyphens]{url} % DO NOT CHAN... | Averaging across all categories, which of the two cases has a larger performance difference, LORA and LEAML or LEAML and fully supervised training? | LORA and LEAML | COMPUTE difference1 = absolute(average performance for LoRA - average performance for LEAML)
COMPUTE difference2 = absolute(average performance for LoRA - average performance for FullySupervised)
IF difference1 > difference2
RETURN “LoRA and LEAML”
RETURN “LEAML and FullySupervised”
|
2510.03232 | [
[
"\\begin{table*}[t!]\n",
" \\centering\n",
" \\vspace{2mm}\n",
" \\caption{Quantitative results of different learning strategies on the SPORTU dataset. All scores are reported in percentage (\\%) of VQA accuracy. ``Easy'', ``Medium'', and ``Hard'' denote different level of difficulty for ... | [
[
"\\begin{figure*}[!t]\n",
" \\centering\n",
" \\includegraphics[width=\\linewidth]{model1fig.pdf}\n",
" \\caption{Overview of the proposed two-stage \\nameshort~framework for OOD VQA adaptation. In \\namestagea, the QA Generator is trained using a small set of labeled question-answer pairs and ... | %File: anonymous-submission-latex-2026.tex
\documentclass[letterpaper]{article} % DO NOT CHANGE THIS
\usepackage[draft]{aaai2026} % DO NOT CHANGE THIS
\usepackage{times} % DO NOT CHANGE THIS
\usepackage{helvet} % DO NOT CHANGE THIS
\usepackage{courier} % DO NOT CHANGE THIS
\usepackage[hyphens]{url} % DO NOT CHAN... | For categories where LORA and LEAML differ in accuracy by more than 10%, what is the difference between the accuracy of the fully supervised model and the average accuracy of all other models? | 34.25 | SELECT all categories
LOOP for each category
COMPUTE gap_lora_leaml = absolute( lora category accuracy − leaml (ours) category accuracy)
IF gap_lora_leaml > 10
COMPUTE others_avg = average of zero-shot, lora, full-tuning, leaml (ours) category accuracies
COMPUTE diff_fs_vs_others = fully-supervi... |
2510.03224 | [
[
"\\begin{table*}[t]\n",
"\\setlength{\\tabcolsep}{0.8pt} \n",
"\\footnotesize\n",
" \\centering\n",
" \\begin{tabular}{c|l|c|c|c|c|c|c|c|c|c|c|c|c}\n",
" &Attack Strength ($\\epsilon$)&\\multicolumn{3}{c|}{0.02}&\\multicolumn{3}{c|}{0.01}&\\multicolumn{3}{c|}{0.005}&\\multicolumn{3}{c}{... | [
[
"\\begin{figure*}[t]\n",
"\\centering\n",
"\\includegraphics[width=\\textwidth]{Figures/diagram.pdf}\n",
" \\caption{\\sl\\small {\\bf Defense against adversarial attacks via stochastic resonance.} Neural networks are highly sensitive to small perturbations in the input space, which adversarial... |
\documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left... | Which attack strength proves to be the most difficult on average to reduce errors on in FGSM with d=2 across all metrics. and what is the average? | 0.002, 12.69 | SELECT all attack strengths in the fgsm section where d is 2
LOOP for each attack_strength
COMPUTE average_reduction = average of error reduced (%) values for mae, rmse, and d1-err for ours d = 2
COMPUTE hardest_strength = argmin attack_strength over average_reduction
RETURN hardest_strength, average_reduction for... |
2510.03223 | [
[
"\\begin{table}\n",
" \\scriptsize\n",
" \\centering\n",
" \\setlength{\\tabcolsep}{4pt}\n",
" \\caption{Evaluation results on six benchmarks. Best results are shown in \\lightgreen{green}, and those indicating a performance drop compared to standard greedy decoding are shown in \\... | [
[
"\\begin{figure*}[ht]\n",
"\\centering\n",
" \\centering\n",
" \\includegraphics[width=\\linewidth]{figure/overview.png}\n",
" \\caption{Comparison between existing reasoning methods and {\\selfanchor}. Due to inherent attention patterns, existing reasoning methods may easily ov... |
\documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left... | What are the average improvements from CoT to Self Anchor across all the bechmarks in the Math and BBH categories respectively? | 6.29,15.39 | SELECT all benchmarks in the Math category
LOOP for each benchmark
COMPUTE improvement = Self Anchor score - CoT score
COMPUTE math_average = average of all improvements in Math category
SELECT all benchmarks in the BBH category
LOOP for each benchmark
COMPUTE improvement = Self Anchor score - CoT score
COMPU... |
2509.06870 | [
[
"\\begin{table}[t]\n",
"\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n",
"\\centering\n",
"\\begin{tabular}{llcccc}\n",
"\\toprule\n",
"\\multicolumn{2}{r}{Aggregation Model} \n",
" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n",... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n",
" \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggreg... | \pdfoutput=1
\documentclass[]{fairmeta}
% Option "twocolumn" available, but please prioritize single-column
\title{The Majority is not always right: \\
%Reinforcement-learned aggregation}
RL training for solution aggregation}
\author[1]{Wenting Zhao}
\author[1,2]{Pranjal Aggarwal}
\author[1]{Swarnadeep Saha}
\author[... | Which dataset's average across aggregation models deviates the most from the average of all 4 datatsets across all aggregation models and how much does it deviate by? | AIME24, 23.74 | SELECT all datasets
LOOP for each dataset
COMPUTE dataset_average = average of all scores for this dataset across all aggregation methods
COMPUTE overall_average = average of dataset_average
SELECT all datasets
LOOP for each dataset
COMPUTE deviation = absolute(dataset_average − overall_average)
COMPUTE targe... |
2509.06870 | [
[
"\\begin{table}[t]\n",
"\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n",
"\\centering\n",
"\\begin{tabular}{llcccc}\n",
"\\toprule\n",
"\\multicolumn{2}{r}{Aggregation Model} \n",
" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n",... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n",
" \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggreg... | \pdfoutput=1
\documentclass[]{fairmeta}
% Option "twocolumn" available, but please prioritize single-column
\title{The Majority is not always right: \\
%Reinforcement-learned aggregation}
RL training for solution aggregation}
\author[1]{Wenting Zhao}
\author[1,2]{Pranjal Aggarwal}
\author[1]{Swarnadeep Saha}
\author[... | Which aggregation method has the second highest average score for the HMMT24 dataset and what is the average score? | Best-of-N (AceMath-72B), 29.58 | SELECT all aggregation methods
LOOP for each aggregation method
COMPUTE average_score = average of all HMMT24 scores for this aggregation_method
COMPUTE rank aggregation methods by average_score descending
COMPUTE second_highest_method = aggregation method of rank 2
RETURN second_highest_method, average_score of ... |
2509.06870 | [
[
"\\begin{table}[t]\n",
"\\caption{Results when aggregating eight solutions sampled from Qwen3-1.7B in thinking mode.}\n",
"\\centering\n",
"\\begin{tabular}{llcccc}\n",
"\\toprule\n",
"\\multicolumn{2}{r}{Aggregation Model} \n",
" & AIME24 & AIME25 & HMMT24 & HMMT25 \\\\ \\midrule\n",... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\includegraphics[width=1.0\\linewidth,trim=2.8cm 4cm 1.2cm 3cm,clip]{llmagg4.pdf}\n",
" \\caption{{\\bf \\method{}}: given a task and sampled LLM solutions as input, \\method{} uses reasoning to review, reconcile, and synthesize a final aggreg... | \pdfoutput=1
\documentclass[]{fairmeta}
% Option "twocolumn" available, but please prioritize single-column
\title{The Majority is not always right: \\
%Reinforcement-learned aggregation}
RL training for solution aggregation}
\author[1]{Wenting Zhao}
\author[1,2]{Pranjal Aggarwal}
\author[1]{Swarnadeep Saha}
\author[... | Which large language model has the best accuracy across all aggregation models for the AIME25 datatset and what is that average score? | Qwen3-8B, 72.82 | SELECT all large language models
LOOP for each model
COMPUTE average_score = average of all AIME25 scores for this language_model across all rows
COMPUTE best_model = argmax large language model over average_score
RETURN best_model, average_score of best_model
|
2510.00024 | [
[
"\\begin{table*}[htbp!]\n",
"\\centering\n",
"\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\n",
"\\renewcommand{\\arraystretch}{1.3}\n",
"\\setlength{\\tabcolsep}{5pt}\n",
"\\begin{tabular}{|>{\\raggedright\\arraybackslash}p{4cm}|\n",
">{\\centering... | [
[
"\\begin{figure}[http]\n",
" \\centering\n",
" \\includegraphics[width=1\\linewidth]{MMMA.pdf}\n",
" \\caption{Multimodal approach for the multi-agent framework for epidemic autonomous research. This framework enhances the power of multi-LLM agents by integrating multimodal data from var... | \documentclass[journal]{IEEEtran}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\providecommand{\authorrefmark}[1]{\textsuperscript{#1}} % fallback if class doesn't define it
\DeclareUnicodeCharacter{202F}{\,}
% ---------- Encoding & Fonts ----------
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepack... | On average, in which category across all 5 questions does AI outperform human answers by the second largest margin? Name the category and the difference between human and AI performance scores. | Experiment and rigour, 1.16 | SELECT all categories
LOOP for each category
SELECT all questions where this category appears
LOOP for each question
COMPUTE difference = ai score − human score
COMPUTE average_difference = average of difference
COMPUTE rank categories by average_difference descending
SELECT second_largest_categor... |
2510.00024 | [
[
"\\begin{table*}[htbp!]\n",
"\\centering\n",
"\\caption{Papers Evaluation of Five Epidemic Questions by AI and Human Reviewers}\n",
"\\renewcommand{\\arraystretch}{1.3}\n",
"\\setlength{\\tabcolsep}{5pt}\n",
"\\begin{tabular}{|>{\\raggedright\\arraybackslash}p{4cm}|\n",
">{\\centering... | [
[
"\\begin{figure}[http]\n",
" \\centering\n",
" \\includegraphics[width=1\\linewidth]{MMMA.pdf}\n",
" \\caption{Multimodal approach for the multi-agent framework for epidemic autonomous research. This framework enhances the power of multi-LLM agents by integrating multimodal data from var... | \documentclass[journal]{IEEEtran}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\providecommand{\authorrefmark}[1]{\textsuperscript{#1}} % fallback if class doesn't define it
\DeclareUnicodeCharacter{202F}{\,}
% ---------- Encoding & Fonts ----------
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepack... | In which catgegory do AI and human performances differ the most when compared on average across all questions? If there are mulltiple categories name all ot them. | Technical Soundness, Readability | SELECT (AI scores and human scores across all questions)
SELECT all categories
LOOP for each category
SELECT all settings
LOOP for each setting
COMPUTE difference = absolute(AI scores - human scores)
COMPUTE average_difference = average over difference
COMPUTE target_category = argmax over average... |
2510.00028 | [
[
"\\begin{table*}[h]\n",
"\\centering\n",
"\\caption{Performance of LLaMA-2-7B on standard LLM benchmarks under different quantization and PI settings. Zero-shot accuracy on 5 tasks plus average and WikiText2 perplexity.}\n",
"\\vspace{-2mm}\n",
"\\label{tab:result-llama-2-7b}\n",
"\\resize... | [
[
"\\begin{figure*}[t]\n",
"\\centering\n",
"\\begin{subfigure}[t]{0.49\\textwidth}\n",
" \\centering\n",
" \\includegraphics[width=\\linewidth]{four_methods_no_pi_style2.pdf}\n",
" \\caption{Non-Interpolated models}\n",
" \\label{left}\n",
"\\end{subfigure}\n",
"\\hf... |
\documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
% Mark sections of captions for referring to divisions of figures
\newcommand{\figleft}{{\em (Left... | On which dataset does extended context improve performance the most when compared on average across all settings and by how much? | WikiText2_PPL, 0.68 | SELECT all datasets
LOOP for each dataset
COMPUTE average_extended = average(extended context performance across all settings)
COMPUTE average_normal = average(normal context performance across all settings)
COMPUTE improvement = average_extended - average_normal
COMPUTE target_dataset = argmax dataset ov... |
2510.01172 | [
[
"\\begin{table*}[t]\n",
"\\centering\n",
"\\caption{Comparison of \\METHODNAME{} with existing methods on sequential editing. \n",
"\\emph{Eff.}, \\emph{Gen.}, \\emph{Spe.}, \\emph{Flu.} and \\emph{Consis.} denote Efficacy, Generalization, Specificity, Fluency and Consistency, respectively. \n",
... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \\vspace{-8mm}\n",
" \\includegraphics[width=0.98\\textwidth]{Figures/sphere_sparse.png} \n",
" \\caption{\n",
" (a) A weight matrix is viewed as a set of neurons (\\textcolor{red}{red dots}) on a hypersphere. \n",
" (b) Cur... |
\documentclass{article} % For LaTeX2e
\usepackage{iclr2026_conference,times}
% Optional math commands from https://github.com/goodfeli/dlbook_notation.
%%%%% NEW MATH DEFINITIONS %%%%%
\usepackage{amsmath,amsfonts,bm}
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{graphicx} % for \rotatebox
\usepackage{ma... | Across both model blocks, keep only methods that are second-best in any ZSRE metric but not best in any Counterfact metric. For each, compute the average of ZSRE Eff. and Counterfact Gen., then find the method with the highest such average. Report its model, method, and the difference between Counterfact Flu. and ZSRE ... | LLaMA3-8B, AlphaEdit, 453.58 | SELECT all model blocks
LOOP for each model block
SELECT model name of this block
SELECT all methods in this block
LOOP for each method
IF any zsre metric for this model block and metric is underlined for this method AND NOT any counterfact metric for this model block and metric is bolded for this m... |
2510.20797 | [
[
"\\begin{table*}[!ht]\n",
" \\small\n",
" \\centering\n",
" \\setlength{\\tabcolsep}{5pt}\n",
" \\resizebox{\\textwidth}{!}{%\n",
"\\begin{tabular}{llcccccccc}\n",
"\\toprule\n",
"\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\text... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \n",
" \\def\\uniformscale{0.23} %\n",
" \n",
" \\newlength{\\fixedheight}\n",
" \\setlength{\\fixedheight}{5.3cm}\n",
" \n",
" \\begin{subfigure}[t]{0.31\\textwidth}\n",
" \\centering\n",
" ... |
\documentclass{article} %
\usepackage{iclr2026_conference,times}
\usepackage{graphicx} %
\usepackage{subcaption} %
\usepackage{adjustbox}
\usepackage{calc}
\usepackage{tikz}
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{float}
\usepackage{amssymb}
\usepackage{wrapfig}
\usepackage{amsmath,amsfonts,bm}
... | Across the proposed methods using 4×Single training only, for each base model select the method whose score is closest to the midpoint between its Original and No Ctx scores. Among these selected methods, which (model, method) achieves the highest 16× Multi score, and what is the difference between 16×Multi and 128×Sin... | Qwen3-8B, Compression-Tokens (Causal), 10.94 | SELECT all base models
LOOP for each base model
COMPUTE midpoint = average(Original score, No Ctx score)
SELECT all methods of this base model under 4× Single
LOOP for each method
COMPUTE distance_to_midpoint = absolute(4× Single score − midpoint)
COMPUTE selected_method = argmin method over dis... |
2510.20797 | [
[
"\\begin{table}[H]\n",
" \\small\n",
" \\centering\n",
" \\setlength{\\tabcolsep}{5pt}\n",
" \\resizebox{\\textwidth}{!}{%\n",
"\\begin{tabular}{llcccccccc}\n",
"\\toprule\n",
"\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{\\textbf{Original}} & \\multicolumn2{c}{\\textbf{... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
" \n",
" \\def\\uniformscale{0.23} %\n",
" \n",
" \\newlength{\\fixedheight}\n",
" \\setlength{\\fixedheight}{5.3cm}\n",
" \n",
" \\begin{subfigure}[t]{0.31\\textwidth}\n",
" \\centering\n",
" ... |
\documentclass{article} %
\usepackage{iclr2026_conference,times}
\usepackage{graphicx} %
\usepackage{subcaption} %
\usepackage{adjustbox}
\usepackage{calc}
\usepackage{tikz}
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{float}
\usepackage{amssymb}
\usepackage{wrapfig}
\usepackage{amsmath,amsfonts,bm}
... | Within the proposed methods, keep only those (model, method) pairs whose change from 4×Multi to 4×Single change has opposite signs when measured by exact match and accuracy. Among those pairs, find the one that maximizes the mean of the absolute difference between 16×Multi and 16×Single computed with both metrics. Repo... | Gemma2-2B, Compression-Tokens (Bidirectional), 2.215 | SELECT all model names under Our Methods
LOOP for each model
SELECT all methods under this model
LOOP for each method
COMPUTE diff_em_4 = 4× Multi exact match score − 4× Single exact match score
COMPUTE diff_acc_4 = 4x Multi accuracy score - 4x Single accuracy score
IF diff_em_4 and diff... |
2509.03962 | [
[
"\\begin{table*}[!t]\n",
" \\centering\n",
" \\small\n",
" \\begin{tabular}{llccccccccc}\n",
" \\hline\n",
" \\textbf{Training Data} & \\textbf{Model} \n",
" & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n",
" & \\multicolumn{3}{... | [
[
"\\begin{figure}[!t]\n",
" \\centering\n",
" \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n",
" \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n",
" \\label{fig:LadinArea}\n",
"\\end{figure}\n"
],
[
"\\begin{figure*}[t]\n",
... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | If we take the ratio of t1 subset to t2 subset for all the models and multiply that value with t3 subset along which metric is the net value highest? For which model? Also, for that model across the table, formulate a polynomial regression function f, what is f(2)? | 55.33,Rouge NLLB 1.3 B,23992.3 | SELECT all metrics
LOOP for each metric
SELECT all models
LOOP for each model
COMPUTE net_value = t1 / t2 × t3
COMPUTE best_pair = argmax model and metric pair over net_value
SELECT all numeric values for best_model across the table in left-to-right order as coeff_list
COMPUTE degree = count of coef... |
2509.03962 | [
[
"\\begin{table*}[!t]\n",
" \\centering\n",
" \\small\n",
" \\begin{tabular}{llccccccccc}\n",
" \\hline\n",
" \\textbf{Training Data} & \\textbf{Model} \n",
" & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n",
" & \\multicolumn{3}{... | [
[
"\\begin{figure}[!t]\n",
" \\centering\n",
" \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n",
" \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n",
" \\label{fig:LadinArea}\n",
"\\end{figure}\n"
],
[
"\\begin{figure*}[t]\n",
... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | If we take all the values across the table for NLLB 1.3B and formulate an polynomial regression function with the last term being the constant, will f(5) be greater than 10000? | Yes | SELECT all numeric values in the NLLB 1.3 B row in left-to-right order as coeff_list
COMPUTE degree = count of coeff_list − 1
LOOP for each coeff in coeff_list with its index i in order
COMPUTE f5 += coeff * (5 ^ (degree − i))
IF f5 > 10000
RETURN yes
RETURN no
|
2509.03962 | [
[
"\\begin{table*}[!t]\n",
" \\centering\n",
" \\small\n",
" \\begin{tabular}{llccccccccc}\n",
" \\hline\n",
" \\textbf{Training Data} & \\textbf{Model} \n",
" & \\multicolumn{3}{c}{\\textbf{BLEU}} & \\multicolumn{3}{c}{\\textbf{Rouge}} \n",
" & \\multicolumn{3}{... | [
[
"\\begin{figure}[!t]\n",
" \\centering\n",
" \\includegraphics[width=2.35in]{latex/Ladin_Italia.jpg}\n",
" \\caption{A map highlighting the Ladin speaking region in South Tyrol, Northern Italy.}\n",
" \\label{fig:LadinArea}\n",
"\\end{figure}\n"
],
[
"\\begin{figure*}[t]\n",
... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | If we take all the values across the table for NLLB 1.3B and formulate an polynomial regression function with the last term being the constant, what is the degree of the polynomial function? | 8 | SELECT all numeric values for model NLLB 1.3 B
COMPUTE term_count = number of selected values
COMPUTE degree = term_count - 1
RETURN degree
|
2510.21604 | [
[
"\\begin{table*}[h]\n",
" \\centering\n",
" \\caption{Performance Comparison of LLMs on BizFinBench~\\citep{lu2025bizfinbench0}. The colors represent the top three performers for each task: \\colorbox{golden}{golden} indicates the top-performing model, \\colorbox{lightblue}{silver} represents the se... | [
[
"\\begin{figure*}\n",
" \\centering\n",
" \\includegraphics[width=0.95\\textwidth]{dataset.pdf}\n",
" \\caption{Overview of data sample for one stock at trading day t.}\n",
" \\label{fig:dataset}\n",
"\\end{figure*}\n"
],
[
"\\begin{figure*}\n",
"\t\\centering\n",
"\t\\... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
% \PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2022
\PassOptionsToPackage{table}{xcolor}
% ready for submission
% \usepackage{neurips_2025}
% \usepackage{iclr2026_conference,times}
% \usepackage[preprint]{iclr2... | Among the proposed LLMs, keep only model families whose Average increases monotonically from Instruct --> SFT --> SFT GRPO, which family has the larger gain from Instruct to SFT GRPO? For that family's SFT GRPO model, on how many metrics does it outperform GPT-4o? | 14B, 3 | SELECT all model families in Our LLMs
LOOP for each family
IF Instruct Average < SFT Average AND SFT Average < SFT GRPO Average
COMPUTE gain = SFT GRPO Average − Instruct Average
COMPUTE target_family = argmax family over gain
COMPUTE outperform_count = 0
SELECT all task metrics excluding average
LOOP for... |
2406.02069 | [
[
"\\begin{table*}[t]\n",
"\n",
"\\centering\n",
"\n",
"\n",
"\n",
"\\resizebox{\\textwidth}{!}{\n",
"\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\... | [
[
"\\begin{figure}\n",
" \\centering\n",
" \\includegraphics[width=\\columnwidth]{Figures/dynamickv4.pdf}\n",
" \\caption{\n",
" Illustration of~\\method compared with existing KV cache compression methods.\n",
" (a) Full KV has all tokens stored in the KV cache in each layer;... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
% \PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2024
% ready for submission
% \usepackage[preprint]{neurips_2024}
\usepackage{iclr2025_conference,times}
\iclrfinalcopy
% \usepackage{neurips_2024}
% \iclrfinalco... | When the proposed method is applied to Llama 8B models, is there a task where, for any of the data sets in it, the KV size of 64 outperforms both full KV cache and KV sixe of 2048. If so, name the task and the margin by which it outperforms KV size of 2048. If not, just say No | Synthetic, 0.25 | SELECT all tasks where method is authors' method AND base model is llama 8b
LOOP for each task
SELECT all datasets in this task
LOOP for each dataset
IF kv size 64 score > full kv cache score AND kv size 64 score > kv size 2048 score
COMPUTE margin = kv size 64 score - kv size 2048 score
... |
2406.02069 | [
[
"\\begin{table*}[t]\n",
"\n",
"\\centering\n",
"\n",
"\n",
"\n",
"\\resizebox{\\textwidth}{!}{\n",
"\\begin{tabular}{l@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\hspace{0.05ex}}c@{\\... | [
[
"\\begin{figure}\n",
" \\centering\n",
" \\includegraphics[width=\\columnwidth]{Figures/dynamickv4.pdf}\n",
" \\caption{\n",
" Illustration of~\\method compared with existing KV cache compression methods.\n",
" (a) Full KV has all tokens stored in the KV cache in each layer;... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
% \PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2024
% ready for submission
% \usepackage[preprint]{neurips_2024}
\usepackage{iclr2025_conference,times}
\iclrfinalcopy
% \usepackage{neurips_2024}
% \iclrfinalco... | When the proposed method is applied to Llama 70B models, is there a task where, for any of the data sets in it, the KV size of 64 outperforms both full KV cache and KV size of 2048. If so, name the task and the margin by which it outperforms KV size of 2048. If not, just say No. | Code, 3.98 | SELECT all tasks where method is authors' method AND base model is llama 70b
LOOP for each task
SELECT all datasets in this task
LOOP for each dataset
IF kv size 64 score > full kv cache score AND kv size 64 score > kv size 2048 score
COMPUTE margin = kv size 64 score - kv size 2048 score
... |
2510.24706 | [
[
"\\begin{table*}[t!]\n",
"\\centering\n",
"\\caption{Overall performance comparison of LLMs across VR games (5-shot setting). Best model performance per metric is \\textbf{bolded}, second best is \\underline{underlined}.}\n",
"\\label{tab:overall_performance_1}\n",
"\\resizebox{\\textwidth}{!}... | [
[
"\\begin{table*}[t!]\n",
"\\centering\n",
"\\caption{Overall performance comparison of LLMs across VR games (5-shot setting). Best model performance per metric is \\textbf{bolded}, second best is \\underline{underlined}.}\n",
"\\label{tab:overall_performance_1}\n",
"\\resizebox{\\textwidth}{!}... |
\documentclass{article} %
\usepackage{iclr2026_conference,times}
%
%
\usepackage{amsmath,amsfonts,bm}
%
\newcommand{\figleft}{{\em (Left)}}
\newcommand{\figcenter}{{\em (Center)}}
\newcommand{\figright}{{\em (Right)}}
\newcommand{\figtop}{{\em (Top)}}
\newcommand{\figbottom}{{\em (Bottom)}}
\newcommand{\captiona}{{... | Among model rows (excluding Human), identify all model-game pairs where the same model has at least one best and one second best metric within that game. Which pair has the highest value for the sum of NSAS-SSC and F1_SOP-SOP? For that model, how many of its metrics exceed the Human row? | GPT-4o -- Vivecraft, 12 | SELECT all models except Human
LOOP for each model
SELECT all games
LOOP for each game
COMPUTE best_metrics_in_game = number of metric types where this model is bolded in this game
COMPUTE second_metrics_in_game = number of metric types where this model is underlined in this game
IF best... |
2511.01815 | [
[
"\\begin{table*}[t!]\n",
" \\caption{\\small Accuracy of KV cache compression methods. Results within $1$ score point of vanilla are in \\textbf{bold}. See Appendix \\ref{sec:appendix_stderr} for standard error analysis. \\methodopcrdef{}{\\mathrm{CR}} denotes \\Method{} set for $\\mathrm{CR}\\times$ c... | [
[
"\\begin{figure*}[t]\n",
" \\centering\n",
" \\subfloat[Keys]{\n",
" \\centering\n",
" \\includegraphics[width=0.48\\linewidth]{figures/cosine_keys.pdf}\n",
" \\label{fig:kv-cache-between-heads-key}\n",
" }\n",
" \\subfloat[Values]{\n",
" \\cente... |
%
%
\documentclass[10pt, logo]{nvidiatechreport} %
%
%
\usepackage{natbib}
\usepackage{xurl} %
\usepackage{hyperref}
\usepackage{url}
%
%
%
%
%
%
\usepackage{graphicx} %
\usepackage{wrapfig}
%
%
%
\usepackage{caption} %
%
%
%
%
%
\usepackage{algorithm}
\usepackage{algorithmic}
%
%
%
%
%
%
%
%
%
%
... | Among methods with compression ratios of at least 30×, for each base model choose the method whose GSM8K/MMLU average is closest to that model’s vanilla GSM8K/MMLU average. Across these chosen methods, which base model’s method has the greatest number of bolded scores across all datasets, and what are that count and it... | Mistral NeMo 12B, 5, -2.1 | SELECT all base models
LOOP for each base model
COMPUTE vanilla_average = average of vanilla GSM8K and MMLU
SELECT all methods with compression ratio ≥ 30×
LOOP for each method
COMPUTE method_average = average of this method’s GSM8K and MMLU
COMPUTE distance = absolute(method_average − vani... |
2505.16986 | [
[
"\\begin{table*}[!ht]\n",
"\\centering\n",
"\\resizebox{\\textwidth}{!}{\n",
" \\begin{tabular}{lcccc|cccc|c|cc|c}\n",
" \\toprule\n",
" \\textbf{Domain} & \\multicolumn{4}{c}{\\textbf{Tool Call}} & \\multicolumn{4}{|c|}{\\textbf{Parameter Matching}} & \\textbf{Code Exec. Rate} & ... | [
[
"\\begin{figure*}[!t]\n",
" \\centering\n",
" \\includegraphics[width=\\textwidth]{assets/pipeline.png}\n",
" \\caption{Illustrative example from the $\\benchmarkname$ dataset. This example showcases a multi-domain scenario involving both flights and hotels, where the user is planning a t... | \documentclass{article}
% if you need to pass options to natbib, use, e.g.:
% \PassOptionsToPackage{numbers, compress}{natbib}
% before loading neurips_2024
\usepackage[square,numbers]{natbib}
\bibliographystyle{abbrvnat}
% ready for submission
% \usepackage[]{neurips_2025}
\usepackage[preprint]{neurips_2025}
... | For the tool call evaluation, what is the largest difference, across all metrics, between the best single-domain result and the best multi-domain result? And what is the metric? | 8.48, Accuracy | SELECT all metrics under tool call evaluation
LOOP for each metric
COMPUTE max_single = max in single-domain
COMPUTE max_multi = max in multi-domain
COMPUTE difference = max_single − max_multi
COMPUTE target_metric = argmax metric over difference
RETURN difference of target_metric, target_metric
|
2511.05407 | [
[
"\\begin{table*}[t]\n",
"\\centering\n",
"\\scalebox{0.92}{\n",
"\\begin{tabular}{lcccccccccccc}\n",
"\\toprule\n",
"\\multirow{2}{*}{Models} & \\multicolumn{4}{c}{Minority} & \\multicolumn{4}{c}{Majority} & \\multicolumn{4}{c}{Minority+Majority} \\\\\n",
"\\cmidrule(lr){2-5} \\cmidrul... | [
[
"\\begin{figure}[t]\n",
" \\centering\n",
"\\includegraphics[width=\\linewidth]{figs/intro7.pdf}\n",
" \\caption{\n",
" \\textcolor{orange}{Majority} and \\textcolor{CBlue}{minority} users may assign different satisfaction ratings to system responses employing the same strategy due to... | % This must be in the first 5 lines to tell arXiv to use pdfLaTeX, which is strongly recommended.
\pdfoutput=1
% In particular, the hyperref package requires pdfLaTeX in order to break URLs across lines.
\documentclass[11pt]{article}
% Change "review" to "final" to generate the final (sometimes called camera-ready) v... | Upon all group-level evaluation setting, in F1 high satisfication metric, which model has the largest improvment to its M^2PC enhanced one? | Llama-3-8B | SELECT all models
LOOP for each model
SELECT all group-level evaluation settings
LOOP for each group-level setting
COMPUTE improvement = F1 high satisfaction score for M2PC-enhanced − F1 high satisfaction score for original model
COMPUTE target_model = argmax model over improvement
RETURN target_model... |
2511.11473 | [
[
"\\begin{table*}[t!]\n",
"\\caption{Evaluation on English (Libri, Candor, SpokenWoZ) and Mandarin (RAMC) testsets.}\n",
"\\vskip -0.1in\n",
"\\centering\n",
" \\setlength{\\tabcolsep}{5.3pt}\n",
"{\\footnotesize\n",
"\\begin{tabular}{lcccccccc}\n",
"\\toprule\n",
"& \\multicol... | [
[
"\\begin{figure}[t!]\n",
" \\centering\n",
" \\vskip -0.1in\n",
" \\includegraphics[width=\\linewidth]{figs/teaser_figure.pdf}\n",
" \\vskip -0.1in\n",
" \\caption{In multi-conversation settings, our proactive hearing assistant uses conversational turn-taking dynamics to au... |
%% IMPORTANT NOTICE:
%%
%% For the copyright see the source file.
%%
%% Any modified versions of this file must be renamed
%% with new filenames distinct from sample-sigconf-authordraft.tex.
%%
%% For distribution of the original source see the terms
%% for copying and modification in the file samples.dtx.
%%
%% T... | Considering only English testsets, find the testset where switching from the Baseline Model to its Dual counterpart yields the largest reduction in non-spatialized CR. Relative to the baseline of the identified testset, which Libri variant has the greatest combined improvement in non-spatialized SISDRi and ΔPESQ, and w... | Libri (2spk), 15.73 | SELECT all table cell values except headers
COMPUTE distinct value, count of that value
COMPUTE value with minimum count
SELECT framework where any value is that value
RETURN framework, value
|
2508.20729 | [
[
"\\begin{table}\n",
"\\begin{center}\n",
"\\def~{\\hphantom{0}}\n",
"\\begin{tabular}{c|c|c|c|c|c|c}\n",
"\\cline{1-7}\n",
"&Reasoning&Expansion&Debugging&Refinement&\\makecell{Review}&\\makecell{Single/Multiple\\\\ LLMs} \\\\ \\cline{1-7}\n",
"\\makecell{Non-reasoning\\\\ LLMs}&$\\usy... | [
[
"\\begin{table}\n",
"\\begin{center}\n",
"\\def~{\\hphantom{0}}\n",
"\\begin{tabular}{c|c|c|c|c|c|c}\n",
"\\cline{1-7}\n",
"&Reasoning&Expansion&Debugging&Refinement&\\makecell{Review}&\\makecell{Single/Multiple\\\\ LLMs} \\\\ \\cline{1-7}\n",
"\\makecell{Non-reasoning\\\\ LLMs}&$\\usy... | \documentclass{article}
\usepackage{arxiv}
\usepackage[utf8]{inputenc} % allow utf-8 input
\usepackage[T1]{fontenc} % use 8-bit T1 fonts
\usepackage{hyperref} % hyperlinks
\usepackage{url} % simple URL typesetting
\usepackage{booktabs} % professional-quality tables
\usepackage{amsfonts} ... | What is the minimum mode value in the given table (apart from the row heads and column heads) and for what LLM agent framework it is? | CodePDE Agent : based on posterior error,Our Agent: Multiple | null |
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