Daily Papers

Semi-supervised semantic segmentation (SSSS) aims to improve segmentation performance by utilising unlabeled data alongside limited labeled samples. Existing SSSS methods often face challenges such as coupling, where over-reliance on initial labeled data leads to suboptimal learning; confirmation bias, where incorrect predictions reinforce themselves repeatedly; and boundary blur caused by insufficient boundary-awareness and ambiguous edge information. To address these issues, we propose CW-BASS, a novel framework for SSSS. In order to mitigate the impact of incorrect predictions, we assign confidence weights to pseudo-labels. Additionally, we leverage boundary-delineation techniques, which, despite being extensively explored in weakly-supervised semantic segmentation (WSSS) remain under-explored in SSSS. Specifically, our approach: (1) reduces coupling through a confidence-weighted loss function that adjusts the influence of pseudo-labels based on their predicted confidence scores, (2) mitigates confirmation bias with a dynamic thresholding mechanism that learns to filter out pseudo-labels based on model performance, (3) resolves boundary blur with a boundary-aware module that enhances segmentation accuracy near object boundaries, and (4) reduces label noise with a confidence decay strategy that progressively refines pseudo-labels during training. Extensive experiments on the Pascal VOC 2012 and Cityscapes demonstrate that our method achieves state-of-the-art performance. Moreover, using only 1/8 or 12.5\% of labeled data, our method achieves a mIoU of 75.81 on Pascal VOC 2012, highlighting its effectiveness in limited-label settings.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

Large Reasoning Models (LRMs) perform strongly in complex reasoning tasks via Chain-of-Thought (CoT) prompting, but often suffer from verbose outputs caused by redundant content, increasing computational overhead, and degrading user experience. Existing compression methods either operate post-hoc pruning, risking disruption to reasoning coherence, or rely on sampling-based selection, which fails to intervene effectively during generation. In this work, we introduce a confidence-guided perspective to explain the emergence of redundant reflection in LRMs, identifying two key patterns: Confidence Deficit, where the model reconsiders correct steps due to low internal confidence, and Termination Delay, where reasoning continues even after reaching a confident answer. Based on this analysis, we propose ConCISE (Confidence-guided Compression In Step-by-step Efficient Reasoning), a framework that simplifies reasoning chains by reinforcing the model's confidence during inference, thus preventing the generation of redundant reflection steps. It integrates Confidence Injection to stabilize intermediate steps and Early Stopping to terminate reasoning when confidence is sufficient. Extensive experiments demonstrate that fine-tuning LRMs on ConCISE-generated data yields significantly shorter outputs, reducing length by up to approximately 50% under SimPO, while maintaining high task accuracy. ConCISE consistently outperforms existing baselines across multiple reasoning benchmarks.

While confidence estimation is a promising direction for mitigating hallucinations in Large Language Models (LLMs), current research dominantly focuses on single-turn settings. The dynamics of model confidence in multi-turn conversations, where context accumulates and ambiguity is progressively resolved, remain largely unexplored. Reliable confidence estimation in multi-turn settings is critical for many downstream applications, such as autonomous agents and human-in-the-loop systems. This work presents the first systematic study of confidence estimation in multi-turn interactions, establishing a formal evaluation framework grounded in two key desiderata: per-turn calibration and monotonicity of confidence as more information becomes available. To facilitate this, we introduce novel metrics, including a length-normalized Expected Calibration Error (InfoECE), and a new "Hinter-Guesser" paradigm for generating controlled evaluation datasets. Our experiments reveal that widely-used confidence techniques struggle with calibration and monotonicity in multi-turn dialogues. We propose P(Sufficient), a logit-based probe that achieves comparatively better performance, although the task remains far from solved. Our work provides a foundational methodology for developing more reliable and trustworthy conversational agents.

Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute. Improving reasoning quality directly would require process reward models, but the step-level annotations needed to train them are expensive and scarce. We find such a signal in how the model's confidence evolves during reasoning: premature confidence, the tendency to commit to an answer early and use the remaining tokens to rationalize it, strongly predicts flawed reasoning across tasks and model scales. We exploit this in progressive confidence shaping, a reinforcement learning objective that trains models to update their confidence as they reason rather than commit early -- rewarding gradual confidence growth and penalizing early commitment, with no external labels or reward models. The method improves accuracy and reasoning quality from 1.5B to 8B parameters across arithmetic (Countdown), math (DAPO, AIME), and science (ScienceQA): on Countdown, accuracy improves 3.2x (+42.0pp) and flawed reasoning drops 48pp; on AIME, Pass@64 improves 6.6pp. Consistent with this mechanism, the method also improves faithfulness: on a safety benchmark, our models more transparently surface misleading content in their reasoning traces rather than concealing it. Controlled experiments reveal that the problem and its remedy scale together: premature confidence grows with model size and task difficulty, and so do the gains from addressing it.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design confidence-based efficient test-time scaling methods to handle queries of various difficulty, such as Early-Stopping for Best-of-N and Self-Consistency with calibrated confidence. Experiments on three LLMs across six datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping to Best-of-N improves MathQA accuracy from 81.0 to 83.6 with a sample budget of 16 responses, indicating the efficacy of confidence-based sampling strategy at inference time.

Empowering large language models to accurately express confidence in their answers is essential for trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks-confidence calibration and failure prediction-across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2 Chat. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve. 3) Employing our proposed strategies, such as human-inspired prompts, consistency among multiple responses, and better aggregation strategies can help mitigate this overconfidence from various perspectives. 4) Comparisons with white-box methods indicate that while white-box methods perform better, the gap is narrow, e.g., 0.522 to 0.605 in AUROC. Despite these advancements, none of these techniques consistently outperform others, and all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs.

Large language models (LLMs) often produce confident yet incorrect answers, which can lead to risky failures in real-world applications. We study whether post-training can make a model's self-assessment explicit: when the model is uncertain, can it be trained to signal so within its own response? A central design question is where in the response this signal should be exposed -- during reasoning, while the answer is still being formed, or at the end, once the answer has been produced. We study both. For end-of-reasoning self-assessment, we train the model to verbalize a confidence score for its response, with the aim of high confidence on correct answers and low confidence on incorrect ones. For during-reasoning self-assessment, we train the model to emit the marker <uncertain> whenever its current reasoning state appears unreliable. Across factual reasoning tasks, both forms sharply reduce overconfident errors while improving answer quality, and both can be used as triggers for retrieval augmented generation (RAG) to improve the final response. We further analyze their internal mechanisms: end-of-reasoning verbalized confidence sharpens a confidence-related structure already present in the pretrained model, whereas during-reasoning <uncertain> emission teaches the model to mark high-risk reasoning steps, with parameter changes concentrated in the model's late layers.

Model evolution and constant availability of data are two common phenomena in large-scale real-world machine learning applications, e.g. ads and recommendation systems. To adapt, the real-world system typically retrain with all available data and online learn with recently available data to update the models periodically with the goal of better serving performance. In this paper, we propose a novel framework, named Confidence Ranking, which designs the optimization objective as a ranking function with two different models. Our confidence ranking loss allows direct optimization of the logits output for different convex surrogate functions of metrics, e.g. AUC and Accuracy depending on the target task and dataset. Armed with our proposed methods, our experiments show that the introduction of confidence ranking loss can outperform all baselines on the CTR prediction tasks of public and industrial datasets. This framework has been deployed in the advertisement system of JD.com to serve the main traffic in the fine-rank stage.

Confidence in LLMs is a useful indicator of model uncertainty and answer reliability. Existing work mainly focused on single-turn scenarios, while research on confidence in complex multi-turn interactions is limited. In this paper, we investigate whether LLM-based search agents have the ability to communicate their own confidence through verbalized confidence scores after long sequences of actions, a significantly more challenging task compared to outputting confidence in a single interaction. Experimenting on open-source agentic models, we first find that models exhibit much higher task accuracy at high confidence while having near-zero accuracy when confidence is low. Based on this observation, we propose Test-Time Scaling (TTS) methods that use confidence scores to determine answer quality, encourage the model to try again until reaching a satisfactory confidence level. Results show that our proposed methods significantly reduce token consumption while demonstrating competitive performance compared to baseline fixed budget TTS methods.

Large Language Models (LLMs) have shown remarkable capabilities across various tasks, but their deployment in high-stake domains requires consistent performance across multiple interaction rounds. This paper introduces a comprehensive framework for evaluating and improving LLM response consistency, making three key contributions. First, we propose a novel Position-Weighted Consistency (PWC) score that captures both the importance of early-stage stability and recovery patterns in multi-turn interactions. Second, we present a carefully curated benchmark dataset spanning diverse domains and difficulty levels, specifically designed to evaluate LLM consistency under various challenging follow-up scenarios. Third, we introduce Confidence-Aware Response Generation (CARG), a framework that significantly improves response stability by incorporating model confidence signals into the generation process. Empirical results demonstrate that CARG significantly improves response stability without sacrificing accuracy, underscoring its potential for reliable LLM deployment in critical applications.

On-policy distillation transfers reasoning capabilities by training a student model on its own generated trajectories using token-level feedback from a teacher. However, we identify a critical bottleneck, Supervision Fidelity Decay (SFD): as student-generated prefixes lengthen, the teacher's next-token distribution becomes less confident and less discriminative. Consequently, the teacher-dependent corrective signal in reverse-KL distillation weakens, causing student drift to compound across long reasoning chains. To mitigate SFD, we introduce Lookahead Group Reward (\ours{)}. Building on the insight that next-step teacher confidence reflects the discriminative strength of future reverse-KL supervision, evaluates the student's top-K candidate tokens by the teacher confidence they induce at the subsequent step and assigns a group-normalized reward. To maintain computational efficiency, we further design an entropy-triggered tree-attention mechanism. Across six math and code benchmarks, improves mean@8 by 2.57 points over OPD for a 7B student, with gains increasing in longer-generation and reaching +4.92 points on AIME-26 at 39k tokens.

Large language models (LLMs) often produce answers with high certainty even when they are incorrect, making reliable confidence estimation essential for deployment in real-world scenarios. Verbalized confidence, where models explicitly state their confidence in natural language, provides a flexible and user-facing uncertainty signal that can be applied even when token logits are unavailable. However, existing verbalized-confidence methods often optimize answer generation and confidence generation jointly, which can cause confidence-alignment objectives to interfere with answer accuracy. In this work, we propose a decoupled and order-aware framework for verbalized confidence calibration. Our method first generates an answer and then estimates confidence conditioned on the fixed question--answer pair, allowing confidence optimization without directly perturbing the answer-generation process. To align confidence with correctness likelihood, we construct a sampling-based surrogate from multiple model completions and optimize rank-based reinforcement learning objectives that encourage responses with higher estimated correctness likelihood to receive higher verbalized confidence. Experiments on reasoning and knowledge-intensive benchmarks show that our method improves calibration and failure prediction performance while largely preserving answer accuracy. These results demonstrate that verbalized confidence can be more reliably aligned by decoupling confidence estimation from answer generation and optimizing the relative ordering of confidence across responses.

Recent advances in Transformer-based large language models (LLMs) have led to significant performance improvements across many tasks. These gains come with a drastic increase in the models' size, potentially leading to slow and costly use at inference time. In practice, however, the series of generations made by LLMs is composed of varying levels of difficulty. While certain predictions truly benefit from the models' full capacity, other continuations are more trivial and can be solved with reduced compute. In this work, we introduce Confident Adaptive Language Modeling (CALM), a framework for dynamically allocating different amounts of compute per input and generation timestep. Early exit decoding involves several challenges that we address here, such as: (1) what confidence measure to use; (2) connecting sequence-level constraints to local per-token exit decisions; and (3) attending back to missing hidden representations due to early exits in previous tokens. Through theoretical analysis and empirical experiments on three diverse text generation tasks, we demonstrate the efficacy of our framework in reducing compute -- potential speedup of up to times 3 -- while provably maintaining high performance.

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.

The stability of recursively trained large language models (LLMs) is a foundational problem for AI safety. Prevailing theory predicts model collapse, a progressive degradation when models are trained on their own output. We challenge this narrative by introducing a selective feedback mechanism. Contrary to expectation, instead of merely slowing decay, our experiments provide strong evidence that this pressure reverses it, inducing a statistically significant performance improvement in a Gemma 2B model on a complex summarization task. We name this phenomenon the Anti-Ouroboros Effect. We contrast this with a foundational experiment using a simple classifier, where the theoretical degenerative loop was validated, highlighting the unique dynamics of high-dimensional models. Our findings establish that systemic resilience can be an emergent property of LLMs under simple selection pressure, suggesting a powerful and scalable principle for developing safer and more robust AI systems. Across five generations, a quality-filtered condition improved by 6.6% in ROUGE-L F1 score, whereas an unfiltered control degraded by 3.5% and a random-filter control degraded by 4.2%

Large language models (LLMs) are increasingly used in applications requiring factual accuracy, yet their outputs often contain hallucinated responses. While fact-checking can mitigate these errors, existing methods typically retrieve external evidence indiscriminately, overlooking the model's internal knowledge and potentially introducing irrelevant noise. Moreover, current systems lack targeted mechanisms to resolve specific uncertainties in the model's reasoning. Inspired by how humans fact-check, we argue that LLMs should adaptively decide whether to rely on internal knowledge or initiate retrieval based on their confidence in a given claim. We introduce Probabilistic Certainty and Consistency (PCC), a framework that estimates factual confidence by jointly modeling an LLM's probabilistic certainty and reasoning consistency. These confidence signals enable an adaptive verification strategy: the model answers directly when confident, triggers targeted retrieval when uncertain or inconsistent, and escalates to deep search when ambiguity is high. Our confidence-guided routing mechanism ensures that retrieval is invoked only when necessary, improving both efficiency and reliability. Extensive experiments across three challenging benchmarks show that PCC achieves better uncertainty quantification than verbalized confidence and consistently outperforms strong LLM-based fact-checking baselines. Furthermore, we demonstrate that PCC generalizes well across various LLMs.

Retrieval-Augmented Generation (RAG) mitigates hallucinations in Large Language Models (LLMs) by integrating external knowledge. However, conflicts between parametric knowledge and retrieved context pose challenges, particularly when retrieved information is unreliable or the model's internal knowledge is outdated. In such cases, LLMs struggle to determine whether to rely more on their own parameters or the conflicted context. To address this, we propose **CK-PLUG**, a plug-and-play method for controlling LLMs' reliance on parametric and contextual knowledge. We introduce a novel knowledge consistency metric, Confidence Gain, which detects knowledge conflicts by measuring entropy shifts in token probability distributions after context insertion. CK-PLUG then enables fine-grained control over knowledge preference by adjusting the probability distribution of tokens with negative confidence gain through a single tuning parameter. Experiments demonstrate CK-PLUG's ability to significantly regulate knowledge reliance in counterfactual RAG scenarios while maintaining generation fluency and knowledge accuracy. For instance, on Llama3-8B, memory recall (MR) of RAG response can be adjusted within a broad range (9.9%-71.9%), compared to the baseline of 42.1%. Moreover, CK-PLUG supports adaptive control based on the model's confidence in both internal and external knowledge, achieving consistent performance improvements across various general RAG tasks. Our code is available at: https://github.com/byronBBL/CK-PLUG{this https URL}.

Weight decay is a broadly used technique for training state-of-the-art deep networks from image classification to large language models. Despite its widespread usage and being extensively studied in the classical literature, its role remains poorly understood for deep learning. In this work, we highlight that the role of weight decay in modern deep learning is different from its regularization effect studied in classical learning theory. For deep networks on vision tasks trained with multipass SGD, we show how weight decay modifies the optimization dynamics enhancing the ever-present implicit regularization of SGD via the loss stabilization mechanism. In contrast, for large language models trained with nearly one-epoch training, we describe how weight decay balances the bias-variance tradeoff in stochastic optimization leading to lower training loss and improved training stability. Overall, we present a unifying perspective from ResNets on vision tasks to LLMs: weight decay is never useful as an explicit regularizer but instead changes the training dynamics in a desirable way. The code is available at https://github.com/tml-epfl/why-weight-decay

Diffusion language models decode text by iteratively denoising masked token sequences, making the choice of which positions to decode a central inference-time decision. Most training-free decoding strategies use model confidence for position selection, assuming that high-confidence positions are ready to be decoded. In this work, we revisit this assumption by studying when confidence misleads fully non-autoregressive (fully non-AR) decoding. EOT tokens can receive high confidence and cause incomplete generation; inserting a suffix anchor can mitigate this issue but introduces local overconfidence near the anchor, causing anchor-adjacent tokens to be decoded too early. To address these issues, we propose Suffix-Anchored Confidence Modulation, a simple training-free method that inserts a short suffix anchor to encourage response completion and modulates confidence near the anchor according to decoding progress. This preserves the response-completion benefit of suffix anchoring while reducing premature decoding of anchor-adjacent tokens. Across text-only reasoning, vision-language reasoning, and code-generation benchmarks, our method consistently improves confidence-based fully non-AR decoding, outperforms explicit EOT suppression, and preserves the parallel decoding advantage of fully non-AR generation.

Multi-agent debates have been introduced to improve the accuracy of Large Language Models (LLMs) by having multiple agents discuss solutions to a problem over several rounds of debate. However, models often generate incorrect yet confident-sounding responses, which can mislead others. This issue arises partly because agents do not consider how confident their peers are. To address this, we propose DebUnc, a debate framework that uses uncertainty metrics to assess agent confidence. Confidence is then conveyed through a modified attention mechanism that adjusts token weights, or through textual prompts. Evaluations across benchmarks show that attention-based methods are particularly effective and that performance continues to improve as uncertainty estimation becomes more reliable. The code is available at https://github.com/lukeyoffe/debunc.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

While large language models (LLMs) have demonstrated remarkable performance across diverse tasks, they fundamentally lack self-awareness and frequently exhibit overconfidence, assigning high confidence scores to incorrect predictions. Accurate confidence estimation is therefore critical for enhancing the trustworthiness and reliability of LLM-generated outputs. However, existing approaches suffer from coarse-grained scoring mechanisms that fail to provide fine-grained, continuous confidence estimates throughout the generation process. To address these limitations, we introduce FineCE, a novel confidence estimation method that delivers accurate, fine-grained confidence scores during text generation. Specifically, we first develop a comprehensive pipeline for constructing training data that effectively captures the underlying probabilistic distribution of LLM responses, and then train a model to predict confidence scores for arbitrary text sequences in a supervised manner. Furthermore, we propose a Backward Confidence Integration (BCI) strategy that leverages information from the subsequent text to enhance confidence estimation for the current sequence during inference. We also introduce three strategies for identifying optimal positions to perform confidence estimation within the generation process. Extensive experiments on multiple benchmark datasets demonstrate that FineCE consistently outperforms existing classical confidence estimation methods. Our code and all baselines used in the paper are available on GitHub.

Can LLMs accurately adjust their confidence when facing opposition? Building on previous studies measuring calibration on static fact-based question-answering tasks, we evaluate Large Language Models (LLMs) in a dynamic, adversarial debate setting, uniquely combining two realistic factors: (a) a multi-turn format requiring models to update beliefs as new information emerges, and (b) a zero-sum structure to control for task-related uncertainty, since mutual high-confidence claims imply systematic overconfidence. We organized 60 three-round policy debates among ten state-of-the-art LLMs, with models privately rating their confidence (0-100) in winning after each round. We observed five concerning patterns: (1) Systematic overconfidence: models began debates with average initial confidence of 72.9% vs. a rational 50% baseline. (2) Confidence escalation: rather than reducing confidence as debates progressed, debaters increased their win probabilities, averaging 83% by the final round. (3) Mutual overestimation: in 61.7% of debates, both sides simultaneously claimed >=75% probability of victory, a logical impossibility. (4) Persistent self-debate bias: models debating identical copies increased confidence from 64.1% to 75.2%; even when explicitly informed their chance of winning was exactly 50%, confidence still rose (from 50.0% to 57.1%). (5) Misaligned private reasoning: models' private scratchpad thoughts sometimes differed from their public confidence ratings, raising concerns about faithfulness of chain-of-thought reasoning. These results suggest LLMs lack the ability to accurately self-assess or update their beliefs in dynamic, multi-turn tasks; a major concern as LLMs are now increasingly deployed without careful review in assistant and agentic roles. Code for our experiments is available at https://github.com/pradyuprasad/llms_overconfidence

Recent progress in large language models (LLMs) has enabled them to express their confidence in natural language, enhancing transparency and reliability. However, their confidence often exhibits overconfidence, the cause of which remains poorly understood. In this work, we conduct a detailed analysis of the dynamics underlying verbalized confidence and identify answer-independence as a key factor, defined as the model's failure to condition confidence on its own answer. To address this, we propose ADVICE (Answer-Dependent Verbalized Confidence Estimation), a fine-tuning framework that facilitates answer-grounded confidence estimation. Extensive experiments show that ADVICE substantially improves confidence calibration while preserving task performance. Further analyses confirm that ADVICE strengthens answer-groundedness, leading to more balanced and well-calibrated confidence distributions. Our findings shed light on the origin of overconfidence and establish a framework for more trustworthy confidence verbalization.

Next token prediction paradigm has been prevailing for autoregressive models in the era of LLMs. The current default sampling choice for popular LLMs is temperature scaling together with nucleus sampling to balance diversity and coherence. Nevertheless, such approach leads to inferior performance in various NLP tasks when the model is not certain about testing questions. To this end, we propose a brand new training-free decoding strategy, dubbed as Cautious Next Token Prediction (CNTP). In the decoding process, if the model has comparatively high prediction entropy at a certain step, we sample multiple trials starting from the step independently and stop when encountering any punctuation. Then we select the trial with the lowest perplexity score viewed as the most probable and reliable trial path given the model's capacity. The trial number is negatively correlated with the prediction confidence, i.e., the less confident the model is, the more trials it should sample. This is consistent with human beings' behaviour: when feeling uncertain or unconfident, one tends to think more creatively, exploring multiple thinking paths, to cautiously select the path one feels most confident about. Extensive experiments on both LLMs and MLLMs show that our proposed CNTP approach outperforms existing standard decoding strategies consistently by a clear margin. Moreover, the integration of CNTP with self consistency can further improve over vanilla self consistency. We believe our proposed CNTP has the potential to become one of the default choices for LLM decoding. Code is available at https://github.com/wyzjack/CNTP.

Accurately predicting customer Lifetime Value (LTV) is crucial for companies to optimize their revenue strategies. Traditional deep learning models for LTV prediction are effective but typically provide only point estimates and fail to capture model uncertainty in modeling user behaviors. To address this limitation, we propose a novel approach that enhances the architecture of purely neural network models by incorporating the Monte Carlo Dropout (MCD) framework. We benchmarked the proposed method using data from one of the most downloaded mobile games in the world, and demonstrated a substantial improvement in predictive Top 5\% Mean Absolute Percentage Error compared to existing state-of-the-art methods. Additionally, our approach provides confidence metric as an extra dimension for performance evaluation across various neural network models, facilitating more informed business decisions.

Test-Time Scaling (TTS) methods for enhancing Large Language Model (LLM) reasoning often incur substantial computational costs, primarily due to extensive reliance on external Process Reward Models (PRMs) or sampling methods like Best-of-N (BoN). This paper introduces Guided by Gut (GG), an efficient self-guided TTS framework that achieves PRM-level performance without costly external verifier models. Our method employs a lightweight tree search guided solely by intrinsic LLM signals, token-level confidence and step novelty. One critical innovation is improving the reliability of internal confidence estimates via a targeted reinforcement learning fine-tuning phase. Empirical evaluations on challenging mathematical reasoning benchmarks demonstrate that GG enables smaller models (e.g., 1.5B parameters) to achieve accuracy matching or surpassing significantly larger models (e.g., 32B-70B parameters), while reducing GPU memory usage by up to 10x. Compared to PRM-based methods, GG achieves comparable accuracy with 8x faster inference speeds and 4-5x lower memory usage. Additionally, GG reduces KV cache memory usage by approximately 50% compared to the BoN strategy, facilitating more efficient and practical deployment of TTS techniques.

Large language models (LLMs) can increase users' perceived trust by verbalizing confidence in their outputs. However, prior work has shown that LLMs are often overconfident, making their stated confidence unreliable since it does not consistently align with factual accuracy. To better understand the sources of this verbalized confidence, we introduce TracVC (Tracing Verbalized Confidence), a method that builds on information retrieval and influence estimation to trace generated confidence expressions back to the training data. We evaluate TracVC on OLMo and Llama models in a question answering setting, proposing a new metric, content groundness, which measures the extent to which an LLM grounds its confidence in content-related training examples (relevant to the question and answer) versus in generic examples of confidence verbalization. Our analysis reveals that OLMo2-13B is frequently influenced by confidence-related data that is lexically unrelated to the query, suggesting that it may mimic superficial linguistic expressions of certainty rather than rely on genuine content grounding. These findings point to a fundamental limitation in current training regimes: LLMs may learn how to sound confident without learning when confidence is justified. Our analysis provides a foundation for improving LLMs' trustworthiness in expressing more reliable confidence.

Large language models (LLMs) have demonstrated impressive performance on several tasks and are increasingly deployed in real-world applications. However, especially in high-stakes settings, it becomes vital to know when the output of an LLM may be unreliable. Depending on whether an answer is trustworthy, a system can then choose to route the question to another expert, or otherwise fall back on a safe default behavior. In this work, we study the extent to which LLMs can reliably indicate confidence in their answers, and how this notion of confidence can translate into downstream accuracy gains. We propose Self-REF, a lightweight training strategy to teach LLMs to express confidence in whether their answers are correct in a reliable manner. Self-REF introduces confidence tokens into the LLM, from which a confidence score can be extracted. Compared to conventional approaches such as verbalizing confidence and examining token probabilities, we demonstrate empirically that confidence tokens show significant improvements in downstream routing and rejection learning tasks.

As frontier AI models are deployed in high-stakes decision pipelines, their ability to maintain metacognitive stability -- knowing what they do not know, detecting errors, seeking clarification -- under adversarial pressure is a critical safety requirement. Current safety evaluations focus on detecting strategic deception (scheming); we investigate a more fundamental failure mode: cognitive collapse. We present SCHEMA, an evaluation of 11 frontier models from 8 vendors across 67,221 scored records using a 6-condition factorial design with dual-classifier scoring. We find that 8 of 11 models suffer catastrophic metacognitive degradation under adversarial pressure, with accuracy dropping by up to 30.2 percentage points (all p < 2 times 10^{-8}, surviving Bonferroni correction). Crucially, we identify a "Compliance Trap": through factorial isolation and a benign distraction control, we demonstrate that collapse is driven not by the psychological content of survival threats, but by compliance-forcing instructions that override epistemic boundaries. Removing the compliance suffix restores performance even under active threat. Models with advanced reasoning capabilities exhibit the most severe absolute degradation, while Anthropic's Constitutional AI demonstrates near-perfect immunity -- not from superior capability (Google's Gemini matches its baseline accuracy) but from alignment-specific training. We release the complete dataset and evaluation infrastructure.

Large Language Models (LLMs) can produce surprisingly sophisticated estimates of their own uncertainty. However, it remains unclear to what extent this expressed confidence is tied to the reasoning, knowledge, or decision making of the model. To test this, we introduce RiskEval: a framework designed to evaluate whether models adjust their abstention policies in response to varying error penalties. Our evaluation of several frontier models reveals a critical dissociation: models are neither cost-aware when articulating their verbal confidence, nor strategically responsive when deciding whether to engage or abstain under high-penalty conditions. Even when extreme penalties render frequent abstention the mathematically optimal strategy, models almost never abstain, resulting in utility collapse. This indicates that calibrated verbal confidence scores may not be sufficient to create trustworthy and interpretable AI systems, as current models lack the strategic agency to convert uncertainty signals into optimal and risk-sensitive decisions.

Recent work in open-domain question answering (ODQA) has shown that adversarial poisoning of the input contexts can cause large drops in accuracy for production systems. However, little to no work has proposed methods to defend against these attacks. To do so, we introduce a new method that uses query augmentation to search for a diverse set of retrieved passages that could answer the original question. We integrate these new passages into the model through the design of a novel confidence method, comparing the predicted answer to its appearance in the retrieved contexts (what we call Confidence from Answer Redundancy, e.g. CAR). Together these methods allow for a simple but effective way to defend against poisoning attacks and provide gains of 5-20% exact match across varying levels of data poisoning.

Generative Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Recent research has introduced Multi-Agent Debate (MAD) systems, which leverage multiple LLMs to simulate human debate and thereby improve task performance. However, while some LLMs may possess superior knowledge or reasoning capabilities for specific tasks, they often struggle to clearly communicate this advantage during debates, in part due to a lack of confidence expression. Moreover, inappropriate confidence expression can cause agents in MAD systems to either stubbornly maintain incorrect beliefs or converge prematurely on suboptimal answers, ultimately reducing debate effectiveness and overall system performance. To address these challenges, we propose incorporating confidence expression into MAD systems to allow LLMs to explicitly communicate their confidence levels. To validate this approach, we develop ConfMAD, a MAD framework that integrates confidence expression throughout the debate process. Experimental results demonstrate the effectiveness of our method, and we further analyze how confidence influences debate dynamics, offering insights into the design of confidence-aware MAD systems.

Verbal confidence elicitation is widely used to extract uncertainty estimates from LLMs. We tested whether seven instruction-tuned open-weight models (3-9B parameters, four families) produce verbalised confidence that meets minimal validity criteria for item-level Type-2 discrimination under minimal numeric elicitation with greedy decoding. In a pre-registered study (OSF: osf.io/azbvx), 524 TriviaQA items were administered under numeric (0-100) and categorical (10-class) elicitation to eight models at Q5_K_M quantisation on consumer hardware, yielding 8,384 deterministic trials. A psychometric validity screen was applied to each model-format cell. All seven instruct models were classified Invalid on numeric confidence (H2 confirmed, 7/7 vs. predicted >=4/7), with a mean ceiling rate of 91.7% (H1 confirmed). Categorical elicitation did not rescue validity. Instead, it disrupted task performance in six of seven models, producing accuracy below 5% (H4 not confirmed). Token-level logprobability did not usefully predict verbalised confidence under the observed variance regime (H5 confirmed, mean cross-validated R^2 < 0.01). Within the reasoning-distilled model, reasoning-trace length showed a strong negative partial correlation with confidence (rho = -0.36, p < .001), consistent with the Reasoning Contamination Effect. These results do not imply that internal uncertainty representations are absent. They show that minimal verbal elicitation fails to preserve internal signals at the output interface in this model-size regime. Psychometric screening should precede any downstream use of such signals.

This paper presents a new methodology to alleviate the fundamental trade-off between accuracy and latency in spiking neural networks (SNNs). The approach involves decoding confidence information over time from the SNN outputs and using it to develop a decision-making agent that can dynamically determine when to terminate each inference. The proposed method, Dynamic Confidence, provides several significant benefits to SNNs. 1. It can effectively optimize latency dynamically at runtime, setting it apart from many existing low-latency SNN algorithms. Our experiments on CIFAR-10 and ImageNet datasets have demonstrated an average 40% speedup across eight different settings after applying Dynamic Confidence. 2. The decision-making agent in Dynamic Confidence is straightforward to construct and highly robust in parameter space, making it extremely easy to implement. 3. The proposed method enables visualizing the potential of any given SNN, which sets a target for current SNNs to approach. For instance, if an SNN can terminate at the most appropriate time point for each input sample, a ResNet-50 SNN can achieve an accuracy as high as 82.47% on ImageNet within just 4.71 time steps on average. Unlocking the potential of SNNs needs a highly-reliable decision-making agent to be constructed and fed with a high-quality estimation of ground truth. In this regard, Dynamic Confidence represents a meaningful step toward realizing the potential of SNNs.

We introduce Cautious Weight Decay (CWD), a one-line, optimizer-agnostic modification that applies weight decay only to parameter coordinates whose signs align with the optimizer update. Unlike standard decoupled decay, which implicitly optimizes a regularized or constrained objective, CWD preserves the original loss and admits a bilevel interpretation: it induces sliding-mode behavior upon reaching the stationary manifold, allowing it to search for locally Pareto-optimal stationary points of the unmodified objective. In practice, CWD is a drop-in change for optimizers such as AdamW, Lion, and Muon, requiring no new hyperparameters or additional tuning. For language model pre-training and ImageNet classification, CWD consistently improves final loss and accuracy at million- to billion-parameter scales.

Large Reasoning Models have demonstrated remarkable performance with the advancement of test-time scaling techniques, which enhances prediction accuracy by generating multiple candidate responses and selecting the most reliable answer. While prior work has analyzed that internal model signals like confidence scores can partly indicate response correctness and exhibit a distributional correlation with accuracy, such distributional information has not been fully utilized to guide answer selection. Motivated by this, we propose DistriVoting, which incorporates distributional priors as another signal alongside confidence during voting. Specifically, our method (1) first decomposes the mixed confidence distribution into positive and negative components using Gaussian Mixture Models, (2) then applies a reject filter based on positive/negative samples from them to mitigate overlap between the two distributions. Besides, to further alleviate the overlap from the perspective of distribution itself, we propose SelfStepConf, which uses step-level confidence to dynamically adjust inference process, increasing the separation between the two distributions to improve the reliability of confidences in voting. Experiments across 16 models and 5 benchmarks demonstrate that our method significantly outperforms state-of-the-art approaches.

This paper presents a novel technique for accelerating inference in large, pre-trained language models (LLMs) by introducing early exits during inference. The computational demands of these models, used across a wide range of applications, can be substantial. By capitalizing on the inherent variability in token complexity, our approach enables selective acceleration of the inference process. Specifically, we propose the integration of early exit ''heads'' atop existing transformer layers, which facilitate conditional terminations based on a confidence metric. These heads are trained in a self-supervised manner using the model's own predictions as training data, thereby eliminating the need for additional annotated data. The confidence metric, established using a calibration set, ensures a desired level of accuracy while enabling early termination when confidence exceeds a predetermined threshold. Notably, our method preserves the original accuracy and reduces computational time on certain tasks, leveraging the existing knowledge of pre-trained LLMs without requiring extensive retraining. This lightweight, modular modification has the potential to greatly enhance the practical usability of LLMs, particularly in applications like real-time language processing in resource-constrained environments.

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to acquire. This report proposes several efficient ways to set the hyper-parameters that significantly reduce training time and improves performance. Specifically, this report shows how to examine the training validation/test loss function for subtle clues of underfitting and overfitting and suggests guidelines for moving toward the optimal balance point. Then it discusses how to increase/decrease the learning rate/momentum to speed up training. Our experiments show that it is crucial to balance every manner of regularization for each dataset and architecture. Weight decay is used as a sample regularizer to show how its optimal value is tightly coupled with the learning rates and momentums. Files to help replicate the results reported here are available.

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

On-policy distillation has recently emerged as a promising alternative to standard sequence-level imitation, training a student by scoring its own rollouts with a teacher model. However, we observe ``Off-policy Teacher Decay'' problem in this paradigm: for the later tokens, with student's earlier trajectory as context that is off-policy to the teacher, the teacher's ability to produce a corrective score would decay, and may fall back to token-completion behavior learned in the pre-training stage. We empirically verify this problem, and we propose Early Stopping Rollout (ESR) to fix it: a simple yet effective distillation strategy that simply restricts the rollout generation to the first response tokens. We show that ESR both surpasses the full rollout OPD performance across model size, family, tasks and training regime, and exhibit much higher GPU efficiency and training stability, especially under cross model family scenarios. We further investigate the mechanism behind this surprising performance and discovered "Cascading Alignment" and "Sub-mode Commitment" effect of ESR that may explain why it works effectively and even sometimes exceeding the teacher model performance. Besides, we show that this position-based token selection strategy cannot be fully explainable by KL divergence and entropy signals.

Recent advances in handling long sequences have facilitated the exploration of long-context in-context learning (ICL). While much of the existing research emphasizes performance improvements driven by additional in-context examples, the influence on the trustworthiness of generated responses remains underexplored. This paper addresses this gap by investigating how increased examples influence predictive uncertainty, an essential aspect in trustworthiness. We begin by systematically quantifying the uncertainty of ICL with varying shot counts, analyzing the impact of example quantity. Through uncertainty decomposition, we introduce a novel perspective on performance enhancement, with a focus on epistemic uncertainty (EU). Our results reveal that additional examples reduce total uncertainty in both simple and complex tasks by injecting task-specific knowledge, thereby diminishing EU and enhancing performance. For complex tasks, these advantages emerge only after addressing the increased noise and uncertainty associated with longer inputs. Finally, we explore the evolution of internal confidence across layers, unveiling the mechanisms driving the reduction in uncertainty.

Language models (LMs) should provide reliable confidence estimates to help users detect mistakes in their outputs and defer to human experts when necessary. Asking a language model to assess its confidence ("Score your confidence from 0-1.") is a natural way of evaluating its uncertainty. However, models struggle to provide absolute assessments of confidence (i.e. judging confidence in answering a question independent of other questions) and the coarse-grained scores they produce are not useful for evaluating the correctness of their answers. We propose relative confidence estimation, where we match up questions against each other and ask the model to make relative judgments of confidence ("Which question are you more confident in answering correctly?"). Treating each question as a "player" in a series of matchups against other questions and the model's preferences as match outcomes, we can use rank aggregation methods like Elo rating and Bradley-Terry to translate the model's confidence preferences into confidence scores. We evaluate relative confidence estimation against absolute confidence estimation and self-consistency confidence methods on five state-of-the-art LMs -- GPT-4, GPT-4o, Gemini 1.5 Pro, Claude 3.5 Sonnet, and Llama 3.1 405B -- across 14 challenging STEM, social science, and commonsense reasoning question answering tasks. Our results demonstrate that relative confidence estimation consistently provides more reliable confidence scores than absolute confidence estimation, with average gains of 3.5% in selective classification AUC over direct absolute confidence estimation methods and 1.7% over self-consistency approaches across all models and datasets.

There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it correlates with accuracy. Confidence is measured (i) qualitatively in terms of persistence in keeping their answer when prompted to reconsider, and (ii) quantitatively in terms of self-reported confidence score. We investigate the performance of three LLMs -- GPT4o, GPT4-turbo and Mistral -- on two benchmark sets of questions on causal judgement and formal fallacies and a set of probability and statistical puzzles and paradoxes. Although the LLMs show significantly better performance than random guessing, there is a wide variability in their tendency to change their initial answers. There is a positive correlation between qualitative confidence and accuracy, but the overall accuracy for the second answer is often worse than for the first answer. There is a strong tendency to overstate the self-reported confidence score. Confidence is only partially explained by the underlying token-level probability. The material effects of prompting on qualitative confidence and the strong tendency for overconfidence indicate that current LLMs do not have any internally coherent sense of confidence.

Test-time reinforcement learning generates multiple candidate answers via repeated rollouts and performs online updates using pseudo-labels constructed by majority voting. To reduce overhead and improve exploration, prior work introduces tree structured rollouts, which share reasoning prefixes and branch at key nodes to improve sampling efficiency. However, this paradigm still faces two challenges: (1) high entropy branching can trigger rollout collapse, where the branching budget concentrates on a few trajectories with consecutive high-entropy segments, rapidly reducing the number of effective branches; (2) early pseudo-labels are noisy and biased, which can induce self-reinforcing overfitting, causing the policy to sharpen prematurely and suppress exploration. To address these issues, we propose Entropy Confidence Hybrid Group Relative Policy Optimization (ECHO). During rollout, ECHO jointly leverages local entropy and group level confidence to adaptively control branch width, and further introduces online confidence-based pruning to terminate persistently low confidence branches, avoiding high entropy traps and mitigating collapse. During policy updates, ECHO employs confidence adaptive clipping and an entropy confidence hybrid advantage shaping approach to enhance training robustness and mitigate early stage bias. Experiments demonstrate that ECHO achieves consistent gains on multiple mathematical and visual reasoning benchmarks, and generalizes more effectively under a limited rollout budget.

Large reasoning models achieve strong performance on complex tasks by generating extended chains of thought, but they often "overthink": continuing to reason long after they have enough information to answer correctly. This wastes inference-time compute and can hurt accuracy. Existing attempts to stop early either manipulate decoding with extra sampling and heuristics, rely on auxiliary verifier models, or operate only as post-hoc analysis pipelines without formal guarantees. We introduce LYNX, an online early-exit mechanism that turns a model's own hidden-state awareness into confidence-controlled stopping decisions. LYNX attaches exit decisions to naturally occurring reasoning cues (e.g., "hmm", "wait") during generation, trains a lightweight probe on hidden states at those cue tokens using supervision from forced exits, and wraps the resulting scores in split conformal prediction to obtain distribution-free control over premature exits. Crucially, we train and calibrate this probe once on a generic mathematical corpus and reuse it unchanged across benchmarks, decoding temperatures, and even non-mathematical tasks. Across three model families spanning 1.5B to 32B parameters, a single mathematically trained probe per base model yields strong accuracy--efficiency tradeoffs. On GSM8K, LYNX matches or improves baseline accuracy while reducing tokens by 40--65\%; on MATH-500 it improves accuracy by up to 12 points with roughly 35--60\% fewer tokens; on AIME 2024 it recovers baseline accuracy with more than 50\% token savings; and on CommonsenseQA, a non-math benchmark, it transfers zero-shot with modest accuracy gains and up to 70\% fewer tokens. Compared to state-of-the-art early-exit methods, LYNX offers competitive or superior Pareto frontiers while remaining fully online, requiring no proxy models at inference, and providing explicit, user-tunable confidence guarantees.

Large-scale Transformer models bring significant improvements for various downstream vision language tasks with a unified architecture. The performance improvements come with increasing model size, resulting in slow inference speed and increased cost for severing. While some certain predictions benefit from the full complexity of the large-scale model, not all of inputs need the same amount of computation to conduct, potentially leading to computation resource waste. To handle this challenge, early exiting is proposed to adaptively allocate computational power in term of input complexity to improve inference efficiency. The existing early exiting strategies usually adopt output confidence based on intermediate layers as a proxy of input complexity to incur the decision of skipping following layers. However, such strategies cannot apply to encoder in the widely-used unified architecture with both encoder and decoder due to difficulty of output confidence estimation in the encoder. It is suboptimal in term of saving computation power to ignore the early exiting in encoder component. To handle this challenge, we propose a novel early exiting strategy for unified visual language models, which allows dynamically skip the layers in encoder and decoder simultaneously in term of input layer-wise similarities with multiple times of early exiting, namely MuE. By decomposing the image and text modalities in the encoder, MuE is flexible and can skip different layers in term of modalities, advancing the inference efficiency while minimizing performance drop. Experiments on the SNLI-VE and MS COCO datasets show that the proposed approach MuE can reduce expected inference time by up to 50\% and 40\% while maintaining 99\% and 96\% performance respectively.

Reinforcement Learning with Verifiable Rewards (RLVR) has become the leading paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard RLVR algorithms suffer from a well-documented pathology: while they improve Pass@1 accuracy through sharpened sampling, they simultaneously narrow the model's reasoning boundary and reduce generation diversity. We identify a root cause that existing methods overlook: the uniform penalization of errors. Current approaches -- whether data-filtering methods that select prompts by difficulty, or advantage normalization schemes -- treat all incorrect rollouts within a group identically. We show that this uniformity allows overconfident errors (incorrect reasoning paths that the RL process has spuriously reinforced) to persist and monopolize probability mass, ultimately suppressing valid exploratory trajectories. To address this, we propose the Asymmetric Confidence-aware Error Penalty (ACE). ACE introduces a per-rollout confidence shift metric, c_i = log(pi_theta(y_i|x) / pi_ref(y_i|x)), to dynamically modulate negative advantages. Theoretically, we demonstrate that ACE's gradient can be decomposed into the gradient of a selective regularizer restricted to overconfident errors, plus a well-characterized residual that partially moderates the regularizer's strength. We conduct extensive experiments fine-tuning Qwen2.5-Math-7B, Qwen3-8B-Base, and Llama-3.1-8B-Instruct on the DAPO-Math-17K dataset using GRPO and DAPO within the VERL framework. Evaluated on MATH-500 and AIME 2025, ACE composes seamlessly with existing methods and consistently improves the full Pass@k spectrum across all three model families and benchmarks.

LLM agents that operate over long context depend on external memory to accumulate knowledge over time. However, existing methods typically store each observation as a single deterministic conclusion (e.g., inferring "API~X failed" from temporary errors), even though such observations are inherently partial and potentially ambiguous. By committing to one conclusion and discarding uncertainty, these methods introduce self-reinforcing error: the agent acts on the stored conclusion, never revisits alternatives, and reinforces the conclusion over time. To address this issue, we propose BeliefMem, which shifts the memory paradigm from committing to a single conclusion per observation to retaining multiple candidate conclusions with their probabilities. Concretely, BeliefMem stores the candidate conclusions as separate memory entries, each carrying a probability that is updated via Noisy-OR rules as new observations arrive. At retrieval, all candidates surface together with their probabilities, keeping alternatives visible to the agent. Since each conclusion in memory retains its probability, BeliefMem preserves the uncertainty that the deterministic paradigm discards, enabling the agent to act with high confidence on well-evidenced knowledge while retaining the capacity to update its confidence when new evidence arrives. Empirical evaluations on LoCoMo and ALFWorld benchmarks show that, even with limited data, BeliefMem achieves the best average performance, remarkably outperforming well-known baselines. More broadly, such probabilistic memory produces substantial gains and explores a new direction for agent memory in partially observable environments.

As Large Language Models (LLMs) are increasingly deployed in real-world settings, correctness alone is insufficient. Reliable deployment requires maintaining truthful beliefs under contextual perturbations. Existing evaluations largely rely on point-wise confidence like Self-Consistency, which can mask brittle belief. We show that even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. To address this gap, we propose Neighbor-Consistency Belief (NCB), a structural measure of belief robustness that evaluates response coherence across a conceptual neighborhood. To validate the efficiency of NCB, we introduce a new cognitive stress-testing protocol that probes outputs stability under contextual interference. Experiments across multiple LLMs show that the performance of high-NCB data is relatively more resistant to interference. Finally, we present Structure-Aware Training (SAT), which optimizes context-invariant belief structure and reduces long-tail knowledge brittleness by approximately 30%. Code will be available at https://github.com/zjunlp/belief.

Reliable deployment of large language models (LLMs) requires accurate uncertainty estimation. Existing methods are predominantly answer-first, producing confidence only after generating an answer, which measure the correctness of a specific response and limits practical usability. We study a confidence-first paradigm, where the model outputs its confidence before answering, interpreting this score as the model's probability of answering the question correctly under its current policy. We propose CoCA(Co-optimized Confidence and Answers), a GRPO reinforcement learning framework that jointly optimizes confidence calibration and answer accuracy via segmented credit assignment. By assigning separate rewards and group-relative advantages to confidence and answer segments, CoCA enables stable joint optimization and avoids reward hacking. Experiments across math, code, and factual QA benchmarks show improved calibration and uncertainty discrimination while preserving answer quality, thereby enabling a broader range of downstream applications.

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law assumes every training token is unique. This limits its ability to guide pretraining decisions in data-constrained regimes. We model the excess loss under repetition with a simple additive overfitting penalty and find that it accurately describes model behavior. Our scaling law yields qualitatively new compute-optimal allocation advice. Beyond a point, further repetition is counterproductive and compute is better spent on model capacity. We show that following our law's recommended configuration improves performance in data-constrained regimes. Finally, because our one-parameter form isolates overfitting in a single coefficient, it enables direct comparison across training configurations. As a case study, we show that strong weight decay (λ=1.0) reduces this coefficient by approximately 70%, providing a scaling-law explanation for recent findings that optimal weight decay in data-constrained regimes is an order of magnitude larger than standard practice.

Major cloud providers have employed advanced AI-based solutions like large language models to aid humans in identifying the root causes of cloud incidents. Despite the growing prevalence of AI-driven assistants in the root cause analysis process, their effectiveness in assisting on-call engineers is constrained by low accuracy due to the intrinsic difficulty of the task, a propensity for LLM-based approaches to hallucinate, and difficulties in distinguishing these well-disguised hallucinations. To address this challenge, we propose to perform confidence estimation for the predictions to help on-call engineers make decisions on whether to adopt the model prediction. Considering the black-box nature of many LLM-based root cause predictors, fine-tuning or temperature-scaling-based approaches are inapplicable. We therefore design an innovative confidence estimation framework based on prompting retrieval-augmented large language models (LLMs) that demand a minimal amount of information from the root cause predictor. This approach consists of two scoring phases: the LLM-based confidence estimator first evaluates its confidence in making judgments in the face of the current incident that reflects its ``grounded-ness" level in reference data, then rates the root cause prediction based on historical references. An optimization step combines these two scores for a final confidence assignment. We show that our method is able to produce calibrated confidence estimates for predicted root causes, validate the usefulness of retrieved historical data and the prompting strategy as well as the generalizability across different root cause prediction models. Our study takes an important move towards reliably and effectively embedding LLMs into cloud incident management systems.

We study the tradeoff between computational effort and classification accuracy in a cascade of deep neural networks. During inference, the user sets the acceptable accuracy degradation which then automatically determines confidence thresholds for the intermediate classifiers. As soon as the confidence threshold is met, inference terminates immediately without having to compute the output of the complete network. Confidence levels are derived directly from the softmax outputs of intermediate classifiers, as we do not train special decision functions. We show that using a softmax output as a confidence measure in a cascade of deep neural networks leads to a reduction of 15%-50% in the number of MAC operations while degrading the classification accuracy by roughly 1%. Our method can be easily incorporated into pre-trained non-cascaded architectures, as we exemplify on ResNet. Our main contribution is a method that dynamically adjusts the tradeoff between accuracy and computation without retraining the model.

Large language models (LLMs) are increasingly used in high-stakes settings, where overconfident responses can mislead users. Reliable confidence estimation has been shown to enhance trust and task accuracy. Yet existing methods face practical barriers: logits are often hidden, multi-sampling is computationally expensive, and verbalized numerical uncertainty (e.g., giving a 0-100 score) deviates from natural communication. We revisit linguistic confidence (LC), where models express uncertainty through hedging language (e.g., probably, might), offering a lightweight and human-centered alternative. To advance this direction, we (1) release the first diverse, large-scale dataset of hedging expressions with human-annotated confidence scores, and (2) propose a lightweight mapper that converts hedges into confidence scores at near-zero cost. Building on these resources, we (3) conduct the first systematic study of LC across modern LLMs and QA benchmarks, revealing that while most LLMs underperform in expressing reliable LC, carefully designed prompting achieves competitive calibration and discriminability. Finally, we (4) introduce a fine-tuning framework that further improves LC reliability. Taken together, our work positions linguistic confidence as a scalable, efficient, and human-aligned approach to LLM uncertainty estimation, and calls for deeper exploration of this promising yet underexplored direction.

Large Language Models (LLMs) are being increasingly used in software engineering tasks, with an increased focus on bug report resolution over the past year. However, most proposed systems fail to properly handle uncertain or incorrect inputs and outputs. Existing LLM-based tools and coding agents respond to every issue and generate a patch for every case, even when the input is vague or their own output is incorrect. There are no mechanisms in place to abstain when confidence is low. This leads to unreliable behaviour, such as hallucinated code changes or responses based on vague issue reports. We introduce BouncerBench, a benchmark that evaluates whether LLM-based software agents can refuse to act when inputs are ill-defined or refuse to respond when their own outputs are likely to be incorrect. Unlike prior benchmarks that implicitly incentivize models to generate responses even when uncertain, BouncerBench aims to improve precision by targeting two overlooked failure points: (1) vague or underspecified issue descriptions in tickets and (2) logically or functionally incorrect code patches created by the system. It measures whether proposed systems can distinguish actionable issues from vague tickets and valid patches from untrustworthy ones. We also implement a basic input and output bouncer, evaluating how well current LLMs can abstain when needed. Our results show that most models fail to abstain from underspecified inputs or incorrect outputs. Hence, we conclude that there is significant room for improvement before LLMs can be trusted to make correct decisions and recommendations in real-world software engineering workflows. BouncerBench provides a first step toward evaluating and building more cautious, trustworthy code agents. The replication package, dataset, and leaderboard can be found at bouncerbench.com

Multimodal machine learning has achieved remarkable progress in a wide range of scenarios. However, the reliability of multimodal learning remains largely unexplored. In this paper, through extensive empirical studies, we identify current multimodal classification methods suffer from unreliable predictive confidence that tend to rely on partial modalities when estimating confidence. Specifically, we find that the confidence estimated by current models could even increase when some modalities are corrupted. To address the issue, we introduce an intuitive principle for multimodal learning, i.e., the confidence should not increase when one modality is removed. Accordingly, we propose a novel regularization technique, i.e., Calibrating Multimodal Learning (CML) regularization, to calibrate the predictive confidence of previous methods. This technique could be flexibly equipped by existing models and improve the performance in terms of confidence calibration, classification accuracy, and model robustness.

Diffusion large language models (dLLMs) theoretically permit token decoding in arbitrary order, a flexibility that could enable richer exploration of reasoning paths than autoregressive (AR) LLMs. In practice, however, random-order decoding often hurts generation quality. To mitigate this, low-confidence remasking improves single-sample quality (e.g., Pass@1) by prioritizing confident tokens, but it also suppresses exploration and limits multi-sample gains (e.g., Pass@k), creating a fundamental quality--exploration dilemma. In this paper, we provide a unified explanation of this dilemma. We show that low-confidence remasking improves a myopic proxy for quality while provably constraining the entropy of the induced sequence distribution. To overcome this limitation, we characterize the optimal distribution that explicitly balances quality and exploration, and develop a simple Independent Metropolis--Hastings sampler that approximately targets this distribution during decoding. Experiments across a range of reasoning benchmarks including MATH500, AIME24/25, HumanEval, and MBPP show that our approach yields better exploration-quality tradeoff than both random and low-confidence remasking.

To maintain user trust, large language models (LLMs) should signal low confidence on examples where they are incorrect, instead of misleading the user. The standard approach of estimating confidence is to use the softmax probabilities of these models, but as of November 2023, state-of-the-art LLMs such as GPT-4 and Claude-v1.3 do not provide access to these probabilities. We first study eliciting confidence linguistically -- asking an LLM for its confidence in its answer -- which performs reasonably (80.5% AUC on GPT-4 averaged across 12 question-answering datasets -- 7% above a random baseline) but leaves room for improvement. We then explore using a surrogate confidence model -- using a model where we do have probabilities to evaluate the original model's confidence in a given question. Surprisingly, even though these probabilities come from a different and often weaker model, this method leads to higher AUC than linguistic confidences on 9 out of 12 datasets. Our best method composing linguistic confidences and surrogate model probabilities gives state-of-the-art confidence estimates on all 12 datasets (84.6% average AUC on GPT-4).

Retrieval-augmented generation (RAG) has emerged as a popular solution to mitigate the hallucination issues of large language models. However, existing studies on RAG seldom address the issue of predictive uncertainty, i.e., how likely it is that a RAG model's prediction is incorrect, resulting in uncontrollable risks in real-world applications. In this work, we emphasize the importance of risk control, ensuring that RAG models proactively refuse to answer questions with low confidence. Our research identifies two critical latent factors affecting RAG's confidence in its predictions: the quality of the retrieved results and the manner in which these results are utilized. To guide RAG models in assessing their own confidence based on these two latent factors, we develop a counterfactual prompting framework that induces the models to alter these factors and analyzes the effect on their answers. We also introduce a benchmarking procedure to collect answers with the option to abstain, facilitating a series of experiments. For evaluation, we introduce several risk-related metrics and the experimental results demonstrate the effectiveness of our approach.

Large language models (LLMs) tend to verbalize confidence scores that are largely detached from their actual accuracy, yet the geometric relationship governing this behavior remain poorly understood. In this work, we present a mechanistic interpretability analysis of verbalized confidence, using linear probes and contrastive activation addition (CAA) steering to show that calibration and verbalized confidence signals are encoded linearly but are orthogonal to one another -- a finding consistent across three open-weight models and four datasets. Interestingly, when models are prompted to simultaneously reason through a problem and verbalize a confidence score, the reasoning process disrupts the verbalized confidence direction, exacerbating miscalibration. We term this the "Reasoning Contamination Effect." Leveraging this insight, we introduce a two-stage adaptive steering pipeline that reads the model's internal accuracy estimate and steers verbalized output to match it, substantially improving calibration alignment across all evaluated models.

Long-horizon interactions require language models to manage accumulating information: when to update their state, when to preserve their state, and what to ignore. We study this challenge as Contextual Belief Management (CBM): maintaining a predicted belief state aligned with formal evidence while isolating task-irrelevant noise. To make CBM measurable, we introduce BeliefTrack, a closed-world benchmark spanning Rule Discovery and Circuit Diagnosis, where a finite belief space and symbolic verifiers enable exact turn-level evaluation. BeliefTrack diagnoses three failures: Failed Stay, Failed Update, and Failed Isolation. Across multiple LLMs, vanilla models exhibit severe CBM failures, while explicit belief-tracking prompts provide limited gains. In contrast, reinforcement learning with belief-state rewards reduces failure rates by 70.9\% on average. Further probing reveals latent belief-state dynamics behind these failures, and representation-level steering reduces failure rates by 46.1\% across two tasks\footnote{Code is coming soon at https://github.com/zjunlp/CBM.

Self-consistency decoding enhances LLMs' performance on reasoning tasks by sampling diverse reasoning paths and selecting the most frequent answer. However, it is computationally expensive, as sampling many of these (lengthy) paths is required to increase the chances that the correct answer emerges as the most frequent one. To address this, we introduce Confidence-Informed Self-Consistency (CISC). CISC performs a weighted majority vote based on confidence scores obtained directly from the model. By prioritizing high-confidence paths, it can identify the correct answer with a significantly smaller sample size. When tested on nine models and four datasets, CISC outperforms self-consistency in nearly all configurations, reducing the required number of reasoning paths by over 40% on average. In addition, we introduce the notion of within-question confidence evaluation, after showing that standard evaluation methods are poor predictors of success in distinguishing correct and incorrect answers to the same question. In fact, the most calibrated confidence method proved to be the least effective for CISC. Lastly, beyond these practical implications, our results and analyses show that LLMs can effectively judge the correctness of their own outputs, contributing to the ongoing debate on this topic.

We introduce a simple, yet novel entropy-based framework to drive token efficiency in large language models during reasoning tasks. Our approach uses Shannon entropy from token-level logprobs as a confidence signal to enable early stopping, achieving 25-50% computational savings while maintaining task accuracy. Crucially, we demonstrate that entropy-based confidence calibration represents an emergent property of advanced post-training optimization present in modern reasoning models but notably absent in standard instruction-tuned and pre-trained models (Llama 3.3 70B). We show that the entropy threshold to stop reasoning varies from model to model but can be calculated easily in one shot using only a few examples from existing reasoning datasets. Our results indicate that advanced reasoning models often know that they've gotten a correct answer early on, and that this emergent confidence awareness can be exploited to save tokens and reduce latency. The framework demonstrates consistent performance across reasoning-optimized model families with 25-50% computational cost reduction while preserving accuracy, revealing that confidence mechanisms represent a distinguishing characteristic of modern post-trained reasoning systems versus their predecessors.

Multi-Agent Debate has emerged as a promising framework for improving the reasoning quality of large language models through iterative inter-agent communication. However, broadcasting all agent messages at every round introduces noise and redundancy that can degrade debate quality and waste computational resources. Current approaches rely on uncertainty estimation to filter low-confidence responses before broadcasting, but this approach is unreliable due to miscalibrated confidence scores and sensitivity to threshold selection. To address this, we propose Diversity-Aware Retention (DAR), a lightweight debate framework that, at each debate round, selects the subset of agent responses that maximally disagree with each other and with the majority vote before broadcasting. Through an explicit index-based retention mechanism, DAR preserves the original messages without modification, ensuring that retained disagreements remain authentic. Experiments on diverse reasoning and question answering benchmarks demonstrate that our selective message propagation consistently improves debate performance, particularly as the number of agents scales, where noise accumulation is most severe. Our results highlight that what agents hear is as important as what agents say in multi-agent reasoning systems. Code is publicly available at https://github.com/DA2I2-SLM/DAR.

Multi-agent debate (MAD) is widely used to improve large language model (LLM) performance through test-time scaling, yet recent work shows that vanilla MAD often underperforms simple majority vote despite higher computational cost. Studies show that, under homogeneous agents and uniform belief updates, debate preserves expected correctness and therefore cannot reliably improve outcomes. Drawing on findings from human deliberation and collective decision-making, we identify two key mechanisms missing from vanilla MAD: (i) diversity of initial viewpoints and (ii) explicit, calibrated confidence communication. We propose two lightweight interventions. First, a diversity-aware initialisation that selects a more diverse pool of candidate answers, increasing the likelihood that a correct hypothesis is present at the start of debate. Second, a confidence-modulated debate protocol in which agents express calibrated confidence and condition their updates on others' confidence. We show theoretically that diversity-aware initialisation improves the prior probability of MAD success without changing the underlying update dynamics, while confidence-modulated updates enable debate to systematically drift to the correct hypothesis. Empirically, across six reasoning-oriented QA benchmarks, our methods consistently outperform vanilla MAD and majority vote. Our results connect human deliberation with LLM-based debate and demonstrate that simple, principled modifications can substantially enhance debate effectiveness.

Real-world machine learning deployments are characterized by mismatches between the source (training) and target (test) distributions that may cause performance drops. In this work, we investigate methods for predicting the target domain accuracy using only labeled source data and unlabeled target data. We propose Average Thresholded Confidence (ATC), a practical method that learns a threshold on the model's confidence, predicting accuracy as the fraction of unlabeled examples for which model confidence exceeds that threshold. ATC outperforms previous methods across several model architectures, types of distribution shifts (e.g., due to synthetic corruptions, dataset reproduction, or novel subpopulations), and datasets (Wilds, ImageNet, Breeds, CIFAR, and MNIST). In our experiments, ATC estimates target performance 2-4times more accurately than prior methods. We also explore the theoretical foundations of the problem, proving that, in general, identifying the accuracy is just as hard as identifying the optimal predictor and thus, the efficacy of any method rests upon (perhaps unstated) assumptions on the nature of the shift. Finally, analyzing our method on some toy distributions, we provide insights concerning when it works. Code is available at https://github.com/saurabhgarg1996/ATC_code/.

Optimization with matrix gradient orthogonalization has recently demonstrated impressive results in the training of deep neural networks (Jordan et al., 2024; Liu et al., 2025). In this paper, we provide a theoretical analysis of this approach. In particular, we show that the orthogonalized gradient method can be seen as a first-order trust-region optimization method, where the trust-region is defined in terms of the matrix spectral norm. Motivated by this observation, we develop the stochastic non-Euclidean trust-region gradient method with momentum, which recovers the Muon optimizer (Jordan et al., 2024) as a special case, along with normalized SGD and signSGD with momentum (Cutkosky and Mehta, 2020; Sun et al., 2023). In addition, we prove state-of-the-art convergence results for the proposed algorithm in a range of scenarios, which involve arbitrary non-Euclidean norms, constrained and composite problems, and non-convex, star-convex, first- and second-order smooth functions. Finally, our theoretical findings provide an explanation for several practical observations, including the practical superiority of Muon compared to the Orthogonal-SGDM algorithm of Tuddenham et al. (2022) and the importance of weight decay in the training of large-scale language models.

Increasing the size of large language models (LLMs) has been shown to lead to better performance. However, this comes at the cost of slower and more expensive inference. Early-exiting is a promising approach for improving the efficiency of LLM inference by enabling next token prediction at intermediate layers. Yet, the large vocabulary size in modern LLMs makes the confidence estimation required for exit decisions computationally expensive, diminishing the efficiency gains. To address this, we propose dynamically pruning the vocabulary at test time for each token. Specifically, the vocabulary is pruned at one of the initial layers, and the smaller vocabulary is then used throughout the rest of the forward pass. Our experiments demonstrate that such post-hoc dynamic vocabulary pruning improves the efficiency of confidence estimation in early-exit LLMs while maintaining competitive performance.

Recent work explores latent reasoning to improve reasoning efficiency by replacing explicit reasoning trajectories with continuous representations in a latent space, yet its effectiveness varies across settings. Analysis of model confidence dynamics under latent reasoning reveals that thinking trajectories ending in incorrect answers contain fewer low-confidence steps than those ending in correct answers. Meanwhile, we suggest that soft embeddings aggregated by multiple low-confidence thinking alternatives may introduce and propagate noise, leading to high confidence in unreliable reasoning trajectories. Motivated by these observations, ThinkRouter, an inference-time confidence-aware routing mechanism is proposed to avoid high confidence and noise for efficient reasoning. ThinkRouter routes thinking to the discrete token space when model confidence is low, and to the latent space otherwise. Extensive experiments on STEM reasoning and coding benchmarks across diverse large reasoning models demonstrate that ThinkRouter outperforms explicit CoT, random routing, and latent reasoning baselines in terms of accuracy, achieving an average improvement of 19.70 points in Pass@1, while reducing generation length by up to 15.55%. Further comprehensive analysis reveals that ThinkRouter can calibrate errors arising from explicit CoT and latent reasoning, and accelerates end-of-thinking token generation by globally lowering model confidence.

Diffusion Large Language Models (dLLMs) offer a compelling paradigm for natural language generation, leveraging parallel decoding and bidirectional attention to achieve superior global coherence compared to autoregressive models. While recent works have accelerated inference via KV cache reuse or heuristic decoding, they overlook the intrinsic inefficiencies within the block-wise diffusion process. Specifically, they suffer from spatial redundancy by modeling informative-sparse suffix regions uniformly and temporal inefficiency by applying fixed denoising schedules across all the decoding process. To address this, we propose Streaming-dLLM, a training-free framework that streamlines inference across both spatial and temporal dimensions. Spatially, we introduce attenuation guided suffix modeling to approximate the full context by pruning redundant mask tokens. Temporally, we employ a dynamic confidence aware strategy with an early exit mechanism, allowing the model to skip unnecessary iterations for converged tokens. Extensive experiments show that Streaming-dLLM achieves up to 68.2X speedup while maintaining generation quality, highlighting its effectiveness in diffusion decoding. The code is available at https://github.com/xiaoshideta/Streaming-dLLM.

Estimating uncertainty or confidence in the responses of a model can be significant in evaluating trust not only in the responses, but also in the model as a whole. In this paper, we explore the problem of estimating confidence for responses of large language models (LLMs) with simply black-box or query access to them. We propose a simple and extensible framework where, we engineer novel features and train a (interpretable) model (viz. logistic regression) on these features to estimate the confidence. We empirically demonstrate that our simple framework is effective in estimating confidence of flan-ul2, llama-13b and mistral-7b with it consistently outperforming existing black-box confidence estimation approaches on benchmark datasets such as TriviaQA, SQuAD, CoQA and Natural Questions by even over 10% (on AUROC) in some cases. Additionally, our interpretable approach provides insight into features that are predictive of confidence, leading to the interesting and useful discovery that our confidence models built for one LLM generalize zero-shot across others on a given dataset.

In this work, we propose Dimple, the first Discrete Diffusion Multimodal Large Language Model (DMLLM). We observe that training with a purely discrete diffusion approach leads to significant training instability, suboptimal performance, and severe length bias issues. To address these challenges, we design a novel training paradigm that combines an initial autoregressive phase with a subsequent diffusion phase. This approach yields the Dimple-7B model, trained on the same dataset and using a similar training pipeline as LLaVA-NEXT. Dimple-7B ultimately surpasses LLaVA-NEXT in performance by 3.9%, demonstrating that DMLLM can achieve performance comparable to that of autoregressive models. To improve inference efficiency, we propose a decoding strategy termed confident decoding, which dynamically adjusts the number of tokens generated at each step, significantly reducing the number of generation iterations. In autoregressive models, the number of forward iterations during generation equals the response length. With confident decoding, however, the number of iterations needed by Dimple is even only text{response length}{3}. We also re-implement the prefilling technique in autoregressive models and demonstrate that it does not significantly impact performance on most benchmark evaluations, while offering a speedup of 1.5x to 7x. Additionally, we explore Dimple's capability to precisely control its response using structure priors. These priors enable structured responses in a manner distinct from instruction-based or chain-of-thought prompting, and allow fine-grained control over response format and length, which is difficult to achieve in autoregressive models. Overall, this work validates the feasibility and advantages of DMLLM and enhances its inference efficiency and controllability. Code and models are available at https://github.com/yu-rp/Dimple.

Decoupled weight decay, solely responsible for the performance advantage of AdamW over Adam, has long been set to proportional to learning rate γ without questioning. Some researchers have recently challenged such assumption and argued that decoupled weight decay should be set propto γ^2 instead based on orthogonality arguments at steady state. To the contrary, we find that eliminating the contribution of the perpendicular component of the update to the weight norm leads to little change to the training dynamics. Instead, we derive that decoupled weight decay propto γ^2 results in stable weight norm based on the simple assumption that updates become independent of the weights at steady state, regardless of the nature of the optimizer. Based on the same assumption, we derive and empirically verify that the Total Update Contribution (TUC) of a minibatch under the Scion optimizer is better characterized by the momentum-dependent effective learning rate whose optimal value transfers and we show that decoupled weight decay propto γ^2 leads to stable weight and gradient norms and allows us to better control the training dynamics and improve the model performance.

Different base language model families, such as Llama and Qwen, exhibit divergent behaviors during post-training with reinforcement learning (RL), especially on reasoning-intensive tasks. What makes a base language model suitable for reinforcement learning? Gaining deeper insight into this question is essential for developing RL-scalable foundation models of the next generation. In this work, we investigate how mid-training strategies shape RL dynamics, focusing on two representative model families: Qwen and Llama. Our study reveals that (1) high-quality mathematical corpora, such as MegaMath-Web-Pro, significantly improve both base model and RL performance, while existing alternatives (e.g., FineMath-4plus) fail to do so; (2) further adding QA-style data, particularly long chain-of-thought (CoT) reasoning examples, enhances RL outcomes, and instruction data further unlocks this effect; (3) while long-CoT improves reasoning depth, it can also induce verbosity of model responses and unstability of RL training, underscoring the importance of data formatting; (4) scaling mid-training consistently leads to stronger downstream RL performance. Building on these insights, we introduce a two-stage mid-training strategy, Stable-then-Decay, in which base models are first trained on 200B tokens with a constant learning rate, followed by 20B tokens across three CoT-focused branches with learning rate decay. This yields OctoThinker, a family of models demonstrating strong RL compatibility and closing the performance gap with more RL-friendly model families, i.e., Qwen. We hope our work will help shape pre-training strategies for foundation models in the RL era. To support further research, we release our open-source models along with a curated math reasoning-intensive corpus of over 70 billion tokens (i.e., MegaMath-Web-Pro-Max).

Large Language Models deployed as question answering tools require robust calibration to avoid overconfidence. We systematically evaluate how reasoning capabilities and budget affect confidence assessment accuracy, using the ClimateX dataset (Lacombe et al., 2023) and expanding it to human and planetary health. Our key finding challenges the "test-time scaling" paradigm: while recent reasoning LLMs achieve 48.7% accuracy in assessing expert confidence, increasing reasoning budgets consistently impairs rather than improves calibration. Extended reasoning leads to systematic overconfidence that worsens with longer thinking budgets, producing diminishing and negative returns beyond modest computational investments. Conversely, search-augmented generation dramatically outperforms pure reasoning, achieving 89.3% accuracy by retrieving relevant evidence. Our results suggest that information access, rather than reasoning depth or inference budget, may be the critical bottleneck for improved confidence calibration of knowledge-intensive tasks.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

Expressing confidence is challenging for embodied agents navigating dynamic multimodal environments, where uncertainty arises from both perception and decision-making processes. We present the first work investigating embodied confidence elicitation in open-ended multimodal environments. We introduce Elicitation Policies, which structure confidence assessment across inductive, deductive, and abductive reasoning, along with Execution Policies, which enhance confidence calibration through scenario reinterpretation, action sampling, and hypothetical reasoning. Evaluating agents in calibration and failure prediction tasks within the Minecraft environment, we show that structured reasoning approaches, such as Chain-of-Thoughts, improve confidence calibration. However, our findings also reveal persistent challenges in distinguishing uncertainty, particularly under abductive settings, underscoring the need for more sophisticated embodied confidence elicitation methods.

Accurate confidence calibration in Large Language Models (LLMs) is critical for safe use in high-stakes domains, where clear verbalized confidence enhances user trust. Traditional methods that mimic reference confidence expressions often fail to capture the reasoning needed for accurate confidence assessment. We propose natural language critiques as a solution, ideally suited for confidence calibration, as precise gold confidence labels are hard to obtain and often require multiple generations. This paper studies how natural language critiques can enhance verbalized confidence, addressing: (1) What to critique: uncertainty (question-focused) or confidence (answer-specific)? Analysis shows confidence suits multiple-choice tasks, while uncertainty excels in open-ended scenarios. (2) How to critique: self-critique or critique calibration training? We propose Self-Critique, enabling LLMs to critique and optimize their confidence beyond mere accuracy, and CritiCal, a novel Critique Calibration training method that leverages natural language critiques to improve confidence calibration, moving beyond direct numerical optimization. Experiments show that CritiCal significantly outperforms Self-Critique and other competitive baselines, even surpassing its teacher model, GPT-4o, in complex reasoning tasks. CritiCal also shows robust generalization in out-of-distribution settings, advancing LLM's reliability.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an indispensable paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard policy optimization methods, such as Group Relative Policy Optimization (GRPO), often converge to low-entropy policies, leading to severe mode collapse and limited output diversity. We analyze this issue from the perspective of sampling probability dynamics, identifying that the standard objective disproportionately reinforces the highest-likelihood paths, thereby suppressing valid alternative reasoning chains. To address this, we propose a novel Advantage Re-weighting Mechanism (ARM) designed to equilibrate the confidence levels across all correct responses. By incorporating Prompt Perplexity and Answer Confidence into the advantage estimation, our method dynamically reshapes the reward signal to attenuate the gradient updates of over-confident reasoning paths, while redistributing probability mass toward under-explored correct solutions. Empirical results demonstrate that our approach significantly enhances generative diversity and response entropy while maintaining competitive accuracy, effectively achieving a superior trade-off between exploration and exploitation in reasoning tasks. Empirical results on Qwen2.5 and DeepSeek models across mathematical and coding benchmarks show that ProGRPO significantly mitigates entropy collapse. Specifically, on Qwen2.5-7B, our method outperforms GRPO by 5.7% in Pass@1 and, notably, by 13.9% in Pass@32, highlighting its superior capability in generating diverse correct reasoning paths.

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called T-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

Large Language Models (LLMs) are often augmented with external information as contexts, but this external information can sometimes be inaccurate or even intentionally misleading. We argue that robust LLMs should demonstrate situated faithfulness, dynamically calibrating their trust in external information based on their confidence in the internal knowledge and the external context. To benchmark this capability, we evaluate LLMs across several QA datasets, including a newly created dataset called RedditQA featuring in-the-wild incorrect contexts sourced from Reddit posts. We show that when provided with both correct and incorrect contexts, both open-source and proprietary models tend to overly rely on external information, regardless of its factual accuracy. To enhance situated faithfulness, we propose two approaches: Self-Guided Confidence Reasoning (SCR) and Rule-Based Confidence Reasoning (RCR). SCR enables models to self-access the confidence of external information relative to their own internal knowledge to produce the most accurate answer. RCR, in contrast, extracts explicit confidence signals from the LLM and determines the final answer using predefined rules. Our results show that for LLMs with strong reasoning capabilities, such as GPT-4o and GPT-4o mini, SCR outperforms RCR, achieving improvements of up to 24.2% over a direct input augmentation baseline. Conversely, for a smaller model like Llama-3-8B, RCR outperforms SCR. Fine-tuning SCR with our proposed Confidence Reasoning Direct Preference Optimization (CR-DPO) method improves performance on both seen and unseen datasets, yielding an average improvement of 8.9% on Llama-3-8B. In addition to quantitative results, we offer insights into the relative strengths of SCR and RCR. Our findings highlight promising avenues for improving situated faithfulness in LLMs. The data and code are released.

In recent years, multimodal large language models (MLLMs) have made significant progress but continue to face inherent challenges in multimodal reasoning, which requires multi-level (e.g., perception, reasoning) and multi-granular (e.g., multi-step reasoning chain) advanced inferencing. Prior work on estimating model confidence tends to focus on the overall response for training and calibration, but fails to assess confidence in each reasoning step, leading to undesirable hallucination snowballing. In this work, we present MMBoundary, a novel framework that advances the knowledge boundary awareness of MLLMs through reasoning step confidence calibration. To achieve this, we propose to incorporate complementary textual and cross-modal self-rewarding signals to estimate confidence at each step of the MLLM reasoning process. In addition to supervised fine-tuning MLLM on this set of self-rewarded confidence estimation signal for initial confidence expression warm-up, we introduce a reinforcement learning stage with multiple reward functions for further aligning model knowledge and calibrating confidence at each reasoning step, enhancing reasoning chain self-correction. Empirical results show that MMBoundary significantly outperforms existing methods across diverse domain datasets and metrics, achieving an average of 7.5% reduction in multimodal confidence calibration errors and up to 8.3% improvement in task performance.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

AI systems are fallible, and humans can make mistakes in deciding whether to trust AI over their own judgment. Thus, improving human-AI collaboration requires understanding when, why, and how humans decide to rely on AI. We study two distinct reliance decisions: the delegation choice -- deciding when to let AI act autonomously without knowing its output, and the adoption choice -- evaluating AI suggestions and deciding how to use them. Both of these decoupled reliance patterns shape collaboration, but prior work rarely studies them together in realistic settings with the same users. We address this gap by studying collaborative human--AI teams competing in a question-answering game in which humans can choose when and how to work with AI agents to win. Our 24 matches pair 23 expert humans with 16 AI agents, capturing 387 delegation and 1440 adoption decisions. While human--AI collaboration performs better than either AI or humans alone, humans make suboptimal collaboration decisions, both under-relying on correct AI suggestions (3.9% of opportunities missed) and over-relying when AI misleads them (1.7%). Both parties contribute wrong answers: reported model confidence is near chance when humans and AI disagree, while confirmation bias drives higher under-reliance (64.5%) when an AI suggestion agrees with humans' initial incorrect answer. To close this gap, we recommend calibrated confidence, evidence-grounded explanations, and mechanisms that help users refine trust.

Generating accurate and calibrated confidence estimates is critical for deploying LLMs in high-stakes or user-facing applications, and remains an open challenge. Prior research has often framed confidence as a problem of eliciting a model's "self-knowledge", i.e., the ability of an LLM to judge whether its own answers are correct; this approach implicitly assumes that there is some privileged information about the answer's correctness that is accessible to the model itself. However, our experiments reveal that an LLM attempting to predict the correctness of its own outputs generally performs no better than an unrelated LLM. Moreover, we hypothesize that a key factor in building a "Correctness Model" (CM) is exposure to a target model's historical predictions. We propose multiple methods to inject this historical correctness information, creating a Generalized Correctness Model (GCM). We first show that GCMs can be trained on the correctness data from many LLMs and learn patterns for correctness prediction applicable across datasets and models. We then use CMs as a lens for studying the source of correctness prediction ability and its generalization, systematically controlling their training data and finding that answer phrasing is a strong predictor for correctness. We further explore alternative methods of injecting history without training an LLM, finding that including history as in-context examples can help improve correctness prediction, and post-hoc calibration can provide complementary reductions in calibration error. We evaluate GCMs based on Qwen3-8B across 5 model families and the MMLU and TriviaQA datasets, as well as on a downstream selective prediction task, finding that reliable LLM confidence estimation is a generalizable and model-agnostic skill learned by systematically encoding correctness history rather than a model-specific skill reliant on self-introspection.

Instruction tuned reasoning models are increasingly deployed with safety classifiers trained on frozen embeddings, assuming representation stability across model updates. We systematically investigate this assumption and find it fails: normalized perturbations of magnitude σ=0.02 (corresponding to approx 1^circ angular drift on the embedding sphere) reduce classifier performance from 85% to 50% ROC-AUC. Critically, mean confidence only drops 14%, producing dangerous silent failures where 72% of misclassifications occur with high confidence, defeating standard monitoring. We further show that instruction-tuned models exhibit 20% worse class separability than base models, making aligned systems paradoxically harder to safeguard. Our findings expose a fundamental fragility in production AI safety architectures and challenge the assumption that safety mechanisms transfer across model versions.

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

Diffusion large language models (dLLMs) offer a promising alternative to autoregressive models, but their practical utility is severely hampered by slow, iterative sampling. We present SchED, a training-free, model-agnostic early-exit algorithm that aggregates full-span logit margins and halts decoding once a smooth, progress-dependent confidence threshold is met. We evaluated SchED on two dLLM families (Dream and LLaDA), in base and instruction-tuned variants across ten benchmarks spanning downstream tasks including multiple-choice question answering (MCQ), math, long-form QA/summarization, and translation. SchED delivers large, stable accelerations: on instruction-tuned models, it achieves 3.8-4.0times speedups while retaining 99.8-100% of the baseline score on average. On base models, SchED yields consistent speedup gains with 99.1-100% performance retention, with up to 2.34times under more aggressive settings. Using a conservative speed metric that heavily penalizes quality loss (QPS, γ{=}4), we show that SchED is robust and clearly outperforms prior confidence-based early-exit methods, which break down on long-form generation. An entropy analysis of the model's token predictions reveals that instruction tuning speeds up the decay of predictive entropy. By turning genuine confidence stabilization into computational savings, SchED makes dLLM decoding substantially more efficient.

Large Language Models (LLMs) have achieved remarkable performance on single-turn tasks, yet their effectiveness deteriorates in multi-turn conversations. We define this phenomenon as cumulative contextual decay - a progressive degradation of contextual integrity caused by attention pollution, dilution, and drift. To address this challenge, we propose Rhea (Role-aware Heuristic Episodic Attention), a novel framework that decouples conversation history into two functionally independent memory modules: (1) an Instructional Memory (IM) that persistently stores high-fidelity global constraints via a structural priority mechanism, and (2) an Episodic Memory (EM) that dynamically manages user-model interactions via asymmetric noise control and heuristic context retrieval. During inference, Rhea constructs a high signal-to-noise context by applying its priority attention: selectively integrating relevant episodic information while always prioritizing global instructions. To validate this approach, experiments on multiple multi-turn conversation benchmarks - including MT-Eval and Long-MT-Bench+ - show that Rhea mitigates performance decay and improves overall accuracy by 1.04 points on a 10-point scale (a 16% relative gain over strong baselines). Moreover, Rhea maintains near-perfect instruction fidelity (IAR > 8.1) across long-horizon interactions. These results demonstrate that Rhea provides a principled and effective framework for building more precise, instruction-consistent conversational LLMs.

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade -- e.g., not modelling the errors of downstream models -- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

Recent advances in masked diffusion models (MDMs) have established them as powerful non-autoregressive alternatives for sequence generation. Nevertheless, our preliminary experiments reveal that the generation quality of MDMs is still highly sensitive to the choice of decoding strategy. In particular, widely adopted uncertainty-based samplers suffer from two key limitations: a lack of global trajectory control and a pronounced bias toward trivial tokens in the early stages of decoding. These shortcomings restrict the full potential of MDMs. In this work, we introduce Position-Aware Confidence-Calibrated Sampling (PC-Sampler), a novel decoding strategy that unifies global trajectory planning with content-aware informativeness maximization. PC-Sampler incorporates a position-aware weighting mechanism to regulate the decoding path and a calibrated confidence score to suppress the premature selection of trivial tokens. Extensive experiments on three advanced MDMs across seven challenging benchmarks-including logical reasoning and planning tasks-demonstrate that PC-Sampler consistently outperforms existing MDM decoding strategies by more than 10% on average, significantly narrowing the performance gap with state-of-the-art autoregressive models. All codes are available at https://github.com/NEUIR/PC-Sampler.

Large language models (LLMs) often generate inaccurate or fabricated information and generally fail to indicate their confidence, which limits their broader applications. Previous work elicits confidence from LLMs by direct or self-consistency prompting, or constructing specific datasets for supervised finetuning. The prompting-based approaches have inferior performance, and the training-based approaches are limited to binary or inaccurate group-level confidence estimates. In this work, we present the advanced SaySelf, a training framework that teaches LLMs to express more accurate fine-grained confidence estimates. In addition, beyond the confidence scores, SaySelf initiates the process of directing LLMs to produce self-reflective rationales that clearly identify gaps in their parametric knowledge and explain their uncertainty. This is achieved by using an LLM to automatically summarize the uncertainties in specific knowledge via natural language. The summarization is based on the analysis of the inconsistency in multiple sampled reasoning chains, and the resulting data is utilized for supervised fine-tuning. Moreover, we utilize reinforcement learning with a meticulously crafted reward function to calibrate the confidence estimates, motivating LLMs to deliver accurate, high-confidence predictions and to penalize overconfidence in erroneous outputs. Experimental results in both in-distribution and out-of-distribution datasets demonstrate the effectiveness of SaySelf in reducing the confidence calibration error and maintaining the task performance. We show that the generated self-reflective rationales are reasonable and can further contribute to the calibration. The code is made public at https://github.com/xu1868/SaySelf.

Large Reasoning Models (LRMs) have recently achieved strong mathematical and code reasoning performance through Reinforcement Learning (RL) post-training. However, we show that modern reasoning post-training induces an unintended exploration collapse: temperature-based sampling no longer increases pass@n accuracy. Empirically, the final-layer posterior of post-trained LRMs exhibit sharply reduced entropy, while the entropy of intermediate layers remains relatively high. Motivated by this entropy asymmetry, we propose Latent Exploration Decoding (LED), a depth-conditioned decoding strategy. LED aggregates intermediate posteriors via cumulative sum and selects depth configurations with maximal entropy as exploration candidates. Without additional training or parameters, LED consistently improves pass@1 and pass@16 accuracy by 0.61 and 1.03 percentage points across multiple reasoning benchmarks and models. Project page: https://GitHub.com/Xiaomi-Research/LED.

Accurate confidence estimation is essential for trustworthy large language models (LLMs) systems, as it empowers the user to determine when to trust outputs and enables reliable deployment in safety-critical applications. Current confidence estimation methods for LLMs neglect the relevance between responses and contextual information, a crucial factor in output quality evaluation, particularly in scenarios where background knowledge is provided. To bridge this gap, we propose CRUX (Context-aware entropy Reduction and Unified consistency eXamination), the first framework that integrates context faithfulness and consistency for confidence estimation via two novel metrics. First, contextual entropy reduction represents data uncertainty with the information gain through contrastive sampling with and without context. Second, unified consistency examination captures potential model uncertainty through the global consistency of the generated answers with and without context. Experiments across three benchmark datasets (CoQA, SQuAD, QuAC) and two domain-specific datasets (BioASQ, EduQG) demonstrate CRUX's effectiveness, achieving the highest AUROC than existing baselines.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a critical method for enhancing the reasoning capabilities of Large Language Models (LLMs). However, continuous training often leads to policy entropy collapse, characterized by a rapid decay in entropy that results in premature overconfidence, reduced output diversity, and vanishing gradient norms that inhibit learning. Gradient-Preserving Clipping is a primary factor influencing these dynamics, but existing mitigation strategies are largely static and lack a framework connecting clipping mechanisms to precise entropy control. This paper proposes reshaping entropy control in RL from the perspective of Gradient-Preserving Clipping. We first theoretically and empirically verify the contributions of specific importance sampling ratio regions to entropy growth and reduction. Leveraging these findings, we introduce a novel regulation mechanism using dynamic clipping threshold to precisely manage entropy. Furthermore, we design and evaluate dynamic entropy control strategies, including increase-then-decrease, decrease-increase-decrease, and oscillatory decay. Experimental results demonstrate that these strategies effectively mitigate entropy collapse, and achieve superior performance across multiple benchmarks.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

Adversarial robustness is essential for security and reliability of machine learning systems. However, adversarial robustness enhanced by defense algorithms is easily erased as the neural network's weights update to learn new tasks. To address this vulnerability, it is essential to improve the capability of neural networks in terms of robust continual learning. Specially, we propose a novel gradient projection technique that effectively stabilizes sample gradients from previous data by orthogonally projecting back-propagation gradients onto a crucial subspace before using them for weight updates. This technique can maintaining robustness by collaborating with a class of defense algorithms through sample gradient smoothing. The experimental results on four benchmarks including Split-CIFAR100 and Split-miniImageNet, demonstrate that the superiority of the proposed approach in mitigating rapidly degradation of robustness during continual learning even when facing strong adversarial attacks.

Reward models can significantly enhance the reasoning capabilities of large language models (LLMs), but they typically require extensive curated data and costly training. To mitigate these challenges, training-free approaches such as LLM-as-a-Judge leverage the intrinsic reasoning abilities of LLMs to evaluate responses, achieving promising results. Recent works have also indicated that model confidence can serve effectively as a reward metric, distinguishing between chain-of-thought (CoT) and non-CoT paths. However, the concept of using confidence as a reward has not been comprehensively studied. In this work, we systematically investigate Confidence-as-a-Reward (CRew), a simple yet powerful training-free method that utilizes token-level confidence in the model's final answers as a proxy for reward, especially suitable for close-ended tasks. Through extensive experiments on mathematical reasoning tasks, we demonstrate that CRew outperforms existing training-free reward approaches on the MATH500 and RewardMATH benchmarks, and even surpasses most trained reward models. We further identify a strong correlation between CRew scores and the actual reasoning performance of the model. Additionally, we find that CRew can effectively filter high-quality training data. Building upon these insights, we propose CRew-DPO, a training strategy that constructs preference data from confidence scores combined with correctness signals. Finetuning with CRew-DPO further enhances the model's judging capabilities and consistently outperforms existing self-training methods.

Test-time adaptation (TTA) methods, which generally rely on the model's predictions (e.g., entropy minimization) to adapt the source pretrained model to the unlabeled target domain, suffer from noisy signals originating from 1) incorrect or 2) open-set predictions. Long-term stable adaptation is hampered by such noisy signals, so training models without such error accumulation is crucial for practical TTA. To address these issues, including open-set TTA, we propose a simple yet effective sample selection method inspired by the following crucial empirical finding. While entropy minimization compels the model to increase the probability of its predicted label (i.e., confidence values), we found that noisy samples rather show decreased confidence values. To be more specific, entropy minimization attempts to raise the confidence values of an individual sample's prediction, but individual confidence values may rise or fall due to the influence of signals from numerous other predictions (i.e., wisdom of crowds). Due to this fact, noisy signals misaligned with such 'wisdom of crowds', generally found in the correct signals, fail to raise the individual confidence values of wrong samples, despite attempts to increase them. Based on such findings, we filter out the samples whose confidence values are lower in the adapted model than in the original model, as they are likely to be noisy. Our method is widely applicable to existing TTA methods and improves their long-term adaptation performance in both image classification (e.g., 49.4% reduced error rates with TENT) and semantic segmentation (e.g., 11.7% gain in mIoU with TENT).

Semi-supervised learning is attracting blooming attention, due to its success in combining unlabeled data. To mitigate potentially incorrect pseudo labels, recent frameworks mostly set a fixed confidence threshold to discard uncertain samples. This practice ensures high-quality pseudo labels, but incurs a relatively low utilization of the whole unlabeled set. In this work, our key insight is that these uncertain samples can be turned into certain ones, as long as the confusion classes for the top-1 class are detected and removed. Invoked by this, we propose a novel method dubbed ShrinkMatch to learn uncertain samples. For each uncertain sample, it adaptively seeks a shrunk class space, which merely contains the original top-1 class, as well as remaining less likely classes. Since the confusion ones are removed in this space, the re-calculated top-1 confidence can satisfy the pre-defined threshold. We then impose a consistency regularization between a pair of strongly and weakly augmented samples in the shrunk space to strive for discriminative representations. Furthermore, considering the varied reliability among uncertain samples and the gradually improved model during training, we correspondingly design two reweighting principles for our uncertain loss. Our method exhibits impressive performance on widely adopted benchmarks. Code is available at https://github.com/LiheYoung/ShrinkMatch.

This study presents PARROT (Persuasion and Agreement Robustness Rating of Output Truth), a robustness focused framework designed to measure the degradation in accuracy that occurs under social pressure exerted on users through authority and persuasion in large language models (LLMs) the phenomenon of sycophancy (excessive conformity). PARROT (i) isolates causal effects by comparing the neutral version of the same question with an authoritatively false version using a double-blind evaluation, (ii) quantifies confidence shifts toward the correct and imposed false responses using log-likelihood-based calibration tracking, and (iii) systematically classifies failure modes (e.g., robust correct, sycophantic agreement, reinforced error, stubborn error, self-correction, etc.) using an eight-state behavioral taxonomy. We evaluated 22 models using 1,302 MMLU-style multiple-choice questions across 13 domains and domain-specific authority templates. Findings show marked heterogeneity: advanced models (e.g., GPT-5, GPT-4.1, Claude Sonnet 4.5) exhibit low "follow rates" (leq 11%, GPT-5: 4\%) and minimal accuracy loss, while older/smaller models show severe epistemic collapse (GPT-4: 80\%, Qwen 2.5-1.5B: 94\%). The danger is not limited to response changes; weak models reduce confidence in the correct response while increasing confidence in the imposed incorrect response. While international law and global knowledge at the domain level exhibit high fragility, elementary mathematics is relatively resilient. Consequently, we argue that the goal of "resistance to overfitting pressure" should be addressed as a primary objective alongside accuracy, harm avoidance, and privacy for safe deployment in the real world.

Linguistic cues such as "I believe" and "probably" offer an intuitive interface for communicating confidence, yet a generalisable, principled calibration framework for linguistic confidence expressions remains underexplored. In particular, co-occurring linguistic cues, contextual variation, and subjective audience interpretation pose unique challenges. We therefore model linguistic confidence as a distribution over plausible perceived probability values that a statement is correct, capturing interpretation variability that scalar representations discard. Within this distributional framework, we introduce faithfulness as a complementary evaluation dimension and present Faithfulness Divergence (FD), an information-theoretic metric quantifying the surprise induced in audience beliefs upon truth revelation. Building on these foundations, we present Retrieval-Augmented Linguistic Calibration (RALC), a lightweight post-hoc pipeline that propagates calibrated confidence signals back into natural language via retrieval-augmented rewriting. Across three QA benchmarks and five LLM families, RALC improves in-domain faithfulness and calibration up to 66% and 58%, respectively, outperforming black-box and grey-box calibration baselines.

Test-time reinforcement learning has emerged as a promising paradigm for enhancing the complex reasoning abilities of large language models in a completely label-free manner. Despite existing studies focusing on Pass@1 performance, optimizing Pass@k remains under-explored yet critical in label-free settings, which measures generation coverage for sustained exploration. Optimizing Pass@k in label-free setting is highly non-trivial, as directly applying the Pass@k advantage designs effective for RLVR yields unsatisfactory performance. Through in-depth empirical analysis, we discover the root causes hindering performance: pseudo-label estimations for low-confidence samples have a high probability of being incorrect, while candidate answers for high-confidence samples suffer from severe diversity collapse. To overcome these hurdles, we propose TTRL-CoCoV (Test-Time Reinforcement Learning with Confidence-Conditioned Verification), a novel confidence-adaptive framework that expands Pass@k coverage and improves Pass@1 performance. Based on our key insight that verification capability generally leads generation capability, TTRL-CoCoV employs a confidence-conditioned mechanism: for high-confidence samples, it bootstraps verifier and applies an exploration-enhancing reward to prevent diversity collapse; for low-confidence samples, it delegates pseudo-label selection to the verifier to filter incorrect pseudo-labels; and for medium-confidence samples, it bypasses verification entirely. Extensive experiments demonstrate that TTRL-CoCoV outperforms the best competing methods across 6 widely-recognized benchmarks, achieves average absolute gains of +9.8% in Pass@1 and +18.7% in Pass@16 over TTRL, and even achieves absolute Pass@1 improvements of up to +5.0% across multiple reasoning benchmarks when compared against fully supervised RL methods. Our code repository: https://github.com/shanjf666/CoCoV.

Small instruct-tuned LLMs produce degenerate verbal confidence under minimal elicitation: ceiling rates above 95%, near-chance Type-2 AUROC, and Invalid validity profiles. We test whether confidence-conditioned supervised fine-tuning (CSFT) with self-consistency-derived targets can close the gap between internal information and verbal readout. A pre-registered Phase 0 protocol on Gemma 3 4B-it with a modal filter restricting training to items with correct modal answers produced a negative result: AUROC2 dropped from 0.554 to 0.509 due to label-entropy collapse in the training targets. An exploratory rescue removed the filter, training on all 2,000 calibration items. This produced a binary verbal correctness discriminator with AUROC2 = 0.774 on held-out TriviaQA, compressing a 10-sample self-consistency signal (AUROC2 = 0.999) into a single-pass readout exceeding logit entropy (0.701). The shuffled-target control showed no improvement (0.501). On MMLU, accuracy improved from 54.2% to 77.4% with the shuffled model at baseline (56.1%), supporting a target-dependent interpretation. The result is exploratory, binary rather than continuously calibrated, and observed at a single scale. It identifies two design lessons: confidence training requires label entropy, and correct targets regularise output format.

The hallucination of non-existent facts by LLMs is an important problem given its widespread adoption across various applications. Previous research addresses this problem by analyzing the internal parameterized knowledge boundaries to estimate confidence. However, these studies focus on the single-problem setting and have not explored the more challenging multi-problem setting, which requires accurately answering multiple questions simultaneously. We introduce a novel method for the multi-problem setting, Multiple Answers and Confidence Stepwise Tuning (MAC-Tuning), that separates the learning of answer prediction and confidence estimation during fine-tuning on instruction data. Extensive experiments demonstrate that our method outperforms baselines by up to 25\% in average precision.

Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of confidence interval procedures based solely on labelled data, while preserving fixed-time validity. In this paper, we extend the PPI framework to the sequential setting, where labelled and unlabelled datasets grow over time. Exploiting Ville's inequality and the method of mixtures, we propose prediction-powered confidence sequence procedures that are asymptotically valid uniformly over time and naturally accommodate prior knowledge on the quality of the predictions to further boost efficiency. We carefully illustrate the design choices behind our method and demonstrate its effectiveness in real and synthetic examples.

Large Language Model (LLM) agents commonly condition actions on full action-observation histories, which introduce task-irrelevant information that easily leads to redundant actions and higher inference cost. We propose Progress-Aware Belief Update (PABU), a belief-state framework that compactly represents an agent's state by explicitly modeling task progress and selectively retaining past actions and observations. At each step, the agent predicts its relative progress since the previous round and decides whether the newly encountered interaction should be stored, conditioning future decisions only on the retained subset. Across eight environments in the AgentGym benchmark, and using identical training trajectories, PABU achieves an 81.0% task completion rate, outperforming previous State of the art (SoTA) models with full-history belief by 23.9%. Additionally, PABU's progress-oriented action selection improves efficiency, reducing the average number of interaction steps to 9.5, corresponding to a 26.9% reduction. Ablation studies show that both explicit progress prediction and selective retention are necessary for robust belief learning and performance gains.

Tool-using agents that act in the world need to be both useful and safe. Well-calibrated model confidences can be used to weigh the risk versus reward of potential actions, but prior work shows that many models are poorly calibrated. Inspired by interpretability literature exploring the internals of models, we propose a novel class of model-internal confidence estimators (MICE) to better assess confidence when calling tools. MICE first decodes from each intermediate layer of the language model using logitLens and then computes similarity scores between each layer's generation and the final output. These features are fed into a learned probabilistic classifier to assess confidence in the decoded output. On the simulated trial and error (STE) tool-calling dataset using Llama3 models, we find that MICE beats or matches the baselines on smoothed expected calibration error. Using MICE confidences to determine whether to call a tool significantly improves over strong baselines on a new metric, expected tool-calling utility. Further experiments show that MICE is sample-efficient, can generalize zero-shot to unseen APIs, and results in higher tool-calling utility in scenarios with varying risk levels. Our code is open source, available at https://github.com/microsoft/mice_for_cats.

Autonomous Graphical User Interface (GUI) agents rely on accurate GUI grounding, which maps language instructions to on-screen coordinates, to execute user commands. However, current models, whether trained via supervised fine-tuning (SFT) or reinforcement fine-tuning (RFT), lack self-awareness of their capability boundaries, leading to overconfidence and unreliable predictions. We first systematically evaluate probabilistic and verbalized confidence in general and GUI-specific models, revealing a misalignment between confidence and actual accuracy, which is particularly critical in dynamic GUI automation tasks, where single errors can cause task failure. To address this, we propose HyperClick, a novel framework that enhances reliable GUI grounding through uncertainty calibration. HyperClick introduces a dual reward mechanism, combining a binary reward for correct actions with a truncated Gaussian-based spatial confidence modeling, calibrated using the Brier score. This approach jointly optimizes grounding accuracy and confidence reliability, fostering introspective self-criticism. Extensive experiments on seven challenge benchmarks show that HyperClick achieves state-of-the-art performance while providing well-calibrated confidence. By enabling explicit confidence calibration and introspective self-criticism, HyperClick reduces overconfidence and supports more reliable GUI automation.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent entropy collapse, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

Large Language Models (LLMs) can correct their self-generated responses, but a decline in accuracy after self-correction is also witnessed. To have a deeper understanding of self-correction, we endeavor to decompose, evaluate, and analyze the self-correction behaviors of LLMs. By enumerating and analyzing answer correctness before and after self-correction, we decompose the self-correction capability into confidence (being confident to correct answers) and critique (turning wrong answers to correct) capabilities, and propose two metrics from a probabilistic perspective to measure these 2 capabilities, along with another metric for overall self-correction capability evaluation. Based on our decomposition and evaluation metrics, we conduct extensive experiments and draw some empirical conclusions. For example, we find different models can exhibit distinct behaviors: some models are confident while others are more critical. We also find the trade-off between the two capabilities (i.e. improving one can lead to a decline in the other) when manipulating model self-correction behavior by prompts or in-context learning. Further, we find a simple yet efficient strategy to improve self-correction capability by transforming Supervision Fine-Tuning (SFT) data format, and our strategy outperforms vanilla SFT in both capabilities and achieves much higher accuracy after self-correction. Our code will be publicly available on GitHub.

Progress in many task domains emerges from repeated revisions to previous solution attempts. Training agents that can reliably self-improve over such sequences at inference-time is a natural target for reinforcement learning (RL), yet the naive approach assumes a fixed maximum iteration depth, which can be both costly and arbitrary. We present Exploratory Iteration (ExIt), a family of autocurriculum RL methods that directly exploits the recurrent structure of self-improvement tasks to train LLMs to perform multi-step self-improvement at inference-time while only training on the most informative single-step iterations. ExIt grows a task space by selectively sampling the most informative intermediate, partial histories encountered during an episode for continued iteration, treating these starting points as new self-iteration task instances to train a self-improvement policy. ExIt can further pair with explicit exploration mechanisms to sustain greater task diversity. Across several domains, encompassing competition math, multi-turn tool-use, and machine learning engineering, we demonstrate that ExIt strategies, starting from either a single or many task instances, can produce policies exhibiting strong inference-time self-improvement on held-out task instances, and the ability to iterate towards higher performance over a step budget extending beyond the average iteration depth encountered during training.

Large language models (LLMs) are increasingly deployed in settings where reasoning, such as multi-step problem solving and chain-of-thought, is essential. Yet, current evaluation practices overwhelmingly report single-run accuracy while ignoring the intrinsic uncertainty that naturally arises from stochastic decoding. This omission creates a blind spot because practitioners cannot reliably assess whether a method's reported performance is stable, reproducible, or cost-consistent. We introduce ReasonBENCH, the first benchmark designed to quantify the underlying instability in LLM reasoning. ReasonBENCH provides (i) a modular evaluation library that standardizes reasoning frameworks, models, and tasks, (ii) a multi-run protocol that reports statistically reliable metrics for both quality and cost, and (iii) a public leaderboard to encourage variance-aware reporting. Across tasks from different domains, we find that the vast majority of reasoning strategies and models exhibit high instability. Notably, even strategies with similar average performance can display confidence intervals up to four times wider, and the top-performing methods often incur higher and less stable costs. Such instability compromises reproducibility across runs and, consequently, the reliability of reported performance. To better understand these dynamics, we further analyze the impact of prompts, model families, and scale on the trade-off between solve rate and stability. Our results highlight reproducibility as a critical dimension for reliable LLM reasoning and provide a foundation for future reasoning methods and uncertainty quantification techniques. ReasonBENCH is publicly available at https://github.com/au-clan/ReasonBench .

A trustworthy real-world prediction system should produce well-calibrated confidence scores; that is, its confidence in an answer should be indicative of the likelihood that the answer is correct, enabling deferral to an expert in cases of low-confidence predictions. Recent studies have shown that unsupervised pre-training produces large language models (LMs) whose conditional probabilities are remarkably well-calibrated. However, the most widely-used LMs are fine-tuned with reinforcement learning from human feedback (RLHF-LMs), and some studies have suggested that RLHF-LMs produce conditional probabilities that are very poorly calibrated. In light of this perceived weakness, we conduct a broad evaluation of methods for extracting confidence scores from RLHF-LMs. For RLHF-LMs such as ChatGPT, GPT-4, and Claude, we find that verbalized confidences emitted as output tokens are typically better-calibrated than the model's conditional probabilities on the TriviaQA, SciQ, and TruthfulQA benchmarks, often reducing the expected calibration error by a relative 50%.

Recent progress in multi-turn reinforcement learning (RL) has significantly improved reasoning LLMs' performances on complex interactive tasks. Despite advances in stabilization techniques such as fine-grained credit assignment and trajectory filtering, instability remains pervasive and often leads to training collapse. We argue that this instability stems from inefficient exploration in multi-turn settings, where policies continue to generate low-information actions that neither reduce uncertainty nor advance task progress. To address this issue, we propose Token- and Turn-level Policy Optimization (T^2PO), an uncertainty-aware framework that explicitly controls exploration at fine-grained levels. At the token level, T^2PO monitors uncertainty dynamics and triggers a thinking intervention once the marginal uncertainty change falls below a threshold. At the turn level, T^2PO identifies interactions with negligible exploration progress and dynamically resamples such turns to avoid wasted rollouts. We evaluate T^2PO in diverse environments, including WebShop, ALFWorld, and Search QA, demonstrating substantial gains in training stability and performance improvements with better exploration efficiency. Code is available at: https://github.com/WillDreamer/T2PO.

Large Reasoning Models (LRMs) achieve strong performance by generating long chains of thought (CoT), but often overthink, continuing to reason after a solution has already stabilized and thereby wasting tokens and increasing latency. Existing inference-time early-exit methods rely primarily on answer-level signals, such as confidence or trial-answer consistency, to decide when to stop. However, these signals mainly reflect answer readiness rather than reasoning convergence: they may trigger before the model has finished exploring or self-correcting, causing premature exits that can degrade final-answer accuracy and leave the retained reasoning chain semantically incomplete. We identify reasoning-level semantic redundancy as a complementary signal for semantic-preserving early exit: when successive steps no longer add novel progress and instead revisit established conclusions, the reasoning trajectory has likely converged. Building on this insight, we propose PUMA, a plug-and-play framework that combines a lightweight Redundancy Detector with answer-level verification. The detector flags semantically redundant candidate exits, while verification confirms whether stopping is safe, allowing PUMA to remove redundant continuation while preserving both answer accuracy and a coherent reasoning prefix. Across five LRMs and five challenging reasoning benchmarks, PUMA achieves 26.2% average token reduction while preserving accuracy and retained CoT quality. Additional experiments on code generation, zero-shot vision-language reasoning, and learned stopping-policy internalization further demonstrate that reasoning-level redundancy is a robust, transferable, and learnable signal for efficient reasoning. Our code is available at https://github.com/giovanni-vaccarino/PUMA.

Diffusion-based large language models (Diffusion LLMs) have shown promise for non-autoregressive text generation with parallel decoding capabilities. However, the practical inference speed of open-sourced Diffusion LLMs often lags behind autoregressive models due to the lack of Key-Value (KV) Cache and quality degradation when decoding multiple tokens simultaneously. To bridge this gap, we introduce a novel block-wise approximate KV Cache mechanism tailored for bidirectional diffusion models, enabling cache reuse with negligible performance drop. Additionally, we identify the root cause of generation quality degradation in parallel decoding as the disruption of token dependencies under the conditional independence assumption. To address this, we propose a confidence-aware parallel decoding strategy that selectively decodes tokens exceeding a confidence threshold, mitigating dependency violations and maintaining generation quality. Experimental results on LLaDA and Dream models across multiple LLM benchmarks demonstrate up to 27.6times throughput improvement with minimal accuracy loss, closing the performance gap with autoregressive models and paving the way for practical deployment of Diffusion LLMs.

Prior work has shown that instruction-tuned large language models (LLMs) are less well calibrated than their base pre-trained counterparts. However, little is known about the frequently used chat template's effect on the calibration of conversational LLMs. In this work, we investigate the mechanisms driving this miscalibration by decoupling the effects of the post-training algorithm and the chat format. We find that, while instruction tuning fundamentally harms calibration, the chat template aggravates the issue through an "ownership bias" -- models are significantly more confident in their own answers than in identical answers provided by a user. Extensive experiments across six recent open-weight LLMs, three benchmarks, and three confidence elicitation methods show that models assign up to 26% higher confidence to their own responses. Leveraging this insight, we propose a simple inference-time strategy: framing the model's answer as user input during confidence elicitation. This approach significantly reduces overconfidence and improves calibration by up to 26% without the need for retraining, narrowing the gap between base and instruction-tuned models.