Daily Papers

Instruction tuning is a standard paradigm for adapting large language models (LLMs), but modern instruction datasets are large, noisy, and redundant, making full-data fine-tuning costly and often unnecessary. Existing data selection methods either build expensive gradient datastores or assign static scores from a weak proxy, largely ignoring evolving uncertainty, and thus missing a key source of LLM interpretability. We propose GRADFILTERING, an objective-agnostic, uncertainty-aware data selection framework that utilizes a small GPT-2 proxy with a LoRA ensemble and aggregates per-example gradients into a Gradient Signal-to-Noise Ratio (G-SNR) utility. Our method matches or surpasses random subsets and strong baselines in most LLM-as-a-judge evaluations as well as in human assessment. Moreover, GRADFILTERING-selected subsets converge faster than competitive filters under the same compute budget, reflecting the benefit of uncertainty-aware scoring.

As models for nature language processing (NLP), computer vision (CV) and recommendation systems (RS) require surging computation, a large number of GPUs/TPUs are paralleled as a large batch (LB) to improve training throughput. However, training such LB tasks often meets large generalization gap and downgrades final precision, which limits enlarging the batch size. In this work, we develop the variance reduced gradient descent technique (VRGD) based on the gradient signal to noise ratio (GSNR) and apply it onto popular optimizers such as SGD/Adam/LARS/LAMB. We carry out a theoretical analysis of convergence rate to explain its fast training dynamics, and a generalization analysis to demonstrate its smaller generalization gap on LB training. Comprehensive experiments demonstrate that VRGD can accelerate training (1sim 2 times), narrow generalization gap and improve final accuracy. We push the batch size limit of BERT pretraining up to 128k/64k and DLRM to 512k without noticeable accuracy loss. We improve ImageNet Top-1 accuracy at 96k by 0.52pp than LARS. The generalization gap of BERT and ImageNet training is significantly reduce by over 65%.

Reinforcement learning with verifiable rewards (e.g. GRPO) is now a common way to improve mathematical reasoning in Large Language Models (LLMs). However, current methods usually broadcast one sequence-level advantage to all tokens, or use costly process reward models (PRMs) for step-level supervision. Uniform advantage distribution assumes that all tokens contribute equally to the final reward. This dilutes the gradient signal, since flawed reasoning steps and filler words are updated as strongly as valid logical inferences. To address this, we introduce Gradient-Reweighted Advantage (GRAIL), an intrinsic token-wise advantage reweighting method. GRAIL uses gradient-activation saliency to place more weight on tokens that are more locally sensitive to the final answer. Evaluations across five models from the Qwen3, R1-distilled and OctoThinker families show that GRAIL consistently outperforms GRPO. GRAIL achieved an average improvement of 3.60% in accuracy and 3.05% in Pass@3, demonstrating that fine-grained reasoning alignment can be achieved without process-level supervision.

Policy gradient computes a backward pass for every sample, even though the backward pass is expensive and most samples carry little learning value. The Delightful Policy Gradient (DG) provides a forward-pass signal of learning value: delight, the product of advantage and surprisal (negative log-probability). We introduce the Kondo gate, which compares delight against a compute price and pays for a backward pass only when the sample is worth it, thereby tracing a quality--cost Pareto frontier. In bandits, zero-price gating preserves useful gradient signal while removing perpendicular noise, and delight is a more reliable screening signal than additive combinations of value and surprise. On MNIST and transformer token reversal, the Kondo gate skips most backward passes while retaining nearly all of DG's learning quality, with gains that grow as problems get harder and backward passes become more expensive. Because the gate tolerates approximate delight, a cheap forward pass can screen samples before expensive backpropagation, suggesting a speculative-decoding-for-training paradigm.

Group Relative Policy Optimization (GRPO) stalls on a model's hardest problems: when no rollout in a group succeeds, the group-relative advantages vanish and the problem contributes no gradient, wasting the frontier examples we most want to learn from. Prepending a correct prefix of a reference solution raises the success rate, making prefix length a continuous knob on difficulty. Concurrent methods set the knob once; AdaPrefix-GRPO turns it into a feedback controller: throughout training it adjusts how much of the solution each problem gets, holding its success rate near 50%, where GRPO's gradient signal is largest, then withdraws the assistance entirely, so the deployed model solves problems unaided. On hard math, at matched training FLOPs, it more than doubles GRPO's accuracy on held-out problems from the training distribution for a 0.6B model (2.1x), with 1.6x on Qwen3-1.7B and 1.7x on AIME, while roughly halving trace length. The method is implemented in data preparation plus a loss mask on prefix tokens; the trainer is otherwise stock. The smaller the model, the larger the gain.

Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse tasks, yet they remain prone to generating hallucinations. Detecting these hallucinations is critical for deploying LLMs reliably in high-stakes applications. We present Grad Detect, a gradient-based approach for predicting hallucinations by analyzing layer-wise gradient patterns from a single forward-backward pass during inference. Our method shows that the internal gradient structure of a model carries rich information about the correctness of its output. This information is not accessible through output-level signals alone. We evaluate Grad Detect on several Q&A benchmarks across both hallucination detection and model abstention prediction, where it consistently outperforms confidence-based and sampling-based baselines. Through comprehensive layer ablation studies across all eleven models from four architectural families, we find that the final five layers concentrate over 97% of the discriminative gradient signal, enabling efficient deployment with minimal performance loss. Grad Detect provides a unified framework for predicting multiple dimensions of LLM reliability, offering strong predictive performance alongside interpretable insights into where and how model failures originate.

Reinforcement learning (RL) has become a powerful paradigm for optimizing large language models (LLMs) to handle complex reasoning tasks. A core challenge in this process lies in managing policy entropy, which reflects the balance between exploration and exploitation during training. Existing methods, such as proximal policy optimization (PPO) and its variants, discard valuable gradient signals from low-probability tokens due to the clipping mechanism. We systematically analyze the entropy dynamics and reveal that these clipped tokens play a critical yet overlooked role in regulating entropy evolution. We propose Controlling Entropy via Gradient-Preserving Policy Optimization (CE-GPPO), a novel algorithm that reintroduces gradients from clipped tokens in native PPO in a gentle and bounded manner. By controlling the magnitude of gradients from tokens outside the clipping interval, CE-GPPO is able to achieve an exploration-exploitation trade-off. We provide theoretical justification and empirical evidence showing that CE-GPPO effectively mitigates entropy instability. Extensive experiments on mathematical reasoning benchmarks show that CE-GPPO consistently outperforms strong baselines across different model scales.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models (LLMs). While Group Relative Policy Optimization (GRPO) is widely adopted, it suffers from sparse reward signals and loses gradients entirely when all responses within a group receive identical rewards. On-policy distillation (OPD) offers a natural remedy by providing dense, token-level supervision from a teacher model. However, naively combining GRPO with OPD leads to degraded performance, due to three underlying causes: not all samples benefit from distillation; fitting too quickly to the teacher undermines the exploratory capacity of RL; and OPD's advantages are asymmetric, suppressing most tokens. To address these challenges, we propose RSTG (Recovering Learning Signals via Adaptive Teacher Guidance), which applies distillation selectively and precisely where it matters most. At the sample level, OPD is restricted to negative zero-variance prompts with each sample weighted by the teacher's confidence score. At the token level, distillation targets only tokens with high student entropy or large teacher-student divergence. We further augment training with SFT on correct trajectories generated by the teacher model, injecting positive gradient signals where RL yields none. Experiments demonstrate that RSTG substantially outperforms naive GRPO+OPD by +4.02% on math and +3.05% on code.

Adaptive prompting mechanisms have been proposed to enhance vision-language models by dynamically tailoring prompts to inputs. However, in frozen few-shot prompt learning with CLIP-style backbones, we systematically observe that adaptive gates and prompt-selection modules often collapse: they produce nearly constant outputs, contribute negligible gradient signals, and frequently fail to outperform fixed prompts. To further explore this issue, we present a systematic diagnostic study to uncover the underlying causes and conditions of adaptation failure. Through controlled experiments across datasets and multiple prompt learning architectures, we identify two recurring failure modes: gradient magnitude imbalance and gate degradation. Our findings invite a re-examination of indiscriminately adding architectural complexity in parameter-efficient learning and clarify when prompt-level adaptive gating is, and is not, effective in this regime.

Retrieval-Augmented Generation (RAG) systems enhance Large Language Models (LLMs) by retrieving relevant documents from external corpora before generating responses. This approach significantly expands LLM capabilities by leveraging vast, up-to-date external knowledge. However, this reliance on external knowledge makes RAG systems vulnerable to corpus poisoning attacks that manipulate generated outputs via poisoned document injection. Existing poisoning attack strategies typically treat the retrieval and generation stages as disjointed, limiting their effectiveness. We propose Joint-GCG, the first framework to unify gradient-based attacks across both retriever and generator models through three innovations: (1) Cross-Vocabulary Projection for aligning embedding spaces, (2) Gradient Tokenization Alignment for synchronizing token-level gradient signals, and (3) Adaptive Weighted Fusion for dynamically balancing attacking objectives. Evaluations demonstrate that Joint-GCG achieves at most 25% and an average of 5% higher attack success rate than previous methods across multiple retrievers and generators. While optimized under a white-box assumption, the generated poisons show unprecedented transferability to unseen models. Joint-GCG's innovative unification of gradient-based attacks across retrieval and generation stages fundamentally reshapes our understanding of vulnerabilities within RAG systems. Our code is available at https://github.com/NicerWang/Joint-GCG.

Scaling inference-time compute for Large Language Models (LLMs) has unlocked unprecedented reasoning capabilities. However, existing inference-time scaling methods typically rely on inefficient and suboptimal discrete search algorithms or trial-and-error prompting to improve the online policy. In this paper, we propose nabla-Reasoner, an iterative generation framework that integrates differentiable optimization over token logits into the decoding loop to refine the policy on the fly. Our core component, Differentiable Textual Optimization (DTO), leverages gradient signals from both the LLM's likelihood and a reward model to refine textual representations. nabla-Reasoner further incorporates rejection sampling and acceleration design to robustify and speed up decoding. Theoretically, we show that performing inference-time gradient descent in the sample space to maximize reward is dual to aligning an LLM policy via KL-regularized reinforcement learning. Empirically, nabla-Reasoner achieves over 20% accuracy improvement on a challenging mathematical reasoning benchmark, while reducing number of model calls by approximately 10-40% compared to strong baselines. Overall, our work introduces a paradigm shift from zeroth-order search to first-order optimization at test time, offering a cost-effective path to amplify LLM reasoning.

As deep learning continues to advance, the transparency of neural network decision-making remains a critical challenge, limiting trust and applicability in high-stakes domains. Class Activation Mapping (CAM) techniques have emerged as a key approach toward visualizing model decisions, yet existing methods face inherent trade-offs. Gradient-based CAM variants suffer from sensitivity to gradient perturbations due to gradient noise, leading to unstable and unreliable explanations. Conversely, gradient-free approaches mitigate gradient instability but incur significant computational overhead and inference latency. To address these limitations, we propose a Cluster Filter Class Activation Map (CF-CAM) technique, a novel framework that reintroduces gradient-based weighting while enhancing robustness against gradient noise. CF-CAM utilizes hierarchical importance weighting strategy to balance discriminative feature preservation and noise elimination. A density-aware channel clustering method via Density-Based Spatial Clustering of Applications with Noise (DBSCAN) groups semantically relevant feature channels and discard noise-prone activations. Additionally, cluster-conditioned gradient filtering leverages Gaussian filters to refine gradient signals, preserving edge-aware localization while suppressing noise impact. Experiment results demonstrate that CF-CAM achieves superior interpretability performance while enhancing computational efficiency, outperforming state-of-the-art CAM methods in faithfulness and robustness. By effectively mitigating gradient instability without excessive computational cost, CF-CAM provides a competitive solution for enhancing the interpretability of deep neural networks in critical applications such as autonomous driving and medical diagnosis.

Proactive Recommender Systems (PRSs) aim to guide user preference shift toward target items by generating paths of intermediate recommendations. Reinforcement learning (RL) provides a principled framework for optimizing such sequential decision tasks, as path rewards can naturally capture both short-term acceptance and long-term guidance effectiveness. However, naively applying policy gradients to PRS results in deficient gradient estimation. We identify two deficiencies: (1) path-level rewards decompose into step-level rewards with positive mean, creating a length-dependent bias that causes gradients to favor path extension over meaningful exploration; (2) weighting each step by the entire path-level reward ignores the decomposition structure, leading to high gradient variance. To rectify these two deficiencies, we propose an effective RL framework ProRL with two novel mechanisms for proactive recommendation. First, Stepwise Reward Centering subtracts expected rewards to neutralize length-dependent bias, ensuring that path extension yields zero expected gradient signal. Second, Position-Specific Advantage Estimation leverages the reward decomposition structure to compute step-dependent baselines, reducing gradient variance. Together, these mechanisms yield policy gradients that precisely target path quality. Our experiments on three real-world datasets demonstrate that ProRL significantly outperforms state-of-the-art PRSs. Our code is available at https://github.com/hongruhou89/ProRL.

Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides the representational plasticity required for high-entropy knowledge injection, Low-Rank Adaptation (LoRA) can match or surpass FFT performance because many tasks only require updates in a low-rank space and benefit from LoRA's additional regularization. Through empirical evaluation across diverse tasks (SQL, Medical QA, and Counterfactual Knowledge) and varying language models (Gemma-3-1B, Qwen2.5-1.5B, and Qwen2.5-3B), we verify both trends and demonstrate that relying solely on either static architecture is structurally limited. To address this challenge, we propose a Mixture of LoRA and Full (MoLF) Fine-Tuning, a unified framework that enables continuous navigation between both training regimes. MoLF dynamically routes updates between FFT and LoRA at the optimizer level to ensure that exact gradient signals are available to both experts throughout training, yielding stable training dynamics. For memory-constrained environments, we also introduce MoLF-Efficient, which freezes base weights and only routes updates among a pair of LoRA experts of potentially varying rank. Our evaluations show that MoLF either improves on or stays within 1.5% of the better of FFT and LoRA across all settings, while MoLF-Efficient outperforms prior adaptive LoRA approaches by up to 20% on Fact and 9% on Med and SQL. Our code is open-sourced at https://github.com/11785T23/molf.git.

Self-tuning algorithms that adapt the learning process online encourage more effective and robust learning. Among all the methods available, meta-gradients have emerged as a promising approach. They leverage the differentiability of the learning rule with respect to some hyper-parameters to adapt them in an online fashion. Although meta-gradients can be accumulated over multiple learning steps to avoid myopic updates, this is rarely used in practice. In this work, we demonstrate that whilst multi-step meta-gradients do provide a better learning signal in expectation, this comes at the cost of a significant increase in variance, hindering performance. In the light of this analysis, we introduce a novel method mixing multiple inner steps that enjoys a more accurate and robust meta-gradient signal, essentially trading off bias and variance in meta-gradient estimation. When applied to the Snake game, the mixing meta-gradient algorithm can cut the variance by a factor of 3 while achieving similar or higher performance.

Gradient signals in LLM training are highly anisotropic: recurrent linguistic structure concentrates energy into a small set of dominant spectral directions, while context specific information resides in a long tail. We show that this spike tail separation persists throughout training, with the spike occupying only about 1.5% of directions yet dominating optimizer statistics. This dominance suppresses tail learning by contracting tail updates through second moment normalization and tightening the globally stable learning rate bound. Motivated by this analysis, we propose Spectra, a spike aware optimizer that suppresses the dominant low rank spike subspace without amplifying the noise sensitive spectral tail. Spectra tracks the spike subspace via cached, warm started power iteration and applies low rank spectral shaping with negligible overhead and substantially reduced optimizer state memory. On LLaMA3 8B trained on 50B tokens, Spectra reaches the same target loss 30% faster than AdamW, reduces per step end to end overhead by 0.7%, cuts optimizer state memory by 49.25%, and improves average downstream accuracy by 1.62%. Compared to Muon, Spectra is 5.1x faster in optimizer processing time, achieves a lower final loss, and improves average accuracy by 0.66%.

Multi-turn tool-use RL is bottlenecked by the rapid depletion of informative samples in static datasets. We observe that the gradient signal in GRPO concentrates on tasks with the highest rollout reward variance, a consequence of the Popoviciu upper bound. Consequently, samples near the agent's capability boundary -- where successes and failures are roughly balanced -- contribute disproportionately large policy gradients. As training progresses, this boundary continuously shifts, which gradually depletes the pool of informative samples in a static dataset. We propose RODS (Reward-driven Online Data Synthesis) to resolve this depletion. RODS closes the loop between RL training and data generation by repurposing the progress reward variance as a practical, zero-cost boundary detector that requires no extra inference beyond the rollouts already computed for training. It continuously identifies such boundary samples, synthesizes new multi-turn variants matching their structural complexity (e.g., API topology and dependency depth) via a skill-aligned resampling pipeline, and manages a dynamic replay buffer that co-evolves with the policy. Starting from 400 human seeds and maintaining an active training pool of ~800 samples, RODS achieves comparable performance to a 17K-sample offline pipeline while requiring roughly 20x fewer trajectories, and improves over fixed-data RL and environment augmentation in our controlled setting.

Large language models (LLMs) primarily rely on supervised fine-tuning (SFT) as a key method to adapt pre-trained models to domain-specific tasks such as mathematical reasoning. However, standard SFT uniformly penalizes all tokens, neglecting that only a small subset of critical tokens determines reasoning correctness. This uniform supervision often causes reduced output diversity and limited generalization. We propose Critical Token Fine-tuning (CFT), a simple yet effective approach that updates only tokens identified as functionally indispensable via counterfactual perturbations. By focusing gradient signals on these decisive reasoning steps while preserving the diversity of non-critical tokens, CFT can enhance both generation and diversity. Extensive experiments on five models across three families (Qwen, OLMo, LLaMA) and eleven mathematical reasoning benchmarks show that CFT, despite fine-tuning on less than 12% of tokens, consistently outperforms standard SFT. Moreover, CFT enables test-time scaling through improved sampling diversity and provides a stronger initialization for reinforcement learning, sustaining performance gains in later training stages while maintaining higher entropy for better exploration. These results highlight CFT as a practical and general framework for efficient and robust LLM fine-tuning.

Aligning diffusion model outputs with downstream objectives is essential for improving task-specific performance. Broadly, inference-time training-free approaches for aligning diffusion models can be categorized into two main strategies: sampling-based methods, which explore multiple candidate outputs and select those with higher reward signals, and gradient-guided methods, which use differentiable reward approximations to directly steer the generation process. In this work, we propose a universal algorithm, UniCoDe, which brings together the strengths of sampling and gradient-based guidance into a unified framework. UniCoDe integrates local gradient signals during sampling, thereby addressing the sampling inefficiency inherent in complex reward-based sampling approaches. By cohesively combining these two paradigms, UniCoDe enables more efficient sampling while offering better trade-offs between reward alignment and divergence from the diffusion unconditional prior. Empirical results demonstrate that UniCoDe remains competitive with state-of-the-art baselines across a range of tasks. The code is available at https://github.com/maurya-goyal10/UniCoDe

Group Relative Policy Optimization (GRPO) is widely used for critic-free Large Language Model (LLM) post-training, but its KL regularization is usually implemented as a local loss-side token penalty. We show that this misses the policy-gradient signal induced by autoregressive KL regularization. Unlike standard KL-regularized Reinforcement Learning (RL) objectives, GRPO's group normalization induces a non-linear prompt-level utility; for binary verifier rewards, this utility is 2arcsinsqrt p. As a result, reward and KL cannot be fused before normalization without changing the implicit objective. We derive the on-policy gradient of GRPO-style objectives with token-wise f-divergence regularization. The reward term recovers the standardized GRPO advantage, while the regularizer term includes a causal future-regularization return-to-go omitted by local KL losses. For reverse KL, this yields a simple future KL correction: add a reverse cumulative sum of per-token log ratios after advantage construction. The resulting method, Future-KL Regularized Policy Optimization (FRPO), requires no critic or extra model passes. On mathematical reasoning tasks, FRPO improves pass@16 in our main large-model setting while maintaining higher entropy and lower policy drift than conventional loss-side KL baselines.

CLI agents are the closest thing language models have to an embodied setting: the model emits commands, the terminal executes them, and the returned stream -- stdout, errors, files, logs, and traces -- records the consequences. We argue that this stream is a supervision signal, but standard agent RL discards it: GRPO-style training updates action tokens with sparse outcome-level rewards while ignoring environment responses already in the rollout. Failed rollouts provide little policy-gradient signal despite containing rich evidence about how the environment responds. We introduce ECHO (Environment Cross-entropy Hybrid Objective), a hybrid objective that combines the standard policy-gradient loss on action tokens with an auxiliary loss that trains the policy to predict environment observation tokens resulting from its own actions. ECHO reuses the same forward pass as GRPO, requires no additional rollouts, and turns terminal feedback into dense supervision for all rollouts. ECHO doubles GRPO pass@1 on TerminalBench-2.0: Qwen3-8B improves from 2.70% to 5.17%, and Qwen3-14B from 5.17% to 10.79%. ECHO also produces policies that better predict terminal dynamics, even on trajectories they did not generate: across held-out rollouts, it sharply reduces environment-token cross-entropy while GRPO alone barely changes it. From base Qwen3-8B, ECHO matches expert-SFT-then-GRPO performance on held-out terminal tasks without expert demonstrations, and recovers roughly half of the expert-SFT initialization benefit on TerminalBench-2.0. In some settings, the environment prediction loss alone enables verifier-free self-improvement, allowing policies to improve on unseen OOD tasks by learning only from environment interactions. Together, these results suggest that environment observations are not merely context for future actions, but a dense, on-policy supervision signal already present in every rollout.

Machine unlearning has emerged as a critical capability for addressing privacy, safety, and regulatory concerns in large language models (LLMs). Existing methods operate at the sequence level, applying uniform updates across all tokens despite only a subset encoding the knowledge targeted for removal. This introduces gradient noise, degrades utility, and leads to suboptimal forgetting. We propose TokenUnlearn, a token-level attribution framework that identifies and selectively targets critical tokens. Our approach combines knowledge-aware signals via masking, and entropy-aware signals to yield importance scores for precise token selection. We develop two complementary strategies: hard selection, applying unlearning only to high-importance tokens, and soft weighting, modulating gradient contributions based on importance scores. Both extend existing methods to token-level variants. Theoretical analysis shows token-level selection improves gradient signal-to-noise ratio. Experiments on TOFU and WMDP benchmarks across three model architectures demonstrate consistent improvements over sequence-level baselines in both forgetting effectiveness and utility preservation.

Diffusion transformers deliver strong image generation, but their training cost grows superlinearly with resolution. Recent work justifies training or sampling at reduced resolution on a spectral premise: at high noise, a downscaled latent preserves almost the full surviving signal. Whether a downscaled step also preserves the native training gradient signal, however, has remained unresolved. We reduce how that signal changes under downscaling to two terms: a noise-dependent term governed by the downscale ratio, which decays at high noise as the spectral premise predicts, and a σ-independent floor governed by the target grid's absolute token count, carried by the compute graph itself and removed by no noise level. The measured (route, σ) map corroborates the account and uncovers structure the spectral picture cannot express: on the 1024->768 route, a window (0.65 < σ< 0.95), predicted by no spectral criterion at any tolerance, where the downscaled gradient stays within a small margin of the native one. Training LoRA adapters with downscaled steps restricted to the routes and noise windows the map validates reduces training time by 14.6% at a fixed step budget while remaining near-native in weight space. Code is available at https://github.com/sorryhyun/anima_lora.

Training large language models (LLMs) with reinforcement learning (RL) methods such as PPO and GRPO commonly relies on ratio clipping to stabilise updates. While effective at preventing instability, clipping discards information and introduces gradient discontinuities. We propose Probability Smoothing Policy Optimisation (PSPO), which smooths the current policy's probabilities toward the old (behaviour) policy before computing the importance ratio, analogous to label smoothing. Unlike clipping, PSPO preserves gradient signal, while interpolation toward the old policy creates a soft trust region that discourages large, destabilising updates, with formal guarantees. We instantiate PSPO within GRPO (GR-PSPO) and fine-tune Qwen2.5-0.5B and Qwen2.5-1.5B on GSM8K, evaluating on GSM8K test and the cross-dataset generalisation on SVAMP, ASDiv, and MATH-500. Relative to unclipped GRPO (single iteration; no data reuse, ratio always = 1), GR-PSPO achieves similar performance but improves the reasoning leading to clearer and more concise responses which are more logical. Compared to clipped GRPO, GR-PSPO substantially improves performance both the 0.5B and 1.5B models, with a boost of over 20% on GSM8K (39.7% vs. 17.6% for 0.5B, 59.4% vs. 37.8% for 1.5B).

Large language models encode impressively broad world knowledge in their parameters. However, the knowledge in static language models falls out of date, limiting the model's effective "shelf life." While online fine-tuning can reduce this degradation, we find that naively fine-tuning on a stream of documents leads to a low level of information uptake. We hypothesize that online fine-tuning does not sufficiently attend to important information. That is, the gradient signal from important tokens representing factual information is drowned out by the gradient from inherently noisy tokens, suggesting that a dynamic, context-aware learning rate may be beneficial. We therefore propose learning which tokens to upweight. We meta-train a small, autoregressive model to reweight the language modeling loss for each token during online fine-tuning, with the objective of maximizing the out-of-date base question-answering model's ability to answer questions about a document after a single weighted gradient step. We call this approach Context-aware Meta-learned Loss Scaling (CaMeLS). Across three different distributions of documents, our experiments find that CaMeLS provides substantially improved information uptake on streams of thousands of documents compared with standard fine-tuning and baseline heuristics for reweighting token losses.

Standard LLM distillation wastes compute on two fronts: problems the student has already mastered (near-zero gradients) and problems far beyond its reach (incoherent gradients that erode existing capabilities). We show that this waste is not merely intuitive but structurally inevitable: the gradient signal-to-noise ratio in distillation provably vanishes at both pass-rate extremes. This theoretical observation leads to Paced, a framework that concentrates distillation on the zone of proximal development -- the frontier of a student model's competence -- via a principled pass-rate weight w(p) = p^α(1 - p)^β derived from the boundary-vanishing structure of distillation gradients. Key results: (1) Theory: We prove that the Beta kernel w(p) = p^α(1-p)^β is a leading-order weight family arising from the SNR structure of distillation, and that it is minimax-robust -- under bounded multiplicative misspecification, worst-case efficiency loss is only O(δ^2). (2)Distillation: On distillation from a larger teacher to a smaller student model with forward KL, Paced achieves significant gain over the base model, while keeping benchmark forgetting at a low level. (3)Self-distillation: On instruction-tuned models with reverse KL, gains are exceeding baselines as well. (4)Two-stage synergy: A forward-KL-then-reverse-KL schedule yields the strongest results in our setting, reaching substantial improvements on standard reasoning benchmarks -- supporting a mode-coverage-then-consolidation interpretation of the distillation process. All configurations require only student rollouts to estimate pass rates, need no architectural changes, and are compatible with any KL direction.

Finetuning data selection requires balancing two competing goals: selecting examples that improve the downstream objective, and doing so without repeatedly finetuning models. Train-free selectors are scalable but rely on proxies such as embedding similarity or clustering, which may not match the target objective. Train-based selectors better reflect downstream utility through gradient signals, subset evaluation, or Shapley attribution, but require many costly train--evaluate iterations. We propose Hierarchical Active Region Pruning (HARP), an efficient train-based selector that preserves downstream alignment while reducing selection cost. HARP organizes the training pool into a node--leaf hierarchy, evaluates only representative leaves, and infers unmeasured utilities with empirical Bayes posteriors. It then selects data using two complementary envelopes: HARP-C, which conservatively controls redundancy, and HARP-E, which additively rewards complementary regions. We theoretically show that, under local smoothness and bounded estimation error, HARP controls selection error while reducing train--evaluate cost. We further validate that HARP variants achieve the best result and outperform the strongest baseline by up to +8.9 points, while using roughly 7times fewer training examples.

On-policy reinforcement learning (RL), particularly Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO), has become the dominant paradigm for fine-tuning large language models (LLMs). While policy ratio clipping stabilizes training, this heuristic hard constraint incurs a fundamental cost: it indiscriminately truncates gradients from high-return yet high-divergence actions, suppressing rare but highly informative "eureka moments" in complex reasoning. Moreover, once data becomes slightly stale, hard clipping renders it unusable, leading to severe sample inefficiency. In this work, we revisit the trust-region objective in policy optimization and show that explicitly constraining the variance (second central moment) of the policy ratio provides a principled and smooth relaxation of hard clipping. This distributional constraint stabilizes policy updates while preserving gradient signals from valuable trajectories. Building on this insight, we propose R^2VPO (Ratio-Variance Regularized Policy Optimization), a novel primal-dual framework that supports stable on-policy learning and enables principled off-policy data reuse by dynamically reweighting stale samples rather than discarding them. We extensively evaluate R^2VPO on fine-tuning state-of-the-art LLMs, including DeepSeek-Distill-Qwen-1.5B and the openPangu-Embedded series (1B and 7B), across challenging mathematical reasoning benchmarks. Experimental results show that R^2VPO consistently achieves superior asymptotic performance, with average relative gains of up to 17% over strong clipping-based baselines, while requiring approximately 50% fewer rollouts to reach convergence. These findings establish ratio-variance control as a promising direction for improving both stability and data efficiency in RL-based LLM alignment.

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.

Reinforcement learning with verifiable rewards has emerged as a powerful paradigm for training intelligent agents. However, existing methods typically employ binary rewards that fail to capture quality differences among trajectories achieving identical outcomes, thereby overlooking potential diversity within the solution space. Inspired by the ``sweet spot'' concept in tennis-the racket's core region that produces optimal hitting effects, we introduce Sweet Spot Learning (SSL), a novel framework that provides differentiated guidance for agent optimization. SSL follows a simple yet effective principle: progressively amplified, tiered rewards guide policies toward the sweet-spot region of the solution space. This principle naturally adapts across diverse tasks: visual perception tasks leverage distance-tiered modeling to reward proximity, while complex reasoning tasks reward incremental progress toward promising solutions. We theoretically demonstrate that SSL preserves optimal solution ordering and enhances the gradient signal-to-noise ratio, thereby fostering more directed optimization. Extensive experiments across GUI perception, short/long-term planning, and complex reasoning tasks show consistent improvements over strong baselines on 12 benchmarks, achieving up to 2.5X sample efficiency gains and effective cross-task transferability. Our work establishes SSL as a general principle for training capable and robust agents.

Recent advancements in Large Reasoning Models (LRMs), exemplified by DeepSeek-R1, have underscored the potential of scaling inference-time compute through Group Relative Policy Optimization (GRPO). However, GRPO frequently suffers from gradient signal attenuation when encountering problems that are either too trivial or overly complex. In these scenarios, the disappearance of inter-group advantages makes the gradient signal susceptible to noise, thereby jeopardizing convergence stability. While variants like DAPO attempt to rectify gradient vanishing, they do not alleviate the substantial computational overhead incurred by exhaustive rollouts on low-utility samples. In this paper, we propose Difficulty-Estimated Policy Optimization (DEPO), a novel framework designed to optimize the efficiency and robustness of reasoning alignment. DEPO integrates an online Difficulty Estimator that dynamically assesses and filters training data before the rollout phase. This mechanism ensures that computational resources are prioritized for samples with high learning potential. Empirical results demonstrate that DEPO achieves up to a 2x reduction in rollout costs without compromising model performance. Our approach significantly lowers the computational barrier for training high-performance reasoning models, offering a more sustainable path for reasoning scaling. Code and data will be released upon acceptance.

Human visual preferences are inherently multi-dimensional, encompassing aesthetics, detail fidelity, and semantic alignment. However, existing datasets provide only single, holistic annotations, resulting in severe label noise: images that excel in some dimensions but are deficient in others are simply marked as winner or loser. We theoretically demonstrate that compressing multi-dimensional preferences into binary labels generates conflicting gradient signals that misguide Diffusion Direct Preference Optimization (DPO). To address this, we propose Semi-DPO, a semi-supervised approach that treats consistent pairs as clean labeled data and conflicting ones as noisy unlabeled data. Our method starts by training on a consensus-filtered clean subset, then uses this model as an implicit classifier to generate pseudo-labels for the noisy set for iterative refinement. Experimental results demonstrate that Semi-DPO achieves state-of-the-art performance and significantly improves alignment with complex human preferences, without requiring additional human annotation or explicit reward models during training. We will release our code and models at: https://github.com/L-CodingSpace/semi-dpo

We introduce Filter Like You Test (FLYT), a method for curating large-scale vision-language datasets that learns the usefulness of each data point as a pretraining example. FLYT trains a scoring model that learns to weigh each example using gradient signals from downstream tasks training sets. Using the same training methodology, we develop Mixing-FLYT (M-FLYT), which takes the per-example scores generated by different scoring methods and learns to unify them into a single score. Our training methodology naturally produces a distribution over the training examples, which we leverage through Soft Cap Sampling (SCS), a strategy for obtaining a filtered pretraining dataset from per-example probabilities that samples examples while preventing over-representation through a repetition penalty. Using all three methods, we achieve 40.1% ImageNet zero-shot accuracy on the DataComp medium scale filtering benchmark, a 1.9% absolute accuracy increase over all previous results and a 5.5% increase over results that -- like us -- use only public resources.

Quantization techniques are essential for the deployment of Large Language Models (LLMs) on edge devices. However, prevailing methods often rely on mixed-precision multiplication that lacks efficient hardware support, making it not feasible. Ternary weight quantization addresses this by constraining weights to {-1, 0, 1}, replacing expensive multiplications with hardware-efficient additions. However, such aggressive compression leads to significant accuracy degradation, even after costly quantization-aware training with massive data. We identify the core issue as deadzone trapping: a large number of weights are trapped at the deadzone boundary. This occurs because these weights receive only noisy, uninformative gradients, preventing stable escape from the deadzone and severely impeding model capacity and optimization. To address this issue, we propose Tequila, a trapping-free quantization optimization method that reactivates deadzone-trapped weights by repurposing them as dynamic biases. This allows the repurposed weights to provide a continuous signal in the forward pass and, critically, receive direct, meaningful gradient signals during backpropagation, thereby enhancing model capacity and optimization with nearly zero inference overhead. Extensive evaluations demonstrate that Tequila outperforms state-of-the-art (SOTA) ternary quantization methods across five benchmarks. Specifically, on the ARC benchmark, it achieves >4% accuracy gain over the SOTA baseline, nearly matching full-precision performance (within <1% gap) with a 3.0x inference speedup. Consequently, Tequila offers a highly practical and efficient implementation for the deployment of advanced LLMs in resource-constrained environments. The code is available at https://github.com/Tencent/AngelSlim.

In this work, we question the necessity of adaptive gradient methods for training deep neural networks. SGD-SaI is a simple yet effective enhancement to stochastic gradient descent with momentum (SGDM). SGD-SaI performs learning rate Scaling at Initialization (SaI) to distinct parameter groups, guided by their respective gradient signal-to-noise ratios (g-SNR). By adjusting learning rates without relying on adaptive second-order momentum, SGD-SaI helps prevent training imbalances from the very first iteration and cuts the optimizer's memory usage by half compared to AdamW. Despite its simplicity and efficiency, SGD-SaI consistently matches or outperforms AdamW in training a variety of Transformer-based tasks, effectively overcoming a long-standing challenge of using SGD for training Transformers. SGD-SaI excels in ImageNet-1K classification with Vision Transformers(ViT) and GPT-2 pretraining for large language models (LLMs, transformer decoder-only), demonstrating robustness to hyperparameter variations and practicality for diverse applications. We further tested its robustness on tasks like LoRA fine-tuning for LLMs and diffusion models, where it consistently outperforms state-of-the-art optimizers. From a memory efficiency perspective, SGD-SaI achieves substantial memory savings for optimizer states, reducing memory usage by 5.93 GB for GPT-2 (1.5B parameters) and 25.15 GB for Llama2-7B compared to AdamW in full-precision training settings.

Large language models can now process increasingly long inputs, yet their ability to effectively use information spread across long contexts remains limited. We trace this gap to how attention budget is spent during supervised fine-tuning (SFT) on long sequences: positional biases and attention sinks cause the model to allocate most of its attention to positionally privileged tokens rather than semantically relevant content. This training-time attention dilution (the starvation of content tokens in the attention distribution) weakens the gradient signal, limiting the model's ability to learn robust long-context capabilities. We introduce FocuSFT, a bilevel optimization framework that addresses this problem at training time. An inner loop adapts lightweight fast-weight parameters on the training context to form a parametric memory that concentrates attention on relevant content, and the outer loop performs SFT conditioned on this sharpened representation. Both loops apply bidirectional attention over context tokens while preserving causal masking for responses, reducing the causal asymmetry that gives rise to attention sinks and aligning inner-outer behavior. On BABILong, FocuSFT improves accuracy by up to +14pp across 4K--32K context lengths; on RULER, it raises CWE aggregation from 72.9\% to 81.1\% at 16K; and on GPQA with agentic tool use, it yields a 24\% relative gain in pass@1. Attention analysis shows that FocuSFT reduces attention sink mass by 529times and triples context engagement during training. Code: https://github.com/JarvisPei/FocuSFT

Standard subword tokenization methods fragment numbers inconsistently, causing large language models (LLMs) to lose positional and decimal structure - a primary driver of errors in arithmetic and scientific reasoning. We introduce Triadic Suffix Tokenization (TST), a deterministic scheme that partitions digits into three-digit triads and annotates each triad with an explicit magnitude marker. Critically, the scheme defines a fixed, one-to-one mapping between suffixes and orders of magnitude for the integer part (thousands, millions, billions, etc.) and a parallel system of replicated markers for fractional depth (tenths, thousandths, millionths, etc.). Unlike approaches that rely on positional inference, this method provides a consistent gradient signal, which should ensure stable convergence. Two implementation variants are proposed: (1) a vocabulary-based approach that adds at most 10,000 fixed tokens to an existing vocabulary, covering 33 orders of magnitude (10^{-15} to 10^{18}); and (2) a suffix-marker approach that uses a small set of special tokens to denote magnitude dynamically. Both variants preserve exact digits while making order-of-magnitude relationships transparent at the token level. The framework is inherently scalable, allowing for linear vocabulary expansion to accommodate arbitrary precision and range. TST is architecture-agnostic and can be integrated as a drop-in preprocessing step. Experimental validation is deferred to future work.

Vision-Language Navigation in Continuous Environments (VLN-CE) requires agents to learn complex reasoning from long-horizon human interactions. While Multi-modal Large Language Models (MLLMs) have driven recent progress, current training paradigms struggle to balance generalization capability, error recovery and training stability. Specifically, (i) policies derived from SFT suffer from compounding errors, struggling to recover from out-of-distribution states, and (ii) Reinforcement Fine-Tuning (RFT) methods e.g. GRPO are bottlenecked by sparse outcome rewards. Their binary feedback fails to assign credit to individual steps, leading to gradient signal collapse in failure dominant batches. To address these challenges, we introduce Step-Aware Contrastive Alignment (SACA), a framework designed to extract dense supervision from imperfect trajectories. At its core, the Perception-Grounded Step-Aware auditor evaluates progress step-by-step, disentangling failed trajectories into valid prefixes and exact divergence points. Leveraging these signals, Scenario-Conditioned Group Construction mechanism dynamically routes batches to specialized resampling and optimization strategies. Extensive experiments on VLN-CE benchmarks demonstrate that SACA achieves state-of-the-art performance.

With the rise in scale for deep learning models to billions of parameters, the computational cost of fine-tuning remains a significant barrier to deployment. While Low-Rank Adaptation (LoRA) has become the standard for parameter-efficient fine-tuning, the need to set a predefined, static rank r requires exhaustive grid searches to balance efficiency and performance. Existing rank-adaptive solutions such as DyLoRA mitigate this by sampling ranks during the training from a predefined distribution. However, they often yield sub-optimal results at higher ranks due to lack of consistent gradient signals across the full hierarchy of ranks, thus making these methods data-inefficient. In this paper, we propose MatryoshkaLoRA, a general, Matryoshka-inspired training framework for LoRA that learns accurate hierarchical low-rank representations by inserting a fixed, carefully crafted diagonal matrix P between the existing LoRA adapters to scale their sub-ranks accordingly. By introducing this simple modification, our general framework recovers LoRA and DyLoRA only by changing P and ensures all sub-ranks embed the available gradient information efficiently. Our MatryoshkaLoRA supports dynamic rank selection with minimal degradation in accuracy. We further propose Area Under the Rank Accuracy Curve (AURAC), a metric that consistently evaluates the performance of hierarchical low-rank adapters. Our results demonstrate that MatryoshkaLoRA learns more accurate hierarchical low-rank representations than prior rank-adaptive approaches and achieves superior accuracy-performance trade-offs across ranks on the evaluated datasets. Our code is available at https://github.com/IST-DASLab/MatryoshkaLoRA.

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, with Group Relative Policy Optimization (GRPO) serving as the dominant algorithm. We identify two overlooked inefficiencies inherent in GRPO. First, a fixed KL coefficient overly restricts policy exploration at moments when the model needs to diverge significantly from the reference policy. Second, uniform question sampling overlooks that moderately difficult problems produce the most informative gradient signals. We propose FG-ExPO, short for Frontier-Guided Exploration-Prioritized Policy Optimization, which integrates two lightweight components. Accuracy-Conditioned KL Scaling (AKL) adjusts the KL penalty strength through a smooth nonlinear function of batch average accuracy, loosening the constraint when the model performs poorly and strengthening it when the model achieves satisfactory results. Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at a moderate accuracy level around 0.5, focusing model training on its learning frontier. We conduct evaluations on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base across six mainstream mathematical reasoning benchmarks. Experimental results demonstrate that FG-ExPO consistently outperforms vanilla GRPO. It delivers an absolute improvement of 13.34 on the AIME 2025 pass@32 metric, rising from 63.33 percent to 76.67 percent, and obtains an average pass@32 gain of 2.66 on the 8B model. The substantially larger performance gains observed on pass@32 compared to pass@1 verify that FG-ExPO enlarges the model's effective exploration space under a fixed inference budget.

Post-Training Quantization (PTQ) is essential for deploying Large Language Models (LLMs) on memory-constrained devices, yet it renders models static and difficult to fine-tune. Standard fine-tuning paradigms, including Reinforcement Learning (RL), fundamentally rely on backpropagation and high-precision weights to compute gradients. Thus they cannot be used on quantized models, where the parameter space is discrete and non-differentiable. While Evolution Strategies (ES) offer a backpropagation-free alternative, optimization of the quantized parameters can still fail due to vanishing or inaccurate gradient. This paper introduces Quantized Evolution Strategies (QES), an optimization paradigm that performs full-parameter fine-tuning directly in the quantized space. QES is based on two innovations: (1) it integrates accumulated error feedback to preserve high-precision gradient signals, and (2) it utilizes a stateless seed replay to reduce memory usage to low-precision inference levels. QES significantly outperforms the state-of-the-art zeroth-order fine-tuning method on arithmetic reasoning tasks, making direct fine-tuning for quantized models possible. It therefore opens up the possibility for scaling up LLMs entirely in the quantized space. The source code is available at https://github.com/dibbla/Quantized-Evolution-Strategies .

We propose Beam Tree Recursive Cell (BT-Cell) - a backpropagation-friendly framework to extend Recursive Neural Networks (RvNNs) with beam search for latent structure induction. We further extend this framework by proposing a relaxation of the hard top-k operators in beam search for better propagation of gradient signals. We evaluate our proposed models in different out-of-distribution splits in both synthetic and realistic data. Our experiments show that BTCell achieves near-perfect performance on several challenging structure-sensitive synthetic tasks like ListOps and logical inference while maintaining comparable performance in realistic data against other RvNN-based models. Additionally, we identify a previously unknown failure case for neural models in generalization to unseen number of arguments in ListOps. The code is available at: https://github.com/JRC1995/BeamTreeRecursiveCells.

Backpropagation (BP), a foundational algorithm for training artificial neural networks, predominates in contemporary deep learning. Although highly successful, it is often considered biologically implausible. A significant limitation arises from the need for precise symmetry between connections in the backward and forward pathways to backpropagate gradient signals accurately, which is not observed in biological brains. Researchers have proposed several algorithms to alleviate this symmetry constraint, such as feedback alignment and direct feedback alignment. However, their divergence from backpropagation dynamics presents challenges, particularly in deeper networks and convolutional layers. Here we introduce the Product Feedback Alignment (PFA) algorithm. Our findings demonstrate that PFA closely approximates BP and achieves comparable performance in deep convolutional networks while avoiding explicit weight symmetry. Our results offer a novel solution to the longstanding weight symmetry problem, leading to more biologically plausible learning in deep convolutional networks compared to earlier methods.

Reinforcement learning (RL) has emerged as an effective post-training paradigm for enhancing the reasoning capabilities of multimodal large language model (MLLM). However, current RL pipelines often suffer from training inefficiencies caused by two underexplored issues: Advantage Collapsing, where most advantages in a batch concentrate near zero, and Rollout Silencing, where the proportion of rollouts contributing non-zero gradients diminishes over time. These issues lead to suboptimal gradient updates and hinder long-term learning efficiency. To address these issues, we propose Shuffle-R1, a simple yet principled framework that improves RL fine-tuning efficiency by dynamically restructuring trajectory sampling and batch composition. It introduces (1) Pairwise Trajectory Sampling, which selects high-contrast trajectories with large advantages to improve gradient signal quality, and (2) Advantage-based Trajectory Shuffle, which increases exposure of valuable rollouts through informed batch reshuffling. Experiments across multiple reasoning benchmarks show that our framework consistently outperforms strong RL baselines with minimal overhead. These results highlight the importance of data-centric adaptations for more efficient RL training in MLLM.

Post-training paradigms for Large Language Models (LLMs), primarily Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), face a fundamental dilemma: SFT provides stability (low variance) but suffers from high fitting bias, while RL enables exploration (low bias) but grapples with high gradient variance. Existing unified optimization strategies often employ naive loss weighting, overlooking the statistical conflict between these distinct gradient signals. In this paper, we provide a rigorous theoretical analysis of this bias-variance trade-off and propose DYPO (Dynamic Policy Optimization), a unified framework designed to structurally mitigate this conflict. DYPO integrates three core components: (1) a Group Alignment Loss (GAL) that leverages intrinsic group dynamics to significantly reduce RL gradient variance; (2) a Multi-Teacher Distillation mechanism that corrects SFT fitting bias via diverse reasoning paths; and (3) a Dynamic Exploitation-Exploration Gating mechanism that adaptively arbitrates between stable SFT and exploratory RL based on reward feedback. Theoretical analysis confirms that DYPO linearly reduces fitting bias and minimizes overall variance. Extensive experiments demonstrate that DYPO significantly outperforms traditional sequential pipelines, achieving an average improvement of 4.8\% on complex reasoning benchmarks and 13.3\% on out-of-distribution tasks. Our code is publicly available at https://github.com/Tocci-Zhu/DYPO.

We revisit a universally accepted but under-examined design choice in every modern LLM: a token index is looked up once at the input embedding layer and then permanently discarded. This single-injection assumption induces two structural failures: (i) the Rare Token Problem, where a Zipf-type distribution of vocabulary causes rare-token embeddings are chronically under-trained due to receiving a fraction of the cumulative gradient signal compared to common tokens; and (ii) the Contextual Collapse Problem, where limited parameters models map distributionally similar tokens to indistinguishable hidden states. As an attempt to address both, we propose TIDE, which augments the standard transformer with EmbeddingMemory: an ensemble of K independent MemoryBlocks that map token indices to context-free semantic vectors, computed once and injected into every layer through a depth-conditioned softmax router with a learnable null bank. We theoretically and empirically establish the benefits of TIDE in addressing the issues associated with single-token identity injection as well as improve performance across multiple language modeling and downstream tasks.

Reinforcement learning with verifiable rewards (RLVR) has become a leading paradigm for improving the reasoning ability of large language models through outcome-based supervision. However, verifiable rewards frequently become uninformative at the group level: when all sampled traces of a given prompt receive identical rewards, group-relative advantage estimation provides no gradient signal, even though the traces may differ substantially in reasoning quality. We propose Reasoning Arena, an adaptive training framework that routes such non-diverse reward groups to a judge system instead of discarding them. Beyond examining the final answer, Reasoning Arena constructs trace tournaments, where reasoning traces are compared head-to-head to expose finer-grained preferences within the group, converting reasoning quality into rich relative reward signals. To make reward estimation efficient, rather than exhaustively comparing every pair, each new trace is evaluated against a small, dynamically updated pool of previously generated traces as anchors to efficiently establish a relative ranking. We then fit a Bradley-Terry model on the incomplete comparison graph, enabling scalable RL integration without quadratic pairwise comparisons. Empirical results demonstrate that Reasoning Arena consistently outperforms the RLVR baseline by 7.6% on average in competition mathematics and coding benchmarks. By converting otherwise wasted zero-advantage samples into useful gradient updates, our method accelerates training by 27% to 41%, saving nearly 50% of generation compute, and substantially improves overall reasoning performance.

Reinforcement learning (RL) plays a central role in large language model (LLM) post-training. Among existing approaches, Group Relative Policy Optimization (GRPO) is widely used, especially for RL with verifiable rewards (RLVR) fine-tuning. In GRPO, each query prompts the LLM to generate a group of rollouts with a fixed group size N. When all rollouts in a group share the same outcome, either all correct or all incorrect, the group-normalized advantages become zero, yielding no gradient signal and wasting fine-tuning compute. We introduce Adaptive Efficient Rollout Optimization (AERO), an enhancement of GRPO. AERO uses an adaptive rollout strategy, applies selective rejection to strategically prune rollouts, and maintains a Bayesian posterior to prevent zero-advantage dead zones. Across three model configurations (Qwen2.5-Math-1.5B, Qwen2.5-7B, and Qwen2.5-7B-Instruct), AERO improves compute efficiency without sacrificing performance. Under the same total rollout budget, AERO reduces total training compute by about 48% while shortening wall-clock time per step by about 45% on average. Despite the substantial reduction in compute, AERO matches or improves Pass@8 and Avg@8 over GRPO, demonstrating a practical, scalable, and compute-efficient strategy for RL-based LLM alignment.

Generative Retrieval (GR) offers a promising paradigm for recommendation through next-token prediction (NTP). However, scaling it to large-scale industrial systems introduces three challenges: (i) within a single request, the identical model inputs may produce inconsistent outputs due to the pagination request mechanism; (ii) the prohibitive cost of encoding long user behavior sequences with multi-token item representations based on semantic IDs, and (iii) aligning the generative policy with nuanced user preference signals. We present GenRec, a preference-oriented generative framework deployed on the JD App that addresses above challenges within a single decoder-only architecture. For training objective, we propose Page-wise NTP task, which supervises over an entire interaction page rather than each interacted item individually, providing denser gradient signal and resolving the one-to-many ambiguity of point-wise training. On the prefilling side, an asymmetric linear Token Merger compresses multi-token Semantic IDs in the prompt while preserving full-resolution decoding, reducing input length by ~2X with negligible accuracy loss. To further align outputs with user satisfaction, we introduce GRPO-SR, a reinforcement learning method that pairs Group Relative Policy Optimization with NLL regularization for training stability, and employs Hybrid Rewards combining a dense reward model with a relevance gate to mitigate reward hacking. In month-long online A/B tests serving production traffic, GenRec achieves 9.5% improvement in click count and 8.7% in transaction count over the existing pipeline.

Continual learning aims to acquire tasks sequentially without catastrophic forgetting, yet standard strategies face a core tradeoff: regularization-based methods (e.g., EWC) can overconstrain updates when task optima are weakly overlapping, while replay-based methods can retain performance but drift due to imperfect replay. We study a hybrid perspective: trust region continual learning that combines generative replay with a Fisher-metric trust region constraint. We show that, under local approximations, the resulting update admits a MAML-style interpretation with a single implicit inner step: replay supplies an old-task gradient signal (query-like), while the Fisher-weighted penalty provides an efficient offline curvature shaping (support-like). This yields an emergent meta-learning property in continual learning: the model becomes an initialization that rapidly re-converges to prior task optima after each task transition, without explicitly optimizing a bilevel objective. Empirically, on task-incremental diffusion image generation and continual diffusion-policy control, trust region continual learning achieves the best final performance and retention, and consistently recovers early-task performance faster than EWC, replay, and continual meta-learning baselines.

Reinforcement learning with verifiable rewards (RLVR) has proven effective in eliciting complex reasoning in large language models (LLMs). However, standard RLVR training often leads to excessively verbose processes (in reasoning tasks) and inefficient exploration trajectories (in agentic settings), as outcome-only rewards provide no incentive for efficiency and the high variance in response length within relatively small rollout groups results in noisy optimization signals. To address this, we propose Rollout Response Recomposition (RoRecomp), a plug-and-play method that guides models toward concise reasoning by strategically recomposing the training data. RoRecomp separates responses into two distinct batch types: 1) priority batches, which combine short-correct and long-incorrect responses selected from online batches to provide a clear gradient signal for brevity, and 2) compensation batches, which utilize remaining responses from a replay buffer to maintain stability and prevent model collapse. To comprehensively evaluate effectiveness, we test RoRecomp across three settings where results demonstrate substantial efficiency gains: reducing reasoning length by 27.7% in zero RL training, reducing unnecessary tool calls by 46.8% while improving accuracy in agentic RL, and achieving up to 52.5% length reduction in thinking compression, all with minimal performance impact.

Graphical User Interface (GUI) grounding maps natural language instructions to precise interface locations for autonomous interaction. Current reinforcement learning approaches use binary rewards that treat elements as hit-or-miss targets, creating sparse signals that ignore the continuous nature of spatial interactions. Motivated by human clicking behavior that naturally forms Gaussian distributions centered on target elements, we introduce GUI Gaussian Grounding Rewards (GUI-G^2), a principled reward framework that models GUI elements as continuous Gaussian distributions across the interface plane. GUI-G^2 incorporates two synergistic mechanisms: Gaussian point rewards model precise localization through exponentially decaying distributions centered on element centroids, while coverage rewards assess spatial alignment by measuring the overlap between predicted Gaussian distributions and target regions. To handle diverse element scales, we develop an adaptive variance mechanism that calibrates reward distributions based on element dimensions. This framework transforms GUI grounding from sparse binary classification to dense continuous optimization, where Gaussian distributions generate rich gradient signals that guide models toward optimal interaction positions. Extensive experiments across ScreenSpot, ScreenSpot-v2, and ScreenSpot-Pro benchmarks demonstrate that GUI-G^2, substantially outperforms state-of-the-art method UI-TARS-72B, with the most significant improvement of 24.7% on ScreenSpot-Pro. Our analysis reveals that continuous modeling provides superior robustness to interface variations and enhanced generalization to unseen layouts, establishing a new paradigm for spatial reasoning in GUI interaction tasks.

Reinforcement Learning (RL) has become a powerful tool for enhancing the reasoning abilities of large language models (LLMs) by optimizing their policies with reward signals. Yet, RL's success relies on the reliability of rewards, which are provided by verifiers. In this paper, we expose and analyze a widespread problem--false negatives--where verifiers wrongly reject correct model outputs. Our in-depth study of the Big-Math-RL-Verified dataset reveals that over 38% of model-generated responses suffer from false negatives, where the verifier fails to recognize correct answers. We show, both empirically and theoretically, that these false negatives severely impair RL training by depriving the model of informative gradient signals and slowing convergence. To mitigate this, we propose tinyV, a lightweight LLM-based verifier that augments existing rule-based methods, which dynamically identifies potential false negatives and recovers valid responses to produce more accurate reward estimates. Across multiple math-reasoning benchmarks, integrating TinyV boosts pass rates by up to 10% and accelerates convergence relative to the baseline. Our findings highlight the critical importance of addressing verifier false negatives and offer a practical approach to improve RL-based fine-tuning of LLMs. Our code is available at https://github.com/uw-nsl/TinyV.

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from entropy collapse and limited reasoning gains. We argue that these issues stem from overemphasizing high-probability output sequences while neglecting rare but informative reasoning paths. To address these challenges, we propose Risk-based Policy Optimization (RiskPO), which substitutes classical mean-based objectives with principled risk measures. Specifically, we introduce a Mixed Value-at-Risk objective that integrates weighted attention over multiple regions of the reward distribution, thereby amplifying gradient signals on challenging instances and preventing overconfident convergence. We further design a bundling scheme that aggregates multiple questions into bundles, thus enriching the feedback signal and yielding more stable and informative training dynamics. Theoretically, we prove that the risk-averse update alleviates entropy collapse and promotes exploration. Numerically, RiskPO achieves consistent and significant improvements in mathematical reasoning, multi-modal reasoning, and code generation benchmarks, surpassing GRPO and its variants on both Pass@1 and Pass@k metrics. Our results demonstrate that risk-based optimization provides a rigorous and effective paradigm for enhancing LLM reasoning capabilities.

The opacity of massive pretraining corpora in Large Language Models (LLMs) raises significant privacy and copyright concerns, making pretraining data detection a critical challenge. Existing state-of-the-art methods typically rely on token likelihoods, yet they often overlook the gap between the target token and the model's top-1 prediction, as well as local correlations between adjacent tokens. In this work, we propose Gap-K%, a novel pretraining data detection method grounded in the optimization dynamics of LLM pretraining. By analyzing the next-token prediction objective, we observe that discrepancies between the model's top-1 prediction and the target token induce strong gradient signals, which are explicitly penalized during training. Motivated by this, Gap-K% leverages the log probability gap between the top-1 predicted token and the target token, incorporating a sliding window strategy to capture local correlations and mitigate token-level fluctuations. Extensive experiments on the WikiMIA and MIMIR benchmarks demonstrate that Gap-K% achieves state-of-the-art performance, consistently outperforming prior baselines across various model sizes and input lengths.

Federated fine-tuning of foundation models with Low-Rank Adaptation (LoRA) provides an efficient solution for reducing communication and computation costs while preserving data locality. However, the direct combination of FedAvg and LoRA suffers from three key issues: limited update space, which restricts the model's effective learning capacity; inter-round state mismatch, which disrupts cross-round local optimization continuity; and a client-agnostic starting state, which slows local convergence on clients. Although recent methods mitigate the limited update space issue by merging LoRA updates into the backbone across communication rounds, inter-round state mismatch and the client-agnostic starting state remain insufficiently addressed. To address these issues, we propose FedSmoothLoRA, a federated LoRA tuning framework that preserves the enlarged update space, improves cross-round local optimization continuity, and provides a client-aware starting state for local training. At each communication round, FedSmoothLoRA constructs the local LoRA initialization using two matrices: a Round-Matching matrix that preserves cross-round local state continuity, and a Gradient-Aligned matrix that provides client-specific optimization guidance from gradient signals estimated on local data. Together, these designs enable smoother and faster convergence. Extensive experiments on image classification and natural language generation tasks demonstrate that FedSmoothLoRA consistently outperforms existing federated LoRA tuning methods. Code: https://github.com/wangzehao0704/FedSmoothLoRA

Speculative decoding accelerates LLM inference, but SOTA hidden-state-based drafters suffer from long-range decay: draft accuracy degrades as the speculative step increases. Existing work attributes this decay to train-inference mismatch and proposes test-time training (TTT) as a remedy, yet we observe that long-range decay persists even in TTT-trained drafters. We revisit long-range decay from the perspective of context information preservation. In hidden-state reuse, we argue the target hidden state acts as a biased context compression: it aggregates historical token information according to the attention query at the current position, yielding a compact representation optimized for immediate next-token prediction. This compression can suppress information less relevant to the current query but important for later speculative steps. In contrast, the target model's KV cache serves as an explicit context, retaining the complete set of token-wise KV representations. We therefore posit the KV-Reuse Hypothesis: allowing the draft model to reuse the target KV cache can provide richer signals for long-horizon drafting. To test this hypothesis, we introduce KVShot, a diagnostic framework that compares three reuse paradigms: hidden-only, KV-only, and hybrid. Extensive evaluations on Qwen3-8B show that KV-Reuse improves long-range acceptance, although end-to-end speedups remain marginal under current training pipelines. Our analysis identifies two key structural bottlenecks: shallow drafters struggle to estimate target queries accurately, and draft-side KV projections receive sparse gradient signals. These findings suggest that realizing the full potential of KV-aware decoding requires moving beyond TTT toward block-wise training paradigms. By exposing these bottlenecks, KVShot provides a foundational diagnostic testbed and a clear roadmap for designing next-generation inference architectures.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for enhancing the reasoning capabilities of Large Language Models (LLMs). However, dominant approaches like Group Relative Policy Optimization (GRPO) face critical stability challenges: they suffer from high estimator variance under computational constraints (small group sizes) and vanishing gradient signals in saturated failure regimes where all responses yield identical zero rewards. To address this, we propose Empirical Bayes Policy Optimization (EBPO), a novel framework that regularizes local group-based baselines by borrowing strength from the policy's accumulated global statistics. Instead of estimating baselines in isolation, EBPO employs a shrinkage estimator that dynamically balances local group statistics with a global prior updated via Welford's online algorithm. Theoretically, we demonstrate that EBPO guarantees strictly lower Mean Squared Error (MSE), bounded entropy decay, and non-vanishing penalty signals in failure scenarios compared to GRPO. Empirically, EBPO consistently outperforms GRPO and other established baselines across diverse benchmarks, including AIME and OlympiadBench. Notably, EBPO exhibits superior training stability, achieving high-performance gains even with small group sizes, and benefits significantly from difficulty-stratified curriculum learning.

Long-horizon reinforcement learning (RL) for large language models faces critical scalability challenges from unbounded context growth, leading to context folding methods that compress interaction history during task execution. However, existing approaches treat summary actions as standard actions, overlooking that summaries fundamentally modify the agent's future observation space, creating a policy-dependent, non-stationary observation distribution that violates core RL assumptions. This introduces three fundamental challenges: (1) gradient dilution where summary tokens receive insufficient training signal, (2) self-conditioning where policy updates change summary distributions, creating a vicious cycle of training collapse, and (3) computational cost from processing unique contexts at each turn. We introduce FoldActhttps://github.com/SHAO-Jiaqi757/FoldAct, a framework that explicitly addresses these challenges through three key innovations: separated loss computation for independent gradient signals on summary and action tokens, full context consistency loss to reduce distribution shift, and selective segment training to reduce computational cost. Our method enables stable training of long-horizon search agents with context folding, addressing the non-stationary observation problem while improving training efficiency with 5.19times speedup.

Subject-driven image generation models face a fundamental trade-off between identity preservation (fidelity) and prompt adherence (editability). While online reinforcement learning (RL), specifically GPRO, offers a promising solution, we find that a naive application of GRPO leads to competitive degradation, as the simple linear aggregation of rewards with static weights causes conflicting gradient signals and a misalignment with the temporal dynamics of the diffusion process. To overcome these limitations, we propose Customized-GRPO, a novel framework featuring two key innovations: (i) Synergy-Aware Reward Shaping (SARS), a non-linear mechanism that explicitly penalizes conflicted reward signals and amplifies synergistic ones, providing a sharper and more decisive gradient. (ii) Time-Aware Dynamic Weighting (TDW), which aligns the optimization pressure with the model's temporal dynamics by prioritizing prompt-following in the early, identity preservation in the later. Extensive experiments demonstrate that our method significantly outperforms naive GRPO baselines, successfully mitigating competitive degradation. Our model achieves a superior balance, generating images that both preserve key identity features and accurately adhere to complex textual prompts.

Training tool-use agents typically relies on outcome-based filtering: Supervised Fine-Tuning (SFT) on successful trajectories and Reinforcement Learning (RL) on pass-rate-selected tasks. However, this paradigm ignores interaction dynamics: successful trajectories may lack error recovery or exhibit redundancy, while pass rates fail to distinguish structurally informative tasks from trivial ones. We propose TopoCurate, an interaction-aware framework that projects multi-trial rollouts from the same task into a unified semantic quotient topology. By merging equivalent action-observation states, this projection transforms scattered linear trajectories into a structured manifold that explicitly captures how tool invocations and environmental responses drive the divergence between effective strategies and failure modes. Leveraging this representation, we introduce a dual-selection mechanism: for SFT, we prioritize trajectories demonstrating reflective recovery, semantic efficiency, and strategic diversity to mitigate covariate shift and mode collapse; for RL, we select tasks with high error branch ratios and strategic heterogeneity, maximizing gradient Signal-to-Noise Ratio to address vanishing signals in sparse-reward settings. Evaluations on BFCLv3 and Tau2 Bench show that TopoCurate achieves consistent gains of 4.2\% (SFT) and 6.9\% (RL) over state-of-the-art baselines. We will release the code and data soon for further investigations.

Large scale 3D scene reconstruction is important for applications such as virtual reality and simulation. Existing neural rendering approaches (e.g., NeRF, 3DGS) have achieved realistic reconstructions on large scenes, but optimize per scene, which is expensive and slow, and exhibit noticeable artifacts under large view changes due to overfitting. Generalizable approaches or large reconstruction models are fast, but primarily work for small scenes/objects and often produce lower quality rendering results. In this work, we introduce G3R, a generalizable reconstruction approach that can efficiently predict high-quality 3D scene representations for large scenes. We propose to learn a reconstruction network that takes the gradient feedback signals from differentiable rendering to iteratively update a 3D scene representation, combining the benefits of high photorealism from per-scene optimization with data-driven priors from fast feed-forward prediction methods. Experiments on urban-driving and drone datasets show that G3R generalizes across diverse large scenes and accelerates the reconstruction process by at least 10x while achieving comparable or better realism compared to 3DGS, and also being more robust to large view changes.

We present SHIFT3D, a differentiable pipeline for generating 3D shapes that are structurally plausible yet challenging to 3D object detectors. In safety-critical applications like autonomous driving, discovering such novel challenging objects can offer insight into unknown vulnerabilities of 3D detectors. By representing objects with a signed distanced function (SDF), we show that gradient error signals allow us to smoothly deform the shape or pose of a 3D object in order to confuse a downstream 3D detector. Importantly, the objects generated by SHIFT3D physically differ from the baseline object yet retain a semantically recognizable shape. Our approach provides interpretable failure modes for modern 3D object detectors, and can aid in preemptive discovery of potential safety risks within 3D perception systems before these risks become critical failures.

Recent studies have examined attention dynamics in large vision-language models (LVLMs) to detect hallucinations. However, existing approaches remain limited in reliably distinguishing hallucinated from factually grounded outputs, as they rely solely on forward-pass attention patterns and neglect gradient-based signals that reveal how token influence propagates through the network. To bridge this gap, we introduce LVLMs-Saliency, a gradient-aware diagnostic framework that quantifies the visual grounding strength of each output token by fusing attention weights with their input gradients. Our analysis uncovers a decisive pattern: hallucinations frequently arise when preceding output tokens exhibit low saliency toward the prediction of the next token, signaling a breakdown in contextual memory retention. Leveraging this insight, we propose a dual-mechanism inference-time framework to mitigate hallucinations: (1) Saliency-Guided Rejection Sampling (SGRS), which dynamically filters candidate tokens during autoregressive decoding by rejecting those whose saliency falls below a context-adaptive threshold, thereby preventing coherence-breaking tokens from entering the output sequence; and (2) Local Coherence Reinforcement (LocoRE), a lightweight, plug-and-play module that strengthens attention from the current token to its most recent predecessors, actively counteracting the contextual forgetting behavior identified by LVLMs-Saliency. Extensive experiments across multiple LVLMs demonstrate that our method significantly reduces hallucination rates while preserving fluency and task performance, offering a robust and interpretable solution for enhancing model reliability. Code is available at: https://github.com/zhangbaijin/LVLMs-Saliency

Reinforcement learning (RL) has enabled the training of large language model (LLM) agents to interact with the environment and to solve multi-turn long-horizon tasks. However, the RL-trained agents often struggle in tasks that require active exploration and fail to efficiently adapt from trial-and-error experiences. In this paper, we present LaMer, a general Meta-RL framework that enables LLM agents to actively explore and learn from the environment feedback at test time. LaMer consists of two key components: (i) a cross-episode training framework to encourage exploration and long-term rewards optimization; and (ii) in-context policy adaptation via reflection, allowing the agent to adapt their policy from task feedback signal without gradient update. Experiments across diverse environments show that LaMer significantly improves performance over RL baselines, with 11%, 14%, and 19% performance gains on Sokoban, MineSweeper and Webshop, respectively. Moreover, LaMer also demonstrates better generalization to more challenging or previously unseen tasks compared to the RL-trained agents. Overall, our results demonstrate that Meta-RL provides a principled approach to induce exploration in language agents, enabling more robust adaptation to novel environments through learned exploration strategies.

We identify a new dimension for enhancing rollout diversity in Group Relative Policy Optimization (GRPO) for LLMs. While GRPO relies on diverse rollouts, prevailing strategies primarily increase diversity by injecting more token-level randomness, which may introduce step-wise noise and lead to incoherent trajectories. We uncover that smaller models within the same model family inherently exhibit higher policy-level diversity, indicated by their superior pass@k relative to larger counterparts as sample counts increase. Unlike token-level noise, this diversity is temporally correlated, preserves logical consistency, and provides structured exploration signals for gradient estimation. We thus propose S2L-PO (Small-to-Large Policy Optimization), a framework that leverages fixed small models as natural explorers to train larger models. To balance exploration and exploitation, we design a progressive annealing strategy that transitions from offline small-model rollouts to the large learner's own sampling. This shift elegantly avoids mid-training performance drops caused by the small model's capacity limits, achieving faster convergence and unlocking a higher performance ceiling. S2L-PO improves accuracy on diverse mathematical reasoning benchmarks (e.g., +8.8% on AIME 24 using a 1.7B explorer to guide the 8B model) while reducing rollout compute.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

Existing Reinforcement Learning with Verifiable Rewards (RLVR) algorithms, such as GRPO, rely on rigid, uniform, and symmetric trust region mechanisms that are fundamentally misaligned with the complex optimization dynamics of Large Language Models (LLMs). In this paper, we identify three critical challenges in these methods: (1) inefficient gradient utilization caused by the binary cutoff of hard clipping, (2) insensitive probability mass arising from uniform ratio constraints that ignore the token distribution, and (3) asymmetric signal reliability stemming from the disparate credit assignment ambiguity between positive and negative samples. To bridge these gaps, we propose Mass-Adaptive Soft Policy Optimization (MASPO), a unified framework designed to harmonize these three dimensions. MASPO integrates a differentiable soft Gaussian gating to maximize gradient utility, a mass-adaptive limiter to balance exploration across the probability spectrum, and an asymmetric risk controller to align update magnitudes with signal confidence. Extensive evaluations demonstrate that MASPO serves as a robust, all-in-one RLVR solution, significantly outperforming baselines. Our code is at: https://github.com/VenomRose-Juri/MASPO-RL{https://github.com/VenomRose-Juri/MASPO-RL}.

Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of the class score function with respect to the input image. This gradient can be interpreted as a sensitivity map, and there are several techniques that elaborate on this basic idea. This paper makes two contributions: it introduces SmoothGrad, a simple method that can help visually sharpen gradient-based sensitivity maps, and it discusses lessons in the visualization of these maps. We publish the code for our experiments and a website with our results.

Gradient descent is the method of choice for training large artificial intelligence systems. As these systems become larger, a better understanding of the mechanisms behind gradient training would allow us to alleviate compute costs and help steer these systems away from harmful behaviors. To that end, we suggest utilizing the circuit perspective brought forward by mechanistic interpretability. After laying out our intuition, we illustrate how it enables us to design a curriculum for efficient learning in a controlled setting. The code is available at https://github.com/facebookresearch/pal.

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the algorithmic perspective, that is, the algorithms of GR that efficiently improve the performance. In this study, we first reveal that a specific finite-difference computation, composed of both gradient ascent and descent steps, reduces the computational cost of GR. Next, we show that the finite-difference computation also works better in the sense of generalization performance. We theoretically analyze a solvable model, a diagonal linear network, and clarify that GR has a desirable implicit bias to so-called rich regime and finite-difference computation strengthens this bias. Furthermore, finite-difference GR is closely related to some other algorithms based on iterative ascent and descent steps for exploring flat minima. In particular, we reveal that the flooding method can perform finite-difference GR in an implicit way. Thus, this work broadens our understanding of GR for both practice and theory.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

Federated Learning (FL) systems are gaining popularity as a solution to training Machine Learning (ML) models from large-scale user data collected on personal devices (e.g., smartphones) without their raw data leaving the device. At the core of FL is a network of anonymous user devices sharing training information (model parameter updates) computed locally on personal data. However, the type and degree to which user-specific information is encoded in the model updates is poorly understood. In this paper, we identify model updates encode subtle variations in which users capture and generate data. The variations provide a strong statistical signal, allowing an adversary to effectively deanonymize participating devices using a limited set of auxiliary data. We analyze resulting deanonymization attacks on diverse tasks on real-world (anonymized) user-generated data across a range of closed- and open-world scenarios. We study various strategies to mitigate the risks of deanonymization. As random perturbation methods do not offer convincing operating points, we propose data-augmentation strategies which introduces adversarial biases in device data and thereby, offer substantial protection against deanonymization threats with little effect on utility.

The growing Synthetic Aperture Radar (SAR) data has the potential to build a foundation model through Self-Supervised Learning (SSL) methods, which can achieve various SAR Automatic Target Recognition (ATR) tasks with pre-training in large-scale unlabeled data and fine-tuning in small labeled samples. SSL aims to construct supervision signals directly from the data, which minimizes the need for expensive expert annotation and maximizes the use of the expanding data pool for a foundational model. This study investigates an effective SSL method for SAR ATR, which can pave the way for a foundation model in SAR ATR. The primary obstacles faced in SSL for SAR ATR are the small targets in remote sensing and speckle noise in SAR images, corresponding to the SSL approach and signals. To overcome these challenges, we present a novel Joint-Embedding Predictive Architecture for SAR ATR (SAR-JEPA), which leverages local masked patches to predict the multi-scale SAR gradient representations of unseen context. The key aspect of SAR-JEPA is integrating SAR domain features to ensure high-quality self-supervised signals as target features. Besides, we employ local masks and multi-scale features to accommodate the various small targets in remote sensing. By fine-tuning and evaluating our framework on three target recognition datasets (vehicle, ship, and aircraft) with four other datasets as pre-training, we demonstrate its outperformance over other SSL methods and its effectiveness with increasing SAR data. This study showcases the potential of SSL for SAR target recognition across diverse targets, scenes, and sensors.Our codes and weights are available in \url{https://github.com/waterdisappear/SAR-JEPA.

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of decoder-only models adapted from the modded NanoGPT codebase, we introduce an empirical protocol based on activation covariance and per-sample gradient SVD spectra. This dual-view reveals three empirical findings and one mechanistic explanation. First, batch size acts as a latent determinant of representation geometry: runs that reach equal loss settle into systematically distinct activation spectra. Second, the activation covariance tail measured early in training reliably forecasts downstream token efficiency. Third, movement of the activation spectrum head (leading modes), together with gradient spectra, characterizes underlying learning-dynamics changes, separating learning-side architectural improvements from primarily execution-side gains. These predictive and diagnostic signals persist across the 12-, 36-, and 48-layer model tiers. Finally, a mechanistic model proves the main observations and explains how activation covariance spectra correlate with task-aligned feature learning.

Large language models (LLMs) are trained on massive web-scale corpora, raising growing concerns about privacy and copyright. Membership inference attacks (MIAs) aim to determine whether a given example was used during training. Existing LLM MIAs largely rely on output probabilities or loss values and often perform only marginally better than random guessing when members and non-members are drawn from the same distribution. We introduce G-Drift MIA, a white-box membership inference method based on gradient-induced feature drift. Given a candidate (x,y), we apply a single targeted gradient-ascent step that increases its loss and measure the resulting changes in internal representations, including logits, hidden-layer activations, and projections onto fixed feature directions, before and after the update. These drift signals are used to train a lightweight logistic classifier that effectively separates members from non-members. Across multiple transformer-based LLMs and datasets derived from realistic MIA benchmarks, G-Drift substantially outperforms confidence-based, perplexity-based, and reference-based attacks. We further show that memorized training samples systematically exhibit smaller and more structured feature drift than non-members, providing a mechanistic link between gradient geometry, representation stability, and memorization. In general, our results demonstrate that small, controlled gradient interventions offer a practical tool for auditing the membership of training-data and assessing privacy risks in LLMs.

Authorship attribution models fine-tuned with the same pretrained encoder, data, and loss can differ four-fold in performance depending only on their scoring mechanism. We use mechanistic interpretability tools to explain this gap. Stylistic features such as word length, punctuation density, and function-word frequency are equally available at every layer in every model, including in an off-the-shelf control encoder, hence the gap not coming from representation quality. Instead, causal intervention shows that the scorer determines where the encoder consolidates authorship signal. Mean pooling forces consolidation by early to mid layers, while late interaction defers it to later layers. We further derive this difference from the gradient structure of each scorer, and training dynamics reveal distinct learning trajectories that follow from that difference.

Long-horizon tool-use reinforcement learning learns from outcome verification, but trajectory-level advantages are broadcast over reasoning, API, and answer tokens. Direct self-distillation can supply a denser signal, but in our experiments it can also destroy tool use by rehearsing teacher behavior without identifying which actions the verifier rewards. We introduce Sibling-Guided Credit Distillation (SGCD), which uses distillation for bounded credit weighting rather than as a competing actor loss. Dynamic sampling produces mixed successful and failed sibling rollouts; an external LLM summarizes their contrast into a training-only credit reference; and detached teacher/student divergence reshapes GRPO token advantages. The deployed student receives only the clean task prompt. Across AppWorld and tau^3-airline, SGCD reports higher held-out point estimates than GRPO-family comparators: AppWorld TGC improves from 42.9 to 45.6 on test_normal and from 24.7 to 27.0 on test_challenge, and tau^3-airline held-out evaluator score improves from 0.583 to 0.602. These results support a narrow design rule for long-horizon tool-use agents: use distillation to guide credit assignment while keeping policy gradient in charge of the actor update.

We propose a desigining method of a flexible sampling operator for graph signals via a difference-of-convex (DC) optimization algorithm. A fundamental challenge in graph signal processing is sampling, especially for graph signals that are not bandlimited. In order to sample beyond bandlimited graph signals, there are studies to expand the generalized sampling theory for the graph setting. Vertex-wise sampling and flexible sampling are two main strategies to sample graph signals. Recovery accuracy of existing vertex-wise sampling methods is highly dependent on specific vertices selected to generate a sampled graph signal that may compromise the accurary especially when noise is generated at the vertices. In contrast, a flexible sampling mixes values at multiple vertices to generate a sampled signal for robust sampling; however, existing flexible sampling methods impose strict assumptions and aggressive relaxations. To address these limitations, we aim to design a flexible sampling operator without such strict assumptions and aggressive relaxations by introducing DC optimization. By formulating the problem of designing a flexible sampling operator as a DC optimization problem, our method ensures robust sampling for graph signals under arbitrary priors based on generalized sampling theory. We develop an efficient solver based on the general double-proximal gradient DC algorithm, which guarantees convergence to a critical point. Experimental results demonstrate the superiority of our method in sampling and recovering beyond bandlimited graph signals compared to existing approaches.

Multi-agent systems (MAS) built on large language models (LLMs) provide a promising framework for solving complex tasks through role specialization and structured interaction. However, their performance is often limited by miscoordination and, more fundamentally, the lack of fine-grained credit assignment across agents. Existing approaches typically rely on coarse-grained feedback, making it difficult to identify which agents or interaction steps are responsible for errors. We propose Gradient-Based Connections (GBC), an approach for fine-grained attribution and optimization of multi-agent systems. GBC models a MAS as a computational graph and introduces gradient-based connection weights to quantify the influence of each agent's output on downstream agents at the token level. By constructing an attribution graph and propagating task-specific loss signals backward, our method enables precise identification of error sources and targeted prompt optimization. We further develop AgentChord, an efficient implementation that leverages prefix-based gradient computation. Experiments on MultiWOZ and τ-bench show that GBC improves multi-agent performance and outperforms strong single-agent and multi-agent baselines, and higher attribution quality is associated with greater optimization effectiveness. Code is available at: https://github.com/yxc-cyber/AgentChord.

We present GDFusion, a temporal fusion method for vision-based 3D semantic occupancy prediction (VisionOcc). GDFusion opens up the underexplored aspects of temporal fusion within the VisionOcc framework, focusing on both temporal cues and fusion strategies. It systematically examines the entire VisionOcc pipeline, identifying three fundamental yet previously overlooked temporal cues: scene-level consistency, motion calibration, and geometric complementation. These cues capture diverse facets of temporal evolution and make distinct contributions across various modules in the VisionOcc framework. To effectively fuse temporal signals across heterogeneous representations, we propose a novel fusion strategy by reinterpreting the formulation of vanilla RNNs. This reinterpretation leverages gradient descent on features to unify the integration of diverse temporal information, seamlessly embedding the proposed temporal cues into the network. Extensive experiments on nuScenes demonstrate that GDFusion significantly outperforms established baselines. Notably, on Occ3D benchmark, it achieves 1.4\%-4.8\% mIoU improvements and reduces memory consumption by 27\%-72\%.

Recent studies have demonstrated that gradient matching-based dataset synthesis, or dataset condensation (DC), methods can achieve state-of-the-art performance when applied to data-efficient learning tasks. However, in this study, we prove that the existing DC methods can perform worse than the random selection method when task-irrelevant information forms a significant part of the training dataset. We attribute this to the lack of participation of the contrastive signals between the classes resulting from the class-wise gradient matching strategy. To address this problem, we propose Dataset Condensation with Contrastive signals (DCC) by modifying the loss function to enable the DC methods to effectively capture the differences between classes. In addition, we analyze the new loss function in terms of training dynamics by tracking the kernel velocity. Furthermore, we introduce a bi-level warm-up strategy to stabilize the optimization. Our experimental results indicate that while the existing methods are ineffective for fine-grained image classification tasks, the proposed method can successfully generate informative synthetic datasets for the same tasks. Moreover, we demonstrate that the proposed method outperforms the baselines even on benchmark datasets such as SVHN, CIFAR-10, and CIFAR-100. Finally, we demonstrate the high applicability of the proposed method by applying it to continual learning tasks.

We propose Q-Guided Value-Gradient Matching (Q-VGM), an off-policy reinforcement learning method for a central difficulty in fine-tuning flow-matching vision-language-action (VLA) policies: improving an expressive flow-matching action expert with a learned Q-function. Effective improvement must exploit the critic's first-order signal nabla_A Q, yet flow policies make this hard: backpropagating values through the multi-step denoising chain is unstable at VLA scale, and the tractable action likelihoods required by policy gradients are unavailable under iterative denoising. Existing value-based methods therefore backpropagate through the full chain, use the critic only for test-time selection or guidance, or distill critic-improved actions as terminal labels that never supervise the velocity field. Q-VGM instead casts policy improvement as optimal control over the denoising dynamics, where the optimal residual velocity is the gradient of a denoising-time value function: clean-action estimates improved by iterative Q-gradient ascent with keep-best selection are converted into residual velocity targets that directly supervise the velocity field -- no action likelihoods, no backpropagation through the denoising chain, fully offline on a fixed replay buffer, and no critic at inference time. The critic is an action-sensitive stepwise IQL critic on compact latent states from the frozen VLA backbone. This enables a few-shot-initialization, learn-from-experience paradigm: starting from a few-shot-SFT π_{0.5} policy, Q-VGM improves the policy from its own rollouts without additional expert supervision, raising the average LIBERO success rate from 79.0% to 92.5%, outperforming all same-backbone, same-critic baselines, and attaining high success rates on four real-robot manipulation tasks, including fine-grained plug insertion.

Distributed reinforcement learning trains on data from stale, buggy, or mismatched actors, producing actions with high surprisal (negative log-probability) under the learner's policy. The core difficulty is not surprising data per se, but negative learning from surprising data. High-surprisal failures can dominate the update direction despite carrying little useful signal, while high-surprisal successes reveal opportunities the current policy would otherwise miss. The Delightful Policy Gradient (DG) separates these cases by gating each update with delight, the product of advantage and surprisal, suppressing rare failures and amplifying rare successes without behavior probabilities. Under contaminated sampling, the cosine similarity between the standard policy gradient and the true gradient collapses, while DG's grows as the policy improves. No sign-blind reweighting, including exact importance sampling, can reproduce this effect. On MNIST with simulated staleness, DG without off-policy correction outperforms importance-weighted PG with exact behavior probabilities. On a transformer sequence task with staleness, actor bugs, reward corruption, and rare discovery, DG achieves roughly 10{times} lower error. When all four frictions act simultaneously, its compute advantage is order-of-magnitude and grows with task complexity.

While bigger and deeper neural network architectures continue to advance the state-of-the-art for many computer vision tasks, real-world adoption of these networks is impeded by hardware and speed constraints. Conventional model compression methods attempt to address this problem by modifying the architecture manually or using pre-defined heuristics. Since the space of all reduced architectures is very large, modifying the architecture of a deep neural network in this way is a difficult task. In this paper, we tackle this issue by introducing a principled method for learning reduced network architectures in a data-driven way using reinforcement learning. Our approach takes a larger `teacher' network as input and outputs a compressed `student' network derived from the `teacher' network. In the first stage of our method, a recurrent policy network aggressively removes layers from the large `teacher' model. In the second stage, another recurrent policy network carefully reduces the size of each remaining layer. The resulting network is then evaluated to obtain a reward -- a score based on the accuracy and compression of the network. Our approach uses this reward signal with policy gradients to train the policies to find a locally optimal student network. Our experiments show that we can achieve compression rates of more than 10x for models such as ResNet-34 while maintaining similar performance to the input `teacher' network. We also present a valuable transfer learning result which shows that policies which are pre-trained on smaller `teacher' networks can be used to rapidly speed up training on larger `teacher' networks.

Recent autoregressive video diffusion methods are increasingly built upon Self Forcing, where the student is trained on histories produced by its own rollout rather than ground-truth video contexts. This reduces exposure bias, but the historical key-value cache is still used by future frames only as frozen rollout state. As a result, future losses cannot supervise how earlier generated latents should be written into more useful keys and values for later video-latent generation. We call this the historical context-gradient gap. We propose Self Gradient Forcing (SGF), a two-pass training strategy that restores this missing supervision signal without backpropagating through the full serial rollout. Pass 1 performs a no-gradient autoregressive rollout matching inference and, at a sampled denoising exit step, records both the self-generated context and the noisy latents fed to the model. Pass 2 performs parallel context-gradient reconstruction for the recorded exit step. The generated context is used as stop-gradient clean-latent input, while the model recomputes the context KV representations and future-to-context causal attention. Thus, SGF provides the missing memory-writing supervision within the native autoregressive training objective, using losses on future video latents to train the model to encode context into more effective causal memory. Across extensive long-horizon frame-wise and chunk-wise experiments under different initializations, SGF achieves stronger native long-video extrapolation than Self Forcing, especially in subject identity, background/layout consistency, and temporal stability. Remarkably, using only a 5-second training window, SGF can extrapolate to videos lasting several minutes. Code and models will be released to advance research on autoregressive video generation.

Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence issues may arise when it is applied to nonconvex penalties, such as SCAD. A recent proposal generalizes Nesterov's AG method to the nonconvex setting. The proposed algorithm requires specification of several hyperparameters for its practical application. Aside from some general conditions, there is no explicit rule for selecting the hyperparameters, and how different selection can affect convergence of the algorithm. In this article, we propose a hyperparameter setting based on the complexity upper bound to accelerate convergence, and consider the application of this nonconvex AG algorithm to high-dimensional linear and logistic sparse learning problems. We further establish the rate of convergence and present a simple and useful bound to characterize our proposed optimal damping sequence. Simulation studies show that convergence can be made, on average, considerably faster than that of the conventional proximal gradient algorithm. Our experiments also show that the proposed method generally outperforms the current state-of-the-art methods in terms of signal recovery.

Inference-time steering methods offer a lightweight alternative to fine-tuning large language models (LLMs) and vision-language models (VLMs) by modifying internal activations at test time without updating model weights. However, most existing approaches rely on fixed, global intervention vectors, overlook the causal influence of individual input tokens, and fail to leverage informative gradients from the model's logits, particularly in multimodal settings where visual and textual inputs contribute unevenly. To address these limitations, we introduce GrAInS, an inference-time steering approach that operates across both language-only and vision-language models and tasks. GrAInS uses contrastive, gradient-based attribution via Integrated Gradients to identify the top-k most influential tokens, both positively and negatively attributed based on their contribution to preferred versus dispreferred outputs. These tokens are then used to construct directional steering vectors that capture semantic shifts from undesirable to desirable behavior. During inference, GrAInS adjusts hidden activations at transformer layers guided by token-level attribution signals, and normalizes activations to preserve representational scale. This enables fine-grained, interpretable, and modular control over model behavior, without retraining or auxiliary supervision. Empirically, GrAInS consistently outperforms both fine-tuning and existing steering baselines: it achieves a 13.22% accuracy gain on TruthfulQA using Llama-3.1-8B, reduces hallucination rates on MMHal-Bench from 0.624 to 0.514 with LLaVA-1.6-7B, and improves alignment win rates on SPA-VL by 8.11%, all while preserving the model's fluency and general capabilities.

Progressive Learning (PL) reduces pre-training computational overhead by gradually increasing model scale. While prior work has extensively explored depth expansion, width expansion remains significantly understudied, with the few existing methods limited to the early stages of training. However, expanding width during the mid-stage is essential for maximizing computational savings, yet it remains a formidable challenge due to severe training instabilities. Empirically, we show that naive initialization at this stage disrupts activation statistics, triggering loss spikes, while copy-based initialization introduces gradient symmetry that hinders feature diversity. To address these issues, we propose SPARKLING (balancing {S}ignal {P}reservation {A}nd symmet{R}y brea{K}ing for width-progressive {L}earn{ING}), a novel framework for mid-stage width expansion. Our method achieves signal preservation via RMS-scale consistency, stabilizing activation statistics during expansion. Symmetry breaking is ensured through asymmetric optimizer state resetting and learning rate re-warmup. Extensive experiments on Mixture-of-Experts (MoE) models demonstrate that, across multiple width axes and optimizer families, SPARKLING consistently outperforms training from scratch and reduces training cost by up to 35% under 2times width expansion.

While online Reinforcement Learning has emerged as a crucial technique for aligning flow matching models with human preferences, current approaches are hindered by inefficient exploration during training rollouts. Relying on undirected stochasticity and sparse outcome rewards, these methods struggle to discover high-reward samples, resulting in data-inefficient and slow optimization. To address these limitations, we propose Euphonium, a novel framework that steers generation via process reward gradient guided dynamics. Our key insight is to formulate the sampling process as a theoretically principled Stochastic Differential Equation that explicitly incorporates the gradient of a Process Reward Model into the flow drift. This design enables dense, step-by-step steering toward high-reward regions, advancing beyond the unguided exploration in prior works, and theoretically encompasses existing sampling methods (e.g., Flow-GRPO, DanceGRPO) as special cases. We further derive a distillation objective that internalizes the guidance signal into the flow network, eliminating inference-time dependency on the reward model. We instantiate this framework with a Dual-Reward Group Relative Policy Optimization algorithm, combining latent process rewards for efficient credit assignment with pixel-level outcome rewards for final visual fidelity. Experiments on text-to-video generation show that Euphonium achieves better alignment compared to existing methods while accelerating training convergence by 1.66x.

Millimeter-wave radar is promising to provide robust and accurate vital sign monitoring in an unobtrusive manner. However, the radar signal might be distorted in propagation by ambient noise or random body movement, ruining the subtle cardiac activities and destroying the vital sign recovery. In particular, the recovery of electrocardiogram (ECG) signal heavily relies on the deep-learning model and is sensitive to noise. Therefore, this work creatively deconstructs the radar-based ECG recovery into three individual tasks and proposes a multi-task learning (MTL) framework, radarODE-MTL, to increase the robustness against consistent and abrupt noises. In addition, to alleviate the potential conflicts in optimizing individual tasks, a novel multi-task optimization strategy, eccentric gradient alignment (EGA), is proposed to dynamically trim the task-specific gradients based on task difficulties in orthogonal space. The proposed radarODE-MTL with EGA is evaluated on the public dataset with prominent improvements in accuracy, and the performance remains consistent under noises. The experimental results indicate that radarODE-MTL could reconstruct accurate ECG signals robustly from radar signals and imply the application prospect in real-life situations. The code is available at: http://github.com/ZYY0844/radarODE-MTL.

Normalization layers are one of the key building blocks for deep neural networks. Several theoretical studies have shown that batch normalization improves the signal propagation, by avoiding the representations from becoming collinear across the layers. However, results on mean-field theory of batch normalization also conclude that this benefit comes at the expense of exploding gradients in depth. Motivated by these two aspects of batch normalization, in this study we pose the following question: "Can a batch-normalized network keep the optimal signal propagation properties, but avoid exploding gradients?" We answer this question in the affirmative by giving a particular construction of an Multi-Layer Perceptron (MLP) with linear activations and batch-normalization that provably has bounded gradients at any depth. Based on Weingarten calculus, we develop a rigorous and non-asymptotic theory for this constructed MLP that gives a precise characterization of forward signal propagation, while proving that gradients remain bounded for linearly independent input samples, which holds in most practical settings. Inspired by our theory, we also design an activation shaping scheme that empirically achieves the same properties for certain non-linear activations.

Domain-specific embedding models have shown promise for applications that require specialized semantic understanding, such as coding agents and financial retrieval systems, often achieving higher performance gains than general models. However, state-of-the-art embedding models are typically based on LLMs, which contain billions of parameters, making deployment challenging in resource-constrained environments. Model compression through pruning offers a promising solution, but existing pruning methods treat all parameters uniformly, failing to distinguish between general semantic representations and domain-specific patterns, leading to suboptimal pruning decisions. Thus, we propose GAPrune, a pruning framework that addresses this challenge by considering both domain importance and preserving general linguistic foundation. Our method uses Fisher Information to measure importance and general-domain gradient alignment to assess parameter behavior, then combines these signals using our Domain Alignment Importance (DAI) scoring. Lower DAI scores indicate that the parameter is either less important for the domain task or creates conflicts between domain and general objectives. Experiments on two domain benchmarks, FinMTEB and ChemTEB, show that GAPrune maintains performance within 2.5% of dense models in one-shot pruning at 50% sparsity, while outperforming all baselines. With retraining in 100 steps, GAPrune achieves +4.51% improvement on FinMTEB and +1.73% on ChemTEB, demonstrating that our pruning strategy not only preserves but enhances domain-specific capabilities. Our findings demonstrate that principled pruning strategies can achieve model compression and enhanced domain specialization, providing the research community with a new approach for development.

Text retrieval plays a crucial role in incorporating factual knowledge for decision making into language processing pipelines, ranging from chat-based web search to question answering systems. Current state-of-the-art text retrieval models leverage pre-trained large language models (LLMs) to achieve competitive performance, but training LLM-based retrievers via typical contrastive losses requires intricate heuristics, including selecting hard negatives and using additional supervision as learning signals. This reliance on heuristics stems from the fact that the contrastive loss itself is heuristic and does not directly optimize the downstream metrics of decision quality at the end of the processing pipeline. To address this issue, we introduce Neural PG-RANK, a novel training algorithm that learns to rank by instantiating a LLM as a Plackett-Luce ranking policy. Neural PG-RANK provides a principled method for end-to-end training of retrieval models as part of larger decision systems via policy gradient, with little reliance on complex heuristics, and it effectively unifies the training objective with downstream decision-making quality. We conduct extensive experiments on various text retrieval benchmarks. The results demonstrate that when the training objective aligns with the evaluation setup, Neural PG-RANK yields remarkable in-domain performance improvement, with substantial out-of-domain generalization to some critical datasets employed in downstream question answering tasks.

Reinforcement learning has become essential for strengthening the reasoning abilities of large language models, yet current exploration mechanisms remain fundamentally misaligned with how these models actually learn. Entropy bonuses and external semantic comparators encourage surface level variation but offer no guarantee that sampled trajectories differ in the update directions that shape optimization. We propose G2RL, a gradient guided reinforcement learning framework in which exploration is driven not by external heuristics but by the model own first order update geometry. For each response, G2RL constructs a sequence level feature from the model final layer sensitivity, obtainable at negligible cost from a standard forward pass, and measures how each trajectory would reshape the policy by comparing these features within a sampled group. Trajectories that introduce novel gradient directions receive a bounded multiplicative reward scaler, while redundant or off manifold updates are deemphasized, yielding a self referential exploration signal that is naturally aligned with PPO style stability and KL control. Across math and general reasoning benchmarks (MATH500, AMC, AIME24, AIME25, GPQA, MMLUpro) on Qwen3 base 1.7B and 4B models, G2RL consistently improves pass@1, maj@16, and pass@k over entropy based GRPO and external embedding methods. Analyzing the induced geometry, we find that G2RL expands exploration into substantially more orthogonal and often opposing gradient directions while maintaining semantic coherence, revealing that a policy own update space provides a far more faithful and effective basis for guiding exploration in large language model reinforcement learning.

Supervised fine-tuning (SFT) is the predominant method for adapting large language models (LLMs), yet it often struggles with generalization compared to reinforcement learning (RL). In this work, we posit that this performance disparity stems not just from the loss function, but from a more fundamental difference: SFT learns from a fixed, pre-collected dataset, whereas RL utilizes on-policy data sampled from the current policy. Building on this hypothesis, we introduce one-token rollout (OTR), a novel fine-tuning algorithm that guides SFT with the policy gradient method. OTR reframes the autoregressive learning process by treating each token generation as a single-step reinforcement learning trajectory. At each step, it performs a Monte Carlo ``rollout'' by sampling multiple candidate tokens from the current policy's distribution. The ground-truth token from the supervised data is then used to provide a reward signal to these samples. Guided by policy gradient, our algorithm repurposes static, off-policy supervised data into a dynamic, on-policy signal at the token level, capturing the generalization benefits of on-policy learning while bypassing the costly overhead of full sentence generation. Through extensive experiments on a diverse suite of challenging benchmarks spanning mathematical reasoning, code generation, and general domain reasoning, we demonstrate that OTR consistently outperforms standard SFT. Our findings establish OTR as a powerful and practical alternative for fine-tuning LLMs and provide compelling evidence that the on-policy nature of data is a critical driver of generalization, offering a promising new direction for fine-tuning LLMs.

In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the transformer model. Our framework can be used to understand and mitigate vanishing/exploding gradients, rank collapse, and instability associated with high attention scores. We also propose DeepScaleLM, an initialization and scaling scheme that conserves unit output/gradient moments throughout the model, enabling the training of very deep models with 100s of layers. We find that transformer models could be much deeper - our deep models with fewer parameters outperform shallow models in Language Modeling, Speech Translation, and Image Classification, across Encoder-only, Decoder-only and Encoder-Decoder variants, for both Pre-LN and Post-LN transformers, for multiple datasets and model sizes. These improvements also translate into improved performance on downstream Question Answering tasks and improved robustness for image classification.

Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient updates through the lens of signal processing and reveal that fixed momentum coefficients inherently distort the balance between bias and variance, leading to skewed or suboptimal parameter updates. To address this, we propose SGDF (SGD with Filter), an optimizer inspired by the principles of Optimal Linear Filtering. SGDF computes an online, time-varying gain to dynamically refine gradient estimation by minimizing the mean-squared error, thereby achieving an optimal trade-off between noise suppression and signal preservation. Furthermore, our approach could extend to other optimizers, showcasing its broad applicability to optimization frameworks. Extensive experiments across diverse architectures and benchmarks demonstrate SGDF surpasses conventional momentum methods and achieves performance on par with or surpassing state-of-the-art optimizers.

Mixture-of-Experts (MoE) architectures achieve parameter efficiency through conditional computation, yet contemporary designs suffer from two fundamental limitations: structural parameter isolation that causes catastrophic forgetting, and instruction-overfitting that degrades performance in instruction-free scenarios. We propose CDSP-MoE (Conflict-Driven Subspace Pruning MoE), a framework that addresses these issues through a paradigm shift from isolated expert containers to dynamic expert instantiation within a shared physical subspace. Grounded in the Universal Weight Subspace Hypothesis, CDSP-MoE maintains a super-complete parameter backbone where logical experts are carved out via learnable topology masks. Unlike prior work that uses gradient conflict for token reassignment or optimization surgery, we leverage it as a structural supervisory signal: a Lagged Gradient Game penalizes interfering connections in the shared manifold, enabling the topology to spontaneously prune conflicting pathways and evolve interpretable modular structures. Experimental results demonstrate that CDSP-MoE achieves robust content-driven routing without human-defined task labels, maintaining semantic specialization even under strict blind inference protocols where explicit instructions are absent. Code is available at: https://github.com/konodiodaaaaa1/Conflict-Driven-Subspace-Pruning-Mixture-of-Experts

This paper describes a novel nonparametric model for modeling diffusion MRI signals in q-space. In q-space, diffusion MRI signal is measured for a sequence of magnetic strengths (b-values) and magnetic gradient directions (b-vectors). We propose a Poly-RBF model, which employs a bidirectional framework with polynomial bases to model the signal along the b-value direction and Gaussian radial bases across the b-vectors. The model can accommodate sparse data on b-values and moderately dense data on b-vectors. The utility of Poly-RBF is inspected for two applications: 1) prediction of the dMRI signal, and 2) harmonization of dMRI data collected under different acquisition protocols with different scanners. Our results indicate that the proposed Poly-RBF model can more accurately predict the unmeasured diffusion signal than its competitors such as the Gaussian process model in {\tt Eddy} of FSL. Applying it to harmonizing the diffusion signal can significantly improve the reproducibility of derived white matter microstructure measures.

Jailbreak attacks on audio language models (ALMs) optimize audio perturbations to elicit unsafe generations, and they typically update the entire waveform densely throughout optimization. In this work, we investigate the necessity of such dense optimization by analyzing the structure of token-aligned gradients in ALMs. We find that gradient energy is highly non-uniform across audio tokens, indicating that only a small subset of token-aligned audio regions dominates the optimization signal. Motivated by this observation, we propose Token-Aware Gradient Optimization (TAGO), which enables sparse jailbreak optimization by retaining only waveform gradients aligned with audio tokens that have high gradient energy, while masking the remaining gradients at each iteration. Across three ALMs, TAGO outperforms baselines, and substantial sparsification preserves strong attack success rates (e.g. on Qwen3-Omni, ASR_{l} remains at 86% with a token retention ratio of 0.25, compared to 87% with full token retention). These results demonstrate that dense waveform updates are largely redundant, and we advocate that future audio jailbreak and safety alignment research should further leverage this heterogeneous token-level gradient structure.

In Recurrent Neural Networks (RNNs), encoding information in a suboptimal or erroneous way can impact the quality of representations based on later elements in the sequence and subsequently lead to wrong predictions and a worse model performance. In humans, challenging cases like garden path sentences (an instance of this being the infamous "The horse raced past the barn fell") can lead their language understanding astray. However, they are still able to correct their representation accordingly and recover when new information is encountered. Inspired by this, I propose an augmentation to standard RNNs in form of a gradient-based correction mechanism: This way I hope to enable such models to dynamically adapt their inner representation of a sentence, adding a way to correct deviations as soon as they occur. This could therefore lead to more robust models using more flexible representations, even during inference time. I conduct different experiments in the context of language modeling, where the impact of using such a mechanism is examined in detail. To this end, I look at modifications based on different kinds of time-dependent error signals and how they influence the model performance. Furthermore, this work contains a study of the model's confidence in its predictions during training and for challenging test samples and the effect of the manipulation thereof. Lastly, I also study the difference in behavior of these novel models compared to a standard LSTM baseline and investigate error cases in detail to identify points of future research. I show that while the proposed approach comes with promising theoretical guarantees and an appealing intuition, it is only able to produce minor improvements over the baseline due to challenges in its practical application and the efficacy of the tested model variants.

Pre-trained Transformers often exhibit over-confidence in source patterns and difficulty in forming new target-domain patterns during fine-tuning. We formalize the mechanism of output saturation leading to gradient suppression through standard cross-entropy and softmax analysis, showing that gradient suppression at inflection layers confines adaptation to high-level recombination of existing features while preventing low-level reconstruction. We introduce a set of layer-wise diagnostic metrics -- attention entropy (saturation proxy), activation gradient norm, parameter gradient norm, and Delta-CKA under a shared PCA basis -- to identify inflection layers characterized by both low attention entropy and steep gradient decay. Building on these findings, we propose a diagnose-first, inject-light fine-tuning strategy: selectively inserting LoRA adapters at inflection layers to restore suppressed backward signals with minimal parameter overhead. Experiments on BERT-base transfer from SST-2 to Rotten Tomatoes under under-trained and over-trained source regimes reveal that over-trained initialization benefits from inflection-layer LoRA injection, while under-trained initialization suffers performance degradation. When base features are strong, unblocking inflection layers facilitates high-level compositional adaptation; when base features are weak, full-pathway unblocking is required for low-level reconstruction, as supported by joint analysis of layer-wise activation gradients and Delta-CKA dynamics.

With the exponential growth of data, traditional object detection methods are increasingly struggling to handle vast vocabulary object detection tasks effectively. We analyze two key limitations of classification-based detectors: positive gradient dilution, where rare positive categories receive insufficient learning signals, and hard negative gradient dilution, where discriminative gradients are overwhelmed by numerous easy negatives. To address these challenges, we propose CQ-DINO, a category query-based object detection framework that reformulates classification as a contrastive task between object queries and learnable category queries. Our method introduces image-guided query selection, which reduces the negative space by adaptively retrieving top-K relevant categories per image via cross-attention, thereby rebalancing gradient distributions and facilitating implicit hard example mining. Furthermore, CQ-DINO flexibly integrates explicit hierarchical category relationships in structured datasets (e.g., V3Det) or learns implicit category correlations via self-attention in generic datasets (e.g., COCO). Experiments demonstrate that CQ-DINO achieves superior performance on the challenging V3Det benchmark (surpassing previous methods by 2.1% AP) while maintaining competitiveness in COCO. Our work provides a scalable solution for real-world detection systems requiring wide category coverage. The code is publicly at https://github.com/RedAIGC/CQ-DINO.

Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only available supervision is a differentiable metric defined on the generated contents. Since the sampling procedure of DPMs involves recursive calls to the denoising UNet, na\"ive gradient backpropagation requires storing the intermediate states of all iterations, resulting in extremely high memory consumption. To overcome this issue, we propose a novel method AdjointDPM, which first generates new samples from diffusion models by solving the corresponding probability-flow ODEs. It then uses the adjoint sensitivity method to backpropagate the gradients of the loss to the models' parameters (including conditioning signals, network weights, and initial noises) by solving another augmented ODE. To reduce numerical errors in both the forward generation and gradient backpropagation processes, we further reparameterize the probability-flow ODE and augmented ODE as simple non-stiff ODEs using exponential integration. Finally, we demonstrate the effectiveness of AdjointDPM on three interesting tasks: converting visual effects into identification text embeddings, finetuning DPMs for specific types of stylization, and optimizing initial noise to generate adversarial samples for security auditing.

The rapid advancement of GAN and Diffusion models makes it more difficult to distinguish AI-generated images from real ones. Recent studies often use image-based reconstruction errors as an important feature for determining whether an image is AI-generated. However, these approaches typically incur high computational costs and also fail to capture intrinsic noisy features present in the raw images. To solve these problems, we innovatively refine error extraction by using bit-plane-based image processing, as lower bit planes indeed represent noise patterns in images. We introduce an effective bit-planes guided noisy image generation and exploit various image normalization strategies, including scaling and thresholding. Then, to amplify the noise signal for easier AI-generated image detection, we design a maximum gradient patch selection that applies multi-directional gradients to compute the noise score and selects the region with the highest score. Finally, we propose a lightweight and effective classification head and explore two different structures: noise-based classifier and noise-guided classifier. Extensive experiments on the GenImage benchmark demonstrate the outstanding performance of our method, which achieves an average accuracy of 98.9\% (11.9\%~uparrow) and shows excellent cross-generator generalization capability. Particularly, our method achieves an accuracy of over 98.2\% from GAN to Diffusion and over 99.2\% from Diffusion to GAN. Moreover, it performs error extraction at the millisecond level, nearly a hundred times faster than existing methods. The code is at https://github.com/hongsong-wang/LOTA.

Current Reinforcement Fine-tuning (RFT) paradigms for Large Language Models (LLMs) suffer from sample inefficiency due to the redundant exposure of identical queries under uniform data sampling. While previous work has explored curriculum learning via heuristic difficulty metrics, these strategies exhibit limitations by neglecting the intrinsic learning signals generated by the model itself, thus leading to suboptimal training regimes. In this paper, we identify a model-inherent signal termed angle concentration that effectively reflects an LLM's capacity to learn from specific data. We theoretically and empirically demonstrate a correlation between the angular distribution of token hidden state vectors and the resulting gradient, revealing a learning preference for data exhibiting higher angle concentration. Inspired by this finding, we propose GAIN-RL, a Gradient-driven Angle-Informed Navigated RL framework. By leveraging the model's intrinsic angle concentration signal, GAIN-RL dynamically selects training data in each epoch, ensuring consistently impactful gradient updates and thus significantly enhancing overall training efficiency. Empirical evaluations show that GAIN-RL (GRPO) achieves over a 2.5x acceleration in training efficiency across diverse mathematical and coding tasks and varying model scales. Furthermore, GAIN-RL (GRPO)'s efficient sampling yields data-efficient training, achieving better performance with half the original data compared to vanilla GRPO with full training data. Code is realsed at https://github.com/wangqinsi1/GAINRL/tree/main.

Diffusion distillation, exemplified by Distribution Matching Distillation (DMD), has shown great promise in few-step generation but often sacrifices quality for sampling speed. While integrating Reinforcement Learning (RL) into distillation offers potential, a naive fusion of these two objectives relies on suboptimal raw sample evaluation. This sample-based scoring creates inherent conflicts with the distillation trajectory and produces unreliable rewards due to the noisy nature of early-stage generation. To overcome these limitations, we propose GDMD, a novel framework that redefines the reward mechanism by prioritizing distillation gradients over raw pixel outputs as the primary signal for optimization. By reinterpreting the DMD gradients as implicit target tensors, our framework enables existing reward models to directly evaluate the quality of distillation updates. This gradient-level guidance functions as an adaptive weighting that synchronizes the RL policy with the distillation objective, effectively neutralizing optimization divergence. Empirical results show that GDMD sets a new SOTA for few-step generation. Specifically, our 4-step models outperform the quality of their multi-step teacher and substantially exceed previous DMDR results in GenEval and human-preference metrics, exhibiting strong scalability potential.

We present Klear-Reasoner, a model with long reasoning capabilities that demonstrates careful deliberation during problem solving, achieving outstanding performance across multiple benchmarks. Although there are already many excellent works related to inference models in the current community, there are still many problems with reproducing high-performance inference models due to incomplete disclosure of training details. This report provides an in-depth analysis of the reasoning model, covering the entire post-training workflow from data preparation and long Chain-of-Thought supervised fine-tuning (long CoT SFT) to reinforcement learning (RL), along with detailed ablation studies for each experimental component. For SFT data, our experiments show that a small number of high-quality data sources are more effective than a large number of diverse data sources, and that difficult samples can achieve better results without accuracy filtering. In addition, we investigate two key issues with current clipping mechanisms in RL: Clipping suppresses critical exploration signals and ignores suboptimal trajectories. To address these challenges, we propose Gradient-Preserving clipping Policy Optimization (GPPO) that gently backpropagates gradients from clipped tokens. GPPO not only enhances the model's exploration capacity but also improves its efficiency in learning from negative samples. Klear-Reasoner exhibits exceptional reasoning abilities in mathematics and programming, scoring 90.5\% on AIME 2024, 83.2\% on AIME 2025, 66.0\% on LiveCodeBench V5 and 58.1\% on LiveCodeBench V6.

Hybrid training methods for large language models combine supervised fine tuning (SFT) on expert demonstrations with reinforcement learning (RL) on model rollouts, typically at the sample level. We propose Entropy Gated Selective Policy Optimization (EGSPO), a three stage framework that extends sample level mixing with token level gradient modulation. Stage 1, SFT expert learning, establishes a reliable warm up policy using expert demonstrations with a pure SFT loss. Stage 2, RL rollout generation, samples trajectories from the current policy and computes per token predictive entropy. Stage 3, the EGSPO mechanism, applies entropy gated gradient allocation: a predictive entropy module routes high entropy tokens to full PPO updates to encourage exploration, and low entropy tokens to attenuated PPO updates to reduce variance and preserve knowledge. Critically, both branches incorporate the advantage function A_t, ensuring that incorrect trajectories receive consistent negative learning signals and preventing reinforcement of confident errors. EGSPO achieves consistent improvements on mathematical reasoning benchmarks, with gains of 3.8 percent on AIME and 2.9 percent on MATH over the CHORD phi baseline, while incurring only 3.4 percent additional computational overhead.

The evolution of Large Language Models (LLMs) has catalyzed a paradigm shift from superficial instruction following to rigorous long-horizon reasoning. While Group Relative Policy Optimization (GRPO) has emerged as a pivotal mechanism for eliciting such post-training reasoning capabilities due to its exceptional performance, it remains plagued by significant training instability and poor sample efficiency. We theoretically identify the root cause of these issues as the lack of distinctiveness within on-policy rollouts: for routine queries, highly homogeneous samples induce destructive gradient conflicts; whereas for hard queries, the scarcity of valid positive samples results in ineffective optimization. To bridge this gap, we propose Distinctiveness-aware Group Relative Policy Optimization (DaGRPO). DaGRPO incorporates two core mechanisms: (1) Sequence-level Gradient Rectification, which utilizes fine-grained scoring to dynamically mask sample pairs with low distinctiveness, thereby eradicating gradient conflicts at the source; and (2) Off-policy Data Augmentation, which introduces high-quality anchors to recover training signals for challenging tasks. Extensive experiments across 9 mathematical reasoning and out-of-distribution (OOD) generalization benchmarks demonstrate that DaGRPO significantly surpasses existing SFT, GRPO, and hybrid baselines, achieving new state-of-the-art performance (e.g., a +4.7% average accuracy gain on math benchmarks). Furthermore, in-depth analysis confirms that DaGRPO effectively mitigates gradient explosion and accelerates the emergence of long-chain reasoning capabilities.

Structure-Based molecule optimization (SBMO) aims to optimize molecules with both continuous coordinates and discrete types against protein targets. A promising direction is to exert gradient guidance on generative models given its remarkable success in images, but it is challenging to guide discrete data and risks inconsistencies between modalities. To this end, we leverage a continuous and differentiable space derived through Bayesian inference, presenting Molecule Joint Optimization (MolJO), the gradient-based SBMO framework that facilitates joint guidance signals across different modalities while preserving SE(3)-equivariance. We introduce a novel backward correction strategy that optimizes within a sliding window of the past histories, allowing for a seamless trade-off between explore-and-exploit during optimization. MolJO achieves state-of-the-art performance on CrossDocked2020 benchmark (Success Rate 51.3%, Vina Dock -9.05 and SA 0.78), more than 4x improvement in Success Rate compared to the gradient-based counterpart, and 2x "Me-Better" Ratio as much as 3D baselines. Furthermore, we extend MolJO to a wide range of optimization settings, including multi-objective optimization and challenging tasks in drug design such as R-group optimization and scaffold hopping, further underscoring its versatility. Code is available at https://github.com/AlgoMole/MolCRAFT.

We introduce a mathematically rigorous framework based on rough path theory to model stochastic spiking neural networks (SSNNs) as stochastic differential equations with event discontinuities (Event SDEs) and driven by c\`adl\`ag rough paths. Our formalism is general enough to allow for potential jumps to be present both in the solution trajectories as well as in the driving noise. We then identify a set of sufficient conditions ensuring the existence of pathwise gradients of solution trajectories and event times with respect to the network's parameters and show how these gradients satisfy a recursive relation. Furthermore, we introduce a general-purpose loss function defined by means of a new class of signature kernels indexed on c\`adl\`ag rough paths and use it to train SSNNs as generative models. We provide an end-to-end autodifferentiable solver for Event SDEs and make its implementation available as part of the diffrax library. Our framework is, to our knowledge, the first enabling gradient-based training of SSNNs with noise affecting both the spike timing and the network's dynamics.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and a lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms other optimizers. Also, we show that diffGrad performs uniformly well for training CNN using different activation functions. The source code is made publicly available at https://github.com/shivram1987/diffGrad.

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

Reasoning ability, a core component of human intelligence, continues to pose a significant challenge for Large Language Models (LLMs) in the pursuit of AGI. Although model performance has improved under the training scaling law, significant challenges remain, particularly with respect to training algorithms, such as catastrophic forgetting, and the limited availability of novel training data. As an alternative, test-time scaling enhances reasoning performance by increasing test-time computation without parameter updating. Unlike prior methods in this paradigm focused on token space, we propose leveraging latent space for more effective reasoning and better adherence to the test-time scaling law. We introduce LatentSeek, a novel framework that enhances LLM reasoning through Test-Time Instance-level Adaptation (TTIA) within the model's latent space. Specifically, LatentSeek leverages policy gradient to iteratively update latent representations, guided by self-generated reward signals. LatentSeek is evaluated on a range of reasoning benchmarks, including GSM8K, MATH-500, and AIME2024, across multiple LLM architectures. Results show that LatentSeek consistently outperforms strong baselines, such as Chain-of-Thought prompting and fine-tuning-based methods. Furthermore, our analysis demonstrates that LatentSeek is highly efficient, typically converging within a few iterations for problems of average complexity, while also benefiting from additional iterations, thereby highlighting the potential of test-time scaling in the latent space. These findings position LatentSeek as a lightweight, scalable, and effective solution for enhancing the reasoning capabilities of LLMs.