Daily Papers

We propose Token-Level Off-Policy Labeling (TOPL), an off-policy training paradigm that reframes post-training as a token-level correctness prediction task. Our key intuition is that by training the model to distinguish good and bad tokens in a response, we naturally guide the model towards generating good tokens, while avoiding the pitfalls that come with directly training the model to generate off-policy tokens. Experiments on document summarization tasks show that TOPL achieves strong out-of-distribution generalization across 11 datasets against a diverse set of sequence-level and token-level baselines. We further demonstrate that TOPL transfers effectively to machine translation, suggesting that its benefits generalize across different faithful generation tasks. Through ablation studies, we confirm that our token-level learning signal is critical to good performance; sequence-level analogues do not confer similar benefits. Finally, we show that TOPL induces interpretable model updates: the LoRA adapters learned through TOPL function as linear classification heads and steering vectors.

Reinforcement learning for large language models faces a fundamental trade-off between sample efficiency and asymptotic performance: strictly on-policy methods discard trajectories after a single update, while off-policy reuse introduces distribution mismatch that existing trust-region techniques mitigate primarily by enforcing conservative optimization, often leaving rich training signals underutilized. To investigate this, we perform extensive off-policy updates on fixed data. Our experiments reveal that aggressive multi-step optimization brings rapid initial gains, but excessive updates cause trajectory probabilities to deviate and entropy to collapse, with performance plateauing early. Tightening KL constraints merely lowers the ceiling without resolving the degradation. This motivates Extreme Region Policy Distillation (ERPD), a two-stage framework that decouples sample efficiency from KL efficiency. The first stage performs weakly constrained off-policy optimization on fixed data to maximally extract training signals. The resulting policy provides token-level supervision. In the second stage, we distill these signals into the base policy under trust-region constraints, filtering harmful drift while preserving useful signals. The distilled policy achieves comparable or better performance with substantially smaller KL divergence, indicating that much of the first-stage divergence was spent on unnecessary drift rather than genuine improvement. Crucially, ERPD accommodates both strong and weak teachers: when aggressive optimization yields no stronger policy, even degenerate teachers provide effective supervision via alternative signal construction strategies. We validate ERPD on mathematical reasoning, showing gains for strong base models where on-policy training plateaus, and reliable improvements with weak teachers.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

On-policy reinforcement learning (RL) methods widely used for language model post-training, like Group Relative Policy Optimization (GRPO), often suffer from limited exploration and early saturation due to low sampling diversity. While off-policy data can help, current approaches that mix entire trajectories cause significant policy mismatch and instability. In this work, we propose the Single-sample Mix-pOlicy Unified Paradigm (SOUP), a framework that unifies off- and on-policy learning within individual samples at the token level. It confines off-policy influence to the prefix of a generated sequence sampled from historical policies, while the continuation is generated on-policy. Through token-level importance ratios, SOUP effectively leverages off-policy information while preserving training stability. Extensive experiments demonstrate that SOUP consistently outperforms standard on-policy training and existing off-policy extensions. Our further analysis clarifies how our fine-grained, single-sample mix-policy training can improve both exploration and final performance in LLM RL.

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.

Reinforcement learning (RL) post-training has increasingly demonstrated strong ability to elicit reasoning behaviors in large language models (LLMs). For training efficiency, rollouts are typically generated in an off-policy manner using an older sampling policy and then used to update the current target policy. To correct the resulting discrepancy between the sampling and target policies, most existing RL objectives rely on a token-level importance sampling ratio, primarily due to its computational simplicity and numerical stability. However, we observe that token-level correction often leads to unstable training dynamics when the degree of off-policyness is large. In this paper, we revisit LLM policy optimization under off-policy conditions and show that the theoretically rigorous correction term is the prefix importance ratio, and that relaxing it to a token-level approximation can induce instability in RL post-training. To stabilize LLM optimization under large off-policy drift, we propose a simple yet effective objective, Minimum Prefix Ratio (MinPRO). MinPRO replaces the unstable cumulative prefix ratio with a non-cumulative surrogate based on the minimum token-level ratio observed in the preceding prefix. Extensive experiments on both dense and mixture-of-experts LLMs, across multiple mathematical reasoning benchmarks, demonstrate that MinPRO substantially improves training stability and peak performance in off-policy regimes.

Autoregressive rollout generation is a major computational cost in reinforcement learning for large language models. Reusing each rollout batch for additional learner updates amortizes this cost, but later updates become increasingly off-policy as the learner departs from the behavior policy. At a token position, exact off-policy correction must account for both the current action and the probability of reaching its prefix. The cumulative importance ratio provides this correction, but its product form can produce an unwieldy dynamic range. We study Prefix-Normalized Policy Optimization (PNPO), which replaces the cumulative ratio with the geometric mean of likelihood ratios along each causal prefix, preserving causal-prefix dependence at each position while compressing the log-weight scale. In controlled long-context mathematical reasoning experiments, we induce two off-policy regimes by using one or four policy-update epochs per rollout batch. PNPO does not consistently outperform GSPO with one epoch. With four epochs, it attains the highest observed Avg@32 on each benchmark; the unweighted mean of the three independently selected benchmark peaks is 50.24, 3.00 percentage points above GSPO. Under a matched 2,400-update budget, four-epoch PNPO reaches a final macro Avg@32 of 49.66 after 150 rollout batches, comparable to the 49.56 reached after 600 batches with one epoch. These results provide preliminary evidence that PNPO can be advantageous as training moves further off-policy.

Reinforcement learning (RL) approaches for Large Language Models (LLMs) frequently use on-policy algorithms, such as PPO or GRPO. However, policy lag from distributed training architectures and differences between the training and inference policies break this assumption, making the data off-policy by design. To rectify this, prior work has focused on making this off-policy data appear more on-policy, either via importance sampling (IS), or by more closely aligning the training and inference policies by explicitly modifying the inference engine. In this work, we embrace off-policyness and propose a novel off-policy RL algorithm that does not require these modifications: Optimal Advantage-based Policy Optimization with Lagged Inference policy (OAPL). We show that OAPL outperforms GRPO with importance sampling on competition math benchmarks, and can match the performance of a publicly available coding model, DeepCoder, on LiveCodeBench, while using 3x fewer generations during training. We further empirically demonstrate that models trained via OAPL have improved test time scaling under the Pass@k metric. OAPL allows for efficient, effective post-training even with lags of more than 400 gradient steps between the training and inference policies, 100x more off-policy than prior approaches.

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.

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

Machine unlearning is an emerging technique that removes the influence of a subset of training data (forget set) from a model without full retraining, with applications including privacy protection, content moderation, and model correction. The key challenge lies in ensuring that the model completely forgets the knowledge of the forget set without compromising its overall utility. Existing unlearning methods for large language models (LLMs) often utilize auxiliary language models, retain datasets, or even commercial AI services for effective unlearning and maintaining the model utility. However, dependence on these external resources is often impractical and could potentially introduce additional privacy risks. In this work, we propose direct token optimization (DTO), a novel self-contained unlearning approach for LLMs that directly optimizes the token level objectives and eliminates the need for external resources. Given a sequence to unlearn, we identify two categories of tokens: target tokens, which capture critical knowledge for unlearning, and the remaining non-target tokens, which are crucial for maintaining the model utility. The former are used to optimize the unlearning objective, while the latter serve to preserve the model's performance. The experimental results show that the proposed DTO achieves up to 16.8times improvement in forget quality on several benchmark datasets than the latest baselines while maintaining a comparable level of model utility.

Reinforcement learning for large language models suffers from high-variance token-level importance sampling (IS) ratios, which would destabilize policy optimization at scale. To improve stability, recent methods typically use a fixed sequence-level IS ratio for all tokens in a sequence or adjust each token's IS ratio separately, thereby neglecting temporal off-policy derivation across tokens in a sequence. In this paper, we first empirically identify that local off-policy deviation is structurally inconsistent at the token level, which may distort policy-gradient updates across adjacent tokens and lead to training collapse. To address the issue, we propose Online Causal Kalman Filtering for stable and effective Policy Optimization (KPO). Concretely, we model the desired IS ratio as a latent state that evolves across tokens and apply a Kalman filter to update this state online and autoregressively based on the states of past tokens, regardless of future tokens. The resulting filtered IS ratios preserve token-wise local structure-aware variation while strongly smoothing noise spikes, yielding more stable and effective policy updates. Experimentally, KPO achieves superior results on challenging math reasoning datasets compared with state-of-the-art counterparts.

Off-policy reinforcement learning (RL) for large language models (LLMs) is attracting growing interest, driven by practical constraints in real-world applications, the complexity of LLM-RL infrastructure, and the need for further innovations of RL methodologies. While classic REINFORCE and its modern variants like Group Relative Policy Optimization (GRPO) are typically regarded as on-policy algorithms with limited tolerance of off-policyness, we present in this work a first-principles derivation for group-relative REINFORCE without assuming a specific training data distribution, showing that it admits a native off-policy interpretation. This perspective yields two general principles for adapting REINFORCE to off-policy settings: regularizing policy updates, and actively shaping the data distribution. Our analysis demystifies some myths about the roles of importance sampling and clipping in GRPO, unifies and reinterprets two recent algorithms -- Online Policy Mirror Descent (OPMD) and Asymmetric REINFORCE (AsymRE) -- as regularized forms of the REINFORCE loss, and offers theoretical justification for seemingly heuristic data-weighting strategies. Our findings lead to actionable insights that are validated with extensive empirical studies, and open up new opportunities for principled algorithm design in off-policy RL for LLMs. Source code for this work is available at https://github.com/modelscope/Trinity-RFT/tree/main/examples/rec_gsm8k.

Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) are two prominent post-training paradigms for refining the capabilities and aligning the behavior of Large Language Models (LLMs). Existing approaches that integrate SFT and RL often face the risk of disrupting established model patterns and inducing overfitting to expert data. To address this, we present a novel investigation into the unified view of SFT and RL through an off-policy versus on-policy lens. We propose CHORD, a framework for the Controllable Harmonization of On- and Off-Policy Reinforcement Learning via Dynamic Weighting, which reframes SFT not as a separate stage but as a dynamically weighted auxiliary objective within the on-policy RL process. Based on an analysis of off-policy expert data's influence at both holistic and granular levels, we incorporate a dual-control mechanism in CHORD. Specifically, the framework first employs a global coefficient to holistically guide the transition from off-policy imitation to on-policy exploration, and then applies a token-wise weighting function that enables granular learning from expert tokens, which preserves on-policy exploration and mitigates disruption from off-policy data. We conduct extensive experiments on widely used benchmarks, providing empirical evidence that CHORD achieves a stable and efficient learning process. By effectively harmonizing off-policy expert data with on-policy exploration, CHORD demonstrates significant improvements over baselines. We release the implementation at https://github.com/modelscope/Trinity-RFT/tree/main/examples/mix_chord to inspire further research.

On-policy distillation (OPD) offers superior capacity transfer by supervising student-sampled trajectories with dense token-level signals. To furnish high-quality supervision sources and thereby elevate the performance frontier of distillation, an intuitive direction is to infuse privileged information to either teacher or student itself. However, this additional input induces a potential failure mode we dub privilege illusion: a pattern that conflates the transferable capability gap that students are meant to close, and the information asymmetry gap that can only be mimicked but never replicated. This issue is further amplified by the inherent non-uniformity of token-level supervision, where only a small subset of tokens carries pivotal capability-bearing signals. To this end, we propose DOPD, an advantage-aware dual distillation paradigm that dynamically routes token-level supervision between privileged teacher and privileged student policies based on their advantage gap and relative probabilities. Each token receives supervision of different strength, objective, and strategy from either teacher or student itself, which transfers credible capability while simultaneously receiving auxiliary signals, to alleviate privilege illusion. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that DOPD consistently outperforms Vanilla OPD and other counterparts. Further results on stability, robustness, continual learning, and out-of-distribution tasks validate its superiority.

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects intrinsic uncertainty induced by the pre-training prior. Ignoring entropy can misidentify noisy or easily replaceable tokens as learning-critical, while ignoring probability fails to reflect target-specific alignment. RankTuner introduces a probability--entropy calibration signal, the Relative Rank Indicator, which compares the rank of the ground-truth token with its expected rank under the prediction distribution. The inverse indicator is used as a token-wise Relative Scale to reweight the fine-tuning objective, focusing updates on truly under-learned tokens without over-penalizing intrinsically uncertain positions. Experiments on multiple backbones show consistent improvements on mathematical reasoning benchmarks, transfer gains on out-of-distribution reasoning, and pre code generation performance over probability-only or entropy-only reweighting baselines.

Recent advancements in reinforcement learning from human feedback have shown that utilizing fine-grained token-level reward models can substantially enhance the performance of Proximal Policy Optimization (PPO) in aligning large language models. However, it is challenging to leverage such token-level reward as guidance for Direct Preference Optimization (DPO), since DPO is formulated as a sequence-level bandit problem. To address this challenge, this work decomposes the sequence-level PPO into a sequence of token-level proximal policy optimization problems and then frames the problem of token-level PPO with token-level reward guidance, from which closed-form optimal token-level policy and the corresponding token-level reward can be derived. Using the obtained reward and Bradley-Terry model, this work establishes a framework of computable loss functions with token-level reward guidance for DPO, and proposes a practical reward guidance based on the induced DPO reward. This formulation enables different tokens to exhibit varying degrees of deviation from reference policy based on their respective rewards. Experiment results demonstrate that our method achieves substantial performance improvements over DPO, with win rate gains of up to 7.5 points on MT-Bench, 6.2 points on AlpacaEval 2, and 4.3 points on Arena-Hard. Code is available at https://github.com/dvlab-research/TGDPO.

Unlearning in large language models (LLMs) has emerged as a promising safeguard against adversarial behaviors. When the forgetting loss is applied uniformly without considering token-level semantic importance, model utility can be unnecessarily degraded. Recent studies have explored token-wise loss regularizers that prioritize informative tokens, but largely rely on ground-truth confidence or external linguistic parsers, which limits their ability to capture contextual information or the model's overall predictive state. Intuitively, function words like "the" primarily serve syntactic roles and are highly predictable with little ambiguity, but informative words admit multiple plausible alternatives with greater uncertainty. Based on this intuition, we propose Entropy-guided Token Weighting (ETW), a token-level unlearning regularizer that uses entropy of the predictive distribution as a proxy for token informativeness. We demonstrate that informative tokens tend to have higher entropy, whereas structural tokens tend to have lower entropy. This behavior enables ETW to achieve more effective unlearning while better preserving model utility than existing token-level approaches.

Deploying large language models in user-facing systems requires efficient output safety filtering. Existing approaches typically rely on a separate moderation model applied after generation, which doubles inference cost and only detects violations after generation completes. We observe that the signal needed for moderation is already present in the model hidden states. Based on this, we train lightweight token-level probes that operate directly on internal activations, producing per-token safety scores that can be aggregated for both offline evaluation and online intervention. The probe reuses activations from the generator and requires no additional forward pass, enabling sub millisecond per-token safety checks inside the decoding loop. A probe applied to a single mid layer recovers most decisions of a strong guard model, acting as a low cost surrogate optimized for latency rather than accuracy. In streaming settings, it can halt or modify unsafe outputs before they are fully generated, replacing end of sequence moderation with continuous token level monitoring. Compared to post hoc and streaming guard models, our method achieves orders of magnitude lower compute overhead with minimal latency cost. We also provide a practical deployment recipe, including layer selection, aggregation strategy, probing frequency, and triggering thresholds. Finally, we show that the probe linear component corresponds to a direction in residual space, enabling both detection and activation steering at negligible cost.

We present a novel approach to feature labeling using gradient descent in token-space. While existing methods typically use language models to generate hypotheses about feature meanings, our method directly optimizes label representations by using a language model as a discriminator to predict feature activations. We formulate this as a multi-objective optimization problem in token-space, balancing prediction accuracy, entropy minimization, and linguistic naturalness. Our proof-of-concept experiments demonstrate successful convergence to interpretable single-token labels across diverse domains, including features for detecting animals, mammals, Chinese text, and numbers. Although our current implementation is constrained to single-token labels and relatively simple features, the results suggest that token-space gradient descent could become a valuable addition to the interpretability researcher's toolkit.

Knowledge distillation is central to LLM post-training, yet its design space remains poorly understood, especially alongside reinforcement learning (RL). We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions: forward KL pairs teacher prefixes with token-level forward KL, and reverse KL pairs student prefixes with token-level reverse KL. We argue this coupling is not intrinsic: decoupling the two axes yields four valid objectives. We establish gradient-level identities showing forward KL gives SFT-style cross-entropy matching with teacher soft targets, whereas reverse KL gives an RL-style policy-gradient objective with a dense teacher-student log-ratio reward, connecting them to off-policy SFT, DAgger-style on-policy SFT, offline-RL-style distillation, and OPD. We conduct an extensive controlled study on math reasoning, evaluating the four objectives both as standalone methods and as initializations for subsequent RL. The results reveal three tradeoffs: KL direction induces an accuracy-entropy tradeoff, prefix source a quality-compute tradeoff, and training length an accuracy-stability tradeoff. Motivated by these findings, we propose KL mixing and an entropy-gated length curriculum. KL mixing shows long-sequence distillation requires substantial forward-KL weight to prevent entropy collapse and length inflation without sacrificing accuracy. The entropy-gated length curriculum improves Avg@k and Pass@k by 3.6 and up to 5.8 points, and cuts average response length by roughly 3x versus fixed long-horizon training. Our results provide a framework and practical methods for designing reasoning distillation objectives that balance accuracy, diversity, compute, and RL behavior.

Large language models (LLMs) demonstrate strong multilingual capabilities, yet often fail to consistently generate responses in the intended language, exhibiting a phenomenon known as language confusion. Prior mitigation approaches based on sequence-level fine-tuning, such as DPO, ORPO, and GRPO, operate at the level of entire responses and can lead to unintended degradation of general model capabilities, motivating the need for more fine-grained alternatives. To address this, we introduce Token-Level Policy Optimization (TLPO), a fine-tuning framework designed to mitigate language confusion through localized, token-level updates. TLPO identifies error-prone positions, explores alternative candidate tokens, and updates the policy using a tailored objective to suppress error-inducing outputs at a granular level. This selective intervention enables effective mitigation of language confusion without compromising the model's general abilities. Experiments on multiple multilingual LLMs across diverse languages demonstrate that TLPO significantly outperforms baselines in improving language consistency while preserving downstream task accuracy.

On-policy distillation (OPD) trains a student on its own rollouts with token-level teacher supervision. Recent selective OPD methods exploit the non-uniformity of OPD signals by prioritizing high-entropy or high-disagreement tokens. We revisit this principle and ask: which token-level teacher signals are actually learnable? Using a fixed-context diagnostic that measures same-context teacher-student KL reduction, we show that raw KL disagreement is a coarse proxy for learning value. It conflates learnable disagreement, where the teacher assigns corrective mass to the student's top-K candidates, with incompatible disagreement, where the teacher places mass mostly off the student's current support. We formalize this local compatibility as token teachability and show that it better predicts fixed-context improvement than raw KL alone. Motivated by this finding, we propose Teachability-Aware OPD (TA-OPD), a lightweight token-position selection method that applies OPD loss to high-teachability positions without reward models or verifiers. Across Qwen2.5 and Qwen 3 teacher-student settings, TA-OPD often surpasses full-token OPD with only 5% retained tokens and improves over entropy- and divergence-based baselines. Our results reframe selective OPD as selecting learnable teacher signals rather than merely salient tokens.

In this paper, we present token labeling -- a new training objective for training high-performance vision transformers (ViTs). Different from the standard training objective of ViTs that computes the classification loss on an additional trainable class token, our proposed one takes advantage of all the image patch tokens to compute the training loss in a dense manner. Specifically, token labeling reformulates the image classification problem into multiple token-level recognition problems and assigns each patch token with an individual location-specific supervision generated by a machine annotator. Experiments show that token labeling can clearly and consistently improve the performance of various ViT models across a wide spectrum. For a vision transformer with 26M learnable parameters serving as an example, with token labeling, the model can achieve 84.4% Top-1 accuracy on ImageNet. The result can be further increased to 86.4% by slightly scaling the model size up to 150M, delivering the minimal-sized model among previous models (250M+) reaching 86%. We also show that token labeling can clearly improve the generalization capability of the pre-trained models on downstream tasks with dense prediction, such as semantic segmentation. Our code and all the training details will be made publicly available at https://github.com/zihangJiang/TokenLabeling.

Off-policy learning (OPL) aims at finding improved policies from logged bandit data, often by minimizing the inverse propensity scoring (IPS) estimator of the risk. In this work, we investigate a smooth regularization for IPS, for which we derive a two-sided PAC-Bayes generalization bound. The bound is tractable, scalable, interpretable and provides learning certificates. In particular, it is also valid for standard IPS without making the assumption that the importance weights are bounded. We demonstrate the relevance of our approach and its favorable performance through a set of learning tasks. Since our bound holds for standard IPS, we are able to provide insight into when regularizing IPS is useful. Namely, we identify cases where regularization might not be needed. This goes against the belief that, in practice, clipped IPS often enjoys favorable performance than standard IPS in OPL.

Unlearning in Multimodal Large Language Models (MLLMs) prevents the model from revealing private information when queried about target images. Existing MLLM unlearning methods largely adopt approaches developed for LLMs. They treat all answer tokens uniformly, disregarding their varying importance in the unlearning process. Moreover, these methods focus exclusively on the language modality, disregarding visual cues that indicate key tokens in answers. In this paper, after formulating the problem of unlearning in multimodal question answering for MLLMs, we propose Visual-Guided Key-Token Regularization (ViKeR). We leverage irrelevant visual inputs to predict ideal post-unlearning token-level distributions and use these distributions to regularize the unlearning process, thereby prioritizing key tokens. Further, we define key tokens in unlearning via information entropy and discuss ViKeR's effectiveness through token-level gradient reweighting, which amplifies updates on key tokens. Experiments on MLLMU and CLEAR benchmarks demonstrate that our method effectively performs unlearning while mitigating forgetting and maintaining response coherence.

Large language model evaluations typically focus on performance under nominal conditions, creating an illusion of capability where models comfortably walk a narrow, highly optimized generation corridor. In real-world deployments, however, complex system prompts, safety guardrails, and structural constraints continuously force models off this nominal path, driving a divergence between benchmark scores and deployment performance. To address this issue, we introduce Decoding-Level Taboo, a zero-prompt diagnostic stress test that intervenes directly in logit space at runtime, forcing models out of their nominal paths. By dynamically masking primary candidate tokens at word boundaries, Taboo forces machine circumlocution. Evaluating Taboo across several open-weight model families reveals that off-path robustness is heavily influenced by both parameter scale and post-training instruction alignment, with robustness generally improving with model size and alignment. Beyond the results presented in this paper, Taboo provides a novel primitive for generating diverse synthetic datasets, stress-testing runtime safety guardrails, and auditing model reliability prior to real-world deployment.

On-Policy Distillation (OPD) improves the learning efficiency of standard reinforcement learning through dense, token-level supervision from teachers. In the standard KL objective of OPD, token-level losses are uniformly averaged, implying equal weights for all tokens. However, we discover that not all tokens are created equal: as student rollouts grow longer, they deviate further from the teacher's distribution, leading to degraded supervision quality at later positions. As a result, OPD using only the first 30% of tokens can perform comparably to using all tokens, whereas OPD using only the last 30% of tokens barely learns anything. In this work, we provide a principled understanding of this issue through the lens of constrained optimization. Based on these insights, we derive Importance-Weighted On-Policy Distillation (IW-OPD), in which the weight assigned to each token depends on the accumulated discrepancy between the student's and teacher's distributions, naturally upweighting earlier tokens and downweighting later ones with larger deviations. We show that IW-OPD converges significantly faster than OPD, with better learning efficiency, and achieves better final performance than standard OPD in both same-size and cross-scale settings, improving performance up to 6.9 points on AIME-2025.

On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. We then develop a scalable targeted-rollout algorithm to estimate this gradient efficiently, even for long chains of intermediate thoughts. The gradient alignment score, defined as the cosine similarity between this ideal gradient and any given distillation gradient, quantifies the extent to which a particular configuration approximates the ideal signal. Across a range of self-distillation settings and external teacher models, we observe that distillation guidance exhibits substantially higher alignment with the ideal on incorrect rollouts than on correct ones, where the student already performs well and the teacher's signal tends to become noisy. Furthermore, we find that the optimal distillation context depends jointly on the student model's capacity and the target task, and that no single universally effective configuration emerges. These findings motivate the use of per-task, per-token diagnostic analyses for distillation.

Adapting large language models (LLMs) to long-context tasks requires post-training methods that remain accurate and coherent over thousands of tokens. Existing approaches are limited in several ways: 1) off-policy methods such as supervised fine-tuning (SFT) and knowledge distillation (KD) suffer from exposure bias and limited recovery from model-generated errors over long horizons; 2) on-policy reinforcement learning methods such as Group Relative Policy Optimization (GRPO) better align training with model-generated states, but are unstable and sample-inefficient due to sparse rewards; 3) on-policy distillation (OPD) provides dense token-level guidance, but does not directly optimize arbitrary reward signals. In this paper, we propose Distilled Group Relative Policy Optimization (dGRPO), a method for long-context reasoning that augments GRPO with dense guidance from a stronger teacher via OPD. We also introduce LongBlocks, a synthetic long-context dataset spanning multi-hop reasoning, contextual grounding, and long-form generation. We conduct extensive experiments and ablations comparing off-policy training, sparse-reward GRPO, and our combined approach, leading to an improved recipe for long-context alignment. Overall, our results show that combining outcome-based policy optimization with knowledge distillation in a single objective provides a more stable and effective path to long-context reasoning, while preserving short-context capabilities.

Current reinforcement learning from human feedback (RLHF) pipelines for large language model (LLM) alignment typically assign scalar rewards to sequences, using the final token as a surrogate indicator for the quality of the entire sequence. However, this leads to sparse feedback and suboptimal token-level credit assignment. In this work, we frame reward shaping as an optimization problem focused on token-level credit assignment. We propose a reward-shaping function leveraging explainability methods such as SHAP and LIME to estimate per-token rewards from the reward model. To learn parameters of this shaping function, we employ a bilevel optimization framework that integrates Bayesian Optimization and policy training to handle noise from the token reward estimates. Our experiments show that achieving a better balance of token-level reward attribution leads to performance improvements over baselines on downstream tasks and finds an optimal policy faster during training. Furthermore, we show theoretically that explainability methods that are feature additive attribution functions maintain the optimal policy as the original reward.

On-policy reinforcement learning has become the dominant paradigm for reasoning alignment in large language models, yet its sparse, outcome-level rewards make token-level credit assignment notoriously difficult. On-Policy Distillation (OPD) alleviates this by introducing dense, token-level KL supervision from a teacher model, but typically applies this supervision uniformly across all rollouts, ignoring fundamental differences in signal quality. We propose Signal-Calibrated On-Policy Distillation Enhancement (SCOPE), a dual-path adaptive training framework that routes on-policy rollouts by correctness into two complementary supervision paths. For incorrect trajectories, SCOPE performs teacher-perplexity-weighted KL distillation to prioritize instances where the teacher demonstrates genuine corrective capability, while down-weighting unreliable guidance. For correct trajectories, it applies student-perplexity-weighted MLE to concentrate reinforcement on low-confidence samples at the capability boundary rather than over-reinforcing already mastered ones. Both paths employ a group-level normalization to adaptively calibrate weight distributions, accounting for the intrinsic difficulty variance across prompts. Extensive experiments on six reasoning benchmarks show that SCOPE achieves an average relative improvement of 11.42% in Avg@32 and 7.30% in Pass@32 over competitive baselines, demonstrating its consistent effectiveness.

Aligning language models with human preferences relies on pairwise preference datasets. While some studies suggest that on-policy data consistently outperforms off -policy data for preference learning, others indicate that the advantages of on-policy data may be task-dependent, highlighting the need for a systematic exploration of their interplay. In this work, we show that on-policy and off-policy data offer complementary strengths in preference optimization: on-policy data is particularly effective for reasoning tasks like math and coding, while off-policy data performs better on open-ended tasks such as creative writing and making personal recommendations. Guided by these findings, we introduce SIMPLEMIX, an approach to combine the complementary strengths of on-policy and off-policy preference learning by simply mixing these two data sources. Our empirical results across diverse tasks and benchmarks demonstrate that SIMPLEMIX substantially improves language model alignment. Specifically, SIMPLEMIX improves upon on-policy DPO and off-policy DPO by an average of 6.03% on Alpaca Eval 2.0. Moreover, it outperforms prior approaches that are much more complex in combining on- and off-policy data, such as HyPO and DPO-Mix-P, by an average of 3.05%.

Policy compliance detection is the task of ensuring that a scenario conforms to a policy (e.g. a claim is valid according to government rules or a post in an online platform conforms to community guidelines). This task has been previously instantiated as a form of textual entailment, which results in poor accuracy due to the complexity of the policies. In this paper we propose to address policy compliance detection via decomposing it into question answering, where questions check whether the conditions stated in the policy apply to the scenario, and an expression tree combines the answers to obtain the label. Despite the initial upfront annotation cost, we demonstrate that this approach results in better accuracy, especially in the cross-policy setup where the policies during testing are unseen in training. In addition, it allows us to use existing question answering models pre-trained on existing large datasets. Finally, it explicitly identifies the information missing from a scenario in case policy compliance cannot be determined. We conduct our experiments using a recent dataset consisting of government policies, which we augment with expert annotations and find that the cost of annotating question answering decomposition is largely offset by improved inter-annotator agreement and speed.

Reinforcement Learning has emerged as the fundamental technique for enhancing reasoning in LLMs. However, existing algorithms apply uniform optimization to all tokens, ignoring their different roles in reasoning process. To address this limitation, we introduce Heterogeneous Adaptive Policy Optimization (HAPO), a comprehensive token-aware algorithm that dynamically adapts optimization based on token entropy. For rollout sampling, we propose Adaptive Temperature Sampling, which adjusts sampling temperature in real time, promoting exploration at high-entropy tokens while preserving coherence at low-entropy ones. For advantage calculation, we introduce Token Level Group Average that normalizes advantages at token level, jointly accounting for sequence-length as in token-mean loss while preserving non-biased treatment. We then develop Differential Advantage Redistribution that leverages entropy and importance ratios to modulate rewards-adjusting updates for tokens with clear signals. For clipping loss, we design Asymmetric Adaptive Clipping, allowing aggressive probability reduction for noisy low-entropy tokens while enabling exploration for high-entropy tokens. Through systematic investigation between entropy and training dynamics, we embedded token-level treatment into every stages to achieve fine-grained control. Extensive experiments demonstrate that HAPO consistently outperforms DAPO across multiple model scales. Our code can be found in https://github.com/starriver030515/HAPO.

Reinforcement learning, including reinforcement learning with verifiable rewards (RLVR), has emerged as a powerful approach for LLM post-training. Central to these approaches is the design of the importance sampling (IS) ratio used in off-policy policy-gradient estimation. Existing methods face a fundamental bias-variance dilemma: token-level IS ratios, as adopted by PPO (Schulman et al., 2017) and GRPO (Shao et al., 2024), introduce bias by ignoring prefix state distribution mismatch; full sequence ratios provide exact trajectory-level correction but suffer from high variance due to the multiplicative accumulation of per-token ratios, while GSPO (Zheng et al., 2025) improves numerical stability via length normalization at the cost of deviating from the exact full-sequence IS correction. In this work, we identify the cumulative token IS ratio, the product of per-token ratios up to position t, as a theoretically principled solution to this dilemma. We prove that, under the token-level policy-gradient formulation, this ratio provides an unbiased prefix correction for each token-level gradient term and has strictly lower variance than the full sequence ratio. Building on this insight, we propose CTPO (Cumulative Token Policy Optimization), which combines the cumulative token IS ratio with position-adaptive clipping that scales log-space clip bounds according to the natural t growth of the cumulative log-ratio. This yields more consistent regularization across token positions. We implement and evaluate CTPO in the tool-integrated reasoning setting on several challenging mathematical reasoning benchmarks, achieving the best average performance across both model scales compared with strong GRPO and GSPO baselines. Code will be available at https://github.com/horizon-llm/CTPO.

On-policy Distillation (OPD) supervises a student model on trajectories sampled from its own policy by minimizing the divergence between the output distributions of the teacher and student at each token position, thereby providing dense token-level supervision. Although existing OPD methods have demonstrated strong performance in improving the reasoning ability of student models, their objectives fundamentally rely on token-level distribution matching. Consequently, they lack an explicit signal for comparing a token's relative compatibility across reasoning modes and thus do not directly model preferences between these modes. To address this limitation, we propose COPD, a contrastive OPD framework. Specifically, for each token generated by the student model, a frozen teacher model scores the same student state under two contrasting instructions that elicit light and heavy reasoning. The difference between the resulting log probabilities serves as a token-level advantage signal to guide the OPD update. Rather than merely imitating a single teacher distribution, COPD directly encourages the student model to learn more concise and efficient reasoning strategies. We conduct experiments on nine multimodal benchmarks covering both reasoning and understanding tasks. The results show that COPD substantially reduces reasoning length without compromising model performance and consistently improves efficiency across different tasks and model scales. Furthermore, the contrastive formulation can be seamlessly integrated into the On-policy Self-distillation (OPSD) framework, where self-contrastive supervision is constructed without an additional teacher model, thereby enabling the model to distill itself toward lightweight reasoning.

On-policy distillation (OPD) has become a core technique in the post-training of large language models, yet its training dynamics remain poorly understood. This paper provides a systematic investigation of OPD dynamics and mechanisms. We first identify that two conditions govern whether OPD succeeds or fails: (i) the student and teacher should share compatible thinking patterns; and (ii) even with consistent thinking patterns and higher scores, the teacher must offer genuinely new capabilities beyond what the student has seen during training. We validate these findings through weak-to-strong reverse distillation, showing that same-family 1.5B and 7B teachers are distributionally indistinguishable from the student's perspective. Probing into the token-level mechanism, we show that successful OPD is characterized by progressive alignment on high-probability tokens at student-visited states, a small shared token set that concentrates most of the probability mass (97%-99%). We further propose two practical strategies to recover failing OPD: off-policy cold start and teacher-aligned prompt selection. Finally, we show that OPD's apparent free lunch of dense token-level reward comes at a cost, raising the question of whether OPD can scale to long-horizon distillation.

Aligning large language models (LLMs) on domain-specific data remains a fundamental challenge. Supervised fine-tuning (SFT) offers a straightforward way to inject domain knowledge but often degrades the model's generality. In contrast, on-policy reinforcement learning (RL) preserves generality but fails to effectively assimilate hard samples that exceed the model's current reasoning level. Recent off-policy RL attempts improve hard sample utilization, yet they suffer from severe training instability due to the forced distribution shift toward off-policy knowledge. To reconcile effective off-policy knowledge absorption with the stability of on-policy RL, we propose Rephrasing Policy Optimization (RePO). In RePO, the policy model is prompted to first comprehend off-policy knowledge and then rephrase it into trajectories that conform to its own stylistic and parametric distribution. RePO dynamically replaces low-reward rollouts with these rephrased, high-quality trajectories. This strategy guides the model toward correct reasoning paths while strictly preserving on-policy training dynamics. Experiments on several benchmarks demonstrate that RePO improves hard-sample utilization and outperforms existing baselines, achieving state-of-the-art performance.

Knowledge distillation improves large language model (LLM) reasoning by compressing the knowledge of a teacher LLM to train smaller LLMs. On-policy distillation advances this approach by having the student sample its own trajectories while a teacher LLM provides dense token-level supervision, addressing the distribution mismatch between training and inference in off-policy distillation methods. However, on-policy distillation typically requires a separate, often larger, teacher LLM and does not explicitly leverage ground-truth solutions available in reasoning datasets. Inspired by the intuition that a sufficiently capable LLM can rationalize external privileged reasoning traces and teach its weaker self (i.e., the version without access to privileged information), we introduce On-Policy Self-Distillation (OPSD), a framework where a single model acts as both teacher and student by conditioning on different contexts. The teacher policy conditions on privileged information (e.g., verified reasoning traces) while the student policy sees only the question; training minimizes the per-token divergence between these distributions over the student's own rollouts. We demonstrate the efficacy of our method on multiple mathematical reasoning benchmarks, achieving 4-8x token efficiency compared to reinforcement learning methods such as GRPO and superior performance over off-policy distillation methods.

On-Policy Distillation (OPD) trains a student model on its own generative trajectories under dense token-level feedback from a stronger teacher, mitigating both the off-policy distribution shift of Supervised Fine-Tuning (SFT) and the sparse credit assignment of Reinforcement Learning (RL). However, standard OPD faces two coupled limitations. First, it requires direct access to the teacher's token-level logits, excluding a broad class of capable proprietary models from serving as teachers. Second, the token-level logit signal itself is brittle, depending on a narrow overlap of plausible next tokens between teacher and student, and prone to amplifying degenerate patterns such as repetition loops. In this paper, we introduce OmniOPD, a novel framework that addresses both limitations through a logit-free, chunk-level supervision signal. OmniOPD replaces deterministic logit matching with Monte Carlo rollouts that approximate the teacher's local preferences through a continuous semantic similarity metric over multi-token chunks, and concentrates this supervision via a peak-entropy scheduler that audits the student only at its high-uncertainty reasoning forks. A Dirichlet-Multinomial Bayesian prior and a base-model KL anchor further bound the variance of discrete sampling and prevent policy collapse across unaudited tokens. Across competitive benchmarks, OmniOPD surpasses the standard OPD approach by up to +28.64% on math, confirming that chunk-level semantic verification extracts a more reliable learning signal than token-level logit matching, whose high information density is offset by significant noise and brittleness. Furthermore, when paired with stronger black-box teachers such as Claude-4.5-Haiku and Gemini-2.5-Flash, OmniOPD achieves an additional +9.54% relative on math over its open-weight teacher counterpart, advancing the student past the performance of self-exploratory RL.

Recent prominent post-training methods, such as Reinforcement Learning (RL) and On-Policy Self-Distillation (OPSD), have driven rapid progress in mathematical reasoning for large language models, yet their reliance on ground-truth labels precludes test-time training (TTT). Replacing ground truth with majority-vote pseudo-labels is a natural alternative, yet it is fragile: an incorrect vote corrupts the teacher and misleads every token. We observe that this failure mode is asymmetric: rollouts that disagree with the pseudo-label are typically wrong regardless of whether the vote itself is correct. Building on this observation, we propose Test-Time Policy Optimization (TTPO), an asymmetric objective that distills agreeing rollouts via OPSD and penalizes disagreeing rollouts with Grouped RL. Token-level selection further refines both branches: distillation down-weights already-converged positions, while RL penalizes only confident errors. Both updates remain well-grounded even under frequent pseudo-label errors, and majority-vote routing yields tighter self-supervision as the model improves. Without any labels, TTPO matches label-supervised OPSD on five competition-level benchmarks, raises Qwen3-1.7B from 38.0% to 45.2% in TTT, yields +25.2% to +36.4% without thinking, and shows strong cross-task generalization.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: Token-level methods (e.g., PPO) aim to provide the fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving 6-12 percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving 7-11 percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

Although language models (LMs) demonstrate exceptional capabilities on various tasks, they are potentially vulnerable to extraction attacks, which represent a significant privacy risk. To mitigate the privacy concerns of LMs, machine unlearning has emerged as an important research area, which is utilized to induce the LM to selectively forget about some of its training data. While completely retraining the model will guarantee successful unlearning and privacy assurance, it is impractical for LMs, as it would be time-consuming and resource-intensive. Prior works efficiently unlearn the target token sequences, but upon subsequent iterations, the LM displays significant degradation in performance. In this work, we propose Privacy Protection via Optimal Parameters (POP), a novel unlearning method that effectively forgets the target token sequences from the pretrained LM by applying optimal gradient updates to the parameters. Inspired by the gradient derivation of complete retraining, we approximate the optimal training objective that successfully unlearns the target sequence while retaining the knowledge from the rest of the training data. Experimental results demonstrate that POP exhibits remarkable retention performance post-unlearning across 9 classification and 4 dialogue benchmarks, outperforming the state-of-the-art by a large margin. Furthermore, we introduce Remnant Memorization Accuracy that quantifies privacy risks based on token likelihood and validate its effectiveness through both qualitative and quantitative analyses.

Reinforcement learning (RL) plays an increasingly important role in enhancing the reasoning capabilities of large language models (LLMs), yet stable and performant policy optimization remains challenging. Token-level importance ratios often exhibit high variance-a phenomenon exacerbated in Mixture-of-Experts models-leading to unstable updates. Existing group-based policy optimization methods, such as GSPO and GRPO, alleviate this problem via hard clipping, making it difficult to maintain both stability and effective learning. We propose Soft Adaptive Policy Optimization (SAPO), which replaces hard clipping with a smooth, temperature-controlled gate that adaptively attenuates off-policy updates while preserving useful learning signals. Compared with GSPO and GRPO, SAPO is both sequence-coherent and token-adaptive. Like GSPO, SAPO maintains sequence-level coherence, but its soft gating forms a continuous trust region that avoids the brittle hard clipping band used in GSPO. When a sequence contains a few highly off-policy tokens, GSPO suppresses all gradients for that sequence, whereas SAPO selectively down-weights only the offending tokens and preserves the learning signal from the near-on-policy ones, improving sample efficiency. Relative to GRPO, SAPO replaces hard token-level clipping with smooth, temperature-controlled scaling, enabling more informative and stable updates. Empirical results on mathematical reasoning benchmarks indicate that SAPO exhibits improved training stability and higher Pass@1 performance under comparable training budgets. Moreover, we employ SAPO to train the Qwen3-VL model series, demonstrating that SAPO yields consistent performance gains across diverse tasks and different model sizes. Overall, SAPO provides a more reliable, scalable, and effective optimization strategy for RL training of LLMs.

On-policy knowledge distillation (OPD) trains a student on its own rollouts under token-level supervision from a teacher. Not all token positions matter equally, but existing views of token importance are incomplete. We ask a direct question: which tokens carry the most useful learning signal in OPD? Our answer is that informative tokens come from two regions: positions with high student entropy, and positions with low student entropy plus high teacher--student divergence, where the student is overconfident and wrong. Empirically, student entropy is a strong first-order proxy: retaining 50% of tokens with entropy-based sampling matches or exceeds all-token training while reducing peak memory by up to 47%. But entropy alone misses a second important region. When we isolate low-entropy, high-divergence tokens, training on fewer than 10% of all tokens nearly matches full-token baselines, showing that overconfident tokens carry dense corrective signal despite being nearly invisible to entropy-only rules. We organize these findings with TIP (Token Importance in on-Policy distillation), a two-axis taxonomy over student entropy and teacher--student divergence, and give a theoretical explanation for why entropy is useful yet structurally incomplete. This view motivates type-aware token selection rules that combine uncertainty and disagreement. We validate this picture across three teacher--student pairs spanning Qwen3, Llama, and Qwen2.5 on MATH-500 and AIME 2024/2025, and on the DeepPlanning benchmark for long-horizon agentic planning, where Q3-only training on <20% of tokens surpasses full-token OPD. Our experiments are implemented by extending the OPD repository https://github.com/HJSang/OPSD_OnPolicyDistillation, which supports memory-efficient distillation of larger models under limited GPU budgets.

We propose a new algorithm for fine-tuning large language models using reinforcement learning. Tapered Off-Policy REINFORCE (TOPR) uses an asymmetric, tapered variant of importance sampling to speed up learning while maintaining stable learning dynamics, even without the use of KL regularization. TOPR can be applied in a fully offline fashion, allows the handling of positive and negative examples in a unified framework, and benefits from the implementational simplicity that is typical of Monte Carlo algorithms. We demonstrate the effectiveness of our approach with a series of experiments on the GSM8K and MATH reasoning benchmarks, finding performance gains for training both a model for solution generation and as a generative verifier. We show that properly leveraging positive and negative examples alike in the off-policy regime simultaneously increases test-time accuracy and training data efficiency, all the while avoiding the ``wasted inference'' that comes with discarding negative examples. We find that this advantage persists over multiple iterations of training and can be amplified by dataset curation techniques, enabling us to match 70B-parameter model performance with 8B language models. As a corollary to this work, we find that REINFORCE's baseline parameter plays an important and unexpected role in defining dataset composition in the presence of negative examples, and is consequently critical in driving off-policy performance.

The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings

Safety alignment often improves robustness to harmful queries at the cost of reasoning ability, a tradeoff known as the safety tax. A common cause is distributional mismatch: supervised fine-tuning trains the target model on safety demonstrations produced by humans, external models, or fixed self-generated traces, rather than on trajectories sampled from its own policy. We identify off-policy training mismatch as a second source of this tax and study on-policy self-distillation for safety alignment, which we call OPSA. The model generates its own rollouts and receives dense per-token KL supervision from a frozen teacher copy of itself conditioned on a privileged safety context. Because this teacher must be safer than the sampled student trajectory, we introduce teacher flip rate: a criterion that measures how often a privileged context converts unsafe responses into safe ones. We use this signal to search for contexts that activate latent safety reasoning rather than merely elicit safe-looking demonstrations. Across two reasoning-model families and five model scales, OPSA achieves a stronger safety--reasoning tradeoff than off-policy self-distillation and external-teacher distillation under matched data and full-parameter fine-tuning, with the largest gains on smaller models (+8.85 points on R1-Distill-1.5B and +5.49 points on Qwen3-0.6B). The gains persist across training-set sizes and adaptive jailbreak evaluations. Token-level analyses further show that OPSA concentrates updates near early compliance-decision tokens, providing a mechanism for improving safety while preserving general reasoning.

Large Audio Language Models (LALMs) have garnered significant research interest. Despite being built upon text-based large language models (LLMs), LALMs frequently exhibit a degradation in knowledge and reasoning capabilities. We hypothesize that this limitation stems from the failure of current training paradigms to effectively bridge the acoustic-semantic gap within the feature representation space. To address this challenge, we propose CORD, a unified alignment framework that performs online cross-modal self-distillation. Specifically, it aligns audio-conditioned reasoning with its text-conditioned counterpart within a unified model. Leveraging the text modality as an internal teacher, CORD performs multi-granularity alignment throughout the audio rollout process. At the token level, it employs on-policy reverse KL divergence with importance-aware weighting to prioritize early and semantically critical tokens. At the sequence level, CORD introduces a judge-based global reward to optimize complete reasoning trajectories via Group Relative Policy Optimization (GRPO). Empirical results across multiple benchmarks demonstrate that CORD consistently enhances audio-conditioned reasoning and substantially bridges the audio-text performance gap with only 80k synthetic training samples, validating the efficacy and data efficiency of our on-policy, multi-level cross-modal alignment approach.

On-policy distillation (OPD) has become a central post-training tool for large language models (LLMs), providing dense per-token teacher supervision along the student's own rollouts. In this work, we identify a common structural cause underlying OPD, which we call prefix failure. Under prefix failure, dense per-token supervision induces a bimodal teacher mixture and fragmented gradients that token-level loss truncation or reweighting fail to address. This observation motivates us to move beyond token-level loss interventions toward trajectory-level output corrections. We thus propose Trajectory-Refined Distillation (TRD), a trajectory-level correction method that revises the student's rollout under the teacher guidance while within on-policy support. By correcting problematic prefixes before distillation, TRD mitigates prefix failure at its source. Moreover, TRD improves the exploration by exposing the student to alternative valid derivations under teacher guidance, even when the original rolls are already correct. TRD can also be applied to on-policy self-distillation (OPSD), a parameter-sharing variant that uses the student model conditioned on privileged informations as the teacher. Across a wide range of benchmarks and base models at multiple scales, TRD consistently outperforms prior baselines, improving single-attempt accuracy and broadening reasoning coverage. Code is available at https://github.com/louieworth/trd

Reinforcement learning for large language models (LLMs) typically relies on trust-region masks to stabilize off-policy updates. The dominant PPO-style approach uses the sampled-token importance ratio for two criteria: a proximity criterion, which asks whether the policy has moved too far from the behavior policy, and a direction criterion, which asks whether the update pushes it farther away. Recent work DPPO improves the proximity criterion by replacing PPO's ratio-based test with a probability divergence between the behavior and training policies. However, its direction criterion is still inherited from PPO. A token can be masked only when the sampled-token importance ratio moves away from one. We observe that this ratio-based direction criterion is a single-sample proxy that can disagree in sign with the change of the divergence that defines the proximity criterion. We therefore propose the predictive divergence mask, which asks whether the next policy-gradient step will increase or decrease the same divergence used by the trust region. For the discrete softmax policies used in LLM RL, we derive this prediction in closed form. Because production rollout engines expose only a truncated (top-K) view of the vocabulary, we develop two lightweight top-K estimators for this prediction. Detailed analysis shows the divergence-based direction is better aligned with the realized change of the divergence than the sampled ratio, and the resulting masks improve RL training across model scales and precision settings.

Reinforcement learning (RL) has become a key driver of progress in large language models, but scaling RL to long chain-of-thought (CoT) trajectories is increasingly constrained by backpropagation over every generated token. Even with optimized rollout engines, full-token updates can consume a large fraction of total training cost, turning token length into a hidden tax on RL. We introduce Not All Tokens Are Needed (NAT), a unified framework that makes the token budget a first-class optimization primitive. NAT updates the policy using only a selected subset of generated tokens while preserving the learning signal of full-sequence RL. The core idea is an unbiased partial-token policy-gradient estimator via Horvitz-Thompson reweighting, which ensures statistically correct gradients despite subsampling. We instantiate NAT with two simple, plug-and-play token selection schemes: Uniform Random Sampling (URS) and Random Prefix Cutting (RPC), both of which reduce forward and backward compute and memory without modifying the reward computation or rollout pipeline. Across mathematical reasoning benchmarks, NAT matches full-token GRPO performance while using as few as 50% of tokens, providing an efficient and orthogonal pathway to scaling RL beyond the limits imposed by long trajectories. In our experiments, RPC saves 18% peak GPU memory and 29% forward and backward RL training time for Qwen3-8B.

Large language models (LLMs) have advanced to encompass extensive knowledge across diverse domains. Yet controlling what a LLMs should not know is important for ensuring alignment and thus safe use. However, effective unlearning in LLMs is difficult due to the fuzzy boundary between knowledge retention and forgetting. This challenge is exacerbated by entangled parameter spaces from continuous multi-domain training, often resulting in collateral damage, especially under aggressive unlearning strategies. Furthermore, the computational overhead required to optimize State-of-the-Art (SOTA) models with billions of parameters poses an additional barrier. In this work, we present ALTER, a lightweight unlearning framework for LLMs to address both the challenges of knowledge entanglement and unlearning efficiency. ALTER operates through two phases: (I) high entropy tokens are captured and learned via the shared A matrix in LoRA, followed by (II) an asymmetric LoRA architecture that achieves a specified forgetting objective by parameter isolation and unlearning tokens within the target subdomains. Serving as a new research direction for achieving unlearning via token-level isolation in the asymmetric framework. ALTER achieves SOTA performance on TOFU, WMDP, and MUSE benchmarks with over 95% forget quality and shows minimal side effects through preserving foundational tokens. By decoupling unlearning from LLMs' billion-scale parameters, this framework delivers excellent efficiency while preserving over 90% of model utility, exceeding baseline preservation rates of 47.8-83.6%.

Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models, even without supervised fine-tuning. However, prevalent reinforcement learning algorithms such as GRPO and its variants like DAPO, suffer from a coarse granularity issue when computing the advantage. Specifically, they compute rollout-level advantages that assign identical values to every token within a sequence, failing to capture token-specific contributions and hindering effective learning. To address this limitation, we propose Key-token Advantage Estimation (KTAE) - a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. This quantified token-level importance is then combined with the rollout-level advantage to obtain a more fine-grained token-level advantage estimation. Empirical results show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks. Notably, they achieve higher accuracy with shorter responses and even surpass R1-Distill-Qwen-1.5B using the same base model.

On-Policy Distillation (OPD) is a fundamental technique for efficient post-training of large language models (LLMs), with broad applications in agent learning, multi-task enhancement, and model compression. However, OPD training becomes unstable when the teacher and student distributions differ substantially, as teacher supervision on student-generated tokens may yield unreliable policy gradients and even cause optimization failure. This work addresses reliable on-policy token-level supervision through credit assignment strategies, and proposes Trust Region On-Policy Distillation, TrOPD. It features the following characteristics: 1) Trust-Region On-Policy Learning: TrOPD performs OPD only in regions where the teacher provides reliable supervision, mitigating the optimization difficulty of the K1 reverse-KL estimator under distribution mismatch. 2) Outlier Estimation: For outlier regions, we explore gradient clipping, masking, and forward-KL estimation to reduce the adverse effects of unreliable supervision. 3) Off-Policy Guidance: The student continues generation from teacher prefixes and uses forward KL to imitate off-policy guidance, encouraging on-policy exploration toward reliable regions. Experiments show that TrOPD consistently outperforms SoTA OPD baselines, including OPD, EOPD, and REOPOLD, across mathematical reasoning, code generation, and general-domain benchmarks.

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

Reinforcement learning from human feedback (RLHF) is a promising solution to align large language models (LLMs) more closely with human values. Off-policy preference optimization, where the preference data is obtained from other models, is widely adopted due to its cost efficiency and scalability. However, off-policy preference optimization often suffers from a distributional gap between the policy used for data collection and the target policy, leading to suboptimal optimization. In this paper, we propose a novel strategy to mitigate this problem by simulating on-policy learning with off-policy preference data. Our Weighted Preference Optimization (WPO) method adapts off-policy data to resemble on-policy data more closely by reweighting preference pairs according to their probability under the current policy. This method not only addresses the distributional gap problem but also enhances the optimization process without incurring additional costs. We validate our method on instruction following benchmarks including Alpaca Eval 2 and MT-bench. WPO not only outperforms Direct Preference Optimization (DPO) by up to 5.6% on Alpaca Eval 2 but also establishes a remarkable length-controlled winning rate against GPT-4-turbo of 48.6% based on Llama-3-8B-Instruct, making it the strongest 8B model on the leaderboard. We will release the code and models at https://github.com/wzhouad/WPO.

On-policy distillation (OPD) is appealing for large language model (LLM) post-training because it evaluates teacher feedback on student-generated rollouts rather than fixed teacher traces. In long-horizon settings, however, the common sampled-token variant is fragile: it reduces distribution matching to a one-token signal and becomes increasingly unreliable as rollouts drift away from prefixes the teacher commonly visits. We revisit OPD from the estimator and implementation sides. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL, but it has a much tighter worst-case variance bound; our toy study shows the same tradeoff empirically, with stronger future-reward coupling producing higher gradient variance and less stable learning. Empirically, we identify three failure modes of sampled-token OPD: an imbalanced one-token signal, unreliable teacher guidance on student-generated prefixes, and distortions caused by tokenizer or special-token mismatch. We address these issues with teacher top-K local support matching, implemented as truncated reverse-KL with top-p rollout sampling and special-token masking. Across single-task math reasoning and multi-task agentic-plus-math training, this objective yields more stable optimization and better downstream performance than sampled-token OPD.

With the help of simple fine-tuning, one can artificially embed hidden text into large language models (LLMs). This text is revealed only when triggered by a specific query to the LLM. Two primary applications are LLM fingerprinting and steganography. In the context of LLM fingerprinting, a unique text identifier (fingerprint) is embedded within the model to verify licensing compliance. In the context of steganography, the LLM serves as a carrier for hidden messages that can be disclosed through a designated trigger. Our work demonstrates that embedding hidden text in the LLM via fine-tuning, though seemingly secure due to the vast number of potential triggers (any sequence of characters or tokens could serve as a trigger), is susceptible to extraction through analysis of the LLM's output decoding process. We propose a novel approach to extraction called Unconditional Token Forcing. It is premised on the hypothesis that iteratively feeding each token from the LLM's vocabulary into the model should reveal sequences with abnormally high token probabilities, indicating potential embedded text candidates. Additionally, our experiments show that when the first token of a hidden fingerprint is used as an input, the LLM not only produces an output sequence with high token probabilities, but also repetitively generates the fingerprint itself. We also present a method to hide text in such a way that it is resistant to Unconditional Token Forcing, which we named Unconditional Token Forcing Confusion.

On-Policy Distillation (OPD) improves large language model reasoning by training a student model on trajectories sampled from its own policy under teacher supervision. Although OPD operates on trajectories, its learning signal remains token-level: it identifies deviations through high-loss tokens and repairs them through local reverse-KL correction. We show that this "trajectory-sampled but token-learned" mechanism cannot reliably bridge student trajectories toward teacher trajectories. About 30% of high-loss tokens fall into the low-divergence regime, indicating that many are surface-form mismatches rather than real reasoning forks. Moreover, even truly divergent tokens are difficult to repair with isolated token-level supervision, since reasoning failures often unfold as short-horizon distributional drift. We propose Trajectory-aware OPD (TOPD), which uses near-future trajectory information to identify real divergent states and distribute guidance across multiple future tokens. Experiments show that suppressing non-divergent high-loss tokens improves standard OPD from 47.8% to 48.2% average accuracy, while TOPD further improves performance to 52.2%, with gains on AIME24 from 60.0% to 63.3% and AIME25 from 46.7% to 53.3%.

Reinforcement learning with verifiable rewards (RLVR) has demonstrated superior performance in enhancing the reasoning capability of large language models (LLMs). However, this accuracy-oriented learning paradigm often suffers from entropy collapse, which reduces policy exploration and limits reasoning capabilities. To address this challenge, we propose an efficient reinforcement learning framework that leverages entropy signals at both the semantic and token levels to improve reasoning. From the data perspective, we introduce semantic entropy-guided curriculum learning, organizing training data from low to high semantic entropy to guide progressive optimization from easier to more challenging tasks. For the algorithmic design, we adopt non-uniform token treatment by imposing KL regularization on low-entropy tokens that critically impact policy exploration and applying stronger constraints on high-covariance portions within these tokens. By jointly optimizing data organization and algorithmic design, our method effectively mitigates entropy collapse and enhances LLM reasoning. Experimental results across 6 benchmarks with 3 different parameter-scale base models demonstrate that our method outperforms other entropy-based approaches in improving reasoning.

On-policy distillation (OPD) offers dense token-level supervision as an alternative to the sparse outcome-level advantages of reinforcement learning with verifiable rewards (RLVR). However, the teacher scores student-generated trajectories that are inherently off-policy for it, so the reliability of its supervision, and hence the source of the student's improvement, remains unclear. We quantitatively analyze teacher supervision during OPD training and find substantial noise whose prevalence increases with teacher scale. Surprisingly, the student policy is insensitive to such noise, converging to comparable performance regardless of whether noisy supervision is retained or removed. Does OPD distill at all? By analyzing what drives its gains, we find that learning concentrates on low log-probability tokens, and using a single fixed negative advantage matches the performance of teacher-provided ones. This suggests that OPD works largely by suppressing low log-probability tokens, which requires no teacher. These findings motivate On-Policy Self-Adaptation (OPSA), a supervision-free method using entropy-adaptive negative advantages. It assigns stronger learning signals to high-entropy positions, suppressing tail tokens, and evenly redistributing probability mass among head tokens. Compared with the base Qwen3-1.7B, OPSA improves Avg@32 by 35.41 points on AIME24, corresponding to a 263\% relative gain, and more than doubles Pass@32 across all three benchmarks. It also outperforms OPD by 16.77 points in Avg@32 on AIME24. Extensive experiments and analyses across model families and tasks further demonstrate its effectiveness and generalizability.

Reinforcement Learning (RL) has significantly improved large language model reasoning, but existing RL fine-tuning methods rely heavily on heuristic techniques such as entropy regularization and reweighting to maintain stability. In practice, they often experience late-stage performance collapse, leading to degraded reasoning quality and unstable training. We derive that the magnitude of token-wise policy gradients in RL is negatively correlated with token probability and local policy entropy. Building on this result, we prove that training instability is driven by a tiny fraction of tokens, approximately 0.01\%, which we term spurious tokens. When such tokens appear in correct responses, they contribute little to the reasoning outcome but inherit the full sequence-level reward, leading to abnormally amplified gradient updates. Motivated by this observation, we propose Spurious-Token-Aware Policy Optimization (STAPO) for large-scale model refining, which selectively masks such updates and renormalizes the loss over valid tokens. Across six mathematical reasoning benchmarks using Qwen 1.7B, 8B, and 14B base models, STAPO consistently demonstrates superior entropy stability and achieves an average performance improvement of 7.13\% over GRPO, 20-Entropy and JustRL.

Reinforcement learning (RL) has emerged as a promising strategy for finetuning small language models (SLMs) to solve targeted tasks such as math and coding. However, RL algorithms tend to be resource-intensive, taking a significant amount of time to train. We propose RAPID, a novel RL algorithm that can substantially reduce the running time of RL. Our key insight is that RL tends to be costly due to the need to perform both inference and backpropagation during training. To maximize use of computational resources, our algorithm performs inference in large batches, and then performs off-policy policy gradient updates in mini-batches. For off-policy updates, we incorporate group advantage estimation into the policy gradient algorithm, and derive an importance weighted estimator to correct for the bias arising from off-policy learning. Our experiments demonstrate that our algorithm can reduce running time by 11%-34% on three benchmarks compared to state-of-the-art RL algorithms while maintaining similar or better accuracy.

Reinforcement Learning From Human Feedback (RLHF) has been a critical to the success of the latest generation of generative AI models. In response to the complex nature of the classical RLHF pipeline, direct alignment algorithms such as Direct Preference Optimization (DPO) have emerged as an alternative approach. Although DPO solves the same objective as the standard RLHF setup, there is a mismatch between the two approaches. Standard RLHF deploys reinforcement learning in a specific token-level MDP, while DPO is derived as a bandit problem in which the whole response of the model is treated as a single arm. In this work we rectify this difference, first we theoretically show that we can derive DPO in the token-level MDP as a general inverse Q-learning algorithm, which satisfies the Bellman equation. Using our theoretical results, we provide three concrete empirical insights. First, we show that because of its token level interpretation, DPO is able to perform some type of credit assignment. Next, we prove that under the token level formulation, classical search-based algorithms, such as MCTS, which have recently been applied to the language generation space, are equivalent to likelihood-based search on a DPO policy. Empirically we show that a simple beam search yields meaningful improvement over the base DPO policy. Finally, we show how the choice of reference policy causes implicit rewards to decline during training. We conclude by discussing applications of our work, including information elicitation in multi-tun dialogue, reasoning, agentic applications and end-to-end training of multi-model systems.

Large language models (LLMs) possess strong semantic understanding, driving significant progress in data mining applications. This is further enhanced by large reasoning models (LRMs), which provide explicit multi-step reasoning traces. On the other hand, the growing need for the right to be forgotten has driven the development of machine unlearning techniques, which aim to eliminate the influence of specific data from trained models without full retraining. However, unlearning may also introduce new security vulnerabilities by exposing additional interaction surfaces. Although many studies have investigated unlearning attacks, there is no prior work on LRMs. To bridge the gap, we first in this paper propose LRM unlearning attack that forces incorrect final answers while generating convincing but misleading reasoning traces. This objective is challenging due to non-differentiable logical constraints, weak optimization effect over long rationales, and discrete forget set selection. To overcome these challenges, we introduce a bi-level exact unlearning attack that incorporates a differentiable objective function, influential token alignment, and a relaxed indicator strategy. To demonstrate the effectiveness and generalizability of our attack, we also design novel optimization frameworks and conduct comprehensive experiments in both white-box and black-box settings, aiming to raise awareness of the emerging threats to LRM unlearning pipelines.

Reinforcement learning (RL) is a pivotal task for enhancing Large Language Model (LLM) reasoning. Conventional algorithms, however, typically adhere to a coarse-grained credit assignment paradigm, applying a uniform reward to all tokens in a sequence, a critical flaw in long-chain reasoning tasks. In this paper, we address this challenge and propose Dynamic Entropy Weighting, a novel mechanism that facilitates fine-grained rewards through two new algorithms: Group Token Policy Optimization (GTPO), which assigns an entropy-weighted reward to each token, and the analogous algorithm Sequence-Level GRPO (GRPO-S). Our approach is founded on the hypothesis that high policy entropy within a reasoning path is a powerful heuristic for cognitive effort at pivotal junctures, which can be repurposed into a learning signal. By repurposing policy entropy for reward shaping, we achieve true per-token credit assignment. Experimental results across challenging reasoning benchmarks validate the superiority of our approach, showing our methods significantly outperform a strong DAPO baseline and confirming our entropy-weighting mechanism as the key driver of this performance boost.

On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher's high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student-teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of +1.37 for Qwen3-0.6B-Base, +2.39 for Qwen3-1.7B-Base, and +5.05 for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer.

Aiming at efficient and dense chain-of-thought (CoT) reasoning, latent reasoning methods fine-tune Large Language Models (LLMs) to substitute discrete language tokens with continuous latent tokens. These methods consume fewer tokens compared to the conventional language CoT reasoning and have the potential to plan in a dense latent space. However, current latent tokens are generally supervised based on imitating language labels. Considering that there can be multiple equivalent but diverse CoT labels for a question, passively imitating an arbitrary one may lead to inferior latent token representations and latent reasoning policies, undermining the potential planning ability and resulting in clear gaps between training and testing. In this work, we emphasize the importance of active planning over the representation space of latent tokens in achieving the optimal latent reasoning policy. So, we propose the Active Latent Planning method (ATP-Latent), which models the supervision process of latent tokens as a conditional variational auto-encoder (VAE) to obtain a smoother latent space. Moreover, to facilitate the most reasonable latent reasoning policy, ATP-Latent conducts reinforcement learning (RL) with an auxiliary coherence reward, which is calculated based on the consistency between VAE-decoded contents of latent tokens, enabling a guided RL process. In experiments on LLaMA-1B, ATP-Latent demonstrates +4.1\% accuracy and -3.3\% tokens on four benchmarks compared to advanced baselines. Codes are available on https://github.com/zz1358m/ATP-Latent-master.

Recent advancements in large language models(LLMs), such as GPT-4 and GPT-4o, have shown exceptional performance, especially in languages with abundant resources like English, thanks to extensive datasets that ensure robust training. Conversely, these models exhibit limitations when processing under-resourced languages such as Chinese and Korean, where issues including hallucinatory responses remain prevalent. This paper traces the roots of these disparities to the tokenization process inherent to these models. Specifically, it explores how the tokenizers vocabulary, often used to speed up the tokenization process and reduce tokens but constructed independently of the actual model training data, inadequately represents non-English languages. This misrepresentation results in the propagation of under-trained or untrained tokens, which perpetuate biases and pose serious concerns related to data security and ethical standards. We aim to dissect the tokenization mechanics of GPT-4o, illustrating how its simplified token-handling methods amplify these risks and offer strategic solutions to mitigate associated security and ethical issues. Through this study, we emphasize the critical need to rethink tokenization frameworks to foster more equitable and secure AI technologies. The code and data are available at https://github.com/yeyimilk/LLMGPT4o

Large Language Models (LLMs) increasingly require selective removal of harmful or sensitive knowledge, called unlearning, yet existing methods and benchmarks fail to evaluate this capability completely. Current approaches rely on disjoint forget and retain sets composed of independent facts, and measure success using simple and direct factual recall. This framing fails to capture a key requirement of unlearning, namely the ability to eliminate harmful behaviors while preserving benign and beneficial knowledge. We argue that effective unlearning must operate at the level of concepts, ensuring complete removal of unsafe applications while maintaining their correct and useful usage, thereby achieving conceptually meaningful and complete unlearning. To better evaluate unlearning techniques from such a practical viewpoint, we introduce the notion of dual-use concepts: concepts that can be used in both harmful and benign contexts. Building on these concepts, we construct a benchmark called ConceptGuard where forget and retain sets are explicitly complementary in concept usage. Our benchmark uniquely enables unlearning to be explored and gauged at the level of concepts, instead of sparse facts, and evaluation is intent-sensitive with the goal of maximizing contextual separation to promote safer behavior. We demonstrate that current unlearning techniques perform poorly under this setting, showing weak contextual separation alongside poor performance in ROUGE and concept-level metrics. Our results reveal strong forgetting-utility trade-offs, limited gains in contextual sensitivity, and poor consistency in concept-level control across methods, and provide ideas for unlearning approaches that better align with real-world safety requirements. Our dataset is publicly available.

Machine unlearning is increasingly important for clinical language models, where privacy regulations and institutional policies may require removing sensitive information from deployed systems without retraining from scratch. In practice, deletion requests must balance effective forgetting of targeted information with preservation of model utility and minimal parameter modification. We introduce Sparse Token Embedding Unlearning (STEU), a parameter-efficient method for behavioral class-level unlearning that updates only PMI-selected token embeddings together with a small classifier head while keeping all encoder layers frozen. Across experiments on MIMIC-IV, MIMIC-III, and eICU using BioClinicalBERT, BERT-base, and DistilBERT, STEU consistently suppresses the target class while largely preserving retained task performance. In the primary MIMIC-IV setting, STEU achieves near-complete forgetting (forget F1 = 0.0004) while maintaining competitive retained utility (retain avg F1 = 0.4766) after modifying only 0.19\% of model parameters. These results suggest that targeted behavioral unlearning can be achieved through sparse embedding edits without modifying deeper encoder representations.

Large language model agents have shown strong potential in complex interactive tasks, yet their reinforcement learning (RL) is often hindered by sparse rewards, as a long multi-turn trajectory may receive only a single outcome-level signal. On-policy self-distillation (OPSD) provides dense token-level supervision from a privileged teacher, but the teacher may not be reliable at every position. Existing methods commonly rely on isolated token-level discrepancies, which can be sensitive to noise, or assign a shared step-level weight that may overlook positional variation. We propose Persistent Consistency Self-Distillation (PCSD), which derives token-level distillation weights from the local persistence of teacher-favoring signals. PCSD combines adaptive windows with exponentially decayed aggregation to capture persistent relative teacher support, applies trend-aware modulation to attenuate locally declining support, and produces continuous weights through sigmoid gating. The resulting objective is jointly optimized with GRPO, combining dense teacher guidance with sparse environmental feedback. Without inference-time skills, PCSD achieves the best ALFWorld Overall results among all baselines on both backbones, exceeding GRPO by 15.6 and 13.3 points and SDAR by 6.2 and 5.5 points, while remaining competitive on WebShop and gaining 15.8 points over GRPO on unseen ALFWorld split.

Video large language models have demonstrated remarkable capabilities in video understanding tasks. However, the redundancy of video tokens introduces significant computational overhead during inference, limiting their practical deployment. Many compression algorithms are proposed to prioritize retaining features with the highest attention scores to minimize perturbations in attention computations. However, the correlation between attention scores and their actual contribution to correct answers remains ambiguous. To address the above limitation, we propose a novel Contribution-aware token Compression algorithm for VIDeo understanding (CaCoVID) that explicitly optimizes the token selection policy based on the contribution of tokens to correct predictions. First, we introduce a reinforcement learning-based framework that optimizes a policy network to select video token combinations with the greatest contribution to correct predictions. This paradigm shifts the focus from passive token preservation to active discovery of optimal compressed token combinations. Secondly, we propose a combinatorial policy optimization algorithm with online combination space sampling, which dramatically reduces the exploration space for video token combinations and accelerates the convergence speed of policy optimization. Extensive experiments on diverse video understanding benchmarks demonstrate the effectiveness of CaCoVID. Codes will be released.

This paper details the methodology behind CoPE, a policy-steerable small language model capable of fast and accurate content labeling. We present a novel training curricula called Contradictory Example Training that enables the model to learn policy interpretation rather than mere policy memorization. We also present a novel method for generating content policies, called Binocular Labeling, which enables rapid construction of unambiguous training datasets. When evaluated across seven different harm areas, CoPE exhibits equal or superior accuracy to frontier models at only 1% of their size. We openly release a 9 billion parameter version of the model that can be run on a single consumer-grade GPU. Models like CoPE represent a paradigm shift for classifier systems. By turning an ML task into a policy writing task, CoPE opens up new design possibilities for the governance of online platforms.

The "end-to-end" label for LLMs is a misnomer. In practice, they depend on a non-differentiable decoding process that requires laborious, hand-tuning of hyperparameters like temperature and top-p. This paper introduces AutoDeco, a novel architecture that enables truly "end-to-end" generation by learning to control its own decoding strategy. We augment the standard transformer with lightweight heads that, at each step, dynamically predict context-specific temperature and top-p values alongside the next-token logits. This approach transforms decoding into a parametric, token-level process, allowing the model to self-regulate its sampling strategy within a single forward pass. Through extensive experiments on eight benchmarks, we demonstrate that AutoDeco not only significantly outperforms default decoding strategies but also achieves performance comparable to an oracle-tuned baseline derived from "hacking the test set"-a practical upper bound for any static method. Crucially, we uncover an emergent capability for instruction-based decoding control: the model learns to interpret natural language commands (e.g., "generate with low randomness") and adjusts its predicted temperature and top-p on a token-by-token basis, opening a new paradigm for steerable and interactive LLM decoding.

During pretraining, LLMs inadvertently memorize sensitive or copyrighted data, posing significant compliance challenges under legal frameworks like the GDPR and the EU AI Act. Fulfilling these mandates demands techniques that can remove information from a deployed model without retraining from scratch. Existing unlearning approaches attempt to address this need, but often leak the very data they aim to erase, sacrifice fluency and robustness, or depend on costly external reward models. We introduce PURGE (Policy Unlearning through Relative Group Erasure), a novel method grounded in the Group Relative Policy Optimization framework that formulates unlearning as a verifiable problem. PURGE uses an intrinsic reward signal that penalizes any mention of forbidden concepts, allowing safe and consistent unlearning. Our approach achieves up to x46 lower token usage per target than state-of-the-art methods, while improving fluency by +5.48% and adversarial robustness by +12.02% over the base model. Extensive evaluation on the Real World Knowledge Unlearning (RWKU) benchmark shows that PURGE reaches 11% unlearning effectiveness while preserving 98% of original utility. PURGE shows that framing LLM unlearning as a verifiable task enables more reliable, efficient, and scalable forgetting, suggesting a promising new direction for unlearning research that combines theoretical guarantees, improved safety, and practical deployment efficiency.

Language models as intelligent agents push the boundaries of sequential decision-making agents but struggle with limited knowledge of environmental dynamics and exponentially huge action space. Recent efforts like GLAM and TWOSOME manually constrain the action space to a restricted subset and employ reinforcement learning to align agents' knowledge with specific environments. However, they overlook fine-grained credit assignments for intra-action tokens, which is essential for efficient language agent optimization, and rely on human's prior knowledge to restrict action space. This paper proposes decomposing language agent optimization from the action level to the token level, offering finer supervision for each intra-action token and manageable optimization complexity in environments with unrestricted action spaces. Beginning with the simplification of flattening all actions, we theoretically explore the discrepancies between action-level optimization and this naive token-level optimization. We then derive the Bellman backup with Action Decomposition (BAD) to integrate credit assignments for both intra-action and inter-action tokens, effectively eliminating the discrepancies. Implementing BAD within the PPO algorithm, we introduce Policy Optimization with Action Decomposition (POAD). POAD benefits from a finer-grained credit assignment process and lower optimization complexity, leading to enhanced learning efficiency and generalization abilities in aligning language agents with interactive environments. We validate POAD across diverse testbeds, with results affirming the advantages of our approach and the correctness of our theoretical analysis.

Reinforcement learning from verifiable rewards (RLVR) has emerged as a central technique for improving the reasoning capabilities of large language models. Despite its effectiveness, how response-level rewards translate into token-level probability changes remains poorly understood. We introduce a discriminator view of RLVR updates, showing that the policy-gradient update direction implicitly acts as a linear discriminator over token-gradient vectors and thereby determines which token probabilities are increased or decreased during learning. Under standard sequence-level RLVR, this discriminator is constructed from positive- and negative-side centroids formed by advantage-weighted averaging of token-gradient vectors. However, such centroid construction can be dominated by shared high-frequency patterns, such as formatting tokens, diluting sparse yet discriminative directions that better distinguish high-reward responses from low-reward ones. To address this limitation, we propose DelTA, a discriminative token credit assignment method that estimates token coefficients to amplify side-specific token-gradient directions and downweight shared or weakly discriminative ones. These coefficients reweight a self-normalized RLVR surrogate, making the effective side-wise centroids more contrastive and thereby reshaping the RLVR update direction. On seven mathematical benchmarks, DelTA outperforms the strongest same-scale baselines by 3.26 and 2.62 average points on Qwen3-8B-Base and Qwen3-14B-Base, respectively. Additional results on code generation, a different backbone, and out-of-domain evaluations further demonstrate the generalization ability of DelTA.

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level rewards introduces a key limitation as uniform credit assignment across all tokens fails to capture fine-grained, token-level contributions. To address this issue, we propose Guidance Contrastive Policy Optimization (GCPO), a novel algorithm that enables per-token credit assignment by contrasting model predictions under positive and negative prompts. Rather than uniformly broadcasting sample-level advantages, GCPO assigns token-level advantages proportional to the difference between these contrastive predictions, allowing more precise and informative learning signals. Empirically, we find that GCPO emphasizes semantically relevant regions such as visual areas aligned with textual prompts in text-to-image generation, and critical keywords within reasoning traces for chain-of-thought tasks. Through extensive experiments, GCPO consistently outperforms GRPO and DAPO baselines on both text-to-image generation and chain-of-thought reasoning benchmarks, demonstrating its effectiveness as a general and scalable optimization strategy for discrete policy learning.

On-Policy distillation (OPD) transfers teacher capabilities by supervising student-sampled trajectories with dense token-level teacher signals. Recent selective OPD methods improve this process by prioritizing signals that are confident, informative, or learnable. However, the assumptions overlook a fundamental failure mode of language models: their token-level judgments can be driven by input-agnostic language priors, formatting conventions, or stereotyped reasoning templates rather than task-specific evidence. We refer to such optimization-relevant but weakly input-grounded supervision as spurious signals in OPD, which may produce large gradients while contributing little task-improving direction. To mitigate this issue, we propose SA-OPD, a Spurious-Signal-Aware On-Policy Distillation framework that identifies and filters misleading token-level supervision based on input-groundedness and optimization impact. SA-OPD introduces a lightweight input-groundedness proxy estimating whether a token-level distillation signal truly depends on the input. It then filters only tokens that simultaneously exhibit low input-groundedness and extreme distillation divergence, thereby removing high-impact spurious updates and achieving fine-grained OPD optimization. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that SA-OPD consistently outperforms Vanilla OPD and competitive selective methods. These results establish input-groundedness as a key dimension for OPD supervision selection and offer a simple, effective strategy for mitigating spurious updates.

Reinforcement-learning-based post-training has become a key approach for improving the reasoning ability of large language models, but its token-level learning signals remain poorly understood. This work studies their heterogeneity through attention entropy, which measures how concentrated or diffuse the contextual support is for each response token. We first show that token-level RL objectives are sparsely estimable: uniformly random 20 percent token subsets preserve much of the full-token held-out performance, suggesting substantial redundancy in token-level updates. However, entropy-structured subsets behave very differently. Low-attention-entropy tokens, which we call anchors, rely on concentrated support, produce stable gradients aligned with full-token updates, and provide a reliable optimization backbone, but tend to plateau on harder benchmarks. High-attention-entropy tokens, which we call explorers, aggregate more diffuse context and induce larger but more volatile gradients. Explorer-only training is unstable on average, though rare successful runs suggest that these tokens may contain useful hard-reasoning signals when optimization remains stable. We support this anchor-explorer spectrum with evidence-gathering analyses, entropy dynamics, gradient-geometry diagnostics, and controls showing that position, predictive entropy, and loss normalization do not explain the observed asymmetry. Finally, a dynamic entropy-aware soft-reweighting intervention improves Qwen3-8B-Base from 34.39 to 37.40 held-out average in the strongest setting. These findings suggest that attention entropy reveals optimization-relevant structure in token-level RL signals, and that uniform token averaging can obscure meaningful heterogeneity in reasoning post-training.

While humans effortlessly draw visual objects and shapes by adaptively allocating attention based on their complexity, existing multimodal large language models (MLLMs) remain constrained by rigid token representations. Bridging this gap, we propose ALTo, an adaptive length tokenizer for autoregressive mask generation. To achieve this, a novel token length predictor is designed, along with a length regularization term and a differentiable token chunking strategy. We further build ALToLLM that seamlessly integrates ALTo into MLLM. Preferences on the trade-offs between mask quality and efficiency is implemented by group relative policy optimization (GRPO). Experiments demonstrate that ALToLLM achieves state-of-the-art performance with adaptive token cost on popular segmentation benchmarks. Code and models are released at https://github.com/yayafengzi/ALToLLM.

Policy-based optimizations are widely adopted today for the training and alignment of language models, where one of the most recent and effective approaches is Group-relative Policy Optimization (GRPO). In this paper, we reveals and analyze two major limitations of GRPO: (i) tokens frequently appear in completions with both positive and negative rewards, leading to conflicting gradient updates that can reduce their output probability, even though can be essential for maintaining proper structure; (ii) negatively rewarded completions may penalize confident responses and shift model decisions toward unlikely tokens, progressively flattening the output distribution and degrading learning. To address these issues and provide a more stable and effective policy optimization strategy, we introduce GTPO (Group-relative Trajectory-based Policy Optimization), which identifies conflict tokens, tokens appearing in the same position across completions with opposite rewards, protects them by skipping negative updates, while amplifying positive ones. To further prevent policy collapse, GTPO filters out completions whose entropy exceeds a provable threshold. Unlike GRPO, GTPO does not rely on KL-divergence regularization, eliminating the need for a reference model during training, while still ensuring greater training stability and improved performance, validated through multiple experiments on GSM8K, MATH and AIME 2024 benchmarks.

Current language models generate chain-of-thought traces by autoregressively sampling tokens from a finite vocabulary. While this discrete sampling has achieved remarkable success, conducting chain-of-thought with continuously-valued tokens (CoT2) offers a richer and more expressive alternative. Our work examines the benefits of CoT2 through logical reasoning tasks that inherently require search capabilities and provide optimization and exploration methods for CoT2. Theoretically, we show that CoT2 allows the model to track multiple traces in parallel and quantify its benefits for inference efficiency. Notably, one layer transformer equipped with CoT2 can provably solve the combinatorial "subset sum problem" given sufficient embedding dimension. These insights lead to a novel and effective supervision strategy where we match the softmax outputs to the empirical token distributions of a set of target traces. Complementing this, we introduce sampling strategies that unlock policy optimization and self-improvement for CoT2. Our first strategy samples and composes K discrete tokens at each decoding step to control the level of parallelism, and reduces to standard CoT when K=1. Our second strategy relies on continuous exploration over the probability simplex. Experiments confirm that policy optimization with CoT2 indeed improves the performance of the model beyond its initial discrete or continuous supervision.

Policy constraint methods to offline reinforcement learning (RL) typically utilize parameterization or regularization that constrains the policy to perform actions within the support set of the behavior policy. The elaborative designs of parameterization methods usually intrude into the policy networks, which may bring extra inference cost and cannot take full advantage of well-established online methods. Regularization methods reduce the divergence between the learned policy and the behavior policy, which may mismatch the inherent density-based definition of support set thereby failing to avoid the out-of-distribution actions effectively. This paper presents Supported Policy OpTimization (SPOT), which is directly derived from the theoretical formalization of the density-based support constraint. SPOT adopts a VAE-based density estimator to explicitly model the support set of behavior policy and presents a simple but effective density-based regularization term, which can be plugged non-intrusively into off-the-shelf off-policy RL algorithms. SPOT achieves the state-of-the-art performance on standard benchmarks for offline RL. Benefiting from the pluggable design, offline pretrained models from SPOT can also be applied to perform online fine-tuning seamlessly.

Open-weight language models from different families exhibit complementary capabilities, motivating their consolidation into a compact student through on-policy distillation (OPD). However, full-vocabulary OPD typically assumes a shared tokenizer, while existing cross-tokenizer methods may discard teacher probability mass or assign it to student tokens with unrelated content. We introduce Byte-Prefix Marginalization (BPM), which re-expresses the teacher's next-token distribution over the student vocabulary in a shared byte space. Specifically, BPM assigns each teacher token's probability to the longest student token whose byte representation is a prefix of the teacher token's bytes, aggregates mass mapped to the same student token, and places otherwise unmatched mass in an explicit residual category. This produces a vocabulary-complete, byte-aligned, and mass-preserving target for dense OPD. The target exactly recovers the teacher-induced byte-prefix marginal when the relevant prefix does not span multiple teacher tokens (a condition satisfied at more than 99% of training positions) and uses a mass-preserving, chain-factorized lower bound otherwise. Across Qwen3-32B, GLM-Z1-9B-0414, and MiniMax-M2.7 as teachers, BPM consistently outperforms current cross-tokenizer methods on six mathematics and programming benchmarks, improving six-benchmark avg@8 by 3.7-6.6 points over the strongest baselines.

Many practical applications, such as recommender systems and learning to rank, involve solving multiple similar tasks. One example is learning of recommendation policies for users with similar movie preferences, where the users may still rank the individual movies slightly differently. Such tasks can be organized in a hierarchy, where similar tasks are related through a shared structure. In this work, we formulate this problem as a contextual off-policy optimization in a hierarchical graphical model from logged bandit feedback. To solve the problem, we propose a hierarchical off-policy optimization algorithm (HierOPO), which estimates the parameters of the hierarchical model and then acts pessimistically with respect to them. We instantiate HierOPO in linear Gaussian models, for which we also provide an efficient implementation and analysis. We prove per-task bounds on the suboptimality of the learned policies, which show a clear improvement over not using the hierarchical model. We also evaluate the policies empirically. Our theoretical and empirical results show a clear advantage of using the hierarchy over solving each task independently.

Reinforcement learning with verifiable rewards (RLVR) has become standard for improving LLM reasoning. However, existing PPO-style trust-region mechanisms remain position-agnostic by enforcing uniform thresholds across all tokens independently. This pointwise treatment conflicts with autoregressive generation in two critical ways. First, uniform thresholds ignore autoregressive asymmetry. Early-stage deviations produce compounding sequence-level drift, causing static thresholds to under-regulate early divergence and excessively constrain late-stage exploration. Second, evaluating token-level divergence in isolation overlooks cumulative prefix drift, granting the same divergence allowance regardless of how far the conditioning history has already deviated from the rollout policy. To address this limitation, we propose CPPO (Cumulative Prefix-divergence Policy Optimization), a token-level masking rule that aligns updates with a finite-horizon policy-improvement bound via two coupled mechanisms. First, a position-weighted threshold imposes stricter limits at early positions whose effects persist longer, relaxing constraints for late-stage tokens. Second, a cumulative prefix budget tracks historical deviations, dynamically restricting further token-level deviation to prevent compounding errors along the prefix. Empirically, CPPO enhances training stability and significantly improves reasoning accuracy across various model scales.

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

Current approaches to reducing undesired capabilities in language models are largely post hoc, and can thus be easily bypassed by adversaries. A natural alternative is to shape capabilities during pretraining itself. On the proxy task of removing medical capabilities, we show that the simple intervention of filtering pretraining data is highly effective, robust, and inexpensive at scale. Inspired by work on data attribution, we show that filtering tokens is more effective than filtering documents, achieving the same hit to undesired capabilities at a lower cost to benign ones. Training models spanning two orders of magnitude, we then demonstrate that filtering gets more effective with scale: for our largest models, token filtering leads to a 7000x compute slowdown on the forget domain. We also show that models trained with token filtering can still be aligned on the forget domain. Along the way, we introduce a methodology for labeling tokens with sparse autoencoders and distilling cheap, high-quality classifiers. We also demonstrate that filtering can be robust to noisy labels with sufficient pretraining compute.

On-policy distillation (OPD) has emerged as a core component of modern LLM post-training pipelines, yet we reveal a failure mode: degenerate agreement, where students exploit repetitive loops to achieve near-perfect token agreement with the teacher despite globally flawed responses. We therefore shift our focus from agreement to teacher-student mismatch, and find that mismatch tokens can be mainly categorized into two types: student-excess tokens and student-deficit tokens. Student-excess tokens are generated by the student but assigned near-zero probability by the teacher; their log-ratio corrections grow unbounded and destabilize the update. Student-deficit tokens, in contrast, are preferred by the teacher but rarely sampled by the student; their absence blocks the transfer of the teacher's reasoning patterns. To tackle these mismatch directions, we propose TIDE (Token-level Independent Deficit-Excess correction), which applies bounded Hellinger shaping to suppress the most severe sampled excesses and an analytic teacher top-K injection to restore deficient probability mass without requiring deficit tokens to be sampled. Across mathematical reasoning benchmarks with multiple Qwen3 teacher-student pairs, TIDE consistently outperforms standard OPD and recent token-selection and reward-shaping baselines. Moreover, the gains of TIDE are more pronounced under strong teacher-student mismatch, where it improves Avg@8 from 6.9% to 20.3%, reduces average response length by a factor of 3.6, and substantially reduces formatting failures. Code is available at https://github.com/yzc-666/TIDE

We propose controlled decoding (CD), a novel off-policy reinforcement learning method to control the autoregressive generation from language models towards high reward outcomes. CD solves an off-policy reinforcement learning problem through a value function for the reward, which we call a prefix scorer. The prefix scorer is used at inference time to steer the generation towards higher reward outcomes. We show that the prefix scorer may be trained on (possibly) off-policy data to predict the expected reward when decoding is continued from a partially decoded response. We empirically demonstrate that CD is effective as a control mechanism on Reddit conversations corpus. We also show that the modularity of the design of CD makes it possible to control for multiple rewards, effectively solving a multi-objective reinforcement learning problem with no additional complexity. Finally, we show that CD can be applied in a novel blockwise fashion at inference-time, again without the need for any training-time changes, essentially bridging the gap between the popular best-of-K strategy and token-level reinforcement learning. This makes CD a promising approach for alignment of language models.

Knowledge distillation has become a primary mechanism for transferring reasoning and domain expertise from frontier Large Language Models (LLMs) to smaller, deployable students. However, the dominant paradigm remains off-policy: students train on static teacher-generated data and never encounter their own errors during learning. This train--test mismatch, an instance of exposure bias, causes prediction errors to compound autoregressively at inference time. On-Policy Distillation (OPD) addresses this by letting the student generate its own trajectories and receive teacher feedback on these self-generated outputs, grounding distillation in the theory of interactive imitation learning. Despite rapid growth spanning divergence minimization, reward-guided learning, and self-play, the OPD literature remains fragmented with no unified treatment. This survey provides the first comprehensive overview of OPD for LLMs. We introduce a unified f-divergence framework over on-policy samples and organize the landscape along three orthogonal dimensions: feedback signal (logit-based, outcome-based, or self-play), teacher access (white-box, black-box, or teacher-free), and loss granularity (token-level, sequence-level, or hybrid). We systematically analyze representative methods, examine industrial deployments, and identify open problems including distillation scaling laws, uncertainty-aware feedback, and agent-level distillation.

Although Large Language Models (LLMs) have demonstrated impressive capabilities across a wide range of tasks, growing concerns have emerged over the misuse of sensitive, copyrighted, or harmful data during training. To address these concerns, unlearning techniques have been developed to remove the influence of specific data without retraining from scratch. However, this paper reveals a critical vulnerability in fine-tuning-based unlearning: a malicious user can craft a manipulated forgetting request that stealthily degrades the model's utility for benign users. We demonstrate this risk through a red-teaming Stealthy Attack (SA), which is inspired by two key limitations of existing unlearning (the inability to constrain the scope of unlearning effect and the failure to distinguish benign tokens from unlearning signals). Prior work has shown that unlearned models tend to memorize forgetting data as unlearning signals, and respond with hallucinations or feigned ignorance when unlearning signals appear in the input. By subtly increasing the presence of common benign tokens in the forgetting data, SA enhances the connection between benign tokens and unlearning signals. As a result, when normal users include such tokens in their prompts, the model exhibits unlearning behaviors, leading to unintended utility degradation. To address this vulnerability, we propose Scope-aware Unlearning (SU), a lightweight enhancement that introduces a scope term into the unlearning objective, encouraging the model to localize the forgetting effect. Our method requires no additional data processing, integrates seamlessly with existing fine-tuning frameworks, and significantly improves robustness against SA. Extensive experiments validate the effectiveness of both SA and SU.

Reinforcement learning with verifiable rewards (RLVR) has become a core technique for post-training of Large Language Models (LLMs). While policy optimization is driven by all sampled tokens under a globally broadcast scalar reward, the heterogeneous policy behaviors exhibited along trajectories are largely overlooked without differentiation. Existing works address this by credit allocation, including token-level advantage reweighting, and selective token optimization, however, the allocation criterion are principally stagnant throughout training, limiting resilient policy evolution. In this work, we argue that when learning signals are scheduled can be as important as where they are allocated across tokens, and introduce the temporal dimension that scheduling the credit allocation criteria over the course of RLVR optimization. We find that prioritizing targeted tokens emphasized with specific policy behaviors, and gradually attenuating toward general optimization leads to more stable and efficient learning dynamics. Furthermore, we show that simple trajectory percentiles provide a natural perspective for distinguishing policy behaviors, and works effectively with temporal scheduling. Our analysis reveals that standard optimization substantially sacrifices policy entropy when simultaneously accommodating heterogeneous behaviors, whereas temporal scheduling yields healthier policy evolution dynamics. Experiments across mathematical and general reasoning benchmarks demonstrate consistent improvements, suggesting that temporal scheduling constitutes a promising optimization dimension.

Rubric-based Reinforcement Learning (RL) has emerged as a promising approach for aligning Large Language Models (LLMs) with complex, open-domain instruction following tasks. However, existing methods predominantly rely on response-level rewards, introducing severe reward sparsity and reward ambiguity problems. To address these issues, we propose Rubrics to Tokens (RTT), a novel rubric-based RL framework that bridges coarse response-level scores and fine-grained token-level credit assignment. RTT introduces a Token-Level Relevance Discriminator to predict which tokens in the response are responsible for a specific constraint, and optimizes the policy model via RTT-GRPO, which integrates response-level and token-level advantages within a unified framework. Furthermore, when transitioning from one-dimensional, outcome-level reward to three-dimensional reward space in the token-level rubric-based RL, we propose a novel group normalization method, called Intra-sample Token Group Normalization, to accommodate this shift. Extensive experiments and benchmarks demonstrate that RTT consistently outperforms other baselines in both instruction- and rubric-level accuracy across different models.

Token-level credit assignment remains a key obstacle for reinforcement learning (RL) in large language models (LLMs), where RL recipes typically treat all tokens equally, failing to distinguish decisive reasoning steps from routine formatting or fluent filler. Recent attempts leverage model-internal signals to assign finer-grained credit, but these are often point-wise heuristics that ignore the global structure of information propagation. We propose FlowTracer, an RL framework that traces answer-targeted reasoning flow on an attention-induced directed acyclic graph in which nodes correspond to tokens and edge capacities come from aggregated attention weights and derives token credit from this global structure. The edge capacities are reweighted to retain only the influence that can reach the answer region, while enforcing local flow conservation so intermediate tokens neither lose nor gain effective mass due to path length or irrelevant branches. On this graph, FlowTracer extracts an information-flow backbone connecting the question to the answer and scores tokens by flow throughput, revealing high-impact hubs and aggregation checkpoints that mediate long-range dependencies. These derived importances are used to shape token-level rewards, enabling learning signals to focus precisely on the tokens that route information toward (or away from) correct answers and delivering consistent performance gains across a range of reasoning tasks.

Reinforcement learning (RL) has emerged as a key paradigm for aligning and optimizing large language models (LLMs). Standard approaches treat the LLM as the policy and apply RL directly over the full vocabulary space. However, this formulation includes the massive tail of contextually irrelevant tokens in the action space, which could distract the policy from focusing on decision-making among the truly reasonable tokens. In this work, we verify that valid reasoning paths could inherently concentrate within a low-rank subspace. Based on this insight, we introduce Reinforcement Learning with Promising Tokens (RLPT), a framework that mitigates the action space issue by decoupling strategic decision-making from token generation. Specifically, RLPT leverages the semantic priors of the base model to identify a dynamic set of promising tokens and constrains policy optimization exclusively to this refined subset via masking. Theoretical analysis and empirical results demonstrate that RLPT effectively reduces gradient variance, stabilizes the training process, and improves sample efficiency. Experiment results on math, coding, and telecom reasoning show that RLPT outperforms standard RL baselines and integrates effectively across various model sizes (4B and 8B) and RL algorithms (GRPO and DAPO).

Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old sampling FLOPs (from prior inference or RL training) in the form of off-policy traces. Standard off-policy methods supervise against off-policy data, causing instabilities during RL optimization. We introduce PrefixRL, where we condition on the prefix of successful off-policy traces and run on-policy RL to complete them, side-stepping off-policy instabilities. PrefixRL boosts the learning signal on hard problems by modulating the difficulty of the problem through the off-policy prefix length. We prove that the PrefixRL objective is not only consistent with the standard RL objective but also more sample efficient. Empirically, we discover back-generalization: training only on prefixed problems generalizes to out-of-distribution unprefixed performance, with learned strategies often differing from those in the prefix. In our experiments, we source the off-policy traces by rejection sampling with the base model, creating a self-improvement loop. On hard reasoning problems, PrefixRL reaches the same training reward 2x faster than the strongest baseline (SFT on off-policy data then RL), even after accounting for the compute spent on the initial rejection sampling, and increases the final reward by 3x. The gains transfer to held-out benchmarks, and PrefixRL is still effective when off-policy traces are derived from a different model family, validating its flexibility in practical settings.

We present DMax, a new paradigm for efficient diffusion language models (dLLMs). It mitigates error accumulation in parallel decoding, enabling aggressive decoding parallelism while preserving generation quality. Unlike conventional masked dLLMs that decode through a binary mask-to-token transition, DMax reformulates decoding as a progressive self-refinement from mask embeddings to token embeddings. At the core of our approach is On-Policy Uniform Training, a novel training strategy that efficiently unifies masked and uniform dLLMs, equipping the model to recover clean tokens from both masked inputs and its own erroneous predictions. Building on this foundation, we further propose Soft Parallel Decoding. We represent each intermediate decoding state as an interpolation between the predicted token embedding and the mask embedding, enabling iterative self-revising in embedding space. Extensive experiments across a variety of benchmarks demonstrate the effectiveness of DMax. Compared with the original LLaDA-2.0-mini, our method improves TPF on GSM8K from 2.04 to 5.47 while preserving accuracy. On MBPP, it increases TPF from 2.71 to 5.86 while maintaining comparable performance. On two H200 GPUs, our model achieves an average of 1,338 TPS at batch size 1. Code is available at: https://github.com/czg1225/DMax

In modern large language models (LLMs), LLM alignment is of crucial importance and is typically achieved through methods such as reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO). However, in most existing methods for LLM alignment, all tokens in the response are optimized using a sparse, response-level reward or preference annotation. The ignorance of token-level rewards may erroneously punish high-quality tokens or encourage low-quality tokens, resulting in suboptimal performance and slow convergence speed. To address this issue, we propose AlignDistil, an RLHF-equivalent distillation method for token-level reward optimization. Specifically, we introduce the reward learned by DPO into the RLHF objective and theoretically prove the equivalence between this objective and a token-level distillation process, where the teacher distribution linearly combines the logits from the DPO model and a reference model. On this basis, we further bridge the accuracy gap between the reward from the DPO model and the pure reward model, by building a contrastive DPO reward with a normal and a reverse DPO model. Moreover, to avoid under- and over-optimization on different tokens, we design a token adaptive logit extrapolation mechanism to construct an appropriate teacher distribution for each token. Experimental results demonstrate the superiority of our AlignDistil over existing methods and showcase fast convergence due to its token-level distributional reward optimization.

Enhancing large vision-language models (LVLMs) with visual slow-thinking reasoning is crucial for solving complex multimodal tasks. However, since LVLMs are mainly trained with vision-language alignment, it is difficult to adopt on-policy reinforcement learning (RL) to develop the slow thinking ability because the rollout space is restricted by its initial abilities. Off-policy RL offers a way to go beyond the current policy, but directly distilling trajectories from external models may cause visual hallucinations due to mismatched visual perception abilities across models. To address these issues, this paper proposes SOPHIA, a simple and scalable Semi-Off-Policy RL for vision-language slow-tHInking reAsoning. SOPHIA builds a semi-off-policy behavior model by combining on-policy visual understanding from a trainable LVLM with off-policy slow-thinking reasoning from a language model, assigns outcome-based rewards to reasoning, and propagates visual rewards backward. Then LVLM learns slow-thinking reasoning ability from the obtained reasoning trajectories using propagated rewards via off-policy RL algorithms. Extensive experiments with InternVL2.5 and InternVL3.0 with 8B and 38B sizes show the effectiveness of SOPHIA. Notably, SOPHIA improves InternVL3.0-38B by 8.50% in average, reaching state-of-the-art performance among open-source LVLMs on multiple multimodal reasoning benchmarks, and even outperforms some closed-source models (e.g., GPT-4.1) on the challenging MathVision and OlympiadBench, achieving 49.08% and 49.95% pass@1 accuracy, respectively. Analysis shows SOPHIA outperforms supervised fine-tuning and direct on-policy RL methods, offering a better policy initialization for further on-policy training.

Knowledge distillation (KD) is a key technique for compressing large-scale language models (LLMs), yet prevailing logit-based methods typically employ static strategies that are misaligned with the dynamic learning process of student models. These methods typically treat all tokens indiscriminately and apply a single, fixed temperature, resulting in suboptimal knowledge transfer. To address these limitations, we propose LLM-Oriented Token-Adaptive Knowledge Distillation (AdaKD), a novel framework that adapts the distillation process to the real-time learning state of each token. AdaKD consists of two synergistic modules driven by a unified token difficulty metric. First, our Loss-Driven Adaptive Token Focusing (LATF) module dynamically adjusts the distillation focus by monitoring the student's learning stability, concentrating computational resources on the most valuable tokens at each training phase. Second, we introduce Inverse Difficulty Temperature Scaling (IDTS), a counterintuitive yet effective token-level temperature strategy. It employs low temperatures for difficult tokens for targeted error correction, and high temperatures for easy tokens to encourage students to learn from the teacher's complete and smooth output distribution, thereby enhancing generalization. As a plug-and-play framework, AdaKD can consistently improve the performance of various distillation methods on multiple model architectures and benchmarks.

Large language models (LLMs) exhibit exceptional performance but pose substantial privacy risks due to training data memorization, particularly within healthcare contexts involving imperfect or privacy-sensitive patient information. We present a hierarchical dual-strategy framework for selective knowledge unlearning that precisely removes specialized knowledge while preserving fundamental medical competencies. Our approach synergistically integrates geometric-constrained gradient updates to selectively modulate target parameters with concept-aware token-level interventions that distinguish between preservation-critical and unlearning-targeted tokens via a unified four-level medical concept hierarchy. Comprehensive evaluations on the MedMCQA (surgical) and MHQA (anxiety, depression, trauma) datasets demonstrate superior performance, achieving an 82.7% forgetting rate and 88.5% knowledge preservation. Notably, our framework maintains robust privacy guarantees while requiring modification of only 0.1% of parameters, addressing critical needs for regulatory compliance, auditability, and ethical standards in clinical research.

Reinforcement learning with verifiable rewards (RLVR) has become a central paradigm for improving reasoning and code generation in large language models, and GRPO-style training is widely adopted for its simplicity and effectiveness. However, an important design choice remains underexplored: how token-level policy gradient terms are aggregated within each sampled group. Standard GRPO uses sequence aggregation, while recent work has advocated token aggregation as a better alternative. We show that these two rules induce different optimization biases: token aggregation introduces sign-length coupling, while sequence aggregation implicitly downweights longer responses through sequence-level equal weighting. To address this tension, we propose Balanced Aggregation (BA), a simple drop-in replacement that computes token-level means separately within the positive and negative subsets and then combines them with sequence-count-based weights. Experiments with Qwen2.5-Math-7B and Qwen3-1.7B on DAPO-17k and Polaris, evaluated on six reasoning and coding benchmarks, show that BA consistently improves training stability and final performance over standard token and sequence aggregation. Our analysis further shows that the relative effectiveness of token and sequence aggregation is largely governed by response-length variation and the positive-negative length gap, highlighting aggregation as a critical design dimension in GRPO-style RLVR.

Multimodal large language models (MLLMs) struggle with numerical regression under long-tailed target distributions. Token-level supervised fine-tuning (SFT) and point-wise regression rewards bias learning toward high-density regions, leading to regression-to-the-mean behavior and poor tail performance. We identify the lack of cross-sample relational supervision as a key limitation of existing MLLM training paradigms. To address it, we propose a distribution-aware reinforcement learning framework based on Group Relative Policy Optimization, which introduces batch-level comparison-based supervision via the Concordance Correlation Coefficient-based reward to align predicted and ground-truth distributions in terms of correlation, scale, and mean. The framework is plug-and-play, requiring no architectural modification. Experiments on a unified suite of long-tailed regression benchmarks show consistent improvements over SFT and existing MLLM regression methods, with particularly strong gains in medium- and few-shot regimes.

On-policy distillation (OPD), which samples trajectories from the student model and supervises them with a teacher at the token level, avoids relying solely on verifiable terminal rewards and can yield better generalization than off-policy distillation. However, OPD requires expensive on-the-fly sampling of the student policy during training, which substantially increases training cost, especially for long responses. Our initial analysis shows that, during OPD, training signals are often concentrated in the prefix of each output, and that even a short teacher-generated prefix can significantly help the student produce the correct answer. Motivated by these observations, we propose a simple yet effective modification of OPD: we apply the distillation objective only to prefixes of student-generated outputs and terminate each sampling early during distillation. Experiments on a suite of AI-for-Math and out-of-domain benchmarks show that on-policy prefix distillation matches the performance of full OPD while reducing training FLOP by 2x-47x.

Tokenization is the first - and often underappreciated - layer of computation in language models. While Chain-of-Thought (CoT) prompting enables transformer models to approximate recurrent computation by externalizing intermediate steps, we show that the success of such reasoning is fundamentally bounded by the structure of tokenized inputs. This work presents a theoretical and empirical investigation into how tokenization schemes, particularly subword-based methods like byte-pair encoding (BPE), impede symbolic computation by merging or obscuring atomic reasoning units. We introduce the notion of Token Awareness to formalize how poor token granularity disrupts logical alignment and prevents models from generalizing symbolic procedures. Through systematic evaluation on arithmetic and symbolic tasks, we demonstrate that token structure dramatically affect reasoning performance, causing failure even with CoT, while atomically-aligned formats unlock strong generalization, allowing small models (e.g., GPT-4o-mini) to outperform larger systems (e.g., o1) in structured reasoning. Our findings reveal that symbolic reasoning ability in LLMs is not purely architectural, but deeply conditioned on token-level representations.

Visual-token pruning can substantially reduce the inference cost of multimodal large language models (MLLMs), yet existing methods largely rely on fixed, handcrafted heuristics and costly expert trial and error. As pruning objectives, budgets, and model architectures diversify, manually navigating the expanding design space becomes increasingly difficult. This paper aims to build an AI4AI framework for visual-token pruning by addressing a natural question: Can large language models automatically design effective visual-token reduction algorithms? Although LLMs possess broad algorithmic knowledge and strong reasoning capabilities, translating such general knowledge into effective solutions for a specialized task remains nontrivial. We argue that the key lies in designing an appropriate search-state representation that connects the internal knowledge of LLMs with the structural requirements and constraints of visual-token pruning. Based on this insight, we propose AutoPrune, a training-free framework for LLM-driven visual-token pruning policy design. At its core, AutoPrune introduces a Token Pruning Domain-Specific Language (TPDSL) comprising 131 reusable atoms for budget control, token scoring, selection constraints, and token reassembly. A key property of TPDSL is that it represents each search state as a residual modification of a strong base policy. This residual formulation narrows the search space and directs the LLM's attention toward the policy components that are most consequential for performance. Experiments on 14 multimodal benchmarks and three MLLM backbones demonstrate the effectiveness, efficiency, and transferability of AutoPrune. Even when removing 94.4% of visual tokens, AutoPrune preserves more than 99% of full-token performance while reducing FLOPs by 9.9x and prefill latency by 6.4x.

Large Language Model (LLM) unlearning has recently gained significant attention, driven by the need to remove unwanted information, such as private, sensitive, or copyrighted content, from LLMs. However, conventional unlearning approaches indiscriminately update model parameters to forget all tokens in a target document, including common tokens (e.g., pronouns, prepositions, general nouns) that carry general knowledge. In this paper, we highlight that not every token needs forgetting. We propose Selective Unlearning (SU), which identifies a critical subset of tokens within the forgetting set that is relevant to the unwanted information, and unlearns only those tokens. Experiments on two benchmarks and six baseline unlearning algorithms demonstrate that SU not only achieves effective unlearning on the targeted forget data, but also significantly preserves the model's utility in the retaining set.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a promising framework for improving reasoning abilities in Large Language Models (LLMs). However, policy optimized with binary verification prone to overlook potential valuable exploration in reasoning trajectory. In view of heavy annotation cost of golden Process Reward Models (PRMs), recent works attempt using auxiliary signals for reward shaping of process tokens, involving entropy and likelihood collected from logit space. In this work, we offer a novel perspective on shaping RLVR with flow rewards derived from latent space, and propose RLFR, where the flow fields of model latents are constructed from either off-policy high-quality data and on-policy rejection sampling data, and the velocity deviations of policy latents within it are quantified to serve as a reward signal. RLFR first demonstrates that a well-established flow field can be a sound environment for reward signal collection, highlighting the expressive latent space is much underexplored. Moreover, RLFR is able to compress any off-policy expert data as reference for constituting reward signals, and we show that the efficient context dependence compressed within the hidden states are utilized, rather than individual token-level denotation for context comprehending. Experiments on both language and multimodal reasoning benchmarks demonstrate the reliability of flow rewards, and suggesting a promising paradigm for reward shaping with auxiliary signals.

Recent advancements in reinforcement learning, particularly through Group Relative Policy Optimization (GRPO), have significantly improved multimodal large language models for complex reasoning tasks. However, two critical limitations persist: 1) they often produce unfocused, verbose reasoning chains that obscure salient spatiotemporal cues and 2) binary rewarding fails to account for partially correct answers, resulting in high reward variance and inefficient learning. In this paper, we propose TW-GRPO, a novel framework that enhances visual reasoning with focused thinking and dense reward granularity. Specifically, we employs a token weighting mechanism that prioritizes tokens with high informational density (estimated by intra-group variance), suppressing redundant tokens like generic reasoning prefixes. Furthermore, we reformulate RL training by shifting from single-choice to multi-choice QA tasks, where soft rewards enable finer-grained gradient estimation by distinguishing partial correctness. Additionally, we propose question-answer inversion, a data augmentation strategy to generate diverse multi-choice samples from existing benchmarks. Experiments demonstrate state-of-the-art performance on several video reasoning and general understanding benchmarks. Notably, TW-GRPO achieves 50.4\% accuracy on CLEVRER (18.8\% improvement over Video-R1) and 65.8\% on MMVU. Our codes are available at https://github.com/longmalongma/TW-GRPO.

Cross-tokenizer knowledge distillation allows a student model to learn from teachers with incompatible vocabularies. Prior work operates on hidden states or logits; the latter is preferred as a drop-in replacement requiring no auxiliary components. Logit-based methods either use only the correct-token probability, missing the full 'dark knowledge' in the teacher's distribution, or operate on the full output distribution, relying on strict token partitioning and/or unprincipled heuristic ranking. We identify two key shortcomings of full-distribution, logit-based methods: (i) an uncommon-token failure, where critical tokens fall into the unmatched subset (e.g., Llama's 1100 multi-digit numerals under digit-splitting Qwen supervision) and are suppressed during training, reducing GSM8k from 12.89 to 2.56 compared to same-tokenizer KD from a weaker teacher; and (ii) over-conservative matching, where strict 1-to-1 matching excludes near-equivalent tokens across surface forms. These failures require distinct remedies: eliminating the partition when critical tokens are misaligned, and refining it when alignment is reliable. We propose X-Token, an approach with two complementary loss formulations targeting these issues. P-KL removes partitioning and aligns the student's distribution with the teacher's via a sparse projection matrix W (initialized from tokenizer-level string rules) to address the uncommon-token failure. H-KL retains the hybrid form while relaxing matching to align each student token with its top-ranked teacher mapping under W. Both objectives share W and extend naturally to multiple teachers. Empirically, on Llama-3.2-1B, X-Token outperforms the current state of the art GOLD by +3.82 average points with a Qwen3-4B teacher and by +0.5 with a Phi-4-Mini teacher. Further, a two-teacher setup (Phi-4-mini + Llama-3B) improves over single-teacher distillation by +1.3 points.

Machine unlearning for large language models (LLMs) aims to selectively remove memorized content such as private data, copyrighted text, or hazardous knowledge, without costly full retraining. Most existing methods require a retain set of curated examples to prevent catastrophic degradation of general model utility, creating an extra data dependency that complicates deployment. We propose SHRED (Self-distillation via High-surprisal-only Retain-set-free Entropy Demotion), a retain-set-free unlearning method built on a key insight: not all tokens within a forget set instance carry memorized information equally. High-information tokens concentrate the model's memorized knowledge, while low-information tokens reflect general language competence. SHRED operates in two stages. (1) Selection: We perform a forward pass on a forget set instance, collect per-token autoregressive probabilities, and select the bottom (lowest probability, highest Shannon information) as forget positions; the remaining positions are retained as benign anchors. (2) Training: We construct modified KL targets that demote the memorized token's logit at forget positions while preserving the original distribution at benign positions. The model is then trained via a single top KL self-distillation objective that simultaneously drives forgetting and utility preservation. We evaluate SHRED across four standard unlearning benchmarks and demonstrate that it establishes a new Pareto-optimal trade-off between forget efficacy and model utility, outperforming retain-set-dependent methods. Our analysis shows that SHRED is robust against relearning attacks and membership-inference attacks, and it maintains stable utility even after many sequential unlearning runs.

On-policy knowledge distillation has proven effective for language models, yet its application to vision-language models (VLMs) remains underexplored. We observe that standard on-policy distillation can improve a student's output quality while failing to strengthen its reliance on visual input: on vision-critical tokens, the student's predictions remain largely unchanged whether or not fine-grained visual detail is present, even though the teacher's predictions depend heavily on it.To make this difference observable, we introduce visual advantage (VA), the token-level log-probability difference when the teacher scores a student-generated rollout with versus without access to fine-grained visual detail. VA is concentrated in a small minority of tokens, and these high-VA tokens are the ones that actually carry the visual supervision signal. This motivates a distillation objective that treats them differently from language scaffolding, so their contribution is not diluted by the abundant surrounding language tokens.We propose Visual-Advantage On-Policy Distillation (VA-OPD), which uses VA at two granularities: rollout-level reweighting by trajectory-averaged VA, and token-level KL averaged within high-VA and low-VA groups separately. We train on two math datasets (Geometry3K and ViRL39K) and evaluate on eight benchmarks covering both mathematical reasoning and visual understanding, across three teacher sizes (4B, 8B, and 32B) on the Qwen3-VL family. VA-OPD improves over standard on-policy distillation on every benchmark, with the gain growing monotonically along both the teacher-size and data-scale axes, suggesting that these factors compound consistently.

Medical Vision-Language Models (Med-VLMs) require reliable reasoning from fine-grained visual evidence, yet existing models can produce plausible clinical answers by relying on language priors or medical templates rather than truly attending to diagnosis-critical regions. On-Policy Distillation (OPD) offers dense token-level supervision on student-generated trajectories and provides a privacy-compatible means of capability transfer without requiring the redistribution of raw patient data. However, standard OPD uniformly distills all tokens, causing sparse evidence-dependent tokens to be diluted by abundant clinical narrative tokens. Inspired by the success of OPD in the large language model community, we propose Med-OPD, to our knowledge the first unified post-training framework that integrates on-policy distillation with medical evidence-aware supervision for Med-VLMs. We introduce Medical Evidence Advantage (MEA), a teacher-grounded counterfactual signal that uses an answer-aware hint to focus teacher scoring on evidence supporting the target diagnosis, and measures each token's dependence on medical visual evidence by comparing teacher likelihoods under the original and evidence-degraded imaging modalities. Based on MEA, Med-OPD redistributes the distillation signal at both the token and trajectory levels, emphasizing diagnosis-critical tokens and evidence-reliant rollouts. Experiments on OmniMedVQA subsets show that Med-OPD consistently outperforms SFT and standard OPD across CT, MRI, Disease Diagnosis, and Lesion Grading. These results demonstrate that evidence-aware distillation can better strengthen medical VLMs' reliance on key visual evidence and improve reliable multimodal medical reasoning. The source code and data is publicly available at: https://github.com/yunhang8658/MedOPD.git

Reinforcement Learning with Verifiable Rewards (RLVR) has propelled Large Language Models in complex reasoning, yet its scalability is often hindered by a training bottleneck where performance plateaus as policy entropy collapses, signaling a loss of exploration. Previous methods typically address this by maintaining high policy entropy, yet the precise mechanisms that govern meaningful exploration have remained underexplored. Our analysis suggests that an unselective focus on entropy risks amplifying irrelevant tokens and destabilizing training. This paper investigates the exploration dynamics within RLVR and identifies a key issue: the gradual elimination of valuable low-probability exploratory tokens, which we term \textit{reasoning sparks}. We find that while abundant in pre-trained models, these sparks are systematically extinguished during RLVR due to over-penalization, leading to a degeneracy in exploration. To address this, we introduce Low-probability Regularization (Lp-Reg). Its core mechanism regularizes the policy towards a heuristic proxy distribution. This proxy is constructed by filtering out presumed noise tokens and re-normalizing the distribution over the remaining candidates. The result is a less-noisy proxy where the probability of reasoning sparks is amplified, which then serves as a soft regularization target to shield these valuable tokens from elimination via KL divergence. Experiments show that Lp-Reg enables stable on-policy training for around 1,000 steps, a regime where baseline entropy-control methods collapse. This sustained exploration leads to state-of-the-art performance, achieving a 60.17% average accuracy on five math benchmarks, an improvement of 2.66% over prior methods. Code is available at https://github.com/CarlanLark/Lp-Reg.

Varied approaches for aligning language models have been proposed, including supervised fine-tuning, RLHF, and direct optimization methods such as DPO. Although DPO has rapidly gained popularity due to its straightforward training process and competitive results, there is an open question of whether there remain practical advantages of using a discriminator, like a reward model, to evaluate responses. We propose D2PO, discriminator-guided DPO, an approach for the online setting where preferences are being collected throughout learning. As we collect gold preferences, we use these not only to train our policy, but to train a discriminative response evaluation model to silver-label even more synthetic data for policy training. We explore this approach across a set of diverse tasks, including a realistic chat setting, we find that our approach leads to higher-quality outputs compared to DPO with the same data budget, and greater efficiency in terms of preference data requirements. Furthermore, we show conditions under which silver labeling is most helpful: it is most effective when training the policy with DPO, outperforming traditional PPO, and benefits from maintaining a separate discriminator from the policy model.