Daily Papers

Long-horizon reasoning in recent LLMs demands that the model switch between distinct skills inside a reasoning chain, such as first doing a math derivation, then using the result to plan a schedule. We call such problems cross-skill long-horizon tasks: multi-step tasks whose steps require different reasoning skills and depend on earlier outputs. Existing benchmarks often evaluate individual skills, lacking a principled way to measure how well a model switches between skills. We address this gap from both the evaluation and training sides. We introduce Skill Entropy, a measure of the difficulty of switching from one skill to another. We then propose Skill^2-Bench, a benchmark of cross-skill long-horizon tasks built over 558 skills across 9 verifiable and open-ended domains. Each task is assigned a task-level skill-entropy score and grouped into three difficulty levels. Evaluating 8 frontier and 4 open-source models on Skill^2-Bench reveals a skill-switching gap: accuracy decreases on higher-entropy tasks. We then turn skill entropy from a benchmark scale into a training signal. We propose Skill-Entropy RL, an RL framework where the model predicts not only the answer at each step but also the skill used to produce it. The reward combines step-level correctness with a skill-entropy reward that measures the alignment between the model-predicted skill sequence and the gold skill sequence. On Qwen3-4B-Instruct and Qwen3-1.7B, Skill-Entropy RL improves the Skill^2-Bench score from 34.4% to 68.4% and from 14.6% to 40.1%, respectively, outperforming competitive baselines. The same pipeline can be applied to off-the-shelf training data such as OpenR1-Math, indicating that skill entropy is a reusable training signal. Code available at: https://github.com/Gen-Verse/Skill-Entropy-RL

Recent advances in multimodal large reasoning models (MLRMs) have substantially improved their ability to solve complex textual and visual tasks. However, these models tend to overthink on simple problems, producing unnecessarily lengthy reasoning traces, while under-exploring on challenging ones, leading to missed solutions. To address this imbalance, we propose ARES, a unified open-source framework for adaptive reasoning that dynamically allocates exploration effort based on task difficulty. Our approach is motivated by two key empirical findings: (i) while single-token entropy is noisy, high window-entropy (HWE) tokens (token-level entropies averaged under a sliding window) can reliably capture reasoning-critical moments; and (ii) reducing HWE usage benefits easy problems, while increasing it is essential for solving hard ones. Building on these insights, ARES introduces a two-stage training pipeline. In the Adaptive Cold-Start stage, we curate multimodal and textual data paired with reasoning traces of length proportional to problem difficulty, equipping the model with initial difficulty awareness. In the second stage, we develop Adaptive Entropy Policy Optimization (AEPO), which uses HWE tokens as exploration triggers to decide when to explore, and a hierarchical entropy reward with dynamic KL control to decide how much to explore. Extensive experiments demonstrate that ARES achieves superior performance and reasoning efficiency across diverse mathematical, logical, and multimodal benchmarks, while closing the gap to leading commercial systems under significantly lower inference costs.

Recent advances in large reasoning models highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing AI's capabilities, particularly in solving complex logical tasks. However, it remains unclear whether RLVR truly expands a model's reasoning boundary or merely amplifies high-reward outputs that the base model already knows for improved precision. This study presents a theoretical and empirical investigation that provides fresh insights into the potential limits of RLVR. First, we offer a new theoretical perspective that RLVR is constrained by the base model's support-unable to sample solutions with zero initial probability-and operates as a conservative reweighting mechanism that may restrict the discovery of entirely original solutions. We also identify an entropy-reward tradeoff: while RLVR reliably enhances precision, it may progressively narrow exploration and potentially overlook correct yet underrepresented solutions. Extensive empirical experiments validate that while RLVR consistently improves pass@1, the shrinkage of empirical support generally outweighs the expansion of empirical support under larger sampling budgets, failing to recover correct answers that were previously accessible to the base model. Interestingly, we also observe that while RLVR sometimes increases token-level entropy, resulting in greater uncertainty at each generation step, answer-level entropy declines, indicating that these seemingly more uncertain paths ultimately converge onto a smaller set of distinct answers. Taken together, these findings reveal potential limits of RLVR in extending reasoning horizons. Breaking this invisible leash may require future algorithmic innovations such as explicit exploration mechanisms or hybrid strategies that seed probability mass into underrepresented solution regions.

Large Reasoning Models (LRMs) have achieved impressive performance on complex reasoning tasks by generating detailed chain-of-thought (CoT) explanations. However, these responses are often excessively long, containing redundant reasoning steps that inflate inference cost and reduce usability. Controlling the length of generated reasoning without sacrificing accuracy remains an open challenge. Through a systematic empirical analysis, we reveal a consistent positive correlation between model entropy and response length at different reasoning stages across diverse LRMs: the thinking phase exhibits higher entropy, reflecting exploratory behavior of longer responses, while the final answer phase shows lower entropy, indicating a more deterministic solution. This observation suggests that entropy at different reasoning stages can serve as a control knob for balancing conciseness and performance. Based on this insight, this paper introduces Phase Entropy Aware Reward (PEAR), a reward mechanism that incorporating phase-dependent entropy into the reward design. Instead of treating all tokens uniformly, PEAR penalize excessive entropy during the thinking phase and allowing moderate exploration at the final answer phase, which encourages models to generate concise reasoning traces that retain sufficient flexibility to solve the task correctly. This enables adaptive control of response length without relying on explicit length targets or rigid truncation rules. Extensive experiments across four benchmarks demonstrate that PEAR consistently reduces response length while sustaining competitive accuracy across model scales. In addition, PEAR demonstrates strong out-of-distribution (OOD) robustness beyond the training distribution. Our code is available at: https://github.com/iNLP-Lab/PEAR.

Reward guidance has been applied to great success in the test-time adaptation of continuous diffusion models; it updates each denoising step using the gradients from a downstream reward model. We study reward guidance for discrete diffusion language models, where one cannot differentiate through the natural outputs of the model because they are discrete tokens. Existing approaches either replace these discrete tokens with continuous relaxations, or employ techniques like the straight-through estimator. In this work, we show the downsides of both these methods. The former degrades gradient feedback because the reward model has never been trained with continuous inputs. The latter involves incorrect optimization because the gradient evaluated at discrete tokens is used to update continuous logits. Our key innovation is to go beyond this tradeoff by introducing a novel mechanism called EntRGi: Entropy aware Reward Guidance that dynamically regulates the gradients from the reward model. By modulating the continuous relaxation using the model's confidence, our approach substantially improves reward guidance while providing reliable inputs to the reward model. We empirically validate our approach on a 7B-parameter diffusion language model across 3 diverse reward models and 3 multi-skill benchmarks, showing consistent improvements over state-of-the-art methods.

Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy reduction, implicitly assuming that low uncertainty is desirable throughout reasoning. We show instead that reasoning efficiency is governed by the trajectory of uncertainty. CoTs with dominant downward entropy trends are substantially shorter. Motivated by this insight, we propose Entropy Trend Reward (ETR), a trajectory-aware objective that encourages progressive uncertainty reduction while allowing limited local exploration. We integrate ETR into Group Relative Policy Optimization (GRPO) and evaluate it across multiple reasoning models and challenging benchmarks. ETR consistently achieves a superior accuracy-efficiency tradeoff, improving DeepSeek-R1-Distill-7B by 9.9% in accuracy while reducing CoT length by 67% across four benchmarks. Code is available at https://github.com/Xuan1030/ETR

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.

While Large Language Models (LLMs) can generate fluent text, producing high-quality creative stories remains challenging. Reinforcement Learning (RL) offers a promising solution but faces two critical obstacles: designing reliable reward signals for subjective storytelling quality and mitigating training instability. This paper introduces the Reinforcement Learning for Creative Storytelling (RLCS) framework to systematically address both challenges. First, we develop a Generative Reward Model (GenRM) that provides multi-dimensional analysis and explicit reasoning about story preferences, trained through supervised fine-tuning on demonstrations with reasoning chains distilled from strong teacher models, followed by GRPO-based refinement on expanded preference data. Second, we introduce an entropy-based reward shaping strategy that dynamically prioritizes learning on confident errors and uncertain correct predictions, preventing overfitting on already-mastered patterns. Experiments demonstrate that GenRM achieves 68\% alignment with human creativity judgments, and RLCS significantly outperforms strong baselines including Gemini-2.5-Pro in overall story quality. This work provides a practical pipeline for applying RL to creative domains, effectively navigating the dual challenges of reward modeling and training stability.

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

This paper examines the exploration-exploitation trade-off in reinforcement learning with verifiable rewards (RLVR), a framework for improving the reasoning of Large Language Models (LLMs). Recent studies suggest that RLVR can elicit strong mathematical reasoning in LLMs through two seemingly paradoxical mechanisms: spurious rewards, which suppress exploitation by rewarding outcomes unrelated to the ground truth, and entropy minimization, which suppresses exploration by pushing the model toward more confident and deterministic outputs, highlighting a puzzling dynamic: both discouraging exploitation and discouraging exploration improve reasoning performance, yet the underlying principles that reconcile these effects remain poorly understood. We focus on two fundamental questions: (i) how policy entropy relates to performance, and (ii) whether spurious rewards yield gains, potentially through the interplay of clipping bias and model contamination. Our results show that clipping bias under spurious rewards reduces policy entropy, leading to more confident and deterministic outputs, while entropy minimization alone is insufficient for improvement. We further propose a reward-misalignment model explaining why spurious rewards can enhance performance beyond contaminated settings. Our findings clarify the mechanisms behind spurious-reward benefits and provide principles for more effective RLVR training.

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

Recently, reinforcement learning with verifiable rewards (RLVR) has been widely used for enhancing the reasoning abilities of large language models (LLMs). A core challenge in RLVR involves managing the exchange between entropy and performance of policies. Despite the importance of this exchange, a fine-grained understanding of when and how this exchange operates most effectively remains limited. To bridge this gap, we conduct a systematic empirical analysis of the entropy-performance exchange mechanism of RLVR across different levels of granularity. Specifically, we first divide the training process into two distinct stages based on entropy dynamics, i.e., rising stage and plateau stage, and then systematically investigate how this mechanism varies across stage-level, instance-level, and token-level granularitiess. Our analysis reveals that, in the rising stage, entropy reduction in negative samples facilitates the learning of effective reasoning patterns, which in turn drives rapid performance gains. Moreover, in the plateau stage, learning efficiency strongly correlates with high-entropy tokens present in low-perplexity samples and those located at the end of sequences. Motivated by these findings, we propose two methods that dynamically adjust the reward signal using perplexity and positional information to focus RL updates on tokens that exhibit high learning potential, achieving improvements compared to the baseline methods on various LLMs.

Offline-to-online RL can make full use of pre-collected offline datasets to initialize policies, resulting in higher sample efficiency and better performance compared to only using online algorithms alone for policy training. However, direct fine-tuning of the pre-trained policy tends to result in sub-optimal performance. A primary reason is that conservative offline RL methods diminish the agent's capability of exploration, thereby impacting online fine-tuning performance. To encourage agent's exploration during online fine-tuning and enhance the overall online fine-tuning performance, we propose a generalized reward augmentation method called Sample Efficient Reward Augmentation (SERA). Specifically, SERA encourages agent to explore by computing Q conditioned entropy as intrinsic reward. The advantage of SERA is that it can extensively utilize offline pre-trained Q to encourage agent uniformly coverage of state space while considering the imbalance between the distributions of high-value and low-value states. Additionally, SERA can be effortlessly plugged into various RL algorithms to improve online fine-tuning and ensure sustained asymptotic improvement. Moreover, extensive experimental results demonstrate that when conducting offline-to-online problems, SERA consistently and effectively enhances the performance of various offline algorithms.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Aligning AI systems with human preferences typically suffers from the infamous reward hacking problem, where optimization of an imperfect reward model leads to undesired behaviors. In this paper, we investigate reward hacking in offline preference optimization, which aims to improve an initial model using a preference dataset. We identify two types of reward hacking stemming from statistical fluctuations in the dataset: Type I Reward Hacking due to subpar choices appearing more favorable, and Type II Reward Hacking due to decent choices appearing less favorable. We prove that many (mainstream or theoretical) preference optimization methods suffer from both types of reward hacking. To mitigate Type I Reward Hacking, we propose POWER, a new preference optimization method that combines Guiasu's weighted entropy with a robust reward maximization objective. POWER enjoys finite-sample guarantees under general function approximation, competing with the best covered policy in the data. To mitigate Type II Reward Hacking, we analyze the learning dynamics of preference optimization and develop a novel technique that dynamically updates preference labels toward certain "stationary labels", resulting in diminishing gradients for untrustworthy samples. Empirically, POWER with dynamic labels (POWER-DL) consistently outperforms state-of-the-art methods on alignment benchmarks, achieving improvements of up to 13.0 points on AlpacaEval 2.0 and 11.5 points on Arena-Hard over DPO, while also improving or maintaining performance on downstream tasks such as mathematical reasoning. Strong theoretical guarantees and empirical results demonstrate the promise of POWER-DL in mitigating reward hacking.

Open-ended real-world interaction admits multiple valid behaviors: an agent may answer directly, ask for clarification, provide progress updates, or confirm before acting. This flexibility breaks a core assumption behind group-based RL: rollouts compared within a group are no longer guaranteed to be behaviorally comparable. As a result, reward-model preferences over interaction style can distort relative advantages and steer optimization toward reward-preferred behaviors rather than context-appropriate ones. We formalize this as a reward fairness problem and propose ARC (Advantage Regularization via Conditioning), a training recipe that restores fairer relative comparison through strategy-conditioned rollout grouping, together with hybrid rewards and entropy regularization. We study ARC in our proposed \inter, a novel paradigm for responsive, steerable, and execution-aware user-agent interaction that decouples user-visible communication from latent reasoning and tool use. \inter\ also provides the annotation and distillation pipeline for constructing \inter-86K, our strategy-annotated training corpus for supervised and RL training. Empirically, ARC substantially strengthens the core τ/τ^2 tool-use benchmarks, while \inter\ reduces time-to-first-token from 4.91s to 1.27s relative to a think-style baseline. Together, these results suggest that a central bottleneck in open-ended interactive learning is not only how agents are rewarded, but whether their behaviors are compared fairly in the first place. The ARC implementation and \inter-86K training data will be released.

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

Existing automatic 3D image segmentation methods usually fail to meet the clinic use. Many studies have explored an interactive strategy to improve the image segmentation performance by iteratively incorporating user hints. However, the dynamic process for successive interactions is largely ignored. We here propose to model the dynamic process of iterative interactive image segmentation as a Markov decision process (MDP) and solve it with reinforcement learning (RL). Unfortunately, it is intractable to use single-agent RL for voxel-wise prediction due to the large exploration space. To reduce the exploration space to a tractable size, we treat each voxel as an agent with a shared voxel-level behavior strategy so that it can be solved with multi-agent reinforcement learning. An additional advantage of this multi-agent model is to capture the dependency among voxels for segmentation task. Meanwhile, to enrich the information of previous segmentations, we reserve the prediction uncertainty in the state space of MDP and derive an adjustment action space leading to a more precise and finer segmentation. In addition, to improve the efficiency of exploration, we design a relative cross-entropy gain-based reward to update the policy in a constrained direction. Experimental results on various medical datasets have shown that our method significantly outperforms existing state-of-the-art methods, with the advantage of fewer interactions and a faster convergence.

Multimodal reward models are crucial for aligning multimodal large language models with human preferences. Recent works have incorporated reasoning capabilities into these models, achieving promising results. However, training these models suffers from two critical challenges: (1) the inherent noise in preference datasets, which degrades model performance, and (2) the inefficiency of conventional training methods, which ignore the differences in sample difficulty. In this paper, we identify a strong correlation between response entropy and accuracy, indicating that entropy can serve as a reliable and unsupervised proxy for annotation noise and sample difficulty. Based on this insight, we propose a novel Entropy-Guided Training (EGT) approach for multimodal reasoning reward models, which combines two strategies: (1) entropy-guided data curation to mitigate the impact of unreliable samples, and (2) an entropy-guided training strategy that progressively introduces more complex examples. Extensive experiments across three benchmarks show that the EGT-trained model consistently outperforms state-of-the-art multimodal reward models.

This paper presents the Entropy-Driven Unified Process Reward Model (EDU-PRM), a novel framework that approximates state-of-the-art performance in process supervision while drastically reducing training costs. EDU-PRM introduces an entropy-guided dynamic step partitioning mechanism, using logit distribution entropy to pinpoint high-uncertainty regions during token generation dynamically. This self-assessment capability enables precise step-level feedback without manual fine-grained annotation, addressing a critical challenge in process supervision. Experiments on the Qwen2.5-72B model with only 7,500 EDU-PRM-generated training queries demonstrate accuracy closely approximating the full Qwen2.5-72B-PRM (71.1% vs. 71.6%), achieving a 98% reduction in query cost compared to prior methods. This work establishes EDU-PRM as an efficient approach for scalable process reward model training.

What drives exploration? Understanding intrinsic motivation is a long-standing challenge in both cognitive science and artificial intelligence; numerous objectives have been proposed and used to train agents, yet there remains a gap between human and agent exploration. We directly compare adults, children, and AI agents in a complex open-ended environment, Crafter, and study how common intrinsic objectives: Entropy, Information Gain, and Empowerment, relate to their behavior. We find that only Entropy and Empowerment are consistently positively correlated with human exploration progress, indicating that these objectives may better inform intrinsic reward design for agents. Furthermore, across agents and humans we observe that Entropy initially increases rapidly, then plateaus, while Empowerment increases continuously, suggesting that state diversity may provide more signal in early exploration, while advanced exploration should prioritize control. Finally, we find preliminary evidence that private speech utterances, and particularly goal verbalizations, may aid exploration in children. Our data is available at https://github.com/alyd/humans_in_crafter_data.

Large Reasoning Models (LRMs) often suffer from overthinking, generating unnecessarily long reasoning chains even for simple tasks. This leads to substantial computational overhead with limited performance gain, primarily due to redundant verification and repetitive generation. While prior work typically constrains output length or optimizes correctness, such coarse supervision fails to guide models toward concise yet accurate inference. In this paper, we propose ENTRA, an entropy-based training framework that suppresses redundant reasoning while preserving performance. ENTRA first estimates the token-level importance using a lightweight Bidirectional Importance Estimation (BIE) method, which accounts for both prediction confidence and forward influence. It then computes a redundancy reward based on the entropy of low-importance tokens, normalized by its theoretical upper bound, and optimizes this reward via reinforcement learning. Experiments on mathematical reasoning benchmarks demonstrate that ENTRA reduces output length by 37% to 53% with no loss-and in some cases, gains-in accuracy. Our approach offers a principled and efficient solution to reduce overthinking in LRMs, and provides a generalizable path toward redundancy-aware reasoning optimization.

Reinforcement learning with verifiable rewards (RLVR) commonly uses entropy for advantage shaping. However, entropy cannot distinguish useful uncertainty from detrimental confusion, limiting its effectiveness as a correctness signal. We propose Contrastive Policy Optimization (CPO), which uses token-level contrastive disagreement between reference-guided and vanilla generation distributions for correctness-aware advantage shaping. Both theoretical and empirical results show that this disagreement reliably indicates token-level correctness. We further show that On-policy Distillation is a special case of CPO, where the posterior distribution is instantiated by an external teacher model. CPO also resolves the zero-advantage problem. Experiments on in-domain and out-of-domain benchmarks demonstrate that CPO substantially outperforms entropy-based RLVR methods while maintaining strong generalization. Further analysis shows that correct and incorrect responses naturally support exploration and exploitation respectively, and balancing both leads to the best performance.

Reinforcement learning with verifiable rewards (RLVR) has shown great promise in enhancing the reasoning abilities of large reasoning models (LRMs). However, it suffers from a critical issue: entropy collapse and premature convergence. Naive entropy regularization, a common approach for encouraging exploration in the traditional RL literature, fails to address this problem in the context of LRM. Our analysis reveals that this failure stems from the vast action space and long trajectories in LRMs, which easily trigger a global entropy explosion as the model indiscriminately explores all possible actions and states. To address this, we propose SIREN (SelectIve entRopy rEgularizatioN), a method that confines exploration to a meaningful subset of actions and states. SIREN achieves this through a two-step entropy masking mechanism, consisting of a top-p mask and a peak-entropy mask. In addition, regularization is transformed into a self-anchored form to stabilize training. Across five mathematical benchmarks, SIREN attains superior average performance over previous entropy-related RLVR approaches, exemplified by a +6.6 maj@k improvement on AIME24/25 with Qwen2.5-Math-7B. Further analysis confirms that SIREN promotes greater response diversity and maintains entropy at an appropriate level, which helps to preserve the validation pass@k throughout training. This effectively mitigates the premature convergence problem common in RLVR for LRM.

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

Tool-using agents based on Large Language Models (LLMs) excel in tasks such as mathematical reasoning and multi-hop question answering. However, in long trajectories, agents often trigger excessive and low-quality tool calls, increasing latency and degrading inference performance, making managing tool-use behavior challenging. In this work, we conduct entropy-based pilot experiments and observe a strong positive correlation between entropy reduction and high-quality tool calls. Building on this finding, we propose using entropy reduction as a supervisory signal and design two reward strategies to address the differing needs of optimizing tool-use behavior. Sparse outcome rewards provide coarse, trajectory-level guidance to improve efficiency, while dense process rewards offer fine-grained supervision to enhance performance. Experiments across diverse domains show that both reward designs improve tool-use behavior: the former reduces tool calls by 72.07% compared to the average of baselines, while the latter improves performance by 22.27%. These results position entropy reduction as a key mechanism for enhancing tool-use behavior, enabling agents to be more adaptive in real-world applications.

Recent advances in large language models (LLMs) have demonstrated significant potential in hardware design automation, particularly in using natural language to synthesize Register-Transfer Level (RTL) code. Despite this progress, a gap remains between model capability and the demands of real-world RTL design, including syntax errors, functional hallucinations, and weak alignment to designer intent. Reinforcement Learning with Verifiable Rewards (RLVR) offers a promising approach to bridge this gap, as hardware provides executable and formally checkable signals that can be used to further align model outputs with design intent. However, in long, structured RTL code sequences, not all tokens contribute equally to functional correctness, and naïvely spreading gradients across all tokens dilutes learning signals. A key insight from our entropy analysis in RTL generation is that only a small fraction of tokens (e.g., always, if, assign, posedge) exhibit high uncertainty and largely influence control flow and module structure. To address these challenges, we present EARL, an Entropy-Aware Reinforcement Learning framework for Verilog generation. EARL performs policy optimization using verifiable reward signals and introduces entropy-guided selective updates that gate policy gradients to high-entropy tokens. This approach preserves training stability and concentrates gradient updates on functionally important regions of code. Our experiments on VerilogEval and RTLLM show that EARL improves functional pass rates over prior LLM baselines by up to 14.7%, while reducing unnecessary updates and improving training stability. These results indicate that focusing RL on critical, high-uncertainty tokens enables more reliable and targeted policy improvement for structured RTL code generation.

Despite the success of reinforcement learning for large language models, a common failure mode is reduced sampling diversity, where the policy repeatedly generates similar erroneous behaviors. Classical entropy regularization encourages randomness under the current policy, but does not explicitly discourage recurrent failure patterns across rollouts. We propose MEDS, a Memory-Enhanced Dynamic reward Shaping framework that incorporates historical behavioral signals into reward design. By storing and leveraging intermediate model representations, we capture features of past rollouts and use density-based clustering to identify frequently recurring error patterns. Rollouts assigned to more prevalent error clusters are penalized more heavily, encouraging broader exploration while reducing repeated mistakes. Across five datasets and three base models, MEDS consistently improves average performance over existing baselines, achieving gains of up to 4.13 pass@1 points and 4.37 pass@128 points. Additional analyses using both LLM-based annotations and quantitative diversity metrics show that MEDS increases behavioral diversity during sampling.

Training LLM agents in multi-turn environments with sparse rewards, where completing a single task requires 30+ turns of interaction within an episode, presents a fundamental challenge for reinforcement learning. We identify a critical failure mode unique to this setting: the exploration-exploitation cascade failure. This cascade begins with early-stage policy premature convergence, where sparse feedback causes agents to commit to flawed, low-entropy strategies. Subsequently, agents enter late-stage policy collapse, where conventional entropy regularization becomes counterproductive, promoting chaotic exploration that destabilizes training. We propose Entropy-regularized Policy Optimization (EPO), a general framework that breaks this failure cycle through three synergistic mechanisms: (1) adopting entropy regularization in multi-turn settings to enhance exploration, (2) an entropy smoothing regularizer that bounds policy entropy within historical averages to prevent abrupt fluctuations, and (3) adaptive phase-based weighting that balances exploration and exploitation across training. Our analysis justifies that EPO guarantees monotonically decreasing entropy variance while maintaining convergence. EPO achieves up to 152% performance improvement on ScienceWorld and up to 19.8% on ALFWorld. Our work demonstrates that multi-turn sparse-reward settings require fundamentally different entropy control than traditional RL, with broad implications for LLM agent training.

Recent reinforcement learning has enhanced the flow matching models on human preference alignment. While stochastic sampling enables the exploration of denoising directions, existing methods which optimize over multiple denoising steps suffer from sparse and ambiguous reward signals. We observe that the high entropy steps enable more efficient and effective exploration while the low entropy steps result in undistinguished roll-outs. To this end, we propose E-GRPO, an entropy aware Group Relative Policy Optimization to increase the entropy of SDE sampling steps. Since the integration of stochastic differential equations suffer from ambiguous reward signals due to stochasticity from multiple steps, we specifically merge consecutive low entropy steps to formulate one high entropy step for SDE sampling, while applying ODE sampling on other steps. Building upon this, we introduce multi-step group normalized advantage, which computes group-relative advantages within samples sharing the same consolidated SDE denoising step. Experimental results on different reward settings have demonstrated the effectiveness of our methods.

This paper introduces EnergyFlow, a framework that unifies generative action modeling with inverse reinforcement learning by parameterizing a scalar energy function whose gradient is the denoising field. We establish that under maximum-entropy optimality, the score function learned via denoising score matching recovers the gradient of the expert's soft Q-function, enabling reward extraction without adversarial training. Formally, we prove that constraining the learned field to be conservative reduces hypothesis complexity and tightens out-of-distribution generalization bounds. We further characterize the identifiability of recovered rewards and bound how score estimation errors propagate to action preferences. Empirically, EnergyFlow achieves state-of-the-art imitation performance on various manipulation tasks while providing an effective reward signal for downstream reinforcement learning that outperforms both adversarial IRL methods and likelihood-based alternatives. These results show that the structural constraints required for valid reward extraction simultaneously serve as beneficial inductive biases for policy generalization. The code is available at https://github.com/sotaagi/EnergyFlow.

Sparse rewards and heterogeneous task sequences remain persistent challenges in Reinforcement Learning (RL), often resulting in slow convergence, weak generalization, and inefficient exploration. We propose Uncertainty-Aware LLM-Guided Policy Shaping (ULPS), a novel framework that integrates a calibrated Large Language Model (LLM) into the RL training loop to provide structured, uncertainty-modulated behavioral guidance. ULPS employs an A*-based oracle to synthesize optimal symbolic trajectories, which are used to fine-tune a BERT-based language model. During training, this model supplies action suggestions whose influence is conditioned on epistemic uncertainty estimated via Monte Carlo (MC) dropout. An entropy-based blending mechanism adaptively balances LLM guidance and the learned policy (via Proximal Policy Optimization, PPO), allowing the agent to prioritize reliable priors while preserving adaptability. We evaluate ULPS on the MiniGridUnlockPickup benchmark and observe consistent improvements in success rate, reward efficiency, and sample complexity over unguided, uncalibrated, and standard RL baselines. ULPS achieves more than 9% improvement in execution accuracy after fine-tuning, requires fewer environment interactions, and yields higher reward AUC. Our results demonstrate that integrating symbolic A* trajectories, pretrained language priors, and uncertainty-aware control offers a principled and effective approach to multi-task reinforcement learning in sparse-reward domains, with potential extensibility to partially observable and multi-agent settings.

Language models are vulnerable to short adversarial suffixes that can reliably alter predictions. Previous works usually find such suffixes with gradient search or rule-based methods, but these are brittle and often tied to a single task or model. In this paper, a reinforcement learning framework is used where the suffix is treated as a policy and trained with Proximal Policy Optimization against a frozen model as a reward oracle. Rewards are shaped using calibrated cross-entropy, removing label bias and aggregating across surface forms to improve transferability. The proposed method is evaluated on five diverse NLP benchmark datasets, covering sentiment, natural language inference, paraphrase, and commonsense reasoning, using three distinct language models: Qwen2-1.5B Instruct, TinyLlama-1.1B Chat, and Phi-1.5. Results show that RL-trained suffixes consistently degrade accuracy and transfer more effectively across tasks and models than previous adversarial triggers of similar genres.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant for applications that require joint compression and retrieval, and in scenarios involving distributional shifts due to processing. We show that the proposed formulation extends the classical minimum entropy coupling framework by integrating a bottleneck, allowing for a controlled degree of stochasticity in the coupling. We explore the decomposition of the Minimum Entropy Coupling with Bottleneck (MEC-B) into two distinct optimization problems: Entropy-Bounded Information Maximization (EBIM) for the encoder, and Minimum Entropy Coupling (MEC) for the decoder. Through extensive analysis, we provide a greedy algorithm for EBIM with guaranteed performance, and characterize the optimal solution near functional mappings, yielding significant theoretical insights into the structural complexity of this problem. Furthermore, we illustrate the practical application of MEC-B through experiments in Markov Coding Games (MCGs) under rate limits. These games simulate a communication scenario within a Markov Decision Process, where an agent must transmit a compressed message from a sender to a receiver through its actions. Our experiments highlight the trade-offs between MDP rewards and receiver accuracy across various compression rates, showcasing the efficacy of our method compared to conventional compression baseline.

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central approach for improving the reasoning ability of large language models. Recent work studies RLVR through token entropy, arguing that high-entropy tokens drive exploration and should receive stronger updates. However, they overlook the fact that most of a reasoning trajectory consists of low-entropy segments that encode stable and reusable structural patterns. Through qualitative and quantitative analyses, we find that the overlap of low-entropy segments across correct responses strongly correlates with model accuracy, while overlaps involving incorrect responses exhibit stable but unproductive patterns. Motivated by these findings, we propose LESS, a correctness-aware reinforcement framework that performs fine-grained advantage modulation over low-entropy segments. LESS amplifies segments unique to correct responses, suppresses those unique to incorrect ones, and neutralizes segments shared by both, while preserving high-entropy exploration in the underlying RL algorithm. Instantiated on top of the popular GRPO, LESS consistently improves accuracy over strong RL baselines across three backbones and six math benchmarks, achieves stronger robustness of the performance floor.

Reinforcement learning with verifiable rewards (RLVR) has recently emerged as the leading approach for enhancing the reasoning capabilities of large language models (LLMs). However, RLVR is prone to entropy collapse, where the LLM quickly converges to a near-deterministic form, hindering exploration and progress during prolonged RL training. In this work, we reveal that the clipping mechanism in PPO and GRPO induces biases on entropy. Through theoretical and empirical analyses, we show that clip-low increases entropy, while clip-high decreases it. Further, under standard clipping parameters, the effect of clip-high dominates, resulting in an overall entropy reduction even when purely random rewards are provided to the RL algorithm. Our findings highlight an overlooked confounding factor in RLVR: independent of the reward signal, the clipping mechanism influences entropy, which in turn affects the reasoning behavior. Furthermore, our analysis demonstrates that clipping can be deliberately used to control entropy. Specifically, with a more aggressive clip-low value, one can increase entropy, promote exploration, and ultimately prevent entropy collapse in RLVR training.

In long-horizon tasks, recent agents based on Large Language Models (LLMs) face a significant challenge that sparse, outcome-based rewards make it difficult to assign credit to intermediate steps. Previous methods mainly focus on creating dense reward signals to guide learning, either through traditional reinforcement learning techniques like inverse reinforcement learning or by using Process Reward Models for step-by-step feedback. In this paper, we identify a fundamental problem in the learning dynamics of LLMs: the magnitude of policy gradients is inherently coupled with the entropy, which leads to inefficient small updates for confident correct actions and potentially destabilizes large updates for uncertain ones. To resolve this, we propose Entropy-Modulated Policy Gradients (EMPG), a framework that re-calibrates the learning signal based on step-wise uncertainty and the final task outcome. EMPG amplifies updates for confident correct actions, penalizes confident errors, and attenuates updates from uncertain steps to stabilize exploration. We further introduce a bonus term for future clarity that encourages agents to find more predictable solution paths. Through comprehensive experiments on three challenging agent tasks, WebShop, ALFWorld, and Deep Search, we demonstrate that EMPG achieves substantial performance gains and significantly outperforms strong policy gradient baselines. Project page is at https://empgseed-seed.github.io/

Large language models (LLMs) are increasingly deployed as multi-step decision-making agents, where effective reward design is essential for guiding learning. Although recent work explores various forms of reward shaping and step-level credit assignment, a key signal remains largely overlooked: the intrinsic uncertainty of LLMs. Uncertainty reflects model confidence, reveals where exploration is needed, and offers valuable learning cues even in failed trajectories. We introduce SELAUR: Self Evolving LLM Agent via Uncertainty-aware Rewards, a reinforcement learning framework that incorporates uncertainty directly into the reward design. SELAUR integrates entropy-, least-confidence-, and margin-based metrics into a combined token-level uncertainty estimate, providing dense confidence-aligned supervision, and employs a failure-aware reward reshaping mechanism that injects these uncertainty signals into step- and trajectory-level rewards to improve exploration efficiency and learning stability. Experiments on two benchmarks, ALFWorld and WebShop, show that our method consistently improves success rates over strong baselines. Ablation studies further demonstrate how uncertainty signals enhance exploration and robustness.

Reinforcement learning (RL) plays a crucial role in shaping the behavior of large language and reasoning models (LLMs/LRMs). However, it often produces brittle and unstable policies, leading to critical failures such as spurious reasoning, deceptive alignment, and instruction disobedience that undermine the trustworthiness and safety of LLMs/LRMs. Currently, these issues lack a unified theoretical explanation and are typically addressed using ad-hoc heuristics. This paper presents a rigorous mathematical framework for analyzing the stability of the mapping from a reward function to the optimal policy. We show that policy brittleness often stems from non-unique optimal actions, a common occurrence when multiple valid traces exist in a reasoning task. This theoretical lens provides a unified explanation for a range of seemingly disparate failures, reframing them as rational outcomes of optimizing rewards that may be incomplete or noisy, especially in the presence of action degeneracy. We extend this analysis from the fundamental single-reward setting to the more realistic multi-reward RL across diverse domains, showing how stability is governed by an "effective reward" aggregation mechanism. We also prove that entropy regularization restores policy stability at the cost of increased stochasticity. Our framework provides a unified explanation for recent empirical findings on deceptive reasoning, instruction-following trade-offs, and RLHF-induced sophistry, and is further validated through perturbation experiments in multi-reward RL. This work advances policy-stability analysis from empirical heuristics towards a principled theory, offering essential insights for designing safer and more trustworthy AI systems.

Joint-embedding predictive architectures (JEPAs) propose that a model should learn more useful abstractions when trained to predict latent representations rather than observed outputs. For autoregressive language-model fine-tuning the principle entails a stricter requirement: the induced hidden-state geometry must reach the language-model head and improve the decoded task metric. We test that requirement under a fixed Llama-3.2-1B-Instruct LoRA harness on natural-language-to-regex generation, comparing twenty-two training-time auxiliaries across trajectory-shape regularisation, distributional constraints, predictor/target asymmetry, Fisher-metric Jacobi residuals, and a decoder-visible JEPA objective constructed to lie in cross-entropy's positive cone. The empirical answer is a structured null: several auxiliaries clear single-cell paired α= 0.10 without correction (T3-Local at Δ= +2.53~pp, p = 0.003 being the strongest), but none survives Bonferroni or Holm--Bonferroni at the relevant family-wise threshold, even though many change curvature, anisotropy, variance, and gradient direction. Decoder-visible JEPA yields the first positive auxiliary--cross-entropy gradient cosine in the study, yet exact match remains inside seed noise; a full-fine-tuning replication of the same auxiliary at n = 5 seeds reproduces the null on both benchmarks (TURK: Δ= +0.04~pp, p_{paired} = 0.96; SYNTH: Δ= +0.52~pp, p_{paired} = 0.28), so the null is robust across LoRA and full fine-tuning for the decoder-visible construction. Hidden-state representation work and decoded-task accuracy are therefore weakly coupled in this regime; we accordingly reframe LLM-domain JEPA evaluation as a coupling problem, in which the operative question is under which metrics useful hidden geometry becomes decoder-visible task signal.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful approach to enhancing the reasoning capabilities of Large Language Models (LLMs), while its mechanisms are not yet well understood. In this work, we undertake a pioneering exploration of RLVR through the novel perspective of token entropy patterns, comprehensively analyzing how different tokens influence reasoning performance. By examining token entropy patterns in Chain-of-Thought (CoT) reasoning, we observe that only a small fraction of tokens exhibit high entropy, and these tokens act as critical forks that steer the model toward diverse reasoning pathways. Furthermore, studying how entropy patterns evolve during RLVR training reveals that RLVR largely adheres to the base model's entropy patterns, primarily adjusting the entropy of high-entropy tokens. These findings highlight the significance of high-entropy tokens (i.e., forking tokens) to RLVR. We ultimately improve RLVR by restricting policy gradient updates to forking tokens and uncover a finding even beyond the 80/20 rule: utilizing only 20% of the tokens while maintaining performance comparable to full-gradient updates on the Qwen3-8B base model and significantly surpassing full-gradient updates on the Qwen3-32B (+11.04 on AIME'25 and +7.71 on AIME'24) and Qwen3-14B (+4.79 on AIME'25 and +5.21 on AIME'24) base models, highlighting a strong scaling trend. In contrast, training exclusively on the 80% lowest-entropy tokens leads to a marked decline in performance. These findings indicate that the efficacy of RLVR primarily arises from optimizing the high-entropy tokens that decide reasoning directions. Collectively, our results highlight the potential to understand RLVR through a token-entropy perspective and optimize RLVR by leveraging high-entropy minority tokens to further improve LLM reasoning.

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.

Realistic and diverse traffic simulation is essential to autonomous driving development. Yet prevailing benchmarks predominantly reward realism, and recent methods have optimized accordingly, leaving diversity underexplored. We introduce Flow-ERD, a multi-agent simulator that pursues realism and diversity jointly. Its backbone, Agent-Type Aware Flow Matching (AFM), couples flow matching's multi-modal expressiveness with type-specific kinematic execution. It preserves fine-grained diversity while keeping motions consistent with each agent type. A second stage, Entropy-Regularized Distillation (ERD), fine-tunes the closed-loop rollout distribution with an entropy-regularized reverse-KL objective. This mitigates covariate shift while explicitly preventing collapse onto high-density modes. We evaluate Flow-ERD with a log-free diversity metric alongside standard realism scores. Flow-ERD ranks first on the WOSAC test benchmark and dominates the realism--diversity Pareto front among reproducible baselines. Our project page is available https://seulbinhwang.github.io/flow-erd-project-page/{here}.

We present a discriminative multimodal reward model that scores all candidate responses in a single forward pass. Conventional discriminative reward models evaluate each response independently, requiring multiple forward passes, one for each potential response. Our approach concatenates multiple responses with separator tokens and applies cross-entropy over their scalar scores, enabling direct comparative reasoning and efficient N-way preference learning. The multi-response design also yields up to Ntimes wall-clock speedup and FLOPs reduction over conventional single-response scoring. To enable N-way reward evaluation beyond existing pairwise benchmarks, we construct two new benchmarks: (1) MR^2Bench-Image contains human-annotated rankings over responses from 8 diverse models; (2) MR^2Bench-Video is a large-scale video-based reward benchmark derived from 94K crowdsourced pairwise human judgments over video question-answering spanning 19 models, denoised via preference graph ensemble. Both benchmarks provide 4-response evaluation variants sampled from the full rankings. Built on a 4B vision-language backbone with LoRA fine-tuning and a lightweight MLP value head, our model achieves state-of-the-art results on six multimodal reward benchmarks, including MR^2Bench-Image, MR^2Bench-Video, and four other existing benchmarks. Our model outperforms existing larger generative and discriminative reward models. We further demonstrate that our reward model, when used in reinforcement learning with GRPO, produces improved policy models that maintain performance across standard multimodal benchmarks while substantially improving open-ended generation quality, outperforming a single-response discriminative reward model (RM) baseline by a large margin in both training stability and open-ended generation quality.

Recent advances in reinforcement learning (RL) have significantly improved the complex reasoning capabilities of large language models (LLMs). Despite these successes, existing methods mainly focus on single-domain RL (e.g., mathematics) with verifiable rewards (RLVR), and their reliance on purely online RL frameworks restricts the exploration space, thereby limiting reasoning performance. In this paper, we address these limitations by leveraging rubrics to provide both fine-grained reward signals and offline guidance. We propose RGR-GRPO (Reward and Guidance through Rubrics), a rubric-driven RL framework for multi-domain reasoning. RGR-GRPO enables LLMs to receive dense and informative rewards while exploring a larger solution space during GRPO training. Extensive experiments across 14 benchmarks spanning multiple domains demonstrate that RGR-GRPO consistently outperforms RL methods that rely solely on alternative reward schemes or offline guidance. Compared with verifiable online RL baseline, RGR-GRPO achieves average improvements of +7.0%, +5.4%, +8.4%, and +6.6% on mathematics, physics, chemistry, and general reasoning tasks, respectively. Notably, RGR-GRPO maintains stable entropy fluctuations during off-policy training and achieves superior pass@k performance, reflecting sustained exploration and effective breakthrough beyond existing performance bottlenecks.

We introduce Entropy-Guided Sequence Weighting (EGSW), a novel approach that enhances the exploration-exploitation tradeoff by dynamically assigning weights to generated outputs based on their advantage and entropy for Reinforcement Learning-based Large Language Model fine-tuning. EGSW integrates entropy regularization with advantage-based weighting to balance policy updates, enabling efficient exploration in high-dimensional state spaces. By employing temperature-scaled softmax weighting over sequences, EGSW prioritizing high-reward, high-uncertainty steps while maintaining training stability. Although originally developed to improve Group Relative Policy Optimization (GRPO) during large language model (LLM) fine-tuning, EGSW is generalizable to other reinforcement learning (RL) algorithms and can be implemented in both step-wise and trajectory-wise settings. Empirical evaluations demonstrate that EGSW enhances GRPO reasoning ability, yielding improvements in sample efficiency. Future work will explore the application of EGSW to advanced RL methodologies.

Recent advances in Reinforcement Learning with Verified Reward (RLVR) have driven the emergence of more sophisticated cognitive behaviors in large language models (LLMs), thereby enhancing their reasoning capabilities. However, in prior RLVR pipelines, the repeated use of static initial-state sampling drawn exactly from the dataset distribution during each sampling phase produced overly deterministic, low diversity model behavior, which manifested as rapid entropy collapse and hindered sustained performance gains during prolonged training. To address this issue, we introduce CURE (Critical-token-gUided Re concatenation for Entropy-collapse prevention), a two-stage framework that balances exploration and exploitation. Specifically, in the first stage, to deliberately steer the model toward novel yet coherent contexts, we re-generate at high-entropy critical tokens and jointly optimize the original and the branched trajectories. The further comparison with vanilla DAPO shows that the regeneration process achieves a better performance on math reasoning tasks while sustaining a high-level entropy degree for exploration. In the second stage, we continue training with static initial-state sampling by DAPO, intentionally placing the model in a familiar state to gradually strengthen exploitation. Extensive experiments on Qwen-2.5-Math-7B show that, compared to other RLVR methods, CURE achieves a 5% performance gain across six math benchmarks, establishing state-of-the-art performance in both entropy and accuracy. A series of experiments further validate the effectiveness of our approach. Code is available at https://github.com/bytedance/CURE.

In the post-training of large language models (LLMs), Reinforcement Learning from Human Feedback (RLHF) is an effective approach to achieve generation aligned with human preferences. Direct Preference Optimization (DPO) allows for policy training with a simple binary cross-entropy loss without a reward model. The objective of DPO is regularized by reverse KL divergence that encourages mode-seeking fitting to the reference policy. Nonetheless, we indicate that minimizing reverse KL divergence could fail to capture a mode of the reference distribution, which may hurt the policy's performance. Based on this observation, we propose a simple modification to DPO, H-DPO, which allows for control over the entropy of the resulting policy, enhancing the distribution's sharpness and thereby enabling mode-seeking fitting more effectively. In our experiments, we show that H-DPO outperformed DPO across various tasks, demonstrating superior results in pass@k evaluations for mathematical tasks. Moreover, H-DPO is simple to implement, requiring only minor modifications to the loss calculation of DPO, which makes it highly practical and promising for wide-ranging applications in the training of LLMs.

When deploying artificial agents in real-world environments where they interact with humans, it is crucial that their behavior is aligned with the values, social norms or other requirements of that environment. However, many environments have implicit constraints that are difficult to specify and transfer to a learning agent. To address this challenge, we propose a novel method that utilizes the principle of maximum causal entropy to learn constraints and an optimal policy that adheres to these constraints, using demonstrations of agents that abide by the constraints. We prove convergence in a tabular setting and provide an approximation which scales to complex environments. We evaluate the effectiveness of the learned policy by assessing the reward received and the number of constraint violations, and we evaluate the learned cost function based on its transferability to other agents. Our method has been shown to outperform state-of-the-art approaches across a variety of tasks and environments, and it is able to handle problems with stochastic dynamics and a continuous state-action space.

Intelligent creatures can explore their environments and learn useful skills without supervision. In this paper, we propose DIAYN ('Diversity is All You Need'), a method for learning useful skills without a reward function. Our proposed method learns skills by maximizing an information theoretic objective using a maximum entropy policy. On a variety of simulated robotic tasks, we show that this simple objective results in the unsupervised emergence of diverse skills, such as walking and jumping. In a number of reinforcement learning benchmark environments, our method is able to learn a skill that solves the benchmark task despite never receiving the true task reward. We show how pretrained skills can provide a good parameter initialization for downstream tasks, and can be composed hierarchically to solve complex, sparse reward tasks. Our results suggest that unsupervised discovery of skills can serve as an effective pretraining mechanism for overcoming challenges of exploration and data efficiency in reinforcement learning.

Reinforcement Learning from Verifiable Rewards (RLVR) improves the reasoning abilities of Large Language Models (LLMs) but it struggles with unstable exploration. We propose FR3E (First Return, Entropy-Eliciting Explore), a structured exploration framework that identifies high-uncertainty decision points in reasoning trajectories and performs targeted rollouts to construct semantically grounded intermediate feedback. Our method provides targeted guidance without relying on dense supervision. Empirical results on mathematical reasoning benchmarks(AIME24) show that FR3E promotes more stable training, produces longer and more coherent responses, and increases the proportion of fully correct trajectories. These results highlight the framework's effectiveness in improving LLM reasoning through more robust and structured exploration.

Reinforcement Learning with Verifiable Rewards algorithms like GRPO have emerged as the dominant post-training paradigm for complex reasoning in LLMs, yet commonly suffer from policy entropy collapse during training. We conduct a first-order gradient analysis of token-level entropy dynamics under GRPO and identify a token-level credit assignment mismatch: the per-token entropy variation decomposes into the product of the trajectory-level advantage and an entropy sensitivity function over the next-token distribution, yielding an advantage-surprisal four-quadrant structure and a near-criticality property. Motivated by it, we propose STARE (Surprisal-guided Token-level Advantage Reweighting for policy Entropy stability), which identifies entropy-critical token subsets via batch-internal surprisal quantiles, selectively reweights their effective advantages, and incorporates a target-entropy closed-loop gate for stable entropy regulation. Across model scales from 1.5B to 32B and three task families (Short CoT, Long CoT, and Multi-Turn Tool Use), STARE sustains stable RL training over thousands of steps while maintaining policy entropy within the target band. On AIME24 and AIME25, STARE outperforms DAPO and other competitive baselines by 4%-8% in average accuracy, with reflection tokens and response length growing in tandem, indicating sustained exploration-exploitation balance that further unlocks RL training potential.Code is available at https://github.com/hp-luo/STARE.

Reinforcement Learning with Verifiable Rewards has recently advanced the capabilities of Large Language Models in complex reasoning tasks by providing explicit rule-based supervision. Among RLVR methods, GRPO and its variants have achieved strong empirical performance. Despite their success, we identify that they suffer from Gradient Misassignment in Positives and Gradient Domination in Negatives, which lead to inefficient and suboptimal policy updates. To address these issues, we propose Rewards as Labels (REAL), a novel framework that revisits verifiable rewards as categorical labels rather than scalar weights, thereby reformulating policy optimization as a classification problem. Building on this, we further introduce anchor logits to enhance policy learning. Our analysis reveals that REAL induces a monotonic and bounded gradient weighting, enabling balanced gradient allocation across rollouts and effectively mitigating the identified mismatches. Extensive experiments on mathematical reasoning benchmarks show that REAL improves training stability and consistently outperforms GRPO and strong variants such as DAPO. On the 1.5B model, REAL improves average Pass@1 over DAPO by 6.7%. These gains further scale to 7B model, REAL continues to outperform DAPO and GSPO by 6.2% and 1.7%, respectively. Notably, even with a vanilla binary cross-entropy, REAL remains stable and exceeds DAPO by 4.5% on average.

Optimization (PPO) has been positioned by recent literature as the canonical method for the RL part of RLHF. PPO performs well empirically but has a heuristic motivation and handles the KL-divergence constraint used in LM-RLHF in an ad-hoc manner and suffers form reward oscillations, entropy collapse, value function drift, and sudden policy divergence that require frequent restarts and extensive hyperparameter tuning. In this paper, we develop a new pure on policy actor-critic RL method for the LM-RLHF setting. We present SAFE (Stable Alignment Finetuning with Entropy-aware control),a novel RLHF algorithm that combines a Double Soft-Min Critic for pessimistic value estimation with a new multi-layer stabilization framework combining entropy-gated KL regulation, and PID-controlled adaptive thresholds. Unlike standard PPO's symmetric KL penalties, SAFE distinguishes high-entropy exploration from low-entropy mode collapse and adjusts penalties dynamically based on reward velocity. Experiments on a 3B parameter model show SAFE achieves +5.15\% training-average reward than PPO (0.725 vs 0.689), negligible reward crashes, and superior KL control than ppo . Our method adds minimal computational overhead and provides an interpretable, crash-resistant RLHF framework that maintains aggressive learning speed while ensuring stable long-horizon optimization suitable for production deployment. Code is available at https://github.com/ryyzn9/SAFE

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for enhancing reasoning in Large Language Models (LLMs). However, it frequently encounters challenges such as entropy collapse, excessive verbosity, and insufficient exploration for hard problems. Crucially, existing reward schemes fail to distinguish between the need for extensive search during problem-solving and the efficiency required for mastered knowledge. In this work, we introduce T2T(Thickening-to-Thinning), a dynamic reward framework inspired by human learning processes. Specifically, it implements a dual-phase mechanism: (1) On incorrect attempts, T2T incentivizes "thickening" (longer trajectories) to broaden the search space and explore novel solution paths; (2) Upon achieving correctness, it shifts to "thinning", imposing length penalties to discourage redundancy, thereby fostering model confidence and crystallizing reasoning capabilities. Extensive experiments on mathematical benchmarks (MATH-500, AIME, AMC) across Qwen-series and Deepseek models demonstrate that T2T significantly outperforms standard GRPO and recent baselines, achieving superior performance.

Process Reward Modeling (PRM) is critical for complex reasoning and decision-making tasks where the accuracy of intermediate steps significantly influences the overall outcome. Existing PRM approaches, primarily framed as classification problems, employ cross-entropy loss to independently evaluate each step's correctness. This method can lead to suboptimal reward distribution and does not adequately address the interdependencies among steps. To address these limitations, we introduce the Process Q-value Model (PQM), a novel framework that redefines PRM in the context of a Markov Decision Process. PQM optimizes Q-value rankings based on a novel comparative loss function, enhancing the model's ability to capture the intricate dynamics among sequential decisions. This approach provides a more granular and theoretically grounded methodology for process rewards. Our extensive empirical evaluations across various sampling policies, language model backbones, and multi-step reasoning benchmarks show that PQM outperforms classification-based PRMs. The effectiveness of the comparative loss function is highlighted in our comprehensive ablation studies, confirming PQM's practical efficacy and theoretical advantage.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful framework for improving the reasoning abilities of Large Language Models (LLMs). However, current methods such as GRPO rely only on problems where the model responses to the same input differ in correctness, while ignoring those where all responses receive the same reward - so-called zero-variance prompts. In this work, we argue that such prompts are not useless but can, in fact, provide meaningful feedback for policy optimization. To this end, we introduce RL with Zero-Variance Prompts (RL-ZVP), a novel algorithm that extract learning signals from zero-variance prompts. RL-ZVP directly rewards correctness and penalizes errors even without contrasting responses, modulating feedback with token-level characteristics to preserve informative, nuanced signals. Across six math reasoning benchmarks, RL-ZVP achieves significant improvements of up to 8.61 points in accuracy and 7.77 points in pass rate over GRPO, while consistently outperforming other baselines that filter out zero-variance prompts. These results highlight the untapped potential of learning from zero-variance prompts in RLVR.

Reinforcement learning (RL) has enabled machine learning models to achieve significant advances in many fields. Most recently, RL has empowered frontier language models to solve challenging math, science, and coding problems. However, central to any RL algorithm is the reward function, and reward engineering is a notoriously difficult problem in any domain. In this paper, we propose RENT: Reinforcement Learning via Entropy Minimization -- a fully unsupervised RL method that requires no external reward or ground-truth answers, and instead uses the model's entropy of its underlying distribution as an intrinsic reward. We find that by reinforcing the chains of thought that yield high model confidence on its generated answers, the model improves its reasoning ability. In our experiments, we showcase these improvements on an extensive suite of commonly-used reasoning benchmarks, including GSM8K, MATH500, AMC, AIME, and GPQA, and models of varying sizes from the Qwen, Mistral, and Llama families. The generality of our unsupervised learning method lends itself to applicability in a wide range of domains where external supervision is unavailable.

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.

Reinforcement learning (RL) has substantially improved the ability of large language model (LLM) agents to interact with environments and solve multi-turn tasks. However, effective agentic RL remains challenging: sparse outcome-only rewards provide limited guidance for assigning credit to individual steps within long interaction trajectories. Existing approaches often introduce dense intermediate supervision, such as process reward models or auxiliary self-supervised signals, which increases supervision and tuning complexity and may limit generalization across tasks and domains. We present AEM, a supervision-free credit assignment method that adaptively modulates entropy dynamics during RL training to improve the exploration-exploitation trade-off. Since in agentic RL the environment is typically affected by a complete response, rather than an individual token, our analysis lifts entropy dynamics from the token level to the response level, aligning uncertainty estimation with the effective action granularity of LLM agents and reducing sensitivity to token-level sampling noise. We further show that entropy drift under natural-gradient updates is governed by the interaction between the sampled-response advantage and its relative surprisal. Motivated by this result, AEM derives a practical response-level uncertainty proxy and uses it to rescale advantages, leveraging the evolving balance between positive and negative samples to naturally transition from exploration to exploitation. Extensive experiments on ALFWorld, WebShop, and SWE-bench-Verified with models ranging from 1.5B to 32B demonstrate that AEM consistently improves strong RL baselines, including a +1.4\% gain when integrated into a state-of-the-art software-engineering RL training framework.

Reinforcement learning algorithms are fundamental to align large language models with human preferences and to enhance their reasoning capabilities. However, current reinforcement learning algorithms often suffer from training instability due to loose on-policy constraints and computational inefficiency due to auxiliary models. In this work, we propose On-Policy RL with Optimal reward baseline (OPO), a novel and simplified reinforcement learning algorithm designed to address these challenges. OPO emphasizes the importance of exact on-policy training, which empirically stabilizes the training process and enhances exploration. Moreover, OPO introduces the optimal reward baseline that theoretically minimizes gradient variance. We evaluate OPO on mathematical reasoning benchmarks. The results demonstrate its superior performance and training stability without additional models or regularization terms. Furthermore, OPO achieves lower policy shifts and higher output entropy, encouraging more diverse and less repetitive responses. These results highlight OPO as a promising direction for stable and effective reinforcement learning in large language model alignment and reasoning tasks. The implementation is provided at https://github.com/microsoft/LMOps/tree/main/opo.

Reinforcement learning (RL) can improve the prompt following capability of text-to-image (T2I) models, yet obtaining high-quality reward signals remains challenging: CLIP Score is too coarse-grained, while VLM-based reward models (e.g., RewardDance) require costly human-annotated preference data and additional fine-tuning. We propose PromptEcho, a reward construction method that requires no annotation and no reward model training. Given a generated image and a guiding query, PromptEcho computes the token-level cross-entropy loss of a frozen VLM with the original prompt as the label, directly extracting the image-text alignment knowledge encoded during VLM pretraining. The reward is deterministic, computationally efficient, and improves automatically as stronger open-source VLMs become available. For evaluation, we develop DenseAlignBench, a benchmark of concept-rich dense captions for rigorously testing prompt following capability. Experimental results on two state-of-the-art T2I models (Z-Image and QwenImage-2512) demonstrate that PromptEcho achieves substantial improvements on DenseAlignBench (+26.8pp / +16.2pp net win rate), along with consistent gains on GenEval, DPG-Bench, and TIIFBench without any task-specific training. Ablation studies confirm that PromptEcho comprehensively outperforms inference-based scoring with the same VLM, and that reward quality scales with VLM size. We will open-source the trained models and the DenseAlignBench.

Large language models (LLMs) and multimodal LLMs (MLLMs) excel at chain-of-thought reasoning but face distribution shift at test-time and a lack of verifiable supervision. Recent test-time reinforcement learning (TTRL) methods derive label-free pseudo-rewards from self-consistency voting over sampled trajectories, yet they often collapse: the majority-vote reward prevails, responses shorten, and Pass@1 declines. We trace this to uniform sequence updates in which most tokens are low-entropy followers, while a small high-entropy subset determines the reasoning branches. Thus we propose SPINE, a token-selective test-time reinforcement learning framework that (i) updates only forking tokens, the high-entropy branch points identified from forward-pass statistics, and (ii) applies an entropy-band regularizer at those tokens to sustain exploration when entropy is too low and to suppress noisy supervision when it is too high. SPINE plugs into GRPO-style objectives, optionally with a KL anchor, and requires no labels or reward models. Across ten benchmarks spanning multimodal VQA, general and expert QA, mathematical reasoning, and medical QA, SPINE consistently improves Pass@1 over TTRL while avoiding response-length collapse and yielding more stable training dynamics on both LLM and MLLM backbones. These results indicate that aligning updates with chain-of-thought branch points is a simple and label-free mechanism for stable and effective test-time adaptation in reasoning models. Code is available at https://github.com/JianghaoWu/SPINE.

Current visual evaluation approaches are typically constrained to a single task. To address this, we propose OmniQuality-R, a unified reward modeling framework that transforms multi-task quality reasoning into continuous and interpretable reward signals for policy optimization. Inspired by subjective experiments, where participants are given task-specific instructions outlining distinct assessment principles prior to evaluation, we propose OmniQuality-R, a structured reward modeling framework that transforms multi-dimensional reasoning into continuous and interpretable reward signals. To enable this, we construct a reasoning-enhanced reward modeling dataset by sampling informative plan-reason trajectories via rejection sampling, forming a reliable chain-of-thought (CoT) dataset for supervised fine-tuning (SFT). Building on this, we apply Group Relative Policy Optimization (GRPO) for post-training, using a Gaussian-based reward to support continuous score prediction. To further stabilize the training and improve downstream generalization, we incorporate standard deviation (STD) filtering and entropy gating mechanisms during reinforcement learning. These techniques suppress unstable updates and reduce variance in policy optimization. We evaluate OmniQuality-R on three key IQA tasks: aesthetic quality assessment, technical quality evaluation, and text-image alignment.

Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally expensive or lack calibration. We propose a three-stage pipeline to post-train LLMs to efficiently infer calibrated uncertainty estimates for their responses. First, we compute fine-grained entropy-based uncertainty scores on the training data, capturing the distributional variability of model outputs in embedding space. Second, these scores are calibrated via Platt scaling, producing reliable and human-interpretable uncertainty signals. Finally, the target LLM is post-trained via reinforcement learning to align its policy with these calibrated signals through a verifiable reward function. Unlike post-hoc uncertainty estimation methods, our approach provides interpretable and computationally efficient uncertainty estimates at test time. Experiments show that models trained with our pipeline achieve better calibration than baselines and generalize to unseen tasks without further processing, suggesting that they learn a robust uncertainty reasoning behavior.

One fascinating aspect of pre-trained vision-language models~(VLMs) learning under language supervision is their impressive zero-shot generalization capability. However, this ability is hindered by distribution shifts between the training and testing data. Previous test time adaptation~(TTA) methods for VLMs in zero-shot classification rely on minimizing the entropy of model outputs, tending to be stuck in incorrect model predictions. In this work, we propose TTA with feedback to rectify the model output and prevent the model from becoming blindly confident. Specifically, a CLIP model is adopted as the reward model during TTA and provides feedback for the VLM. Given a single test sample, the VLM is forced to maximize the CLIP reward between the input and sampled results from the VLM output distribution. The proposed reinforcement learning with CLIP feedback~(RLCF) framework is highly flexible and universal. Beyond the classification task, with task-specific sampling strategies and a proper reward baseline choice, RLCF can be easily extended to not only discrimination tasks like retrieval but also generalization tasks like image captioning, improving the zero-shot generalization capacity of VLMs. According to the characteristics of these VL tasks, we build different fully TTA pipelines with RLCF to improve the zero-shot generalization ability of various VLMs. Extensive experiments along with promising empirical results demonstrate the effectiveness of RLCF. The code is available at https://github.com/mzhaoshuai/RLCF.

Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an implicit PRM can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models, which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline \'a la Math-Shepherd using less than 1/38 of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.

Reasoning ability has become a defining capability of Large Language Models (LLMs), with Reinforcement Learning with Verifiable Rewards (RLVR) emerging as a key paradigm to enhance it. However, RLVR training often suffers from policy entropy collapse, where the policy becomes overly deterministic, hindering exploration and limiting reasoning performance. While entropy regularization is a common remedy, its effectiveness is highly sensitive to the fixed coefficient, making it unstable across tasks and models. In this work, we revisit entropy regularization in RLVR and argue that its potential has been largely underestimated. Our analysis shows that (i) tasks of varying difficulty demand distinct exploration intensities, and (ii) balanced exploration may require the policy entropy to be maintained within a moderate range below its initial level. Therefore, we propose Adaptive Entropy Regularization (AER)--a framework that dynamically balances exploration and exploitation via three components: difficulty-aware coefficient allocation, initial-anchored target entropy, and dynamic global coefficient adjustment. Experiments on multiple mathematical reasoning benchmarks show that AER consistently outperforms baselines, improving both reasoning accuracy and exploration capability.

Large language models are typically post-trained using supervised fine-tuning (SFT) and reinforcement learning (RL), yet effectively unifying efficient knowledge injection with robust generalization remains challenging. In this work, we provide a training-dynamics analysis showing that SFT can be interpreted as a special case of policy gradient optimization with an extremely sparse implicit reward and unstable inverse-probability weighting, which together lead to single-path dependency, entropy collapse, and gradient explosion. Motivated by this diagnosis, we propose Group Fine-Tuning (GFT), a unified post-training framework that addresses these intrinsic limitations through two mechanisms: Group Advantage Learning, which constructs diverse response groups and derives normalized contrastive supervision to alleviate reward sparsity, and Dynamic Coefficient Rectification, which adaptively bounds inverse-probability weights to stabilize optimization while preserving efficient knowledge injection. Experiments demonstrate that GFT consistently surpasses SFT-based methods and yields policies that integrate more smoothly with subsequent RL training.

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts Entropy-Driven Advantage and Guided Error Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.

Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs) performance on challenging math, physics, and coding tasks. We explore three approaches: (1) EM-FT minimizes token-level entropy similarly to instruction finetuning, but on unlabeled outputs drawn from the model; (2) EM-RL: reinforcement learning with negative entropy as the only reward to maximize; (3) EM-INF: inference-time logit adjustment to reduce entropy without any training data or parameter updates. On Qwen-7B, EM-RL, without any labeled data, achieves comparable or better performance than strong RL baselines such as GRPO and RLOO that are trained on 60K labeled examples. Furthermore, EM-INF enables Qwen-32B to match or exceed the performance of proprietary models like GPT-4o, Claude 3 Opus, and Gemini 1.5 Pro on the challenging SciCode benchmark, while being 3x more efficient than self-consistency and sequential refinement. Our findings reveal that many pretrained LLMs possess previously underappreciated reasoning capabilities that can be effectively elicited through entropy minimization alone, without any labeled data or even any parameter updates.

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

Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an off-policy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy. That is, to succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as Q-learning methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.

We trained 13,440 large language models and found that entropy minimization requires only a single unlabeled data and 10 steps optimization to achieve performance improvements comparable to or even greater than those obtained using thousands of data and carefully designed rewards in rule-based reinforcement learning. This striking result may prompt a rethinking of post-training paradigms for large language models. Our code is avaliable at https://github.com/zitian-gao/one-shot-em.

Entropy-based deep reasoning has emerged as a promising direction for improving the reasoning capabilities of Large Language Models (LLMs), but existing methods often either increase response length indiscriminately or shorten responses at the cost of accuracy. To better balance this trade-off, we introduce Conditional Entropy Shaping (CES), a framework that dynamically controls token-level response entropy, enabling LLMs to produce concise solutions on simple problems while encouraging deeper exploration on hard ones. Built on DAPO, CES uses token-level entropy as an uncertainty signal and applies a conditional bidirectional policy: it penalizes high-entropy "forking point" tokens on correct reasoning paths to improve conciseness, and rewards them on incorrect paths to encourage exploration and error correction. We implement CES on DeepSeek-R1-Distill-7B and evaluate it on 12 mathematical benchmarks. CES consistently improves average accuracy while reducing response length relative to DAPO, and supplementary experiments show similar trends on a smaller 1.5B backbone and on out-of-domain benchmarks.

Recent reasoning-first models (e.g., OpenAI o1, DeepSeek R1) have spurred a resurgence of interest in RLVR. Nevertheless, advances are dominated by mathematics (e.g., AIME), with competitive-programming code generation underexplored and data curation receiving less attention than RL algorithm design. We investigate how to construct RLVR datasets (i.e., RL prompts) and present practical training techniques that yield strong performance on competitive-programming code generation. Our pipeline begins with supervised fine-tuning (SFT) distilled from strong open-source models, augmented with general-purpose and reasoning-intensive data. RL then follows a two-stage process with executable, testcase-driven rewards: first, training on a large, uniformly distributed set of competitive-programming problems using Group Relative Policy Optimization (GRPO) with 8 rollouts per prompt and a relatively short response-generation window (e.g., 32k during SFT and 24k in this stage) to expand entropy and mitigate repetition and truncation; second, we perform Pre-GRPO: updating on a small, high-quality set of challenging problems with a large rollout budget (64 rollouts per prompt) under a hard-focus curriculum that continuously retains the most difficult instances throughout training. We implement our method on Qwen2.5-32B and evaluate on LeetCode and Codeforces weekly contests to avoid data leakage. The resulting model achieves state-of-the-art performance among models of similar scale and is comparable to leading systems such as DeepSeek v3.1 and Doubao-1.5-Thinking. We also examine scaling trends and observe strong RL scaling on an internal large-scale MoE model. Our study distills concise best practices for data curation, entropy expansion, and curriculum design in RLVR for competitive-programming code generation.

Reinforcement learning (RL) has been effective for post-training autoregressive (AR) language models, but extending these methods to diffusion language models (DLMs) is challenging due to intractable sequence-level likelihoods. Existing approaches therefore rely on surrogate likelihoods or heuristic approximations, which can introduce bias and obscure the sequential structure of denoising. We formulate diffusion-based sequence generation as a finite-horizon Markov decision process over the denoising trajectory and derive an exact, unbiased policy gradient that decomposes over denoising steps and is expressed in terms of intermediate advantages, without requiring explicit evaluation of the sequence likelihood. To obtain a practical and compute-efficient estimator, we (i) select denoising steps for policy updates via an entropy-guided approximation bound, and (ii) estimate intermediate advantages using a one-step denoising reward naturally provided by the diffusion model, avoiding costly multi-step rollouts. Experiments on coding and logical reasoning benchmarks demonstrate state-of-the-art results, with strong competitive performance on mathematical reasoning, outperforming existing RL post-training approaches for DLMs. Code is available at https://github.com/vishnutez/egspo-dllm-rl.

The varying significance of distinct primitive behaviors during the policy learning process has been overlooked by prior model-free RL algorithms. Leveraging this insight, we explore the causal relationship between different action dimensions and rewards to evaluate the significance of various primitive behaviors during training. We introduce a causality-aware entropy term that effectively identifies and prioritizes actions with high potential impacts for efficient exploration. Furthermore, to prevent excessive focus on specific primitive behaviors, we analyze the gradient dormancy phenomenon and introduce a dormancy-guided reset mechanism to further enhance the efficacy of our method. Our proposed algorithm, ACE: Off-policy Actor-critic with Causality-aware Entropy regularization, demonstrates a substantial performance advantage across 29 diverse continuous control tasks spanning 7 domains compared to model-free RL baselines, which underscores the effectiveness, versatility, and efficient sample efficiency of our approach. Benchmark results and videos are available at https://ace-rl.github.io/.

Although RLVR has become an essential component for developing advanced reasoning skills in LLMs, contemporary studies have documented training plateaus that emerge following thousands of optimization steps, demonstrating notable decreases in performance gains despite increased computational investment. This limitation stems from the sparse exploration patterns inherent in current RLVR practices, where models rely on limited rollouts that often miss critical reasoning paths and fail to provide systematic coverage of the solution space. We present DeepSearch, a framework that integrates Monte Carlo Tree Search directly into RLVR training. In contrast to existing methods that rely on tree search only at inference, DeepSearch embeds structured search into the training loop, enabling systematic exploration and fine-grained credit assignment across reasoning steps. Through training-time exploration, DeepSearch addresses the fundamental bottleneck of insufficient exploration, which leads to diminishing performance improvements over prolonged training steps. Our contributions include: (1) a global frontier selection strategy that prioritizes promising nodes across the search tree, (2) selection with entropy-based guidance that identifies confident paths for supervision, and (3) adaptive replay buffer training with solution caching for efficiency. Experiments on mathematical reasoning benchmarks show that DeepSearch achieves 62.95% average accuracy and establishes a new state-of-the-art for 1.5B reasoning models - using 5.7x fewer GPU hours than extended training approaches. These results highlight the importance of strategic exploration over brute-force scaling and demonstrate the promise of algorithmic innovation for advancing RLVR methodologies. DeepSearch establishes a new direction for scaling reasoning capabilities through systematic search rather than prolonged computation.

Chain-of-Thought (CoT) has substantially empowered Large Language Models (LLMs) to tackle complex reasoning tasks, yet the verbose nature of explicit reasoning steps incurs prohibitive inference latency and computational costs, limiting real-world deployment. While existing compression methods - ranging from self-training to Reinforcement Learning (RL) with length constraints - attempt to mitigate this, they often sacrifice reasoning capability for brevity. We identify a critical failure mode in these approaches: explicitly optimizing for shorter trajectories triggers rapid entropy collapse, which prematurely shrinks the exploration space and stifles the discovery of valid reasoning paths, particularly for challenging questions requiring extensive deduction. To address this issue, we propose Compress responses for Easy questions and Explore Hard ones (CEEH), a difficulty-aware approach to RL-based efficient reasoning. CEEH dynamically assesses instance difficulty to apply selective entropy regularization: it preserves a diverse search space for currently hard questions to ensure robustness, while permitting aggressive compression on easier instances where the reasoning path is well-established. In addition, we introduce a dynamic optimal-length penalty anchored to the historically shortest correct response, which effectively counteracts entropy-induced length inflation and stabilizes the reward signal. Across six reasoning benchmarks, CEEH consistently reduces response length while maintaining accuracy comparable to the base model, and improves Pass@k relative to length-only optimization.

Most unified large multimodal models (LMMs) that support both visual understanding and image generation still rely on curated post-training supervision, such as human annotations, preference labels, or external reward models. We ask whether a unified LMM can improve both abilities autonomously using only unlabeled images. We propose a self-evolving training framework with three internal roles: a Proposer that generates visual questions, a Solver that answers and evaluates them, and a Generator that synthesizes images. Training uses only self-derived consistency signals, without human annotations, preference labels, or task-trained external reward/judge models. To stabilize learning, we introduce Solver Token Entropy (STE), a continuous difficulty signal based on token-level prediction uncertainty that remains useful even when sample-level consistency becomes unreliable. For image generation, we design a multi-scale internal evaluation scheme that combines question-answer fidelity scoring with cycle-consistent captioning. This creates a solver-mediated coupling, where better visual understanding enables more reliable generation assessment and stronger internal training signals. The framework preserves the same role decomposition, reward logic, and training schedule across diffusion-based BLIP3o, rectified-flow BAGEL, and autoregressive VARGPT-v1.1 architectures, requiring only each backbone's native prompting and generation interface. Across eight understanding metrics, our method consistently improves over the corresponding base models. On BAGEL, it achieves a +3.5% absolute gain on MMMU and improves GenEval image generation performance from 82% to 85%. Code and models are publicly released.

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

Reinforcement learning (RL) is the dominant paradigm for sharpening strategic tool use capabilities of LLMs on long-horizon, sparsely-rewarded agent tasks, yet it faces a fundamental challenge of exploration-exploitation trade-off. Existing studies stimulate exploration through the lens of policy entropy, but such mechanical entropy maximization is prone to RL training instability due to the multi-turn distribution shifting. In this paper, we target the progressive exploration-exploitation balance under the guidance of the agent own experiences without succumbing to either entropy collapsing or runaway divergence. We propose SPEAR, a curriculum-based self-imitation learning (SIL) recipe for training agentic LLMs. It extends the vanilla SIL framework, where a replay buffer stores self-generated promising trajectories for off-policy update, by gradually steering the policy evolution within a well-balanced range of entropy across stages. Specifically, our approach incorporates a curriculum to manage the exploration process, utilizing intrinsic rewards to foster skill-level exploration and facilitating action-level exploration through SIL. At first, the auxiliary tool call reward plays a critical role in the accumulation of tool-use skills, enabling broad exposure to the unfamiliar distributions of the environment feedback with an upward entropy trend. As training progresses, self-imitation gets strengthened to exploit existing successful patterns from replayed experiences for comparative action-level exploration, accelerating solution iteration without unbounded entropy growth. To further stabilize training, we recalibrate the advantages of experiences in the replay buffer to address the potential policy drift. Reugularizations such as the clipping of tokens with high covariance between probability and advantage are introduced to the trajectory-level entropy control to curb over-confidence.

Entropy serves as a critical metric for measuring the diversity of outputs generated by large language models (LLMs), providing valuable insights into their exploration capabilities. While recent studies increasingly focus on monitoring and adjusting entropy to better balance exploration and exploitation in reinforcement fine-tuning (RFT), a principled understanding of entropy dynamics during this process is yet to be thoroughly investigated. In this paper, we establish a theoretical framework for analyzing the entropy dynamics during the RFT process, which begins with a discriminant expression that quantifies entropy change under a single logit update. This foundation enables the derivation of a first-order expression for entropy change, which can be further extended to the update formula of Group Relative Policy Optimization (GRPO). The corollaries and insights drawn from the theoretical analysis inspire the design of entropy control methods, and also offer a unified lens for interpreting various entropy-based methods in existing studies. We provide empirical evidence to support the main conclusions of our analysis and demonstrate the effectiveness of the derived entropy-discriminator clipping methods. This study yields novel insights into RFT training dynamics, providing theoretical support and practical strategies for optimizing the exploration-exploitation balance during LLM fine-tuning.

Reinforcement learning (RL) algorithms aim to balance exploiting the current best strategy with exploring new options that could lead to higher rewards. Most common RL algorithms use undirected exploration, i.e., select random sequences of actions. Exploration can also be directed using intrinsic rewards, such as curiosity or model epistemic uncertainty. However, effectively balancing task and intrinsic rewards is challenging and often task-dependent. In this work, we introduce a framework, MaxInfoRL, for balancing intrinsic and extrinsic exploration. MaxInfoRL steers exploration towards informative transitions, by maximizing intrinsic rewards such as the information gain about the underlying task. When combined with Boltzmann exploration, this approach naturally trades off maximization of the value function with that of the entropy over states, rewards, and actions. We show that our approach achieves sublinear regret in the simplified setting of multi-armed bandits. We then apply this general formulation to a variety of off-policy model-free RL methods for continuous state-action spaces, yielding novel algorithms that achieve superior performance across hard exploration problems and complex scenarios such as visual control tasks.

Finding meaningful and accurate dense rewards is a fundamental task in the field of reinforcement learning (RL) that enables agents to explore environments more efficiently. In traditional RL settings, agents learn optimal policies through interactions with an environment guided by reward signals. However, when these signals are sparse, delayed, or poorly aligned with the intended task objectives, agents often struggle to learn effectively. Dense reward functions, which provide informative feedback at every step or state transition, offer a potential solution by shaping agent behavior and accelerating learning. Despite their benefits, poorly crafted reward functions can lead to unintended behaviors, reward hacking, or inefficient exploration. This problem is particularly acute in complex or high-dimensional environments where handcrafted rewards are difficult to specify and validate. To address this, recent research has explored a variety of approaches, including inverse reinforcement learning, reward modeling from human preferences, and self-supervised learning of intrinsic rewards. While these methods offer promising directions, they often involve trade-offs between generality, scalability, and alignment with human intent. This proposal explores several approaches to dealing with these unsolved problems and enhancing the effectiveness and reliability of dense reward construction in different RL applications.

Reinforcement learning usually uses the feedback rewards of environmental to train agents. But the rewards in the actual environment are sparse, and even some environments will not rewards. Most of the current methods are difficult to get good performance in sparse reward or non-reward environments. Although using shaped rewards is effective when solving sparse reward tasks, it is limited to specific problems and learning is also susceptible to local optima. We propose a model-free method that does not rely on environmental rewards to solve the problem of sparse rewards in the general environment. Our method use the minimum number of transitions between states as the distance to replace the rewards of environmental, and proposes a goal-distance gradient to achieve policy improvement. We also introduce a bridge point planning method based on the characteristics of our method to improve exploration efficiency, thereby solving more complex tasks. Experiments show that our method performs better on sparse reward and local optimal problems in complex environments than previous work.

Balancing exploration and exploitation is a central goal in reinforcement learning (RL). Despite recent advances in enhancing language model (LM) reasoning, most methods lean toward exploitation, and increasingly encounter performance plateaus. In this work, we revisit entropy -- a signal of exploration in RL -- and examine its relationship to exploratory reasoning in LMs. Through empirical analysis, we uncover strong positive correlations between high-entropy regions and three types of exploratory reasoning actions: (1) pivotal tokens that determine or connect logical steps, (2) reflective actions such as self-verification and correction, and (3) rare behaviors under-explored by the base LMs. Motivated by this, we introduce a minimal modification to standard RL with only one line of code: augmenting the advantage function with an entropy-based term. Unlike traditional maximum-entropy methods which encourage exploration by promoting uncertainty, we encourage exploration by promoting longer and deeper reasoning chains. Notably, our method achieves significant gains on the Pass@K metric -- an upper-bound estimator of LM reasoning capabilities -- even when evaluated with extremely large K values, pushing the boundaries of LM reasoning.

Let p denote a generative language model. Let r denote a reward model that returns a scalar that captures the degree at which a draw from p is preferred. The goal of language model alignment is to alter p to a new distribution phi that results in a higher expected reward while keeping phi close to p. A popular alignment method is the KL-constrained reinforcement learning (RL), which chooses a distribution phi_Delta that maximizes E_{phi_{Delta}} r(y) subject to a relative entropy constraint KL(phi_Delta || p) leq Delta. Another simple alignment method is best-of-N, where N samples are drawn from p and one with highest reward is selected. In this paper, we offer a closed-form characterization of the optimal KL-constrained RL solution. We demonstrate that any alignment method that achieves a comparable trade-off between KL divergence and reward must approximate the optimal KL-constrained RL solution in terms of relative entropy. To further analyze the properties of alignment methods, we introduce two simplifying assumptions: we let the language model be memoryless, and the reward model be linear. Although these assumptions may not reflect complex real-world scenarios, they enable a precise characterization of the asymptotic behavior of both the best-of-N alignment, and the KL-constrained RL method, in terms of information-theoretic quantities. We prove that the reward of the optimal KL-constrained RL solution satisfies a large deviation principle, and we fully characterize its rate function. We also show that the rate of growth of the scaled cumulants of the reward is characterized by a proper Renyi cross entropy. Finally, we show that best-of-N is asymptotically equivalent to KL-constrained RL solution by proving that their expected rewards are asymptotically equal, and concluding that the two distributions must be close in KL divergence.

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) for Large Language Model (LLM) reasoning have been hindered by a persistent challenge: exploration collapse. The semantic homogeneity of random rollouts often traps models in narrow, over-optimized behaviors. While existing methods leverage policy entropy to encourage exploration, they face inherent limitations. Global entropy regularization is susceptible to reward hacking, which can induce meaningless verbosity, whereas local token-selective updates struggle with the strong inductive bias of pre-trained models. To address this, we propose Latent Policy Optimization via Iterative Information Bottleneck (IIB-LPO), a novel approach that shifts exploration from statistical perturbation of token distributions to topological branching of reasoning trajectories. IIB-LPO triggers latent branching at high-entropy states to diversify reasoning paths and employs the Information Bottleneck principle both as a trajectory filter and a self-reward mechanism, ensuring concise and informative exploration. Empirical results across four mathematical reasoning benchmarks demonstrate that IIB-LPO achieves state-of-the-art performance, surpassing prior methods by margins of up to 5.3% in accuracy and 7.4% in diversity metrics.

Exploration in sparse reward environments remains one of the key challenges of model-free reinforcement learning. Instead of solely relying on extrinsic rewards provided by the environment, many state-of-the-art methods use intrinsic rewards to encourage exploration. However, we show that existing methods fall short in procedurally-generated environments where an agent is unlikely to visit a state more than once. We propose a novel type of intrinsic reward which encourages the agent to take actions that lead to significant changes in its learned state representation. We evaluate our method on multiple challenging procedurally-generated tasks in MiniGrid, as well as on tasks with high-dimensional observations used in prior work. Our experiments demonstrate that this approach is more sample efficient than existing exploration methods, particularly for procedurally-generated MiniGrid environments. Furthermore, we analyze the learned behavior as well as the intrinsic reward received by our agent. In contrast to previous approaches, our intrinsic reward does not diminish during the course of training and it rewards the agent substantially more for interacting with objects that it can control.

Large Language Models (LLMs) are increasingly deployed in business-critical domains such as finance, education, healthcare, and customer support, where users expect consistent and reliable recommendations. Yet LLMs often exhibit variability when prompts are phrased with minor differences, even when semantically equivalent. Such inconsistency undermines trust, complicates compliance, and disrupts user experience. While personalization is desirable in certain contexts, many enterprise scenarios-such as HR onboarding, customer support, or policy disclosure-require invariant information delivery regardless of phrasing or prior conversational history. Existing approaches, including retrieval-augmented generation (RAG) and temperature tuning, improve factuality or reduce stochasticity but cannot guarantee stability across equivalent prompts. In this paper, we propose a reinforcement learning framework based on Group Relative Policy Optimization (GRPO) to directly optimize for consistency. Unlike prior applications of GRPO, which have been limited to reasoning and code generation, we adapt GRPO to enforce stability of information content across groups of semantically equivalent prompts. We introduce entropy-based helpfulness and stability rewards, treating prompt variants as groups and resetting conversational context to isolate phrasing effects. Experiments on investment and job recommendation tasks show that our GRPO-trained model reduces variability more effectively than fine-tuning or decoding-based baselines. To our knowledge, this is a novel application of GRPO for aligning LLMs toward information consistency, reframing variability not as an acceptable feature of generative diversity but as a correctable flaw in enterprise deployments.

Reinforcement learning (RL) has become essential for post-training large language models (LLMs) in reasoning tasks. While scaling rollouts can stabilize training and enhance performance, the computational overhead is a critical issue. In algorithms like GRPO, multiple rollouts per prompt incur prohibitive costs, as a large portion of prompts provide negligible gradients and are thus of low utility. To address this problem, we investigate how to select high-utility prompts before the rollout phase. Our experimental analysis reveals that sample utility is non-uniform and evolving: the strongest learning signals concentrate at the ``learning edge", the intersection of intermediate difficulty and high uncertainty, which shifts as training proceeds. Motivated by this, we propose HIVE (History-Informed and online-VErified prompt selection), a dual-stage framework for data-efficient RL. HIVE utilizes historical reward trajectories for coarse selection and employs prompt entropy as a real-time proxy to prune instances with stale utility. By evaluating HIVE across multiple math reasoning benchmarks and models, we show that HIVE yields significant rollout efficiency without compromising performance.

Extrinsic rewards can effectively guide reinforcement learning (RL) agents in specific tasks. However, extrinsic rewards frequently fall short in complex environments due to the significant human effort needed for their design and annotation. This limitation underscores the necessity for intrinsic rewards, which offer auxiliary and dense signals and can enable agents to learn in an unsupervised manner. Although various intrinsic reward formulations have been proposed, their implementation and optimization details are insufficiently explored and lack standardization, thereby hindering research progress. To address this gap, we introduce RLeXplore, a unified, highly modularized, and plug-and-play framework offering reliable implementations of eight state-of-the-art intrinsic reward methods. Furthermore, we conduct an in-depth study that identifies critical implementation details and establishes well-justified standard practices in intrinsically-motivated RL. Our documentation, examples, and source code are available at https://github.com/RLE-Foundation/RLeXplore.

Automatically synthesizing dense rewards from natural language descriptions is a promising paradigm in reinforcement learning (RL), with applications to sparse reward problems, open-ended exploration, and hierarchical skill design. Recent works have made promising steps by exploiting the prior knowledge of large language models (LLMs). However, these approaches suffer from important limitations: they are either not scalable to problems requiring billions of environment samples, due to requiring LLM annotations for each observation, or they require a diverse offline dataset, which may not exist or be impossible to collect. In this work, we address these limitations through a combination of algorithmic and systems-level contributions. We propose \oni, a distributed architecture that simultaneously learns an RL policy and an intrinsic reward function using LLM feedback. Our approach annotates the agent's collected experience via an asynchronous LLM server, which is then distilled into an intrinsic reward model. We explore a range of algorithmic choices for reward modeling with varying complexity, including hashing, classification, and ranking models. By studying their relative tradeoffs, we shed light on questions regarding intrinsic reward design for sparse reward problems. Our approach achieves state-of-the-art performance across a range of challenging, sparse reward tasks from the NetHack Learning Environment in a simple unified process, solely using the agent's gathered experience, without requiring external datasets. We make our code available at https://github.com/facebookresearch/oni.

The Sachdev-Ye-Kitaev (SYK) model, known for its strong quantum correlations and chaotic behavior, serves as a key platform for quantum gravity studies. However, variationally preparing thermal states on near-term quantum processors for large systems (N>12, where N is the number of Majorana fermions) presents a significant challenge due to the rapid growth in the complexity of parameterized quantum circuits. This paper addresses this challenge by integrating reinforcement learning (RL) with convolutional neural networks, employing an iterative approach to optimize the quantum circuit and its parameters. The refinement process is guided by a composite reward signal derived from entropy and the expectation values of the SYK Hamiltonian. This approach reduces the number of CNOT gates by two orders of magnitude for systems Ngeq12 compared to traditional methods like first-order Trotterization. We demonstrate the effectiveness of the RL framework in both noiseless and noisy quantum hardware environments, maintaining high accuracy in thermal state preparation. This work advances a scalable, RL-based framework with applications for quantum gravity studies and out-of-time-ordered thermal correlators computation in quantum many-body systems on near-term quantum hardware. The code is available at https://github.com/Aqasch/solving_SYK_model_with_RL.

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) have empowered large language models (LLMs) to tackle challenging reasoning tasks such as mathematics and programming. RLVR leverages verifiable outcome rewards to guide policy optimization, enabling LLMs to progressively improve output quality in a grounded and reliable manner. Despite its promise, the RLVR paradigm poses significant challenges, as existing methods often suffer from sparse reward signals and unstable policy gradient updates, particularly in RL-based approaches. To address the challenges, we propose PACS, a novel RLVR framework that achieves imPlicit Actor Critic coupling via a Supervised learning framework. By treating the outcome reward as a predictable label, we reformulate the RLVR problem into a supervised learning task over a score function parameterized by the policy model and optimized using cross-entropy loss. A detailed gradient analysis shows that this supervised formulation inherently recovers the classical policy gradient update while implicitly coupling actor and critic roles, yielding more stable and efficient training. Benchmarking on challenging mathematical reasoning tasks, PACS outperforms strong RLVR baselines, such as PPO and GRPO, achieving superior reasoning performance. For instance, PACS achieves 59.78\% at pass@256 on AIME 2025, representing improvements of 13.32 and 14.36 points over PPO and GRPO. This simple yet powerful framework offers a promising avenue for LLMs post-training with verifiable rewards. Our code and data are available as open source at https://github.com/ritzz-ai/PACS.

Large language models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks. However, existing approaches mainly rely on imitation learning and struggle to achieve effective test-time scaling. While reinforcement learning (RL) holds promise for enabling self-exploration and learning from feedback, recent attempts yield only modest improvements in complex reasoning. In this paper, we present T1 to scale RL by encouraging exploration and understand inference scaling. We first initialize the LLM using synthesized chain-of-thought data that integrates trial-and-error and self-verification. To scale RL training, we promote increased sampling diversity through oversampling. We further employ an entropy bonus as an auxiliary loss, alongside a dynamic anchor for regularization to facilitate reward optimization. We demonstrate that T1 with open LLMs as its base exhibits inference scaling behavior and achieves superior performance on challenging math reasoning benchmarks. For example, T1 with Qwen2.5-32B as the base model outperforms the recent Qwen QwQ-32B-Preview model on MATH500, AIME2024, and Omni-math-500. More importantly, we present a simple strategy to examine inference scaling, where increased inference budgets directly lead to T1's better performance without any additional verification. We will open-source the T1 models and the data used to train them at https://github.com/THUDM/T1.

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.

Reading text from images or scanned documents via OCR models has been a longstanding focus of researchers. Intuitively, text reading is perceived as a straightforward perceptual task, and existing work primarily focuses on constructing enriched data engineering to enhance SFT capabilities. In this work, we observe that even advanced OCR models exhibit significantly higher entropy in formatted text (e.g., formula, table, etc.) compared to plain text, often by an order of magnitude. These statistical patterns reveal that advanced OCR models struggle with high output uncertainty when dealing with format sensitive document, suggesting that reasoning over diverse reading pathways may improve OCR performance. To address this, we propose format decoupled reinforcement learning (FD-RL), which leverages high-entropy patterns for targeted optimization. Our approach employs entropy-based data filtration strategy to identify format-intensive instances, and adopt format decoupled rewards tailored to different format types, enabling format-level validation rather than token-level memorization. FD-RL achieves an average score of 90.41 on OmniDocBench, setting a new record for end-to-end models on this highly popular benchmark. More importantly, we conduct comprehensive ablation studies over data, training, filtering, and rewarding strategies, thoroughly validating their effectiveness.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a popular paradigm for aligning models with human intent. Typically RLHF algorithms operate in two phases: first, use human preferences to learn a reward function and second, align the model by optimizing the learned reward via reinforcement learning (RL). This paradigm assumes that human preferences are distributed according to reward, but recent work suggests that they instead follow the regret under the user's optimal policy. Thus, learning a reward function from feedback is not only based on a flawed assumption of human preference, but also leads to unwieldy optimization challenges that stem from policy gradients or bootstrapping in the RL phase. Because of these optimization challenges, contemporary RLHF methods restrict themselves to contextual bandit settings (e.g., as in large language models) or limit observation dimensionality (e.g., state-based robotics). We overcome these limitations by introducing a new family of algorithms for optimizing behavior from human feedback using the regret-based model of human preferences. Using the principle of maximum entropy, we derive Contrastive Preference Learning (CPL), an algorithm for learning optimal policies from preferences without learning reward functions, circumventing the need for RL. CPL is fully off-policy, uses only a simple contrastive objective, and can be applied to arbitrary MDPs. This enables CPL to elegantly scale to high-dimensional and sequential RLHF problems while being simpler than prior methods.

Reinforcement learning with verifiable rewards (RLVR) for Large Reasoning Models hinges on baseline estimation for variance reduction, but existing approaches pay a heavy price: PPO requires a policy-model scale critic, while GRPO needs multiple rollouts per prompt to keep its empirical group mean stable. We introduce Policy Optimization with Internal State Value Estimation), which obtains a baseline at negligible cost by using the policy model's internal signals already computed during the policy forward pass. A lightweight probe predicts the expected verifiable reward from the hidden states of the prompt and generated trajectory, as well as token-entropy statistics, and is trained online alongside the policy. To preserve gradient unbiasedness despite using trajectory-conditioned features, we introduce a cross-rollout construction that predicts each rollout's value from an independent rollout's internal states. Because POISE estimates prompt value using only a single rollout, it enables higher prompt diversity for a fixed compute budget during training. This reduces gradient variance for more stable learning and also eliminates the compute overhead of sampling costs for detecting zero-advantage prompts. On Qwen3-4B and DeepSeek-R1-Distill-Qwen-1.5B across math reasoning benchmarks, POISE matches DAPO while requiring less compute. Moreover, its value estimator shows similar performance to a separate LLM-scale value model and generalizes to various verifiable tasks. By leveraging the model's own internal representations, POISE enables more stable and efficient policy optimization.

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

Recent vision-language models (VLMs) achieve remarkable reasoning through reinforcement learning (RL), which provides a feasible solution for realizing continuous self-evolving large vision-language models (LVLMs) in the era of experience. However, RL for VLMs requires abundant high-quality multimodal data, especially challenging in specialized domains like chemistry, earth sciences, and multimodal mathematics. Existing strategies such as synthetic data and self-rewarding mechanisms suffer from limited distributions and alignment difficulties, ultimately causing reward hacking: models exploit high-reward patterns, collapsing policy entropy and destabilizing training. We propose DoGe (Decouple to Generalize), a dual-decoupling framework that guides models to first learn from context rather than problem solving by refocusing on the problem context scenarios overlooked by synthetic data methods. By decoupling learning process into dual components (Thinker and Solver), we reasonably quantify the reward signals of this process and propose a two-stage RL post-training approach from freely exploring context to practically solving tasks. Second, to increase the diversity of training data, DoGe constructs an evolving curriculum learning pipeline: an expanded native domain knowledge corpus and an iteratively evolving seed problems pool. Experiments show that our method consistently outperforms the baseline across various benchmarks, providing a scalable pathway for realizing self-evolving LVLMs.

As trajectories sampled by policies used by reinforcement learning (RL) and generative flow networks (GFlowNets) grow longer, credit assignment and exploration become more challenging, and the long planning horizon hinders mode discovery and generalization. The challenge is particularly pronounced in entropy-seeking RL methods, such as generative flow networks, where the agent must learn to sample from a structured distribution and discover multiple high-reward states, each of which take many steps to reach. To tackle this challenge, we propose an approach to incorporate the discovery of action abstractions, or high-level actions, into the policy optimization process. Our approach involves iteratively extracting action subsequences commonly used across many high-reward trajectories and `chunking' them into a single action that is added to the action space. In empirical evaluation on synthetic and real-world environments, our approach demonstrates improved sample efficiency performance in discovering diverse high-reward objects, especially on harder exploration problems. We also observe that the abstracted high-order actions are interpretable, capturing the latent structure of the reward landscape of the action space. This work provides a cognitively motivated approach to action abstraction in RL and is the first demonstration of hierarchical planning in amortized sequential sampling.

Reinforcement Learning with Verifiable Rewards (RLVR) has shown significant promise for enhancing the reasoning capabilities of large language models (LLMs). However, prevailing algorithms like GRPO broadcast a uniform advantage signal across all tokens in a sequence. This coarse-grained approach overlooks the pivotal role of uncertain, high-stakes decisions during reasoning, leading to inefficient exploration and the well-documented problem of entropy collapse. To address this, we introduce UnCertainty-aware Advantage Shaping (UCAS), a model-free method that refines credit assignment by leveraging the model's internal uncertainty signals. UCAS operates in two stages: it first modulates the response-level advantage using the model's overall self-confidence, and then applies a token-level penalty based on raw logit certainty. This dual mechanism encourages exploration of high-uncertainty paths that yield correct answers while penalizing overconfident yet erroneous reasoning, effectively balancing the exploration-exploitation trade-off. Extensive experiments on five mathematical reasoning benchmarks show that UCAS significantly outperforms strong RLVR baselines across multiple model scales, including 1.5B and 7B. Our analysis confirms that UCAS not only achieves higher rewards but also promotes greater reasoning diversity and successfully mitigates entropy collapse.

Exploration is essential for solving complex Reinforcement Learning (RL) tasks. Maximum State-Visitation Entropy (MSVE) formulates the exploration problem as a well-defined policy optimization problem whose solution aims at visiting all states as uniformly as possible. This is in contrast to standard uncertainty-based approaches where exploration is transient and eventually vanishes. However, existing approaches to MSVE are theoretically justified only for discrete state-spaces as they are oblivious to the geometry of continuous domains. We address this challenge by introducing Geometric Entropy Maximisation (GEM), a new algorithm that maximises the geometry-aware Shannon entropy of state-visits in both discrete and continuous domains. Our key theoretical contribution is casting geometry-aware MSVE exploration as a tractable problem of optimising a simple and novel noise-contrastive objective function. In our experiments, we show the efficiency of GEM in solving several RL problems with sparse rewards, compared against other deep RL exploration approaches.

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.

LLM agents have emerged as powerful systems for tackling multi-turn tasks by interleaving internal reasoning and external tool interactions. Agentic Reinforcement Learning has recently drawn significant research attention as a critical post-training paradigm to further refine these capabilities. In this paper, we present AT^2PO (Agentic Turn-based Policy Optimization via Tree Search), a unified framework for multi-turn agentic RL that addresses three core challenges: limited exploration diversity, sparse credit assignment, and misaligned policy optimization. AT^2PO introduces a turn-level tree structure that jointly enables Entropy-Guided Tree Expansion for strategic exploration and Turn-wise Credit Assignment for fine-grained reward propagation from sparse outcomes. Complementing this, we propose Agentic Turn-based Policy Optimization, a turn-level learning objective that aligns policy updates with the natural decision granularity of agentic interactions. ATPO is orthogonal to tree search and can be readily integrated into any multi-turn RL pipeline. Experiments across seven benchmarks demonstrate consistent improvements over the state-of-the-art baseline by up to 1.84 percentage points in average, with ablation studies validating the effectiveness of each component. Our code is available at https://github.com/zzfoutofspace/ATPO.

Post-training of large language models routinely interleaves supervised fine-tuning (SFT) with reinforcement learning (RL). These two methods have different objectives: SFT minimizes the cross-entropy loss between model outputs and expert responses, while RL maximizes reward signals derived from human preferences or rule-based verifiers. Modern reasoning models have widely adopted the practice of alternating SFT and RL training. However, there is no theoretical account of whether they can be decoupled. We prove that decoupling is impossible in either order: (1) SFT-then-RL coupling: RL increases SFT loss under SFT optimality and (2) RL-then-SFT coupling: SFT lowers the reward achieved by RL. Experiments on Qwen3-0.6B confirm the predicted degradation, verifying that SFT and RL cannot be separated without loss of prior performance in the post-training

Reinforcement Learning (RL) has emerged as a powerful tool for neural combinatorial optimization, enabling models to learn heuristics that solve complex problems without requiring expert knowledge. Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast combinatorial action spaces, leading to inefficiency. In this paper, we propose Preference Optimization, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling, emphasizing the superiority among sampled solutions. Methodologically, by reparameterizing the reward function in terms of policy and utilizing preference models, we formulate an entropy-regularized RL objective that aligns the policy directly with preferences while avoiding intractable computations. Furthermore, we integrate local search techniques into the fine-tuning rather than post-processing to generate high-quality preference pairs, helping the policy escape local optima. Empirical results on various benchmarks, such as the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP) and the Flexible Flow Shop Problem (FFSP), demonstrate that our method significantly outperforms existing RL algorithms, achieving superior convergence efficiency and solution quality.

Fast weight architectures offer a promising alternative to attention-based transformers for long-context modeling by maintaining constant memory overhead regardless of context length. However, their potential is limited by the next-token prediction (NTP) training paradigm. NTP optimizes single-token predictions and ignores semantic coherence across multiple tokens following a prefix. Consequently, fast weight models, which dynamically update their parameters to store contextual information, learn suboptimal representations that fail to capture long-range dependencies. We introduce REFINE (Reinforced Fast weIghts with Next sEquence prediction), a reinforcement learning framework that trains fast weight models under the next-sequence prediction (NSP) objective. REFINE selects informative token positions based on prediction entropy, generates multi-token rollouts, assigns self-supervised sequence-level rewards, and optimizes the model with group relative policy optimization (GRPO). REFINE is applicable throughout the training lifecycle of pre-trained language models: mid-training, post-training, and test-time training. Our experiments on LaCT-760M and DeltaNet-1.3B demonstrate that REFINE consistently outperforms supervised fine-tuning with NTP across needle-in-a-haystack retrieval, long-context question answering, and diverse tasks in LongBench. REFINE provides an effective and versatile framework for improving long-context modeling in fast weight architectures.

While advancements in the reasoning abilities of LLMs have significantly enhanced their performance in solving mathematical problems, coding tasks, and general puzzles, their effectiveness in accurately adhering to instructions remains inconsistent, particularly with more complex directives. Our investigation identifies lazy reasoning during the thinking stage as the primary factor contributing to poor instruction adherence. To mitigate this issue, we propose a comprehensive framework designed to enable rigorous reasoning processes involving preview and self-checking, essential for satisfying strict instruction constraints. Specifically, we first generate instructions with complex constraints and apply a filtering process to obtain valid prompts, resulting in three distinct prompt datasets categorized as hard, easy, and pass. Then, we employ rejection sampling on the pass prompts to curate a small yet high-quality dataset, enabling a cold-start initialization of the model and facilitating its adaptation to effective reasoning patterns. Subsequently, we employ an entropy-preserving supervised fine-tuning (Entropy-SFT) strategy coupled with token-wise entropy-adaptive (TEA-RL) reinforcement learning guided by rule-based dense rewards. This approach encourages the model to transform its reasoning mechanism, ultimately fostering generalizable reasoning abilities that encompass preview and self-checking. Extensive experiments conducted on instruction-following benchmarks demonstrate remarkable performance improvements across various model scales. Notably, our Light-IF-32B model surpasses both larger open-source models such as DeepSeek-R1 and closed-source models like Doubao-1.6.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). Unlike traditional RL approaches, RLVR leverages rule-based feedback to guide LLMs in generating and refining complex reasoning chains -- a process critically dependent on effective exploration strategies. While prior work has demonstrated RLVR's empirical success, the fundamental mechanisms governing LLMs' exploration behaviors remain underexplored. This technical report presents a systematic investigation of exploration capacities in RLVR, covering four main aspects: (1) exploration space shaping, where we develop quantitative metrics to characterize LLMs' capability boundaries; (2) entropy-performance exchange, analyzed across training stages, individual instances, and token-level patterns; and (3) RL performance optimization, examining methods to effectively translate exploration gains into measurable improvements. By unifying previously identified insights with new empirical evidence, this work aims to provide a foundational framework for advancing RLVR systems.

A significant amount of the world's knowledge is stored in relational databases. However, the ability for users to retrieve facts from a database is limited due to a lack of understanding of query languages such as SQL. We propose Seq2SQL, a deep neural network for translating natural language questions to corresponding SQL queries. Our model leverages the structure of SQL queries to significantly reduce the output space of generated queries. Moreover, we use rewards from in-the-loop query execution over the database to learn a policy to generate unordered parts of the query, which we show are less suitable for optimization via cross entropy loss. In addition, we will publish WikiSQL, a dataset of 80654 hand-annotated examples of questions and SQL queries distributed across 24241 tables from Wikipedia. This dataset is required to train our model and is an order of magnitude larger than comparable datasets. By applying policy-based reinforcement learning with a query execution environment to WikiSQL, our model Seq2SQL outperforms attentional sequence to sequence models, improving execution accuracy from 35.9% to 59.4% and logical form accuracy from 23.4% to 48.3%.

Entropy control has become an effective tool in reinforcement learning (RL) of large language models (LLMs), helping balance exploration-exploitation trade-off during alignment process. Such RL paradigm is often conducted on mixtures of heterogeneous tasks, which induce distinct entropy regimes under the same policy, making global or token-level entropy regulation insufficient to corresponding heterogeneous needs of exploration. This heterogeneity further makes GRPO-style normalized advantages induce an entropy-dependent bias, making advantage signals across prompt groups statistically non-comparable. To address this issue, we propose Group Entropy-Controlled Policy Optimization (GEPO), a lightweight extension to GRPO that uses group entropy, estimated from existing grouped samples to perform entropy-conditioned asymmetric advantage shaping. GEPO attenuates positive advantages in low-entropy groups to reduce over-exploitation, and negative advantages in high-entropy groups to preserve exploration, with adaptive thresholds derived from historical entropy statistics. Extensive experiments on two base models across thirteen benchmarks spanning mathematics, physics, science, code generation, and instruction following show that GEPO consistently outperforms GRPO and recent entropy-controlled methods, delivering balanced cross-task improvements while preserving task-specific exploration levels throughout training.

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid premature convergence to sub-optimal solutions. However, existing reinforcement learning methods struggle to maintain an appropriate level of entropy, as the training process involves a mix of positive and negative samples, each affecting entropy in different ways across steps. To address this, we propose Entropy stablilization via Proportional-Integral Control (EntroPIC), a novel method that adaptively adjusts the influence of positive and negative samples by dynamically tuning their loss coefficients. This approach stabilizes entropy throughout training, ensuring efficient exploration and steady progress. We provide a comprehensive theoretical analysis for both on-policy and off-policy learning settings, demonstrating that EntroPIC is effective at controlling entropy in large-scale LLM training. Experimental results show that our method successfully maintains desired entropy levels, enabling stable and optimal RL training for LLMs.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6%, and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7%. This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which includes the aforementioned example. Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples (many of which yield approximately 30% or greater improvement on MATH500 when employed as a single training example). In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-domain generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by adding entropy loss with an appropriate coefficient) in 1-shot RLVR training. As a bonus, we observe that applying entropy loss alone, without any outcome reward, significantly enhances Qwen2.5-Math-1.5B's performance on MATH500 by 27.4%. These findings can inspire future work on RLVR data efficiency and encourage a re-examination of both recent progress and the underlying mechanisms in RLVR. Our code, model, and data are open source at https://github.com/ypwang61/One-Shot-RLVR