Entropy Collapse in RL

Test-time reinforcement learning (TTRL) adapts a model without labels by rewarding answers that agree with the majority, but it collapses the policy onto its majority answer and can remove the correct answer from the samples. Exploration can prevent this collapse, yet its strength is chosen by trial and error, and how the training algorithm changes the required strength is unclear. We model training on a single problem as a continuous flow of the logits of a softmax policy and analyze which policies are stable as the exploration coefficient varies. Only collapsed policies are stable below a lower boundary and only policies spread over many answers above an upper boundary, and we derive these boundaries in closed form for an agreement reward with smoothing toward the uniform policy, compute them for the majority reward of TTRL on policies with one leading answer and bound them with interval arithmetic for actions on ordered bins. We prove that under exact gradients, the learning rate and, in a mean-field model, the normalization of GRPO leave these boundaries unchanged when exploration passes through them together with the reward but shift them when exploration bypasses them. Exact sums on these policies then show that a bonus for rare answers needs a coefficient above $1/\log(G-1)$ for groups of $G$ samples before the normalization and about two to three times that after it. In free-form TTRL on MATH-500, a bonus placed before the normalization prevented collapse and kept more correct answers among the samples, although it lowered pass@1.

Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning by scoring sampled responses with a rule-based verifier and reinforcing those that pass. Where a classifier's training couples predicted probability to labels, nothing ties an RLVR policy's confidence in a response to its reward: aligned training would drive responses with the same advantage toward equal confidence, yet the advantage is blind to confidence. Under this sequence-confidence misalignment, a success the policy barely found earns the same update as one it produces with near certainty, and a confident error is corrected no harder than an exploratory one. We propose SCARL (Sequence Confidence-Aligned Reinforcement Learning), which reshapes, but never re-signs, each advantage with the alignment gap between the response's group-relative confidence and the outcome its advantage certifies, normalized into shares of each class's advantage budget. Misaligned samples absorb the force, responses with the same advantage are driven toward equal confidence, and repairing the misalignment doubles as a remedy for the entropy collapse that erodes exploration. SCARL provably reduces to its base estimator when a class's confidences agree, adds no extra passes and one hyperparameter. On Qwen3-4B-Base it lifts average Pass@32 by 2.4 points over DAPO and is best among nine compute-matched methods on both coverage and per-draw accuracy; applied unchanged across four estimators and four backbones, it improves 14 of 16 settings while preserving policy entropy and widening the confidence-correctness separation. Our code is available at https://github.com/kezhh163/scarl.

Reinforcement learning (RL) methods such as GRPO substantially improve large language model reasoning but often suffer from policy entropy collapse: the loss of sampling diversity weakens exploration and limits further improvement. Existing methods address this issue either through algorithm-level interventions, such as reward modification and entropy/KL regularization, or through token-level reweighting. We investigate a complementary perspective: entropy collapse can also be mitigated by changing which generated rollouts contribute to policy updates. Under the same sampling budget, not all rollouts contribute positively to an update, and selectively excluding some can improve learning. To address this, we propose GRPODropout: before the standard update, we use a simple strategy that selectively removes a small number of high-probability positive-advantage rollouts and recenters the retained advantages. To motivate this design, we develop a rollout-level theoretical analysis that guides method design and threshold selection. The method changes only rollout usage, and adds negligible computational overhead. Experiments show higher accuracy than original GRPO and higher actor entropy while using fewer rollout samples for updates, illustrating "less is more." This work provides insight into RL rollout usage: removing some rollouts can improve performance. Code is available at https://github.com/hexuandeng/GRPODropout/.

While Reinforcement Learning (RL) effectively incentivizes reasoning in Large Language Models, current pipelines are hindered by training instability and rapid entropy collapse. These limitations often stem from "Rollout Silencing" and low-quality gradient signals in standard sampling procedures. In this work, we propose a robust, data-centric framework to stabilize RL training. We first introduce Potential-Aware Query Mining (PAQM), which filters data dynamically to focus on the "Distillation Zone"---samples with high potential for capability elicitation. Furthermore, we present Hybrid Stratified Replay (HSR), a novel mechanism that restructures batches by stratifying rollouts based on Path Entropy, a rollout-level confidence proxy, and outcome reward. Within each optimization step, HSR reuses current-policy "Stability Anchors" and "Hard Negatives" to construct high-contrast optimization groups, then clears its buffers before the next step. This approach mitigates entropy collapse while improving the utilization of learning signals under limited compute. Our method outperforms strong baselines on complex reasoning tasks, offering a principled solution for stable and efficient RL fine-tuning.

Reinforcement Learning with Verifiable Rewards (RLVR) significantly improves LLM reasoning but often causes a drop in policy entropy, leading to narrowed reasoning coverage and degraded pass@$k$ for large $k$. While existing methods mitigate this entropy collapse through algorithmic regularizations, cross-model non-parametric perturbation is also neglected. In this work, we propose a simple yet effective approach to preserve the generative diversity of LLMs during RLVR. Instead of relying solely on internal exploration, we force the target model to generate answers based on partial reasoning trajectories generated by a smaller, weaker language models. These unfamiliar prefixes effectively disrupt over-confidence and encourage the exploration of distinct reasoning paths. We empirically study the potential of outer prefixes, revealing the mechanism of the impact of distributional discrepancy to the exploration dynamics in RLVR training. Experiments across multiple mathematical benchmarks show that our method consistently outperforms vanilla RLVR. Notably, the performance gain becomes increasingly pronounced as $k$ scales up, demonstrating a substantial expansion of reasoning coverage. Furthermore, our approach efficiently mitigates entropy collapse without requiring additional SFT, intricate reward designs, or complex prompting.

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 (RLVR) has become an effective paradigm for improving the reasoning ability of large language models. However, widely used RLVR algorithms, such as GRPO, often suffer from entropy collapse, leading to premature determinism and unstable optimization. Existing remedies, including entropy regularization and ratio-based clipping heuristics, either control entropy in a coarse-grained manner or rely on approximate on-policy training. In this paper, we revisit entropy collapse from a token-level entropy flow perspective. Our analysis reveals that entropy-decreasing tokens consistently outweigh entropy-increasing ones, resulting in a severely imbalanced entropy flow. This perspective provides a unified explanation of entropy collapse in existing RLVR algorithms and highlights the importance of balancing entropy dynamics. Motivated by this analysis, we propose On-Policy Entropy Flow Optimization (OPEFO), an adaptive entropy flow balancing mechanism that rescales entropy-increasing and entropy-decreasing updates according to their contributions to entropy change, while remaining strict on-policy. Experiments on six mathematical reasoning benchmarks demonstrate that OPEFO improves training stability and final performance. We will release the code and models upon publication.

Reinforcement learning (RL) has enabled complex reasoning abilities in large language models (LLMs). However, most RL algorithms suffer from performance saturation, preventing continued gains as RL training scales. This problem can be characterized by the collapse of entropy, a key diagnostic for exploration in RL. Existing attempts focus on preventing entropy collapse through regularization or clipping. However, their resulting entropy curves often exhibit instability in the long term, which hinders performance gains. In this paper, we introduce Entrocraft, a simple rejection-sampling approach that realizes user-customized entropy schedule by biasing the advantage distributions. Entrocraft requires no objective regularization and is advantage-estimator-agnostic. Theoretically, we relate per-step entropy change to the advantage distribution under minimal assumptions. This explains the behavior of existing RL and entropy-preserving methods. Entrocraft also enables a systematic study of entropy schedules, which reveals that linear annealing, which starts high and decays to a slightly lower target, performs best. Empirically, Entrocraft addresses performance saturation, significantly improving generalization, output diversity, and long-term training. It enables a 4B model to outperform an 8B baseline, sustains improvement for up to 4x longer before plateauing, and raises pass@K by 50% over the baseline.

Recent advances in reinforcement learning (RL) have improved the reasoning capabilities of large language models (LLMs) and vision-language models (VLMs). However, the widely used Group Relative Policy Optimization (GRPO) consistently suffers from entropy collapse, causing the policy to converge prematurely and lose diversity. Existing exploration methods introduce additional bias or variance during exploration, making it difficult to maintain optimization stability. We propose Unified Entropy Control for Reinforcement Learning (UEC-RL), a framework that provides targeted mechanisms for exploration and stabilization. UEC-RL activates more exploration on difficult prompts to search for potential and valuable reasoning trajectories. In parallel, a stabilizer prevents entropy from growing uncontrollably, thereby keeping training stable as the model consolidates reliable behaviors. Together, these components expand the search space when needed while maintaining robust optimization throughout training. Experiments on both LLM and VLM reasoning tasks show consistent gains over RL baselines on both Pass@1 and Pass@$k$. On Geometry3K, UEC-RL achieves a 37.9% relative improvement over GRPO, indicating that it sustains effective exploration without compromising convergence and underscoring UEC-RL as a key for scaling RL-based reasoning in large models. Our code is available at https://github.com/597358816/UEC-RL.

Policy gradient algorithms have driven many recent advancements in language model reasoning. An appealing property is their ability to learn from exploration on their own trajectories, a process crucial for fostering diverse and creative solutions. As we show in this paper, many policy gradient algorithms naturally reduce the entropy -- and thus the diversity of explored trajectories -- as part of training, yielding a policy increasingly limited in its ability to explore. In this paper, we argue that entropy should be actively monitored and controlled throughout training. We formally analyze the contributions of leading policy gradient objectives on entropy dynamics, identify empirical factors (such as numerical precision) that significantly impact entropy behavior, and propose explicit mechanisms for entropy control. These include REPO, a family of algorithms that modify the advantage function to regulate entropy, and ADAPO, an adaptive asymmetric clipping approach. Models trained with our entropy-preserving methods maintain diversity throughout training, yielding final policies that are more performant and retain their trainability for sequential learning in new environments.

Reinforcement learning (RL) is a key paradigm for post-training large language models (LLMs), but the widely used Group Relative Policy Optimization (GRPO) often suffers from entropy collapse: exploration quickly disappears, policies converge prematurely, and sample diversity declines, ultimately harming training effectiveness. Existing remedies, including entropy bonuses and clip-based methods, rarely keep entropy within a stable exploration regime and often introduce oscillatory entropy or reward degradation. In this work, we identify a previously overlooked asymmetry in entropy dynamics: under high-temperature sampling, positive and negative samples have opposite effects on policy entropy. Specifically, high-temperature positive samples promote entropy growth, whereas negative samples suppress it. We provide a qualitative theoretical explanation for this phenomenon: when entropy decreases during policy updates, its derivative with respect to temperature is strictly positive under positive sample updates, indicating that high-temperature positive samples can counteract entropy decay, thereby slowing entropy collapse and potentially reversing it. Motivated by this insight, we propose SCOPE-RL, a stable entropy control framework through a regularization term constructed from temperature-adaptive positive samples. Extensive experiments show that SCOPE-RL consistently outperforms strong RL baselines on both Pass@1 and Pass@k. Our results provide evidence that escaping entropy collapse can improve reasoning performance, while our quantitative empirical analysis further reveals a non-monotonic entropy-performance relationship, with an optimal level of exploration for RL post-training in reasoning LLMs. Our code is available at https://github.com/597358816/SCOPE-RL.

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.