Entropy polarity from a first-order entropy change approximation enables Polarity-Aware Policy Optimization (PAPO) that preserves complementary polarity branches and outperforms baselines on math and agentic RL fine-tuning tasks.
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The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models
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abstract
This paper aims to overcome a major obstacle in scaling RL for reasoning with LLMs, namely the collapse of policy entropy. Such phenomenon is consistently observed across vast RL runs without entropy intervention, where the policy entropy dropped sharply at the early training stage, this diminished exploratory ability is always accompanied with the saturation of policy performance. In practice, we establish a transformation equation R=-a*e^H+b between entropy H and downstream performance R. This empirical law strongly indicates that, the policy performance is traded from policy entropy, thus bottlenecked by its exhaustion, and the ceiling is fully predictable H=0, R=-a+b. Our finding necessitates entropy management for continuous exploration toward scaling compute for RL. To this end, we investigate entropy dynamics both theoretically and empirically. Our derivation highlights that, the change in policy entropy is driven by the covariance between action probability and the change in logits, which is proportional to its advantage when using Policy Gradient-like algorithms. Empirical study shows that, the values of covariance term and entropy differences matched exactly, supporting the theoretical conclusion. Moreover, the covariance term stays mostly positive throughout training, further explaining why policy entropy would decrease monotonically. Through understanding the mechanism behind entropy dynamics, we motivate to control entropy by restricting the update of high-covariance tokens. Specifically, we propose two simple yet effective techniques, namely Clip-Cov and KL-Cov, which clip and apply KL penalty to tokens with high covariances respectively. Experiments show that these methods encourage exploration, thus helping policy escape entropy collapse and achieve better downstream performance.
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- abstract This paper aims to overcome a major obstacle in scaling RL for reasoning with LLMs, namely the collapse of policy entropy. Such phenomenon is consistently observed across vast RL runs without entropy intervention, where the policy entropy dropped sharply at the early training stage, this diminished exploratory ability is always accompanied with the saturation of policy performance. In practice, we establish a transformation equation R=-a*e^H+b between entropy H and downstream performance R. This empirical law strongly indicates that, the policy performance is traded from policy entropy, thus b
- background [145] Yingqian Cui, Pengfei He, Jingying Zeng, Hui Liu, Xianfeng Tang, Zhenwei Dai, Yan Han, Chen Luo, Jing Huang, Zhen Li, et al. Stepwise perplexity-guided refinement for efficient chain-of-thought reasoning in large language models. arXiv preprint arXiv:2502.13260, 2025. [146] Yu Cui and Cong Zuo. Practical reasoning interruption attacks on reasoning large language models. arXiv preprint arXiv:2505.06643, 2025. [147] Yu Cui, Bryan Hooi, Yujun Cai, and Yiwei Wang. Process or result? manipulate
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Entrocraft uses rejection sampling to enforce precise entropy schedules in LLM RL by biasing advantages, enabling longer training, better generalization, and higher performance than baselines.
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HiRO-Nav adaptively triggers reasoning only on high-entropy actions via a hybrid training pipeline and shows better success-token trade-offs than always-reason or never-reason baselines on the CHORES-S benchmark.
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InternVL3.5 advances open-source multimodal models with Cascade RL for +16% reasoning gains and ViR for 4x inference speedup, with the 241B model reaching SOTA among open-source MLLMs on multimodal, reasoning, and agentic tasks.
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