On the Entropy Dynamics in Reinforcement Fine-Tuning of Large Language Models
Shumin Wang, Yuexiang Xie, Wenhao Zhang, Yuchang Sun, Yanxi Chen, Yaliang Li, Yanyong Zhang
TL;DR
This paper develops a theoretical framework to analyze entropy dynamics in reinforcement fine-tuning of large language models, offering insights and practical methods to improve exploration-exploitation balance.
Contribution
It introduces a principled theoretical analysis of entropy changes during RFT and proposes entropy control methods based on this analysis.
Findings
Theoretical expressions for entropy change during RFT.
Empirical validation of entropy-discriminator clipping methods.
Enhanced understanding of exploration-exploitation trade-offs in LLM fine-tuning.
Abstract
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…
Peer Reviews
Decision·Submitted to ICLR 2026
1. The authors provide a theoretical analysis of entropy variation under changes in logits caused by individual tokens and by gradients derived from the GRPO loss, and they propose a metric for assessing entropy change. 2、 Building on the new metric, the authors establish connections with previous reinforcement learning methods and introduce two new algorithms. 3. Both new algorithms achieve performance improvements on downstream tasks.
All the analysis is done on "tabular" cases. However, for the RL in LLMs, the updates of different positions and different tokens will be combined by shared parameters in LLM. Why can the theoretical analysis still apply to the scenarios.
1. This paper’s key strength is to provide a very clean expression of the change of entropy during policy updates. 2. This expression motivates clean and simple clipping techniques (ClipB and ClipV) to improve exploration without destabilizing training. Overall, the work contributes both theoretical depth and practical utility, marking a valuable advance in understanding and stabilizing reinforcement fine-tuning for LLMs
1. From an empirical perspective, the experiments are limited to the Qwen model family, leaving uncertainty regarding the generality of the proposed methods across other architectures or training setups. As pointing out in previous paper, Qwen is very different from other models in terms of reasoning. 2. The theoretical analysis presented in Section 3.2 appears broadly applicable to generic policy-gradient algorithms, including not only GRPO but also other methods such as PPO. It is therefore u
1. This paper provides a clear, simple theoretical insight on the entropy dynamics in the RFT process. The paper derives a compact first-order expression that links a single-logit update to entropy change. This gives an intuitive discriminator that predicts whether an update increases or decreases entropy. The derivation is straightforward and easy to follow (Lemma 1 / Theorem 1). The authors extend the single-token result to a GRPO optimization step. This links per-token effects to the actual o
1. Corollary 1 appears to be incorrect. It claims that the expected entropy change within GRPO optimization is zero. If I understand correctly, this is proved by calculating the expectation of the first-order entropy change $\Delta H$ under the token distribution $k \sim p$. However, $\Delta H$ contains the advantage $A$, which depends on the token $k$. The paper seems to ignore this dependence. 2. The scope of the theoretical analysis is limited. The analysis is first-order (small perturbation)
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Taxonomy
TopicsNatural Language Processing Techniques · Topic Modeling · Explainable Artificial Intelligence (XAI)