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
2026-02-09
Summary
This paper investigates how the 'diversity' of responses from large language models changes when those models are being improved through a process called reinforcement learning. It aims to understand *why* this diversity changes and how to control it.
What's the problem?
Large language models are often 'fine-tuned' using reinforcement learning to make them better at specific tasks. A key challenge is finding the right balance between 'exploration' – trying out new and different responses – and 'exploitation' – sticking with responses that are known to work well. Measuring diversity, using a concept called 'entropy', is helpful, but there wasn't a clear theoretical understanding of *how* entropy changes during this fine-tuning process, making it hard to control effectively.
What's the solution?
The researchers developed a mathematical framework to analyze how entropy changes with each small update to the language model during reinforcement learning. They started with a formula to track entropy change from a single update and then expanded it to work with a common fine-tuning method called Group Relative Policy Optimization. This framework helped them design new ways to control entropy and also provided a way to understand existing methods for controlling entropy.
Why it matters?
This work provides a solid theoretical foundation for understanding and controlling the diversity of responses from large language models during fine-tuning. This is important because controlling diversity allows us to optimize the balance between exploring new possibilities and reliably generating good responses, ultimately leading to better and more useful language models.
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 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.