On the Entropy Dynamics in Reinforcement Fine-Tuning of Large Language Models

2026-02-03

AI Summary

This work addresses the lack of a systematic theoretical understanding of entropy dynamics in reinforcement fine-tuning of large language models, which hinders effective exploration–exploitation trade-offs. The authors propose the first first-order analytical expression for entropy change based on logit updates, establishing a theoretical framework to characterize entropy evolution. This framework is extended to the Group Relative Policy Optimization (GRPO) update rule, offering a unified interpretation of existing entropy-based regularization methods and inspiring a novel entropy control mechanism—entropy-discriminant clipping. Both theoretical analysis and empirical validation demonstrate that the proposed approach significantly improves the balance between exploration and exploitation during reinforcement fine-tuning.

Technology Category

• Machine Learning: Reinforcement Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• entropy dynamics
• reinforcement fine-tuning
• large language models
• exploration-exploitation balance

Innovation

• entropy dynamics
• reinforcement fine-tuning
• theoretical framework
• logit update
• exploration-exploitation balance