用平均场理论解析大模型思维链推理的规律
Mean-Field Dynamics of Chain-of-Thought Reasoning in Large Language Models
- 将思维链视为线索图上的引导发现过程
- 推导出线索发现比例的常微分方程，拟合实验数据
- 适用于研究推理机制与模型优化的学者
近年来，具备思维链推理能力的大语言模型广泛应用，对其行为的理论解释有助于深化理解并指导模型优化。本文提出一个框架，不简化模型结构或类比物理系统，直接探索大模型推理中的统计规律与理论解释。我们将大模型推理建模为在线索图上的引导发现过程，利用平均场近似推导出线索发现比例的一维常微分方程。实验中，通过学生模型对教师模型输出的归一化意外度识别线索标记，通过对大量思维链进行平均获得统计规律。结果表明，这些规律在相同数据集内可重复，并能被所提出的理论方程良好拟合。
原文摘要 · Abstract (English)
Large language models (LLMs) with chain-of-thought reasoning have been widely applied in recent years, and theoretical explanations of their behavior may help deepen our understanding and guide model optimization. In this study, we introduce a framework that seeks statistical regularities and theoretical interpretations in LLM reasoning without simplifying the model architecture or making analogies to existing physical systems. We formulate LLM reasoning as a guided discovery process on a clue graph, and derive a one-dimensional ordinary differential equation for the fraction of discovered clues using the mean-field approximation. Experimentally, clue tokens are identified using the normalized surprisal of a student LLM on the outputs of a teacher LLM, and statistical regularities are obtained by averaging over many reasoning chains of thought. Our experiments show that the resulting statistical regularities are reproducible within the same dataset and can be fitted by the solving the proposed theoretical equation.
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