Mean-Field Dynamics of Chain-of-Thought Reasoning in Large Language Models

大型语言模型中思维链推理的平均场动力学

Abstract: 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. 摘要： 近年来，具备思维链（Chain-of-Thought）推理能力的大型语言模型（LLMs）得到了广泛应用，对其行为的理论解释有助于加深我们的理解并指导模型优化。

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. 在本研究中，我们引入了一个框架，旨在探索大模型推理中的统计规律和理论解释，且无需简化模型架构或将其类比为现有的物理系统。

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. 我们将大模型的推理过程表述为在“线索图”（clue graph）上的引导式发现过程，并利用平均场近似推导出了关于已发现线索比例的一维常微分方程。

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. 在实验中，我们通过计算学生大模型对教师大模型输出的归一化惊奇度（normalized surprisal）来识别线索词元（clue tokens），并通过对大量思维链进行平均来获取统计规律。

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. 实验结果表明，所得的统计规律在同一数据集内具有可重复性，并且可以通过求解所提出的理论方程进行拟合。