Unlocking the Boundaries of Thought: A Reasoning Granularity Framework to Quantify and Optimize Chain-of-Thought

Chain-of-Thought (CoT) reasoning has emerged as a promising approach for enhancing the performance of large language models (LLMs) on complex reasoning tasks. Recently, a series of studies attempt to explain the mechanisms underlying CoT, aiming to deepen the understanding of its efficacy. Nevertheless, the existing research faces two major challenges: (1) a lack of quantitative metrics to assess CoT capabilities and (2) a dearth of guidance on optimizing CoT performance. Motivated by this, in this work, we introduce a novel reasoning granularity framework (RGF) to address these challenges. To solve the lack of quantification, we first define a reasoning granularity (RG) to quantify the upper bound of CoT and establish a combination law for RG, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RGs. We further optimize these categories with combination laws focused on RG promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 25 models and 4 tasks, the study validates the existence and rationality of the proposed framework. Furthermore, it explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives. We hope this work can provide a comprehensive understanding of the boundaries and optimization strategies for reasoning in LLMs. Our code and data are available at https://github.com/LightChen233/reasoning-granularity.