Unlocking the Capabilities of Thought: A Reasoning Boundary Framework to Quantify and Optimize Chain-of-Thought

TL;DR

This paper introduces a reasoning boundary framework (RBF) to quantify and optimize Chain-of-Thought reasoning in large language models, providing a new way to assess and improve complex reasoning capabilities.

Contribution

The work proposes a novel reasoning boundary framework with quantitative metrics and optimization strategies for CoT, addressing key challenges in understanding and enhancing LLM reasoning.

Findings

Validated the framework on 27 models and 5 tasks

Explained the effectiveness of 10 CoT strategies

Guided optimization of reasoning paths

Abstract

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 boundary framework (RBF) to address these challenges. To solve the lack of quantification, we first define a reasoning boundary (RB) to quantify the upper-bound of CoT and establish a combination law for RB, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RBs. We further optimize these categories with combination laws focused on RB promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 27 models and 5 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-boundary.