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

Qiguang Chen, Libo Qin, Jiaqi Wang, Jinxuan Zhou, Wanxiang Che

TL;DR

A novel reasoning boundary framework (RBF) is introduced to solve the lack of quantification and address the lack of optimization in chain-of-Thought reasoning, and explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives.

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.

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

TL;DR

A novel reasoning boundary framework (RBF) is introduced to solve the lack of quantification and address the lack of optimization in chain-of-Thought reasoning, and explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives.

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.
Paper Structure (68 sections, 19 equations, 21 figures, 3 tables)

This paper contains 68 sections, 19 equations, 21 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Quantification Methodology
  3. Reasoning Boundary
  4. Combination Law of Reasoning Boundary
  5. Categories of Reasoning Boundary
  6. Experimental Setup
  7. Benchmark Settings
  8. Model Settings
  9. Empirical Analysis of Reasoning Boundary
  10. Existence Verification for Reasoning Boundary
  11. Basic Arithmetic Calculation
  12. Nature Language Planning
  13. Code Planning
  14. Combination Law Verification on Different Tasks
  15. Combination Law in Complex Arithmetic Calculation
  16. ...and 53 more sections

Figures (21)

  • Figure 1: Overview of the introduced concepts.
  • Figure 1: Main experimental results on GPT-3.5-Turbo. Results on different benchmarks are shown in Table \ref{['exp:additional-exp']}.
  • Figure 2: Existence Verification for Reasoning Boundary.
  • Figure 2: Extended experimental results on GPT-3.5-Turbo.
  • Figure 3: Combination law verification of RB on different tasks. More verification results on other tasks are shown in Figure \ref{['fig:med-prob']}.
  • ...and 16 more figures

Theorems & Definitions (2)

  • Definition 1
  • Definition 2