Learning Global Hypothesis Space for Enhancing Synergistic Reasoning Chain

TL;DR

This paper introduces GHS-TDA, a novel method that constructs a global hypothesis graph and applies topological data analysis to improve reasoning accuracy, robustness, and interpretability in large language models' chain-of-thought reasoning.

Contribution

It proposes a global hypothesis graph and topological data analysis framework to enhance reasoning correction, stability, and interpretability in chain-of-thought methods for LLMs.

Findings

Outperforms strong baselines in accuracy and robustness.

Produces high-confidence, interpretable reasoning paths.

Achieves self-adaptive convergence in reasoning processes.

Abstract

Chain-of-Thought (CoT) has been shown to significantly improve the reasoning accuracy of large language models (LLMs) on complex tasks. However, due to the autoregressive, step-by-step generation paradigm, existing CoT methods suffer from two fundamental limitations. First, the reasoning process is highly sensitive to early decisions: once an initial error is introduced, it tends to propagate and amplify through subsequent steps, while the lack of a global coordination and revision mechanism makes such errors difficult to correct, ultimately leading to distorted reasoning chains. Second, current CoT approaches lack structured analysis techniques for filtering redundant reasoning and extracting key reasoning features, resulting in unstable reasoning processes and limited interpretability. To address these issues, we propose GHS-TDA. GHS-TDA first constructs a semantically enriched global hypothesis graph to aggregate, align, and coordinate multiple candidate reasoning paths, thereby providing alternative global correction routes when local reasoning fails. It then applies topological data analysis based on persistent homology to capture stable multi-scale structures, remove redundancy and inconsistencies, and extract a more reliable reasoning skeleton. By jointly leveraging reasoning diversity and topological stability, GHS-TDA achieves self-adaptive convergence, produces high-confidence and interpretable reasoning paths, and consistently outperforms strong baselines in terms of both accuracy and robustness across multiple reasoning benchmarks.