GHS-TDA: A Synergistic Reasoning Framework Integrating Global Hypothesis Space with Topological Data Analysis

TL;DR

This work addresses limitations in chain-of-thought reasoning by introducing GHS-TDA, a two-stage framework that first constructs a Global Hypothesis Graph to integrate diverse candidate reasoning paths and then applies persistent homology to extract stable backbones and self-consistent loops. The topological analysis yields high-confidence, interpretable reasoning skeletons (backbones from $H_0$ and verification loops from $H_1$) that guide robust answer assembly. Empirical results across eight benchmarks and multiple backbones show consistent accuracy gains, improved robustness to perturbations, and substantial token- and call-based efficiency, with persistence metrics serving as a task-agnostic indicator of correctness. The proposed method offers a principled fusion of semantic alignment and topological stability, enabling scalable, interpretable, and reliable multipath reasoning for complex tasks.

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.

Figures (4)

• Figure 1: The method consists of two stages: (1) Global Hypothesis Space Modeling, where multiple reasoning paths sampled from an LLM are semantically aligned and merged into a unified Global Hypothesis Graph encoding adjacency, support, and refutation relations; and (2) Skeleton Extraction, where the graph is embedded into a feature space, analyzed via Vietoris–Rips filtration and persistent homology, and reduced to stable backbones and self-consistent loops. The resulting skeleton provides both accurate answers and interpretable reasoning structures.
• Figure 2: Global relation between H$_1$ persistence and reasoning correctness.
• Figure 3: Validation of the predictive role of topological persistence. Left: correct reasoning chains have consistently higher H$_1$ persistence values than incorrect ones. Right: ROC analysis shows persistence alone achieves an AUC of 0.74.
• Figure 4: Overall results across eight experimental settings.