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

2026-02-10

AI Summary

This work addresses the limitations of existing chain-of-thought methods in complex reasoning, which are prone to early errors and lack structured mechanisms, leading to error propagation and poor interpretability. The authors propose a semantic-enhanced global hypothesis graph that integrates multiple reasoning paths and, for the first time, incorporates topological data analysis based on persistent homology to extract a stable, de-redundant reasoning skeleton. This approach enables adaptive convergence and global error correction. Evaluated across multiple reasoning benchmarks, the method consistently outperforms strong baselines, achieving significant gains in both accuracy and robustness while generating high-confidence, structurally coherent, and interpretable reasoning trajectories.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

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.

Problem

• Chain-of-Thought
• reasoning error propagation
• global coordination
• redundant reasoning
• interpretability

Innovation

• Global Hypothesis Space
• Topological Data Analysis
• Persistent Homology
• Chain-of-Thought Reasoning
• Reasoning Skeleton