Learning Global Hypothesis Space for Enhancing Synergistic Reasoning Chain

Chain-of-Thought (CoT) has emerged as an effective paradigm to enhance the reasoning ability of large language models (LLMs) in complex tasks. However, existing approaches still face two major challenges: (1) the lack of a global mechanism to integrate and interact across diverse reasoning hypotheses, and (2) the absence of structured analysis techniques to filter redundancy and extract salient reasoning features. To address these challenges, we propose GHS-TDA (Global Hypothesis Space with Topological Data Analysis), a two-stage reasoning framework that achieves synergistic enhancement through global information integration and topological feature analysis. Specifically, (i) Global Hypothesis Space (GHS) constructs a semantically enriched global hypothesis graph via agenda-driven multi-agent interactions, integrating diverse hypotheses and their semantic relations; (ii) Topological Data Analysis (TDA) applies persistent homology to extract multi-scale topological features, identify stable connected components and self-consistent loops, and derive a redundancy-free reasoning skeleton chain. GHS-TDA preserves reasoning diversity while leveraging topological stability to achieve self-aware convergence, ultimately producing high-confidence and interpretable reasoning paths. Experimental results show that GHS-TDA consistently outperforms existing methods across multiple benchmark datasets, demonstrating its effectiveness and competitiveness in complex reasoning scenarios.