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[2512.19135] Understanding Chain-of-Thought in Large Language Models via Topological Data Analysis
Summary
This paper explores the structural analysis of reasoning chains in large language models (LLMs) using Topological Data Analysis (TDA), revealing insights into their effectiveness in problem-solving.
Why It Matters
Understanding the structural mechanisms behind reasoning chains in LLMs is crucial for enhancing their performance in complex tasks. This research provides a novel perspective that could lead to improved model designs and applications in AI.
Key Takeaways
- The study introduces a structural perspective to evaluate reasoning chains in LLMs.
- Topological Data Analysis (TDA) reveals semantic coherence and logical gaps in reasoning.
- More complex reasoning chains correlate with higher accuracy in problem-solving.
- Simpler topologies enhance efficiency and interpretability of reasoning.
- This research offers guidance for optimizing reasoning chains in future AI models.
Computer Science > Artificial Intelligence arXiv:2512.19135 (cs) [Submitted on 22 Dec 2025 (v1), last revised 13 Feb 2026 (this version, v2)] Title:Understanding Chain-of-Thought in Large Language Models via Topological Data Analysis Authors:Chenghao Li, Chaoning Zhang, Yi Lu, Shuxu Chen, Xudong Wang, Jiaquan Zhang, Zhicheng Wang, Zhengxun Jin, Kuien Liu, Sung-Ho Bae, Guoqing Wang, Yang Yang, Heng Tao Shen View a PDF of the paper titled Understanding Chain-of-Thought in Large Language Models via Topological Data Analysis, by Chenghao Li and 12 other authors View PDF HTML (experimental) Abstract:With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging the power of long reasoning chains, we cannot help but wonder: Why do different reasoning chains perform differently in reasoning? What components of the reasoning chains play a key role? Existing studies mainly focus on evaluating reasoning chains from a functional perspective, with little attention paid to their structural mechanisms. To address this gap, this work is the first to analyze and evaluate the quality of the reasoning chain from a structural perspective. We apply persistent homology from Topological Data Analysis (TDA) to map reasoning steps into semantic space, extract topological features, and analyze structural changes. These change...