TDA-RC: Task-Driven Alignment for Knowledge-Based Reasoning Chains in Large Language Models

TL;DR

This paper introduces TDA-RC, a topology-based optimization method that enhances the reasoning quality of large language models by repairing logical gaps in single-round chains using topological analysis.

Contribution

It proposes a novel topological optimization framework that embeds reasoning structures into CoT, improving reasoning accuracy while maintaining efficiency.

Findings

Outperforms multi-round methods like ToT and GoT in accuracy and efficiency.

Uses persistent homology to unify and analyze reasoning chain structures.

Provides a practical single-round reasoning enhancement with multi-round capabilities.

Abstract

Enhancing the reasoning capability of large language models (LLMs) remains a core challenge in natural language processing. The Chain-of-Thought (CoT) paradigm dominates practical applications for its single-round efficiency, yet its reasoning chains often exhibit logical gaps. While multi-round paradigms like Graph-of-Thoughts (GoT), Tree-of-Thoughts (ToT), and Atom of Thought (AoT) achieve strong performance and reveal effective reasoning structures, their high cost limits practical use. To address this problem, this paper proposes a topology-based method for optimizing reasoning chains. The framework embeds essential topological patterns of effective reasoning into the lightweight CoT paradigm. Using persistent homology, we map CoT, ToT, and GoT into a unified topological space to quantify their structural features. On this basis, we design a unified optimization system: a Topological Optimization Agent diagnoses deviations in CoT chains from desirable topological characteristics and simultaneously generates targeted strategies to repair these structural deficiencies. Compared with multi-round reasoning methods like ToT and GoT, experiments on multiple datasets show that our approach offers a superior balance between reasoning accuracy and efficiency, showcasing a practical solution to ``single-round generation with multi-round intelligence''.