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

Jiaquan Zhang; Qigan Sun; Chaoning Zhang; Xudong Wang; Zhenzhen Huang; Yitian Zhou; Pengcheng Zheng; Chi-lok Andy Tai

cs.CLMar 13, 2026

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

Authors: Jiaquan Zhang, Qigan Sun, Chaoning Zhang, Xudong Wang, Zhenzhen Huang, Yitian Zhou, Pengcheng Zheng, Chi-lok Andy Tai, +6 more

Organizations: School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China · School of Computing, Kyung Hee University, Yongin-si, South Korea · School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China · College of Professional and Continuing Education, The Hong Kong Polytechnic University, Hong Kong, China · School of Robotics and Advanced Manufacture, Harbin Institute of Technology, Shenzhen, China · School of Computer Science and Technology, Tongji University, Shanghai, China

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''.

Figures & tables

Fig. 1 : The upper part illustrates the offline procedure for constructing task-specific health bands, where reasoning chains are modeled as topological graphs and persistent homology features are extracted to characterize their structural properties. The lower part presents the online usage pipeline of TDA-RC, which performs a single-round closed-loop optimization consisting of health evaluation, structural diagnosis, and agent-based prompt repair. By combining persistent homology with reasoning feature analysis, TDA-RC identifies structural inconsistencies in LLM reasoning and generates targeted repair strategies, enabling one-shot refinement of the prompt to improve structural coherence and task accuracy.

Fig. 2 : Topological profiles of six metrics, averaged across datasets for CoT, ToT, GoT, and AoT, computed via TDA.

Fig. 3 : Task-specific Topological Health Bands derived from core topological metrics computed on correct reasoning traces.

Metric	$F_{\text{coh}}$	$F_{\text{div}}$	$F_{\text{val}}$	$F_{\text{pen}}$	$\delta$	$F_{\text{complexity}}$
$F_{\text{coh}}$	1.00	0.18	0.22	0.11	0.27	0.19
$F_{\text{div}}$	0.18	1.00	0.31	0.09	0.33	0.42
$F_{\text{val}}$	0.22	0.31	1.00	0.28	0.21	0.36
$F_{\text{pen}}$	0.11	0.09	0.28	1.00	0.25	0.29
$\delta$	0.27	0.33	0.21	0.25	1.00	0.31
$F_{\text{complexity}}$	0.19	0.42	0.36	0.29	0.31	1.00

TABLE I : Spearman correlation matrix among TDA structural metrics (computed on correct reasoning traces of GSM8K and MATH combined).

Panel of Figure 6 — Fig. 4 : Accuracy vs. relative cost (CoT = 1.0) for reasoning methods on GPT-4o-mini, Qwen-Turbo, and DeepSeek-V3. Each point represents a reasoning approach, with accuracy on the y-axis and generation cost on the x-axis. CoT, AoT, and TDA-RC are highlighted for reference. Methods closer to the upper-left region achieve a more favorable.

Target Task	Source Task	Self-band	Transferred
MATH	GSM8K	82.7	82.4
GSM8K	MATH	94.2	94.1
HotpotQA	MuSiQue	70.6	70.4
MuSiQue	HotpotQA	37.8	37.6

TABLE V: Accuracy (%) of TDA-RC under self-band vs. transferred-band settings. Small differences indicate strong cross-task transferability.

Metric	G $\to$ M	M $\to$ G	H $\to$ Q	Q $\to$ H
$F_{\mathrm{coh}}$	0.07	0.05	0.04	0.05
$F_{\mathrm{div}}$	0.09	0.06	0.05	0.06
$F_{\mathrm{val}}$	0.05	0.04	0.03	0.03
$F_{\mathrm{pen}}$	0.08	0.05	0.04	0.04
$\delta$	0.06	0.04	0.03	0.03
$F_{\mathrm{complexity}}$	0.10	0.07	0.06	0.06

TABLE VI: 1-Wasserstein distances (

W_{1}

) between topological metric distributions across tasks. Lower values indicate higher structural similarity.

Dataset	[Q1,Q3]	[Q1,Q4]	[Q2,Q3]	[Q2,Q4]
MATH	$82.7$	$82.2$	$82.9$	83.0
OlympiadBench (Math)	$12.6$	$12.3$	$12.8$	12.9
GSM8K	$94.2$	$93.8$	$94.0$	94.4
BBH	$82.5$	$82.0$	82.7	$82.1$
MMLU-CF	70.8	$70.3$	$70.6$	$70.7$
LongBench	59.3	$58.6$	$58.8$	$58.7$

TABLE VII: Ablation results of different health threshold ranges in the TDA-RC framework on GPT-4o-mini. Higher values indicate better accuracy (%).

Dataset	A1	A2	A3	A4	A5
MATH	82.7	$81.1$	$81.2$	$81.3$	$81.4$
OlympiadBench (Math)	12.6	$11.8$	$11.9$	$12.0$	$12.1$
GSM8K	94.2	$91.9$	$91.9$	$92.0$	$92.0$
BBH	82.5	$80.6$	$80.6$	$80.5$	$80.7$
MMLU-CF	70.8	$70.4$	$70.4$	$70.4$	$70.5$
LongBench	59.3	$58.7$	$58.6$	$58.7$	$58.7$

TABLE VIII: Ablation study results (%) of the proposed TDA-RC framework under different module configurations (A1–A5) on the GPT-4o-mini model. A1–A5 denote progressively modified variants removing or replacing specific modules.

Topological Metric	Initial Value	Health Band	Optimized
$F_{\text{coh}}$	0.00	$[0.34,\,0.71]$	0.65
$F_{\text{val}}$	0.00	$[0.45,\,0.76]$	0.56
$F_{\text{div}}$	1.00	$[1.42,\,3.91]$	2.31
$F_{\text{pen}}$	4.20	$[1.40,\,3.30]$	3.10
$\delta$	0.22	$[0.23,\,0.54]$	0.26
$F_{\text{complexity}}$	14.50	$[10.20,\,23.7]$	22.10

TABLE IX: Topological reasoning metrics for the MATH (Algebra) task, reporting initial values, task-specific health bands, and the post-optimization improvements. Missing optimized values indicate metrics not directly targeted during the refinement process.

Topological Metric	Initial Value	Health Band	Optimized
$F_{\text{coh}}$	0.80	$[0.08,\,0.35]$	0.28
$F_{\text{val}}$	0.85	$[0.15,\,0.43]$	0.39
$F_{\text{div}}$	1.30	$[2.31,\,5.88]$	4.10
$F_{\text{pen}}$	1.20	$[0.40,\,1.90]$	1.40
$\delta$	0.22	$[0.22,\,0.48]$	0.25
$F_{\text{complexity}}$	4.80	$[16.20,\,32.70]$	22.10

TABLE X: Topological reasoning metrics for the MMLU-CF (Physics / General Science) task, reporting initial values, task-specific health bands, and the corresponding optimized improvements.

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Open paper AskPDF arXiv

Chain-of-Thought (CoT) prompting has significantly improved the reasoning capabilities of large language models (LLMs). However, conventional CoT often relies on unstructured, flat reasoning chains that suffer from redundancy and suboptimal performance. In this work, we introduce Hierarchical Chain-of-Thought (Hi-CoT), a structured reasoning paradigm specifically designed to address the challenges of complex, multi-step reasoning. Hi-CoT decomposes the reasoning process into hierarchical substeps by alternating between instructional planning and step-by-step execution. This decomposition enables LLMs to better manage long reasoning horizons and maintain logical coherence. Extensive evaluations across diverse LLMs and mathematical reasoning benchmarks show that Hi-CoT consistently improves average accuracy by 6.2% (up to 61.4% on certain models and tasks) while reducing reasoning trace length by 13.9% compared to CoT. We further show that accuracy and efficiency are maximized when models strictly adhere to the hierarchical structure. Our code is available at https://github.com/XingshuaiHuang/Hi-CoT.

Abstract

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