# The Shape of Reasoning: Topological Analysis of Reasoning Traces in Large Language Models

arXiv: https://arxiv.org/abs/2510.20665 · HTML: https://mlsanity.com/paper/2510.20665/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 6 of 6)

- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Faithfulness vs. Plausibility: On the (Un)Reliability of Explanations from Large Language Models](https://mlsanity.com/paper/2402.04614/) (2024)
- [A Survey of Reasoning with Foundation Models](https://mlsanity.com/paper/2312.11562/) (2023)
- [Evaluating Step-by-step Reasoning Traces: A Survey](https://mlsanity.com/paper/2502.12289/) (2025)
- [Topology of Reasoning: Understanding Large Reasoning Models through Reasoning Graph Properties](https://mlsanity.com/paper/2506.05744/) (2025)
- [Mapping the Minds of LLMs: A Graph-Based Analysis of Reasoning LLM](https://mlsanity.com/paper/2505.13890/) (2025)

## Built on by (most cited first, 9 of 9)

- [SARL: Label-Free Reinforcement Learning by Rewarding Reasoning Topology](https://mlsanity.com/paper/2603.27977/) (2026)
- [SliceGraph: Mapping Process Isomers in Multi-Run Chain-of-Thought Reasoning](https://mlsanity.com/paper/2605.14619/) (2026)
- [TraceGraph: Shared Decision Landscapes for Diagnosing and Improving Agent Trajectories](https://mlsanity.com/paper/2605.31308/) (2026)
- [Metacognitive Behavioral Tuning of Large Language Models for Multi-Hop Question Answering](https://mlsanity.com/paper/2602.22508/) (2026)
- [Topology-Aware Layer Pruning for Large Vision-Language Models](https://mlsanity.com/paper/2604.16502/) (2026)
- [CoDA: Towards Effective Cross-domain Knowledge Transfer via CoT-guided Domain Adaptation](https://mlsanity.com/paper/2604.19488/) (2026)
- [Do Large Language Models Play Six Degrees of Separation? Measuring Topological Compression in Long-Context Manifolds](https://mlsanity.com/paper/2608.17950/) (2026)
- [From Concentration to Differentiation and Back: Routing Effective Rank in MoE Reasoning Cohorts](https://mlsanity.com/paper/2609.06403/) (2026)
- [Selecting Diverse SFT Traces Improves Post-RL Generalization](https://mlsanity.com/paper/2609.33780/) (2026)

## Abstract (arXiv)

Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are dominated by graph-based proxies that quantify structural connectivity but do not clarify what constitutes high-quality reasoning; such abstractions can be overly simplistic for inherently complex processes. We introduce a topological data analysis (TDA)-based evaluation framework that captures the geometry of reasoning traces and enables label-efficient, automated assessment. In our empirical study, topological features yield substantially higher predictive power for assessing reasoning quality than standard graph metrics, suggesting that effective reasoning is better captured by higher-dimensional geometric structures rather than purely relational graphs. We further show that a compact, stable set of topological features reliably indicates trace quality, offering a practical signal for future reinforcement learning algorithms.