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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 ","title":"The Shape of Reasoning: Topological Analysis of Reasoning Traces in Large Language Models","url":"https://arxiv.org/abs/2510.20665","vendor":"arxiv_cs_ai"},"summary":"arXiv:2510.20665v3 Announce Type: replace \nAbstract: 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. 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