[2510.19842] DAG-Math: Graph-of-Thought Guided Mathematical Reasoning in LLMs

Computer Science > Artificial Intelligence arXiv:2510.19842 (cs) [Submitted on 19 Oct 2025 (v1), last revised 1 Mar 2026 (this version, v2)] Title:DAG-Math: Graph-of-Thought Guided Mathematical Reasoning in LLMs Authors:Yuanhe Zhang, Ilja Kuzborskij, Jason D. Lee, Chenlei Leng, Fanghui Liu View a PDF of the paper titled DAG-Math: Graph-of-Thought Guided Mathematical Reasoning in LLMs, by Yuanhe Zhang and 4 other authors View PDF HTML (experimental) Abstract:Large Language Models (LLMs) demonstrate strong performance on mathematical problems when prompted with Chain-of-Thought (CoT), yet it remains unclear whether this success stems from search, rote procedures, or rule-consistent reasoning. To address this, we propose modeling CoT as a certain rule-based stochastic process over directed acyclic graphs (DAGs), where nodes represent intermediate derivation states and edges encode rule applications. Within this framework, we introduce \textbf{logical closeness}, a metric that quantifies how well a model's CoT trajectory (i.e., the LLM's final output) adheres to the DAG structure, providing evaluation beyond classical PASS@$k$ metrics. Building on this, we introduce the \emph{DAG-MATH} CoT format and construct a benchmark that guides LLMs to generate CoT trajectories in this format, thereby enabling the evaluation of their reasoning ability under our framework. Across standard mathematical reasoning datasets, our analysis uncovers statistically significant differences in reaso...