URSA: Understanding and Verifying Chain-of-thought Reasoning in Multimodal Mathematics

Chain-of-Thought (CoT) reasoning is widely used to enhance the mathematical reasoning capabilities of large language models (LLMs). The introduction of process supervision for CoT trajectories has sparked discussions on improving test-time scaling, thereby unlocking the System 2-style thinking capabilities of these models. However, in multimodal mathematical reasoning, the scarcity of high-quality CoT training data has hindered existing models from achieving both deliberate reasoning and fine-grained verification. In this work, we propose a novel framework that introduces System 2-style thinking to multimodal mathematical reasoning. We introduce a three-module CoT data synthesis process that integrates CoT distillation, trajectory-format rewriting, and format unification. This process generates MMathCoT-1M, a high-quality CoT reasoning instruction fine-tuning dataset. Furthermore, we implement a dual-view trajectory labeling automation that targets both visual grounding fidelity and deductive chain validity, resulting in the DualMath-1.1M dataset. The URSA-8B model, trained on MMathCoT-1M, achieves new state-of-the-art (SOTA) performance among similarly sized multimodal LLMs on six popular reasoning benchmarks. Training URSA-8B further on the DualMath-1.1M dataset yields URSA-RM-8B, a verifier that enhances URSA-8B's test-time performance and surpasses strong closed-source multimodal MLLMs like GPT-4o. The model weights, training data, and code have been open-sourced: https://github.com/URSA-MATH/URSA-MATH.
Comment: Add benchmarks and baselines. 27 pages, 11 tables, 17 figures. Models, training data and code have been open-sourced. Project url: https://ursa-math.github.io