URSA: Understanding and Verifying Chain-of-thought Reasoning in
  Multimodal Mathematics
Authors: name: Ruilin Luo, name: Zhuofan Zheng, name: Yifan Wang, name: Yiyao Yu, name: Xinzhe Ni, name: Zicheng Lin, name: Jin Zeng, name: Yujiu Yang

Chain-of-thought (CoT) reasoning has been widely applied in the mathematical
reasoning of Large Language Models (LLMs). Recently, the introduction of
derivative process supervision on CoT trajectories has sparked discussions on
enhancing scaling capabilities during test time, thereby boosting the potential
of these models. However, in multimodal mathematical reasoning, the scarcity of
high-quality CoT training data has hindered existing models from achieving
high-precision CoT reasoning and has limited the realization of reasoning
potential during test time. In this work, we propose a three-module synthesis
strategy that integrates CoT distillation, trajectory-format rewriting, and
format unification. It results in a high-quality CoT reasoning instruction
fine-tuning dataset in multimodal mathematics, MMathCoT-1M. We comprehensively
validate the state-of-the-art (SOTA) performance of the trained URSA-7B model
on multiple multimodal mathematical benchmarks. For test-time scaling, we
introduce a data synthesis strategy that automatically generates process
annotation datasets, known as DualMath-1.1M, focusing on both interpretation
and logic. By further training URSA-7B on DualMath-1.1M, we transition from CoT
reasoning capabilities to robust supervision abilities. The trained URSA-RM-7B
acts as a verifier, effectively enhancing the performance of URSA-7B at test
time. URSA-RM-7B also demonstrates excellent out-of-distribution (OOD)
verifying capabilities, showcasing its generalization. Model weights, training
data and code will be open-sourced.