MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning

• URL: http://arxiv.org/abs/2510.14958v1
• Date: Thu, 16 Oct 2025 17:58:58 GMT
• Title: MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning
• Authors: Weikang Shi, Aldrich Yu, Rongyao Fang, Houxing Ren, Ke Wang, Aojun Zhou, Changyao Tian, Xinyu Fu, Yuxuan Hu, Zimu Lu, Linjiang Huang, Si Liu, Rui Liu, Hongsheng Li,
• Abstract summary: We present a comprehensive framework designed to endow unified Large Multimodal Models with intrinsic VCoT capabilities for mathematics.<n>Our model, BAGEL-canvas, trained under this framework, achieves an 86% relative improvement over strong LMM baselines.<n>Our work provides a complete toolkit-framework, datasets, and benchmark-to unlock complex, human-like visual-aided reasoning in LMMs.
• Score: 58.776297011268845
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While Large Language Models (LLMs) have excelled in textual reasoning, they struggle with mathematical domains like geometry that intrinsically rely on visual aids. Existing approaches to Visual Chain-of-Thought (VCoT) are often limited by rigid external tools or fail to generate the high-fidelity, strategically-timed diagrams necessary for complex problem-solving. To bridge this gap, we introduce MathCanvas, a comprehensive framework designed to endow unified Large Multimodal Models (LMMs) with intrinsic VCoT capabilities for mathematics. Our approach consists of two phases. First, a Visual Manipulation stage pre-trains the model on a novel 15.2M-pair corpus, comprising 10M caption-to-diagram pairs (MathCanvas-Imagen) and 5.2M step-by-step editing trajectories (MathCanvas-Edit), to master diagram generation and editing. Second, a Strategic Visual-Aided Reasoning stage fine-tunes the model on MathCanvas-Instruct, a new 219K-example dataset of interleaved visual-textual reasoning paths, teaching it when and how to leverage visual aids. To facilitate rigorous evaluation, we introduce MathCanvas-Bench, a challenging benchmark with 3K problems that require models to produce interleaved visual-textual solutions. Our model, BAGEL-Canvas, trained under this framework, achieves an 86% relative improvement over strong LMM baselines on MathCanvas-Bench, demonstrating excellent generalization to other public math benchmarks. Our work provides a complete toolkit-framework, datasets, and benchmark-to unlock complex, human-like visual-aided reasoning in LMMs. Project Page: https://mathcanvas.github.io/

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