MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal
  Mathematical Reasoning
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/
68f1a3346e0bef323a68fcde
Weikang Shi
68f1a3346e0bef323a68fcdf
Aldrich Yu
68f1a3346e0bef323a68fce0
Rongyao Fang
68f1a3346e0bef323a68fce1
Houxing Ren
68f1a3346e0bef323a68fce2
Ke Wang
claimed_verified
2025-10-18T04:49:41.913Z
64d592c28767727dffa1f002
/avatars/fe38bcac944a2742dc12c624e62d24ef.svg
WangKe
user
scikkk
68f1a3346e0bef323a68fce3
Aojun Zhou
68f1a3346e0bef323a68fce4
Changyao Tian
68f1a3346e0bef323a68fce5
Xinyu Fu
68f1a3346e0bef323a68fce6
Yuxuan Hu
68f1a3346e0bef323a68fce7
Zimu Lu
68f1a3346e0bef323a68fce8
Linjiang Huang
68f1a3346e0bef323a68fce9
Si Liu
68f1a3346e0bef323a68fcea
Rui Liu
68f1a3346e0bef323a68fceb
Hongsheng Li
MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal
  Mathematical Reasoning
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/
MathCanvas enhances Large Multimodal Models with Visual Chain-of-Thought capabilities for mathematics through pre-training on diagram generation and fine-tuning on visual-textual reasoning, achieving significant improvements on math benchmarks.
Large Language Models Visual Chain-of-Thought Large Multimodal Models Visual Manipulation Strategic Visual-Aided Reasoning MathCanvas-Imagen MathCanvas-Edit MathCanvas-Instruct MathCanvas-Bench BAGEL-Canvas