@inproceedings{shi-etal-2026-mathcanvas,
title = "{M}ath{C}anvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning",
author = "Shi, Weikang and
Yu, Aldrich and
Fang, Rongyao and
Ren, Houxing and
Wang, Ke and
Zhou, Aojun and
Tian, Changyao and
Fu, Xinyu and
Hu, Yuxuan and
Lu, Zimu and
Huang, Linjiang and
Liu, Si and
Liu, Rui and
Li, Hongsheng",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.acl-long.1287/",
pages = "27933--27954",
ISBN = "979-8-89176-390-6",
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 reasoning in LMMs."
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<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 reasoning in LMMs.</abstract>
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%0 Conference Proceedings
%T MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning
%A Shi, Weikang
%A Yu, Aldrich
%A Fang, Rongyao
%A Ren, Houxing
%A Wang, Ke
%A Zhou, Aojun
%A Tian, Changyao
%A Fu, Xinyu
%A Hu, Yuxuan
%A Lu, Zimu
%A Huang, Linjiang
%A Liu, Si
%A Liu, Rui
%A Li, Hongsheng
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F shi-etal-2026-mathcanvas
%X 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 reasoning in LMMs.
%U https://aclanthology.org/2026.acl-long.1287/
%P 27933-27954
Markdown (Informal)
[MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning](https://aclanthology.org/2026.acl-long.1287/) (Shi et al., ACL 2026)
ACL
- 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, and Hongsheng Li. 2026. MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 27933–27954, San Diego, California, United States. Association for Computational Linguistics.