---
title: "MathCanvas — paper by Shi et al. (2026) — summary and ideas"
description: "The authors also release MathCanvas-Bench and use it to evaluate 20 LMMs. 60 references, cited by 3 papers here."
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"]
year: 2026
venue: "Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)"
source: "https://aclanthology.org/2026.acl-long.1287/"
doi: "10.18653/v1/2026.acl-long.1287"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/shi-2026-mathcanvas-intrinsic-visual-chain-thought/"
---
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# MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning

**Authors:** [Weikang Shi](https://md.research.elamur.ai/free/en/authors/weikang-shi/), Aldrich Yu, [Rongyao Fang](https://md.research.elamur.ai/free/en/authors/rongyao-fang/), [Houxing Ren](https://md.research.elamur.ai/free/en/authors/houxing-ren/), [Ke Wang](https://md.research.elamur.ai/free/en/authors/ke-wang/), [Aojun Zhou](https://md.research.elamur.ai/free/en/authors/aojun-zhou/), Changyao Tian, Xinyu Fu, [Yuxuan Hu](https://md.research.elamur.ai/free/en/authors/yuxuan-hu/), [Zimu Lu](https://md.research.elamur.ai/free/en/authors/zimu-lu/), Linjiang Huang, Si Liu, Rui Liu and [Hongsheng Li](https://md.research.elamur.ai/free/en/authors/hongsheng-li/) · **Year:** 2026 · **Venue:** [Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2026](https://md.research.elamur.ai/free/en/venues/acl/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.acl-long.1287/) · [PDF](https://aclanthology.org/2026.acl-long.1287.pdf) · [DOI 10.18653/v1/2026.acl-long.1287](https://doi.org/10.18653/v1/2026.acl-long.1287) · [OpenAlex](https://openalex.org/W7166870864)

**Citations:** 0 citations (OpenAlex, 2026-10-14) · [3](https://md.research.elamur.ai/free/en/papers/shi-2026-mathcanvas-intrinsic-visual-chain-thought/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Text-only chain-of-thought is a poor fit for areas such as geometry and function analysis, where people solve problems by sketching and modifying diagrams. Earlier Visual Chain-of-Thought (VCoT) methods either depend on inflexible external tools or, in the intrinsic setting, produce inaccurate figures that are drawn without a clear purpose. MathCanvas trains a unified LMM to create and edit diagrams within its own reasoning, in two stages. The Visual Manipulation stage pre-trains on 15.2M diagram pairs to build drawing and editing skill. The Strategic Visual-Aided Reasoning stage then fine-tunes on interleaved text-and-image solutions so the model learns when a drawing helps and what to draw. The authors also release MathCanvas-Bench and use it to evaluate 20 LMMs. The resulting model, BAGEL-Canvas, is built on BAGEL and improves by 86% relative to strong baselines on this benchmark. It also transfers well to other math benchmarks. Ablations indicate that interleaved training improves the model's text-only reasoning as well.

## Key points
- **Pre-training corpus (15.2M pairs):**
  - MathCanvas-Imagen contains 10M caption-to-diagram pairs.
  - MathCanvas-Edit contains 5.2M stepwise editing trajectories, produced by LLM mining of competition problems combined with programmatic synthesis.
- **Fine-tuning data and benchmark:**
  - MathCanvas-Instruct has 219K interleaved visual-textual solutions.
  - MathCanvas-Bench has 3K problems that require mixed image-and-text answers.
- **Pre-training ablation (weighted score):**
  - Full BAGEL-Canvas scores 34.4.
  - Removing MathCanvas-Edit lowers this to 32.0.
  - Removing all pre-training lowers it to 30.8.
- **Visual-modality ablation:**
  - A variant trained only on text (BAGEL-Canvas-Text) scores 30.9.
  - The full model with image generation switched off at inference scores 31.9, which is still above the text-only variant.
- **Generalization and limitations:**
  - BAGEL-Canvas gains roughly 5–23 points over BAGEL across MathVerse, MathVision and MathVista.
  - The method relies on supervised fine-tuning only and targets school-level, geometry-heavy mathematics.
  - The evaluation does not check whether the intermediate diagrams are correct.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Chinese University of Hong Kong](https://md.research.elamur.ai/free/en/universities/chinese-university-of-hong-kong/) — University, Hong Kong, China · 126 works · 14,073 citations
- [Beihang University](https://md.research.elamur.ai/free/en/universities/beihang-university/) — University, Beijing, China · 65 works · 8,452 citations

📚 Shelves (3): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 16,667 works · [👁️ Computer Vision and Pattern Recognition](https://md.research.elamur.ai/free/en/shelves/computer-science/computer-vision-and-pattern-recognition/) · 2,869 works · [🧮 Computational Theory and Mathematics](https://md.research.elamur.ai/free/en/shelves/computer-science/computational-theory-and-mathematics/) · 252 works

🧭 Topics (2): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,426 works · [🖼️ Vision & language](https://md.research.elamur.ai/free/en/topics/multimodal/) · 657 works

## Cite

Cite as: 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. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{shi2026mathcanvas,
  title = {{MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning}},
  author = {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},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.1287},
  url = {https://doi.org/10.18653/v1/2026.acl-long.1287}
}
```

- [← previous MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis](https://md.research.elamur.ai/free/en/papers/yu-2026-mathagent-adversarial-evolution-constraint-graphs/)
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- [↑ back to papers of 2026](https://md.research.elamur.ai/free/en/papers/2026/page/5/)

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38. ByteDance Seed, :, Jiaze Chen, Tiantian Fan, Xin Liu, Lingjun Liu, Zhiqi Lin, Mingxuan Wang, Chengyi Wang, Xiangpeng Wei, Wenyuan Xu, Yufeng Yuan, Yu Yue, Lin Yan, Qiying Yu, Xiaochen Zuo, Chi Zhang, Ruofei Zhu, Zhecheng An, and 255 others. 2025. [Seed1.5-thinking: Advancing superb reasoning models w…](https://md.research.elamur.ai/free/en/papers/bytedance-seed-2025-seed1-5-thinking-advancing/)
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*Updated 1 November 2026*