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home / papers / 2024 / MathGLM-Vision: Solving Mathematical Problems with Multi-Modal Large Language Model

MathGLM-Vision: Solving Mathematical Problems with Multi-Modal Large Language Model

Paper · 2024 · Zhen Yang, Jinhao Chen, Zhengxiao Du et al.

Summary

Most math-focused multi-modal LLMs (MLLMs) are trained almost entirely on geometry, using small public sets such as GeoQA and Geometry3K whose answers rarely show the reasoning. The authors argue that this ignores the visual material found in other branches of school mathematics. They note that roughly 63% of Chinese K12 math questions contain images. To address this, they built MathVL, a supervised fine-tuning corpus with two parts. The first is a set of public datasets whose short answers were expanded into step-by-step solutions using GPT-4o and then checked. The second is a large new Chinese K12 collection covering arithmetic, algebra, geometry, statistics and word problems, in several question formats and sometimes with multiple images per problem. Fine-tuning three backbones on MathVL produced the MathGLM-Vision family. These models clearly beat their base models on MathVista's geometry subset and on a new 2,000-problem MathVL-test, and the authors report that general vision-language ability is preserved. The work shows that diverse, solution-rich training data matters for visual math reasoning.

Key points

  • Models: MathGLM-Vision-9B, -19B and -32B are fine-tuned from GLM-4V-9B, CogVLM2 and CogVLM-32B, respectively.
  • Data: The Chinese K12 portion contains 341,346 problems. The open-source portion contains 145,568 samples drawn from ChartQA, UniGeo-Calculation, Geometry3K, GeoQA+, Geo170K and GeomVerse.
  • Main result: Relative gains over the backbones on the MathVista GPS minitest are about 39.7% (9B), 65.1% (19B) and 51–54% (32B). For the 32B model, the paper reports 51.05% in the introduction and 53.7% in the conclusion.
  • Evaluation: Models were tested on four public benchmarks plus the curated MathVL-test (2,000 problems). Ablations with and without image input confirm that visual information substantially boosts accuracy, both for MathGLM-Vision and for commercial models such as GPT-4o.
  • Error analysis (32B model): Knowledge errors account for about 12.7% of mistakes and vision recognition errors for 11.4%. Calculation errors (4.3%) and question misunderstanding (2.5%) are comparatively rare.

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

🎓Tsinghua UniversityBeijing · China333 works · 87,019 citations🎓Beihang UniversityBeijing · China65 works · 8,452 citations🏢Zhipu AIBeijing · China22 works · 2,364 citations

 Fields, topics and concepts

📚 Shelves 6The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksComputer Vision and Pattern Recognition · 2,869 worksComputational Theory and Mathematics · 252 works

🧭 Topics 3Research subjects and languages the work is about.Language models & pretraining · 3,320 worksReasoning · 1,426 worksVision & language · 657 works

Cite

Cite as Zhen Yang, Jinhao Chen, Zhengxiao Du, Wenmeng Yu, Weihan Wang, Wenyi Hong, Zhihuan Jiang, Bin Xu and Jie Tang. 2024. MathGLM-Vision: Solving Mathematical Problems with Multi-Modal Large Language Model. arXiv:2409.13729.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2409.13729 · arXiv 2409.13729

@misc{yang2024mathglm,
  title = {{MathGLM-Vision: Solving Mathematical Problems with Multi-Modal Large Language Model}},
  author = {Zhen Yang, Jinhao Chen, Zhengxiao Du, Wenmeng Yu, Weihan Wang, Wenyi Hong, Zhihuan Jiang, Bin Xu and Jie Tang},
  year = {2024},
  doi = {10.48550/arxiv.2409.13729},
  eprint = {2409.13729},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2409.13729}
}

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