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home / papers / 2024 / DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models

DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models

Paper · 2024 · Chengke Zou, Xingang Guo, Rui Yang et al.

Summary

Vision-language models (VLMs) now score well on visual math benchmarks. Those benchmarks are fixed question sets, though, so they cannot show whether a model's reasoning survives small changes to a problem, and they may reward memorized patterns. The authors build DynaMath, where each of 501 seed questions is a hand-written Python program. Each program randomly alters numbers, function types, graph structures, geometric layouts or operations, then renders the matching image and ground-truth answer. Seeds cover nine topics, from Plane Geometry and Algebra to Graph Theory and Scientific Figures, mostly at high-school and undergraduate level. The authors tested 14 closed- and open-source VLMs on 5,010 generated items, ten per seed. They compared average accuracy with worst-case accuracy, which credits a seed only if all ten variants are answered correctly. For every model, the worst-case score falls near or below half of the average. Repeated sampling indicates these errors are largely systematic, not random noise. The work gives a reusable tool for measuring reasoning robustness beyond memorization.

Key points

  • DynaMath contains 501 seed questions, each a Python program generating visual and textual variants with automatically computed answers. The project page is dynamath.github.io.
  • The nine subject areas are Arithmetic, Algebra, three branches of geometry (Plane, Solid and Analytic), Puzzle Tests, Graph Theory, Statistics and Scientific Figures.
  • Evaluated models include GPT-4o, Gemini Pro, Claude-3.5 Sonnet, InternVL2, LLaVA-v1.6, Qwen2-VL, DeepSeek-VL and Llama 3.2, tested on 5,010 concrete questions.
  • All models show worst-case accuracy close to or under 50% of their average-case accuracy. A repetition-consistency metric confirms that many failures recur on specific variants.
  • Example: GPT-4o repeatedly claims a shifted |x − a| has its corner at x = 0. It answered one such variant wrongly with 90% repetition consistency.

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

🎓University of California, BerkeleyBerkeley · United States243 works · 251,774 citations🎓University of Illinois Urbana-ChampaignUrbana · United States228 works · 74,590 citations

 Fields, topics and concepts

📚 Shelves 7The field of science this work belongs to (OpenAlex fields).Computer Science · 19,503 worksArtificial Intelligence · 18,805 worksArts and Humanities · 17,959 worksLanguage and Linguistics · 17,789 worksComputer Vision and Pattern Recognition · 3,621 worksMathematics · 233 worksApplied Mathematics · 73 works

🧭 Topics 4Research subjects and languages the work is about.Language models & pretraining · 4,145 worksReasoning · 1,948 worksEvaluation & benchmarks · 1,394 worksVision & language · 827 works

Cite

Cite as Chengke Zou, Xingang Guo, Rui Yang, Junyu Zhang, Bin Hu and Huan Zhang. 2024. DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models. arXiv:2411.00836.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2411.00836 · arXiv 2411.00836

@misc{zou2024dynamath,
  title = {{DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models}},
  author = {Chengke Zou, Xingang Guo, Rui Yang, Junyu Zhang, Bin Hu and Huan Zhang},
  year = {2024},
  doi = {10.48550/arxiv.2411.00836},
  eprint = {2411.00836},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2411.00836}
}

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