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A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning

Paper · 2026 · Tianyu Yang, Sihong Wu, Yilun Zhao et al.

Summary

This survey covers multimodal mathematical reasoning (MMR), where a model must solve math problems that combine text with diagrams, plots, charts, tables or images. The authors note three common failures of current multimodal LLMs: they misread visuals, fail to connect symbols with visual evidence, and produce inconsistent intermediate steps. Most evaluations also check only the final answer.

Earlier surveys mainly list benchmarks. This one takes a process-oriented view built on four questions: what to extract, how to represent and align modalities, how to reason, and how to judge correctness. Methods are arranged in a Perception–Alignment–Reasoning (PAR) pipeline, and benchmarks are mapped to an Answer–Process–Executable (APE) evaluation hierarchy. Coverage spans geometry, chart/table tasks and visual math word problems. Approaches range from symbolic parsers to LMM-based pipelines, RL, tool use and process reward models.

The authors argue that faithful reasoning depends on structured perception, executable intermediates and step-level verification. The survey gives researchers a shared map for comparing methods and diagnosing failures. An open GitHub repository tracks new work.

Key points

  • PAR framework:
    • Perception extracts primitives, relations and quantities.
    • Alignment maps these facts to symbolic or executable forms.
    • Reasoning covers CoT, RL, tool-augmented methods and process verification.
  • APE hierarchy: evaluation is graded at three levels: answer accuracy, faithfulness of intermediate steps, and executable checking.
  • Datasets and systems surveyed:
    • Geometry: Geometry3K, GeoQA/GeoQA+, PGPS9K, FormalGeo, Inter-GPS, E-GPS, Pi-GPS, AlphaGeometry.
    • Charts and tables: ChartQA, PlotQA, TABMWP.
    • Process evaluation: MPBench, ErrorRadar, We-Math, MathVerse.
  • Open challenges:
    • Perception is shallow and breaks under layout changes.
    • Domain-specific languages are fragmented and unit handling is inconsistent.
    • Long reasoning chains drift away from visual evidence.
    • RL is costly and sensitive to reward design.
  • Scope limits: 3D, video and interactive tutoring settings are only briefly mentioned. Suggested applications include tutoring, automated grading and accessibility tools such as MathCAT.

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

🎓New York UniversityNew York · United States219 works · 103,487 citations🎓Columbia UniversityNew York · United States254 works · 56,747 citations🎓Yale UniversityNew Haven · United States101 works · 13,302 citations🎓University of Notre DameNotre Dame · United States59 works · 37,127 citations🎓Pennsylvania State UniversityState College · United States67 works · 5,865 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksComputer Vision and Pattern Recognition · 3,486 worksComputational Theory and Mathematics · 321 works

🧭 Topics 2Research subjects and languages the work is about.Reasoning · 1,685 worksVision & language · 811 works

Cite

Cite as Tianyu Yang, Sihong Wu, Yilun Zhao, Zhenwen Liang, Lisen Dai, Chen Zhao, Minhao Cheng, Arman Cohan and Xiangliang Zhang. 2026. A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to 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. DOI 10.18653/v1/2026.acl-long.1961

@inproceedings{yang2026survey,
  title = {{A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning}},
  author = {Tianyu Yang, Sihong Wu, Yilun Zhao, Zhenwen Liang, Lisen Dai, Chen Zhao, Minhao Cheng, Arman Cohan and Xiangliang Zhang},
  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.1961},
  url = {https://doi.org/10.18653/v1/2026.acl-long.1961}
}

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