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home / papers / 2026 / Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language

Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language

Paper · 2026 · Peijie Wang, Ming-Liang Zhang, Jun Cao et al.

Summary

Multimodal LLMs often fail at geometry problems because they misread diagrams. They miss or invent points, lines, and relations. Prior diagram-parsing work, such as PGDP5K and FormalGeo7K, handled only plane figures. The authors build a single formal language that adopts the predicate-style notation of PGPS9K and adds solid-geometry elements, including planes and named solids like prisms and pyramids. With it they release GDP-29K, a parsing dataset drawn from varied real-world sources. It contains printed and hand-drawn plane figures plus 3D figures, each annotated with a reference formal description. Their parser is trained first with supervised fine-tuning, then with reinforcement learning using verifiable rewards. A rule-based checker rewards outputs that are syntactically well-formed and geometrically consistent. The model scores 96.4 on the plane benchmark and 94.9 on the solid one, ahead of GPT-5.2 and Gemini-3-Flash. Feeding its parses to other MLLMs improves their geometry problem solving. This shows that explicit perception can support reasoning, especially for plane diagrams.

Key points

  • GDP-29K: a plane subset, PGDP-20K (printed and handwritten), and a solid subset, SGDP-9K. The test splits PGDP-2K and SGDP-1K are used for evaluation.
  • Training: SFT followed by RLVR with a rule-based verifier. The authors describe this as the first use of RL for geometry diagram parsing. GDP-4B-RL fully parses 72.8% of PGDP-2K diagrams and 70.9% of SGDP-1K diagrams (Perfect Parsing Rate).
  • Downstream gains for Qwen3-VL-8B: +10.1% on Geometry3K, +9.0% on PGPS9K, and +3.1% on SolidGeo. GPT-5.2 gains +4.1% on PGPS9K. Gains on solid geometry are smaller, and a few model–benchmark pairs drop slightly.
  • Formal vs. natural language: on PGPS9K, giving models the formal parse beats giving them an equivalent natural-language rewrite for all five models tested.
  • Limitations: the formalism does not mark hidden (dashed) elements as different from visible ones, and the solid-geometry annotations are semantically sparse.

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

🏢Alibaba GroupHangzhou · China201 works · 17,172 citations🏛️Chinese Academy of SciencesBeijing · China246 works · 24,952 citations🔬Institute of AutomationBeijing · China87 works · 14,883 citations🎓University of Chinese Academy of SciencesBeijing · China188 works · 8,744 citations🏢Alibaba Group (United States)San Mateo · United States8 works · 329 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 worksComputational Theory and Mathematics · 321 works

Cite

Cite as Peijie Wang, Ming-Liang Zhang, Jun Cao, Chao Deng, Dekang Ran, Pi Bu, Hongda Sun, Xuan Zhang, Yingyao Wang, Jun Song, Bo Zheng, Fei Yin and Cheng-Lin Liu. 2026. Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.findings-acl.1494

@inproceedings{wang2026geoparsing,
  title = {{Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language}},
  author = {Peijie Wang, Ming-Liang Zhang, Jun Cao, Chao Deng, Dekang Ran, Pi Bu, Hongda Sun, Xuan Zhang, Yingyao Wang, Jun Song, Bo Zheng, Fei Yin and Cheng-Lin Liu},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1494},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1494}
}

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