@inproceedings{wang-etal-2026-geoparsing,
title = "Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language",
author = "Wang, Peijie and
Zhang, Ming-Liang and
Cao, Jun and
Deng, Chao and
Ran, Dekang and
Bu, Pi and
Sun, Hongda and
Zhang, Xuan and
Wang, Yingyao and
Song, Jun and
Zheng, Bo and
Yin, Fei and
Liu, Cheng-Lin",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-acl.1494/",
pages = "29876--29903",
ISBN = "979-8-89176-395-1",
abstract = "Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. We propose a training paradigm combining Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards, which effectively enforces syntactic correctness and geometric consistency. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs' capabilities for downstream geometry reasoning tasks."
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<abstract>Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. We propose a training paradigm combining Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards, which effectively enforces syntactic correctness and geometric consistency. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs’ capabilities for downstream geometry reasoning tasks.</abstract>
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%0 Conference Proceedings
%T Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language
%A Wang, Peijie
%A Zhang, Ming-Liang
%A Cao, Jun
%A Deng, Chao
%A Ran, Dekang
%A Bu, Pi
%A Sun, Hongda
%A Zhang, Xuan
%A Wang, Yingyao
%A Song, Jun
%A Zheng, Bo
%A Yin, Fei
%A Liu, Cheng-Lin
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F wang-etal-2026-geoparsing
%X Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. We propose a training paradigm combining Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards, which effectively enforces syntactic correctness and geometric consistency. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs’ capabilities for downstream geometry reasoning tasks.
%U https://aclanthology.org/2026.findings-acl.1494/
%P 29876-29903
Markdown (Informal)
[Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language](https://aclanthology.org/2026.findings-acl.1494/) (Wang et al., Findings 2026)
ACL
- 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. In Findings of the Association for Computational Linguistics: ACL 2026, pages 29876–29903, San Diego, California, United States. Association for Computational Linguistics.