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

Peijie Wang; Ming-Liang Zhang; Jun Cao; Chao Deng; Dekang Ran; Hongda Sun; Pi Bu; Xuan Zhang; Yingyao Wang; Jun Song; Bo Zheng; Fei Yin; Cheng-Lin Liu

arXiv · 2604.11600

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

Peijie Wang·Ming-Liang Zhang·Jun Cao·Chao Deng·Dekang Ran·Hongda Sun·Pi Bu·Xuan Zhang·Yingyao Wang·Jun Song·Bo Zheng·Fei Yin·Cheng-Lin Liu

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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. To ensure syntactic correctness and geometric consistency, we propose a training paradigm that combines Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards. 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. Our data and code are available at Geoparsing.

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BibTeX RIS

Peijie Wang, Ming-Liang Zhang, Jun Cao, Chao Deng, Dekang Ran, Hongda Sun, Pi Bu, Xuan Zhang, Yingyao Wang, Jun Song, Bo Zheng, Fei Yin, Cheng-Lin Liu. 2026-04-13. Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language. https://arxiv.org/abs/2604.11600

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