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

• URL: http://arxiv.org/abs/2604.11600v2
• Date: Thu, 16 Apr 2026 11:28:39 GMT
• Title: Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language
• Abstract summary: We design a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations.<n>We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources.
• Score: 60.70116693224378
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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