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

arXiv: https://arxiv.org/abs/2604.11600 · HTML: https://mlsanity.com/paper/2604.11600/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 24 of 24)

- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Engine](https://mlsanity.com/paper/2407.08739/) (2024)
- [LongDocURL: a Comprehensive Multimodal Long Document Benchmark Integrating Understanding, Reasoning, and Locating](https://mlsanity.com/paper/2412.18424/) (2024)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solving](https://mlsanity.com/paper/2402.10104/) (2024)
- [DetermLR: Augmenting LLM-based Logical Reasoning from Indeterminacy to Determinacy](https://mlsanity.com/paper/2310.18659/) (2023)
- [MV-MATH: Evaluating Multimodal Math Reasoning in Multi-Visual Contexts](https://mlsanity.com/paper/2502.20808/) (2025)
- [AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understanding](https://mlsanity.com/paper/2409.09039/) (2024)
- [FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solving](https://mlsanity.com/paper/2310.18021/) (2023)
- [GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training](https://mlsanity.com/paper/2412.11863/) (2024)
- [SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry](https://mlsanity.com/paper/2505.21177/) (2025)
- [EAGLE: Elevating Geometric Reasoning through LLM-empowered Visual Instruction Tuning](https://mlsanity.com/paper/2408.11397/) (2024)
- [PeRL: Permutation-Enhanced Reinforcement Learning for Interleaved Vision-Language Reasoning](https://mlsanity.com/paper/2506.14907/) (2025)
- [Towards Geometry Problem Solving in the Large Model Era: A Survey](https://mlsanity.com/paper/2506.02690/) (2025)
- [GeoVLMath: Enhancing Geometry Reasoning in Vision-Language Models via Cross-Modal Reward for Auxiliary Line Creation](https://mlsanity.com/paper/2510.11020/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [VLM-Loc: Localization in Point Cloud Maps via Vision-Language Models](https://mlsanity.com/paper/2603.09826/) (2026)

## Built on by (most cited first, 1 of 1)

- [Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry](https://mlsanity.com/paper/2608.30457/) (2026)

## Abstract (arXiv)

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.