GeoFM: Enhancing Geometric Reasoning of MLLMs via Synthetic Data Generation through Formal Language

• URL: http://arxiv.org/abs/2510.27448v1
• Date: Fri, 31 Oct 2025 12:56:32 GMT
• Title: GeoFM: Enhancing Geometric Reasoning of MLLMs via Synthetic Data Generation through Formal Language
• Authors: Yuhao Zhang, Dingxin Hu, Tinghao Yu, Hao Liu, Yiting Liu,
• Abstract summary: Multi-modal Large Language Models (MLLMs) have gained significant attention in both academia and industry.<n>These models face challenges in mathematical geometric reasoning due to the scarcity of high-quality geometric data.<n>We propose GeoFM, a novel method for synthesizing geometric data.
• Score: 11.134307550723037
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multi-modal Large Language Models (MLLMs) have gained significant attention in both academia and industry for their capabilities in handling multi-modal tasks. However, these models face challenges in mathematical geometric reasoning due to the scarcity of high-quality geometric data. To address this issue, synthetic geometric data has become an essential strategy. Current methods for generating synthetic geometric data involve rephrasing or expanding existing problems and utilizing predefined rules and templates to create geometric images and problems. However, these approaches often produce data that lacks diversity or is prone to noise. Additionally, the geometric images synthesized by existing methods tend to exhibit limited variation and deviate significantly from authentic geometric diagrams. To overcome these limitations, we propose GeoFM, a novel method for synthesizing geometric data. GeoFM uses formal languages to explore combinations of conditions within metric space, generating high-fidelity geometric problems that differ from the originals while ensuring correctness through a symbolic engine. Experimental results show that our synthetic data significantly outperforms existing methods. The model trained with our data surpass the proprietary GPT-4o model by 18.7\% on geometry problem-solving tasks in MathVista and by 16.5\% on GeoQA. Additionally, it exceeds the performance of a leading open-source model by 5.7\% on MathVista and by 2.7\% on GeoQA.

Related papers

• Visual Diffusion Models are Geometric Solvers [54.31602846693932]
  We show that visual diffusion models can serve as effective geometric solvers by working in pixel space.<n>We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry.<n>We extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem.
  arXiv  Detail & Related papers  (2025-10-24T17:57:31Z)
• GeoRef: Referring Expressions in Geometry via Task Formulation, Synthetic Supervision, and Reinforced MLLM-based Solutions [45.70578816057097]
  We introduce the task of Referring Expression (REC) for geometric problems.<n>REC evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts.<n>We generate a large-scale synthetic training dataset using a structured geometric formal language.
  arXiv  Detail & Related papers  (2025-09-25T12:00:52Z)
• Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Models [63.331590876872944]
  We propose a method for deriving Riemannian metrics directly from pretrained Energy-Based Models.<n>These metrics define spatially varying distances, enabling the computation of geodesics.<n>We show that EBM-derived metrics consistently outperform established baselines.
  arXiv  Detail & Related papers  (2025-05-23T12:18:08Z)
• Geo-LLaVA: A Large Multi-Modal Model for Solving Geometry Math Problems with Meta In-Context Learning [4.4615747404424395]
  Geometry mathematics problems pose significant challenges for large language models (LLMs)<n>We collect a geometry question-answer dataset by sourcing geometric data from Chinese high school education websites, referred to as GeoMath.<n>We propose a Large Multi-modal Model (LMM) framework named Geo-LLaVA, which incorporates retrieval augmentation with supervised fine-tuning (SFT) in the training stage, called meta-training, and employs in-context learning (ICL) during inference to improve performance.
  arXiv  Detail & Related papers  (2024-12-12T07:34:09Z)
• Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning [53.13514542825493]
  We introduce a two-stage Theorem-d Reverse Chain-of-Thought Reasoning Synthesis (TRCoT) framework.<n>The first stage, TR-Engine, synthesizes theorem-grounded geometric diagrams with structured descriptions and properties.<n>The second stage, TR-Reasoner, employs reverse reasoning to iteratively refine question-answer pairs by cross-validating geometric properties and description fragments.
  arXiv  Detail & Related papers  (2024-10-23T13:58:39Z)
• Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver [11.69164802295844]
  We introduce a new framework that integrates visual features, geometric formal language, and natural language representations. We propose a novel synthetic data approach and create a large-scale geometric dataset, SynthGeo228K, annotated with both formal and natural language captions. Our framework improves MLLMs' ability to process geometric diagrams and extends their application to open-ended tasks on the formalgeo7k dataset.
  arXiv  Detail & Related papers  (2024-09-06T12:11:06Z)
• GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generation [15.931398242118073]
  GPT-4 and GPT-4V are used to generate basic geometry problems with aligned text and images. We have produced a dataset of 4.9K geometry problems and combined it with 19K open-source data to form our GeoGPT4V dataset. Results demonstrate that the GeoGPT4V dataset significantly improves the geometry performance of various models on the MathVista and MathVision benchmarks.
  arXiv  Detail & Related papers  (2024-06-17T13:04:27Z)
• A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications [71.809127869349]
  This paper formalizes geometric graph as the data structure, on top of which we provide a unified view of existing models from the geometric message passing perspective.<n>We also summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation.
  arXiv  Detail & Related papers  (2024-03-01T12:13:04Z)
• Adaptive Surface Normal Constraint for Geometric Estimation from Monocular Images [56.86175251327466]
  We introduce a novel approach to learn geometries such as depth and surface normal from images while incorporating geometric context. Our approach extracts geometric context that encodes the geometric variations present in the input image and correlates depth estimation with geometric constraints. Our method unifies depth and surface normal estimations within a cohesive framework, which enables the generation of high-quality 3D geometry from images.
  arXiv  Detail & Related papers  (2024-02-08T17:57:59Z)
• G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model [121.07873620883322]
  Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities.<n>G-LLaVA demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.
  arXiv  Detail & Related papers  (2023-12-18T17:36:20Z)
• GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning [172.36214872466707]
  We focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. We propose a Geometric Question Answering dataset GeoQA, containing 5,010 geometric problems with corresponding annotated programs.
  arXiv  Detail & Related papers  (2021-05-30T12:34:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.