Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver

TL;DR

This paper introduces DFE-GPS, a framework that combines visual, formal, and natural language representations to improve AI's understanding and solving of geometry problems involving diagrams.

Contribution

It presents a novel synthetic dataset and a formalization method to enhance multi-modal models' ability to interpret geometric diagrams.

Findings

Improved performance on geometric problem solving tasks.

Enhanced understanding of geometric diagrams by MLLMs.

Effective integration of visual and formal language representations.

Abstract

Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to understand geometric diagrams, performing no better in geometry problem solving than LLMs that only process text. This limitation is amplified by the lack of effective methods for representing geometric relationships. To address these issues, we introduce the Diagram Formalization Enhanced Geometry Problem Solver (DFE-GPS), 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, designed to enhance the vision encoder for a better understanding of geometric structures. Our framework improves MLLMs' ability to process geometric diagrams and extends their application to open-ended tasks on the formalgeo7k dataset.