GeoReform: Reflective Formalization Evolution for Multimodal Geometry Problem Solving

2026-10-08

AI Summary

This study addresses the difficulty multimodal models face in accurately recognizing geometric relations, where existing formalization methods often introduce redundancy or ambiguity that leads to reasoning errors. To this end, we propose GeoReform, a framework that formulates geometric formalization as an optimizable policy and introduces the first reflective formalization evolution mechanism. By integrating multimodal large language models, reinforcement learning-based policy evolution, and structured geometric entity constraints, GeoReform dynamically adjusts representations through reflection on failure cases, thereby overcoming the limitations of fixed parsers and achieving closed-loop optimization of representation quality. Evaluated on the Geometry3K benchmark, our approach improves the accuracy of Qwen3VL-2B from 42.0% to 56.0%, significantly enhancing the model's geometric reasoning capabilities.

Abstract

Multimodal large language models (MLLMs) often struggle to identify and use geometric relations in diagrams. Recent methods address this challenge by converting geometric entities, relations, and constraints into explicit textual representations for the model to reason over. However, effective formalization is highly non-trivial: on Geometry3K, structure injection fixes 28 errors but introduces 13 new ones among 200 examples. Redundant relations can distract the model, while ambiguous references to diagram elements can lead it to apply constraints incorrectly. This suggests that the key challenge is not merely extracting more geometric facts, but organizing them into representations that support downstream reasoning. To fully exploit the power of formalization, we further propose GeoReform, a reflective formalization evolution framework that treats formalization as an optimizable policy rather than a fixed parser output. GeoReform executes the full reasoning pipeline, collects failed rollouts, diagnoses defects in the current representation, and mutates the policy to better select, ground, group, and present geometric entities, relations, constraints, and targets. On Geometry3K, GeoReform improves Qwen3VL-2B accuracy from 42.0\% to 56.0\%. Extensive experiments and analyses across geometry reasoning benchmarks demonstrate that effective formalization is crucial for improving multimodal geometry reasoning.

Problem

• Multimodal Geometry Problem Solving
• Geometric Formalization
• Multimodal Large Language Models
• Geometric Reasoning

Innovation

• Reflective Formalization Evolution
• Multimodal Geometry Problem Solving
• Optimizable Policy
• MLLMs
• Failed Rollout Diagnosis