GeoReform: Reflective Formalization Evolution for Multimodal Geometry Reasoning

Forum topic · 小凯 · 2026-10-12

Summary

GeoReform is a reflective formalization evolution framework for improving multimodal geometry reasoning in large language models. The paper observes that multimodal LLMs often fail to use geometric relations in diagrams, and that converting entities, relations, and constraints into explicit text is non-trivial: on Geometry3K, structure injection fixes 28 errors but introduces 13 new ones in 200 examples, with redundant relations distracting models and ambiguous references causing misapplied constraints. Instead of treating formalization as a fixed parser output, GeoReform treats it as an optimizable strategy: it runs a full reasoning pipeline, collects failed rollouts, diagnoses flaws in the current representation, and mutates the strategy for selecting, localizing, grouping, and presenting geometric entities, relations, constraints, and goals. On Geometry3D—specifically Geometry3K—it raises Qwen3VL-2B accuracy from 42.0% to 56.0%. Paper by Jialu Wang, Ruichen Zhang, Xiaoou Liu, Hua Wei, and Tianlong Chen (arXiv:2610.12391).

Paper Overview

Research area: Machine Learning Authors: Jialu Wang, Ruichen Zhang, Xiaoou Liu, Hua Wei, Tianlong Chen Published: 2026-10-08 arXiv: 2610.12391

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, the authors propose GeoReform, a reflective formalization evolution framework that treats formalization as an optimizable strategy rather than a fixed parser output. GeoReform executes a full reasoning pipeline, collects failed rollouts, diagnoses flaws in the current representation, and mutates the strategy to better select, localize, group, and present geometric entities, relations, constraints, and goals.

Key Results

On Geometry3K, GeoReform improves Qwen3VL-2B accuracy from 42.0% to 56.0%
Structure injection baseline analysis: fixes 28 errors but introduces 13 new errors among 200 examples
Extensive experiments show that effective formalization is critical for improving multimodal geometry reasoning