GeoReform: Reflective Formalization Evolution for Multimodal Geometry Problem Solving

arXiv:2610.12391v1 Announce Type: new 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.

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.

Artificial Intelligence (cs.AI)

arXiv:2610.12391 [cs.AI]

(or arXiv:2610.12391v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.12391 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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GeoReform: Reflective Formalization Evolution for Multimodal Geometry Problem Solving

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