GeoReform: Reflective Formalization Evolution for Multimodal Geometry Problem Solving
GeoReform revises geometric formalizations, lifting Qwen3VL-2B from 42% to 56% on Geometry3K.
Multimodal models often mishandle geometric relations in diagrams, and naive structure injection on Geometry3K fixed 28 errors while introducing 13 new ones among 200 examples. GeoReform treats formalization as an optimizable policy: it runs the reasoning pipeline, diagnoses failed rollouts, and mutates how entities, relations, constraints, and targets are selected and presented. On Geometry3K, it raises Qwen3VL-2B accuracy from 42.0% to 56.0%.
- Formalization treated as an evolvable policy, not a fixed parser
- Structure injection fixed 28 errors but added 13 on 200 examples
- Qwen3VL-2B accuracy rises from 42% to 56% on Geometry3K
- Failed rollouts drive selection, grounding, and grouping changes
Full article189 words · extracted from arxiv.org · click to collapse
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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2610.12391