发表机构
Tongji University; University of North Carolina at Chapel Hill; Arizona State University（同济大学; 北卡罗来纳大学教堂山分校; 亚利桑那州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
GeoReform是将形式化视为可优化策略的反思式演化框架，通过优化几何表示提升多模态几何推理，使Qwen3VL-2B在Geometry3K上准确率达56.0%。
AI 中文摘要
多模态大语言模型（MLLMs）常难以识别和利用图表中的几何关系。现有方法通过将几何实体、关系和约束转换为显式文本表示供模型推理来应对这一挑战，但有效的形式化过程极具挑战性：在Geometry3K数据集的200个示例中，结构注入修复了28个错误，却引入了13个新错误；冗余关系会干扰模型，对图表元素的模糊引用会导致模型错误应用约束。这表明关键挑战不仅是提取更多几何事实，而是将其组织为支持下游推理的表示。为充分发挥形式化的作用，我们提出GeoReform，一种将形式化视为可优化策略而非固定解析器输出的反思式形式化演化框架。GeoReform执行完整推理流程，收集失败的推演，诊断当前表示的缺陷，并对策略进行变异，以更好地选择、定位、分组和呈现几何实体、关系、约束及目标。在Geometry3K上，GeoReform将Qwen3VL-2B的准确率从42.0%提升至56.0%。在多个几何推理基准上的大量实验和分析表明，有效的形式化对提升多模态几何推理至关重要。
英文摘要
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.
