用于几何推理的定理验证逆向思维链问题生成
Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning
AI总结：
针对大型多模态模型几何推理数据不足的问题，提出两阶段TR-CoT框架，通过定理验证的逆向思维链合成图文数据，显著提升了模型在MathVista和GeoQA等基准上的几何推理能力。
摘要：
大型多模态模型（LMMs）由于缺乏思维链（CoT）图文训练数据，在几何推理方面存在局限。现有方法利用基于模板或LLM辅助的方法创建几何CoT数据，但往往难以兼顾多样性与精确性。为弥补这一不足，我们提出了两阶段的定理验证逆向思维链推理合成（TR-CoT）框架。第一阶段TR-Engine合成具有结构化描述和属性的定理几何图形。第二阶段TR-Reasoner采用逆向推理，通过交叉验证几何属性和描述片段来迭代优化问答对。该方法扩展了定理类型覆盖范围，纠正了长期存在的误解，并增强了几何推理。细粒度CoT提升了定理理解，将逻辑一致性提高了24.5%。我们的最佳模型在MathVista和GeoQA上分别以10.1%和4.7%的优势超越基线，优于GPT-4o等先进闭源模型。
英文摘要：
Large Multimodal Models (LMMs) face limitations in geometric reasoning due to insufficient Chain of Thought (CoT) image-text training data. While existing approaches leverage template-based or LLM-assisted methods for geometric CoT data creation, they often face challenges in achieving both diversity and precision. To bridge this gap, we introduce a two-stage Theorem-Validated Reverse Chain-of-Thought Reasoning Synthesis (TR-CoT) framework. The first stage, TR-Engine, synthesizes theorem-grounded geometric diagrams with structured descriptions and properties. The second stage, TR-Reasoner, employs reverse reasoning to iteratively refine question-answer pairs by cross-validating geometric properties and description fragments. Our approach expands theorem-type coverage, corrects long-standing misunderstandings, and enhances geometric reasoning. Fine-grained CoT improves theorem understanding and increases logical consistency by 24.5%. Our best models surpass the baselines in MathVista and GeoQA by 10.1% and 4.7%, outperforming advanced closed-source models like GPT-4o.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
