用定理验证的逆向思维生成几何推理数据，提升模型理解能力
Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning
- 基于定理构建几何图示与描述，逆向迭代优化问答对
- 逻辑一致性提升24.5%，在两个数据集上分别领先10.1%和4.7%
- 适合需要高精度几何推理的AI研究者与教育技术开发者
大型多模态模型在几何推理方面受限于缺乏链式思维（CoT）图像-文本训练数据。现有模板或大语言模型辅助方法常难以兼顾多样性与准确性。为此，我们提出两阶段定理验证逆向链式思维合成框架（TR-CoT）。第一阶段TR-Engine生成基于定理的几何图示，附带结构化描述与属性；第二阶段TR-Reasoner通过逆向推理，结合几何属性与描述片段交叉验证，迭代优化问题与答案对。该方法扩展了定理类型覆盖范围，纠正长期误解，增强几何推理能力。细粒度链式思维使定理理解更深入，逻辑一致性提升24.5%。最佳模型在MathVista和GeoQA上分别优于基线10.1%和4.7%，超越GPT-4o等先进闭源模型。
原文摘要 · Abstract (English)
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.
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