Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

本研究解决了大型多模态模型在几何数学推理中因高质量图像-文本配对数据不足而面临的问题。提出的反向思维链（R-CoT）生成管道通过引入GeoChain生成高保真几何图像及其描述，并采用反向问答法进行逐步推理，从而生成问题。实验证明，该方法在多个基准上显著提升了性能，尤其在MathVista和GeoQA数据集上，R-CoT-8B超越了现有的开源数学模型和GPT-4o。 

R-CoT：反向思维链几何推理问题生成用于大型多模态模型