GeoThought：用于增强视觉语言模型中数学几何推理能力的数据集
GeoThought: A Dataset for Enhancing Mathematical Geometry Reasoning in Vision-Language Models
AI总结：
针对LLM在几何视觉推理中性能下降的问题，本文构建了GeoThoughts数据集并训练GeoThought-MLLM模型，通过思维链训练显著提升了领域内外几何推理能力。
摘要：
大型语言模型（LLMs）在基于文本的数学问题求解中已展现出强大的推理能力；然而，当它们被应用于视觉推理任务，尤其是几何问题求解时，其性能显著下降，因为几何问题带来了独特的挑战。具体而言，这些挑战源于两个关键因素：第一，几何问题本身固有的复杂性，需要详细的图像理解和多步推理；第二，现有数据集的局限性，这些数据集缺乏足够的规模、多样性和显式的推理轨迹，从而阻碍了有效的模型训练。为了解决这些挑战，我们开发了GeoThoughts数据集，这是一个全面的几何推理语料库，包含两个子集：包含6,243个样本的Geo-Thought-6K及其增强版本Geo-Thought-Augmented-10K，后者包含10,834个样本。每个条目都包含视觉描述、逐步解决方案、显式推理链、反思步骤和最终答案。利用该数据集，我们开发了GeoThought-MLLM，一个数学推理多模态模型，该模型在问题求解过程中会生成详细的思考过程。我们的模型在几何任务上优于现有基准，表明使用我们的思维链（Chain-of-Thought）数据集进行训练能够提高模型在领域内和领域外场景中的几何推理能力。最后，我们分析了失败案例，并观察到错误主要源于对数学概念的错误解释或空间判断失误。通过调用思维链（CoT）来纠正这些错误，模型能够产生正确的答案。
英文摘要：
Large language models (LLMs) have demonstrated strong reasoning capabilities in text-based mathematical problem solving; however, when adapted to visual reasoning tasks, particularly geometric problem solving, their performance substantially declines because geometric problems present unique challenges. Specifically, these challenges stem from two key factors: first, the intrinsic complexity of geometry requiring detailed image comprehension and multi-step reasoning, and second, the limitations of existing datasets which lack sufficient scale, diversity, and explicit reasoning traces, consequently hindering effective model training. To address these challenges, we developed the GeoThoughts dataset, a comprehensive geometric reasoning corpus with two subsets: Geo-Thought-6K with 6,243 samples and its augmented version Geo-Thought-Augmented-10K containing 10,834 samples. Each entry includes visual descriptions, step-by-step solutions, explicit reasoning chains, reflection steps, and final answers. Using this dataset, we developed GeoThought-MLLM, a mathematical reasoning multimodal model that generates detailed thinking processes during problem-solving. Our model outperforms existing benchmarks in geometric tasks, demonstrating that training with our Chain-of-Thought dataset improves geometric reasoning capabilities across both in-domain and out-of-domain settings. Finally, we analyze failure cases and observe that errors primarily arise from incorrect interpretation of mathematical concepts or spatial misjudgment. By invoking CoT to correct these mistakes, the model produces correct answers.
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。
