简洁几何描述作为桥梁：释放LLM在平面几何问题求解中的潜力
Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solving
AI总结：
本文提出通过训练多模态大语言模型解释器生成几何描述，再利用通用LLM进行推理，以解决平面几何问题。通过设计CDL匹配奖励机制，提升生成几何描述的效率，并在新构建的Formalgeo7k-Rec-CoT数据集上验证了方法的有效性。
摘要：
平面几何问题求解（PGPS）是一种多模态推理任务，旨在基于几何图示和问题文本描述解决平面几何问题。尽管大型语言模型（LLMs）具有强大的推理能力，但其直接应用于PGPS受限于无法处理视觉图示。现有工作通常端到端微调多模态大语言模型（MLLMs）在大规模PGPS数据上以增强视觉理解和推理。然而，这种联合优化可能损害基础LLMs的固有推理能力。本文观察到LLM本身在适当将视觉信息转化为文本描述时可能成为强大的PGPS求解器。我们提出训练MLLM解释器生成几何描述，然后利用现成LLM进行推理。具体而言，我们选择条件声明语言（CDL）作为几何描述，因其简洁性有助于MLLM解释器训练。MLLM解释器通过CoT（链式推理）增强的SFT后接GRPO进行微调以生成CDL。而非使用传统基于解决方案的奖励比较推理结果与地面真相答案，我们设计CDL匹配奖励以促进更有效的GRPO训练，从而为CDL生成提供更直接和密集的指导。为支持训练，我们构建了新的数据集Formalgeo7k-Rec-CoT，通过手动审查Formalgeo7k v2并加入CoT注释。在Formalgeo7k-Rec-CoT、Unigeo和MathVista上的广泛实验表明，我们的方法（仅在5.5k数据上微调）在领先的开源和闭源MLLMs中表现优异。
英文摘要：
Plane Geometry Problem Solving (PGPS) is a multimodal reasoning task that aims to solve a plane geometric problem based on a geometric diagram and problem textual descriptions. Although Large Language Models (LLMs) possess strong reasoning skills, their direct application to PGPS is hindered by their inability to process visual diagrams. Existing works typically fine-tune Multimodal LLMs (MLLMs) end-to-end on large-scale PGPS data to enhance visual understanding and reasoning simultaneously. However, such joint optimization may compromise base LLMs' inherent reasoning capability. In this work, we observe that LLM itself is potentially a powerful PGPS solver when appropriately formulating visual information as textual descriptions. We propose to train a MLLM Interpreter to generate geometric descriptions for the visual diagram, and an off-the-shelf LLM is utilized to perform reasoning. Specifically, we choose Conditional Declaration Language (CDL) as the geometric description as its conciseness eases the MLLM Interpreter training. The MLLM Interpreter is fine-tuned via CoT (Chain-of-Thought)-augmented SFT followed by GRPO to generate CDL. Instead of using a conventional solution-based reward that compares the reasoning result with the ground-truth answer, we design CDL matching rewards to facilitate more effective GRPO training, which provides more direct and denser guidance for CDL generation. To support training, we construct a new dataset, Formalgeo7k-Rec-CoT, by manually reviewing Formalgeo7k v2 and incorporating CoT annotations. Extensive experiments on Formalgeo7k-Rec-CoT, Unigeo, and MathVista show our method (finetuned on only 5.5k data) performs favorably against leading open-source and closed-source MLLMs.
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。
