Geo-Qwen: A Geometry Problem-Solving Method Based on Generative Large Language Models and Heuristic Reasoning

Research on geometry problem solving is gaining increasing attention in the field of Natural Language Processing (NLP). Currently, research in geometry problem solving often relies on formal logical language systems and traditional rule-based reasoning. However, the transformation from natural language to formal language inevitably leads to information loss, which impacts the accuracy and completeness of reasoning. In recent years, with the development of large language models (LLM) exemplified by the GPT architecture and significant improvements in natural language comprehension, research on purely natural language-based geometric reasoning has become increasingly popular. This paper presents a novel heuristic method for geometric reasoning, called Geo-Qwen, which enables the automatic generation of geometry problem-solving steps from natural language to natural language. To support reasoning, we introduce a geometric theorem library composed of 38 theorems as the reasoning knowledge base. Geo-Qwen employs a heuristic single-step reasoning strategy, automatically generating the next solution step based on a selected theorem, previously generated steps, and the problem information. The generation process of the solution steps can be viewed as constructing a reasoning tree. Additionally, to address the combinatorial explosion issue during reasoning, we utilize the T5 model as a theorem predictor to limit the number of theorems used at each step of reasoning. Finally, extensive experiments conducted on the UniGeo dataset and the Geometry3K dataset demonstrate that Geo-Qwen significantly outperforms existing methods.