Geometry problem solving presents a formidable challenge within the NLP community. Existing approaches often rely on models designed for solving math word problems, neglecting the unique characteristics of geometry math problems. Additionally, the current research predominantly focuses on geometry calculation problems, while overlooking other essential aspects like proving. In this study, we address these limitations by proposing the Geometry-Aware Problem Solver (GAPS) model. GAPS is specifically designed to generate solution programs for geometry math problems of various types with the help of its unique problem-type classifier. To achieve this, GAPS treats the solution program as a composition of operators and operands, segregating their generation processes. Furthermore, we introduce the geometry elements enhancement method, which enhances the ability of GAPS to recognize geometry elements accurately. By leveraging these improvements, GAPS showcases remarkable performance in resolving geometry math problems. Our experiments conducted on the UniGeo dataset demonstrate the superiority of GAPS over the state-of-the-art model, Geoformer. Specifically, GAPS achieves an accuracy improvement of more than 5.3% for calculation tasks and an impressive 41.1% for proving tasks. Notably, GAPS achieves an impressive accuracy of 97.5% on proving problems, representing a significant advancement in solving geometry proving tasks.

翻译：几何问题求解是自然语言处理领域中的一项严峻挑战。现有方法通常依赖于为求解数学文字题而设计的模型，忽视了几何数学问题的独特特征。此外，当前研究主要聚焦于几何计算问题，而忽略了证明等其他关键方面。在本研究中，我们通过提出几何感知问题求解器（GAPS）模型来解决这些局限性。GAPS专门设计用于借助其独特的问题类型分类器，为各种类型的几何数学问题生成求解程序。为此，GAPS将求解程序视为运算符和操作数的组合，并分离它们的生成过程。此外，我们引入了几何元素增强方法，提升了GAPS准确识别几何元素的能力。借助这些改进，GAPS在解决几何数学问题中展现出卓越性能。我们在UniGeo数据集上进行的实验表明，GAPS的性能优于当前最先进的模型Geoformer。具体而言，在计算任务中GAPS的准确率提升了超过5.3%，而在证明任务中更是实现了惊人的41.1%的准确率提升。值得注意的是，GAPS在证明问题上达到了97.5%的出色准确率，标志着在解决几何证明任务方面取得了重大进展。