摘要：

数学应用题(MWP)的计算机自动求解是当前学术界的研究热点。尽管现有研究已取得显著进展, 但多数研究将MWP中的数值替换为占位符并作为普通文本进行处理, 忽略了数值语义对于MWP求解的重要性。因此, 基于"编码器-解码器"的通用架构提出了一种增强数值表示的MWP求解模型。该模型引入了两项新颖的设计来增强数值编码能力并提升MWP的求解性能, 利用图卷积神经网络(GCNN)来显示建模数值之间以及数值与上下文文本之间的语义关系; 引入辅助学习任务来指导模型充分捕捉与任务相关的数值语义, 显著增强编码器的数值建模能力。在常用的MWP数据集Math23K和MAWPS上的实验结果表明, 所提出的模型充分利用到了数值语义, 模型整体性能优于现有的主流MWP求解模型。

关键词: 数学应用题, 图卷积神经网络, 辅助学习任务, 图编码层, 图变换层

Abstract:

The automatic resolution of Math Word Problems (MWP) is a current research hotspot in the academic community. Despite the significant progress made in the existing research, most studies treat numerical values in MWPs as placeholders and simply process them as ordinary text, overlooking the importance of numerical semantics in solving MWPs. To address this issue, this study proposes an enhanced numerical representation model for MWP solving based on the generic "encoder-decoder" architecture. The model achieves this by utilizing Graph Convolutional Neural Networks (GCNN) to explicitly model the semantic relationships between numerical values and between numerical values and context text and introducing auxiliary learning tasks to guide the model to fully capture task-related numerical semantics. This significantly enhances the numerical modeling capability of the encoder. Empirical evidence from the commonly used MWP datasets, Math23K and MAWPS, shows that the proposed model can fully consider numerical semantics and outperform mainstream classical models in solving large-scale Chinese application problem sets.

Key words: Math Word Problems (MWP), Graph Convolutional Neural Networks (GCNN), auxiliary learning tasks, graph encoding layer, graph transformation layer