Towards Better Quantity Representations for Solving Math Word Problems

Solving a math word problem requires selecting quantities in it and performing appropriate arithmetic operations to obtain the answer. For deep learning-based methods, it is vital to obtain good quantity representations, i.e., to selectively and emphatically aggregate information in the context of quantities. However, existing works have not paid much attention to this aspect. Many works simply encode quantities as ordinary tokens, or use some implicit or rule-based methods to select information in their context. This leads to poor results when dealing with linguistic variations and confounding quantities. This paper proposes a novel method to identify question-related distinguishing features of quantities by contrasting their context with the question and the context of other quantities, thereby enhancing the representation of quantities. Our method not only considers the contrastive relationship between quantities, but also considers multiple relationships jointly. Besides, we propose two auxiliary tasks to further guide the representation learning of quantities: 1) predicting whether a quantity is used in the question; 2) predicting the relations (operators) between quantities given the question. Experimental results show that our method outperforms previous methods on SVAMP and ASDiv-A under similar settings, even some newly released strong baselines. Supplementary experiments further confirm that our method indeed improves the performance of quantity selection by improving the representation of both quantities and questions.