A Knowledge-Aware Sequence-to-Tree Network for Math Word Problem Solving

Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing, pages 7137–7146, November 16–20, 2020. c⃝2020 Association for Computational Linguistics 7137 A Knowledge-Aware Sequence-to-Tree Network for Math Word Problem Solving Qinzhuo Wu, Qi Zhang∗, Jinlan Fu, Xuanjing Huang Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, China (qzwu17,qz,fujl16,xjhuang)@fudan.edu.cn Abstract With the advancements in natural language processing tasks, math word problem solving has received increasing attention. Previous methods have achieved promising results but ignore background common-sense knowledge not directly provided by the problem. In addition, during generation, they focus on local features while neglecting global informa- tion. To incorporate external knowledge and global expression information, we propose a novel knowledge-aware sequence-to-tree (KA- S2T) network in which the entities in the problem sequences and their categories are modeled as an entity graph. Based on this entity graph, a graph attention network is used to capture knowledge-aware problem repre- sentations. Further, we use a tree-structured decoder with a state aggregation mechanism to capture the long-distance dependency and global expression information. Experimental results on the Math23K dataset revealed that the KA-S2T model can achieve better perfor- mance than previously reported best results. 1 Introduction Math word problem solving has attracted increas- ing attention, and many math word problem solving systems have been developed. Early statisti- cal learning methods (Feigenbaum et al., 1963; Fletcher, 1985; Bakman, 2007; Roy and Roth, 2016) extracted templates or features from prob- lems and generated corresponding math expres- sions based on these templates or features. These methods require a large number of manually for- mulated features or can only be applied to small application problems in small areas. In recent years, many methods (Wang et al., 2017, 2018b; Xie and Sun, 2019) have been developed that apply neural networks to analyze math word problems, with ∗Corresponding author. Problem: Alan bought 2 green apples, 3 red apples, and 4 oranges for a total of $50. Each apple weighed 0.4 kg and is worth $6. Each orange weighs half as much as an apple. How much does each orange cost? Knowledge: Expression tree: Expression sequence: apple orange fruit apple orange fruit food green red color / - 50 * + 23 6 4 8 step + 2 3 * ? 0.4 apple weight / - 50 4 1 step 6 apple price or Figure 1: An example of a math word problem. With external knowledge, a model can capture the relationships between the entities in the problem. With the global information of a generated expression tree, a model can capture information between long-distance nodes. promising results. These methods use end-to-end models to directly generate the corresponding math expressions from the problem text. Although previous methods have achieved promising results, several problems remain that need to be addressed: 1) Background knowledge and common sense should be incorporated. For example, as shown in Figure 1, both apples and oranges are fruit. Humans are naturally aware of this common-sense information, but it is difficult for the model …

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