Tree-structured Decoding for Solving Math Word Problems

Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing, pages 2370–2379, Hong Kong, China, November 3–7, 2019. c⃝2019 Association for Computational Linguistics 2370 Tree-structured Decoding for Solving Math Word Problems Qianying Liu∗1, Wenyu Guan∗23, Sujian Li2 and Daisuke Kawahara1 1 Graduate School of Informatics, Kyoto University 2 Key Laboratory of Computational Linguistics, MOE, Peking University 3 School of Software and Microelectronics, Peking University ying@nlp.ist.i.kyoto-u.ac.jp; guanwy@pku.edu.cn; lisujian@pku.edu.cn; dk@i.kyoto-u.ac.jp Abstract Automatically solving math word problems is an interesting research topic that needs to bridge natural language descriptions and for- mal math equations. Previous studies intro- duced end-to-end neural network methods, but these approaches did not efficiently consider an important characteristic of the equation, i.e., an abstract syntax tree. To address this problem, we propose a tree-structured decod- ing method that generates the abstract syntax tree of the equation in a top-down manner. In addition, our approach can automatically stop during decoding without a redundant stop to- ken. The experimental results show that our method achieves single model state-of-the-art performance on Math23K, which is the largest dataset on this task. 1 Introduction Math word problem (MWP) solving is the task of obtaining a solution from math problems that are described in natural language. One example of MWP is illustrated in Figure 1. Early approaches rely on either predefined rules or statistical ma- chine learning-based methods to map the prob- lems into several predefined templates in classifi- cation style or retrieval style. The major drawback of these approaches is that they are inflexible for new templates and require extra effort to design rules, features and templates. Modeling the tree structure of math equations has been considered as an important factor when building models for MWP. As shown in Figure 1, each equation could be transformed into an ab- stract syntax tree (AST). Roy and Roth (2017) built an expression tree and combined two classi- fiers for quantity relevance prediction and operator classification. Koncel-Kedziorski et al. (2015) de- signed a template ranking function based on the ∗ This denotes equal contribution. Problem The distance between the two places A and B is 660 km, the car start- ing from A drives 32 km/h, and the car starting from B drives 34 km/h. The two cars are starting from the two places at the same time in inverse di- rection. How many hours later would the two cars meet? Equation x = 660 / ( 32 + 34 ) Prefix x = / 660 + 32 34 Answer 10 AST / 660 + 34 32 Figure 1: One example of MWP. Problem refers to the natural language descriptions. Equation refers to the formal math equation. Prefix refers to the prefix nota- tion of the equation. Answer refers to the final quantity solution. AST refers to the AST of the equation. AST of the equations. However, these approaches are based on traditional methods and require fea- ture engineering. Recently, the appearance of large-scale datasets …

Content truncated to 500 words