Text2Math: End-to-end Parsing Text into Math Expressions

Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing, pages 5327–5337, Hong Kong, China, November 3–7, 2019. c⃝2019 Association for Computational Linguistics 5327 Text2Math: End-to-end Parsing Text into Math Expressions Yanyan Zou and Wei Lu StatNLP Research Group Singapore University of Technology and Design yanyan zou@mymail.sutd.edu.sg, luwei@sutd.edu.sg Abstract We propose Text2Math, a model for seman- tically parsing text into math expressions. The model can be used to solve different math related problems including arithmetic word problems (Roy and Roth, 2017; Liang et al., 2018) and equation parsing problems (Roy et al., 2016). Unlike previous approaches, we tackle the problem from an end-to-end struc- tured prediction perspective where our algo- rithm aims to predict the complete math ex- pression at once as a tree structure, where min- imal manual efforts are involved in the pro- cess. Empirical results on benchmark datasets demonstrate the efficacy of our approach. 1 Introduction Designing computer algorithms that can automat- ically solve math word problems is a challenge for the AI research community (Bobrow, 1964). Two representative tasks have been proposed and studied recently – solving arithmetic word prob- lems (Wang et al., 2017; Roy and Roth, 2018; Zou and Lu, 2019b) and equation parsing (Roy et al., 2016), as illustrated in Figure 1. The former task focuses on mapping the input paragraph (which may involve multiple sentences) into a target math expression, from which an answer can be calcu- lated. The latter task focuses on mapping a de- scription (usually a single sentence) into a math equation that typically involves one or more un- knowns. As we can observe from Figure 1, in both cases, the output can be represented as a tree struc- ture. Earlier approaches to solving arithmetic word problems focused on rule-based methods where hand-crafted rules have been used (Mukherjee and Garain, 2008; Hosseini et al., 2014). Re- cently, learning-based approaches based on statis- tical classifiers (Kushman et al., 2014; Roy and Roth, 2015; Roy et al., 2016; Liang et al., 2018) or Problem 1 Mike picked 7 apples. Nancy picked 3 apples and Keith picked 6 apples at the farm. In total, how many apples were picked? Expressionion (7 + (3 + 6)) + 7 + 3 6 Answerioniion 16 Problem 2 3 times one of the numbers is 11 less than 5 times the other. Expressionionio (3 × X1) = (5 × X2) − 11 = − × 11 5 X2 × 3 X1 Figure 1: An example arithmetic word problem (top) and an example equation parsing problem (bottom) where the outputs can be represented as trees. neural networks (Wang et al., 2017, 2018b) have been used for making decisions in the expression1 construction process. However, these models do not focus on predicting the target tree as a com- plete structure at once, but locally trained classi- fiers are often used and local decisions are then combined. Such local classifiers often make pre- dictions on the choice …

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