Math Word Problem Solving with Explicit Numerical Values

Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, pages 5859–5869 August 1–6, 2021. ©2021 Association for Computational Linguistics 5859 Math Word Problem Solving with Explicit Numerical Values Qinzhuo Wu, Qi Zhang, Zhongyu Wei, Xuanjing Huang∗ Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, China (qzwu17,qz,zywei,xjhuang)@fudan.edu.cn Abstract In recent years, math word problem solving has received considerable attention and achieved promising results, but previous methods rarely take numerical values into consideration. Most methods treat the numerical values in the problems as number symbols, and ignore the prominent role of the numerical values in solving the problem. In this paper, we propose a novel approach called NumS2T, which enhances math word problem solving performance by explicitly incorporating numerical values into a sequence-to-tree network. In addition, a numerical properties prediction mechanism is used to capture the category and comparison information of numerals and measure their importance in global expressions. Experimental results on the Math23K and APE datasets demonstrate that our model achieves better performance than existing state-of-the-art models. 1 1 Introduction Taking a math word problem as input, the math word problem solving task aims to generate a cor- responding solvable expression and answer. With the advancements in natural language processing, math word problem solving has received growing attention in recent years (Roy and Roth, 2015; Mitra and Baral, 2016; Ling et al., 2017; Huang et al., 2018). Many methods have been proposed that use sequence-to-sequence (seq2seq) models with an attention mechanism (Bahdanau et al., 2014) for math word problem solving (Wang et al., 2017b, 2018b, 2019). To better utilize expression structure information, some methods use sequence- to-tree (seq2tree) models to generate expressions ∗ Corresponding author. 1Code is available at https://github.com/ qinzhuowu/NumS2T/ Problem: A school purchased several pairs of new desks and chairs for grade students. Each desk is worth $ , and each chair is worth $ . The price difference between the tables and the chairs is $ . There are more students than chairs. How many students are there? Expression 1: 𝑣4 / ( 𝑣2 - 𝑣3 ) + 𝑣5 Numerical expression: 100 / ( 15 – 10 ) + 25 Expression 2: 𝑣4 / ( 𝑣2 - 𝑣3 ) * ( 1 + 𝑣5 ) Numerical expression: 64 / (9.9 – 8.3) * (1+20%) Expression 3: 𝑣4 / ( 𝑣3 - 𝑣2 ) * ( 1 + 𝑣5 ) Numerical expression: 18 / (8 – 6.5) * (1 + (1/3)) 31𝑣1 7 15 9.9 6.5 𝑣2 10 8.3 8 𝑣3 𝑣4 100 64 18 𝑣5 25 20% (1/3) Figure 1: Example of a math word problem. The same problem with different numerical values may correspond to different math expressions. Without numerical value information, the model can hardly determine which expression is correct. and have achieved promising results (Liu et al., 2019; Xie and Sun, 2019; Wu et al., 2020). These methods convert the target expression into a binary tree, …

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