Point to the Expression: Solving Algebraic Word Problems using the Expression-Pointer Transformer Model

Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing, pages 3768–3779, November 16–20, 2020. c⃝2020 Association for Computational Linguistics 3768 Point to the Expression: Solving Algebraic Word Problems using the Expression-Pointer Transformer Model Bugeun Kim Kyung Seo Ki Donggeon Lee Department of Transdisciplinary Studies,Gahgene Gweon Seoul National University, Seoul, Republic of Korea {cd4209,kskee88,lsw5835,ggweon}@snu.ac.kr Abstract Solving algebraic word problems has recently emerged as an important natural language pro- cessing task. To solve algebraic word prob- lems, recent studies suggested neural mod- els that generate solution equations by using ‘Op (operator/operand)’ tokens as a unit of input/output. However, such a neural model suffered two issues: expression fragmentation and operand-context separation. To address each of these two issues, we propose a pure neural model, Expression-Pointer Transformer (EPT), which uses (1) ‘Expression’ token and (2) operand-context pointers when generat- ing solution equations. The performance of the EPT model is tested on three datasets: ALG514, DRAW-1K, and MAWPS. Com- pared to the state-of-the-art (SoTA) models, the EPT model achieved a comparable perfor- mance accuracy in each of the three datasets; 81.3% on ALG514, 59.5% on DRAW-1K, and 84.5% on MAWPS. The contribution of this paper is two-fold; (1) We propose a pure neural model, EPT, which can address the expression fragmentation and the operand- context separation. (2) The fully automatic EPT model, which does not use hand-crafted features, yields comparable performance to existing models using hand-crafted features, and achieves better performance than existing pure neural models by at most 40%. 1 Introduction Solving algebraic word problems has recently become an important research task in that auto- matically generating solution equations requires understanding natural language. Table 1 shows a sample algebraic word problem, along with corresponding solution equations that are used to generate answers for the problem. To solve such problems with deep learning technology, researchers recently suggested neural models that generate solution equations automatically (Huang Problem One number is eight more than twice another and their sum is 20. What are their numbers? Numbers 1(‘one’), 8(‘eight’), 2(‘twice’), 20. Equations x0 − 2x1 = 8, x0 + x1 = 20 Answers (16, 4) Table 1: A sample algebraic word problem et al., 2018; Amini et al., 2019; Chiang and Chen, 2019; Wang et al., 2019). However, suggested neural models showed a fairly large performance gap compared to existing state-of-the-art models based on hand-crafted features in popular algebraic word problem datasets, such as ALG514 (44.5% for pure neural model vs. 83.0% for using hand-crafted features) (Huang et al., 2018; Upadhyay and Chang, 2016). To address the large performance gap in this study, we propose a larger unit of input/output (I/O) token called “Expressions” for a pure neural model. Figure 1 illustrates conventionally used “Op (operator/operands)” versus our newly proposed “Expression” token. To improve the performance of pure neural models that can solve algebraic word problems, we identified two issues that can be addressed using Expression tokens, which are shown in Figure 1: (1) expression fragmentation and (2) operand- context separation. First, the expression fragmen- …

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