Solving Math Word Problems with Multi-Encoders and Multi-Decoders

Proceedings of the 28th International Conference on Computational Linguistics, pages 2924–2934 Barcelona, Spain (Online), December 8-13, 2020 2924 Solving Math Word Problems with Multi-Encoders and Multi-Decoders Yibin Shen East China Normal University ybshen@stu.ecnu.edu.cn Cheqing Jin� East China Normal University cqjin@dase.ecnu.edu.cn Abstract Math word problems solving remains a challenging task where potential semantic and mathe- matical logic need to be mined from natural language. Although previous researches employ the Seq2Seq technique to transform text descriptions into equation expressions, most of them achieve inferior performance due to insufficient consideration in the design of encoder and de- coder. Specifically, these models only consider input/output objects as sequences, ignoring the important structural information contained in text descriptions and equation expressions. To overcome those defects, a model with multi-encoders and multi-decoders is proposed in this paper, which combines sequence-based encoder and graph-based encoder to enhance the repre- sentation of text descriptions, and generates different equation expressions via sequence-based decoder and tree-based decoder. Experimental results on the dataset Math23K show that our model outperforms existing state-of-the-art methods. 1 Introduction Math word problems (MWPs) solving, a task that transforms text descriptions into solvable equation expressions, is considered a crucial step towards general AI (Wang et al., 2018b). Since semantic under- standing and mathematical logic reasoning both contribute to correct answers, MWPs solving remains a challenging topic in NLP. Table 1 shows a typical example of MWPs. Problem: A slow car drives 58(n1) km/h, and a fast car drives 85(n2) km/h. The two cars drive at the same time in inverse direction, and they meet after 5(n3) hours. How many kilometers does the fast car drive more than the slow car when they meet? AST: Equation: (n2 − n1) × n3 × − �� �� �� Prefix: × − n2n1n3 Suffix: n2n1 − n3× Answer: 135 Table 1: A typical example of MWPs. Researches on MWPs solving has a long history. Early researches focused on rule-based meth- ods (Fletcher, 1985; Bakman, 2007; Yuhui et al., 2010) and statistical machine learning methods (Kush- man et al., 2014; Hosseini et al., 2014; Mitra and Baral, 2016) that map problems into predefined tem- plates. The main drawbacks of these methods lie in their heavy dependency on manual features and incapacity to generate new templates for new problems. Consequently, they can only achieve satisfac- tory results on small-scale datasets (Zhang et al., 2018). This work is licensed under a Creative Commons Attribution 4.0 International License. License details: http:// creativecommons.org/licenses/by/4.0/. 2925 Recently, more researchers have been introducing Seq2Seq models, which are capable of generating new equation expressions that do not exist in the training set (Wang et al., 2017; Wang et al., 2018a; Wang et al., 2019; Li et al., 2019). However, these models may generate invalid expressions since the sequence- based decoder cannot control the generation process. Based on the fact that each equation expression could be transformed into an abstract syntax tree (AST), some studies (Liu et al., 2019; Xie and Sun, 2019) changed the pattern of sequence generation from left …

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