Structure-Unified M-Tree Coding Solver for Math Word Problem

Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pages 8122 - 8132 December 7-11, 2022 ©2022 Association for Computational Linguistics Structure-Unified M-Tree Coding Solver for Math Word Problem Bin Wang, Jiangzhou Ju, Yang Fan, Xinyu Dai∗, Shujian Huang, Jiajun Chen National Key Laboratory for Novel Software Technology, Nanjing University Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing {wangbin, jujiangzhou, fanyang}@smail.nju.edu.cn {daixinyu, huangsj, chenjj}@nju.edu.cn Abstract As one of the challenging NLP tasks, design- ing math word problem (MWP) solvers has attracted increasing research attention for the past few years. In previous work, models de- signed by taking into account the properties of the binary tree structure of mathematical expressions at the output side have achieved better performance. However, the expressions corresponding to a MWP are often diverse (e.g., n1+n2×n3−n4, n3×n2−n4+n1, etc.), and so are the corresponding binary trees, which creates difficulties in model learning due to the non-deterministic output space. In this pa- per, we propose the Structure-Unified M-Tree Coding Solver (SUMC-Solver), which applies a tree with any M branches (M-tree) to unify the output structures. To learn the M-tree, we use a mapping to convert the M-tree into the M-tree codes, where codes store the informa- tion of the paths from tree root to leaf nodes and the information of leaf nodes themselves, and then devise a Sequence-to-Code (seq2code) model to generate the codes. Experimental re- sults on the widely used MAWPS and Math23K datasets have demonstrated that SUMC-Solver not only outperforms several state-of-the-art models under similar experimental settings but also performs much better under low-resource conditions1. 1 Introduction Given the description text of a MWP, an automatic solver needs to output an expression for solving the unknown variable asked in the problem that consists of mathematical operands (numerical val- ues) and operation symbols (+, −, ×, ÷), as shown in Fig. 1. It requires that the solver not only un- derstand the natural-language problem but also be able to model the relationships between the numer- ical values to perform arithmetic reasoning. These *Corresponding author 1Code and data are available at https://github.com/ devWangBin/SUMC-Solver Problem: Mike bought a new book. He read 3 pages every day on the first 2 days. Then, on the third day, he read 4 pages in the morning and 5 pages in the afternoon. How many pages has Mike read so far? Solution expressions: 2 × 3 + 4 + 5 3 × 2 + (5 + 4) 5 + 3 × 2 + 4 …… Post expression sequences: 2 3 × 4 + 5 + 3 2 × 5 4 + + 5 3 2 × + 4 + …… Expression binary trees: …… M-Tree of expressions: Answer: 15 Figure 1: An example of math word problems, which has multiple solution expressions and binary trees, but only one M-tree output. challenges mean MWP solvers are often broadly considered good test beds for evaluating the intelli- gence level of agents (Lin et al., 2021). In recent years, the research on …

Content truncated to 500 words