Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems

Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing, pages 3780–3789, November 16–20, 2020. c⃝2020 Association for Computational Linguistics 3780 Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems Jinghui Qin1, Lihui Lin2, Xiaodan Liang1,2,∗, Rumin Zhang2, Liang Lin1,2 1 Sun Yat-sen University 2 Dark Matter AI Inc. qinjingh@mail2.sysu.edu.cn, linlh23@mail2.sysu.edu.cn, xdliang328@gmail.com, rm zhang@foxmail.com, linliang@ieee.org Abstract A practical automatic textual math word prob- lems (MWPs) solver should be able to solve various textual MWPs while most existing works only focused on one-unknown linear MWPs. Herein, we propose a simple but efficient method called Universal Expression Tree (UET) to make the first attempt to rep- resent the equations of various MWPs uni- formly. Then a semantically-aligned univer- sal tree-structured solver (SAU-Solver) based on an encoder-decoder framework is proposed to resolve multiple types of MWPs in a uni- fied model, benefiting from our UET represen- tation. Our SAU-Solver generates a universal expression tree explicitly by deciding which symbol to generate according to the generated symbols’ semantic meanings like human solv- ing MWPs. Besides, our SAU-Solver also includes a novel subtree-level semantically- aligned regularization to further enforce the se- mantic constraints and rationality of the gener- ated expression tree by aligning with the con- textual information. Finally, to validate the universality of our solver and extend the re- search boundary of MWPs, we introduce a new challenging Hybrid Math Word Problems dataset (HMWP), consisting of three types of MWPs. Experimental results on several MWPs datasets show that our model can solve universal types of MWPs and outperforms sev- eral state-of-the-art models1. 1 Introduction Math word problems (MWPs) solving aims to au- tomatically answer a math word problem by un- derstanding the textual description of the problem and reasoning out the underlying answer. A typ- ical MWP is a short story that describes a partial state of the world and poses a question about an ∗Corresponding Author 1The code and the new HMWP dataset are available at https://github.com/QinJinghui/SAU-Solver. = 3 5 * y x * + x = y ; 24 = 3 6 x * = 3 6 x * = 3 5 * y x * + x = y 24 Expression Trees Universal Expression Trees Equation Set Problem Arithmetic Word Problem Figure 1: Universal Expression Trees (UET). In our UET representation, multiple expression trees underly- ing a MWP will be integrated as an universal expres- sion tree (UET) via symbol extension. UET can enable a solver to handle multiple types of MWPs in an unified manner like a single expression tree of an equation. unknown quantity or multiple unknown quantities. Thus, a machine should have the ability of natural language understanding and reasoning. To solve an MWP, the relevant quantities need to be identified from the text, and the correct operators and their computation order among these quantities need to be determined. Many traditional methods (Yuhui et al., 2010; Kushman et al., 2014; Shi et al., 2015) have been proposed to address this problem, but they relied on tedious hand-crafted …

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