Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks

Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, pages 5870–5881 August 1–6, 2021. ©2021 Association for Computational Linguistics 5870 Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks Jinghui Qin1, Xiaodan Liang1,2, Yining Hong3, Jianheng Tang1 and Liang Lin1,2∗ 1 Sun Yat-sen University 2 Dark Matter AI Inc. 3 University of California, Los Angeles qinjingh@mail2.sysu.edu.cn,{xdliang328,sqrt3tjh}@gmail.com, yininghong@cs.ucla.edu,linliang@ieee.org Abstract Previous math word problem solvers follow- ing the encoder-decoder paradigm fail to ex- plicitly incorporate essential math symbolic constraints, leading to unexplainable and un- reasonable predictions. Herein, we propose Neural-Symbolic Solver (NS-Solver) to explic- itly and seamlessly incorporate different lev- els of symbolic constraints by auxiliary tasks. Our NS-Solver consists of a problem reader to encode problems, a programmer to generate symbolic equations, and a symbolic executor to obtain answers. Along with target expres- sion supervision, our solver is also optimized via 4 new auxiliary objectives to enforce dif- ferent symbolic reasoning: a) self-supervised number prediction task predicting both num- ber quantity and number locations; b) com- monsense constant prediction task predicting what prior knowledge (e.g. how many legs a chicken has) is required; c) program con- sistency checker computing the semantic loss between predicted equation and target equa- tion to ensure reasonable equation mapping; d) duality exploiting task exploiting the quasi duality between symbolic equation generation and problem’s part-of-speech generation to en- hance the understanding ability of a solver. Be- sides, to provide a more realistic and challeng- ing benchmark for developing a universal and scalable solver, we also construct a new large- scale MWP benchmark CM17K consisting of 4 kinds of MWPs (arithmetic, one-unknown linear, one-unknown non-linear, equation set) with more than 17K samples. Extensive exper- iments on Math23K and our CM17k demon- strate the superiority of our NS-Solver com- pared to state-of-the-art methods1. ∗Corresponding Author 1The code and the new CM17k dataset are available at https://github.com/QinJinghui/NS-Solver. 1 Introduction Deep neural networks have achieved remarkable successes in natural language processing recently. Although neural models have demonstrated per- formance superior to humans on some tasks, e.g. reading comprehension (Rajpurkar et al., 2016; De- vlin et al., 2019; Lan et al.), it still lacks the ability of discrete reasoning, resulting in low accuracy on math reasoning. Thus, it is hard for pure neural network approaches to tackle the task of solving math word problems (MWPs), which requires a model to be capable of natural language under- standing and discrete reasoning. MWP solving aims to automatically answer a math word prob- lem by understanding the textual description of the problem and reasoning out the underlying answer. A typical MWP is a short story that describes a par- tial state of the world and poses a question about an unknown quantity or multiple unknown quan- tities. To solve an MWP, the relevant quantities need to be identified from the text. Furthermore, the correct operators along with their computation order among these quantities need to be determined. Therefore, integrating neural networks with …

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