DISK: Domain-constrained Instance Sketch for Math Word Problem Generation

Proceedings of the 29th International Conference on Computational Linguistics, pages 6327–6339 October 12–17, 2022. 6327 DISK: Domain-constrained Instance Sketch for Math Word Problem Generation Tianyang Cao1∗, Shuang Zeng1,2∗, Xiaodan Xu1,3, Mairgup Mansur2, Baobao Chang1† 1Key Laboratory of Computational Linguistics, MOE, Peking University 2Tencent Inc. 3School of Software and Microelectronics, Peking University {ctymy, zengs, diane1968, chbb}@pku.edu.cn, mairgupma@tencent.com Abstract A math word problem (MWP) is a coherent narrative which reflects the underlying logic of math equations. Successful MWP gener- ation can automate the writing of mathemat- ics questions. Previous methods mainly gener- ate MWP text based on inflexible pre-defined templates. In this paper, we propose a neu- ral model for generating MWP text from math equations. Firstly, we incorporate a matching model conditioned on the domain knowledge to retrieve a MWP instance which is most consis- tent with the ground-truth, where the domain is a latent variable extracted with a domain sum- marizer. Secondly, by constructing a Quantity Cell Graph (QCG) from the retrieved MWP instance and reasoning over it, we improve the model’s comprehension of real-world scenar- ios and derive a domain-constrained instance sketch to guide the generation. Besides, the QCG also interacts with the equation encoder to enhance the alignment between math tokens (e.g., quantities and variables) and MWP text. Experiments and empirical analysis on educa- tional MWP set show that our model achieves impressive performance in both automatic eval- uation metrics and human evaluation metrics. 1 Introduction Text generation has been broadly studied as an important task in the field of natural language pro- cessing. It aims to generate natural language text that is fluent, readable and faithful to the original input. Recent text generation studies mainly focus on the data-to-text generation, which generates tex- tual output from structured data such as tables of records or knowledge graphs (KGs) (Puduppully et al., 2019a; Chen et al., 2019; Gong et al., 2019b; Zhao et al., 2020). In this paper, we focus on a rela- tively new type of data-to-text generation task: gen- erating Math Word Problems (MWP) from equa- tions (Zhou and Huang, 2019), which does not ∗Equal contribution. † Corresponding author. Equations: x = 6 * y ; (x + y) * 3= 147 Problem: Jane travels 6 times faster than mike. Traveling in opposite directions they are 147 miles apart after 3 hrs. Find their rates of travel. Equations: (1 – 1/3 – 9/20) * x = 245 Problem: At a local high school, 3/8 of the students are freshman. 1/4 are juniors. And 245 are seniors. Find the total number of students. Figure 1: Two examples selected from the MWP gener- ation dataset. seem to have been fully studied by the community. Figure 1 shows two examples of this task. We aim to automatically generate coherent narratives which reflect the computational relationship within given equations. Successful math word problems gener- ation has the potential to automate the writing of mathematics questions given equations to be solved. It can alleviate the burden of school teachers and further help …

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