Graph-to-Tree Learning for Solving Math Word Problems

Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 3928–3937 July 5 - 10, 2020. c⃝2020 Association for Computational Linguistics 3928 Graph-to-Tree Learning for Solving Math Word Problems Jipeng Zhang1,2,∗, Lei Wang2,∗, Roy Ka-Wei Lee3, Yi Bin1, Yan Wang4, Jie Shao1,5,#, Ee-Peng Lim2 1Center for Future Media, University of Electronic Science and Technology of China 2School of Information Systems, Singapore Management University 3Department of Computer Science, University of Saskatchewan 4Tencent AI Lab 5Sichuan Artificial Intelligence Research Institute zhangjipeng20@std.uestc.edu.cn, lei.wang.2019@phdcs.smu.edu.sg, roylee@cs.usask.ca, yi.bin@hotmail.com, bradenwang@tencent.com, shaojie@uestc.edu.cn, eplim@smu.edu.sg Abstract While the recent tree-based neural models have demonstrated promising results in gener- ating solution expression for the math word problem (MWP), most of these models do not capture the relationships and order infor- mation among the quantities well. This re- sults in poor quantity representations and in- correct solution expressions. In this paper, we propose Graph2Tree, a novel deep learning architecture that combines the merits of the graph-based encoder and tree-based decoder to generate better solution expressions. In- cluded in our Graph2Tree framework are two graphs, namely the Quantity Cell Graph and Quantity Comparison Graph, which are de- signed to address limitations of existing meth- ods by effectively representing the relation- ships and order information among the quan- tities in MWPs. We conduct extensive ex- periments on two available datasets. Our ex- periment results show that Graph2Tree out- performs the state-of-the-art baselines on two benchmark datasets significantly. We also discuss case studies and empirically examine Graph2Tree’s effectiveness in translating the MWP text into solution expressions1. 1 Introduction Math Word Problem (MWP), which involves au- tomatically answering a mathematical question ac- cording to a textual description, is an important natural language understanding task that has been studied by researchers since the 1960s (Bobrow, 1964). A typical MWP is a short narrative that de- scribes a problem and poses a question about an unknown quantity. Table 1 provides an example of a typical MWP where the reader is required to in- fer the revenue of a store after selling all the teddy *Equal Contribution #Corresponding Author 1Code could be found at https://github.com/ 2003pro/Graph2Tree Problem: 348 teddy bears are sold for $23 each. There are total 470 teddy bears in a store and the remaining teddy bears are sold for $17 each. How much did the store earn after selling all the teddy bears? Expression: x = 348×23+(470−348)×17 Solution: 10078 Table 1: A math word problem. bears. Earlier studies have attempted to perform the MWP task via statistical machine learning methods (Kushman et al., 2014; Hosseini et al., 2014; Mitra and Baral, 2016; Roy and Roth, 2018) and seman- tic parsing approaches (Shi et al., 2015; Koncel- Kedziorski et al., 2015; Roy and Roth, 2015; Huang et al., 2017). However, these methods are non- scalable as tremendous efforts are required to de- sign suitable features and expression templates. In recent years, deep learning-based models have been developed to solve MWPs. These deep learn- ing methods are able to automate the learning of features and …

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