Deep Neural Solver for Math Word Problems

Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 845–854 Copenhagen, Denmark, September 7–11, 2017. c⃝2017 Association for Computational Linguistics Deep Neural Solver for Math Word Problems Yan Wang Xiaojiang Liu Tencent AI LabShuming Shi {brandenwang, kieranliu, shumingshi}@tencent.com Abstract This paper presents a deep neural solver to automatically solve math word prob- lems. In contrast to previous statistical learning approaches, we directly translate math word problems to equation templates using a recurrent neural network (RNN) model, without sophisticated feature engi- neering. We further design a hybrid mod- el that combines the RNN model and a similarity-based retrieval model to achieve additional performance improvement. Ex- periments conducted on a large dataset show that the RNN model and the hy- brid model significantly outperform state- of-the-art statistical learning methods for math word problem solving. 1 Introduction Developing computer models to automatically solve math word problems has been an interest of NLP researchers since 1963 Feigenbaum et al. (1963); Bobrow (1964); Briars and Larkin (1984); Fletcher (1985). Recently, machine learning tech- niques Kushman et al. (2014); Amnueypornsakul and Bhat (2014); Zhou et al. (2015); Mitra and Baral (2016) and semantic parsing methods Shi et al. (2015); Koncel-Kedziorski et al. (2015) are proposed to tackle this problem and promising re- sults are reported on some datasets. Although progress has been made in this task, performance of state-of-the-art techniques is still quite low on large datasets having diverse problem types Huang et al. (2016). A typical math word problems are shown in Ta- ble 1. The reader is asked to infer how many pens Dan and Jessica have, based on constraints pro- vided. Given the success of deep neural network- s (DNN) on many NLP tasks (like POS tagging, Problem: Dan have 2 pens, Jessica have 4 pens. How many pens do they have in total ? Equation: x = 4+2 Solution: 6 Table 1: A math word problem syntactic parsing, and machine translation), it may be interesting to study whether DNN could also help math word problem solving. In this paper, we propose a recurrent neural network (RNN) model for automatic math word problem solving. It is a sequence to sequence (seq2seq) model that trans- forms natural language sentences in math word problems to mathematical equations. Experiments conducted on a large dataset show that the RNN model significantly outperforms state-of-the-art s- tatistical learning approaches. Since it has been demonstrated Huang et al. (2016) that a simple similarity based method per- forms as well as more sophisticated statistical learning approaches on large datasets, we imple- ment a similarity-based retrieval model and com- pare with our seq2seq model. We observe that al- though seq2seq performs better on average, the re- trieval model is able to correctly solve many prob- lems for which RNN generates wrong results. We also find that the accuracy of the retrieval model positively correlate with the maximal similarity s- core between the target problem and the problems in training data: the larger the similarity score, the higher the …

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