Learning Fine-Grained Expressions to Solve Math Word Problems

Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 805–814 Copenhagen, Denmark, September 7–11, 2017. c⃝2017 Association for Computational Linguistics Learning Fine-Grained Expressions to Solve Math Word Problems Danqing Huang1∗, Shuming Shi2, Jian Yin1, and Chin-Yew Lin3 {huangdq2@mail2,issjyin@mail}.sysu.edu.cn shumingshi@tencent.com cyl@microsoft.com 1 Guangdong Key Laboratory of Big Data Analysis and Processing, Sun Yat-sen University 2Tencent AI Lab 3 Microsoft Research Abstract This paper presents a novel template- based method to solve math word prob- lems. This method learns the mappings between math concept phrases in math word problems and their math expressions from training data. For each equation tem- plate, we automatically construct a rich template sketch by aggregating informa- tion from various problems with the same template. Our approach is implemented in a two-stage system. It first retrieves a few relevant equation system templates and aligns numbers in math word problems to those templates for candidate equation generation. It then does a fine-grained in- ference to obtain the final answer. Ex- periment results show that our method achieves an accuracy of 28.4% on the lin- ear Dolphin18K benchmark, which is 10% (54% relative) higher than previous state- of-the-art systems while achieving an ac- curacy increase of 12% (59% relative) on the TS6 benchmark subset. 1 Introduction The research topic of automatically solving math word problems dates back to the 1960s (Bobrow, 1964a,b; Charniak, 1968). Recently many sys- tems have been proposed to these types of prob- lems (Kushman et al., 2014; Hosseini et al., 2014; Koncel-Kedziorski et al., 2015; Zhou et al., 2015; Roy and Roth, 2015; Shi et al., 2015; Upadhyay et al., 2016; Mitra and Baral, 2016). On a re- cent evaluation conducted by Huang et al. (2016), current state-of-the-art systems only achieved an ∗Work done while this author was an intern at Microsoft Research. 18.3% accuracy on their published dataset Dol- phin18K. Their results indicate that math word problem solving is a very challenging task. To solve a math word problem, a system needs to understand natural language text to extract in- formation from the problem as local context. Also, it should provide an external knowledge base, in- cluding commonsense knowledge (e.g. ”a chicken has two legs”) and mathematical knowledge (e.g. ”the perimeter of a rectangle = 2 * length + 2 * width”). The system can then perform reasoning based on the above two resources to generate an answer. P1: What's 25% off $139.99? Equation: (1-0.25)*139.99 = x P2: How much will the ipod now be if the original price is $260 and I get 10% discount? Equation: (1-0.1)*260 = x Template: (1-n1)*n2 = x P3: I bought something for $306.00 dollars. I got a 20% discount. What was the original price? Equation: (1-0.2)*x = 306 Template: (1-n1)*x = n2 Figure 1: Math Word Problem Examples. In this paper, we focus on the acquisition of mathematical knowledge, or deriving math con- cepts from natural language. Consider the first two problems P1 and P2 in Figure 1. The math con- cept in the …

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