Quantity Tagger: A Latent-Variable Sequence Labeling Approach to Solving Addition-Subtraction Word Problems

Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 5246–5251 Florence, Italy, July 28 - August 2, 2019. c⃝2019 Association for Computational Linguistics 5246 Quantity Tagger: A Latent-Variable Sequence Labeling Approach to Solving Addition-Subtraction Word Problems Yanyan Zou and Wei Lu StatNLP Research Group Singapore University of Technology and Design yanyan zou@mymail.sutd.edu.sg, luwei@sutd.edu.sg Abstract An arithmetic word problem typically includes a textual description containing several con- stant quantities. The key to solving the prob- lem is to reveal the underlying mathematical relations (such as addition and subtraction) among quantities, and then generate equa- tions to find solutions. This work presents a novel approach, Quantity Tagger, that auto- matically discovers such hidden relations by tagging each quantity with a sign correspond- ing to one type of mathematical operation. For each quantity, we assume there exists a latent, variable-sized quantity span surrounding the quantity token in the text, which conveys in- formation useful for determining its sign. Em- pirical results show that our method achieves 5 and 8 points of accuracy gains on two datasets respectively, compared to prior approaches. 1 Introduction Teaching machines to automatically solve arith- metic word problems, exemplified by two prob- lems in Figure 1, is a long-standing Artificial Intel- ligence (AI) task (Bobrow, 1964; Mukherjee and Garain, 2008). Recent research (Hosseini et al., 2014; Kushman et al., 2014; Roy and Roth, 2015; Wang et al., 2017, 2018b,a) focused on designing algorithms to automatically solve arithmetic word problems. One line of prior works designed rules (Mukherjee and Garain, 2008; Hosseini et al., 2014) or templates (Kushman et al., 2014; Zhou et al., 2015; Mitra and Baral, 2016) to map prob- lems to expressions, where rules or templates are collected from training data. However, it would be non-trivial and expensive to acquire a general set of rules or templates. Fur- thermore, such approaches typically require addi- tional annotations. The addition-subtraction prob- lems, which constitute the most fundamental class of arithmetic word problems, have been the focus Problem 1: A worker at a medical lab is studying blood samples. 2 samples contained a total of 7341 blood cells. The first sample contained 4221 blood cells. How many blood cells were in the second sample? Prediction: (0)×2+(+1)×7341+(−1)×4221+(−1)×x = 0 Equation: 7341 − 4221 − x = 0 Solution: x = 3120 Problem 2: There are 22 walnut trees currently in the park. Park workers will plant walnut trees today. When the workers are fin- ished there will be 55 walnut trees in the park. How many walnut trees did the workers plant today? Prediction: (+1)×22 + (−1)×55 + (+1)×x = 0 Equation: 22 − 55 + x = 0 Solution: x = 33 Figure 1: Two examples of arithmetic word problems described in English with answers. for many previous works (Hosseini et al., 2014; Mitra and Baral, 2016). We also focus on this im- portant task in this work. Our key observation is that essentially solving such a class of problems can be tackled from a sequence …

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