Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems

Proceedings of NAACL-HLT 2019, pages 2656–2668 Minneapolis, Minnesota, June 2 - June 7, 2019. c⃝2019 Association for Computational Linguistics 2656 Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems Ting-Rui Chiang Yun-Nung Chen National Taiwan University, Taipei, Taiwan r07922052@csie.ntu.edu.tw y.v.chen@ieee.org Abstract Solving math word problems is a challeng- ing task that requires accurate natural language understanding to bridge natural language texts and math expressions. Motivated by the intu- ition about how human generates the equations given the problem texts, this paper presents a neural approach to automatically solve math word problems by operating symbols accord- ing to their semantic meanings in texts. This paper views the process of generating equa- tions as a bridge between the semantic world and the symbolic world, where the proposed neural math solver is based on an encoder- decoder framework. In the proposed model, the encoder is designed to understand the se- mantics of problems, and the decoder focuses on tracking semantic meanings of the gener- ated symbols and then deciding which sym- bol to generate next. The preliminary exper- iments are conducted in a benchmark dataset Math23K, and our model significantly outper- forms both the state-of-the-art single model and the best non-retrieval-based model over about 10% accuracy, demonstrating the effec- tiveness of bridging the symbolic and semantic worlds from math word problems.1 1 Introduction Automatically solving math word problems has been an interesting research topic and also been viewed as a way of evaluating machines’ abil- ity (Mandal and Naskar, 2019). For human, writ- ing down an equation that solves a math word problem requires the ability of reading compre- hension, reasoning, and sometimes real world un- derstanding. Specifically, to solve a math word problem, we first need to know the goal of the given problem, then understand the semantic 1The source code is available at https://github. com/MiuLab/E2EMathSolver. meaning of each numerical number in the prob- lem, perform reasoning based on the comprehen- sion in the previous step, and finally decide what to write in the equation. Most prior work about solving math word prob- lems relied on hand-crafted features, which re- quired more human knowledge. Because those features are often in the lexical level, it is not clear whether machines really understand the math problems. Also, most prior work evaluated their approaches on relatively small datasets, and the capability of generalization is concerned. This paper considers the reasoning procedure when writing down the associated equation given a problem. Figure 1 illustrates the problem solving process. The illustration shows that human actu- ally assigns the semantic meaning to each number when manipulating symbols, including operands (numbers) and operators (+ − ×÷). Also, we be- lieve that the semantic meaning of operands can help us decide which operator to use. For example, the summation of “price of one pen” and “number of pens Tom bought” is meaningless; therefore the addition would not be chosen. Following the observation above, this paper proposes a novel encoder decoder model, where the encoder extracts semantic meanings of num- …

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