Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction

Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics Volume 1: Long Papers, pages 5944 - 5955 May 22-27, 2022 c⃝2022 Association for Computational Linguistics Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction Zhanming Jie♥♦, Jierui Li♣♦ and Wei Lu♦ ♥ByteDance AI Lab, ♣University of Texas at Austin ♦StatNLP Research Group, Singapore University of Technology and Design allan@bytedance.com, jierui@cs.utexas.edu, luwei@sutd.edu.sg Abstract Solving math word problems requires deduc- tive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational rea- soning between quantities in the given con- text. While empirically effective, such ap- proaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation ex- traction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive opera- tion over two quantities defining their rela- tion. Through extensive experiments on four benchmark datasets, we show that the pro- posed model significantly outperforms exist- ing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.1 1 Introduction Math word problem (MWP) solving (Bobrow, 1964) is a task of answering a mathematical ques- tion that is described in natural language. Solving MWP requires logical reasoning over the quantities presented in the context (Mukherjee and Garain, 2008) to compute the numerical answer. Various recent research efforts regarded the problem as a generation problem – typically, such models focus on generating the complete target mathematical ex- pression, often represented in the form of a linear sequence or a tree structure (Xie and Sun, 2019). Figure 1 (top) depicts a typical approach that attempts to generate the target expression in the 1Our code and data are released at https://github. com/allanj/Deductive-MWP. Question: In a division sum , the remainder is 8 and the divisor is 6 times the quotient and is obt- -ained by adding 3 to the thrice of the remainder. What is the divident? Answer: 129.5 Expr: ((8 × 3 + 3)×(8 × 3 + 3)÷6)+8 Tree generation: 7 ops + × 8 + ÷ × 3 + 6 8 3 × 3 8 3 Our deductive procedure: 5 ops 8 × 3 = 24 1 24 + 3 = 27 2 27 ÷ 6 = 4.5 3 27 × 4.5 = 121.5 4 121.5 + 8 = 129.5 5 Figure 1: A MWP example taken from MathQA. Top: tree generation. Bottom: deductive procedure. form of a tree structure, which is adopted in re- cent research efforts (Xie and Sun, 2019; Zhang et al., 2020; Patel et al., 2021; Wu et al., 2021). Specifically, the output is an expression that can be obtained from such a generated structure. We note that, however, there are several limitations with such a structure …

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