Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems

Findings of the Association for Computational Linguistics: ACL 2022, pages 2486 - 2496 May 22-27, 2022 c⃝2022 Association for Computational Linguistics Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems Zhongli Li1∗, Wenxuan Zhang2∗†, Chao Yan2†, Qingyu Zhou1, Chao Li1, Hongzhi Liu2, Yunbo Cao1 1Tencent Cloud Xiaowei 2Peking University {neutrali,qingyuzhou,diegoli,yunbocao}@tencent.com {zwx980624@stu,cyan@stu,liuhz@ss}.pku.edu.cn Abstract Math Word Problem (MWP) solving needs to discover the quantitative relationships over natural language narratives. Recent work shows that existing models memorize proce- dures from context and rely on shallow heuris- tics to solve MWPs. In this paper, we look at this issue and argue that the cause is a lack of overall understanding of MWP patterns. We first investigate how a neural network under- stands patterns only from semantics, and ob- serve that, if the prototype equations like n1 + n2 are the same, most problems get closer representations and those representations apart from them or close to other prototypes tend to produce wrong solutions. Inspired by it, we propose a contrastive learning approach, where the neural network perceives the diver- gence of patterns. We collect contrastive ex- amples by converting the prototype equation into a tree and seeking similar tree structures. The solving model is trained with an auxiliary objective on the collected examples, resulting in the representations of problems with simi- lar prototypes being pulled closer. We conduct experiments1 on the Chinese dataset Math23k and the English dataset MathQA. Our method greatly improves the performance in monolin- gual and multilingual settings. 1 Introduction A Math Word Problem (MWP) is described as a natural language narrative with a math question. The MWP solver is required to generate a solution equation, which can be calculated to get the nu- merical answer, by understanding the contextual problem description. In teaching, students are encouraged to recog- nize that mathematics is really about patterns and ∗ Zhongli Li and Wenxuan Zhang contributed equally. Qingyu Zhou is the corresponding author. † Contribution done during internship at Tencent Cloud Xiaowei. 1The code is available at https://github.com/ zwx980624/mwp-cl. n1 + n2 n1 / n2 Prob. C: A bee has 6 legs. How many legs do 2 bees have? Eq: 2 * 6 Prob. B: Joyce starts with 75 apples. She gives 52 to Larry. How many apples does Joyce end with? Eq: 75 - 52 Prob. A: Norma has 88 cards. She loses 70. How many cards will Norma have ? Eq: 88 - 70 Prob. D: 2 bee have 12 legs. How many legs does a bee have? Eq: 12 / 2 𝑛1 + 𝑛2 𝑛1 − 𝑛2 (𝑛1 + 𝑛2) ÷ 𝑛3 (𝑛1 + 𝑛2) × 𝑛3 𝑛1 × 𝑛2 𝑛1 ÷ 𝑛2 (n1 + n2) * n3 n1 − n2 n1 * n2 (n1 + n2) / n3 Figure 1: The visualization of the problem representa- tions by T-SNE. "Prob." and "Eq" are short for the math word problem and its solution equation. The problem A and B are in the same prototype equation "n1 − …

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