Using Intermediate Representations to Solve Math Word Problems

By Danqing Huang, Jin-ge Yao, Chin-Yew Lin, Qingyu Zhou, Jian Yin. 2018

29 citations recorded by the source corpus.

To solve math word problems, previous statistical approaches attempt at learning a direct mapping from a problem description to its corresponding equation system. However, such mappings do not include the information of a few higher-order operations that cannot be explicitly represented in equations but are required to solve the problem. The gap between natural language and equations makes it difficult for a learned model to generalize from limited data. In this work we present an intermediate meaning representation scheme that tries to reduce this gap. We use a sequence-to-sequence model with a novel attention regularization term to generate the intermediate forms, then execute them to obtain the final answers. Since the intermediate forms are latent, we propose an iterative labeling framework for learning by leveraging supervision signals from both equations and answers. Our experiments show using intermediate forms outperforms directly predicting equations.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Natural Language Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Lei Wang
2. Jipeng Zhang
3. Jierui Li
4. Hannaneh Hajishirzi
5. Xuanjing Huang
6. Yan Wang
7. Bing Tian Dai
8. Jie Shao

In Computational Theory and Mathematics

1. Jipeng Zhang
2. Lei Wang
3. Yan Wang
4. Qinzhuo Wu
5. Xuanjing Huang
6. Qi Zhang
7. Jie Shao
8. Bing Tian Dai

In Natural Language Processing

1. Lei Wang
2. Jipeng Zhang
3. Jierui Li
4. Bing Tian Dai
5. Yan Wang
6. Dongxiang Zhang
7. Hannaneh Hajishirzi
8. Jie Shao

Citations in the corpus

• MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms (2019, methodology): “…features introduced by prior work are arguably “interpretable” due to the relative sparsity of features as well as the clear alignments between inputs and outputs, new neuralized approaches present new challenges to model interpretability of math word problem solvers (Huang et al., 2018a).”
• Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions (2019, background): “In recent years, a growing number of deep learning models for MWPs (Wang et al., 2017; Ling et al., 2017; Wang et al., 2018b,a; Huang et al., 2018a,b; Wang et al., 2019) have drawn inspiration from advances in machine translation.”
• Graph-to-Tree Learning for Solving Math Word Problems (2020, background): “Huang et al. (2018) designed a new intermediate form to generate.”
• Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems (2021, background): “…(Fletcher, 1985; Bakman, 2007), statistical machine learning methods (Kushman et al., 2014; Hosseini et al., 2014), semantic parsing methods (Shi et al., 2015; Koncel-Kedziorski et al., 2015) and deep learning methods (Wang et al., 2017; Huang et al., 2018; Xie and Sun, 2019; Zhang et al., 2020).”
• Math Word Problem Solving with Explicit Numerical Values (2021, background): “With the advancements in natural language processing, math word problem solving has received growing attention in recent years (Roy and Roth, 2015; Mitra and Baral, 2016; Ling et al., 2017; Huang et al., 2018).”