The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers

By Dongxiang Zhang, Lei Wang, Nuo Xu, Bing Tian Dai, Heng Tao Shen. 2018

149 citations recorded by the source corpus.

Solving mathematical word problems (MWPs) automatically is challenging, primarily due to the semantic gap between human-readable words and machine-understandable logics. Despite the long history dated back to the 1960s, MWPs have regained intensive attention in the past few years with the advancement of Artificial Intelligence (AI). Solving MWPs successfully is considered as a milestone towards general AI. Many systems have claimed promising results in self-crafted and small-scale datasets. However, when applied on large and diverse datasets, none of the proposed methods in the literature achieves high precision, revealing that current MWP solvers still have much room for improvement. This motivated us to present a comprehensive survey to deliver a clear and complete picture of automatic math problem solvers. In this survey, we emphasize on algebraic word problems, summarize their extracted features and proposed techniques to bridge the semantic gap, and compare their performance in the publicly accessible datasets. We also cover automatic solvers for other types of math problems such as geometric problems that require the understanding of diagrams. Finally, we identify several emerging research directions for the readers with interests in MWPs.

Subfields: Artificial Intelligence, Information Systems, Natural Language Processing

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Citations in the corpus

MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers (2021, background): “More work on math word and geometric problem solving can be found in the survey paper (Zhang et al., 2019).”
Are NLP Models really able to Solve Simple Math Word Problems? (2021, methodology): “Following the setting of Zhang et al. (2020), the arithmetic word problems from MAWPS are divided into ﬁve folds, each of equal test size.”
Giving BERT a Calculator: Finding Operations and Arguments with Reading Comprehension (2019, background): “Mathematical Word Problems have been addressed with a wide variety of datasets and approaches; see Zhang et al. (2018) for an overview.”
A Goal-Driven Tree-Structured Neural Model for Math Word Problems (2019, methodology): “For a more thorough review of automatic MWPs solver, please refer to a recent survey paper [Zhang et al., 2018].”
Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions (2019, background): “More related work and feature-related information can be found in Zhang et al. (2018).”
Template-Based Math Word Problem Solvers with Recursive Neural Networks (2019, background): “For more comprehensive review on MWP solvers, readers can refer to a recent survey paper (Zhang et al. 2018).”
HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem (2021, background): “Therefore, successfully solving MWP can be considered as a milestone towards general AI in the broad domains (Zhang et al. 2019).”
Translating a Math Word Problem to an Expression Tree (2018, background): “For more literatures about solving math word problems automatically, refer to a recent survey paper Zhang et al. (2018).”
Solving Math Word Problems with Teacher Supervision (2021, background): “Building automatic MWP solvers remains a challenging task due to the wide semantic gap to parse the human-readable words into machine-understandable logics so as to facilitate quantitative reasoning [Zhang et al. , 2019].”
PTR: A Benchmark for Part-based Conceptual, Relational, and Physical Reasoning (2021, background): “Also, while previous datasets emphasize reasoning based on spatial relationships, humans possess diverse reasoning abilities, including analogy [62], geometry[48, 40], arithmetic[63, 20, 21], and physics [13].”
Point to the Expression: Solving Algebraic Word Problems Using the Expression-Pointer Transformer Model (2020, methodology): “We copied the accuracy of DNS on DRAW-1K from Zhang et al. (2019).”
Solving Math Word Problems with Multi-Encoders and Multi-Decoders (2020, background): “The work presented in (Zhang et al., 2018) reviews more early approaches.”
Neural Mathematical Solver with Enhanced Formula Structure (2020, background): “Letting computers learn and apply knowledge to answer mathematical problems is a crucial issue, which has attracted much attention in information retrieval and natural language processing for a long history [15].”
A Survey of Deep Learning for Mathematical Reasoning (2022, background): “Previous literature has been limited to the discussion of specific aspects, such as solving math word problems (Bhattacharya, 2017; Zhang et al., 2019; Ughade and Kumbhar, 2019), representing numbers representation (Thawani et al.”
A Weakly Supervised Model for Solving Math word Problems (2021, background): “For a more comprehensive review on automatic MWP solvers, readers can refer to a recent survey paper (Zhang et al., 2018).”