Equation Parsing : Mapping Sentences to Grounded Equations

By Manish Gupta, Arun Mallya, Subhro Roy, Jason H. D. Cho, Jiawei Han. 2016

49 citations recorded by the source corpus.

Identifying mathematical relations expressed in text is essential to understanding a broad range of natural language text from election reports, to financial news, to sport commentaries to mathematical word problems. This paper focuses on identifying and understanding mathematical relations described within a single sentence. We introduce the problem of Equation Parsing -- given a sentence, identify noun phrases which represent variables, and generate the mathematical equation expressing the relation described in the sentence. We introduce the notion of projective equation parsing and provide an efficient algorithm to parse text to projective equations. Our system makes use of a high precision lexicon of mathematical expressions and a pipeline of structured predictors, and generates correct equations in $70\%$ of the cases. In $60\%$ of the time, it also identifies the correct noun phrase $\rightarrow$ variables mapping, significantly outperforming baselines. We also release a new annotated dataset for task evaluation.

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

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Citations in the corpus

Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems (2017, background): “Other work has focused on learning to map math expressions into formal languages (Roy et al., 2016).”
Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (2018, methodology): “…the quantities in the problems (Kushman et al., 2014; Hosseini et al., 2014; Roy et al., 2015; Roy and Roth, 2015; Koncel-Kedziorski et al., 2015; Roy et al., 2016; Upadhyay et al., 2016; Upadhyay and Chang, 2017; Roy and Roth, 2018; Wang et al., 2018 In terms of how to learn the model for…”
Learning a Neural Semantic Parser from User Feedback (2017, background): “…et al., 2016), Abstract Meaning Representations (AMR) (Artzi et al., 2015; Misra and Artzi, 2016), and systems of equations (Kushman et al., 2014; Roy et al., 2016) – parsers for querying databases have typically used either logic programs (Zelle and Mooney, 1996), lambda calculus (Zettlemoyer…”
Mapping to Declarative Knowledge for Word Problem Solving (2017, methodology): “There has been some work to extract meaning of variables (Roy et al., 2016) in algebra word problems; an extension of this can possibly support the application of rules in algebra word problems.”
Neural Math Word Problem Solver with Reinforcement Learning (2018, background): “Roy and Roth (2015), Roy et al. (2016) leverage the tree structure of equations.”
A Bottom-Up DAG Structure Extraction Model for Math Word Problems (2021, methodology): “Koncel-Kedziorski et al. (2015) generated several complete expression trees by integer programming and chose the correct one by SVM. Roy et al. (2016) predicted the expression tree by Cocke-Younger-Kasami algorithm (Cocke 1969) and SVM.”
A Weakly Supervised Model for Solving Math word Problems (2021, methodology): “Tree-based meth-ods (Roy and Roth, 2015; Koncel-Kedziorski et al., 2015; Roy et al., 2016; Roy and Roth, 2017, 2018) replaced the process of deriving an equation by constructing an equivalent tree structure, step by step, in a bottom-up manner.”
Using Intermediate Representations to Solve Math Word Problems (2018, background): “Roy and Roth (2015); Roy et al. (2016) leverage the tree structure of equations.”