Mapping to Declarative Knowledge for Word Problem Solving

By Subhro Roy, Dan Roth. 2017

112 citations recorded by the source corpus.

Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several mathematical concepts such as dimensional analysis, subset relationships, etc. In this paper, we develop declarative rules which govern the translation of natural language description of these concepts to math expressions. We then present a framework for incorporating such declarative knowledge into word problem solving. Our method learns to map arithmetic word problem text to math expressions, by learning to select the relevant declarative knowledge for each operation of the solution expression. This provides a way to handle multiple concepts in the same problem while, at the same time, supporting interpretability of the answer expression. Our method models the mapping to declarative knowledge as a latent variable, thus removing the need for expensive annotations. Experimental evaluation suggests that our domain knowledge based solver outperforms all other systems, and that it generalizes better in the realistic case where the training data it is exposed to is biased in a different way than the test data.

Subfields: Artificial Intelligence, Information Systems, Natural Language Processing

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Citations in the corpus

Are NLP Models really able to Solve Simple Math Word Problems? (2021, neutral): “A wide variety of methods and datasets have been proposed to solve MWPs; e.g. statistical machine learning (Roy and Roth, 2018), semantic parsing (Huang et al., 2017) and most recently deep learning (Wang et al., 2017; Xie and Sun, 2019; Zhang et al., 2020); see (Zhang et al., 2020) for an…”
MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms (2019, background): “This has led to an increasing focus on finding semantic alignment of math word problems and mentions of numbers (Roy and Roth, 2018).”
Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2022, background): “Kushman et al. (2014) and Roy and Roth (2018) designed templates to ﬁnd the alignments between the declarative language and equations.”
Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (2018, background): “…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 solving math word problems, the prior work can be categorized into…”
A Goal-Driven Tree-Structured Neural Model for Math Word Problems (2019, methodology): “…1985; Bakman, 2007; Yuhui et al. , 2010], statistical machine learning methods [Kushman et al. , 2014; Zhou et al. , 2015; Mitra and Baral, 2016; Roy and Roth, 2018] and semantic parsing methods [ Shi et al. , 2015; Koncel-Kedziorski et al. , 2015; Huang et al. , 2017] RNN [Wang et al. , 2017].”
Text Modular Networks: Learning to Decompose Tasks in the Language of Existing Models (2021, background): “However, much of this prior work is limited to pre-determined composition structures (Berant et al., 2013; Seo et al., 2015; Neelakantan et al., 2017; Roy and Roth, 2018).”
Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks (2022, background): “Earlier, there have been studies in understanding NLP models’ capabilities to solve arithmetic/algebraic questions (Hosseini et al., 2014; Koncel-Kedziorski et al., 2015; Roy and Roth, 2015; Ling et al., 2017; Roy and Roth, 2018).”
Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions (2019, methodology): “This indicates part-whole relation(i.e., one quantity is part of a larger quantity), mentioned in (Mitra and Baral, 2016; Roy and Roth, 2018), which is of great importance in MWPs solving.”
Template-Based Math Word Problem Solvers with Recursive Neural Networks (2019, background): “…efforts have been mainly based on statistical machine learning (Kushman et al. 2014; Am-nueypornsakul and Bhat 2014; Zhou, Dai, and Chen 2015; Mitra and Baral 2016; Roy and Roth 2018) and semantic parsing (Shi et al. 2015; Koncel-Kedziorski et al. 2015; Roy and Roth 2015; Huang et al. 2017).”
Graph-to-Tree Learning for Solving Math Word Problems (2020, methodology): “works can be broadly divided into statistical machine learning based (Kushman et al., 2014; Hosseini et al., 2014; Mitra and Baral, 2016; Roy and Roth, 2018; Zou and Lu, 2019a) and semantic parsing based (Shi et al.”
Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning (2021, methodology): “Unlike existing methods (Seo et al., 2015; Sachan et al., 2017; Alvin et al., 2017; Sachan et al., 2020), Inter-GPS achieves the explicit symbolic reasoning with the theorem knowledge base and the humanreadable search process, shown in Figure 4.”
Text2Math: End-to-end Parsing Text into Math Expressions (2019, methodology): “We note that some prior systems (Roy and Roth, 2017, 2018) require extra inverse operators – inverse subtraction “−r” and inverse division “÷r” to handle the scenarios where the order of quantities appearing in the text is not consistent with the order that they appear in the expression.”
A Knowledge-Aware Sequence-to-Tree Network for Math Word Problem Solving (2020, background): “Roy and Roth (2018) developed declarative rules to transform math concepts into expressions.”
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.”
Neural Math Word Problem Solver with Reinforcement Learning (2018, background): “On the other hand, the feature-based statistical learning approaches (Kushman et al., 2014; Roy and Roth, 2018) generate equation candidates and ﬁnd the most probable equation by using predeﬁned features.”
Using Intermediate Representations to Solve Math Word Problems (2018, background): “Mitra and Baral (2016); Roy and Roth (2018) design features for a few math concepts (e.g. Part-Whole, Comparison).”
Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks (2021, methodology): “…statistical machine learning methods (Kushman et al., 2014; Zhou et al., 2015; Roy and Roth, 2015, 2016; Mitra and Baral, 2016; Huang et al., 2016; Roy and Roth, 2018), semantic parsing methods (Shi et al., 2015; Koncelkedziorski et al., 2015; Huang et al., 2017; Liang et al., 2018a), to deep…”