Unit Dependency Graph and Its Application to Arithmetic Word Problem Solving

By Subhro Roy, Dan Roth. 2016

107 citations recorded by the source corpus.

Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms .

Subfields: Artificial Intelligence, Information Systems, Natural Language Processing, Prompting & Reasoning

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Citations in the corpus

Generate & Rank: A Multi-task Framework for Math Word Problems (2021, neutral): “ARIS (Hosseini et al., 2014) (Roy and Roth, 2017) proposes Unit Depen-dency Graph to enhance the scoring function.”
A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers (2020, methodology): “(addition, subtraction, multiplication and division) with either single-step or multi-step operations; (3) the Algebraic Word Problem corpora (Kushman et al., 2014; Koncel-Kedziorski et al., 2015; Roy and Roth, 2017; Upadhyay & Chang, 2015; Wang et al., 2017), which focus on algebraic MWPs; and (4) ”
A Goal-Driven Tree-Structured Neural Model for Math Word Problems (2019, methodology): “We use the same 5-fold cross-3 validation as in [Roy and Roth, 2017].”
Text Modular Networks: Learning to Decompose Tasks in the Language of Existing Models (2021, background): “, 2013), math QA systems (Roy and Roth, 2017) and textual NMNs (Gupta et al.”
MathDQN: Solving Arithmetic Word Problems via Deep Reinforcement Learning (2018, methodology): “Recently, UnitDep (Roy and Roth 2017) augments the scoring function of the expression tree in (Roy and Roth 2015) by further considering the consistence of rate unit associated with the quantities.”
Mapping to Declarative Knowledge for Word Problem Solving (2017, methodology): “Results on the AllArith datasets are slightly different from (Roy and Roth, 2017), since we fixed several ungrammatical sentences in the dataset”
Template-Based Math Word Problem Solvers with Recursive Neural Networks (2019, background): “UnitDep (Roy and Roth 2017) further took into account the consistence of rate unit associated with the quantities and treated it as a scoring factor.”
The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers (2018, methodology): “As shown in Table 5, a binary indicator to determine whether a quantity refers to a rate is adopted in many solvers [26] [28] [15] [40] [45].”
Learning by Fixing: Solving Math Word Problems with Weak Supervision (2020, background): “…(Fletcher 1985; Bakman 2007; Yu-hui et al. 2010), statistical learning methods (Kushman et al. 2014; Zhou, Dai, and Chen 2015; Mitra and Baral 2016; Roy and Roth 2017; Huang et al. 2016), semantic-parsing meth-ods (Shi et al. 2015; Koncel-Kedziorski et al. 2015; Huang et al. 2017) to recent deep…”
Point to the Expression: Solving Algebraic Word Problems Using the Expression-Pointer Transformer Model (2020, background): “…capture the semantic content of a word, such as the unit of a given number (Roy and Roth, 2015; Koncel-Kedziorski et al., 2015; Zhou et al., 2015; Upadhyay et al., 2016; Roy and Roth, 2017) or dependency relationship between numbers (Kushman et al., 2014; Zhou et al., 2015; Upadhyay et al., 2016).”
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.”
Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks (2021, methodology): “…ranging from rule-based meth-ods (Bakman, 2007; Yuhui et al., 2010), 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;…”
Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems (2020, unknown): “Alg514 (Kushman et al., 2014) 514 28 - Dolphin1878 (Shi et al., 2015) 1,878 1,183 - AllArith (Roy and Roth, 2017) 831 - - MAWPS (Koncel-Kedziorski et al., 2016) 2,373 - - Dolphin18K (Huang et al., 2016) 18,460 5,871 - Math23K (Wang et al., 2017) 23,160 2,187 0.80% Ape210K 210,488 56,532 37.70%…”
LILA: A Unified Benchmark for Mathematical Reasoning (2022, methodology): “Here we discuss the construction and composition of the benchmark and provide descriptive statistics of the datasets.”
HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem (2021, methodology): “For MAWPS, we apply the 5-fold cross-validation.”
Tree-structured Decoding for Solving Math Word Problems (2019, methodology): “This two-step pipeline model was further extended with tree-based features, ranking style retrieval models and so on (Upadhyay and Chang, 2017; Roy and Roth, 2017).”