Learning to Solve Arithmetic Word Problems with Verb Categorization

By Mohammad Javad Hosseini, Hannaneh Hajishirzi, Oren Etzioni, Nate Kushman. 2014

485 citations recorded by the source corpus.

This paper presents a novel approach to learning to solve simple arithmetic word problems. Our system, ARIS, analyzes each of the sentences in the problem statement to identify the relevant variables and their values. ARIS then maps this information into an equation that represents the problem, and enables its (trivial) solution as shown in Figure 1. The paper analyzes the arithmetic-word problems “genre”, identifying seven categories of verbs used in such problems. ARIS learns to categorize verbs with 81.2% accuracy, and is able to solve 77.7% of the problems in a corpus of standard primary school test questions. We report the first learning results on this task without reliance on predefined templates and make our data publicly available. 1

Subfields: Artificial Intelligence, Natural Language Processing

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Citations in the corpus

SQuAD: 100,000+ Questions for Machine Comprehension of Text (2016, background): “Algebra word problems require understanding a story well enough to turn it into a system of equations, which can be easily solved to produce the answer (Kushman et al., 2014; Hosseini et al., 2014).”
Chain of Thought Prompting Elicits Reasoning in Large Language Models (2022, neutral): “√ √ √ √ √ Answer Choices: (a) 5 MAWPS: AddSub 395 There were 6 roses in the vase.”
NumNet: Machine Reading Comprehension with Numerical Reasoning (2019, neutral): “Hosseini et al. (2014) proposed a simple method to address arithmetic word problems, but mostly focusing on subsets of problems which only require addition and subtraction.”
DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs (2019, background): “also contain similar phenomena to what is in DROP (Koncel-Kedziorski et al., 2015; Kushman et al., 2014; Hosseini et al., 2014; Clark et al., 2016; Ling et al., 2017).”
Solving Quantitative Reasoning Problems with Language Models (2022, background): “Solving quantitative reasoning problems expressed in natural language has been an active area of study [13, 14].”
Self-Consistency Improves Chain of Thought Reasoning in Language Models (2022, methodology): “For these tasks, we used the Math Word Problem Repository (Koncel-Kedziorski et al., 2016), including AddSub (Hosseini et al., 2014), MultiArith (Roy & Roth, 2015), and ASDiv (Miao et al., 2020).”
MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms (2019, background): “Some effort has been made on parsing the problems to extract salient entities (Hosseini et al., 2017).”
Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems (2017, background): “…language speciﬁcations of algebraic word problems, and solved these by either learning to ﬁll in templates that can be solved with equation solvers (Hosseini et al., 2014; Kushman et al., 2014) or inferring and modeling operation sequences (programs) that lead to the ﬁnal answer (Roy and Roth,…”
MAWPS: A Math Word Problem Repository (2016, methodology): “• AddSub: Collection of addition, subtraction problems (Hosseini et al., 2014).”
Large Language Models are Zero-Shot Reasoners (2022, positive): “Our method gives on-par performances for the remaining two arithmetic reasoning tasks (SingleEq and AddSub), which is expected since they do not require multi-step reasoning.”
A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers (2020, background): “, 2015), which contains number word problems only; (2) the Arithmetic Word Problem corpora (Hosseini et al., 2014; Roy et al., 2015), which involve the four basic arithmetic operations Math Word Problem”
Injecting Numerical Reasoning Skills into Language Models (2020, methodology): “Therefore, we use the framework of Hosseini et al. (2014), who proposed to model math word problems with a simple structure.”
Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (2018, background): “…as POS tags, paths in the dependency trees, keywords, etc., to allow the model to focus on 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…”
Solving General Arithmetic Word Problems (2016, methodology): “(Hosseini et al., 2014) mentions the result of running the system of (Kushman et al.”
Parsing Algebraic Word Problems into Equations (2015, methodology): “In addition, ALGES overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.”
How well do Computers Solve Math Word Problems? Large-Scale Dataset Construction and Evaluation (2016, background): “The system of Hosseini et al. (2014) is not included in our evaluation because it only handles homogeneous addition/subtraction problems.”
Combining Retrieval, Statistics, and Inference to Answer Elementary Science Questions (2016, background): “A few systems have attempted standardized tests, e.g., in geometry (Seo et al. 2014) and mathematics (Hosseini et al. 2014; Kushman et al. 2014), and work well due to their limited domains and stylized wording of questions.”
Automatically Solving Number Word Problems by Semantic Parsing and Reasoning (2015, methodology): “Statistical learning methods have been proposed recently in two papers: Hosseini et al. (2014) solve single step or multi-step homogenous addition and subtraction problems by learning verb categories from the training data.”