Solving General Arithmetic Word Problems

By Subhro Roy, Dan Roth. 2016

656 citations recorded by the source corpus.

This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional annotations or predefined templates. We develop a theory for expression trees that can be used to represent and evaluate the target arithmetic expressions; we use it to uniquely decompose the target arithmetic problem to multiple classification problems; we then compose an expression tree, combining these with world knowledge through a constrained inference framework. Our classifiers gain from the use of quantity schemas that supports better extraction of features. Experimental results show that our method outperforms existing systems, achieving state of the art performance on benchmark datasets of arithmetic word problems.

Subfields: Artificial Intelligence, Natural Language Processing

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Citations in the corpus

Chain of Thought Prompting Elicits Reasoning in Large Language Models (2022, neutral): “• Math Word Problem Repository (Koncel-Kedziorski et al., 2016): AddSub (Hosseini et al., 2014): https://www.cs.washington.edu/nlp/arithmetic ; MultiArith (Roy and Roth, 2015), license: CC BY 4.0.”
NumNet: Machine Reading Comprehension with Numerical Reasoning (2019, neutral): “After that, Roy and Roth (2015) proposed an algorithmic approach which could handle arithmetic word problems with multiple steps and operations.”
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).”
Training Verifiers to Solve Math Word Problems (2021, background): “Early math word problem datasets (Kushman et al., 2014; Roy and Roth, 2015) are relatively small and are not well suited for testing the limits of modern language models.”
Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems (2017, background): “Extensive efforts have been made in the domain of math problem solving (Hosseini et al., 2014; Kushman et al., 2014; Roy and Roth, 2015), which aim at obtaining the correct answer to a given math problem.”
MAWPS: A Math Word Problem Repository (2016, background): “, 2015), logic puzzle problems (Mitra and Baral, 2015), arithmetic word problems (Hosseini et al., 2014; Roy and Roth, 2015), algebra word problems (Kushman et al.”
Large Language Models Are Human-Level Prompt Engineers (2022, methodology): “Known as Zero-Shot-CoT, this prompting strategy improves the zero-shot performance of InstructGPT on MultiArith (Roy & Roth, 2016) from 17.7 to 78.7 and improves performance on GSM8K(Cobbe et al., 2021) from 10.4 to 40.7.”
Large Language Models are Zero-Shot Reasoners (2022, background): “While our Zero-shot-CoT underperforms Few-shot-CoT with carefully-crafted and task-speciﬁc step-by-step examples, Zero-shot-CoT achieves enormous score gains compared to the zero-shot baseline, e.g. from 17.7% to 78.7% on MultiArith and from 10.4% to 40.7% on GSM8K with large-scale InstructGPT model”
Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2022, background): “As a result we also consider the “reverse operation” for division and subtraction (Roy and Roth, 2015).”
Generate & Rank: A Multi-task Framework for Math Word Problems (2021, neutral): “Roy et al. (2015) proposes three types of classiﬁers to identify different elements of problems.”
A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers (2020, methodology): “Current MWP corpora can be classified into four categories: (1) the Number Word Problem corpus (Shi et al., 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”
Giving BERT a Calculator: Finding Operations and Arguments with Reading Comprehension (2019, methodology): “The model can learn to predict new operations when appropriate in a math word problem setting (Roy and Roth, 2015) with very few training examples.”
Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (2018, methodology): “The The results are consistent with those hand-craft features for solving math word problems proposed by the prior research (Hos-seini et al., 2014; Roy and Roth, 2015; Roy et al., 2015).”
Parsing Algebraic Word Problems into Equations (2015, background): “, 2015), logic puzzle problems (Mitra and Baral, 2015), arithmetic word problems (Hosseini et al., 2014; Roy and Roth, 2015), algebra word problems (Kushman et al.”
Deep Neural Solver for Math Word Problems (2017, background): “In addition, Roy and Roth Roy et al. (2015); Roy and Roth (2016) tries to handle arithmetic problems with multiple steps and operations without depending on additional annotations or predeﬁned templates.”
How well do Computers Solve Math Word Problems? Large-Scale Dataset Construction and Evaluation (2016, background): “Koncel-Kedziorski et al. (2015) and Roy and Roth (2015) target math problems that can be solved by one single linear equation.”
DeepProbLog: Neural Probabilistic Logic Programming (2018, methodology): “As in their work, we consider three tasks: addition, sorting [26] and word algebra problems (WAPs) [27].”
Programming with a Differentiable Forth Interpreter (2016, background): “In previous work, local classifiers (Roy & Roth, 2015; Roy et al., 2015), hand-crafted grammars (Koncel-Kedziorski et al.”
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).”