Parsing Algebraic Word Problems into Equations

By Rik Koncel-Kedziorski, Hannaneh Hajishirzi, Ashish Sabharwal, Oren Etzioni, Siena Dumas Ang. 2015

366 citations recorded by the source corpus.

This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as Alges. We compare Alges with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. 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.

Subfields: Artificial Intelligence, Information Systems, Natural Language Processing

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Citations in the corpus

Chain of Thought Prompting Elicits Reasoning in Large Language Models (2022, neutral): “, 2015), (2) SingleEq (Koncel-Kedziorski et al., 2015), (3) AddSub (Hosseini et al.”
NumNet: Machine Reading Comprehension with Numerical Reasoning (2019, neutral): “Koncel-Kedziorski et al. (2015) The framework of our NumNet model.”
DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs (2019, background): “Many existing algebra word problem datasets also contain similar phenomena to what is in DROP (Koncel-Kedziorski et al., 2015; 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].”
Large Language Models are Zero-Shot Reasoners (2022, methodology): “SingleEq and AddSub contain easier problems, which do not require multi-step calculation to solve the tasks.”
Generate & Rank: A Multi-task Framework for Math Word Problems (2021, neutral): “ALGES (Koncel-Kedziorski et al., 2015) converts the process of searching valid expressions to an integer linear programming prob-”
A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers (2020, background): “For AI2, IL, KAZB, ALGES, AllArith, DRAW, and MathQA, we follow their own either n-fold cross-validation setting or the train/dev/test splits originally specified in each dataset.”
Injecting Numerical Reasoning Skills into Language Models (2020, methodology): “All models that were ﬁne-tuned on DROP were evaluated in a zero-shot setup on 395 examples from A DD S UB (Hosseini et al., 2014), 321 from SO P (Roy et al., 2015), and 305 from SE Q (Koncel-Kedziorski et al., 2015).”
Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (2018, methodology): “…word problems as a parsing task about transforming natural language into the logical form (Roy et al., 2015; Roy and Roth, 2015; Shi et al., 2015; Koncel-Kedziorski et al., 2015; Roy et al., 2016; Roy and Roth, 2018), 2) the second one focuses on retrieving proper predeﬁned equation templates…”
Deep Neural Solver for Math Word Problems (2017, background): “…machine learning techniques Kushman et al. (2014); Amnueypornsakul and Bhat (2014); Zhou et al. (2015); Mitra and Baral (2016) and semantic parsing methods Shi et al. (2015); Koncel-Kedziorski et al. (2015) are proposed to tackle this problem and promising re-sults are reported on some datasets.”
Programming with a Differentiable Forth Interpreter (2016, background): “, 2015), hand-crafted grammars (Koncel-Kedziorski et al., 2015), and recurrent neural models (Bouchard et al.”
My Computer Is an Honor Student - but How Intelligent Is It? Standardized Tests as a Measure of AI (2016, background): “Kushman et al. (2014) report results on story problems that translate to simultaneous algebraic equations.”
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].”
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 & Roth, 2015; Ling et al., 2017; Roy & Roth, 2018).”
MathDQN: Solving Arithmetic Word Problems via Deep Reinforcement Learning (2018, methodology): “ALGES works well in IL and CC, but its accuracy in AI2 is not satisfactory.”
Mapping to Declarative Knowledge for Word Problem Solving (2017, background): “Koncel-Kedziorski et al. (2015) looks at single equation problems, and Shi et al. (2015) focuses on number word problems.”