Learn to Solve Algebra Word Problems Using Quadratic Programming

By Lipu Zhou, Shuaixiang Dai, Liwei Chen. 2015

90 citations recorded by the source corpus.

This paper presents a new algorithm to automatically solve algebra word problems. Our algorithm solves a word problem via analyzing a hypothesis space containing all possible equation systems generated by assigning the numbers in the word problem into a set of equation system templates extracted from the training data. To obtain a robust decision surface, we train a log-linear model to make the margin between the correct assignments and the false ones as large as possible. This results in a quadratic programming (QP) problem which can be efficiently solved. Experimental results show that our algorithm achieves 79.7% accuracy, about 10% higher than the state-of-the-art baseline (Kushman et al., 2014).

Subfields: Artificial Intelligence, Natural Language Processing, Reinforcement Learning

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Citations in the corpus

MAWPS: A Math Word Problem Repository (2016, background): “* denotes equal contribution types of math word problems (Hosseini et al., 2014; Kushman et al., 2014; Roy and Roth, 2015; Zhou et al., 2015; Koncel-Kedziorski et al., 2015).”
Parsing Algebraic Word Problems into Equations (2015, background): “, 2014; Roy and Roth, 2015), algebra word problems (Kushman et al., 2014; Zhou et al., 2015), and geometry word problems (Seo et al.”
Deep Neural Solver for Math Word Problems (2017, methodology): “Although ZDC and the retrieval model cannot generate new templates, their accuracy is not zero in the new settings.”
How well do Computers Solve Math Word Problems? Large-Scale Dataset Construction and Evaluation (2016, methodology): “For example, the Alg514 dataset used in Kushman et al. (2014) and Zhou et al. (2015) only contains 514 problems of 28 types.”
MathDQN: Solving Arithmetic Word Problems via Deep Reinforcement Learning (2018, methodology): “In (Zhou et al. 2015), an improved method was proposed to reduce the hypothesis space by only enumerating the permutation of number slots.”
Annotating Derivations: A New Evaluation Strategy and Dataset for Algebra Word Problems (2016, methodology): “Zhou et al. (2015) also reconciled templates, but do not describe how it was performed.”
EQUATE: A Benchmark Evaluation Framework for Quantitative Reasoning in Natural Language Inference (2019, methodology): “tic word problems (Hosseini et al., 2014; Mitra and Baral, 2016; Zhou et al., 2015; Upadhyay et al., 2016; Huang et al., 2017; Kushman et al., 2014a; Koncel-Kedziorski et al., 2015; roy; Roy, 2017; Ling et al., 2017a).”
Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions (2019, methodology): “Compared to statistical machine learning-based methods (Kushman et al., 2014; Mitra and Baral, 2016; Roy and Roth, 2018; Zhou et al., 2015; Huang et al., 2016) and semantic parsing-based methods (Shi et al., 2015; Koncel-Kedziorski et al., 2015; Roy and Roth, 2015; Huang et al., 2017), these…”
Template-Based Math Word Problem Solvers with Recursive Neural Networks (2019, methodology): “In (Zhou, Dai, and Chen 2015), an improved method was proposed to reduce the hypothesis space by only enumerating the permutation of number slots.”
Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks (2021, methodology): “, 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.”
Investigating Math Word Problems using Pretrained Multilingual Language Models (2021, background): “Various approaches have been proposed to solve MWPs. Template-based approaches (Kushman et al., 2014; Zhou et al., 2015; Upadhyay et al., 2016; Huang et al., 2017) are widely adopted as numbers appeared in the expressions are usually sparse in the representation space and the expressions may fall…”
DRAW: A Challenging and Diverse Algebra Word Problem Set (2015, methodology): “Following previous work (Kushman et al., 2014; Zhou et al., 2015), we mainly focus on the semantic parsing component and leave the question answering component as future work.”
Point to the Expression: Solving Algebraic Word Problems Using the Expression-Pointer Transformer Model (2020, methodology): “Upadhyay et al. (2016) designed a model using a set of hand-crafted features similar to those used by Zhou et al. (2015).”
Using Intermediate Representations to Solve Math Word Problems (2018, background): “…(1) generate equation candidates; They either re- place numbers of existing equations in the training data as new equations (Kushman et al., 2014; Zhou et al., 2015; Upadhyay et al., 2016), or enumerate possible combinations of math operators and numbers and variables (Koncel-Kedziorski et…”
Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems (2020, methodology): “machine learning methods (Kushman et al., 2014; Zhou et al., 2015; Mitra and Baral, 2016; Huang et al., 2016; Roy and Roth, 2018),semantic parsing methods (Shi et al.”
Learning Fine-Grained Expressions to Solve Math Word Problems (2017, methodology): “Kushman et al. (2014) aligns nouns to variable slots {x1, x2, ...} which leads to a huge hypothesis space and does not perform as well as the number slot alignment only method proposed later by (Zhou et al., 2015).”
A Meaning-Based Statistical English Math Word Problem Solver (2018, background): “…2014), which make all related decisions based on a set of rules; (2) Purely statistics-based approaches (Kushman et al., 2014; Roy et al., 2015; Zhou et al., 2015; Upadhyay et al., 2016), in which all related decisions are done via a statistical classifier; (3) DNNbased approaches (Ling et…”
TM-generation model: a template-based method for automatically solving mathematical word problems (2021, methodology): “In contrast, Zhou et al. [14] used equation template slotting only numbers to improve Kushman’s model.”