Learning To Use Formulas To Solve Simple Arithmetic Problems

By Arindam Mitra, Chitta Baral. 2016

123 citations recorded by the source corpus.

Solving simple arithmetic word problems is one of the challenges in Natural Language Understanding. This paper presents a novel method to learn to use formulas to solve simple arithmetic word problems. Our system, analyzes each of the sentences to identify the variables and their attributes; and automatically maps this information into a higher level representation. It then uses that representation to recognize the presence of a formula along with its associated variables. An equation is then generated from the formal description of the formula. In the training phase, it learns to score the pair from the systematically generated higher level representation. It is able to solve 86.07% of the problems in a corpus of standard primary school test questions and beats the state-of-the-art by

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Natural Language Processing

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Citations in the corpus

Generate & Rank: A Multi-task Framework for Math Word Problems (2021, methodology): “Other works (Sundaram and Khemani, 2015; Mitra and Baral, 2016; Liang et al., 2016) follow a similar process with different templates and annotations.”
Deep Neural Solver for Math Word Problems (2017, methodology): “Mitra et al. Mitra and Baral (2016) presents a novel method to learn to use formulas to solve simple addition-subtraction arithmetic problems.”
A Goal-Driven Tree-Structured Neural Model for Math Word Problems (2019, methodology): “…methods [Fletcher, 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]…”
MathDQN: Solving Arithmetic Word Problems via Deep Reinforcement Learning (2018, methodology): “An alternative template-based method was proposed in (Mitra and Baral 2016).”
EQUATE: A Benchmark Evaluation Framework for Quantitative Reasoning in Natural Language Inference (2019, background): “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).”
Mapping to Declarative Knowledge for Word Problem Solving (2017, methodology): “tra and Baral (2016) maps problems to a set of formulas. Both require extensive annotations for intermediate steps (verb classiﬁcation for Hosseini et al. (2014), alignment of numbers to formulas for Mitra and Baral (2016), etc). In contrast, our method can handle a more general class of problems, w”
Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions (2019, methodology): “This indicates part-whole relation(i.e., one quantity is part of a larger quantity), mentioned in (Mitra and Baral, 2016; Roy and Roth, 2018), which is of great importance in MWPs solving.”
Template-Based Math Word Problem Solvers with Recursive Neural Networks (2019, background): “ARIS (Hosseini et al. 2014) and Formula (Mitra and Baral 2016) are two systems that only support the operators of addition and subtraction.”
Graph-to-Tree Learning for Solving Math Word Problems (2020, methodology): “works can be broadly divided into statistical machine learning based (Kushman et al., 2014; Hosseini et al., 2014; Mitra and Baral, 2016; Roy and Roth, 2018; Zou and Lu, 2019a) and semantic parsing based (Shi et al.”
TAT-QA: A Question Answering Benchmark on a Hybrid of Tabular and Textual Content in Finance (2021, background): “…question answering (Dua et al., 2019; Ran et al., 2019; Andor et al., 2019; Chen et al., 2020a; Pasupat and Liang, 2015; Herzig et al., 2020; Yin et al., 2020; Zhang and Balog, 2020) and arithmetic word problems (Kush-man et al., 2014; Mitra and Baral, 2016; Huang et al., 2017; Ling et al., 2017).”
Neural Math Word Problem Solver with Reinforcement Learning (2018, background): “Mitra and Baral (2016), Roy and Roth (2018) design features for a few math concepts (e.g. Part-Whole, Comparison).”
A Meaning-Based Statistical English Math Word Problem Solver (2018, background): “, 2017), which does not check the entity-attribute consistency between each quantity and the target of the given question; and (b) With understanding (Lin et al., 2015; Mitra and Baral, 2016; Roy and Roth, 2017), which also checks the entity-attribute consistency while solving the problem.”
Using Intermediate Representations to Solve Math Word Problems (2018, background): “Mitra and Baral (2016); Roy and Roth (2018) design features for a few math concepts (e.g. Part-Whole, Comparison).”
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.”
Learning by Fixing: Solving Math Word Problems with Weak Supervision (2020, methodology): “…rule-based methods (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.…”
Learning Fine-Grained Expressions to Solve Math Word Problems (2017, background): “Mitra and Baral (2016) considers addition and sub-traction problems in three basic problem types: “Change”, “Part Whole” and “Comparison”.”
Solving Math Word Problems with Multi-Encoders and Multi-Decoders (2020, background): “, 2010) and statistical machine learning methods (Kushman et al., 2014; Hosseini et al., 2014; Mitra and Baral, 2016) that map problems into predefined templates.”