Abstract

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

Highlights

  • Developing algorithms to solve math word problems (Table 1) has been an interest of NLP researchers for a long time (Feigenbaum and Feldman, 1963)

  • It is an interesting topic of study from the point of view of natural language understanding and reasoning for several reasons

  • Our contributions are three-fold: (a) We model the application of a formula and present a novel method to learn to apply a formula; (b) We annotate the publicly available AddSub corpus with the correct formula and its associated variables; and (c) We make the code publicly available. 2

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Summary

Introduction

Developing algorithms to solve math word problems (Table 1) has been an interest of NLP researchers for a long time (Feigenbaum and Feldman, 1963). It maps that formula into an algebraic equation Examples of such formulas in the arithmetic domain includes part whole which says, ‘the whole is equal to the sum of its parts’, or the Unitary Method that is used to solve problems like ‘A man walks seven miles in two hours. Our system currently considers three mathematical concepts: 1) the concept of part whole, 2) the concept of change and 3) the concept of comparison These concepts are sufficient to solve the arithmetic word problems in AddSub. Table 2 illustrates each of these three concepts with examples. Part Whole TOTAL SET UNKNOWN Tom went to 4 hockey games this year , but missed 7.

Problem Formulation
Modelling Formulas And their Applications
The Space of Possible Applications
Probabilistic Model
Parameter Estimation
Feature Function φ
Attributes of Variables
Cross Attribute Relations
Features
Handling Arbitrary Number of Variables
Related Works
Dataset
Result
Error Analysis
Findings
Conclusion
Full Text
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