In this website, you will find all materials for a tutorial on machine learning for automatic word problem solving. This will be held at the premier conference for machine learning in Europe, ECML - PKDD, at Würzburg, Germany from September 16 - 20, 2019.

Abstract

In the recent past, and more specifically over the last five years, there has been a growing interest in applying machine learning techniques for understanding and solving mathematical word problems. Advances in this rapidly evolving field that seek to address an interesting but sophisticated task is yet to receive more widespread attention within the broader ML community. This tutorial aims to summarize this flourishing and growing field, focusing on two major trends of approaching this problem; viz., building probabilistic models and designing sequence-to-sequence (seq2seq) architectures. We will start by providing a concrete specification of the task and historical context comprising early approaches to the problem. We then cover the recent research within this field using our categorization across the two major families as alluded to earlier, and then offer perspectives on general trends and future evolution of the area.

What is a word problem?

A word problem is a textual description of a situation, followed by a pertinent question. The answer is a numerical quantity obtained after analysing the word problem. An example of a simple mathematical word problem appears below.

Word Problem: Kevin had 5 books. Kristen took 2 books from Kevin. How many books does he have now?

Equation: x = 5 - 2

Answer: 3

Machine Learning and Natural Language Processing

The complexity of the task may be evident if one observes that small changes to the word problem can change the meaning of the word problem. If the second statement was changed to 'Kristen gave 2 books to Kevin', the equation will change to x = 5 + 2. This makes it challenging for ML paradigms to solve such word problems. Also, the interplay between linguistic and mathematical cues needs specific attention, offering interesting ML challenges.

Overview

The focus of this three and a half hour tutorial is to introduce the recent work done on automatically solving word problems using machine learning and deep learning techniques. Within the tutorial, we provide two primers on Probabilistic Modelling and Seq2Seq learning in this domain.

Contents

• Introduction to Math Word Problem Solving
• Categorization
• Datasets
• Symbolic Semantic Parsing
• Probabilistic Modelling
  • Introduction to Probabilistic Modelling
  • Equation Template based Approaches
  • Expression Tree based Approaches
• Seq2Seq Learning
  • Recurrent Neural Networks (RNN)
  • Long Short term Memory Networks (LSTM)
  • Gated Recurrent Unit (GRU)
  • Sequence-to-Sequence Learning
  • Solvers that use Seq2Seq Learning
• Summary
• Future Directions

[ Slides ]

Highlighted Relevant Papers

1. Anirban Mukherjee and Utpal Garain (2008) - A review of methods for automatic understanding of natural language mathematical problems - Artificial Intelligence Review, 29(2):93–122 [link]
2. Nate Kushman, Yoav Artzi, Luke Zettlemoyer, and Regina Barzilay (2014) - Learning to automatically solve algebra word problems - ACL(1), pages 271–281. [pdf] [code] [data]
3. Mohammad Javad Hosseini, Hannaneh Hajishirzi, Oren Etzioni, and Nate Kushman (2014) - Learning to solve arithmetic word problems with verb categorization - In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 523–533. [pdf] [code] [data]
4. Subhro Roy, Tim Vieira, and Dan Roth (2015) - Reasoning about quantities in natural language - Transactions of the Association for Computational Linguistics, 3:1–13. [pdf]
5. Lipu Zhou, Shuaixiang Dai, and Liwei Chen (2015) - Learn to solve algebra word problems using quadratic programming - In EMNLP, pages 817–822. [pdf]
6. Rik Koncel-Kedziorski, Hannaneh Hajishirzi, Ashish Sabharwal, Oren Etzioni, and Siena Dumas Ang (2015) - Parsing algebraic word problems into equations - Transactions of the Association for Computational Linguistics, 3:585–597. [pdf]
7. Arindam Mitra and Chitta Baral - (2016) - Learning to use formulas to solve simple arithmetic problems - ACL [pdf]
8. Subhro Roy and Dan Roth (2016) - Solving general arithmetic word problems - arXiv preprint arXiv:1608.01413 [pdf]
9. Shyam Upadhyay, Ming-Wei, Chang, Kai-Wei Chang, and Wen-tau Yih (2016) - Learning from explicit and implicit supervision jointly for algebra word problems - In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pages 297–306 [pdf]
10. Yan Wang, Xiaojiang Liu, and Shuming Shi (2017) - Deep neural solver for math word problems - In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 845–854 [pdf]
11. Lei Wang, Yan Wang, Deng Cai, Dongxiang Zhang, and Xiaojiang Liu (2018) - Translating a math word problem to an expression tree - arXiv preprint arXiv:1811.05632 [pdf]

Citation Policy

If you wish to cite this tutorial, please use the following citation styles.

Sowmya S. Sundaram, Savitha Sam Abraham, Deepak P. (2019). Tutorial on Machine Learning for Automatic Word Problem Solving [https://sites.google.com/view/nlp-word-problem-solving/].

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