Deep Learning: An Introduction for Applied Mathematicians

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This art...

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Bibliographic Details
Published in:arXiv.org 2018-01
Main Authors: Higham, Catherine F, Higham, Desmond J
Format: Article
Language:English
Subjects:
Applications of mathematics
Applied mathematics
Artificial neural networks
Computational mathematics
Deep learning
Graduate studies
Image classification
Linear algebra
Mathematical analysis
Neural networks
Optimization
Teachers
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Summary:Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very brief introduction to the basic ideas that underlie deep learning from an applied mathematics perspective. Our target audience includes postgraduate and final year undergraduate students in mathematics who are keen to learn about the area. The article may also be useful for instructors in mathematics who wish to enliven their classes with references to the application of deep learning techniques. We focus on three fundamental questions: what is a deep neural network? how is a network trained? what is the stochastic gradient method? We illustrate the ideas with a short MATLAB code that sets up and trains a network. We also show the use of state-of-the art software on a large scale image classification problem. We finish with references to the current literature.
ISSN:2331-8422