Deep learning: an introduction for applied mathematicians

Higham, C. F. and Higham, D. J. (2019) Deep learning: an introduction for applied mathematicians. SIAM Review, 61(4), pp. 860-891. (doi: 10.1137/18M1165748)

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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 from 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 demonstrate the use of state-of-the-art software on a large scale image classification problem. We finish with references to the current literature.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Higham, Dr Catherine
Authors: Higham, C. F., and Higham, D. J.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:SIAM Review
Publisher:Society for Industrial and Applied Mathematics
ISSN (Online):1095-7200
Copyright Holders:Copyright © 2019 SIAM
First Published:First published in SIAM Review 61(4):860-891
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
190841UK Quantum Technology Hub in Enhanced Quantum ImagingMiles PadgettEngineering and Physical Sciences Research Council (EPSRC)EP/M01326X/1P&S - Physics & Astronomy