Deep learning : an introduction for applied mathematicians
Higham, Catherine F. and Higham, Desmond J. (2019) Deep learning : an introduction for applied mathematicians. SIAM Review, 61 (4). 860–891. ISSN 0036-1445 (https://doi.org/10.1137/18M1165748)
Preview |
Text.
Filename: Higham_Higham_SIAM_2019_Deep_learning_an_introduction_for_applied.pdf
Final Published Version License: Download (5MB)| Preview |
Abstract
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.
ORCID iDs
Higham, Catherine F. and Higham, Desmond J. ORCID: https://orcid.org/0000-0002-6635-3461;-
-
Item type: Article ID code: 66954 Dates: DateEvent6 November 2019Published7 February 2019AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 13 Feb 2019 18:19 Last modified: 12 Dec 2024 07:39 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/66954