Deep Learning: An Introduction for Applied Mathematicians

TL;DR

This paper introduces deep learning concepts from an applied mathematics perspective, focusing on neural networks, training methods, and practical implementation, aimed at students and educators in mathematics.

Contribution

It provides an accessible introduction to deep learning for applied mathematicians, connecting mathematical concepts with neural network training and applications.

Findings

Illustrates neural network training with MATLAB code

Demonstrates large-scale image classification using state-of-the-art software

Clarifies fundamental deep learning questions for mathematical audience

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.