Mathematics of Deep Learning

An Introduction

Leonid Berlyand, Pierre-Emmanuel Jabin

• Publisher: De Gruyter
• Year: 2023
• eBook ISBN: 9783111025803
• Edition: 1
• Topic: Computer Science
• Subtopic: Human-Computer Interaction
• Index: Computer Science

The goal of this book is to provide a mathematical perspective on some key elements of the so-called deep neural networks (DNNs). Much of the interest in deep learning has focused on the implementation of DNN-based algorithms. Our hope is that this compact textbook will offer a complementary point of view that emphasizes the underlying mathematical ideas. We believe that a more foundational perspective will help to answer important questions that have only received empirical answers so far.

The material is based on a one-semester course Introduction to Mathematics of Deep Learning" for senior undergraduate mathematics majors and first year graduate students in mathematics. Our goal is to introduce basic concepts from deep learning in a rigorous mathematical fashion, e.g introduce mathematical definitions of deep neural networks (DNNs), loss functions, the backpropagation algorithm, etc. We attempt to identify for each concept the simplest setting that minimizes technicalities but still contains the key mathematics.

Table of contents

• Title Page
• Copyright
• Contents
• 1 About this book
• 2 Introduction to machine learning: what and why?
• 3 Classification problem
• 4 The fundamentals of artificial neural networks
• 5 Supervised, unsupervised, and semisupervised learning
• 6 The regression problem
• 7 Support vector machine
• 8 Gradient descent method in the training of DNNs
• 9 Backpropagation
• 10 Convolutional neural networks
• Subject Index