TY - BOOK

T1 - Mathematics of deep learning

T2 - An introduction

AU - Berlyand, Leonid

AU - Jabin, Pierre Emmanuel

N1 - Publisher Copyright:
© 2023 Walter de Gruyter GmbH, Berlin/Boston. All rights reserved.

PY - 2023/4/26

Y1 - 2023/4/26

N2 - 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. Accessible for students with no prior knowledge of deep learning. Focuses on the foundational mathematics of deep learning. Provides quick access to key deep learning techniques. Includes relevant examples that readers can relate to easily.

AB - 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. Accessible for students with no prior knowledge of deep learning. Focuses on the foundational mathematics of deep learning. Provides quick access to key deep learning techniques. Includes relevant examples that readers can relate to easily.

UR - http://www.scopus.com/inward/record.url?scp=85159421906&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85159421906&partnerID=8YFLogxK

U2 - 10.1515/9783111025551

DO - 10.1515/9783111025551

M3 - Book

AN - SCOPUS:85159421906

SN - 9783111025803

BT - Mathematics of deep learning

PB - de Gruyter

ER -