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Deep Learning Architectures

A Mathematical Approach

  • Textbook
  • © 2020

Overview

  • Contains a fair number of end-of chapter exercises
  • Full solutions provided to all exercises
  • Appendices including topics needed in the book exposition

Part of the book series: Springer Series in the Data Sciences (SSDS)

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About this book

This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter.

This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates.  In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.

 

 


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Table of contents (20 chapters)

  1. Introduction to Neural Networks

  2. Analytic Theory

  3. Information Processing

  4. Geometric Theory

  5. Other Architectures

Reviews

“This book is useful to students who have already had an introductory course in machine learning and are further interested to deepen their understanding of the machine learning material from the mathematical point of view.” (T. C. Mohan, zbMATH 1441.68001, 2020)

Authors and Affiliations

  • Department of Mathematics & Statistics, Eastern Michigan University, Ypsilanti, USA

    Ovidiu Calin

About the author

Ovidiu Calin, a graduate from University of Toronto, is a professor at Eastern Michigan University and a former visiting professor at Princeton University and University of Notre Dame. He has delivered numerous lectures at several universities in Japan, Hong Kong, Taiwan, and Kuwait over the last 15 years. His publications include over 60 articles and 8 books in the fields of machine learning, computational finance, stochastic processes, variational calculus and geometric analysis.

Bibliographic Information

  • Book Title: Deep Learning Architectures

  • Book Subtitle: A Mathematical Approach

  • Authors: Ovidiu Calin

  • Series Title: Springer Series in the Data Sciences

  • DOI: https://doi.org/10.1007/978-3-030-36721-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-36720-6Published: 14 February 2020

  • Softcover ISBN: 978-3-030-36723-7Published: 14 February 2021

  • eBook ISBN: 978-3-030-36721-3Published: 13 February 2020

  • Series ISSN: 2365-5674

  • Series E-ISSN: 2365-5682

  • Edition Number: 1

  • Number of Pages: XXX, 760

  • Number of Illustrations: 172 b/w illustrations, 35 illustrations in colour

  • Topics: Mathematical Applications in Computer Science, Machine Learning

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