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  • Textbook
  • © 2020

Deep Learning Architectures

A Mathematical Approach

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  • 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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USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-36721-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 79.99
Price excludes VAT (USA)
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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxx
  2. Introduction to Neural Networks

    1. Front Matter

      Pages 1-1
    2. Introductory Problems

      • Ovidiu Calin
      Pages 3-19
    3. Activation Functions

      • Ovidiu Calin
      Pages 21-39
    4. Cost Functions

      • Ovidiu Calin
      Pages 41-68
    5. Finding Minima Algorithms

      • Ovidiu Calin
      Pages 69-131
    6. Abstract Neurons

      • Ovidiu Calin
      Pages 133-165
    7. Neural Networks

      • Ovidiu Calin
      Pages 167-198
  3. Analytic Theory

    1. Front Matter

      Pages 199-199
    2. Approximation Theorems

      • Ovidiu Calin
      Pages 201-225
    3. Learning with One-dimensional Inputs

      • Ovidiu Calin
      Pages 227-250
    4. Universal Approximators

      • Ovidiu Calin
      Pages 251-284
    5. Exact Learning

      • Ovidiu Calin
      Pages 285-313
  4. Information Processing

    1. Front Matter

      Pages 315-315
    2. Information Representation

      • Ovidiu Calin
      Pages 317-349
    3. Information Capacity Assessment

      • Ovidiu Calin
      Pages 351-413
  5. Geometric Theory

    1. Front Matter

      Pages 415-415
    2. Output Manifolds

      • Ovidiu Calin
      Pages 417-464
    3. Neuromanifolds

      • Ovidiu Calin
      Pages 465-504
  6. Other Architectures

    1. Front Matter

      Pages 505-505

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.

 

 


Keywords

  • neural networks
  • deep learning
  • machine learning
  • Kullback-Leibler divergence
  • Entropy
  • Fisher information metric
  • Boltzmann machine

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

Buying options

eBook
USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-36721-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 79.99
Price excludes VAT (USA)
Hardcover Book
USD 109.99
Price excludes VAT (USA)