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Deep Learning Architectures: A Mathematical Approach (Springer Series in the Data Sciences) 1st ed. 2020 Edition

by Ovidiu Calin (Author)
4.3 4.3 out of 5 stars 26 ratings
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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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  1. ISBN-10
    3030367231
  2. ISBN-13
    978-3030367237
  3. Edition
    1st ed. 2020
  4. Publisher
    Springer
  5. Publication date
    February 14, 2021
  6. Part of series
    Springer Series in the Data Sciences
  7. Language
    English
  8. Dimensions
    6.14 x 1.57 x 9.21 inches
  9. Print length
    790 pages
  10. See all details
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Editorial Reviews

Review

“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)

From the Back Cover

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.

Product details

  • Publisher ‏ : ‎ Springer; 1st ed. 2020 edition (February 14, 2021)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 790 pages
  • ISBN-10 ‏ : ‎ 3030367231
  • ISBN-13 ‏ : ‎ 978-3030367237
  • Item Weight ‏ : ‎ 3.26 pounds
  • Dimensions ‏ : ‎ 6.14 x 1.57 x 9.21 inches
  • Customer Reviews:
    4.3 4.3 out of 5 stars 26 ratings

About the author

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Ovidiu Calin

Ovidiu Calin

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Ovidiu Calin is Professor of Mathematics and Statistics at Eastern Michigan University. He obtained his PhD. from the University of Toronto in 2000. He was a Visiting professor at Princeton University (2016-2017) and University of Notre Dame (2000-2002). His variate mathematical interests includes deep learning, mathematical finance, stochastic calculus, information theory, geometric analysis and calculus of variations.

Customer reviews

4.3 out of 5 stars
26 global ratings

Top reviews from the United States

Alexandru Stere
5.0 out of 5 stars Remarkable book on Deep Learning
Reviewed in the United States on May 10, 2022
Verified Purchase
If you are interested in the mathematical aspects of deep learning, especially those more advanced ones connecting it with various mathematical representations, then this book is highly recommended. Almost 700 pages of rich math but very well explained. Rigorous proofs are illuminating and provide the theoretical background necessary to elevate one from a good ML practitioner to a great one.
4 people found this helpful
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Teddy Oscar
5.0 out of 5 stars Excellent book
Reviewed in the United States on July 14, 2020
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I think this is good book for deep learning method. Highly recommended it.
One person found this helpful
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Allan Zhang
2.0 out of 5 stars Good book material to read
Reviewed in the United States on November 19, 2021
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Good content to read. Useful for those who like theory behind boilerplate code. Shipping is really bad, my new book's corner is seriously damaged
One person found this helpful
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D Lim
2.0 out of 5 stars This is a book without any proof reading
Reviewed in the United States on July 29, 2024
The book seemed to be nice. It has a good approach on explanation on convergence of neural networks and some geometric implication of the models.

But the book is in overall sense, horrible.

The author often makes wrong notations.
Ex. Mistaking x with x*, suddenly introducing a new aphabetical symbo D, when it is suposed to be B. Wrong directions of mathematical operator such as set inclusion, set substraciton, etc.

The author mentions some un-explaned terms, which seems to be only used by him in his own imagination or his lectures.
I tried to figure out the meaning of "digenerate direction" for an hour.

These mistakes make the reader hard to figure out what the hack is going on.
Sometimes I had to figure out which one of the statements are mistake, and it gives me headaches.

There was a wrong proof.
Lemma 4.2.2.
It was a non-rigorous proof which made assumed some approximation,
but even that non-rigorous proof had wrong logic, I figured out my own proof to correct the problem.

Some statements omit some important assumptions(such as the function does not have multiple local minimum or local maximum) which make the statements wrong.

There are so many "so what?" lemmas and prepositions.
I don't know what to do with some lemmas and prepositions.
The author broght up some lemmas and prepositions, and those do not give any explanation or ideas related to the the topics of the chapters.

I stopped reading book at the chapters about information theory.

The author states that (I have made the statements simpler, so that it is easier to understand)

1. a network that outputs only recoverable information is a network that has lost all information.
2. a network that has lost all information is uselss.
3. a network that has lost all informmation does not tell any information.

statement 2 is never explained why.
statement 3 is contradictory with 1,
According to 1, a network that has lost all information may output recoverable information,
but the author suddenly statets that the netowrk does not give any information.

It seems the author was hallucinating while writhing this chapter.

I spent some money to buy this book. I am disappointed and had some headaches figuring out the correction of the errors made by the author.

To author,
if you are selling a book, you should have done some proof readings before publishing it. People are spending money to buy the book.
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Abhimanyu Alexander
1.0 out of 5 stars Terrible book on deep learning
Reviewed in the United States on July 4, 2020
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Poorly written, haphazardly organized, book.
One person found this helpful
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Top reviews from other countries

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Enki Barra
5.0 out of 5 stars The best theoric DL book
Reviewed in Mexico on August 19, 2024
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DLAAMA is a really good book to fully understand the theory of DL. However, if you're not really into heavy maths, I wouldn't advice you to purchase this book.

Tbh, this is one of the best books about DL I own, if not "THE" best; Printing quality is really good:)
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Nico
5.0 out of 5 stars Nuovissimo
Reviewed in Italy on November 30, 2023
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Completamente nuovo e con pellicola.
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Severus
4.0 out of 5 stars Valuable reference
Reviewed in Germany on May 27, 2021
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This book is well-written and comprehensive. Its coverage of optimization for neural network learning is the best in any book so far. The part on information geometry is superb too. However, the „Analytic Theory“ part is disappointing: It reflects the classical results (on shallow(!) neural network approximation theory!) quite nicely, but lately there has been a lot of activity in harmonic analysis, using e.g. wavelet to understand the expressiveness of deep neural networks. Maybe it’s still a bit too early to present positive results in a book, but I personally find this matter quite confusing and it would have been nice to have at least a survey of „common wisdom“ and a (qualitative) discussion of current research revolving around the question why deep neural networks outperform shallow networks and when/why/in what sense they apparently can break the curse of dimensionality. That’s why I give only 4 and not 5 stars.
( BTW: G. Kutyniok and P. Grohs are writing a book „Deep Learning Theory,“ which is about to appear in Cambridge University Press soon; those are two leading researchers, I have very high hopes for the book to close this gap on analytic theory )

I personally like the somewhat large font (and therefore short lines) in the book, which makes it pleasant to read, but others may disagree.

Needless to say, this is not a book for the average computer science graduate student. It’s a book for readers with curiosity who bring the necessary mathematical maturity.
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summukhe
5.0 out of 5 stars Unique collection of topics
Reviewed in India on September 8, 2020
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This is not a traditional deep learning book. Covers very unique theoretical topics of deep learning, viz. universal approximators, exact learning, information capacity assessment, neuromanifold. The author explained these unique topics in great detail. The book has a detailed chapter on optimization techniques, though it is not the strong point of the book.
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Mauro Gatti
5.0 out of 5 stars The best book on Deep Learning for those having an adequate mathematical background
Reviewed in Italy on February 28, 2023
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This is the best book on Deep Learning I have ever read. I strongly recommend it. The reader should pay attention to the fact that an adequate mathematical background is required.
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