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Geometry of deep learning = a signal...

Ye, Jong Chul.

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Geometry of deep learning = a signal processing perspective /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometry of deep learning/ by Jong Chul Ye.
Reminder of title:	a signal processing perspective /
Author:	Ye, Jong Chul.
Published:	Singapore :Springer Singapore : : 2022.,
Description:	xvi, 330 p. :ill., digital ;24 cm.
[NT 15003449]:	Part I Basic Tools for Machine Learning: 1. Mathematical Preliminaries -- 2. Linear and Kernel Classifiers -- 3. Linear, Logistic, and Kernel Regression -- 4. Reproducing Kernel Hilbert Space, Representer Theorem -- Part II Building Blocks of Deep Learning: 5. Biological Neural Networks -- 6. Artificial Neural Networks and Backpropagation -- 7. Convolutional Neural Networks -- 8. Graph Neural Networks -- 9. Normalization and Attention -- Part III Advanced Topics in Deep Learning -- 10. Geometry of Deep Neural Networks -- 11. Deep Learning Optimization -- 12. Generalization Capability of Deep Learning -- 13. Generative Models and Unsupervised Learning -- Summary and Outlook -- Bibliography -- Index.
Contained By:	Springer Nature eBook
Subject:	Deep learning (Machine learning) - Mathematics. -
Online resource:	https://doi.org/10.1007/978-981-16-6046-7
ISBN:	9789811660467

Geometry of deep learning = a signal processing perspective /
Ye, Jong Chul.

Geometry of deep learninga signal processing perspective /[electronic resource] :by Jong Chul Ye. - Singapore :Springer Singapore :2022. - xvi, 330 p. :ill., digital ;24 cm. - Mathematics in industry,v. 372198-3283 ;. - Mathematics in industry ;v. 37..

Part I Basic Tools for Machine Learning: 1. Mathematical Preliminaries -- 2. Linear and Kernel Classifiers -- 3. Linear, Logistic, and Kernel Regression -- 4. Reproducing Kernel Hilbert Space, Representer Theorem -- Part II Building Blocks of Deep Learning: 5. Biological Neural Networks -- 6. Artificial Neural Networks and Backpropagation -- 7. Convolutional Neural Networks -- 8. Graph Neural Networks -- 9. Normalization and Attention -- Part III Advanced Topics in Deep Learning -- 10. Geometry of Deep Neural Networks -- 11. Deep Learning Optimization -- 12. Generalization Capability of Deep Learning -- 13. Generative Models and Unsupervised Learning -- Summary and Outlook -- Bibliography -- Index.

The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems. Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.

ISBN: 9789811660467

Standard No.: 10.1007/978-981-16-6046-7doiSubjects--Topical Terms:

3593338
Deep learning (Machine learning)
--Mathematics.

LC Class. No.: Q325.73 / .Y4 2022

Dewey Class. No.: 006.310151

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505 0 $a Part I Basic Tools for Machine Learning: 1. Mathematical Preliminaries -- 2. Linear and Kernel Classifiers -- 3. Linear, Logistic, and Kernel Regression -- 4. Reproducing Kernel Hilbert Space, Representer Theorem -- Part II Building Blocks of Deep Learning: 5. Biological Neural Networks -- 6. Artificial Neural Networks and Backpropagation -- 7. Convolutional Neural Networks -- 8. Graph Neural Networks -- 9. Normalization and Attention -- Part III Advanced Topics in Deep Learning -- 10. Geometry of Deep Neural Networks -- 11. Deep Learning Optimization -- 12. Generalization Capability of Deep Learning -- 13. Generative Models and Unsupervised Learning -- Summary and Outlook -- Bibliography -- Index.
520 $a The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems. Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
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650 1 4 $a Functional Analysis. $3 893943
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