Title
Geometry of deep learning : a signal processing perspective / Jong Chul Ye.
ISBN
9789811660467 (electronic bk.)
9811660468 (electronic bk.)
9789811660450
981166045X
Published
Singapore : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource (338 pages).
Item Number
10.1007/978-981-16-6046-7 doi
Call Number
Q325.73 .Y4 2022
Dewey Decimal Classification
006.3/10151
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Description based upon print version of record.
Series
Mathematics in industry ; 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.
