Ridge Functions and Applications in Neural Networks (Mathematical Surveys and Monographs) - Softcover

Vugar E. Ismailov (author)

 
9781470467654: Ridge Functions and Applications in Neural Networks (Mathematical Surveys and Monographs)
Softcover
ISBN 10: 1470467658 ISBN 13: 9781470467654
Publisher: American Mathematical Society, 2022

Synopsis

Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed.

This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.

"synopsis" may belong to another edition of this title.

About the Author

Vugar E. Ismailov, Azerbaijan National Academy of Sciences, Baku, Azerbaijan.

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2022
Language
English
ISBN 10 
1470467658
ISBN 13 
9781470467654
Binding
Paperback
Number of pages
186