Ridge Functions and Applications in Neural Networks (Mathematical Surveys and Monographs, 263) - Softcover

Ismailov, Vugar E.

9781470467654: Ridge Functions and Applications in Neural Networks (Mathematical Surveys and Monographs, 263)

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ISBN 10: 1470467658 ISBN 13: 9781470467654

Verlag: American Mathematical Society, 2022

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Ridge functions appear in various fields and under various guises, says Ismailov, for example in partial differential equations-where they are called plane waves-, computerized tomography, and statistics. Here he is interested in them as the underpinnings of many central models in neural networks, and from the perspective of approximation theory. He covers properties of linear combinations of ridge functions, the smoothness problem in ridge function representation, approximation of multivariate functions by sums of univariate functions, generalized ridge functions and linear superpositions, and applications to neural networks. Annotation �2022 Ringgold, Inc., Portland, OR (protoview.com)

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

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Verlag: American Mathematical Society
Erscheinungsdatum: 2022
Sprache: Englisch
ISBN 10: 1470467658
ISBN 13: 9781470467654
Einband: Taschenbuch
Anzahl der Seiten: 186
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Ridge Functions and Applications in Neural Networks (Mathematical Surveys and Monographs, 263)

Vugar E. Ismailov

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ISBN 10: 1470467658 ISBN 13: 9781470467654

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Ridge Functions and Applications in Neural Networks (eng)

Vugar E. Ismailov (author)

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Ismailov

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Ridge Functions and Applications in Neural Networks

Ismailov, Vugar E.

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ISBN 10: 1470467658 ISBN 13: 9781470467654

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Ridge Functions and Applications in Neural Networks

Vugar E. Ismailov

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ISBN 10: 1470467658 ISBN 13: 9781470467654

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Paperback. Zustand: New. 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. Bestandsnummer des Verk�ufers LU-9781470467654

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Ridge Functions and Applications in Neural Networks

Vugar E. Ismailov

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Ridge Functions and Applications in Neural Networks (Paperback)

Vugar E. Ismailov

Verlag: American Mathematical Society, Providence, 2022

ISBN 10: 1470467658 ISBN 13: 9781470467654

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Paperback. Zustand: new. Paperback. 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. Describes various approximation theoretic properties of ridge functions. The book also discusses 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verk�ufers 9781470467654

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