Ridge functions and applications in neural networks
- Providence : American Mathematical Society, 2021
- ix, 186 p. ; ill., 26 cm
- Mathematical surveys and monographs, 0076-5376 ; v. 263 .
Includes bibliographical references and index.
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 Kolmogo.
9781470467654
Function spaces Multivariate analysis Approximation theory Linear operators Numbers, Real Neural networks Plane wave Kolmogorov's superposition theorem Banach-Alaoglu theorem Complexity problem Diliberto-Straus-algorithm Fubini's theorem Hahn-Banach theorem MLP model Proximinality ReLU function Sigmoidel function Uniqueness problem