Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any Hölder smooth function up to a given approximation error in Hölder norms in such...

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Vydané v:	Neural networks Ročník 161; s. 242 - 253
Hlavní autori:	Belomestny, Denis, Naumov, Alexey, Puchkin, Nikita, Samsonov, Sergey
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States Elsevier Ltd 01.04.2023
Predmet:	Algorithms Approximation complexity Deep neural networks Hölder class Machine Learning Neural Networks, Computer ReLUk activations ReQU activations Approximation complexity Deep neural networks Hölder class ReQU activations ReLUk activations ReLU(k) activations
ISSN:	0893-6080, 1879-2782, 1879-2782
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