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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Veröffentlicht in:	Neural networks 2023-04, Vol.161, p.242-253
Hauptverfasser:	Belomestny, Denis, Naumov, Alexey, Puchkin, Nikita, Samsonov, Sergey
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Approximation complexity Deep neural networks Hölder class Machine Learning Neural Networks, Computer ReLUk activations ReQU activations
Online-Zugang:	Volltext
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