Optimal approximation of piecewise smooth functions using deep ReLU neural networks

We study the necessary and sufficient complexity of ReLU neural networks – in terms of depth and number of weights – which is required for approximating classifier functions in an Lp-sense. As a model class, we consider the set Eβ(Rd) of possibly discontinuous piecewise Cβ functions f:[−12,12]d→R, w...

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Veröffentlicht in:	Neural networks Jg. 108; S. 296 - 330
Hauptverfasser:	Petersen, Philipp, Voigtlaender, Felix
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	United States Elsevier Ltd 01.12.2018
Schlagworte:	Curse of dimension Deep neural networks Function approximation Metric entropy Neural Networks (Computer) Piecewise smooth functions Sparse connectivity Deep neural networks Function approximation Curse of dimension Metric entropy Piecewise smooth functions Sparse connectivity
ISSN:	0893-6080, 1879-2782, 1879-2782
Online-Zugang:	Volltext
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