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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Bibliographic Details

Published in:	Neural networks Vol. 108; pp. 296 - 330
Main Authors:	Petersen, Philipp, Voigtlaender, Felix
Format:	Journal Article
Language:	English
Published:	United States Elsevier Ltd 01.12.2018
Subjects:	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 Access:	Get full text
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