131 citations · 174 across the 21 of their papers we have counts for
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math.FA2017★ 1 cited
Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces
Philipp Petersen, Mones Raslan
In this paper, we study a newly developed shearlet system on bounded domains which yields frames for for some , . We will derive ap…
math.FA2017
Optimal approximation of piecewise smooth functions using deep ReLU neural networks
Philipp Petersen, Felix Voigtlaender
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 $L^…
cs.LG2017
Optimal Approximation with Sparsely Connected Deep Neural Networks
Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok +1
We derive fundamental lower bounds on the connectivity and the memory requirements of deep neural networks guaranteeing uniform approximation rates for arbitrary function classes i…