131 citations · 174 across the 21 of their papers we have counts for
5 papers · 1 filter
Approximation in with deep ReLU neural networks
Felix Voigtlaender, Philipp Petersen
We discuss the expressive power of neural networks which use the non-smooth ReLU activation function by analyzing the approximation theoretic properties…
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
Gitta Kutyniok, Philipp Petersen, Mones Raslan +1
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge…
Error bounds for approximations with deep ReLU neural networks in norms
Ingo Gühring, Gitta Kutyniok, Philipp Petersen
We analyze approximation rates of deep ReLU neural networks for Sobolev-regular functions with respect to weaker Sobolev norms. First, we construct, based on a calculus of ReLU net…
The Oracle of DLphi
Dominik Alfke, Weston Baines, Jan Blechschmidt +24
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of l…
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks
Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem +1
Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importanc…