131 citations · 174 across the 21 of their papers we have counts for
6 papers · 1 filter
VC dimensions of group convolutional neural networks
Philipp Christian Petersen, Anna Sepliarskaia
We study the generalization capacity of group convolutional neural networks. We identify precise estimates for the VC dimensions of simple sets of group convolutional neural networ…
Limitations of neural network training due to numerical instability of backpropagation
Clemens Karner, Vladimir Kazeev, Philipp Christian Petersen
We study the training of deep neural networks by gradient descent where floating-point arithmetic is used to compute the gradients. In this framework and under realistic assumption…
Deep Microlocal Reconstruction for Limited-Angle Tomography
Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem +1
We present a deep learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging. The algorithm is based on a rece…
The Modern Mathematics of Deep Learning
Julius Berner, Philipp Grohs, Gitta Kutyniok +1
We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of…
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…
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…