131 citations · 174 across the 21 of their papers we have counts for
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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 neural networks can stably solve high-dimensional, noisy, non-linear inverse problems
Andrés Felipe Lerma Pineda, Philipp Christian Petersen
We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensio…