131 citations · 174 across the 21 of their papers we have counts for
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Gamma-convergence of a shearlet-based Ginzburg--Landau energy
Philipp Christian Petersen, Endre Süli
We introduce two shearlet-based Ginzburg--Landau energies, based on the continuous and the discrete shearlet transform. The energies result from replacing the elastic energy term o…
Equivalence of approximation by convolutional neural networks and fully-connected networks
Philipp Petersen, Felix Voigtlaender
Convolutional neural networks are the most widely used type of neural networks in applications. In mathematical analysis, however, mostly fully-connected networks are studied. In t…
Topological properties of the set of functions generated by neural networks of fixed size
Philipp Petersen, Mones Raslan, Felix Voigtlaender
We analyze the topological properties of the set of functions that can be implemented by neural networks of a fixed size. Surprisingly, this set has many undesirable properties. It…