2 citations · 4 across the 6 of their papers we have counts for
7 papers
Experimental data re-uploading with provable enhanced learning capabilities
Martin F. X. Mauser, Solène Four, Lena Marie Predl +7
The last decades have seen the development of quantum machine learning, stemming from the intersection of quantum computing and machine learning. This field is particularly promisi…
Causal pieces: analysing and improving spiking neural networks piece by piece
Dominik Dold, Philipp Christian Petersen
We introduce "causal pieces", a novel concept for analysing spiking neural networks (SNNs), inspired by "linear pieces" used to study expressivity and trainability in artificial ne…
The sampling complexity of learning invertible residual neural networks
Yuanyuan Li, Philipp Grohs, Philipp Petersen
In recent work it has been shown that determining a feedforward ReLU neural network to within high uniform accuracy from point samples suffers from the curse of dimensionality in t…
First Order System Least Squares Neural Networks
Joost A. A. Opschoor, Philipp C. Petersen, Christoph Schwab
We introduce a conceptual framework for numerically solving linear elliptic, parabolic, and hyperbolic PDEs on bounded, polytopal domains in euclidean spaces by deep neural network…
Mathematical theory of deep learning
Philipp Petersen, Jakob Zech
This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learni…
Regularized Gauss-Newton for Optimizing Overparameterized Neural Networks
Adeyemi D. Adeoye, Philipp Christian Petersen, Alberto Bemporad
The generalized Gauss-Newton (GGN) optimization method incorporates curvature estimates into its solution steps, and provides a good approximation to the Newton method for large-sc…
Stable Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders
A. Martina Neuman, Dominik Dold, Philipp Christian Petersen
We study the learning problem associated with spiking neural networks. Specifically, we focus on spiking neural networks composed of simple spiking neurons having only positive syn…