98 citations · 308 across the 30 of their papers we have counts for
34 papers
Traces left by random walks on large random graphs: local limits
Steffen Dereich
In this article, we develop a theory for understanding the traces left by a random walk in the vicinity of a randomly chosen reference vertex. The analysis is related to interlacem…
On the existence of optimal shallow feedforward networks with ReLU activation
Steffen Dereich, Sebastian Kassing
We prove existence of global minima in the loss landscape for the approximation of continuous target functions using shallow feedforward artificial neural networks with ReLU activa…
On the existence of minimizers in shallow residual ReLU neural network optimization landscapes
Steffen Dereich, Arnulf Jentzen, Sebastian Kassing
In this article, we show existence of minimizers in the loss landscape for residual artificial neural networks (ANNs) with multi-dimensional input layer and one hidden layer with R…
On minimal representations of shallow ReLU networks
S. Dereich, S. Kassing
The realization function of a shallow ReLU network is a continuous and piecewise affine function , where the domain is partitioned by a…
Quasi-processes for branching Markov chains
Steffen Dereich, Martin Maiwald
Potential theory is a central tool to understand and analyse Markov processes. In this article, we develop its probabilistic counterpart for branching Markov chains. Specifically,…
Cooling down stochastic differential equations: almost sure convergence
S. Dereich, S. Kassing
We consider almost sure convergence of the SDE under the existence of a -Lyapunov function . More explicitly, we show t…