26 citations · 96 across the 22 of their papers we have counts for
8 papers · 1 filter
On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks
Arnulf Jentzen, Adrian Riekert
In this article we study fully-connected feedforward deep ReLU ANNs with an arbitrarily large number of hidden layers and we prove convergence of the risk of the GD optimization me…
Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions
Martin Hutzenthaler, Arnulf Jentzen, Katharina Pohl +2
In many numerical simulations stochastic gradient descent (SGD) type optimization methods perform very effectively in the training of deep neural networks (DNNs) but till this day…
Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation
Simon Eberle, Arnulf Jentzen, Adrian Riekert +1
The training of artificial neural networks (ANNs) with rectified linear unit (ReLU) activation via gradient descent (GD) type optimization schemes is nowadays a common industrially…
A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions
Arnulf Jentzen, Adrian Riekert
Gradient descent (GD) type optimization methods are the standard instrument to train artificial neural networks (ANNs) with rectified linear unit (ReLU) activation. Despite the gre…
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation
Arnulf Jentzen, Adrian Riekert
Gradient descent (GD) type optimization schemes are the standard methods to train artificial neural networks (ANNs) with rectified linear unit (ReLU) activation. Such schemes can b…
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions
Arnulf Jentzen, Adrian Riekert
In this article we study the stochastic gradient descent (SGD) optimization method in the training of fully-connected feedforward artificial neural networks with ReLU activation. T…
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions
Patrick Cheridito, Arnulf Jentzen, Adrian Riekert +1
Gradient descent optimization algorithms are the standard ingredients that are used to train artificial neural networks (ANNs). Even though a huge number of numerical simulations i…
Convergence Rates for Empirical Measures of Markov Chains in Dual and Wasserstein Distances
Adrian Riekert
We consider a Markov chain on with invariant measure . We are interested in the rate of convergence of the empirical measures towards the invariant measure with r…