On bounds for norms of reparameterized ReLU artificial neural network parameters: sums of fractional powers of the Lipschitz norm control the network parameter vector

no code implementations • 27 Jun 2022 • Arnulf Jentzen, Timo Kröger

Furthermore, we prove that this upper bound only holds for sums of powers of the Lipschitz norm with the exponents $ 1/2 $ and $ 1 $ but does not hold for the Lipschitz norm alone.

Convergence rates for gradient descent in the training of overparameterized artificial neural networks with biases

no code implementations • 23 Feb 2021 • Arnulf Jentzen, Timo Kröger

In recent years, artificial neural networks have developed into a powerful tool for dealing with a multitude of problems for which classical solution approaches reach their limits.