Arnulf Jentzen

Full error analysis for the training of deep neural networks

2019 · arXiv (Cornell University)

Deep learning algorithms have been applied very successfully in recent years to a range of problems out of reach for classical solution paradigms. Nevertheless, there is no completely rigorous mathematical error and convergence analysis which …

Landscape analysis for shallow ReLU neural networks: complete classification of critical points for affine target functions.

2021 · arXiv (Cornell University)

In this paper, we analyze the landscape of the true loss of a ReLU neural network with one hidden layer. We provide a complete classification of the critical points in the case where the target …

Deep neural network approximation theory for high-dimensional functions

2021 · arXiv (Cornell University)

The purpose of this article is to develop a machinery to study the capacity of deep neural networks (DNNs) to approximate high-dimensional functions. In particular, we show that DNNs have the expressive power to overcome …