4 citations · 5 across the 2 of their papers we have counts for
4 papers
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the -sense
Julia Ackermann, Arnulf Jentzen, Thomas Kruse +2
Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have gener…
Deep neural network approximation theory for high-dimensional functions
Pierfrancesco Beneventano, Patrick Cheridito, Robin Graeber +2
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 DN…
Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger
This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including…
On the logical skills of large language models: evaluations using arbitrarily complex first-order logic problems
Shokhrukh Ibragimov, Arnulf Jentzen, Benno Kuckuck
We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several data…