88 citations · 204 across the 14 of their papers we have counts for
3 papers · 1 filter
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…
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations
Julia Ackermann, Arnulf Jentzen, Benno Kuckuck +1
It is a challenging topic in applied mathematics to solve high-dimensional nonlinear partial differential equations (PDEs). Standard approximation methods for nonlinear PDEs suffer…
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…