6 citations · 9 across the 8 of their papers we have counts for
8 papers · 1 filter
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces
Philipp Grohs, Felix Voigtlaender
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by…
Approximations with deep neural networks in Sobolev time-space
Ahmed Abdeljawad, Philipp Grohs
Solutions of evolution equation generally lies in certain Bochner-Sobolev spaces, in which the solution may has regularity and integrability properties for the time variable that c…
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning
Julius Berner, Markus Dablander, Philipp Grohs
We present a deep learning algorithm for the numerical solution of parametric families of high-dimensional linear Kolmogorov partial differential equations (PDEs). Our method is ba…
Towards a regularity theory for ReLU networks -- chain rule and global error estimates
Julius Berner, Dennis Elbrächter, Philipp Grohs +1
Although for neural networks with locally Lipschitz continuous activation functions the classical derivative exists almost everywhere, the standard chain rule is in general not app…
The Oracle of DLphi
Dominik Alfke, Weston Baines, Jan Blechschmidt +24
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of l…
Deep Neural Network Approximation Theory
Dennis Elbrächter, Dmytro Perekrestenko, Philipp Grohs +1
This paper develops fundamental limits of deep neural network learning by characterizing what is possible if no constraints are imposed on the learning algorithm and on the amount…