22 citations · 123 across the 18 of their papers we have counts for
7 papers · 1 filter
The inhomogeneous -Laplacian equation with Neumann boundary conditions in the limit
Leon Bungert
We investigate the limiting behavior of solutions to the inhomogeneous -Laplacian equation subject to Neumann boundary conditions. For right hand sides which are…
Eigenvalue Problems in : Optimality Conditions, Duality, and Relations with Optimal Transport
Leon Bungert, Yury Korolev
In this article we characterize the eigenvalue problem associated to the Rayleigh quotient $\left.{\|\nabla u\|_{\mathrm{L}^\infty}}\middle/{\|u\|_\infty}\right…
Neural Architecture Search via Bregman Iterations
Leon Bungert, Tim Roith, Daniel Tenbrinck +1
We propose a novel strategy for Neural Architecture Search (NAS) based on Bregman iterations. Starting from a sparse neural network our gradient-based one-shot algorithm gradually…
Gradient Flows and Nonlinear Power Methods for the Computation of Nonlinear Eigenfunctions
Leon Bungert, Martin Burger
This chapter describes how gradient flows and nonlinear power methods in Banach spaces can be used to solve nonlinear eigenvector-dependent eigenvalue problems, and how convergence…
A Bregman Learning Framework for Sparse Neural Networks
Leon Bungert, Tim Roith, Daniel Tenbrinck +1
We propose a learning framework based on stochastic Bregman iterations, also known as mirror descent, to train sparse neural networks with an inverse scale space approach. We deriv…
CLIP: Cheap Lipschitz Training of Neural Networks
Leon Bungert, René Raab, Tim Roith +2
Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulne…
Identifying Untrustworthy Predictions in Neural Networks by Geometric Gradient Analysis
Leo Schwinn, An Nguyen, René Raab +5
The susceptibility of deep neural networks to untrustworthy predictions, including out-of-distribution (OOD) data and adversarial examples, still prevent their widespread use in sa…