22 citations · 123 across the 18 of their papers we have counts for
18 papers
Introduction to Nonlinear Spectral Analysis
Leon Bungert, Yury Korolev
These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding no…
Convergence rates of the fractional to the local Dirichlet problem
Leon Bungert, Félix del Teso
We prove non-asymptotic rates of convergence in the -norm for the solution of the fractional Dirichlet problem to the solution of the local Dirichlet problem…
The convergence rate of -harmonic to infinity-harmonic functions
Leon Bungert
The purpose of this paper is to prove a uniform convergence rate of the solutions of the -Laplace equation with Dirichlet boundary conditions to the solution of the…
Improving Robustness against Real-World and Worst-Case Distribution Shifts through Decision Region Quantification
Leo Schwinn, Leon Bungert, An Nguyen +5
The reliability of neural networks is essential for their use in safety-critical applications. Existing approaches generally aim at improving the robustness of neural networks to e…
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…
Variational regularisation for inverse problems with imperfect forward operators and general noise models
Leon Bungert, Martin Burger, Yury Korolev +1
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lat…
The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
Farid Bozorgnia, Leon Bungert, Daniel Tenbrinck
In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigen…
Structural analysis of an -infinity variational problem and relations to distance functions
Leon Bungert, Yury Korolev, Martin Burger
In this work we analyse the functional defined on Lipschitz functions with homogeneous Dirichlet boundary conditions. Our analysis is performed di…
Asymptotic Profiles of Nonlinear Homogeneous Evolution Equations of Gradient Flow Type
Leon Bungert, Martin Burger
This work is concerned with the gradient flow of absolutely -homogeneous convex functionals on a Hilbert space, which we show to exhibit finite () or infinite extinction ti…
Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
Leon Bungert, Martin Burger, Daniel Tenbrinck
In this work we investigate the computation of nonlinear eigenfunctions via the extinction profiles of gradient flows. We analyze a scheme that recursively subtracts such eigenfunc…
Nonlinear Spectral Decompositions by Gradient Flows of One-Homogeneous Functionals
Leon Bungert, Martin Burger, Antonin Chambolle +1
This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimens…
Solution Paths of Variational Regularization Methods for Inverse Problems
Leon Bungert, Martin Burger
We consider a family of variational regularization functionals for a generic inverse problem, where the data fidelity and regularization term are given by powers of a Hilbert norm…