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pro vyhledávání: '"Bungert, Leon"'
Autor:
Bungert, Leon, del Teso, Félix
We prove non-asymptotic rates of convergence in the $W^{s,2}(\mathbb R^d)$-norm for the solution of the fractional Dirichlet problem to the solution of the local Dirichlet problem as $s\uparrow 1$. For regular enough boundary values we get a rate of
Externí odkaz:
http://arxiv.org/abs/2408.03299
In this paper we prove discrete to continuum convergence rates for Poisson Learning, a graph-based semi-supervised learning algorithm that is based on solving the graph Poisson equation with a source term consisting of a linear combination of Dirac d
Externí odkaz:
http://arxiv.org/abs/2407.06783
We connect adversarial training for binary classification to a geometric evolution equation for the decision boundary. Relying on a perspective that recasts adversarial training as a regularization problem, we introduce a modified training scheme tha
Externí odkaz:
http://arxiv.org/abs/2404.14402
Autor:
Bungert, Leon, Trillos, Nicolás García, Jacobs, Matt, McKenzie, Daniel, Nikolić, Đorđe, Wang, Qingsong
Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated examples. Thus, considerable effort has been invested into reformulatin
Externí odkaz:
http://arxiv.org/abs/2305.18779
Autor:
Bungert, Leon
Publikováno v:
Communications in Partial Differential Equations, 48:10-12, 1323-1339, 2024
The purpose of this paper is to prove a uniform convergence rate of the solutions of the $p$-Laplace equation $\Delta_p u = 0$ with Dirichlet boundary conditions to the solution of the infinity-Laplace equation $\Delta_\infty u = 0$ as $p\to\infty$.
Externí odkaz:
http://arxiv.org/abs/2302.08462
Autor:
Bungert, Leon, Stinson, Kerrek
In this paper we prove Gamma-convergence of a nonlocal perimeter of Minkowski type to a local anisotropic perimeter. The nonlocal model describes the regularizing effect of adversarial training in binary classifications. The energy essentially depend
Externí odkaz:
http://arxiv.org/abs/2211.15223
In this paper we propose polarized consensus-based dynamics in order to make consensus-based optimization (CBO) and sampling (CBS) applicable for objective functions with several global minima or distributions with many modes, respectively. For this,
Externí odkaz:
http://arxiv.org/abs/2211.05238
In this paper we prove the first quantitative convergence rates for the graph infinity Laplace equation for length scales at the connectivity threshold. In the graph-based semi-supervised learning community this equation is also known as Lipschitz le
Externí odkaz:
http://arxiv.org/abs/2210.09023
Autor:
Schwinn, Leo, Bungert, Leon, Nguyen, An, Raab, René, Pulsmeyer, Falk, Precup, Doina, Eskofier, Björn, Zanca, Dario
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 either real-world distribution shifts (e.g., common corruptions and per
Externí odkaz:
http://arxiv.org/abs/2205.09619
Autor:
Bungert, Leon
Publikováno v:
Adv Cont Discr Mod 2023, 8 (2023)
We investigate the limiting behavior of solutions to the inhomogeneous $p$-Laplacian equation $-\Delta_p u = \mu_p$ subject to Neumann boundary conditions. For right hand sides which are arbitrary signed measures we show that solutions converge to a
Externí odkaz:
http://arxiv.org/abs/2112.07401