24 citations · 75 across the 13 of their papers we have counts for
15 papers
Quantifying Concentration Phenomena of Mean-Field Transformers in the Low-Temperature Regime
Albert Alcalde, Leon Bungert, Konstantin Riedl +1
Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the e…
Duality for the Adversarial Total Variation
Leon Bungert, Lucas Schmitt
Adversarial training of binary classifiers can be reformulated as regularized risk minimization involving a nonlocal total variation. Building on this perspective, we establish a c…
Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies
Tim Roith, Leon Bungert, Philipp Wacker
Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence…
MirrorCBO: A consensus-based optimization method in the spirit of mirror descent
Leon Bungert, Franca Hoffmann, Dohyeon Kim +1
In this work we propose MirrorCBO, a consensus-based optimization (CBO) method which generalizes standard CBO in the same way that mirror descent generalizes gradient descent. For…
Convergence rates for Poisson learning to a Poisson equation with measure data
Leon Bungert, Jeff Calder, Max Mihailescu +2
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 equ…
A mean curvature flow arising in adversarial training
Leon Bungert, Tim Laux, Kerrek Stinson
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…
It begins with a boundary: A geometric view on probabilistically robust learning
Leon Bungert, Nicolás García Trillos, Matt Jacobs +3
Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated e…
Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning
Leon Bungert, Kerrek Stinson
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 adversa…
Polarized consensus-based dynamics for optimization and sampling
Leon Bungert, Tim Roith, Philipp Wacker
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 g…
Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian
Leon Bungert, Jeff Calder, Tim Roith
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-sup…
The Geometry of Adversarial Training in Binary Classification
Leon Bungert, Nicolás García Trillos, Ryan Murray
We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where…
Uniform Convergence Rates for Lipschitz Learning on Graphs
Leon Bungert, Jeff Calder, Tim Roith
Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a w…
Complete Deterministic Dynamics and Spectral Decomposition of the Linear Ensemble Kalman Inversion
Leon Bungert, Philipp Wacker
The ensemble Kalman inversion (EKI) for the solution of Bayesian inverse problems of type , with being an unknown parameter, a given datum, and $\vare…
Continuum Limit of Lipschitz Learning on Graphs
Tim Roith, Leon Bungert
Tackling semi-supervised learning problems with graph-based methods has become a trend in recent years since graphs can represent all kinds of data and provide a suitable framework…
The lion in the attic -- A resolution of the Borel--Kolmogorov paradox
Leon Bungert, Philipp Wacker
The Borel--Kolmogorov paradox of conditioning with respect to events of prior probability zero has fascinated students and researchers since its discovery more than 100 years ago.…