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05/30/2023
It begins with a boundary: A geometric view on probabilistically robust learning
Although deep neural networks have achieved super-human performance on m...
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11/28/2022
Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning
In this paper we prove Gamma-convergence of a nonlocal perimeter of Mink...
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11/09/2022
Polarized consensus-based dynamics for optimization and sampling
In this paper we propose polarized consensus-based dynamics in order to ...
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10/17/2022
Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian
In this paper we prove the first quantitative convergence rates for the ...
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11/26/2021
The Geometry of Adversarial Training in Binary Classification
We establish an equivalence between a family of adversarial training pro...
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11/24/2021
Uniform Convergence Rates for Lipschitz Learning on Graphs
Lipschitz learning is a graph-based semi-supervised learning method wher...
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06/04/2021
Neural Architecture Search via Bregman Iterations
We propose a novel strategy for Neural Architecture Search (NAS) based o...
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05/18/2021
Gradient Flows, Nonlinear Power Methods, and Computation of Nonlinear Eigenfunctions
This chapter describes how gradient flows and nonlinear power methods in...
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05/10/2021
A Bregman Learning Framework for Sparse Neural Networks
We propose a learning framework based on stochastic Bregman iterations t...
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04/27/2021
Complete Deterministic Dynamics and Spectral Decomposition of the Ensemble Kalman Inversion
The Ensemble Kalman inversion (EKI), proposed by Iglesias et al. for the...
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03/23/2021
CLIP: Cheap Lipschitz Training of Neural Networks
Despite the large success of deep neural networks (DNN) in recent years,...
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02/24/2021
Identifying Untrustworthy Predictions in Neural Networks by Geometric Gradient Analysis
The susceptibility of deep neural networks to untrustworthy predictions,...
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12/07/2020
Continuum Limit of Lipschitz Learning on Graphs
Tackling semi-supervised learning problems with graph-based methods have...
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05/28/2020
Variational regularisation for inverse problems with imperfect forward operators and general noise models
We study variational regularisation methods for inverse problems with im...
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04/17/2020
The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
In this work we present an alternative formulation of the higher eigenva...
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04/01/2020
Robust Image Reconstruction with Misaligned Structural Information
Multi-modality (or multi-channel) imaging is becoming increasingly impor...
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02/27/2019
Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
In this work we investigate the computation of nonlinear eigenfunctions ...
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10/04/2017