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Found 15 papers, 8 papers with code
A mean curvature flow arising in adversarial training
We connect adversarial training for binary classification to a geometric evolution equation for the decision boundary.
It begins with a boundary: A geometric view on probabilistically robust learning
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.
Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning
In this paper we prove Gamma-convergence of a nonlocal perimeter of Minkowski type to a local anisotropic perimeter.
Improving Robustness against Real-World and Worst-Case Distribution Shifts through Decision Region Quantification
The reliability of neural networks is essential for their use in safety-critical applications.
The Geometry of Adversarial Training in Binary Classification
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 the regularizer is a nonlocal perimeter functional.
Uniform Convergence Rates for Lipschitz Learning on Graphs
In this work we prove uniform convergence rates for solutions of the graph infinity Laplace equation as the number of vertices grows to infinity.
Neural Architecture Search via Bregman Iterations
We propose a novel strategy for Neural Architecture Search (NAS) based on Bregman iterations.
A Bregman Learning Framework for Sparse Neural Networks
In contrast to established methods for sparse training the proposed family of algorithms constitutes a regrowth strategy for neural networks that is solely optimization-based without additional heuristics.
Ranked #164 on
Image Classification
on CIFAR-10
CLIP: Cheap Lipschitz Training of Neural Networks
Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability.
Identifying Untrustworthy Predictions in Neural Networks by Geometric Gradient Analysis
The susceptibility of deep neural networks to untrustworthy predictions, including out-of-distribution (OOD) data and adversarial examples, still prevent their widespread use in safety-critical applications.
Continuum Limit of Lipschitz Learning on Graphs
In particular, we define a sequence of functionals which approximate the largest local Lipschitz constant of a graph function and prove $\Gamma$-convergence in the $L^\infty$-topology to the supremum norm of the gradient as the graph becomes denser.
Variational regularisation for inverse problems with imperfect forward operators and general noise models
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 lattice.
Numerical Analysis Numerical Analysis Optimization and Control 47A52, 65J20, 65J22, 65K10
Robust Image Reconstruction with Misaligned Structural Information
Multi-modality (or multi-channel) imaging is becoming increasingly important and more widely available, e. g. hyperspectral imaging in remote sensing, spectral CT in material sciences as well as multi-contrast MRI and PET-MR in medicine.
Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
In this work we investigate the computation of nonlinear eigenfunctions via the extinction profiles of gradient flows.
Blind Image Fusion for Hyperspectral Imaging with the Directional Total Variation
In this paper, we propose a method for increasing the spatial resolution of a hyperspectral image by fusing it with an image of higher spatial resolution that was obtained with a different imaging modality.
