On the existence of solutions to adversarial training in multiclass classification
We study three models of the problem of adversarial training in multiclass classification
designed to construct robust classifiers against adversarial perturbations of data in the …
designed to construct robust classifiers against adversarial perturbations of data in the …
On adversarial robustness and the use of wasserstein ascent-descent dynamics to enforce it
CG Trillos, NG Trillos - arXiv preprint arXiv:2301.03662, 2023 - arxiv.org
We propose iterative algorithms to solve adversarial problems in a variety of supervised
learning settings of interest. Our algorithms, which can be interpreted as suitable ascent …
learning settings of interest. Our algorithms, which can be interpreted as suitable ascent …
A mean curvature flow arising in adversarial training
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 …
the decision boundary. Relying on a perspective that recasts adversarial training as a …
An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification
Despite the success of deep learning-based algorithms, it is widely known that neural
networks may fail to be robust. A popular paradigm to enforce robustness is adversarial …
networks may fail to be robust. A popular paradigm to enforce robustness is adversarial …
An elliptic approximation for phase separation in a fractured material
K Stinson, S Wittig - arXiv preprint arXiv:2408.03776, 2024 - arxiv.org
We consider a free-boundary and free-discontinuity energy connecting phase separation
and fracture in an elastic material. The energy excludes the contribution of phase …
and fracture in an elastic material. The energy excludes the contribution of phase …
Adversarial flows: A gradient flow characterization of adversarial attacks
A popular method to perform adversarial attacks on neuronal networks is the so-called fast
gradient sign method and its iterative variant. In this paper, we interpret this method as an …
gradient sign method and its iterative variant. In this paper, we interpret this method as an …
Can We Rely on AI?
DJ Higham - arXiv preprint arXiv:2308.15092, 2023 - arxiv.org
Over the last decade, adversarial attack algorithms have revealed instabilities in deep
learning tools. These algorithms raise issues regarding safety, reliability and interpretability …
learning tools. These algorithms raise issues regarding safety, reliability and interpretability …
Uniform Convergence of Adversarially Robust Classifiers
R Morris, R Murray - arXiv preprint arXiv:2406.14682, 2024 - arxiv.org
In recent years there has been significant interest in the effect of different types of adversarial
perturbations in data classification problems. Many of these models incorporate the …
perturbations in data classification problems. Many of these models incorporate the …
On De Giorgi's Conjecture of Nonlocal approximations for free-discontinuity problems: The symmetric gradient case
We prove that E. De Giorgi's conjecture for the nonlocal approximation of free-discontinuity
problems extends to the case of functionals defined in terms of the symmetric gradient of the …
problems extends to the case of functionals defined in terms of the symmetric gradient of the …
On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it
CA García Trillos, N García Trillos - Information and Inference: A …, 2024 - academic.oup.com
We propose iterative algorithms to solve adversarial training problems in a variety of
supervised learning settings of interest. Our algorithms, which can be interpreted as suitable …
supervised learning settings of interest. Our algorithms, which can be interpreted as suitable …