16 citations · 56 across the 11 of their papers we have counts for
14 papers
On the existence of solutions to adversarial training in multiclass classification
Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim
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…
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…
Lagrangian solutions to the Porous Media Equation and Reaction Diffusion Systems
Matt Jacobs
In this paper, we construct global-in-time forward and backward Lagrangian flow maps along the pressure gradient generated by weak solutions of the Porous Media Equation. The main…
Tumor Growth with Nutrients: Regularity and Stability
Matt Jacobs, Inwon Kim, Jiajun Tong
In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nu…
The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification
Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim
We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in…
Existence of solutions to reaction cross diffusion systems
Matt Jacobs
Reaction cross diffusion systems are a two species generalization of the porous media equation. These systems play an important role in the mechanical modeling of living tissues an…