4 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…
Semi-discrete optimization through semi-discrete optimal transport: a framework for neural architecture search
Nicolas Garcia Trillos, Javier Morales
In this paper we introduce a theoretical framework for semi-discrete optimization using ideas from optimal transport. Our primary motivation is in the field of deep learning, and s…
From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds
Nicolas Garcia Trillos, Ryan Murray, Matthew Thorpe
In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of C…
Gromov-Hausdorff limit of Wasserstein spaces on point clouds
Nicolas Garcia Trillos
We consider a point cloud uniformly distributed on the flat torus , and construct a geometric graph on…