30 citations · 180 across the 40 of their papers we have counts for
8 papers · 1 filter
A New Perspective On Denoising Based On Optimal Transport
Nicolas Garcia Trillos, Bodhisattva Sen
In the standard formulation of the denoising problem, one is given a probabilistic model relating a latent variable and an observation $Z \…
Spectral Neural Networks: Approximation Theory and Optimization Landscape
Chenghui Li, Rishi Sonthalia, Nicolas Garcia Trillos
There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of the…
Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms
Nicolás García Trillos, Anna Little, Daniel McKenzie +1
We analyze the convergence properties of Fermat distances, a family of density-driven metrics defined on Riemannian manifolds with an associated probability measure. Fermat distanc…
Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds
Nicolas Garcia Trillos, Melanie Weber
Let denote a low-dimensional manifold embedded in Euclidean space and let be a collection of points uniformly sampled from it. We study the relatio…
FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization
Jose A. Carrillo, Nicolas Garcia Trillos, Sixu Li +1
Federated learning is an important framework in modern machine learning that seeks to integrate the training of learning models from multiple users, each user having their own loca…
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…
From Optimization to Sampling Through Gradient Flows
N. Garcia Trillos, B. Hosseini, D. Sanz-Alonso
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, s…
On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it
Camilo Garcia Trillos, Nicolas Garcia Trillos
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-…