25 citations · 35 across the 8 of their papers we have counts for
8 papers
An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification
Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim +1
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 traini…
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…
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…
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…
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-…
Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning
Nicolas García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
In recent decades, science and engineering have been revolutionized by a momentous growth in the amount of available data. However, despite the unprecedented ease with which data a…