30 citations · 180 across the 40 of their papers we have counts for
5 papers · 1 filter
Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks
Aditya Kumar Akash, Sixu Li, Nicolás García Trillos
Based on the concepts of Wasserstein barycenter (WB) and Gromov-Wasserstein barycenter (GWB), we propose a unified mathematical framework for neural network (NN) model fusion and u…
Rates of Convergence for Regression with the Graph Poly-Laplacian
Nicolás García Trillos, Ryan Murray, Matthew Thorpe
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be ob…
Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective
Yuetian Luo, Nicolas Garcia Trillos
We study a general matrix optimization problem with a fixed-rank positive semidefinite (PSD) constraint. We perform the Burer-Monteiro factorization and consider a particular Riema…
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…
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…