6 papers
Sampling in the Euclidean Motion Group and a Problem from Brain's Primary Visual Cortex
Davide Barbieri
We study a sampling problem for the abstract wavelet transform associated with the quasiregular representation of the group, for a modulated gaussian mother wavelet. This p…
Scattering Networks on Noncommutative Finite Groups
Maria Teresa Arias, Davide Barbieri, Eugenio Hernández
Scattering Networks were initially designed to elucidate the behavior of early layers in Convolutional Neural Networks (CNNs) over Euclidean spaces and are grounded in wavelets. In…
Is Stochastic Gradient Descent Effective? A PDE Perspective on Machine Learning processes
Davide Barbieri, Matteo Bonforte, Peio Ibarrondo
In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimizatio…
Learning optimal smooth invariant subspaces for data approximation
Davide Barbieri, Eugenio Hernández, Carlos Cabrelli +1
In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functio…
The structure of group preserving operators
Davide Barbieri, Carlos Cabrelli, Diana Carbajal +2
In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of where is a second coun…
Data approximation with time-frequency invariant systems
D. Barbieri, C. Cabrelli, E. Hernández +1
In this paper we prove the existence of a time-frequency space that best approximates a given finite set of data. Here best approximation is in the least square sense, among all ti…