72 citations · 536 across the 51 of their papers we have counts for
7 papers · 1 filter
Geometry of tree-based tensor formats in tensor Banach spaces
Antonio Falcó, Wolfgang Hackbusch, Anthony Nouy
In the paper `On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces', we provided a geometrical description of manifolds of tensors in Tucker format with fixed multili…
Approximation of Smoothness Classes by Deep Rectifier Networks
Mazen Ali, Anthony Nouy
We consider approximation rates of sparsely connected deep rectified linear unit (ReLU) and rectified power unit (RePU) neural networks for functions in Besov spaces …
A PAC algorithm in relative precision for bandit problem with costly sampling
Marie Billaud-Friess, Arthur Macherey, Anthony Nouy +1
This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem. We first propose a naive stochastic bandit algorithm for obt…
Learning with tree tensor networks: complexity estimates and model selection
Bertrand Michel, Anthony Nouy
Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspo…
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part II
Mazen Ali, Anthony Nouy
We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p(…
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part I
Mazen Ali, Anthony Nouy
We study the approximation of functions by tensor networks (TNs). We show that Lebesgue -spaces in one dimension can be identified with tensor product spaces of arbitrary orde…
A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds
Marie Billaud-Friess, Antonio Falcó, Anthony Nouy
In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introdu…