72 citations · 536 across the 51 of their papers we have counts for
6 papers · 1 filter
Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions
Mazen Ali, Anthony Nouy
We study the approximation of multivariate functions with tensor networks (TNs), providing some answers to the following two questions: ``what are the approximation capabilities of…
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 …
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…
Singular Value Decomposition in Sobolev Spaces: Part II
Mazen Ali, Anthony Nouy
Under certain conditions, an element of a tensor product space can be identified with a compact operator and the singular value decomposition (SVD) applies to the latter. These con…
Singular Value Decomposition in Sobolev Spaces: Part I
Mazen Ali, Anthony Nouy
A well known result from functional analysis states that any compact operator between Hilbert spaces admits a singular value decomposition (SVD). This decomposition is a powerful t…