11 citations · 44 across the 12 of their papers we have counts for
5 papers · 1 filter
Ranks of Tensor Networks for Eigenspace Projections and the Curse of Dimensionality
Mazen Ali
The hierarchical (multi-linear) rank of an order- tensor is key in determining the cost of representing a tensor as a (tree) Tensor Network (TN). In general, it is known that, f…
-Stability of the -Projection onto Finite Element Spaces on Adaptively Refined Quadrilateral Meshes
Mazen Ali, Stefan A. Funken, Anja Schmidt
The -orthogonal projection onto a finite element (FE) space is called -stable iff $\|\nablaΠ_h u\|_{L^2(Ω)}\leq C\|u\|_…
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…