Gradient-based dimension reduction of multivariate vector-valued functions
Multivariate functions encountered in high-dimensional uncertainty quantification problems
often vary most strongly along a few dominant directions in the input parameter space. We …
often vary most strongly along a few dominant directions in the input parameter space. We …
[BOOK][B] Ridge functions
A Pinkus - 2015 - books.google.com
Ridge functions are a rich class of simple multivariate functions which have found
applications in a variety of areas. These include partial differential equations (where they are …
applications in a variety of areas. These include partial differential equations (where they are …
[BOOK][B] Ridge functions and applications in neural networks
VE Ismailov - 2021 - books.google.com
Recent years have witnessed a growth of interest in the special functions called ridge
functions. These functions appear in various fields and under various guises. They appear in …
functions. These functions appear in various fields and under various guises. They appear in …
Tractability of sampling recovery on unweighted function classes
D Krieg - Proceedings of the American Mathematical Society …, 2024 - ams.org
It is well-known that the problem of sampling recovery in the $ L_2 $-norm on unweighted
Korobov spaces (Sobolev spaces with mixed smoothness) as well as classical smoothness …
Korobov spaces (Sobolev spaces with mixed smoothness) as well as classical smoothness …
Counting via entropy: new preasymptotics for the approximation numbers of Sobolev embeddings
In this paper, we reveal a new connection between approximation numbers of periodic
Sobolev type spaces, where the smoothness weights on the Fourier coefficients are induced …
Sobolev type spaces, where the smoothness weights on the Fourier coefficients are induced …
Robust and resource-efficient identification of two hidden layer neural networks
We address the structure identification and the uniform approximation of two fully nonlinear
layer neural networks of the type f (x)= 1^ T h (B^ T g (A^ T x)) f (x)= 1 T h (BT g (AT x)) …
layer neural networks of the type f (x)= 1^ T h (B^ T g (A^ T x)) f (x)= 1 T h (BT g (AT x)) …
[HTML][HTML] Gelfand numbers related to structured sparsity and Besov space embeddings with small mixed smoothness
We consider the problem of determining the asymptotic order of the Gelfand numbers of
mixed-(quasi-) norm embeddings ℓ pb (ℓ qd)↪ ℓ rb (ℓ ud) given that p≤ r and q≤ u, with …
mixed-(quasi-) norm embeddings ℓ pb (ℓ qd)↪ ℓ rb (ℓ ud) given that p≤ r and q≤ u, with …
Robust and resource efficient identification of shallow neural networks by fewest samples
We address the structure identification and the uniform approximation of sums of ridge
functions on, representing a general form of a shallow feed-forward neural network, from a …
functions on, representing a general form of a shallow feed-forward neural network, from a …
Stable recovery of entangled weights: Towards robust identification of deep neural networks from minimal samples
In this paper we approach the problem of unique and stable identifiability from a finite
number of input-output samples of generic feedforward deep artificial neural networks of …
number of input-output samples of generic feedforward deep artificial neural networks of …
Tractability of the approximation of high-dimensional rank one tensors
We study the approximation of high-dimensional rank one tensors using point evaluations
and consider deterministic as well as randomized algorithms. We prove that for certain …
and consider deterministic as well as randomized algorithms. We prove that for certain …