3 papers
math.FA2025
Bases of Lebesgue spaces formed by neural networks
Vladimir Kulbatov, Jan Lang, Cornelia Schneider +1
The seminal work of Daubechies, DeVore, Foucart, Hanin, and Petrova introduced in 2022 a sequence of univariate piece-wise linear functions, which resemble the classical Fourier ba…
cs.LG2025
Nonlocal techniques for the analysis of deep ReLU neural network approximations
Cornelia Schneider, Mario Ullrich, Jan Vybiral
Recently, Daubechies, DeVore, Foucart, Hanin, and Petrova introduced a system of piece-wise linear functions, which can be easily reproduced by artificial neural networks with the…
math.FA2025
Improved universal approximation with neural networks studied via affine-invariant subspaces of
Cornelia Schneider, Samuel Probst
We show that there are no non-trivial closed subspaces of that are invariant under invertible affine transformations. We apply this result to neural networks sh…