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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…
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…