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We investigate the best $L_2$ approximation of mixed Sobolev spaces by shallow neural networks with $n$ neurons and general activation functions.
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We investigate the best $L_2$ approximation of mixed Sobolev spaces by shallow neural networks with $n$ neurons and general activation functions. We first establish an activation-independent Fourier-block principle: if an activation has univariate approximation order $ρ$ in the sense of the Fourier-block property, then the global approximation rate has algebraic order $\min\{α,ρ\}$ for target functions of mixed smoothness $α$, up to explicit logarithmic factors. To verify this property for concrete activations, we introduce a structured univariate approximation condition that implies the Fouri...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.05263v1 · Indexed 7 days ago