$L^p$ sampling numbers for the Fourier-analytic Barron space

@article{Voigtlaender2022LpSN,
  title={\$L^p\$ sampling numbers for the Fourier-analytic Barron space},
  author={F. Voigtlaender},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.07605}
}
In this paper, we consider Barron functions f : [0 , 1] d → R of smoothness σ > 0, which are functions that can be written as f ( x ) = Z R d F ( ξ ) e 2 πi h x,ξ i dξ with Z R d | F ( ) | · σ < ∞ . For σ = 1, these functions play a prominent role in machine learning, since they can be efficiently approximated by (shallow) neural networks without suffering from the curse of dimensionality. For these functions, we study the following question: Given m point samples f ( x 1 ) , . . . , f ( x m ) of… 
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