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math.FA2025
Does the Barron space really defy the curse of dimensionality?
Olov Schavemaker
The Barron space has become famous in the theory of (shallow) neural networks because it seemingly defies the curse of dimensionality. And while the Barron space (and generalizatio…
math.FA2025
On best approximation by multivariate ridge functions with applications to generalized translation networks
Paul Geuchen, Palina Salanevich, Olov Schavemaker +1
In this paper, we prove sharp upper and lower bounds for the approximation of Sobolev functions by sums of multivariate ridge functions, i.e., for approximation by functions of the…