A phi-weighted generalized Barron space B^phi_sigma is defined for shallow networks and shown to embed into Sobolev spaces, to unify known Barron-type spaces, and to yield approximation and regularization bounds.
Breaking the curse of dimensionality with convex neutral networks.J
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On Generalized Barron Spaces for Shallow Neural Networks
A phi-weighted generalized Barron space B^phi_sigma is defined for shallow networks and shown to embed into Sobolev spaces, to unify known Barron-type spaces, and to yield approximation and regularization bounds.