Stephan Wojtowytsch

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method

We prove that harmonic functions with Dirichlet boundary data in Barron space, a function class tailored to wide ReLU networks with a single hidden layer and suitably bounded weights, are generally neither Lipschitz continuous nor in the Sobolev class $H^2$. A fortiori, they are not in any function class in which the n...