arXiv stat.ML
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Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method
arXiv:2607.25100v1 Announce Type: cross Abstract: 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,