Sharp approximation rates for shallow ReLU neuralnetworks on critical Besov classes

Let $\mathbb D$ be the normalized ridge dictionary generated by $\operatorname{ReLU}^k$ on a bounded Lipschitz domain $Ω\subset\mathbb R^d$. We determine the sharp algebraic rate of finite $n$-term approximation from $\mathbb D$ when the outer $\ell^1$ coefficient budget is independent of $n$. More