Noisy Interpolation Learning with Shallow Univariate ReLU Networks

We study the asymptotic overfitting behavior of interpolation with minimum norm ($\ell_2$ of the weights) two-layer ReLU networks for noisy univariate regression. We show that overfitting is tempered for the $L_1$ loss, and any $L_p$ loss for $p<2$, but catastrophic for $p\geq 2$.