(Submitted) Minimum norm interpolation by shallow networks: Explicit regularization and implicit bias.

We investigate how shallow ReLU networks interpolate between known regions as the number of data points and parameters tends to infinity. Our analysis yields convergence to a minimum norm interpolant when a weight decay regularizer is penalized with a coefficient which vanishes at a precise rate as the network width and the number of data points grow. With and without explicit regularization, we numerically study the implicit bias of common optimization algorithms towards known minimum norm interpolants.