Before revision:  It is assumed that the number of i.i.d. Gaussian features grows superlinear in the number of samples. The main result is that under these conditions the Euclidean error of recovering the true regressor is of the order of the average noise level .
After revision:  A quantitative bound for the prediction error is given, relating it to the Rademacher complexity of the covariates, the norm of the minimum norm interpolator of the errors and the shape of the subdifferential around the true parameter. The general theory is illustrated with several examples: the sparse linear model with minimum \ell_1-norm or group Lasso penalty interpolation, the low rank trace regression model with nuclear norm minimization, and minimum Euclidean norm interpolation in the linear model. In case of sparsity or low-rank inducing norms, minimum norm interpolation yields a prediction error of the order of the average noise level .