Before revision:  The generalization error turns out to be smaller than the estimate {\|\hat f\|^2_{L^1(\mathbb{R}^d)}}/{( LK )} of the generalization error for random Fourier features with one hidden layer and the same total number of nodes LK , in the case the L^\infty-norm of f is much less than the L^1-norm of its Fourier transform \hat f.
After revision:  The generalization error turns out to be smaller than the estimate {\|\hat f\|^2_{L^1(\mathbb{R}^d)}}/{( LK )} of the generalization error for random Fourier features with one hidden layer and the same total number of nodes KL , in the case the L^\infty-norm of f is much less than the L^1-norm of its Fourier transform \hat f.