In this paper, we consider the generalization ability of deep wide
feedforward ReLU neural networks defined on a bounded domain XβRd. We first demonstrate that the generalization ability of
the neural network can be fully characterized by that of the corresponding deep
neural tangent kernel (NTK) regression. We then investigate on the spectral
properties of the deep NTK and show that the deep NTK is positive definite on
X and its eigenvalue decay rate is (d+1)/d. Thanks to the well
established theories in kernel regression, we then conclude that multilayer
wide neural networks trained by gradient descent with proper early stopping
achieve the minimax rate, provided that the regression function lies in the
reproducing kernel Hilbert space (RKHS) associated with the corresponding NTK.
Finally, we illustrate that the overfitted multilayer wide neural networks can
not generalize well on Sd. We believe our technical contributions
in determining the eigenvalue decay rate of NTK on Rd might be of
independent interests