  We study the training and generalization of deep neural networks (DNNs) in
the over-parameterized regime, where the network width (i.e., number of hidden
nodes per layer) is much larger than the number of training data points. We
show that, the expected $0$-$1$ loss of a wide enough ReLU network trained with
stochastic gradient descent (SGD) and random initialization can be bounded by
the training loss of a random feature model induced by the network gradient at
initialization, which we call a neural tangent random feature (NTRF) model. For
data distributions that can be classified by NTRF model with sufficiently small
error, our result yields a generalization error bound in the order of
$\tilde{\mathcal{O}}(n^{-1/2})$ that is independent of the network width. Our
result is more general and sharper than many existing generalization error
bounds for over-parameterized neural networks. In addition, we establish a
strong connection between our generalization error bound and the neural tangent
kernel (NTK) proposed in recent work.
