Before revision:  This papershows that gradient descent can identify a global minimizer of the optimization problem with a well-controlled generalization error in the case of two-layer neural networks in the over-parameterization regime (i. e., the network width is sufficiently large). The generalization error of the gradient descent solution does not suffer from the curse of dimensonality if the solution is in a Barron-type space .
After revision:  This papershows that gradient descent can identify a global minimizer of the optimization problem with a well-controlled generalization error in the case of two-layer neural networks under the assumption of over-parametrization. We also analyze the generalization error of the gradient descent solution does not suffer from the curse of dimensonality if the solution is in a Barron-type space .