Before revision:  Moreover, we prove that only O(|\log(\epsilon)|) layers are needed for an \epsilon accurate solution to the inverse problem (exponential convergence), and that the inner dimensions in the layers do not exceed the dimension of the inverse problem.
After revision:  Moreover, we prove that only O(|\log(\epsilon)|) layers are needed for an \epsilon -accurate solution to the inverse problem (exponential convergence), and that the inner dimensions in the layers do not exceed the dimension of the inverse problem.