Appendix

We extra define the following notations for the proof. In Assumption 3.2, we assume the Lipschitz continuity and smoothness for all the activation functions. In the proof of lemmas, e.g., Lemma B.1 and B.2, we only use the fact that they are Lipschitz continuous and smooth, as well as bounded by a constant 0 > 0 at point 0, hence we use () to denote all the activation functions like what we do in Assumption 3.2 for simplicity. Additionally, in the following we introduce notations of the derivatives, mainly used in the proof of Lemma B.1 and Lemma B.2. By definition of feedforward neural networks in Section 2, different from the standard neural networks such as FCNs and CNNs in which the connection between neurons are generally only in adjacent layers, the neurons in feedforward neural networks can be arbitrarily connected as long as there is no loop.