A Proof of Theorem 1 Proof

Theorem 6 is stated in terms of Gaussian complexity. Ben-David (2014) has a full proof. M (α)null is the linear class following the depth-K neural network. The second term relies on the Lipschitz constant of DNN, which we bound with the following lemma. Similar results are given by Scaman and Virmaux (2018); Fazlyab et al. (2019).