Notes on Lipschitz Margin, Lipschitz Margin Training, and Lipschitz Margin p-Values for Deep Neural Network Classifiers

A variety of papers have been recently produced on "robustifying " Deep Neural Networks (DNNs), particularly to adversarial Test-Time Evasion (TTE) attacks [14, 15, 13]. We discuss some of this work in Sections III.A and IV.A of [9 ] and argue for the need for TTE-attack detection [8] for robustness . In this note, we derive a local class purity result under the assumption of Lipschitz continuity, discuss Lipschitz margin training, and define an associated p-value. Estimation of the Lipschitz parameter for a given DNN is disc ussed in, e.g., [12, 14, 16, 4].