A Dynamical System Perspective for Lipschitz Neural Networks

The Lipschitz constant of neural networks has been established as a key quantity to enforce the robustness to adversarial examples. In this paper, we tackle the problem of building 1-Lipschitz Neural Networks. By studying Residual Networks from a continuous time dynamical system perspective, we provide a generic method to build 1-Lipschitz Neural Networks and show that some previous approaches are special cases of this framework. Then, we extend this reasoning and show that ResNet flows derived from convex potentials define 1-Lipschitz transformations, that lead us to define the Convex Potential Layer (CPL). A comprehensive set of experiments on several datasets demonstrates the scalability of our architecture and the benefits as an l(2)-provable defense against adversarial examples. Our code is available at https://github.com/MILES- PSL/Convex- Potential-Layer