Lipschitz Bound Analysis of Neural Networks

Abstract

Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. This is useful in a variety of applications ranging from reinforcement learning to autonomous systems. In this paper, we highlight the significant gap in obtaining a non-trivial Lipschitz bound certificate for Convolutional Neural Networks (CNNs) and empirically support it with extensive graphical analysis. We also show that unrolling Convolutional layers or Toeplitz matrices can be employed to convert Convolutional Neural Networks (CNNs) to a Fully Connected Network. Further, we propose a simple algorithm to show the existing 20x-50x gap in a particular data distribution between the actual lipschitz constant and the obtained tight bound. We also ran sets of thorough experiments on various network architectures and benchmark them on datasets like MNIST and CIFAR-10. All these proposals are supported by extensive testing, graphs, histograms and comparative analysis.