CLIP: Cheap Lipschitz Training of Neural Networks
This addresses stability issues in neural networks for safety-critical applications like biomedical imaging and autonomous driving, though it is an incremental improvement over existing regularization methods.
The authors tackled the instability of deep neural networks to adversarial perturbations by proposing CLIP, a variational regularization method for controlling the Lipschitz constant, which they evaluated on regression and classification tasks like MNIST and Fashion-MNIST, showing competitive results compared to weight regularization.
Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so called adversarial examples, that can cause false predictions. This instability can have severe consequences in applications which influence the health and safety of humans, e.g., biomedical imaging or autonomous driving. While bounding the Lipschitz constant of a neural network improves stability, most methods rely on restricting the Lipschitz constants of each layer which gives a poor bound for the actual Lipschitz constant. In this paper we investigate a variational regularization method named CLIP for controlling the Lipschitz constant of a neural network, which can easily be integrated into the training procedure. We mathematically analyze the proposed model, in particular discussing the impact of the chosen regularization parameter on the output of the network. Finally, we numerically evaluate our method on both a nonlinear regression problem and the MNIST and Fashion-MNIST classification databases, and compare our results with a weight regularization approach.