Parseval Networks: Improving Robustness to Adversarial Examples

TL;DR

Parseval networks are a new deep learning architecture that constrains layer weights to improve robustness against adversarial attacks while maintaining high accuracy and training efficiency.

Contribution

We propose Parseval networks that enforce weight matrices to be Parseval tight frames, enhancing adversarial robustness and training speed compared to traditional networks.

Findings

Achieve state-of-the-art accuracy on CIFAR-10/100 and SVHN datasets.

Demonstrate increased robustness to adversarial examples.

Train faster and utilize network capacity more effectively.

Abstract

We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically motivated by an analysis of the robustness of the predictions made by deep neural networks when their input is subject to an adversarial perturbation. The most important feature of Parseval networks is to maintain weight matrices of linear and convolutional layers to be (approximately) Parseval tight frames, which are extensions of orthogonal matrices to non-square matrices. We describe how these constraints can be maintained efficiently during SGD. We show that Parseval networks match the state-of-the-art in terms of accuracy on CIFAR-10/100 and Street View House Numbers (SVHN) while being more robust than their vanilla counterpart against adversarial examples. Incidentally, Parseval networks also tend to train faster and make a better usage of the full capacity of the networks.