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Parseval Networks: Improving Robustness to Adversarial Examples
Moustapha Cisse · Piotr Bojanowski · Edouard Grave · Yann Dauphin · Nicolas Usunier

Mon Aug 07 09:06 PM -- 09:24 PM (PDT) @ Darling Harbour Theatre
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 regarding 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.

Author Information

Moustapha Cisse (Facebook AI Research)
Piotr Bojanowski (Facebook)
Edouard Grave (Facebook AI Research)
Yann Dauphin (Facebook AI Research)
Nicolas Usunier (Facebook AI Research)

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