Improved techniques for deterministic l2 robustnessDownload PDF

Published: 31 Oct 2022, Last Modified: 12 Mar 2024NeurIPS 2022 AcceptReaders: Everyone
Keywords: provable defenses, adversarial examples, Lipschitz CNNs, formal guarantees
TL;DR: we introduce several new techniques that lead to significant improvements on CIFAR-10 and CIFAR-100 for both standard and provable robust accuracy and establishes a new state-of-the-art.
Abstract: Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the l_{2} norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing each layer to have an orthogonal Jacobian matrix (for all inputs) to prevent the gradients from vanishing during backpropagation. However, their performance often significantly lags behind that of heuristic methods to enforce Lipschitz constraints where the resulting CNN is not provably 1-Lipschitz. In this work, we reduce this gap by introducing (a) a procedure to certify robustness of 1-Lipschitz CNNs by replacing the last linear layer with a 1-hidden layer MLP that significantly improves their performance for both standard and provably robust accuracy, (b) a method to significantly reduce the training time per epoch for Skew Orthogonal Convolution (SOC) layers (>30\% reduction for deeper networks) and (c) a class of pooling layers using the mathematical property that the l_{2} distance of an input to a manifold is 1-Lipschitz. Using these methods, we significantly advance the state-of-the-art for standard and provable robust accuracies on CIFAR-10 (gains of +1.79\% and +3.82\%) and similarly on CIFAR-100 (+3.78\% and +4.75\% across all networks.
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