Disentangling Adversarial Robustness and Generalization

Obtaining deep networks that are robust against adversarial examples and generalize well is an open problem. A recent hypothesis even states that both robust and accurate models are impossible, i.e., adversarial robustness and generalization are conflicting goals. In an effort to clarify the relationship between robustness and generalization, we assume an underlying, low-dimensional data manifold and show that: 1. regular adversarial examples leave the manifold; 2. adversarial examples constrained to the manifold, i.e., on-manifold adversarial examples, exist; 3. on-manifold adversarial examples are generalization errors, and on-manifold adversarial training boosts generalization; 4. regular robustness and generalization are not necessarily contradicting goals. These assumptions imply that both robust and accurate models are possible. However, different models (architectures, training strategies etc.) can exhibit different robustness and generalization characteristics. To confirm our claims, we present extensive experiments on synthetic data (with known manifold) as well as on EMNIST, Fashion-MNIST and CelebA.Comment: Conference on Computer Vision and Pattern Recognition 201

Efficient Two-Step Adversarial Defense for Deep Neural Networks

In recent years, deep neural networks have demonstrated outstanding performance in many machine learning tasks. However, researchers have discovered that these state-of-the-art models are vulnerable to adversarial examples: legitimate examples added by small perturbations which are unnoticeable to human eyes. Adversarial training, which augments the training data with adversarial examples during the training process, is a well known defense to improve the robustness of the model against adversarial attacks. However, this robustness is only effective to the same attack method used for adversarial training. Madry et al.(2017) suggest that effectiveness of iterative multi-step adversarial attacks and particularly that projected gradient descent (PGD) may be considered the universal first order adversary and applying the adversarial training with PGD implies resistance against many other first order attacks. However, the computational cost of the adversarial training with PGD and other multi-step adversarial examples is much higher than that of the adversarial training with other simpler attack techniques. In this paper, we show how strong adversarial examples can be generated only at a cost similar to that of two runs of the fast gradient sign method (FGSM), allowing defense against adversarial attacks with a robustness level comparable to that of the adversarial training with multi-step adversarial examples. We empirically demonstrate the effectiveness of the proposed two-step defense approach against different attack methods and its improvements over existing defense strategies.Comment: 12 page