On the transferability of adversarial examples between convex and 01 loss models

Abstract

The 01 loss gives different and more accurate boundaries than convex loss models in the presence of outliers. Could the difference of boundaries translate to adversarial examples that are non-transferable between 01 loss and convex models? We explore this empirically in this paper by studying transferability of adversarial examples between linear 01 loss and convex (hinge) loss models, and between dual layer neural networks with sign activation and 01 loss vs sigmoid activation and logistic loss. We first show that white box adversarial examples do not transfer effectively between convex and 01 loss and between 01 loss models compared to between convex models. As a result of this non-transferability we see that convex substitute model black box attacks are less effective on 01 loss than convex models. Interestingly we also see that 01 loss substitute model attacks are ineffective on both convex and 01 loss models mostly likely due to the non-uniqueness of 01 loss models. We show intuitively by example how the presence of outliers can cause different decision boundaries between 01 and convex loss models which in turn produces adversaries that are non-transferable. Indeed we see on MNIST that adversaries transfer between 01 loss and convex models more easily than on CIFAR10 and ImageNet which are likely to contain outliers. We show intuitively by example how the non-continuity of 01 loss makes adversaries non-transferable in a dual layer neural network. We discretize CIFAR10 features to be more like MNIST and find that it does not improve transferability, thus suggesting that different boundaries due to outliers are more likely the cause of non-transferability. As a result of this non-transferability we show that our dual layer sign activation network with 01 loss can attain robustness on par with simple convolutional networks.