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The 01 loss gives different and more accurate boundaries than convex lossmodels in the presence of outliers. Could the difference of boundariestranslate to adversarial examples that are non-transferable between 01 loss andconvex models? We explore this empirically in this paper by studyingtransferability of adversarial examples between linear 01 loss and convex(hinge) loss models, and between dual layer neural networks with signactivation and 01 loss vs sigmoid activation and logistic loss. We first showthat white box adversarial examples do not transfer effectively between convexand 01 loss and between 01 loss models compared to between convex models. As aresult of this non-transferability we see that convex substitute model blackbox attacks are less effective on 01 loss than convex models. Interestingly wealso see that 01 loss substitute model attacks are ineffective on both convexand 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 differentdecision boundaries between 01 and convex loss models which in turn producesadversaries that are non-transferable. Indeed we see on MNIST that adversariestransfer between 01 loss and convex models more easily than on CIFAR10 andImageNet which are likely to contain outliers. We show intuitively by examplehow the non-continuity of 01 loss makes adversaries non-transferable in a duallayer neural network. We discretize CIFAR10 features to be more like MNIST andfind that it does not improve transferability, thus suggesting that differentboundaries due to outliers are more likely the cause of non-transferability. Asa result of this non-transferability we show that our dual layer signactivation network with 01 loss can attain robustness on par with simpleconvolutional networks.

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