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تسجيل مستخدم جديدProvable defenses against adversarial examples via the convex outer adversarial polytope
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We propose a method to learn deep ReLU-based classifiers that are provably robust against norm-bounded adversarial perturbations on the training data. For previously unseen examples, the approach is guaranteed to detect all adversarial examples, though it may flag some non-adversarial examples as well. The basic idea is to consider a convex outer approximation of the set of activations reachable through a norm-bounded perturbation, and we develop a robust optimization procedure that minimizes the worst case loss over this outer region (via a linear program). Crucially, we show that the dual problem to this linear program can be represented itself as a deep network similar to the backpropagation network, leading to very efficient optimization approaches that produce guaranteed bounds on the robust loss. The end result is that by executing a few more forward and backward passes through a slightly modified version of the original network (though possibly with much larger batch sizes), we can learn a classifier that is provably robust to any norm-bounded adversarial attack. We illustrate the approach on a number of tasks to train classifiers with robust adversarial guarantees (e.g. for MNIST, we produce a convolutional classifier that provably has less than 5.8% test error for any adversarial attack with bounded $ell_infty$ norm less than $epsilon = 0.1$), and code for all experiments in the paper is available at https://github.com/locuslab/convex_adversarial.
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Recent work has developed methods for learning deep network classifiers that are provably robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this paper, in
an effort to scale these approaches to substantially larger models, we extend previous work in three main directions. First, we present a technique for extending these training procedures to much more general networks, with skip connections (such as ResNets) and general nonlinearities; the approach is fully modular, and can be implemented automatically (analogous to automatic differentiation). Second, in the specific case of $ell_infty$ adversarial perturbations and networks with ReLU nonlinearities, we adopt a nonlinear random projection for training, which scales linearly in the number of hidden units (previous approaches scaled quadratically). Third, we show how to further improve robust error through cascade models. On both MNIST and CIFAR data sets, we train classifiers that improve substantially on the state of the art in provable robust adversarial error bounds: from 5.8% to 3.1% on MNIST (with $ell_infty$ perturbations of $epsilon=0.1$), and from 80% to 36.4% on CIFAR (with $ell_infty$ perturbations of $epsilon=2/255$). Code for all experiments in the paper is available at https://github.com/locuslab/convex_adversarial/.
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