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In the past two decades we have seen the popularity of neural networksincrease in conjunction with their classification accuracy. Parallel to this,we have also witnessed how fragile the very same prediction models are: tinyperturbations to the inputs can cause misclassification errors throughoutentire datasets. In this paper, we consider perturbations bounded by the$\ell_0$--norm, which have been shown as effective attacks in the domains ofimage-recognition, natural language processing, and malware-detection. To thisend, we propose a novel defense method that consists of "truncation" and"adversarial training". We then theoretically study the Gaussian mixturesetting and prove the asymptotic optimality of our proposed classifier.Motivated by the insights we obtain, we extend these components to neuralnetwork classifiers. We conduct numerical experiments in the domain of computervision using the MNIST and CIFAR datasets, demonstrating significantimprovement for the robust classification error of neural networks.

Efficient and Robust Classification for Sparse Attacks