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Machine learning models are vulnerable to adversarial perturbations, thatwhen added to an input, can cause high confidence misclassifications. Theadversarial learning research community has made remarkable progress in theunderstanding of the root causes of adversarial perturbations. However, mostproblems that one may consider important to solve for the deployment of machinelearning in safety critical tasks involve high dimensional complex manifoldsthat are difficult to characterize and study. It is common to developadversarially robust learning theory on simple problems, in the hope thatinsights will transfer to `real world datasets'. In this work, we discuss asetting where this approach fails. In particular, we show with a linearclassifier, it is always possible to solve a binary classification problem onGaussian data under arbitrary levels of adversarial corruption during training,and that this property is not observed with non-linear classifiers on theCIFAR-10 dataset.

Unique properties of adversarially trained linear classifiers on Gaussian data