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We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations, we propose an easy-to-use, end-to-end trainable, low-rank regularizer (LR) that can be applied to any intermediate layer representation of a DNN. This regularizer forces the feature representations to (mostly) lie in a low-dimensional linear subspace. WearXiv:1804.07090v5 fatcat:qq4gnlix6rbqha5hz6f2eykd2e