Explaining adversarial vulnerability with a data sparsity hypothesis

Abstract

Despite many proposed algorithms to provide robustness to deep learning (DL) models, DL models remain susceptible to adversarial attacks. We hypothesize that the adversarial vulnerability of DL models stems from two factors. The first factor is data sparsity which is that in the high dimensional input data space, there exist large regions outside the support of the data distribution. The second factor is the existence of many redundant parameters in the DL models. Owing to these factors, different models are able to come up with different decision boundaries with comparably high prediction accuracy. The appearance of the decision boundaries in the space outside the support of the data distribution does not affect the prediction accuracy of the model. However, it makes an important difference in the adversarial robustness of the model. We hypothesize that the ideal decision boundary is as far as possible from the support of the data distribution. In this paper, we develop a training framework to observe if DL models are able to learn such a decision boundary spanning the space around the class distributions further from the data points themselves. Semi-supervised learning was deployed during training by leveraging unlabeled data generated in the space outside the support of the data distribution. We measured adversarial robustness of the models trained using this training framework against well-known adversarial attacks and by using robustness metrics. We found that models trained using our framework, as well as other regularization methods and adversarial training support our hypothesis of data sparsity and that models trained with these methods learn to have decision boundaries more similar to the aforementioned ideal decision boundary. We show that the unlabeled data generated by noise in our framework is almost as effective on adversarial robustness as unlabeled data sourced from existing datasets or generated by synthesis algorithms. The code for our training framework is available online.