Title: Leveraging Adversarial Examples to Obtain Robust Second-Order Representations. Abstract: Deep neural networks represent data as projections on trained weights in a high dimensional manifold. This is a first-order based absolute representation that is widely used due to its interpretable nature and simple mathematical functionality. However, in the application of visual recognition, first-order representations trained on pristine images have shown a vulnerability to distortions. Visual distortions including imaging acquisition errors and challenging environmental conditions like blur, exposure, snow and frost cause incorrect classification in first-order neural nets. To eliminate vulnerabilities under such distortions, we propose representing data points by their relative positioning in a high dimensional manifold instead of their absolute positions. Such a positioning scheme is based on a data point’s second-order property. We obtain a data point’s second-order representation by creating adversarial examples to all possible decision boundaries and tracking the movement of corresponding boundaries. We compare our representation against first-order methods and show that there is an increase of more than 14% under severe distortions for ResNet-18. We test the generalizability of the proposed representation on larger networks and on 19 complex and real-world distortions from CIFAR-10-C. Furthermore, we show how our proposed representation can be used as a plug-in approach on top of any network. We also provide methodologies to scale our proposed representation to larger datasets.