The Robustness of Deep Networks: A Geometrical Perspective

When building predictive models, it is important to take into account the geometric structure of the data - how the observations are located in a multidimensional space. Usually, the location of observations is well described by a manifold. It is obvious that its properties affect the accuracy of the corresponding predictive models. By learning the data manifold, we can identify areas on the manifold in which the predictive model is not robust, and thus it becomes possible both to generate effective adversarial attacks on the model and to protect against them. The presentation describes approaches to generating adversarial attacks and to protecting against them by taking into account properties of the data manifold, as well as, in general, how to compare the real data manifold and data generated by a generative model, and thereby, for example, to identify artificially generated (potentially fake) observations.