Curse of Dimensionality in Adversarial Examples
Nandish Chattopadhyay, Anupam Chattopadhyay, Sourav Sen Gupta, Michael E. Kasper · 2019
While machine learning and deep neural networks in particular, have undergone massive progress in the past years, this ubiquitous paradigm faces a relatively newly discovered challenge, adversarial attacks. An adversary can leverage a plethora of attacking algorithms to severely reduce the performance of existing models, therefore threatening the use of AI in many safety-critical applications. Several attempts have been made to try and understand the root cause behind the generation of adversarial examples. In this paper, we try to relate the geometry of the high-dimensional space in which the model operates and optimizes, and the properties and problems therein, to such adversarial attacks. We present the mathematical background, the intuition behind the existence of adversarial examples and substantiate them with empirical results from our experiments.