Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustness
This work addresses the problem of adversarial robustness in machine learning for researchers, offering theoretical insights that challenge the notion of unavoidable adversarial examples.
The paper investigates whether adversarial examples are unavoidable by showing that data concentration on small-volume subsets determines robust classifier existence, and demonstrates that for data on low-dimensional linear subspaces, classifiers can achieve data-dependent polyhedral robustness guarantees.
The susceptibility of modern machine learning classifiers to adversarial examples has motivated theoretical results suggesting that these might be unavoidable. However, these results can be too general to be applicable to natural data distributions. Indeed, humans are quite robust for tasks involving vision. This apparent conflict motivates a deeper dive into the question: Are adversarial examples truly unavoidable? In this work, we theoretically demonstrate that a key property of the data distribution -- concentration on small-volume subsets of the input space -- determines whether a robust classifier exists. We further demonstrate that, for a data distribution concentrated on a union of low-dimensional linear subspaces, utilizing structure in data naturally leads to classifiers that enjoy data-dependent polyhedral robustness guarantees, improving upon methods for provable certification in certain regimes.