From Characterizing Intrinsic Robustness to Adversarially Robust Machine Learning

The prevalence of adversarial examples raises questions about the reliability of machine learning systems, especially for their deployment in critical applications. Numerous defense mechanisms have been proposed that aim to improve a machine learning system's robustness in the presence of adversarial examples. However, none of these methods are able to produce satisfactorily robust models, even for simple classification tasks on benchmarks. In addition to empirical attempts to build robust models, recent studies have identified intrinsic limitations for robust learning against adversarial examples. My research aims to gain a deeper understanding of why machine learning models fail in the presence of adversaries and design ways to build better robust systems. In this dissertation, I develop a concentration estimation framework to characterize the intrinsic limits of robustness for typical classification tasks of interest. The proposed framework leads to the discovery that compared with the concentration of measure which was previously argued to be an important factor, the existence of uncertain inputs may explain more fundamentally the vulnerability of state-of-the-art defenses. Moreover, to further advance our understanding of adversarial examples, I introduce a notion of representation robustness based on mutual information, which is shown to be related to an intrinsic limit of model robustness for downstream classification tasks. Finally in this dissertation, I advocate for a need to rethink the current design goal of robustness and shed light on ways to build better robust machine learning systems, potentially escaping the intrinsic limits of robustness.