ICLR 2022: Understanding Intrinsic Robustness Using Label Uncertainty
(Blog post written by Xiao Zhang)
Motivated by the empirical hardness of developing robust classifiers against adversarial perturbations, researchers began asking the question “Does there even exist a robust classifier?”. This is formulated as the intrinsic robustness problem (Mahloujifar et al., 2019), where the goal is to characterize the maximum adversarial robustness possible for a given robust classification problem. Building upon the connection between adversarial robustness and classifier’s error region, it has been shown that if we restrict the search to the set of imperfect classifiers, the intrinsic robustness problem can be reduced to the concentration of measure problem.
Improved Estimation of Concentration (ICLR 2021)
Our paper on Improved Estimation of Concentration Under ℓp-Norm Distance Metrics Using Half Spaces (Jack Prescott, Xiao Zhang, and David Evans) will be presented at ICLR 2021.
Abstract: Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. Mahloujifar et al. (2019) presented an empirical way to measure the concentration of a data distribution using samples, and employed it to find lower bounds on intrinsic robustness for several benchmark datasets. However, it remains unclear whether these lower bounds are tight enough to provide a useful approximation for the intrinsic robustness of a dataset. To gain a deeper understanding of the concentration of measure phenomenon, we first extend the Gaussian Isoperimetric Inequality to non-spherical Gaussian measures and arbitrary ℓp-norms (p ≥ 2). We leverage these theoretical insights to design a method that uses half-spaces to estimate the concentration of any empirical dataset under ℓp-norm distance metrics. Our proposed algorithm is more efficient than Mahloujifar et al. (2019)’s, and experiments on synthetic datasets and image benchmarks demonstrate that it is able to find much tighter intrinsic robustness bounds. These tighter estimates provide further evidence that rules out intrinsic dataset concentration as a possible explanation for the adversarial vulnerability of state-of-the-art classifiers.