We develop a method to measure the concentration of image benchmarks using empirical samples and show that concentration of measure does not prohibit the existence of adversarially robust classifiers.

We propose a notion of cost-sensitive robustness for measuring classifier’s performance when adversarial transformations are not equally important, and provide a certified robust training method to optimize for it.

We present a new gradient-based optimization algorithm for inductive matrix completion, which achieves both linear rate of convengence and sample complexities linearly depending on the feature dimension.