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Built upon on a novel definition of label uncertainty, we develop an empirical method to estimate a more realistic intirnsic robustness limit for image classification tasks.

We show that concentration of measure does not prohibit the existence of adversarially robust classifiers using a novel method of empirical concentration estimation.

We propose a way to characterize the intrinsic robustness of image distributions under L2 perturbations using conditional generative models.

We propose an unsupervised learning method for obtaining robust representations based on a notion of representation vulnerability.

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 prove theoretical guarantees of learning one-hidden-layer neural networks with ReLU activations.

A primal-dual based framework for analyzing the global optimality of nonconvex low-rank matrix recovery.

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.

A unified framework for solving general low-rank plus sparse matrix recovery problems.