We study data-dependent uniform generalization bounds by approaching the problem from a PAC-Bayesian perspective. We first apply the PAC-Bayesian framework on ``random sets'' in a rigorous way, where the training algorithm is assumed to output a data-dependent hypothesis set after

Neural network compression has been an increasingly important subject, not only due to its practical relevance, but also due to its theoretical implications, as there is an explicit connection between compressibility and generalization error. In this talk, I will present