“…To address this limitation, several works, inspired by some PAC-Bayesian literature, have proposed fast-rate information-theoretic bounds [24,25,64], demonstrating a good characterization in some instances of non-convex settings such as deep learning. More recently, [65,66,71] present IOMI bounds for the Gaussian mean estimation problem, that achieve optimal convergence rates, contrasting previous bounds [9,70].…”