  In this work, we propose a novel prior learning method for advancing
generalization and uncertainty estimation in deep neural networks. The key idea
is to exploit scalable and structured posteriors of neural networks as
informative priors with generalization guarantees. Our learned priors provide
expressive probabilistic representations at large scale, like Bayesian
counterparts of pre-trained models on ImageNet, and further produce non-vacuous
generalization bounds. We also extend this idea to a continual learning
framework, where the favorable properties of our priors are desirable. Major
enablers are our technical contributions: (1) the sums-of-Kronecker-product
computations, and (2) the derivations and optimizations of tractable objectives
that lead to improved generalization bounds. Empirically, we exhaustively show
the effectiveness of this method for uncertainty estimation and generalization.
