  Recent advances in variational inference enable the modelling of highly
structured joint distributions, but are limited in their capacity to scale to
the high-dimensional setting of stochastic neural networks. This limitation
motivates a need for scalable parameterizations of the noise generation
process, in a manner that adequately captures the dependencies among the
various parameters. In this work, we address this need and present the
Kronecker Flow, a generalization of the Kronecker product to invertible
mappings designed for stochastic neural networks. We apply our method to
variational Bayesian neural networks on predictive tasks, PAC-Bayes
generalization bound estimation, and approximate Thompson sampling in
contextual bandits. In all setups, our methods prove to be competitive with
existing methods and better than the baselines.
