  Bayesian neural networks (BNNs) allow us to reason about uncertainty in a
principled way. Stochastic Gradient Langevin Dynamics (SGLD) enables efficient
BNN learning by drawing samples from the BNN posterior using mini-batches.
However, SGLD and its extensions require storage of many copies of the model
parameters, a potentially prohibitive cost, especially for large neural
networks. We propose a framework, Adversarial Posterior Distillation, to
distill the SGLD samples using a Generative Adversarial Network (GAN). At
test-time, samples are generated by the GAN. We show that this distillation
framework incurs no loss in performance on recent BNN applications including
anomaly detection, active learning, and defense against adversarial attacks. By
construction, our framework not only distills the Bayesian predictive
distribution, but the posterior itself. This allows one to compute quantities
such as the approximate model variance, which is useful in downstream tasks. To
our knowledge, these are the first results applying MCMC-based BNNs to the
aforementioned downstream applications.
