  Learning a sequence of tasks without access to i.i.d. observations is a
widely studied form of continual learning (CL) that remains challenging. In
principle, Bayesian learning directly applies to this setting, since recursive
and one-off Bayesian updates yield the same result. In practice, however,
recursive updating often leads to poor trade-off solutions across tasks because
approximate inference is necessary for most models of interest. Here, we
describe an alternative Bayesian approach where task-conditioned parameter
distributions are continually inferred from data. We offer a practical deep
learning implementation of our framework based on probabilistic
task-conditioned hypernetworks, an approach we term posterior meta-replay.
Experiments on standard benchmarks show that our probabilistic hypernetworks
compress sequences of posterior parameter distributions with virtually no
forgetting. We obtain considerable performance gains compared to existing
Bayesian CL methods, and identify task inference as our major limiting factor.
This limitation has several causes that are independent of the considered
sequential setting, opening up new avenues for progress in CL.
