  This work identifies the existence and cause of a type of posterior collapse
that frequently occurs in the Bayesian deep learning practice. For a general
linear latent variable model that includes linear variational autoencoders as a
special case, we precisely identify the nature of posterior collapse to be the
competition between the likelihood and the regularization of the mean due to
the prior. Our result suggests that posterior collapse may be related to neural
collapse and dimensional collapse and could be a subclass of a general problem
of learning for deeper architectures.
