  We propose to learn a hierarchical prior in the context of variational
autoencoders to avoid the over-regularisation resulting from a standard normal
prior distribution. To incentivise an informative latent representation of the
data, we formulate the learning problem as a constrained optimisation problem
by extending the Taming VAEs framework to two-level hierarchical models. We
introduce a graph-based interpolation method, which shows that the topology of
the learned latent representation corresponds to the topology of the data
manifold---and present several examples, where desired properties of latent
representation such as smoothness and simple explanatory factors are learned by
the prior.
