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.

本文提出了在变分自编码器中学习分层先验以避免标准正态先验分布造成的过度规则化。为了激励数据的具有信息的潜在表示，我们将学习问题公式化为带有约束的优化问题，并将 Taming VAEs 框架扩展为两层分层模型。我们引入了基于图形的插值方法，该方法显示所学习的潜在表示的拓扑结构对应于数据流形的拓扑结构，并呈现了几个例子，在这些例子中，优先考虑的是潜在表示的所需属性，例如平滑性和简单的解释因素。