  Capsule networks are a neural network architecture specialized for visual
scene recognition. Features and pose information are extracted from a scene and
then dynamically routed through a hierarchy of vector-valued nodes called
'capsules' to create an implicit scene graph, with the ultimate aim of learning
vision directly as inverse graphics. Despite these intuitions, however, capsule
networks are not formulated as explicit probabilistic generative models;
moreover, the routing algorithms typically used are ad-hoc and primarily
motivated by algorithmic intuition. In this paper, we derive an alternative
capsule routing algorithm utilizing iterative inference under sparsity
constraints. We then introduce an explicit probabilistic generative model for
capsule networks based on the self-attention operation in transformer networks
and show how it is related to a variant of predictive coding networks using
Von-Mises-Fisher (VMF) circular Gaussian distributions.
