This work presents the Poincaré Wasserstein Autoencoder, a reformulation of
 the recently proposed Wasserstein autoencoder framework on a non-Euclidean
 manifold, the Poincaré ball model of the hyperbolic space H n . By assuming the
 latent space to be hyperbolic, we can use its intrinsic hierarchy to impose structure
 on the learned latent space representations. We show that for datasets with latent
 hierarchies, we can recover the structure in a low-dimensional latent space. We
 also demonstrate the model in the visual domain to analyze some of its properties
 and show competitive results on a graph link prediction task.
Wasserstein Autoencoder with hyperbolic latent space