Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders

The Variational Auto-Encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. We therefore endow VAEs with a Poincaré ball model of hyperbolic geometry as a latent space and rigorously derive the necessary methods to work with two main Gaussian generalisations on that space. We empirically show better generalisation to unseen data than the Euclidean counterpart, and can qualitatively and quantitatively better recover hierarchical structures.