Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders

Emile Mathieu, Charline Le Lan, Chris J Maddison, Ryota Tomioka, Yee Whye Teh

Abstract: The Variational Auto-Encoder (VAE) is a popular method for learning a generative model and embeddings of data living in high-dimensional spaces. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot efficiently embed tree-like structures. Hyperbolic spaces with negative curvature can. 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.

Code Link: https://github.com/emilemathieu/pvae

CMT Num: 6826