Continuous Hierarchical Representations with Poincar\'e Variational Auto-Encoders

TL;DR

This paper introduces Poincaré Variational Auto-Encoders that utilize hyperbolic geometry in the latent space to effectively model and recover hierarchical data structures, outperforming traditional Euclidean VAEs.

Contribution

It develops a novel hyperbolic latent space for VAEs using Poincaré geometry, enabling better embedding of hierarchical data structures.

Findings

Better generalization to unseen data.

More accurate recovery of hierarchical structures.

Outperforms Euclidean VAEs in experiments.

Abstract

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. 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 Poincar\'e 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.