Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders
This addresses the inefficiency of Euclidean latent spaces in capturing tree-like structures for datasets with hierarchical organization, representing an incremental improvement in generative modeling.
The authors tackled the problem of embedding hierarchically structured data in variational auto-encoders by using a Poincaré ball model of hyperbolic geometry as the latent space, resulting in better generalization to unseen data and improved recovery of hierarchical structures compared to Euclidean counterparts.
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 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.