Continuous Hierarchical Representations with Poincar\'e Variational Auto-Encoders
Machine Learning
2019-11-27 v3 Machine Learning
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.
Cite
@article{arxiv.1901.06033,
title = {Continuous Hierarchical Representations with Poincar\'e Variational Auto-Encoders},
author = {Emile Mathieu and Charline Le Lan and Chris J. Maddison and Ryota Tomioka and Yee Whye Teh},
journal= {arXiv preprint arXiv:1901.06033},
year = {2019}
}
Comments
Advances in Neural Information Processing Systems