Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders

Emile Mathieu, Charline Le Lan, Chris J. Maddison, Ryota Tomioka, Yee Whye Teh
1/17/2019
stat.MLcs.LG

Official code: emilemathieu/pvae (133 stars, MIT, PyTorch, last commit 2023-10-03).

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 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.

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Code Implementations(1)

emilemathieu/pvaeOfficial100%
PyTorchMIT

code for "Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders".

13344PythonApr 23, 20193 years agoMIT
hierarchical-datahyperbolic-geometrypoincare-embeddingspytorchvae

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Cite this paper

@article{mathieu2019continuous,
  title  = {Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders},
  author = {Emile Mathieu and Charline Le Lan and Chris J. Maddison and Ryota Tomioka and Yee Whye Teh},
  year   = {2019},
  eprint = {1901.06033},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1901.06033}
}

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