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

2019/01/17 by Émile Mathieu, Mathieu, Emile, Charline Le Lan +7 · 14 citations
Computer Science · #Generative Adversarial Networks and Image Synthesis #Image Processing and 3D Reconstruction #Computational Physics and Python Applications

paper · pdf · doi:10.48550/arxiv.1901.06033

Abstract

The variational auto-encoder (VAE) is a popular method for learning a\ngenerative model and embeddings of the data. Many real datasets are\nhierarchically structured. However, traditional VAEs map data in a Euclidean\nlatent space which cannot efficiently embed tree-like structures. Hyperbolic\nspaces with negative curvature can. We therefore endow VAEs with a Poincar 'e\nball model of hyperbolic geometry as a latent space and rigorously derive the\nnecessary methods to work with two main Gaussian generalisations on that space.\nWe empirically show better generalisation to unseen data than the Euclidean\ncounterpart, and can qualitatively and quantitatively better recover\nhierarchical structures.\n

Citations

• Auto-Encoding Variational Bayes

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