Abstract

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders DeltaVAE with arbitrary (closed) manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence.
We show that the DeltaVAE is indeed capable of capturing topological properties for datasets with a known underlying latent structure derived from generative processes such as rotations and translations.
Original languageEnglish
Publication statusAccepted/In press - 11 Jul 2020
Event29th International Joint Conference on Artificial Intelligence - 17th Pacific Rim International Conference on Artificial Intelligence. - Pacifico Convention Plaza Yokohama, Yokohama, Japan
Duration: 11 Jul 202017 Jul 2020
Conference number: 29
https://ijcai20.org/

Conference

Conference29th International Joint Conference on Artificial Intelligence - 17th Pacific Rim International Conference on Artificial Intelligence.
Abbreviated titleIJCAI-PRICAI 2020
CountryJapan
CityYokohama
Period11/07/2017/07/20
Internet address

Keywords

  • Brownian Movement
  • Topology
  • Deep learning

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  • Cite this

    Perez Rey, L. A., Menkovski, V., & Portegies, J. W. (Accepted/In press). Diffusion Variational Autoencoders. Paper presented at 29th International Joint Conference on Artificial Intelligence - 17th Pacific Rim International Conference on Artificial Intelligence., Yokohama, Japan.