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Variational Autoencoders with Riemannian Brownian Motion Priors
Dimitris Kalatzis · David Eklund · Georgios Arvanitidis · Søren Hauberg

Thu Jul 16 02:00 PM -- 02:45 PM & Fri Jul 17 03:00 AM -- 03:45 AM (PDT) @

Variational Autoencoders (VAEs) represent the given data in a low-dimensional latent space, which is generally assumed to be Euclidean. This assumption naturally leads to the common choice of a standard Gaussian prior over continuous latent variables. Recent work has, however, shown that this prior has a detrimental effect on model capacity, leading to subpar performance. We propose that the Euclidean assumption lies at the heart of this failure mode. To counter this, we assume a Riemannian structure over the latent space, which constitutes a more principled geometric view of the latent codes, and replace the standard Gaussian prior with a Riemannian Brownian motion prior. We propose an efficient inference scheme that does not rely on the unknown normalizing factor of this prior. Finally, we demonstrate that this prior significantly increases model capacity using only one additional scalar parameter.

Author Information

Dimitris Kalatzis (Technical University of Denmark)
David Eklund (Research Institutes of Sweden)
Georgios Arvanitidis (MPI for Intelligent Systems, Tübingen)
Søren Hauberg (Technical University of Denmark)

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