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.
|Title of host publication||Proceedings of the 37th International Conference on Machine Learning|
|Editors||Hal Daume, Aarti Singh|
|Publisher||International Machine Learning Society (IMLS)|
|Publication status||Published - 2020|
|Event||37th International Conference on Machine Learning - Virtual event, Virtual, Online|
Duration: 13 Jul 2020 → 18 Jul 2020
|Conference||37th International Conference on Machine Learning|
|Period||13/07/2020 → 18/07/2020|
Bibliographical noteFunding Information:
SH and DE were supported by a research grant (15334) from VILLUM FONDEN. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no 757360). We gratefully acknowledge the support of the NVIDIA Corporation with the donation of GPU hardware.
© 2020 by the Authors.