Pulling back information geometry
Georgios Arvanitidis, Miguel González-Duque, Alison Pouplin, Dimitrios Kalatzis, Soren Hauberg
Abstract
Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, relies on the decoder being a Gaussian distribution as its simple reparametrization allows us to interpret the generating process as a random projection of a deterministic manifold. Consequently, this approach breaks down when applied to decoders that are not as easily reparametrized. We here propose to use the Fisher-Rao metric associated with the space of decoder distributions as a reference metric, which we pull back to the latent space. We show that we can achieve meaningful latent geometries for a wide range of decoder distributions for which the previous theory was not applicable, opening the door to ’black box’ latent geometries.
BibTeX
@InProceedings{pmlr-v151-arvanitidis22b,
title = { Pulling back information geometry },
author = {Arvanitidis, Georgios and Gonz\'alez-Duque, Miguel and Pouplin, Alison and Kalatzis, Dimitrios and Hauberg, Soren},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {4872--4894},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/arvanitidis22b/arvanitidis22b.pdf},
url = {https://proceedings.mlr.press/v151/arvanitidis22b.html},
abstract = { Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, relies on the decoder being a Gaussian distribution as its simple reparametrization allows us to interpret the generating process as a random projection of a deterministic manifold. Consequently, this approach breaks down when applied to decoders that are not as easily reparametrized. We here propose to use the Fisher-Rao metric associated with the space of decoder distributions as a reference metric, which we pull back to the latent space. We show that we can achieve meaningful latent geometries for a wide range of decoder distributions for which the previous theory was not applicable, opening the door to ’black box’ latent geometries. }
}