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.
@article{arxiv.2106.05367,
title = {Pulling back information geometry},
author = {Georgios Arvanitidis and Miguel González-Duque and Alison Pouplin and Dimitris Kalatzis and Søren Hauberg},
journal= {arXiv preprint arXiv:2106.05367},
year = {2022}
}