Pulling back information geometry
Enables latent geometry analysis for non-Gaussian decoders in deep generative models, which is incremental but extends applicability.
The paper tackles the limitation of existing latent space geometry theory that only works with Gaussian decoders by proposing to use the Fisher-Rao metric from decoder distributions and pulling it back to latent space, achieving meaningful latent geometries for a wide range of decoder distributions.
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.