Pulling back information geometry

• URL: http://arxiv.org/abs/2106.05367v1
• Date: Wed, 9 Jun 2021 20:16:28 GMT
• Title: Pulling back information geometry
• Authors: Georgios Arvanitidis, Miguel Gonz\'alez-Duque, Alison Pouplin, Dimitris Kalatzis, S{\o}ren Hauberg
• Abstract summary: We show that we can achieve meaningful latent geometries for a wide range of decoder distributions. We show that we can achieve meaningful latent geometries for a wide range of decoder distributions.
• Score: 3.0273878903284266
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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