We present Multi-chart flows, a flow-based model for concurrently learning topologically non-trivial manifolds and statistical densities on them. Current methods focus on manifolds that are topologically Euclidean, enforce strong structural priors on the learned models or use operations that do not scale to high dimensions. In contrast, our model learns the local manifold topology piecewise by "gluing" it back together through a collection of learned coordinate charts. We demonstrate the efficiency of our approach on synthetic data of known manifolds, as well as higher dimensional manifolds of unknown topology, where we show better sample efficiency and competitive or superior performance against current state-of-the-art.
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. * Equal contribution.Preprint. Under review.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.