Multi-chart flows.
Year: 2021
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institution: Technical University of Denmark
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3167427103