Equivariant Manifold FlowsDownload PDF

Published: 15 Jun 2021, Last Modified: 22 Oct 2023INNF+ 2021 posterReaders: Everyone
Keywords: manifold, normalizing flow, equivariant, invariant
TL;DR: We construct manifold normalizing flows which are equivariant to isometric actions.
Abstract: Tractably modelling distributions over manifolds has long been an important goal in the natural sciences. Recent work has focused on developing general machine learning models to learn such distributions. However, for many applications these distributions must respect manifold symmetries---a trait which most previous models disregard. In this paper, we lay the theoretical foundations for learning symmetry-invariant distributions on arbitrary manifolds via equivariant manifold flows. We demonstrate the utility of our approach by using it to learn gauge invariant densities over SU(n) in the context of quantum field theory.
Community Implementations: [![CatalyzeX](/images/catalyzex_icon.svg) 1 code implementation](https://www.catalyzex.com/paper/arxiv:2107.08596/code)
4 Replies