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.
@article{arxiv.2107.08596,
title = {Equivariant Manifold Flows},
author = {Isay Katsman and Aaron Lou and Derek Lim and Qingxuan Jiang and Ser-Nam Lim and Christopher De Sa},
journal= {arXiv preprint arXiv:2107.08596},
year = {2022}
}