Equivariant Manifold Flows

Anonymous

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. Though these are significant advances, many problems require the learned distribution to obey symmetries inherent to the manifold. Up until now, the theory of invariant learning on manifolds was underdeveloped—models were unable to incorporate these symmetries while learning. In this paper, we lay the theoretical foundations for learning symmetry invariant distributions on arbitrary manifolds via equivariant manifold flows. We demonstrate the efficacy of our approach in the context of quantum field theory in learning gauge invariant densities over SU(n).

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2107.08596/code)