Equivariant Manifold Flows

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 learning quantum field theorymotivated invariant SU (n) densities and by correcting meteor impact dataset bias. * indicates equal contribution 1 SU (n) denotes the special unitary group SU (n) = X ∈ C n×n | X * X = I, det(X) = 1. 35th Conference on Neural Information Processing Systems (NeurIPS 2021).