Equivariant Manifold Flows

Part of Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)

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Authors

Isay Katsman, Aaron Lou, Derek Lim, Qingxuan Jiang, Ser Nam Lim, Christopher M. De Sa

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 learning quantum field theory-motivated invariant SU(n) densities and by correcting meteor impact dataset bias.