Equivariant Manifold Flows

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

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

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Code: https://github.com/CUAI/Equivariant-Manifold-Flows

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