Equivariant Manifold Flows
This work addresses the need for symmetry-invariant distribution modeling in fields like quantum field theory, representing a novel method for a known bottleneck.
The paper tackled the problem of modeling distributions over manifolds that respect symmetries, which previous models often disregarded, by developing equivariant manifold flows and demonstrated its utility by learning gauge invariant densities over SU(n) in quantum field theory.
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.