Equivariant Hamiltonian Flows

TL;DR

This paper presents equivariant Hamiltonian flows, a novel method for modeling data with known symmetries that enhances data efficiency and generalization by incorporating symmetry invariance into the learning process.

Contribution

It introduces equivariant Hamiltonian flows, demonstrating how to learn invariant densities and connect to disentangled representation learning.

Findings

Symmetry invariance improves data efficiency.

Equivariant flows can be learned with proof of concept demonstrations.

Connections to disentangled representation learning are established.

Abstract

This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the data. We provide proof of principle demonstrations of how such flows can be learnt, as well as how the addition of symmetry invariance constraints can improve data efficiency and generalisation. Finally, we make connections to disentangled representation learning and show how this work relates to a recently proposed definition.