  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.
