Equivariant Hamiltonian Flows
This work addresses the challenge of incorporating symmetry constraints in density estimation for machine learning, offering incremental improvements in data efficiency and generalization.
The paper tackles the problem of learning expressive densities invariant to known symmetry transformations while providing equivariant data representations, demonstrating improved data efficiency and generalization through proof-of-principle experiments.
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.