Commutativity and Disentanglement from the Manifold Perspective

In this paper, we interpret disentanglement as the discovery of local charts and trace how that definition naturally leads to an equivalent condition for disentanglement: the disentangled factors must commute with each other. We discuss the practical and theoretical implications of commutativity, in particular the compression and disentanglement of generative models. Finally, we conclude with a discussion of related approaches to disentanglement and how they relate to our view of disentanglement from the manifold perspective.