Commutativity and Disentanglement from the Manifold Perspective

In this paper, we interpret disentanglement from the manifold perspective and trace how it naturally leads to a necessary and sufficient condition for disentanglement: the disentangled factors must commute with each other. Along the way, we show how some technical results have consequences for the compression and disentanglement of generative models, and we also discuss the practical and theoretical implications of commutativity. Finally, we conclude with a discussion of related approaches to disentanglement and how they relate to our view of disentanglement from the manifold perspective.