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.

翻译：在本文中,我们从多方面的角度解释分解问题,并追踪它如何自然地导致分解的必要和充分条件:分解的因素必须相互交织。 顺便说一下,我们展示一些技术结果如何对基因模型的压缩和分解产生影响,我们还讨论了同化的实际和理论影响。 最后,我们讨论了解解脱的相关方法,以及它们如何与我们从多重角度分解的观点相关。