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.

翻译：本文从流形视角将解耦解释为局部坐标系的发现，并追溯该定义如何自然导出解耦的等价条件：解耦因子必须相互交换。我们讨论了交换性的实践与理论意义，特别是生成模型中的压缩与解耦问题。最后，我们探讨了与解耦相关的现有方法，以及它们与我们基于流形视角的解耦观点之间的关系。