When Is Unsupervised Disentanglement Possible?

A common assumption in many domains is that high dimensional data are a smooth nonlinear function of a small number of independent factors. When is it possible to recover the factors from unlabeled data? In the context of deep models this problem is called "disentanglement" and was recently shown to be impossible without additional strong assumptions [17, 19]. In this paper, we show that the assumption of local isometry together with non-Gaussianity of the factors, is sufficient to provably recover disentangled representations from data. We leverage recent advances in deep generative models to construct manifolds of highly realistic images for which the ground truth latent representation is known, and test whether modern and classical methods succeed in recovering the latent factors.