Independent Subspace Analysis for Unsupervised Learning of Disentangled Representations

Recently there has been an increased interest in unsupervised learning of disentangled representations using the Variational Autoencoder (VAE) framework. Most of the existing work has focused largely on modifying the variational cost function to achieve this goal. We first show that these modifications, e.g. beta-VAE, simplify the tendency of variational inference to underfit, causing pathological over-pruning and over-orthogonalization of learned components. Second, we propose a complementary approach: to modify the probabilistic model with a structured latent prior. This prior discovers latent variable representations that are structured into a hierarchy of independent vector spaces. The proposed prior has three major advantages: First, in contrast to the standard VAE normal prior, the proposed prior is not rotationally invariant. This feature of our approach resolves the problem of unidentifiability of the standard VAE normal prior. Second, we demonstrate that the proposed prior encourages a disentangled latent representation which facilitates learning of disentangled representations. Third, extensive quantitative experiments demonstrate that the prior significantly mitigates the trade-off between reconstruction loss and disentanglement over the state of the art.