Geometric Inductive Biases for Identifiable Unsupervised Learning of Disentangled Representations

The model identifiability is a considerable issue in the unsupervised learning of disentangled representations. The PCA inductive biases revealed recently for unsupervised disentangling in VAE-based models are shown to improve local alignment of latent dimensions with principal components of the data. In this paper, in additional to the PCA inductive biases, we propose novel geometric inductive biases from the manifold perspective for unsupervised disentangling, which induce the model to capture the global geometric properties of the data manifold with guaranteed model identifiability. We also propose a Geometric Disentangling Regularized AutoEncoder (GDRAE) that combines the PCA and the proposed geometric inductive biases in one unified framework. The experimental results show the usefulness of the geometric inductive biases in unsupervised disentangling and the effectiveness of our GDRAE in capturing the geometric inductive biases.