C$^2$VAE: Gaussian Copula-based VAE Differing Disentangled from Coupled
  Representations with Contrastive Posterior
Zhangkai Wu Longbing Cao
We present a self-supervised variational autoencoder (VAE) to jointly learn
disentangled and dependent hidden factors and then enhance disentangled
representation learning by a self-supervised classifier to eliminate coupled
representations in a contrastive manner. To this end, a Contrastive Copula VAE
(C$^2$VAE) is introduced without relying on prior knowledge about data in the
probabilistic principle and involving strong modeling assumptions on the
posterior in the neural architecture. C$^2$VAE simultaneously factorizes the
posterior (evidence lower bound, ELBO) with total correlation (TC)-driven
decomposition for learning factorized disentangled representations and extracts
the dependencies between hidden features by a neural Gaussian copula for copula
coupled representations. Then, a self-supervised contrastive classifier
differentiates the disentangled representations from the coupled
representations, where a contrastive loss regularizes this contrastive
classification together with the TC loss for eliminating entangled factors and
strengthening disentangled representations. C$^2$VAE demonstrates a strong
effect in enhancing disentangled representation learning. C$^2$VAE further
contributes to improved optimization addressing the TC-based VAE instability
and the trade-off between reconstruction and representation.