Analyzing the Posterior Collapse in Hierarchical Variational Autoencoders

Hierarchical Variational Autoencoders (VAEs) are among the most popular likelihood-based generative models. There is rather a consensus that the top-down hierarchical VAEs allow to effectively learn deep latent structures and avoid problems like the posterior collapse. Here, we show that it is not necessarily the case and the problem of collapsing posteriors remains. To discourage the posterior collapse, we propose a new deep hierarchical VAE with a partly fixed encoder, specifically, we use Discrete Cosine Transform to obtain top latent variables. In a series of experiments, we observe that the proposed modification allows us to achieve better utilization of the latent space. Further, we demonstrate that the proposed approach can be useful for compression and robustness to adversarial attacks.