AR-ELBO: Preventing Posterior Collapse Induced by Oversmoothing in Gaussian VAE

Variational autoencoders (VAEs) often suffer from posterior collapse, which is a phenomenon that the learned latent space becomes uninformative. This is related to local optima introduced by a fixed hyperparameter resembling the data variance in the objective function. We suggest that this variance parameter regularizes the VAE and affects its smoothness, which is the magnitude of its gradient. An inappropriate choice of this parameter causes oversmoothness and leads to posterior collapse. This is shown theoretically by analysis on the linear approximated objective function and empirically in general cases. We propose AR-ELBO, which stands for adaptively regularized ELBO~(Evidence Lower BOund). It controls the strength of regularization by adapting the variance parameter, and thus avoids oversmoothing the model. Generation models trained by proposed objectives show improved Frechet inception distance~(FID) of images generated from the MNIST and CelebA datasets.