The Polarised Regime of Variational Autoencoders

Variational Autoencoders ( VAEs ) learn in a polarised regime, a sparsity-enforcing regime where a subset of latent representations (the active variables) are used for reconstruction while the others (the passive variables) are ignored by the decoder. While this regime is well-studied for "standard" VAEs given a single data example, a more general analysis of its properties and impact is lacking. This work extends the polarised regime to a larger family of VAEs (including identifiable VAEs ) and to multiple data examples. After analysing the properties of this extended version, we prove that latent representations of different models learned in a polarised regime have the same number of active and passive variables when they have a high representational similarity. We further show that the polarised regime can be used to explain discrepancies between mean and sampled representations and predict a good number of latent dimensions for VAEs and deterministic Autoencoders ( AEs ). Overall, we demonstrate that the polarised regime is a valuable tool which can be used to assess, explain, and improve the quality of the latent representations learned by VAEs.