Relaxed-Responsibility Hierarchical Discrete VAEs

Successfully training Variational Autoencoders (VAEs) with a hierarchy of discrete latent variables remains an area of active research. Leveraging insights from classical methods of inference we introduce $\textit{Relaxed-Responsibility Vector-Quantisation}$, a novel way to parameterise discrete latent variables, a refinement of relaxed Vector-Quantisation. This enables a novel approach to hierarchical discrete variational autoencoder with numerous layers of latent variables that we train end-to-end. Unlike discrete VAEs with a single layer of latent variables, we can produce realistic-looking samples by ancestral sampling: it is not essential to train a second generative model over the learnt latent representations to then sample from and then decode. Further, we observe different layers of our model become associated with different aspects of the data.