Topographic VAEs learn Equivariant Capsules (Machine Learning Research Paper Explained)

#tvae #topographic #equivariant Variational Autoencoders model the latent space as a set of independent Gaussian random variables, which the decoder maps to a data distribution. However, this independence is not always desired, for example when dealing with video sequences, we know that successive frames are heavily correlated. Thus, any latent space dealing with such data should reflect this in its structure. Topographic VAEs are a framework for defining correlation structures among the latent variables and induce equivariance within the resulting model. This paper shows how such correlation structures can be built by correctly arranging higher-level variables, which are themselves independent Gaussians. OUTLINE: 0:00 - Intro 1:40 - Architecture Overview 6:30 - Comparison to regular VAEs 8:35 - Generative Mechanism Formulation 11:45 - Non-Gaussian Latent Space 17:30 - Topographic Product of Student-t 21:15 - Introducing Temporal Coherence 24:50 - Topographic VAE 27:50 - Experimental Results 31:15 - Conclus