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 - Conclusion & Comments Paper: https://ift.tt/3tXsw93 Code: https://ift.tt/3Cv1XeC Abstract: In this work we seek to bridge the concepts of topographic organization and equivariance in neural networks. To accomplish this, we introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. Furthermore, through topographic organization over time (i.e. temporal coherence), we demonstrate how predefined latent space transformation operators can be encouraged for observed transformed input sequences -- a primitive form of unsupervised learned equivariance. We demonstrate that this model successfully learns sets of approximately equivariant features (i.e. "capsules") directly from sequences and achieves higher likelihood on correspondingly transforming test sequences. Equivariance is verified quantitatively by measuring the approximate commutativity of the inference network and the sequence transformations. Finally, we demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks. Authors: T. Anderson Keller, Max Welling Links: TabNine Code Completion (Referral): http://bit.ly/tabnine-yannick YouTube: https://www.youtube.com/c/yannickilcher Twitter: https://twitter.com/ykilcher Discord: https://ift.tt/3dJpBrR BitChute: https://ift.tt/38iX6OV Minds: https://ift.tt/37igBpB Parler: https://ift.tt/38tQU7C LinkedIn: https://ift.tt/3qcgOFy BiliBili: https://ift.tt/3mfyjkW If you want to support me, the best thing to do is to share out the content :) If you want to support me financially (completely optional and voluntary, but a lot of people have asked for this): SubscribeStar: https://ift.tt/2DuKOZ3 Patreon: https://ift.tt/390ewRH Bitcoin (BTC): bc1q49lsw3q325tr58ygf8sudx2dqfguclvngvy2cq Ethereum (ETH): 0x7ad3513E3B8f66799f507Aa7874b1B0eBC7F85e2 Litecoin (LTC): LQW2TRyKYetVC8WjFkhpPhtpbDM4Vw7r9m Monero (XMR): 4ACL8AGrEo5hAir8A9CeVrW8pEauWvnp1WnSDZxW7tziCDLhZAGsgzhRQABDnFy8yuM9fWJDviJPHKRjV4FWt19CJZN9D4n