Topographic VAE

Topographic VAE is a method for efficiently training deep generative models with topographically organized latent variables. The model learns sets of approximately equivariant features (i.e. "capsules") directly from sequences and achieves higher likelihood on correspondingly transforming test sequences. The combined color/rotation transformation in input space $\tau\_{g}$ becomes encoded as a $\mathrm{Roll}$ within the capsule dimension. The model is thus able decode unseen sequence elements by encoding a partial sequence and Rolling activations within the capsules. This resembles a commutative diagram.