  Variational Autoencoders (VAEs) have been shown to be remarkably effective in
recovering model latent spaces for several computer vision tasks. However,
currently trained VAEs, for a number of reasons, seem to fall short in learning
invariant and equivariant clusters in latent space. Our work focuses on
providing solutions to this problem and presents an approach to disentangle
equivariance feature maps in a Lie group manifold by enforcing deep,
group-invariant learning. Simultaneously implementing a novel separation of
semantic and equivariant variables of the latent space representation, we
formulate a modified Evidence Lower BOund (ELBO) by using a mixture model pdf
like Gaussian mixtures for invariant cluster embeddings that allows superior
unsupervised variational clustering. Our experiments show that this model
effectively learns to disentangle the invariant and equivariant representations
with significant improvements in the learning rate and an observably superior
image recognition and canonical state reconstruction compared to the currently
best deep learning models.
