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Variational Autoencoders (VAEs) have been shown to be remarkably effective inrecovering model latent spaces for several computer vision tasks. However,currently trained VAEs, for a number of reasons, seem to fall short in learninginvariant and equivariant clusters in latent space. Our work focuses onproviding solutions to this problem and presents an approach to disentangleequivariance feature maps in a Lie group manifold by enforcing deep,group-invariant learning. Simultaneously implementing a novel separation ofsemantic and equivariant variables of the latent space representation, weformulate a modified Evidence Lower BOund (ELBO) by using a mixture model pdflike Gaussian mixtures for invariant cluster embeddings that allows superiorunsupervised variational clustering. Our experiments show that this modeleffectively learns to disentangle the invariant and equivariant representationswith significant improvements in the learning rate and an observably superiorimage recognition and canonical state reconstruction compared to the currentlybest deep learning models.

Invariance-based Multi-Clustering of Latent Space Embeddings for Equivariant Learning