Encoded Prior Sliced Wasserstein AutoEncoder for learning latent manifold representations

While variational autoencoders have been successful in several tasks, the use of conventional priors are limited in their ability to encode the underlying structure of input data. We introduce an Encoded Prior Sliced Wasserstein AutoEncoder wherein an additional prior-encoder network learns an embedding of the data manifold which preserves topological and geometric properties of the data, thus improving the structure of latent space. The autoencoder and prior-encoder networks are iteratively trained using the Sliced Wasserstein distance. The effectiveness of the learned manifold encoding is explored by traversing latent space through interpolations along geodesics which generate samples that lie on the data manifold and hence are more realistic compared to Euclidean interpolation. To this end, we introduce a graph-based algorithm for exploring the data manifold and interpolating along network-geodesics in latent space by maximizing the density of samples along the path while minimizing total energy. We use the 3D-spiral data to show that the prior encodes the geometry underlying the data unlike conventional autoencoders, and to demonstrate the exploration of the embedded data manifold through the network algorithm. We apply our framework to benchmarked image datasets to demonstrate the advantages of learning data representations in outlier generation, latent structure, and geodesic interpolation.