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While variational autoencoders have been successful in several tasks, the useof conventional priors are limited in their ability to encode the underlyingstructure of input data. We introduce an Encoded Prior Sliced WassersteinAutoEncoder wherein an additional prior-encoder network learns an embedding ofthe data manifold which preserves topological and geometric properties of thedata, thus improving the structure of latent space. The autoencoder andprior-encoder networks are iteratively trained using the Sliced Wassersteindistance. The effectiveness of the learned manifold encoding is explored bytraversing latent space through interpolations along geodesics which generatesamples that lie on the data manifold and hence are more realistic compared toEuclidean interpolation. To this end, we introduce a graph-based algorithm forexploring the data manifold and interpolating along network-geodesics in latentspace by maximizing the density of samples along the path while minimizingtotal energy. We use the 3D-spiral data to show that the prior encodes thegeometry underlying the data unlike conventional autoencoders, and todemonstrate the exploration of the embedded data manifold through the networkalgorithm. We apply our framework to benchmarked image datasets to demonstratethe advantages of learning data representations in outlier generation, latentstructure, and geodesic interpolation.

Encoded Prior Sliced Wasserstein AutoEncoder for learning latent manifold representations