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The generation of discontinuous distributions is a difficult task for mostknown frameworks such as generative autoencoders and generative adversarialnetworks. Generative non-invertible models are unable to accurately generatesuch distributions, require long training and often are subject to modecollapse. Variational autoencoders (VAEs), which are based on the idea ofkeeping the latent space to be Gaussian for the sake of a simple sampling,allow an accurate reconstruction, while they experience significant limitationsat generation task. In this work, instead of trying to keep the latent space tobe Gaussian, we use a pre-trained contrastive encoder to obtain a clusteredlatent space. Then, for each cluster, representing a unimodal submanifold, wetrain a dedicated low complexity network to generate this submanifold from theGaussian distribution. The proposed framework is based on theinformation-theoretic formulation of mutual information maximization betweenthe input data and latent space representation. We derive a link between thecost functions and the information-theoretic formulation. We apply our approachto synthetic 2D distributions to demonstrate both reconstruction and generationof discontinuous distributions using continuous stochastic networks.

Generation of data on discontinuous manifolds via continuous stochastic non-invertible networks