Coulomb Autoencoders.

Learning the true density in high-dimensional feature spaces is a well-known problem in machine learning. In this work, we improve the recent Wasserstein autoencoders (WAEs) by proposing Coulomb autoencoders. We demonstrate that a source of sub-optimality in WAEs is the choice of kernel function, because of the additional local minima in the objective. To mitigate this problem, we propose to use Coulomb kernels. We show that, under some conditions on the capacity of the encoder and the decoder, global convergence in the function space can be achieved. Finally, we provide an upper bound on the generalization performance, which can be improved by increasing the capacity of the encoder and the decoder networks. The theory is corroborated by experimental comparisons on synthetic and real-world datasets against several approaches from the families of generative adversarial networks and autoencoder-based models.