A GAN that learns the Brenier potential using cubic-activation neural networks and a convexity penalty is shown to be statistically consistent, so the Jensen-Shannon distance from the generated to the target distribution can be made arbitrarily small.
Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations,
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Learning Brenier Potentials with Convex Generative Adversarial Neural Networks
A GAN that learns the Brenier potential using cubic-activation neural networks and a convexity penalty is shown to be statistically consistent, so the Jensen-Shannon distance from the generated to the target distribution can be made arbitrarily small.