Generalization and Equilibrium in Generative Adversarial Nets (GANs)

This paper makes progress on several open theoretical issues related to Generative Adversarial Networks. A definition is provided for what it means for the training to generalize, and it is shown that generalization is not guaranteed for the popular distances between distributions such as Jensen-Shannon or Wasserstein. We introduce a new metric called neural net distance for which generalization does occur. We also show that an approximate pure equilibrium in the 2-player game exists for a natural training objective (Wasserstein). Showing such a result has been an open problem (for any training objective). Finally, the above theoretical ideas lead us to propose a new training protocol, MIX+GAN, which can be combined with any existing method. We present experiments showing that it stabilizes and improves some existing methods.