  Generative adversarial networks (GANs) are a family of generative models that
do not minimize a single training criterion. Unlike other generative models,
the data distribution is learned via a game between a generator (the generative
model) and a discriminator (a teacher providing training signal) that each
minimize their own cost. GANs are designed to reach a Nash equilibrium at which
each player cannot reduce their cost without changing the other players'
parameters. One useful approach for the theory of GANs is to show that a
divergence between the training distribution and the model distribution obtains
its minimum value at equilibrium. Several recent research directions have been
motivated by the idea that this divergence is the primary guide for the
learning process and that every step of learning should decrease the
divergence. We show that this view is overly restrictive. During GAN training,
the discriminator provides learning signal in situations where the gradients of
the divergences between distributions would not be useful. We provide empirical
counterexamples to the view of GAN training as divergence minimization.
Specifically, we demonstrate that GANs are able to learn distributions in
situations where the divergence minimization point of view predicts they would
fail. We also show that gradient penalties motivated from the divergence
minimization perspective are equally helpful when applied in other contexts in
which the divergence minimization perspective does not predict they would be
helpful. This contributes to a growing body of evidence that GAN training may
be more usefully viewed as approaching Nash equilibria via trajectories that do
not necessarily minimize a specific divergence at each step.
