  Recent work demonstrated the benefits of studying continuous-time dynamics
governing the GAN training. However, this dynamics is analyzed in the model
parameter space, which results in finite-dimensional dynamical systems. We
propose a novel perspective where we study the local dynamics of adversarial
training in the general functional space and show how it can be represented as
a system of partial differential equations. Thus, the convergence properties
can be inferred from the eigenvalues of the resulting differential operator. We
show that these eigenvalues can be efficiently estimated from the target
dataset before training. Our perspective reveals several insights on the
practical tricks commonly used to stabilize GANs, such as gradient penalty,
data augmentation, and advanced integration schemes. As an immediate practical
benefit, we demonstrate how one can a priori select an optimal data
augmentation strategy for a particular generation task.
