  In this paper, we analyze the numerics of common algorithms for training
Generative Adversarial Networks (GANs). Using the formalism of smooth
two-player games we analyze the associated gradient vector field of GAN
training objectives. Our findings suggest that the convergence of current
algorithms suffers due to two factors: i) presence of eigenvalues of the
Jacobian of the gradient vector field with zero real-part, and ii) eigenvalues
with big imaginary part. Using these findings, we design a new algorithm that
overcomes some of these limitations and has better convergence properties.
Experimentally, we demonstrate its superiority on training common GAN
architectures and show convergence on GAN architectures that are known to be
notoriously hard to train.
