Reviews: Gradient descent GAN optimization is locally stable

The authors present a dynamical system based analysis of simultaneous gradient descent updates for GANs, by considering the limit dynamical system that corresponds to the discrete updates. They show that under a series of assumptions, an equilibrium point of the dynamical system is locally asymptotically stable, implying convergence to the equilibrium if the system is initialized in a close neighborhood of it. Then they show how some types of GANs fail to satisfy some of their conditions and propose a fix to the gradient updates that re-instate local stability. They give experimental evidence that the local-stability inspired fix yields improvements in practice on MNIST digit generation and simple multi-modal distributions. However, I do think that these drawbacks are remedied by the fact that their modification, based on local asymptotic theory, did give noticeable improvements.