GANs have been very popular in data generation and unsupervised learning, but our understanding of GAN training is still very limited. One major reason is that GANs are often formulated as non-convex-concave min-max optimization. As a result, most recent studies focused on the analysis in the local region around the equilibrium. In this work, we perform a global analysis of GANs from two perspectives: the global landscape of the outer-optimization problem and the global behavior of the gradient descent dynamics. We find that the original GAN has exponentially many bad strict local minima which are perceived as mode-collapse, and the training dynamics (with linear discriminators) cannot escape mode collapse. To address these issues, we propose a simple modification to the original GAN, by coupling the generated samples and the true samples. We prove that the new formulation has no bad basins, and its training dynamics (with linear discriminators) has a Lyapunov function that leads to global convergence. Our experiments on standard datasets show that this simple loss outperforms the original GAN and WGAN-GP.
In this paper, the authors introduce a new training loss for GANs.  This loss allows the outer optimization problem to have no spurious local minima, under an appropriate finite sample analysis.  In contrast, the authors establish that there are exponentially many spurious local minima under the conventional GAN training loss.  Under a linear discriminator model, the authors show that a standard GAN can not escape from collapsed modes in a finite sample analysis, whereas the new trining loss allows for such an escape (due to the presence of a Lyapunov functional with favorable properties).  The authors use this new training loss to train GANS on MNIST, CIFAR10, CelebA, and LSUN datasets, and observe mild improvements in Inception Scores and Frechet Inception Distances of the resulting generated images.
I recommend the paper be accepted because it provides a new formulation for training GANs that both demonstrates improved empirical performance while also allowing theoretically favorable properties (on spurious local minima and avoidance of mode collapse) that specifically do not hold for a standard GAN.
The primary question I am left with after reading the paper is: is there a probabilistic interpretation of the new loss function (equation 4a).  The authors justify this formulation because it allows analysis via Lyapunov functions, but it would be very useful to know if it itself is the maximum likelihood estimate under an alternate data model.  Such an explanation would improve the understandability of this method.
Minor comment: 
The fourth bullet point under the contributions section should specific the sense in which the new GAN "performs better"