Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
This paper proposes a model for adversarial learning of the spiked covariance model. The proposed model is solvable in the high-dimensional limit, and this paper provides analysis of the dynamics of the proposed model, both in the macroscopic and microscopic levels. The macroscopic dynamics is represented by a set of ODEs as shown in Theorem 1, whereas the microscopic dynamics is described stochastically, in terms of the SDE (10). Local stability analysis of the macroscopic dynamics is also provided in Section 4, which shows that a proper level of background noise in the learning process can prevent oscillation and help stabilize the learning in some cases. The review scores are above the acceptance threshold. I feel that the model studied in this paper is not really a GAN in the usual sense of this term, because the common goal of GAN is generative modeling, i.e., to learn the (possibly complex) distribution from which real data are generated, whereas the generator in the model in general may not have capability of implementing a true data distribution. Nevertheless, all the reviewers agree that this paper contains nice contributions. They are also basically satisfied with the authors' rebuttal. I would therefore like to recommend acceptance of this paper.