Training generative adversarial networks is unstable in high-dimensions as the true data distribution tends to be concentrated in a small fraction of the ambient space. The discriminator is then quickly able to classify nearly all generated samples as fake, leaving the generator without meaningful gradients and causing it to deteriorate after a point in training. In this work, we propose training a single generator simultaneously against an array of discriminators, each of which looks at a different random low-dimensional projection of the data. Individual discriminators, now provided with restricted views of the input, are unable to reject generated samples perfectly and continue to provide meaningful gradients to the generator throughout training. Meanwhile, the generator learns to produce samples consistent with the full data distribution to satisfy all discriminators simultaneously. We demonstrate the practical utility of this approach experimentally, and show that it is able to produce image samples with higher quality than traditional training with a single discriminator.
The paper proposes to stabilize GAN training by using an ensemble of discriminators, each workin on a random projection of the input data, to provide the training signal for the generator model.
Q1: “In relation to “Theorem 3.1. … will produce samples from a distribution whose marginals along each of the projections W_k match those of the true distribution”.. I presume an infinite number of generator distributions could give rise to the correct marginals however not necessarily be converged to the data distribution. In Theorem A.2 the authors upperbound this residual as a function of the smoothness and support of the distributions as well as the projections presented to the discriminators. Can the authors comment on how tight this bound is e.g. as a function the number of used discriminators or the choosen projection methods ? 
Q2: Related to the above. Did the authors do or considered any frequency analysis of the ensemble of random projection? I guess you could easily do a numeric simulation of the expected frequency spectrum of the combined set discriminators?
Q3: My primary concern with the work is the above mentioned computational complexity of running K discriminators in parallel. This is especially in relation to the experimental results showing significant high-frequency artefacts when running with K=12 classifiers (K=12 celebA results and “Random Imagenet-Canine Images: Proposed Method” in suplementary results). I think this is as expected as the authors are effectively fitting each classifier to the distributions of smoothed  (with 8x8 random kernel)  subsampled version of the input image. I would expect that each discriminator sees none or only a very limited amount  the high frequency component in the images.  Do the authors have any comments on how the sampling of the projection kernels affects the image results especially if the number of needed classifiers can be reduced somehow? I would expect that a combination of smoothing and high frequency filters would be needed to remove the high frequency artefacts?
Q4: Whats the explanation of the oscilating patterns in figure 2?
Q5: In the conclusion the authors mention that their framework is currently limited by the computational of running K discriminators and proposes:
“In our current framework, the number of discriminators is limited by computational cost. In future work, we plan to investigate training with a much larger set of discriminators, employing only a small subset of them at each iteration, or every set of iterations”
In the extreme case of only using a single randomly discriminator the approach is quite similar to the quite widely used input dropout to the discriminator?
Overall I like the simplicity of the proposed idea. However i’m not completely convinced that the “marginal” convergence proof holds for the relative low number of discriminators possible to use in practice. At least i would like the authors to touch on this key aspect of the method both theoretically and with experiments/simulations. Also several other methods have recently been proposed to improve stability of GANs, however no experimental comparisons is made with these methods (WGAN, EGAN, LSGAN etc.)