  Self-supervised (SS) learning is a powerful approach for representation
learning using unlabeled data. Recently, it has been applied to Generative
Adversarial Networks (GAN) training. Specifically, SS tasks were proposed to
address the catastrophic forgetting issue in the GAN discriminator. In this
work, we perform an in-depth analysis to understand how SS tasks interact with
learning of generator. From the analysis, we identify issues of SS tasks which
allow a severely mode-collapsed generator to excel the SS tasks. To address the
issues, we propose new SS tasks based on a multi-class minimax game. The
competition between our proposed SS tasks in the game encourages the generator
to learn the data distribution and generate diverse samples. We provide both
theoretical and empirical analysis to support that our proposed SS tasks have
better convergence property. We conduct experiments to incorporate our proposed
SS tasks into two different GAN baseline models. Our approach establishes
state-of-the-art FID scores on CIFAR-10, CIFAR-100, STL-10, CelebA, Imagenet
$32\times32$ and Stacked-MNIST datasets, outperforming existing works by
considerable margins in some cases. Our unconditional GAN model approaches
performance of conditional GAN without using labeled data. Our code:
https://github.com/tntrung/msgan
