  Generative Adversarial Networks (GANs), though powerful, is hard to train.
Several recent works (brock2016neural,miyato2018spectral) suggest that
controlling the spectra of weight matrices in the discriminator can
significantly improve the training of GANs. Motivated by their discovery, we
propose a new framework for training GANs, which allows more flexible spectrum
control (e.g., making the weight matrices of the discriminator have slow
singular value decays). Specifically, we propose a new reparameterization
approach for the weight matrices of the discriminator in GANs, which allows us
to directly manipulate the spectra of the weight matrices through various
regularizers and constraints, without intensively computing singular value
decompositions. Theoretically, we further show that the spectrum control
improves the generalization ability of GANs. Our experiments on CIFAR-10,
STL-10, and ImageNet datasets confirm that compared to other methods, our
proposed method is capable of generating images with competitive quality by
utilizing spectral normalization and encouraging the slow singular value decay.
