This paper addresses the ability of generative adversarial networks (GANs) to model complex distributions of data in high-dimensional spaces. Our proposition is that the more effective the adversary is in discriminating the output of the generator, the more effective the generator will be at modeling (or generating) the distribution represented by the training data. The most extreme failure of GANs in this context is mode collapse, and there are several proposed methods to address that problem. However, mode collapse is merely a symptom of a more general problem of GANs, where the generator fools the adversary while failing to faithfully model the distribution of the training data. Here, we address the challenge of constructing and evaluating GANs that more effectively represent the input distribution. We introduce an adversarial architecture that processes sets of generated and real samples, and discriminates between the origins of these sets (i.e., training versus generated data) in a flexible, permutation invariant manner. We present quantitative and qualitative results that demonstrate the effectiveness of this approach relative to state-of-the-art methods for avoiding mode collapse.
In recent years, several training strategies have been proposed to mitigate model collapse in GANs. Metz @cite_0 , for instance, modified the training strategy, such that at each gradient update step @math , the generator's update is computed based on the discriminator's state at step @math to match those that the optimal discriminator would allow. This strategy stabilizes GAN training and decreases mode collapse, but it significantly increases the computational complexity of each update step, as the discriminator calculates derivatives @math times more than the vanilla GAN. Other strategies modify the GAN's loss function and network architecture. For instance, Zhao @cite_18 proposed a nonstochastic alternative loss and an autoencoder-like architecture for the discriminator to learn the manifold of the training data.
@cite_0 @cite_18
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Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the Frechet Inception Distance'' (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark. Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the "Frechet Inception Distance" (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.