A New Formulation of Lipschitz Constrained With Functional Gradient Learning for GANs

This paper introduces a promising alternative method for training Generative Adversarial Networks (GANs) on large-scale datasets with clear theoretical guarantees. GANs are typically learned through a minimax game between a generator and a discriminator, which is known to be empirically unstable. Previous learning paradigms have encountered mode collapse issues without a theoretical solution. To address these challenges, we propose a novel Lipschitz-constrained Functional Gradient GANs learning (Li-CFG) method to stabilize the training of GAN and provide a theoretical foundation for effectively increasing the diversity of synthetic samples by reducing the neighborhood size of the latent vector. Specifically, we demonstrate that the neighborhood size of the latent vector can be reduced by increasing the norm of the discriminator gradient, resulting in enhanced diversity of synthetic samples. To efficiently enlarge the norm of the discriminator gradient, we introduce a novel {\epsilon}-centered gradient penalty that amplifies the norm of the discriminator gradient using the hyper-parameter {\epsilon}. In comparison to other constraints, our method enlarging the discriminator norm, thus obtaining the smallest neighborhood size of the latent vector. Extensive experiments on benchmark datasets for image generation demonstrate the efficacy of the Li-CFG method and the {\epsilon}-centered gradient penalty. The results showcase improved stability and increased diversity of synthetic samples.

Nested Annealed Training Scheme for Generative Adversarial Networks

Recently, researchers have proposed many deep generative models, including generative adversarial networks(GANs) and denoising diffusion models. Although significant breakthroughs have been made and empirical success has been achieved with the GAN, its mathematical underpinnings remain relatively unknown. This paper focuses on a rigorous mathematical theoretical framework: the composite-functional-gradient GAN (CFG)[1]. Specifically, we reveal the theoretical connection between the CFG model and score-based models. We find that the training objective of the CFG discriminator is equivalent to finding an optimal D(x). The optimal gradient of D(x) differentiates the integral of the differences between the score functions of real and synthesized samples. Conversely, training the CFG generator involves finding an optimal G(x) that minimizes this difference. In this paper, we aim to derive an annealed weight preceding the weight of the CFG discriminator. This new explicit theoretical explanation model is called the annealed CFG method. To overcome the limitation of the annealed CFG method, as the method is not readily applicable to the SOTA GAN model, we propose a nested annealed training scheme (NATS). This scheme keeps the annealed weight from the CFG method and can be seamlessly adapted to various GAN models, no matter their structural, loss, or regularization differences. We conduct thorough experimental evaluations on various benchmark datasets for image generation. The results show that our annealed CFG and NATS methods significantly improve the quality and diversity of the synthesized samples. This improvement is clear when comparing the CFG method and the SOTA GAN models.