Neural Stability Enhancement Through Dynamic Lipschitz Constraints in Generative Adversarial Networks

Abstract

Generative Adversarial Networks (GANs) are widely used for generative modeling in neural networks, yet their practical use is hindered by training instability and mode collapse. Existing stabilization approaches predominantly rely on enforcing fixed 1-Lipschitz constraints on the discriminator through techniques such as gradient penalty, spectral normalization, and gradient normalization. However, these methods fail to account for the dynamic nature of neural network training, where the appropriate Lipschitz constant target may vary with evolving system dynamics. This work challenges the conventional fixed-constraint paradigm by formalizing how the effective constraint strength and a bound-implied Lipschitz constant target can depend on architecture and training state. We provide theoretical analysis to motivate adaptive Lipschitz constraint control and introduce Adaptive Lipschitz Constraint (ALC), a modular mechanism that adjusts the Lipschitz constant target rather than introducing another standalone regularization term. Experiments across multiple stable GAN architectures show improvements in generation quality and training stability in several evaluated settings. Our contributions advance the understanding of neural system stability in adversarial learning and provide a practical approach to adaptive Lipschitz constraint control in adversarial objectives.