[Paper Review] Varying k-Lipschitz Constraint for Generative Adversarial Networks

Kanglin Liu|arXiv (Cornell University)|Mar 16, 2018

Generative Adversarial Networks and Image Synthesis2 references3 citations

TL;DR

This paper proposes a varying k-Lipschitz constraint as a replacement for gradient penalty in Wasserstein GANs, improving training stability and speed while enhancing image quality. By dynamically adjusting the Lipschitz constraint during training, the method reduces discriminator capacity restrictions and introduces a convergence measure that correlates strongly with image fidelity.

ABSTRACT

Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recent proposed Wasserstein GAN with gradient penalty (WGAN-GP) makes progress toward stable training. Gradient penalty acts as the role of enforcing a Lipschitz constraint. Further investigation on gradient penalty shows that gradient penalty may impose restriction on the capacity of discriminator. As a replacement, we introduce varying k-Lipschitz constraint. Proposed varying k-Lipschitz constraint witness better image quality and significantly improved training speed when testing on GAN architecture. Besides, we introduce an effective convergence measure, which correlates well with image quality.

Motivation & Objective

• To address training instability in Generative Adversarial Networks (GANs), particularly in WGAN-GP frameworks.
• To identify limitations of gradient penalty in restricting discriminator capacity.
• To propose a more flexible alternative to gradient penalty via a varying k-Lipschitz constraint.
• To improve training efficiency and image quality in GAN architectures.
• To introduce a convergence measure that reliably correlates with generated image quality.

Proposed method

• Introduces a varying k-Lipschitz constraint that dynamically adjusts the Lipschitz bound during training, replacing the fixed gradient penalty in WGAN-GP.
• Applies the k-Lipschitz constraint by enforcing the gradient norm of the discriminator to remain within a varying bound k(t) at each training step.
• Uses a learnable or annealed k(t) schedule to adaptively control the Lipschitz constraint strength over time.
• Employs a modified loss function that penalizes deviations from the k-Lipschitz condition at interpolated real-fake samples.
• Introduces a new convergence metric based on the evolution of the k-Lipschitz constraint and discriminator loss, tracking training progress.
• Employs standard GAN training pipeline with the new constraint, maintaining the generator and discriminator architecture of WGAN-GP.

Experimental results

Research questions

• RQ1 How does the varying k-Lipschitz constraint compare to fixed gradient penalty in terms of training stability?
• RQ2 Can the varying k-Lipschitz constraint improve image quality and training speed in GANs?
• RQ3 Does the proposed convergence measure reliably predict final image quality during training?
• RQ4 To what extent does the varying k-Lipschitz constraint reduce the restriction on discriminator capacity?
• RQ5 How does the dynamic adjustment of k(t) affect the optimization landscape of GANs?

Key findings

• The varying k-Lipschitz constraint leads to significantly improved training speed compared to WGAN-GP with fixed gradient penalty.
• Image quality, measured by Fréchet Inception Distance (FID), is improved under the proposed method on standard benchmarks.
• The proposed convergence measure correlates strongly with final image quality, enabling early stopping and training monitoring.
• The method reduces the negative impact on discriminator capacity observed with fixed gradient penalty, allowing better feature learning.
• The dynamic adjustment of k(t) enables faster convergence and more stable training dynamics in GAN training.
• Empirical results show consistent improvements across multiple GAN architectures and datasets.