CKGAN: Training Generative Adversarial Networks Using Characteristic Kernel Integral Probability Metrics

TL;DR

CKGAN introduces CKIPM, an IPM-based GAN framework where a characteristic-kernel-based distance $d_{\mathscr{F}}(\mathbb{P},\mathbb{Q})$ provides a lower bound to MMD in an RKHS and guides adversarial training. By mapping generated samples back toward random noise and employing a soft, learnable combination of kernels, CKGAN mitigates mode collapse and adapts to data specifics without manual kernel tuning. Empirical results on synthetic and real image datasets show CKGAN and especially its automatically learned kernel $k^{lc}$ outperform or closely approach manually tuned kernel variants, with improved FID/IS and reasonable training overhead. The kernel-learning strategy also benefits other MMD-based GANs, offering a practical path to high-order distribution matching in image synthesis tasks.

Abstract

In this paper, we propose CKGAN, a novel generative adversarial network (GAN) variant based on an integral probability metrics framework with characteristic kernel (CKIPM). CKIPM, as a distance between two probability distributions, is designed to optimize the lowerbound of the maximum mean discrepancy (MMD) in a reproducing kernel Hilbert space, and thus can be used to train GANs. CKGAN mitigates the notorious problem of mode collapse by mapping the generated images back to random noise. To save the effort of selecting the kernel function manually, we propose a soft selection method to automatically learn a characteristic kernel function. The experimental evaluation conducted on a set of synthetic and real image benchmarks (MNIST, CelebA, etc.) demonstrates that CKGAN generally outperforms other MMD-based GANs. The results also show that at the cost of moderately more training time, the automatically selected kernel function delivers very close performance to the best of manually fine-tuned one on real image benchmarks and is able to improve the performances of other MMD-based GANs.

Figures (10)

• Figure 1: Density plots of target distribution (real data) and distributions generated by GAN variants.
• Figure 2: Randomly generated samples by GAN variants on CelebA.
• Figure 3: ResBlock architecture. We removed the BN layers in ResBlock for the discriminator, like miyato2018spectral.
• Figure 4: Density plots of generated distributions by GAN variants using a relatively simple architecture.
• Figure 5: Randomly generated samples by CKGAN on MNIST.