Cumulant GAN
This work addresses stability and performance issues in GAN training for image generation, offering a partially unified theoretical perspective, but it is incremental as it builds on existing GAN frameworks.
The paper tackles the problem of training Generative Adversarial Networks (GANs) by proposing a novel loss function based on cumulant generating functions, called Cumulant GAN, which improves stability and performance, with experimental results showing enhanced image generation robustness and substantial gains in inception score and Fréchet inception distance compared to Wasserstein GAN.
In this paper, we propose a novel loss function for training Generative Adversarial Networks (GANs) aiming towards deeper theoretical understanding as well as improved stability and performance for the underlying optimization problem. The new loss function is based on cumulant generating functions giving rise to \emph{Cumulant GAN}. Relying on a recently-derived variational formula, we show that the corresponding optimization problem is equivalent to R{é}nyi divergence minimization, thus offering a (partially) unified perspective of GAN losses: the R{é}nyi family encompasses Kullback-Leibler divergence (KLD), reverse KLD, Hellinger distance and $χ^2$-divergence. Wasserstein GAN is also a member of cumulant GAN. In terms of stability, we rigorously prove the linear convergence of cumulant GAN to the Nash equilibrium for a linear discriminator, Gaussian distributions and the standard gradient descent ascent algorithm. Finally, we experimentally demonstrate that image generation is more robust relative to Wasserstein GAN and it is substantially improved in terms of both inception score and Fréchet inception distance when both weaker and stronger discriminators are considered.