Dynamics of Fourier Modes in Torus Generative Adversarial Networks

Generative Adversarial Networks (GANs) are powerful Machine Learning models capable of generating fully synthetic samples a desired phenomenon with high resolution. Despite their success, the training process GAN is highly unstable and typically it necessary to implement several accessory heuristics networks reach an acceptable convergence model. In this paper, we introduce novel method analyze stability in Networks. For purpose, propose decompose objective function adversary min-max game defining periodic into its Fourier series. By studying dynamics truncated series for continuous Alternating Gradient Descend algorithm, able approximate real flow identify main features GAN. This approach confirmed empirically by $2$-parametric aiming generate unknown exponential distribution. As byproduct, show that convergent orbits GANs small perturbations so Nash equillibria spiral attractors. theoretically justifies slow observed GANs.