Soft-margin Ellipsoid generative adversarial networks

Generative adversarial networks (GANs) are of great significance for synthetizing realistic images. However, GANs are potentially unstable during the training process, posing some challenges for their development. By defining an integral probability metric (IPM) on the hypersphere, Sphere GAN enforces the discriminator to satisfy Lipschitz continuity and stabilizes the training process. Developed from Sphere GAN, a soft-margin Ellipsoid GAN is proposed for improving the quality of generated samples and the stability of training process. In the presented method, the geometric moment difference defined on the hypersphere is generalized to the hyperellipsoid. The hyperellipsoid is realized to relax the upper bound of the IPM by extending measurable functions space, thus the quality of generated samples can be improved. Furthermore, a nonlinear separating hyperellipsoid is designed to prevent the discriminator from gradient vanishing and exploding on the classification boundary. The proposed soft-margin Ellipsoid GAN is proved theoretically to have a global optimal solution, i.e., the probability density of generated samples approaches to that of real samples infinitely when both the discriminator and the generator are optimal. The CIFAR10 and LSUN-bedrooms datasets are selected to evaluate the performance of the proposed methods. The quantitative results show that the proposed approach decreases the Frechet inception distance (FID) on the two datasets by 8.2% and 16.0%, respectively. The qualitative results show that the proposed soft-margin mechanism improves the stability of the training process.