α-EGAN: a-Energy distance GAN with an early stopping rule

Generative adversarial networks (GANs) are popular tools for learning the distribution of real samples and generating new ones, where the qualities of the generated images and the degree of preserved variation are two major concerns currently. In view of this, we propose an a-EGAN with energy distance as the loss function of the generator, which is proven to be effective in mitigating mode collapse. Moreover, an early stopping rule is proposed in the frame of hypothesis testing to avoid the unhealthy competition between the generator and the discriminator, thus achieving a trade-off between image qualities and variations. As a byproduct, the energy distance under the Euclidean norm can serve as a novel metric for evaluating generated samples in GAN. Experiments are conducted on simulated manifold datasets, as well as real MNIST and CelebA face datasets, showing that the proposed a-EGAN outperforms several competitors in both training stability and image quality.