Research On Generative Adversarial Networks Based On Improved Loss Functions

Generative Adversarial Networks(GANs)belong to deep generative models and are widely used in computer vision and image processing.However,GANs are often subjected to problem linked to instability.Some works related to loss functions are of great significance for the stability of GANs.As the metrics of probability distributions,the design of loss functions should ensure the global convergence of probability distributions.From the engineering perspective,the loss function should provide a reasonable gradient to avoid gradient vanishing and exploding during the training process.Therefore,this thesis analyzes and designs the loss functions of GANs.The main contributions of this thesis are as follows:(1)The Suboptimal Saturated GAN(SOSA GAN)is designed.Firstly,the dynamics of generator’s vanishing gradient of Vanilla GAN are analyzed.Then,the loss function of discriminator is approximated by adding an additional Taylor’s higher-order term,preventing the outputs of discriminator from going to the saturation region of the sigmoid activation which results in the vanishing of the gradient.The experimental results of stability show that SOSA GAN can maintain its stability under the increasing discriminator iterations.Unsupervised experimental results show that SOSA GAN improves the quality of generated samples,which decreases the Fréchet inception distance(FID)on CIFAR10 dataset by 3.8%.(2)The Soft-Margin Ellipsoid GAN(SME GAN)is designed.Firstly,the geometric moments difference defined on the hyperellipsoid is adopted as the loss function of GANs,and the method for calculating the Riemannian distance on the hyperellipsoid is designed to obtain the new loss function of Ellipsoid GAN.Then,the reasons of gradient vanishing and exploding of Ellipsoid GAN are analyzed,and a nonlinear separating hyperellipsoid is designed to obtain the new loss function of SME GAN.Finally,the designed SME GAN is theoretically proved to have a global optimal solution.The experimental results of stability show that SME GAN can maintain its stability under a large learning rate and the increasing discriminator iterations.Unsupervised experimental results show that SME GAN improves the quality of generated samples,which decreases the FID on CIFAR10 and LSUN-bedrooms datasets by 8.2% and 16%,respectively.