# Improvement of Learning Stability of Generative Adversarial Network Using Variational Learning
## 1 Introduction  
The generative adversarial network (GAN) [1] is a deep generative model that is composed of artificial neural networks. Numerous studies have recently been undertaken on GAN in various fields based on the use of generative models, such as super resolution [2], image translation [3], medical image analysis [4], and three-dimensional (3D) modelling [5]. GAN has a structure that comprises two competing models--referred to as the discriminator and generator--that learn from each other. When it was first introduced, it gained considerable attention by researchers because it produced results with considerably higher quality (more realistic, higher resolution) as compared to many conventional generative models. However, given that the learning of networks could become unstable, owing to the competitive learning structure used in GAN, it was necessary to either a) apply techniques, such as the deep convolutional generative adversarial network (DCGAN) [6], or b) undergo a tedious hyperparameter tuning process [7] to achieve the learning of GAN. The widespread use of GAN is restricted by these issues, and research on various methods to resolve them is ongoing. The most common cause of the unstable learning of GAN is the so-called 'vanishing gradient' [8], whereby th gradient vanishes during the learning process of the generator for generating new samples that can deceive the discriminator. This occurs when the discriminator reaches the local optimum [9]. The learning of early GAN models was performed based on the minimization of the Jensen Shannon divergence (JSD) between the distribution of real data and the distribution the generator. Herein, the JSD does not converge when the intersection set of the support of the two compared distributions is the null set. This leads to a learning failure for GAN. Research studies that were conducted on the least-squares generative adversarial network (LSGAN) [10], Wasserstein generative adversarialnetwork (WGAN) [11], Wasserstein generative adversarial network-gradient penalty (WGAN-GP) [9], \(f\)-GAN [12], and on the deep regret analytic generative adversarial network (DRAGAN) [13], attempted to improve the performance of GAN by solving the vanishing gradient problem by replacing the JSD following the identification of a new divergence that could always converge. However, experiments on extensive hyperparametric searches while using the same dataset and architecture [7] showed that the algorithmic differences of these GAN did not significantly improve the original GAN. A study on an energy-based generative adversarial network (EBGAN) [14] proposed a method that stabilized energy based on reconstruction errors by designing the discriminator as an autoencoder structure. A boundary equilibrium generative adversarial network (BEGAN) [15] was inspired by WGAN and EBGAN, and it produced high-quality data. A representative feature-based generative adversarial network (RFGAN) [16] improved the learning stability of GAN based on the use of a pretrained autoencoder to provide the discriminator with representative features for training data. [PERSON] et al. [17] analyzed the vanishing gradient of GAN more systematically and suggested a few methods to solve the 'vanishing gradient' problem, yet the approach was not able to solve the problem that occurred in real problems. Some other studies proposed a model that combined the variational autoencoder (VAE) [18], another generative model with GAN, which resulted in the improvement of the learning stability of networks. VAE shows low performance (e.g., blurry results for image data) in many cases in terms of the quality of the generated data compared to GAN, yet ensures a stable convergence and yields a better likelihood than GAN [19]. By applying these characteristics of VAE to GAN, the adversarial autoencoder (AAE) [20] and adversarial variational Bayes (AVB) [21] models were combined based on the use of the GAN discriminator instead of the Kullback-Leibler divergence (KLD) that was used as regularizer in the objective function of VAE.