# Improvement of Learning Stability of Generative Adversarial Network Using Variational Learning
## 1 Introduction
In [22], a GAN model was introduced that combined the reconstruction, GAN, and classification losses of the pretrained classifier. VAE-GAN [23] improved the image quality of VAE based on the use of the discriminator to separate the perceptual information [24] of the input and output instead of using the reconstruction loss between the input and output data in the structure of VAE. Adversarially learned inference (ALI) [25] and bidirectional GAN (BIGAN) [26] combined the autoencoder and GAN based on the use of an adversarial learning method, whereby the encoder and decoder generated fake data and fake code, respectively, and the discriminator identified whether data and code were one pair or not. Adversarial symmetric AS-VAE [27] learned the symmetric VAE with the adversarial learning method of ALI. [PERSON] et al. [28] found the mathematical linkages and similarities between VAE and GAN, and showed that VAE can be expressed as the GAN formula, which included the perfect discriminator (i.e., fully learned the ideal discriminator). Furthermore, at the same time, they proved that various methods, such as the importance weighting method that is used to improve VAE, could be applied to GAN. [PERSON] et al. [29] revealed the possibility of combining variational inference with GAN, and proposed the \(\alpha\)-GAN method that solves the mode collapse of the generator by combining AAE and GAN. DePSiM [30] proposed a loss function that can generate clear data by combining the pixel-wise reconstruction loss of VAE, the perceptual loss obtained from feature space, and the adversarial loss obtained by inserting the generated and real data into the discriminator. CycleGAN [31] has a structure that translates data into each domain for paired datasets that are based on the use of two GANs and reconstruction errors. In this study, its structure is similar to that of \(\alpha\)-GAN based on the assumption that one of the domains is a latent space domain. In this paper, we propose a generative adversarial model using variational learning to improve the learning stability of GAN. We conceived this idea based on the common properties of the GAN generator and the VAE decoder that aided the identification of an approximate distribution of the original data distribution. Based on the assumption that the prior distribution of VAE is equal to the noise distribution of GAN, we built a combined model that was composed of the encoder, generator, and discriminator. The proposed method obtained the latent code based on the use of a reparameterization trick after inputting the given data into the VAE encoder along with the learning of GAN, and generated new data by inputting this latent code in the GAN generator. Subsequently,it trained the GAN generator along with the VAE encoder based on the use of the input data, and generated data and latent code with the loss of VAE. Unlike the conventional methods that extracted better features or found a mathematical linkage between two models that were based on the combination of GAN and VAE, the proposed method focused on the solution of the vanishing gradient problem of GAN and used VAE as an auxiliary model for GAN. Given that this structure does not change the model structure or the input/output forms of the conventional GAN, it has the advantage that it can be naturally applied to problems that to-this-date have utilized GAN. In addition, by solving the vanishing gradient problem of GAN according to economic terms, we built simpler and more efficient networks based on the use of the VAE structure instead of the AAE structure [29]. Finally, we conducted experiments in order to observe the occurrence of the vanishing gradient for the MNIST dataset [32] that contained handwritten images, and the CelebA dataset [33] that was made up of facial images of celebrities, which were extensively used in the GAN evaluation.