# Improvement of Learning Stability of Generative Adversarial Network Using Variational Learning
## 4 Experimental Results and Discussions
### Quality of Data Generated by the Proposed Method  
We evaluated the quality of the data generated based on the use of the proposed method and compared the performance of the proposed method with that of the DCGAN [6], and \(\alpha\)-GAN [29], which attempted to improve the learning stability of GAN. Figure 5 shows newly generated image data after learning with the use of images from the CelebA dataset and the MNIST dataset with each of the referred methods. In Figure 5, it is shown that both the proposed and conventional methods, which were based on GAN, generated good quality data, as confirmed by the naked eye. We evaluated the quality of each method using the latent space walk (LSP) method [1]. The LSP can be used to verify whether the deep generative model is overfitting the actual data. This can be achieved by observing the aspect of the data generated by the latent variables, as the latent variable \(a\) gradually changes toward the other latent variable \(b\) in the latent space. To address this issue, the model first underwent learning with the use of the training data, and then recorded the latent variables that produced two samples based on the sampling of two data units from the trained model denoted as \(a\) and \(b\). In the latent space, we observed the data that were generated by the generator using variable values along a straight line between points \(a\) and \(b\). Accordingly, if there was a semantically natural change between the data generated by the generator with values that corresponded to \(a\) and \(b\), then the generator was not overfitting. Figure 6a,b show the LSP results using the proposed VLGAN for the CelebA dataset and the MNIST dataset, respectively. Relative to the images at the top left (\(A\)), top right (\(B\)), bottom left (\(C\)), and the bottom right (\(D\)) in Figure 6, the generated images show that the semantic aspect of changes is well presented among the reference images as the latent variables change. We measured the multi-scale structural similarity (MS-SSIM) [42] for the generated images and the training time taken by each method for single iteration to quantitatively evaluate the performance of each method (Figure 7). The MS-SSIM is extensively used for evaluating image quality, and takes values between 0 and 1. Given that the MS-SSIM measures the similarity between images belonging to the same category, we conducted experiments only for the CelebA dataset that has the same property for face. The MS-SSIM indicates that the similarity between the two images is higher as the resulting value becomes closer to one. Figure 7 shows that the proposed method is slightly slower than DCGAN in terms of speed, yet the MS-SSIM value was slightly higher than that of DCGAN in terms of image quality. Conversely, in comparison with \(\alpha\)-GAN, \(\alpha\)-GAN yields slightly higher MS-SSIM values compared to VLGAN, yet VLGAN is two times faster than \(\alpha\)-GAN in terms of speed. This is because \(\alpha\)-GAN learns the generator again by using the restored data as the input of GAN using AAE. Therefore, additional discriminator models and additional learning about them are required in the execution process of AAE. The results of Figure 7 confirm that, when the simplicity of the model and the trade-off between the training speed and image quality are considered, the proposed method efficiently maintains the data quality achieved by GAN, while it simultaneously improves the learning stability with a low-calculation cost. Figure 4: Plots of the variations of the sum of absolute values of gradient when the ‘vanishing gradient’ phenomenon artificially occurs. (**a**) GAN for the MNIST dataset; (**b**) VLGAN for the MNIST dataset; (**c**) GAN for the CelebA dataset; (**d**) VLGAN for the CelebA dataset. Figure 5: Data samples generated from the (**a**) CelebA dataset and (**b**) MNIST dataset with each model. From left to right, DCGAN, \(\alpha\)-GAN, VLGAN.