Generative Adversarial Networks in Computer Vision: A Survey and Taxonomy <s> Loss Sensitive GAN (LS-GAN) <s> Unsupervised learning with generative adversarial networks (GANs) has proven hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process. To overcome such a problem, we propose in this paper the Least Squares Generative Adversarial Networks (LSGANs) which adopt the least squares loss function for the discriminator. We show that minimizing the objective function of LSGAN yields minimizing the Pearson X2 divergence. There are two benefits of LSGANs over regular GANs. First, LSGANs are able to generate higher quality images than regular GANs. Second, LSGANs perform more stable during the learning process. We evaluate LSGANs on LSUN and CIFAR-10 datasets and the experimental results show that the images generated by LSGANs are of better quality than the ones generated by regular GANs. We also conduct two comparison experiments between LSGANs and regular GANs to illustrate the stability of LSGANs. <s> BIB001 </s> Generative Adversarial Networks in Computer Vision: A Survey and Taxonomy <s> Loss Sensitive GAN (LS-GAN) <s> While Generative Adversarial Networks (GANs) have seen wide success at the problem of synthesizing realistic images, they have seen little application to the problem of unsupervised audio generation. Unlike for images, a barrier to success is that the best discriminative representations for audio tend to be non-invertible, and thus cannot be used to synthesize listenable outputs. In this paper, we introduce WaveGAN, a first attempt at applying GANs to raw audio synthesis in an unsupervised setting. Our experiments on speech demonstrate that WaveGAN can produce intelligible words from a small vocabulary of human speech, as well as synthesize audio from other domains such as bird vocalizations, drums, and piano. Qualitatively, we find that human judges prefer the generated examples from WaveGAN over those from a method which naively apply GANs on image-like audio feature representations. <s> BIB002 </s> Generative Adversarial Networks in Computer Vision: A Survey and Taxonomy <s> Loss Sensitive GAN (LS-GAN) <s> In this paper, we present the Lipschitz regularization theory and algorithms for a novel Loss-Sensitive Generative Adversarial Network (LS-GAN). Specifically, it trains a loss function to distinguish between real and fake samples by designated margins, while learning a generator alternately to produce realistic samples by minimizing their losses. The LS-GAN further regularizes its loss function with a Lipschitz regularity condition on the density of real data, yielding a regularized model that can better generalize to produce new data from a reasonable number of training examples than the classic GAN. We will further present a Generalized LS-GAN (GLS-GAN) and show it contains a large family of regularized GAN models, including both LS-GAN and Wasserstein GAN, as its special cases. Compared with the other GAN models, we will conduct experiments to show both LS-GAN and GLS-GAN exhibit competitive ability in generating new images in terms of the Minimum Reconstruction Error (MRE) assessed on a separate test set. We further extend the LS-GAN to a conditional form for supervised and semi-supervised learning problems, and demonstrate its outstanding performance on image classification tasks. <s> BIB003
LS-GAN was introduced to train the generator to produce realistic samples by minimizing the designated margins between real and generated samples BIB003 . This work argues that the problems such as the vanishing gradient and mode collapse as appearing in the original GAN is caused by a non-parametric hypothesis that the discriminator is able to distinguish any type of probability distribution between real samples and generated samples. As mentioned before, it is very normal for the overlap between the real samples distribution and the generated samples distribution to be negligible. Moreover, D is also able to separate real samples and generated samples. The JS divergence will become a constant under this situation, where the vanishing gradient arises for G. In LS-GAN, the classification ability of D is restricted and is learned by a loss function L θ (x) parameterized with θ, which assumed that a real sample ought to have smaller loss than a generated sample. The loss function can be trained as the following constraint where ∆(x, G(z)) is the margin measuring the difference between real samples and generated samples. This constraint indicates that a real sample is separated from a generated sample by at least a margin of ∆(x, G(z)). The optimization for the LS-GAN is then stated as where λ is a positive balancing parameter, (a) + = max(a, 0) and θ are the parameters in D. From the second term in L D in the equation BIB002 , ∆(x, G(z)) is added as a regularization term for optimizing D in order to prevent D from overfitting the real samples and the generated samples. Figure 14 demonstrates the efficacy of equation BIB002 . The loss for D puts a restriction on the ability of D i.e., It challenges the ability of D for to separate well generated samples from real samples, which is the original cause for the vanishing gradient. More formally, LS-GAN assumes that p r lies in a set of Lipschitz densities with a compact support. . Decision boundary of D for the original GAN. It has small errors for the generated samples, which is far away from the decision boundary (in green), for updating G. (c). Decision boundary for D of LSGAN. It penalizes the large error for any generated sample that is far away from the boundary (in green). Thus it pushes generated samples (in green) toward the boundary BIB001 . Fig. 14. Demonstration of the loss in equation BIB002 . ∆(x, G(z)) is used to separate real samples and generated samples. If some generated samples are close enough to the real samples, LS-GAN will focus on other generated samples that are far away from the real samples. This optimization loss puts restriction on D to prevent it from separating generated and real samples too well. Thus, it solves the vanishing gradient problem which arises in original GANs. (G φ (z) here is equivalent to G(z) where φ represents the parameters for generator). 