## 2 What Is a Generative Adversarial Network?
### Advantages and Constrains of Generative Adversarial Networks
#### 2.5.2 Constraints  
Conversely, GANs exhibit limitations in terms of replication rate, which exhibits an exponential decay concerning dataset size and complexity, resulting in image quality shortcomings. The authors in [57] posit a hypothesis that an increase in dataset size leads to heightened dataset complexity, thereby causing a decline in the replication rate. Additionally, they present that the quality of generated samplings initially deteriorates but later improves as the number of training samplings increases. The practical aim of the study in [79] is to enhance our understanding of the relationship between dataset size and replication in the context of GANs during image synthesis. To achieve this, they have developed a tool capable of predicting the required number of training iterations before the onset of exponential decay in the replication rate. This exploration sheds light on the underlying mechanisms behind GAN replication and over-fitting, contributing to a more comprehensive understanding of these phenomena. GANs are potent models for generating synthetic data, but they are notorious for their unstable training process, which is plagued by several challenges. This section will review some of the critical challenges that arise during GAN training. The following list shows the common obstacles:  
* _Vanishing gradient_: This problem can lead to the gradients of the generator, concerning weights in the early layers of the network, becoming so small that those layers stop learning, resulting in poor-quality image generation [80]. In addition, a well-trained discriminator network may confidently reject the generator-generated samplings due to this problem. The challenge of optimizing the generator is compounded by the fact that the discriminator does not share any information, which can damage the overall learning capacity model [81]. * _Mode collapse_: Mode collapse poses a critical challenge in GAN training, leading to the generator consistently producing identical outputs. This failure in GAN training is attributed to the generator exhibiting low diversity in its generated data or producing only a limited range of specific real samplings. Consequently, the utility of the learned GANs becomes restricted in numerous computer vision applications and computer graphics tasks [82]. * _Shortcoming of accurate evaluation metrics_: The lack of accurate evaluation metrics is a critical challenge in generative adversarial network (GAN) research. Evaluating the quality of images generated by GANs remains an active area of research, especially with regard to unstable training. Despite the demonstrated successes of GANs in a variety of applications, determining which method is superior to another in terms of evaluation remains a complex problem. Currently, there is no universally accepted standard for evaluation, and each paper introducing a new GAN proposes its own evaluation techniques. This results in a lack of agreed-upon parameters that make a fair comparison of models difficult [57; 83; 84]. One of the main challenges of current GAN evaluation metrics is to have a measure that assesses both diversity and visual fidelity simultaneously. Diversity implies that all modes are covered, while visual fidelity implies that the generated samples must have a high probability. Another challenge is that some measures are less practical to calculate for large sample sizes. Also, there is currently no powerful universal measure for assessing GANs, which may hinder progress in this field [83; 85]. While various quantitative and qualitative metrics have been proposed to evaluate generative models, their complexity and limitations make the choice of a single metric a complicated process. This complexity is reflected in the fact that the precise evaluation of GANs remains an active and evolving research topic.