## 2 An Overview of GA and GAN Architectures
### Generative Adversarial Networks and Deep Convolutional GANs  
Generative Adversarial Networks (GANs) [31] are a prominent class of machine learning models designed to generate realistic synthetic data. GANs operate within an adversarial framework in which two neural networks, the generator and the discriminator, participate in a continuous competition. This adversarial process, structured as a zero-sum game, encourages both networks to iteratively refine their capabilities: the generator learns to create data that increasingly resemble true samples, while the discriminator enhances its ability to distinguish synthetic data from genuine examples. This dynamic interaction is fundamental to GANs, facilitating significant advancements in data realism and fidelity with each training iteration. At the core of a GAN is its dual-network architecture. The generator synthesizes new data samples from random noise, aiming to produce outputs indistinguishable from the real dataset. Concurrently, the discriminator evaluates these samples, assigning a likelihood score based on how closely they resemble actual data. As training progresses, the generator's outputs improve in authenticity, while the discriminator adapts to increasingly challenging inputs. This interplay between generation and evaluation is fundamental to GANs' effectiveness across a variety of applications, including image synthesis, style transfer, and data augmentation. The GAN architecture is illustrated in Figure 2.  
A significant advancement in the evolution of GANs was the introduction of Convolutional Neural Networks (CNNs) into the framework, as demonstrated by the development of Deep Convolutional GANs (DCGANs). While the original GAN framework introduced in [1] was not inherently convolutional, the adaptation of CNNs, particularly in DCGANs [14], has proven especially beneficial for image-based applications. CNNs are specialized for processing grid-like data structures, such as images, using convolutional layers to automatically learn hierarchical features. This makes them particularly well-suited for capturing the spatial hierarchies essential to high-quality image generation. By replacing the fully connected layers in traditional GAN architectures with convolutional layers in both the generator and discriminator, DCGANs significantly enhance performance in visual data processing. This architectural shift allows DCGANs to capture detailed features such as edges, textures, and shapes with greater precision, thereby improving the fidelity and resolution of generated images. To illustrate the DCGAN workflow, Figure 3 presents the structure of the generator, while Figure 4 depicts the discriminator. Figure 2: General overview of the GAN architecture workflow. More specifically, the DCGAN generator architecture in Figure 3 starts with a latent vector of size 100, which is progressively transformed through several layers to produce a final 64 \(\times\) 64 image with 3 channels. Initially, the input is reshaped to 4 \(\times\) 4 \(\times\) 1024, followed by convolutional layers that unsampled the tensor to 8 \(\times\) 8 \(\times\) 512, 16 \(\times\) 16 \(\times\) 256, 32 \(\times\) 32 \(\times\) 128, and finally to 64 \(\times\) 64 \(\times\) 3. On the other hand, the DCGAN discriminator architecture in Figure 4 takes a 64 \(\times\) 64 image as input and applies a series of convolutional layers to downscale it. The image size is reduced through layers of 32 \(\times\) 32 \(\times\) 64, 16 \(\times\) 16 \(\times\) 128, and 8 \(\times\) 8 \(\times\) 256, before a fully connected layer outputs a single classification score, determining whether the image is real or fake. The use of CNNs in DCGANs results in more stable training and enables the generation of higher-quality images, making DCGANs particularly effective for tasks like image synthesis, facial recognition, and other applications requiring high-resolution, photorealistic outputs.