## 3 Experiment
### Training Analysis  
Our experiment harnesses a training approach that leans on the foundations of WGAN, making apt modifications to cater to our specific requirements. The WGAN, or Wasserstein Generative Adversarial Network, presents an advanced twist to the traditional GAN paradigm. It seeks to ameliorate challenges linked with unstable training and the inconsistent quality of generated samples endemic to conventional GANs. The innovation lies in the adoption of the Wasserstein distance, manifested in Equations (6) and (7), to serve as the loss function. This unique integration is coupled with pivotal refinements ensuring that GAN training remains steadfast and stable. \[\text{Loss\_D}=\text{D}(G(z))-\text{ D}(x) \tag{6}\]  
\[\text{Loss\_G}=-\text{ D}(G(z)) \tag{7}\]  
To elucidate, \(D\) symbolizes the discriminator, \(G\) denotes the generator, \(x\) characterizes real samples, and \(z\) stands for random noise. Zooming into the specifics, our experimental training unfolds in two distinct stages, graphically depicted in Figure 7, which showcases the loss trajectory across both stages. The onset of the initial stage witnesses the initialization of parameters for both \(G\) and \(D\), achieved either through random seeding or leveraging weights from pre-trained models. This is followed by an iterative training regimen where the generator gets refreshed every five iterations and the discriminator sees an update every single iteration. This sequential structure primarily ensures that the discriminator first attains robust capabilities, subsequently enabling a more efficient and effective guidance for the generator's training. During each generative update, a batch of samples emanates from the input random noise vectors. These samples, once produced, are channeled into the discriminator, \(D\). The ensuing outcome from \(D\) for these generated samples sets the stage for computing the associated loss function. Here, the Wasserstein distance serves as a metric to discern discrepancies between genuine and fabricated samples. The overarching aim is to curtail this generated sample loss by initiating backward propagation and fine-tuning the generator parameters. One of the cornerstones of the WGAN approach is the imposition of constraints on \(D\)'s parameters. In our experiments, we diligently clip the model parameters within a range of \(-0.1\) to \(0.1\). This meticulous curation pre-empts potential pitfalls like an overpowered discriminator or gradient anomalies during the training trajectory. These enumerated steps recur till a stipulated training cycle count is met or until the loss function exhibits signs of convergence. The payoff of adopting the Wasserstein distance as the linchpin loss function is manifold: it crafts a more nuanced portrayal of disparities between data distributions, amplifying the caliber of generated samples while anchoring GAN training in stability. The second training chapter is marked by resuscitating the parameters of \(G\) and \(D\) honed during the initial stage, followed by simultaneous updates in each iteration. This modus operandi mirrors its predecessor in the first phase. One of the inherent tribulations with legacy GANs resides in the disproportionate training dynamics between the generator and discriminator. This imbalance often culminates in a scenario where one model might overshadow the other prematurely, thus injecting instability into the training phase. By modulating the update cadence of the generator to every fifth iteration, we furnish the discriminator with an augmented window of opportunity for updates and learning. This strategic recalibration harmonizes the learning trajectories of both the generator and the discriminator, bolstering the overarching stability of the training process. Only after the discriminator has displayed a proficiency level comparable to the generator do we pivot to simultaneous updates for both entities. This shift in strategy not only amplifies the equilibrium during the training phase but also propels the overall training efficiency.