## 4 Results
### Quantitative Evaluation
#### 4.3.2 Evaluation Results  
Here, we employed the IS, FID, and loss function as quantitative evaluation metrics. The generator's loss function typically hinges on the discriminator's predictions concerning the generated samples. Specifically, the generator aims to minimize the probability of the discriminator classifying the generated sample as fake. Conversely, the discriminator's loss function typically relies on its classification outcomes for both real and generated samples. Figure 8 illustrates the fluctuation patterns of the generator's and discriminator's loss functions across different model variants. The graph indicates that the discriminator's loss function experienced notable fluctuations during the early stages. On the other hand, the generator's loss function exhibited significant fluctuations in the beginning due to its limited capacity to create authentic defect images. This made it susceptible to being identified as a fake sample by the discriminator. As the training progressed, the generator's loss function gradually increased, signifying an improved ability to generate samples resembling real defect images. In comparison with our proposed approach, we can see that the error between the maximum value of the loss function of the generator and the discriminator was one to three times in the GAN and DCGAN models. The loss of the generator and discriminator of our approach was significantly lower than for the other two models, and it also demonstrated robust convergence and performance.  
Figure 9 depicts the performance for the FID and IS values across different models and defect cases. In all three defect cases, the FID value consistently decreased as the optimization and training of the model progressed. This trend signifies that the quality of the generated images steadily approached that of real images, reflecting an overall enhancement in the performance of the generated model. Conversely, the IS value exhibited a more intricate pattern of change. The IS value tended to increase over time, indicating an enhancement in the quality and diversity of the generated images. However, changes in the IS can be complex due to its potential sensitivity to specific categories of generated images during diversity evaluation. Consequently, the improvement in the quality of certain categories of generated images may be very slow. We can see that the GAN model showed a sharp downward trend in terms of the IS value for the LCC defect, similar to the trend observed for the BAF defect with the DCGAN model. This indicates that the training process of these models was not stable. In contrast, when employing imbalanced learning rates for training both the generator and discriminator within our proposed model, the  
generated images consistently exhibited a monotonic change with respect to the FID and the IS values throughout the training process.  
We also detail the FID and IS values in Table 4. We can see that the image generation model introduced in this paper achieved better results.  
For the IS value, our model outperformed both the DCGAN and GAN models for all defect types, showing substantial improvements. For the BAF defect, our model significantly outperformed both comparison models. For MAF and LCC defects, our model also demonstrated notable improvements over the DCGAN and GAN models.  
Figure 8: Comparison of the loss function of the generator and discriminator under different models.  
Figure 9: Comparison of the IS and FID metrics under different models.  
Regarding the FID values, our model achieved impressively low scores for all defect types, significantly lower than those of the DCGAN and GAN models. These results indicate that the proposed model consistently produced superior images compared to the existing models.