## 3 Proposed Methodology
### Masking  
In order for the augmentation method to be applied in the industry, stable augmentation performance must be guaranteed. However, it is already widely known that GAN-based models are difficult to train and easily become unstable due to issues such as mode collapse, Nash equilibrium, and non-convergence. These problems degrade the quality of the augmented WBMs and cannot guarantee the quality of the generated WBMs. Moreover, there was a problem with broken edges in some wafers in the WM-811k dataset. Augmented WBMs using imperfect WBMs, such as broken-edge WBMs, are a factor that can impact the overall quality of the classification model's reliability. To alleviate the imperfections of the augmented WBM and ensure the reliability of the generative model, it is effective to properly calibrate the augmented wafer. In [38], the authors improved the quality of augmented wafers through wafer repair when the shape of the wafer was deformed, or when a good bit or failed bit was in the wrong location on the wafer map (e.g., outside the wafer area).  
As mentioned above, GAN-based augmentation model learning can be unstable, which can sometimes lead to the production of low-quality augmented images. It is labor-intensive to manually remove these low-quality augmented images, and even if such manual work is performed it is difficult to solve the problem of deviation in the quality of the augmented WBMs due to problems caused by worker bias. Therefore, we refined the augmented WBMs through a defined process. We performed the masking process on the augmented WBMs to correct the errors in the WBMs. The masking process was performed with the following steps. First, assuming that the size of the generated WBM was \(2r\times 2r\), a circle with a radius of \(r\) was formed. The circle formed was called the masking wafer. The inner region of this circle was assumed to be the inner area of the original wafer. After overlapping the masking wafer and the generated WBM, the good bits and the failed bits which formed outside the wafer of the generated WBMs were removed. The removed bits were marked as areas outside the wafer. Figure 6 shows the process of refining the WBMs via the masking process (Figure 6a is an example of a WBM augmented with poor quality by an augmentation model). Then, the masking wafers on the augmented  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Kernel Size, Stride** & **No. of Parameters** & **Output Shape** \\ \hline Input & - & - & (64, 64, 3) \\ Convolutional & \(5\times 5\times 64\), 2 & 4864 & (32, 32, 64) \\ Dropout (0.4) & - & - & (32, 32, 64) \\ Convolutional & \(5\times 5\times 128\), 2 & 204,928 & (16, 16, 128) \\ Dropout (0.4) & - & - & (16, 16, 128) \\ Flatten & - & - & (32,768) \\ Dense & - & 32,769 & (1) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Discriminator network architecture and hyperparameters.  
WBMs were covered, as shown in Figure 6b,c. The good /failed bits were removed from the areas outside the wafer. The masking process had the advantage of being able to check whether a defect pattern occurred at the incorrect spatial position on a given wafer. A WBM augmented through the DCGAN-based model tended to be augmented by focusing on the features constituting the defect pattern on the wafer rather than the absolute spatial shape of the wafer; thus, the boundary between the wafer itself and the outside of the wafer may appear ambiguous. The masking process thus ensures that the generated WBM maintains the shape of the original wafer. It is possible to ensure the quality of the augmented wafer while reducing the labor (human power) required for manual operation by an engineer.