## 3 Proposed Methodology
### Polymorphic Generative Index  
To evaluate the effectiveness of the proposed generative model, a quantitative index is needed to evaluate how diversely the model augments the data. Although many studies \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 & \(3\times 3\times 32,1\) & 896 & (64, 64, 32) \\ Max-Pooling & \(2\times 2,2\) & - & (32, 32, 32) \\ Convolutional & \(3\times 3\times 64,1\) & 18,496 & (32, 32, 64) \\ Max-Pooling & \(2\times 2,2\) & - & (16, 16, 64) \\ Convolutional & \(3\times 3\times 64,1\) & 36,928 & (16, 16, 64) \\ Max-Pooling & \(2\times 2,2\) & - & (8, 8, 64) \\ Flatten & - & - & (4096) \\ Fully Connected & - & 1,048,832 & (256) \\ Fully Connected & - & 2313 & (9) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: CNN architecture and hyperparameters. Figure 6: Masking process for wafer refining: (**a**) augmented WBM with poor quality; (**b**) masking wafer; (**c**) refined augmented WBM. have been conducted to evaluate the performance of the generative model, agreed-upon criteria for evaluating the GAN model have not yet been clearly established. The most common and intuitive method for evaluating the performance of GAN is manual evaluation, which entails a visual evaluation by human judges, such as via the use of Rating and Preference Judgment and the use of Rapid Scene Categorization. However, this qualitative method is subjective because the indicators vary based on the evaluator's stereotypes or biases, and its application is limited because it is greatly influenced by the evaluator's domain knowledge. In addition, it is difficult to verify the problem of GAN methods, such as mode collapse. Therefore, to solve this problem, the need for quantitative evaluation indicators has emerged. In general, GANs are evaluated in terms of 'quality', or how similar the generated images are to the original images, and 'diversity', i.e., whether they can generate a variety of images across different kinds of noise vectors. The representative metrics used to evaluate GAN are IS (inception score) [39] and FID (Frechet inception distance). In general, IS is measured using the ImageNet pre-trained model, Inception v3, and the calculation of IS is performed as follows:  
\[\text{IS}=\exp\big{(}\mathbb{E}_{x\sim p_{data}}D_{KL}(P(y\mid x)\parallel P(y)) \big{)} \tag{2}\]  
where \(x\sim p_{data}\) means that \(x\) is an image sampled from \(p_{data}\); \(D_{KL}(P(y\mid x)\parallel P(y))\) is the Kullback-Leibler divergence between the distributions \(P(y\mid x)\) and \(P(y)\); \(P(y\mid x)\) is the conditional class distribution; and \(P(y)=\int_{x}P(y\mid x)P_{data}(x)dx\) is the marginal class distribution for noise vectors z. In the present work, IS was calculated for each class according to the preceding equation, with a large IS value indicating that the generation model had a better generation performance. However, IS has the following disadvantages: large IS values are achieved even if the augmentation model repeatedly generates one good quality identical image for each class of the classifier. This means that IS cannot measure inner diversity within a class of generative models. In other words, IS is vulnerable to mode collapse evaluation. Furthermore, high IS values are achieved even when a GAN replicates training data exactly. When the augmentation model generates only one image per class, \(P(y)\) comes close to a uniform distribution, even if the diversity is low. This causes IS to exhibit a distorted performance. Additionally, unlike human cognition, deep learning networks consider style to be more important than content. That is, image classification networks consider texture more than shape in terms of input data [40; 41]. Thus, even if the augmented model outputs results that differ from human thinking, IS can achieve high numbers. Therefore, sometimes IS may not be suitable for evaluating the performance of the augmentation model.