## 3 Bin2 Vec: A Convolutional Neural Network-Based WBM Coloring Scheme
### Word2 Vec and Bin2 Vec
#### 3.2.2 Bin2 Vec
Figure 4: Example of wafer bin map and resized image from wafer chip size. step size by one. For example, Group 1 products have \(23\times 27\) dies on a wafer, and we assign the index from top to bottom, and from left to right. The first training instance is made by taking 25 dies with index of 1-5 (horizontal) and 1-5 (vertical). If horizontal sliding is done first, then the second training instance is made by taking 25 dies with index of 2-6 (horizontal) and 1-5 (vertical). This process is repeated until the 25 dies with index 19-23 (horizontal) and 23-27 (vertical) are taken. With these vectorized bin codes, we employed the Skip-Gram structure [27] to learn the embedding vectors. The bin codes in the middle, i.e., the bin code in the third row and third column in the \(5\times 5\) bin matrix, or the 13 th bin code in the 25-dimensional vector, were used as the input while the other 24 bin codes were used as the target of the Skip-Gram model, as shown in the first two steps in Figure 6. During the Skip-Gram model training, we excluded the following two cases because they do not have any significant information: (1) instances when all elements have the same bin code, and (2) instances that contain only \"-2\" (non-wafer part) and \"0\" (the die passed all the EDS tests). For the Bin2 Vec model, the input vector dimension (\(|V|\)) is set to 401, which is the number of total bin codes that appeared at least once in the WBM dataset. The number of hidden nodes is set to 3 to assign the RGB code to the embedded bin codes. In an Natural language processing task, it is common to use a negative sampling technique or noise-contrastive estimation [30] for Word2 Vec training to reduce the number of words used for the denominator of the softmax function, as shown in Equation (2). Without these techniques, Word2 Vec would consider more than 100,000 words to compute the softmax function, causing a heavy computational burden. On the other hand, in the  
Figure 5: Data converted from WBM to Bin2 Vec input structure. Figure 6: Bin code RGB color mapping framework based on Bin2 Vec. Bin2 Vec, we used all bins to compute the softmax function because there were only 401 distinctive bin codes. Once the Bin2 Vec model training is completed, the range of three embedded dimensions can be different. To fully use the RGB code coverage, the embedded bin vectors are min-max scaled for all dimensions, as shown in Figure 6. Accordingly, each bin code has a value between 0 and 1 in the R-, G-, and B-axis, respectively. Figure 7a is an example of a WBM with binary colorization scheme. The white color indicates that the dies in those areas passed all the EDS tests while the gray color indicates that the dies in those areas failed at least one of the EDS tests. The only information delivered to process engineers by the binary colorization scheme is whether each die passed all the tests or not. The failed tests cannot be distinguished because these are presented as the same gray color. To provide both types of information, the random RGB coloring scheme assigns different colors to different bin codes, as shown in Figure 7b. Although different bin codes are colored differently, it is not possible to determine which bins are semantically similar to others; the colors only serve as identifiers. Bin2 Vec can provide all three types of information: (1) whether each die passed all the tests, (2) what die failed which tests, and (3) which bin codes are semantically related. Figure 7c shows the same WBM with the Bin2 Vec coloring scheme. Compared with random RGB coloring, bin patterns are more noticeable with the Bin2 Vec. The areas A, B, and C have similar green colors in Figure 8a, whereas black, purple, and brown are assigned to the dies in areas A, B, and C by the Bin2 Vec, respectively (Figure 8b). In addition, Figure 8b shows that the bin codes along the edge are semantically similar since they are represented in yellow.