## 2 Contributions of the Paper
### Why the Proposed Methodology Satisfies XAI Dimensions  
The illustration of the proposed ICNN is presented in Figure 2. This executive diagram describes the step-by-step procedure of how the proposed network architecture was designed and why it satisfies the three dimensions (\(\mathcal{D}1\), \(\mathcal{D}2\), and \(\mathcal{D}3\)) in the definition of interpretability and, hence, can be the benchmark in addressing XAI problems. **Proposed Architecture**. The executive diagram of the proposed architecture is presented in Figure 2. First, the architecture starts with image data that consists of X-ray pictures sized 128 \(\times\) 128 (see detailed discussion of COVID-19 data set in Section 4). The architecture proposes using a 2 \(\times\)2 rolling window (we use a 2 \(\times\) 2 window for simplicity; larger sizes can be applicable as well in practice depending on the data). Since the window size is 2 \(\times\) 2, this means there are four variables every time the window rests on a certain location of the image. Within this subset of variables, we execute the proposed backward dropping algorithm (BDA). This procedure finely selects a subset of variables that is highly predictive by omitting the noisy variables in this small neighborhood on the image. Next, the selected variables (which can be any subset of the original four) undergo a proposed procedure called interaction-based feature engineer (see (6) for a definition). The BDA procedure is illustrated in the bottom left corner of Figure 2 (we use a \(2\times 2\) window for demonstration purpose). In addition, we set the starting point to be \(12\) which means we start from the pixel in the \(12\)th row and the \(12\)th column. From data (size of \(128\times 128\)) to the \(1\)st layer (\(58\times 58\)), this procedure produces a new feature matrix with size \(\lfloor(128-12-2+1)/2+1\rfloor=58\) on both edges, which means the new feature matrix has \(58\times 58\) variables (the formula is presented in Equation (18)). This feature matrix constitutes the first interaction-based convolutional layer. We can then use the same methodology to construct the second and third interaction-based convolutional layers. The third interaction-based convolutional layer can be used as the input layer for a neural network classifier. For each layer, we can compute the proposed I-score and the AUC value (see Section 4.4 for a detailed discussion of AUC values) for each variable (assuming using this variable as a predictor when computing the AUC value). The paths of the I-score and AUC values have parallel behavior, which is shown in the color palette of the spectrum in Figure 2.  
**Why the Proposed I-score Satisfies XAI Dimensions**. The design of the proposed architecture in Figure 2 mainly focuses on using the I-score and the BDA to extract and engineer features from the original images. The proposed I-score is nonparametric (see Section 3.1 for a definition of this measure). This means the impact of the explanatory variables on the response variable measured by the I-score does not rely on the knowledge of the correct specification of the underlying model. In other words, the computation of the I-score does not rely on any model fitting procedure. This characteristic satisfies the first dimension, \(\mathcal{D}1\), defined in Section 1 about interpretable measures. Next, the proposed architecture is transparent at disclosing to its human users what locations of the image are important in making decisions about prediction and what locations are noisy. In every interaction-based convolutional layer, we can compute the proposed I-score for any single variable. We can also compute the I-score and finely select predictive variables from any combination of variables. The larger the I-score, the more important the variables in making predictions. With the simple visualization presented in Figure 2, we are able to use a spectrum of different colors to illustrate this phenomenon.