## 3 Proposed Model  
The proposed model is built with two primary components: the generator (\(G\)) and the discriminator (\(D\)) as shown in Figure 1. The generator includes an encoder with two cascading parallel sub-networks, a conventional convolutional pipeline (CNN), and a dilated convolutional pipeline (DCN) with a dilation factor of two. Both pipelines are four layers deep. Each layer uses \(3\times 3\) convolutional filters, followed by a rectified linear unit (ReLU) activation function, a batch normalization operation [35], and a max-pooling operation for spatial dimension reduction. This also means that the computational cost is identical between both the CNN and DCN (dilation rate has no effect on the computational complexity). The reasoning behind the parallel DCN is that the dilated convolutions increase the receptive field of the network while keeping the number of coefficients the same as its conventional counterpart, causing it to capture more global features [36]. The latent space vector created by the concatenation of the features obtained from CNN and DCN becomes the input of the decoder part of the generator. The four layer-deep up-sampling layers also concatenate the skip-connections from CNN and DCN to enable multi-scale capturing of the image space with high capability [37]. In the scenario of replacing the DCN with a CNN with \(5\times 5\) convolutions, the computational cost would increase 2.78 times due to the massive increase in the number of trainable parameters (from 387,840 trainable parameters to 1,077,334 trainable parameters). Moreover, \(3\times 3\) convolutions are highly optimized for modern computing libraries on GPU and CPU. Winograd algorithm [38] which is designed specifically for \(3\times 3\) convolutions with stride 1, is well supported by libraries like cuDNN [39]. The generator reconstructs a corresponding image \(\hat{x}\) from the input image \(x\) such that \(G\): \(x\to z\) where \(x\in\mathbb{R}^{(w\times h\times c)}\) and \(z\in\mathbb{R}^{d}\). The input image is sent through both CNN and DCN, and at the end of each network, the feature vectors are concatenated into the latent space vector \(z\). The discriminator (\(D\)) is comprised of a four-layer cascading CNN that is responsible for predicting the correct class (i.e., real or fake) based on the features of the input image. Its structure is identical to the CNN sub-network in the generator, with \(3\times 3\) convolutional filters, ReLU activation, and a batch normalization operation. At the end of the fully connected layer, there is a prediction layer that classifies normal images \(x\) and corresponding reconstructed images \(\hat{x}\). When adversarially trained, the discriminator improves its capability to predict until the convergence is reached. A Softmax layer is also added at the end of the concatenated feature vector as an individual classification layer as an ablation study of the model. In this ablation study, the parallel feature extracting encoder is trained in a supervised method with the labeled dataset. The dataset is split into the training set \(D_{tr}\) containing \(N\) normal images where \(D_{tr}=\{x_{1},\dots,x_{N}\}\), and a test set \(D_{te}\) of \(A\) normal and abnormal images combined \(D_{te}=\{(\hat{x}_{1},y_{1}),\dots,\{\hat{x}_{A},y_{A}\}\) where \(y_{A}\in[0,1]\) denoting normal and abnormal classes, respectively. The main task is to train the model \(f\) on \(D_{tr}\) and perform inference on \(D_{te}\). In an ideal scenario, the size of the training set should be much larger than the testing set. Training helps the model map the dataset distribution in all vector spaces, causing it to learn both higher and lower-level features distinctly different from abnormal samples. The task of the training is to capture and map the distribution of the training set \(D_{tr}\) in both the image space and the latent vector space. It is hypothesized that defining an anomaly score \(\mathcal{A}(.