## 2 Proposed Methodology  
The proposed filter pruning is performed to learn more about filters from different aspects and prune accordingly. The overall process is shown in Figure 1. This is an iterative pruning approach where additional importance weights are applied to identify unimportant filters. This filter pruning is performed in a way to minimize the damage to the original network and obtain a compact network. The different filters contain various kinds of features, thus preserving additional useful information for further processing. Under this assumption, additional importance weights are applied to each filter. These importance weights will help the model learn efficiently and maintain the diversity among different feature maps by constraining the representation error. Certain filters in the convolutional layer contribute less or not at all. These filters are less reliable than others for any computer vision task. In these cases, it is assumed that the importance weights assist filters in capturing the discriminant characteristics of the input data and contribute efficiently in the final decision. Furthermore, similar to the traditional convolutional layer, the initialization of importance weights influences the convergence process and learning ability of the model. Hence, to analyze the impact of initialization, we adopted and compared various weight initialization methods. The stochastic nature of weights and the dynamic behavior of the back propagation algorithm cause the CNN with random weight initialization to be trained in an uncontrollable manner, leading to highly redundant filters with a non-uniform contribution in the overall performance of the model. Therefore, we used different initialization methods for additional importance weight initialization such as random uniform initialization, chaotic initialization, i.e., logistic map [57], He initialization [58], LeCun uniform initialization [59], and Xavier initialization [60]. Initialization also depends on the activation function used in the network. For example, using ReLU activation, He initialization is superior to Xavier-Glorot initialization. However, additional importance weights do not interfere in the process of gradient descent. Hence, this conclusion is irrelevant in our approach. Let M be an original network model and M' a compact network. The original network \(M\) with \(L\) layers consists of \(N\) convolutional filters in each layer. The parameters of the filters in each \(l^{th}\) layer are denoted as \(F_{l}eR^{c\times N\times h\times\omega}\), where \(c\) is the number of filter kernels and \(h\times\omega\) denotes the size of the filter kernels. \(F_{l}\) is composed of \(c\) 3D kernels \(W_{l}^{i}eR^{c\times h\times\omega},ie(1,\,2,\ldots,\,N)\). In the proposed filter pruning model, we introduced additional importance weights \(w_{i}\) to each convolutional filter \(F_{i}\). The aim of the proposed filter pruning was to iteratively prune unimportant filters. Let us assume that the larger the importance weight \(w_{i}\), the more the convolutional filter \(F_{i}\) contributes to the decision-making process, and vice versa. The initial importance weights are applied using one of the above-mentioned initialization strategies. The importance weights are updated every subsequent iteration \((t+1)\) as  
\[w_{i}^{t+1}=w_{i}^{t}\frac{e^{m_{i}^{t}}-1}{e^{m_{i}^{t}}+1} \tag{1}\]  
Figure 1: Overall procedure for the proposed filter pruning. where, for each filter with \(c\) kernels and \(k\) the absolute weight of each 2D kernel, \(m_{i}^{t}\) can be computed as the sum of the absolute values of the filter weights:  
\[m_{i}^{t}=\sum_{j=1}^{c}\abs{k_{j}} \tag{2}\]  
Let us consider \(E(F)\) to be the original cost function or loss related to the original unpruned model \(M\) and \(E(F^{\prime})\) the loss representing the pruned model \(M^{\prime}\). Let \(F^{\prime}\) be the set of retained filters.