## 3 Methods  
### Depthwise Separable Convolution  
This section is based on [37; 38]. Figure 3 illustrates the process of standard convolution, which performs spatial-wise and channel-wise computation in a single step. In this process, a kernel is applied simultaneously over the height, width, and channel dimensions of the image.  
Figure 3: Standard convolution, applying a 3 \(\times\) 3 3-channel kernel to a 3 \(\times\) 7 3-channel image, obtaining a 1-channel 6 \(\times\) 6 output.  
The number of parameters in standard convolution can be calculated using Equation (1), where \(k_{h}\) and \(k_{w}\) represent the kernel dimensions (height and width), \(c_{in}\) is the number of input channels, and \(c_{out}\) is the number of output channels.  
\[\text{Cost}_{Conv}=k_{h}\times k_{w}\times c_{in}\times c_{out} \tag{1}\]  
As an alternative to standard convolution, depthwise separable convolution was proposed, dividing the process into two more efficient steps. The first step, called depthwise convolution, is represented by Figure 4. In this operation, spatial-wise computation is performed by applying a kernel separately to each channel, meaning the kernel is applied over the height and width dimensions of each channel individually.  
The number of parameters in depthwise convolution is calculated using Equation (2).  
\[\text{Cost}_{DConv}=k_{h}\times k_{w}\times c_{in} \tag{2}\]  
The second step of depthwise separable convolution is pointwise convolution, represented by Figure 5. This operation performs channel-wise computation by applying a standard convolution with a \(1\times 1\) kernel over the channel dimension. This allows combining the input channels to produce the desired number of output channels.  
The number of parameters in pointwise convolution is calculated using Equation (3).  
\[\text{Cost}_{PConv}=1\times 1\times c_{in}\times c_{out} \tag{3}\]  
In this proposal, standard convolution is replaced by depthwise separable convolution with the aim of reducing the number of parameters in the model. The total computational cost of depthwise separable convolution can be calculated using Equation (4), which sums the costs of the two steps, depthwise convolution and pointwise convolution.  
\[\text{Cost}_{DSConv}=\text{Cost}_{DConv}+\text{Cost}_{PConv}=k_{h}\times k_{ w}\times c_{in}+1\times 1\times c_{in}\times c_{out} \tag{4}\]  
The reduction in parameters can be justified by the ratio between the number of parameters in standard convolution and the number of parameters in depthwise separable  
Figure 4: Depthwise convolution, applying a \(3\times 3\) kernel separately to each channel of a 3-channel \(7\times 7\) image, resulting in a 3-channel \(6\times 6\) output.  
Figure 5: Pointwise convolution, applying a \(1\times 1\) kernel on a 3-channel \(6\times 6\) image, resulting in a 1-channel \(6\times 6\) output.  
convolution, as presented in Equation (5) [23]. Given that \(k_{h}\times k_{w}>1\) and \(c_{out}>1\), the ratio \(R\) demonstrates the efficiency of depthwise separable convolution compared to standard convolution.  
\[R=\frac{\text{Cost}_{Conv}}{\text{Cost}_{DSConv}}=\frac{k_{h}\times k_{w}\times c _{in}\times c_{out}}{k_{h}\times k_{w}\times c_{in}+1\times 1\times c_{in}\times c_{out}}= \frac{1}{c_{out}}+\frac{1}{k_{h}\times k_{w}} \tag{5}\]  
In this way, this approach significantly reduces the computational cost, making depthwise separable convolution an efficient alternative for building lighter and faster models without compromising feature extraction capability.