## 2 Methods
### Convolution
#### 2.3.1 Depthwise Separable Convolution  
Depthwise separable convolution is a special convolution operation that decomposes the traditional convolution operation into two separate parts: depthwise convolution and pointwise convolution. In the realm of deep learning, pointwise convolution, typically characterized as \(1\times 1\) convolution, stands out as an elementary yet potent instrument [32]. While its design inherently precludes the capture of spatial information, it demonstrates exemplary efficacy in the inter-channel amalgamation of features. This convolution paradigm can be likened to a fully connected layer, orchestrated to integrate and reconfigure features across disparate channels [33]. Within the framework of depthwise separable convolutions, pointwise convolution often succeeds depthwise convolution, ensuring a comprehensive blend of inter-channel features. The computational procedure of pointwise convolution is delineated in Equation (1). \[Y_{\{n\}}=\sum_{m^{\prime}}X_{m^{\prime}}*K_{n} \tag{1}\]  
where \(n\) represents the nth channel of the output, \(m^{\prime}\) is the channel index, and \(K_{n}\) is the \(1\times 1\) convolution kernel for the nth output channel. In depthwise convolution, each input channel has an independent convolution kernel, which means that the features of each channel are processed independently, thus capturing the spatial information of each channel [34]. The calculation process is shown in Formula (2). \[X_{m^{\prime}}=X_{m}*K_{m^{\prime}} \tag{2}\]  
where \(X\) represents the input data, \(m\) represents the channel index, \({}^{*}\) represents the convolution operation, and \(K_{m^{\prime}}\) represents the \(m^{\prime}\)th convolution kernel. Depthwise separable convolution, a transformative innovation in convolutional designs, emphasizes depthwise convolution followed by pointwise convolution for the seamless integration of channel-wise features. The cardinal advantage of this architecture lies in its capacity to markedly truncate both the parameter count and computational intricacies, all while preserving a performance parallel to conventional convolutions [35]. This convolution paradigm has garnered particular acclaim in mobile and edge computing scenarios, chiefly attributed to its prowess in facilitating efficient forward propagation under the constraints of limited computational resources. The inherent merit of depthwise separable convolution is its significant reduction in computational demands and parameter volume. To elucidate, consider a comparative evaluation between standard convolution and depthwise separable convolution when processing input dimensions of \(D\times D\), input channels numbered at \(M\), output channels at \(N\), and with a convolutional kernel size of \(K\times K\). The ratio of computational magnitude is represented in Equation (3). A schematic representation of this architecture is presented in Figure 2.  
\[\frac{N_{\text{C}}}{N_{\text{DW}}}=\frac{D*D*M*N*K*K}{D*D*M*K*K+D*D*M*N}=\frac{N*K* K}{K*K+1} \tag{3}\]  
where \(N_{\text{C}}\) represents the computational cost of standard convolution, and \(N_{\text{DW}}\) represents the computational cost of depthwise separable convolution. Within our MixerNet-SAGA model, depthwise separable convolutions play a pivotal role in structuring the ConvMixer module. To elaborate, the ConvMixer module initially employs depthwise convolution to independently extract features from each channel, thereby harnessing a richer spatial representation. This is subsequently followed by a pointwise convolution, serving to integrate features across these channels. The incorporation of depthwise separable convolution in the MixerNet-SAGA model stems from several key considerations:  
1. Computational Efficiency: Depthwise separable convolutions, while preserving feature extraction capabilities, remarkably reduce the model's parameter count and computational intricacy. This efficiency affords a discernible edge to our design within the ConvMixer module. 2.