## 3 Methods and Data
### Construction of the WaveNet Network Model
#### 3.2.2 SE Residual Block  
The squeeze and excitation (SE) residual block, illustrated in Figure 7, represents an essential architectural component within WaveNet. It combines the benefits of a traditional residual block with a channel-wise attention mechanism. This integration enhances the model's capability to capture and leverage crucial global information across feature chan  
Figure 6: Residual block structure in WaveNet. nels, facilitating the recognition of important patterns and relationships within the data. The SE residual block plays a pivotal role in enhancing the overall performance of the WaveNet model. The initial size of the input feature map \(X_{0}\) of the SE residual block is C \(\times\) H \(\times\) W. and the output feature map X after two layers of convolution operations will be used as the input of global average pooling. We will perform feature compression on the feature map X along the spatial dimension by applying global average pooling. This operation transforms each two-dimensional feature channel into a single scalar value. Each scalar, in a sense, possesses a global receptive field and shares the same dimensionality as the number of input feature channels. These scalars represent the global response distribution across feature channels and enable layers closer to the input to access global information. Consequently, feature compression transforms the size of the feature map from C \(\times\) H \(\times\) W to C \(\times\) 1 \(\times\) 1. Following feature compression, the resulting compressed feature vector serves as the input to the channel-wise attention mechanism. This integrated mechanism effectively allows the model to capture and leverage global information across feature channels, thereby enhancing its capacity to recognize important patterns and relationships within the data. The formula of global average pooling of the SE residual block can be expressed as follows:  
\[F_{c}(X)=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j=1}^{W}X(i,j) \tag{4}\]  
In the equation, \(F_{c}\) represents the compressed feature map, and \(X\) represents the output feature map of the last convolutional layer. The subsequent two fully connected layers are used to model the correlations between channels and output weights equal to the number of input feature channels. Firstly, in the first fully connected layer, we reduce the dimensionality of the channel features to 1/16 of the original size. Then, a ReLU activation function is applied for non-linear transformation, followed by another fully connected layer to increase the dimensionality back to the dimension of the original feature channels. This design, compared to using  
Figure 7: The squeeze and excitation attention mechanism in the residual block (SE residual block) structure. only one fully connected layer, offers greater non-linear capability, enabling better fitting of complex correlations between channels, while also reducing the number of parameters and computational complexity. For the fully connected layer input FC, the output can be expressed as:  
\[F_{o}=(ReLU(F_{c}\times w_{1}+b_{1}))\times w_{2}+b_{2} \tag{5}\]  
In the equation, \(F_{o}\) represents the final output of the fully connected layer, and \(w_{1}\) and \(b_{1}\) denote the weight and bias of the first fully connected layer, respectively. Similarly, \(w_{2}\) and \(b_{2}\) represent the weight and bias of the second fully connected layer. The output from the final fully connected layer undergoes a non-linear transformation facilitated by a sigmoid activation function. The formula of the sigmoid function is as follows. \[Sigmoid(x)=\frac{1}{1+e^{-x}} \tag{6}\]  
The sigmoid function generates a normalized weight for each channel within the range of 0 to 1. These normalized weights are then applied in an element-wise multiplication operation with the original channel features, thus finalizing the re-scaling of the original features along the channel dimension.