## 3 The Proposed Model Architecture
### MSCA-Res2 Block  
The multi-scale channel adaptive (MSCA) module is an attention mechanism that allows convolutional neural networks to adaptively learn the importance of different scale channels, in order to improve the model's representation and generalization performance. The structure of MSCA, as shown in Figure 2, can be obtained through the following steps. The first step of the MSCA module is to obtain multi-scale feature maps through n dilated convolutions of different size scales. Dilated convolution is a technique that increases the receptive field of the convolutional kernel while keeping the same number of parameters. This means that dilated convolution can capture information from larger regions of the input feature map, allowing the network to learn more meaningful features. Assuming the input feature is \(X\), the multi-scale feature maps obtained through dilated convolution can be described as a set of matrices, where each matrix represents the response of different filters to the input feature. The filters are defined by the convolution kernel size \(k_{i}\) and dilation rate \(d\), which determine the size of their receptive field. By using multiple filters with different receptive fields, the MSCA module can capture features of different scales \(F_{i}\), allowing it to learn more complex patterns and improve the accuracy of dialect identification. This can be described as:  
\[k_{i}=2i-1\quad(i=1,2\cdots n) \tag{8}\]  
\[F_{i}=Conv(k_{i},d)(X)\quad(i=1,2\cdots n) \tag{9}\]  
Figure 1: MSCA-TDNN. In order to reduce parameters and save computational resources, we used a dimension reduction \(m\) in the channel dimension, which reduces the output channels to \(1/m\) of the original feature map. In this experiment, we set the dimension reduction factor \(m\) to 4 and the number of dilation convolution \(n\) to 4. The Squeeze-and-Excitation (SE) module is highly effective in enhancing the performance of neural networks. The SE module enhances the influence of useful feature channels by learning the weights of each channel. The basic idea is to use another neural network to learn the weights of each channel, and then apply the weights to each channel of the input feature map, allowing the neural network to focus on the useful feature channels. In a multi-scale scenario, we can apply the SE module on different scale feature maps \(F_{i}\) to obtain multi-scale channel attention \(z_{i}\), which can help the network to better understand the input feature maps and improve the model performance. We applied squeeze operations on multiple scale features \(F_{i}\) to compute the average vector \(s_{i}\) of frame-level features at different scales:  
\[s_{i}=\frac{1}{T}\sum_{t=1}^{T}F_{i}(t)\ \ \ \ (i=1,2\cdots n) \tag{10}\]  
Here, \(T\) denotes the total number of frames on the scale, and \(F_{i}(t)\) represents the feature vector of the \(t\)-th frame on the \(i\)-th scale. Next, we perform the excitation operation to calculate the weights of the multi-scale channels, which can be defined as:  
\[z_{i}=\sigma(W_{2}f(W_{1}s_{i}+b_{1})+b_{2})\ \ \ \ (i=1,2\cdots n) \tag{11}\]  
Here, \(\sigma\) represents the sigmoid function, \(f\) represents a non-linear function, \(b_{1}\) and \(b_{2}\) are bias terms, and \(W_{1}\in\mathbb{R}^{R\times C}\), \(W_{2}\in\mathbb{R}^{C\times R}\) (where \(C\) and \(R\) represent the number of input channels and the reduction factor, respectively, and in our experiments, \(C\) is set to 64 and \(R\) is set to 1/2). After the multi-scale attention processing, the SE module obtains the channel attention of each scale feature map, but not all scales have equal importance for the task. Therefore, it is necessary to further calibrate the different scale feature maps to obtain more effective feature representations. To address this issue, this paper proposes a method for adaptively calibrating the channel attention vectors of different scale convolutions. Specifically, the  
Figure 2: Structure of MSCA.