## 2 Background and Proposed Method
### Proposed Method Overview
#### 2.4.3. Fusion Res2 net and SE-Attentive Mean  
In Figure 6a, the input is divided into \(n\) feature groups by Res2 net. The \(i\)-th feature is fused with the \((i+1)\)th feature through a \(3\times 3\) convolutional residual connection, except for the first feature, which is preserved in an unchanged state. Inspired by multi-rate tracking in navigation system [54], this study utilizes the multi-scale fusion capability of the U-net architecture. Figure 4b illustrates the convolutional fusion process within the U-net architecture. In the downsampling phase, features are combined by applying a \(3\times 3\) convolution, where the \(i\)th-level feature is integrated with the \((i+1)\)th level feature.  
Figure 5: The algorithm of Canopy/Mini Batch k-means++.  
Conversely, during the upsampling phase, the \(i\)th-level feature is concatenated with the \((i-1)\)th-level feature through a similar \(3\times 3\) convolutional process. Furthermore, at the deepest level (\(nt\)th feature), convolution is applied, and the result is directly propagated to the subsequent layer. This mechanism facilitates the integration of contextual information and the fusion of neighboring channels.  
Equations (8)-(10) illustrate the three steps executed by the SE (Squeeze Excitation) module within the ECAPA-TDNN framework. (1) \(x(B,F,T)\) obtains \(x_{mean}(B,F,1)\) in the \(T\) dimension mean, as shown in Figure 4c, \"Mean Parameter\"; (2) \(x_{mean}\) is squeezed and excited to obtain weight coefficients for all \(F\) channels \(x_{f}(B,F,1)\). The linear operation corresponding to \(W_{1}\) and \(b_{1}\) represents squeeze, whereas \(W_{2}\) and \(b_{2}\) represent excitation, as shown in Figure 4c, \"Fully Connected\"; (3) \(x_{f}\) is extended to \(x_{ft}\) (in \(T\) dimension), and subsequently, \(x_{f}\) is re-weighted with \(x\) to obtain \(\widetilde{x}(B,F,T)\), as shown in Figure 6c, \"Re-weight\".  
\[x_{mean}=\frac{1}{T}\sum_{t=1}^{T}x_{t} \tag{8}\]  
\[x_{f}=sigmoid(W_{2}\cdot relu(W_{1}\cdot x_{mean}+b_{1})+b_{2}) \tag{9}\]  
\[\tilde{x}=x_{ft}\cdot x \tag{10}\]  
This study introduces an attentive channel mean mechanism to replace the traditional mean operation, acknowledging the varying contributions of different frames to the speaker's message, particularly in the differentiation between vocalized and silent states. Concretely, \(x(B,F,T)\) is sequentially processed through compression, recovery, and probability estimation to yield the attentive channel mean score \(\alpha\).  
In Equation (11), \(x\) undergoes squeeze and recovery operations along the \(F\) channel. The linear transformations corresponding to weight matrix \(W_{3}\) and bias vector \(b_{3}\) denote the squeeze operation, while \(W_{4}\) and \(b_{4}\) denote the recovery operation, as illustrated in Figure 4(c1), \"Fully Connected\". The hyperbolic tangent function, \(tanh\), is used as the activation function. After the above operation, we further obtain the linear relationship between all \(F\) channels. Subsequently, the Softmax activation function is applied to the \(T\) channel, resulting in the fractional distribution of different time frames. Equation (12) illustrates that \(\alpha\) is element-wise multiplied with \(x\), followed by the aggregation of the resulting values across the \(T\) channel. Conclusively, the optimized mean feature \(\widetilde{x}_{mean}\) is derived, as shown in Figure 4(c1), \"Hadamard Product+Sum\".  
\[\alpha=Softmax(W_{4}\cdot\tanh(W_{3}\cdot x+b_{3})+b_{4}) \tag{11}\]  
\[\tilde{x}_{mean}=\sum_{t=1}^{T}\alpha_{t}\cdot x_{t} \tag{12}\]  
Figure 6: Different Res2 nets comparisons.