## 2 Methods
### Model Design
#### 2.2.2 Separation Network
\[e^{(3)}=\text{Conv2d}(\text{PReLU}(e^{(2)})), \tag{4}\]  
\[e^{(4)}=\text{OverlapAdd}(e^{(3)}), \tag{5}\]  
where OverlapAdd(\(\cdot\)) denotes the process of adding small blocks of overlap back into the sequence. The FFW is shown in Formula (6):  
\[e^{(4)}=\text{Conv1d}(\text{Tanh}(\text{Conv1d}\ (e^{(4)}))+\text{Sigmoid}( \text{Conv1d}\ (e^{(4)}))), \tag{6}\]  
Finally, we split \(e^{(4)}\) into \(N\) speaker features \(spk_{1},spk_{2},\dots,spk_{N}\), as Formula (7):  
\[(spk_{1},spk_{2},\dots,spk_{N})=(e^{(4)}[0],e^{(4)}[1],\dots,e^{(4)}[N]). \tag{7}\]  
2. SuperFormer Block  
Figure 2 shows the detailed structure of the SuperFormer Block. The SuperFormer Block includes Intra-SuperFormer and Inter-SuperFormer. After segmentation, the local and global dependencies between fusion channels and spatial adaptive features are extracted utilizing a dual-path framework. The Intra-SuperFormer module models the local dependence of the channel on the K-dimension of \(e^{(1)}\), and then adds the original input of \(e^{(1)}\) of the module to form the residual connection input to the Inter-Superformer module. Thus, the Inter-SuperFormer module forms spatial global dependence on sequence blocks  
of the S-dimension direction of \(z^{(1)}\). Therefore, the overall definition of the SuperFormer Block is shown in Formula (8):  
\[e^{(2)}=f_{\text{inter}}(\text{P}(f_{\text{intra}}(e^{(1)})+e^{(1)})+z, \tag{8}\]  
where \(f_{\text{intra}}(\cdot)\) and \(f_{\text{inter}}(\cdot)\) represent Intra-SuperFormer and Inter-SuperFormer, respectively. P is the conversion function permute resorted to representing the data dimension--that is, to exchange the dimensions of \(K\) and \(S\). * Forward Adaptive Module  
In order to enhance the feature learning ability of the separation network, a module to enhance the adaptability of the model is designed, the Forward Adapative Module, which has the same structure in Intra-SuperFormer and Inter-SuperFormer, as shown in Figure 3. The adaptive module exploits MLP to connect with Depth wise Convolution (Dw-Conv2d) and Depth wise Group Convolution (Dw-G-Conv2d) respectively, which helps the model to acquire corresponding knowledge from the transformed data structure [7,8], and as the expression of the local and global features of the speaker's speech, it improves the adaptability of the model. The specific calculation process is shown in Formulas (9)-(11). \[e_{1}^{(1)}=\text{Sigmoid (MLP}(e^{(1)})\cdot e^{(1)}), \tag{9}\]  
\[e_{2}^{(1)}=\text{Sigmoid (Norm (Dw-Conv2d (PReLU(Norm(Dw-Conv2d (e_{1}^{(1)})))))}\cdot e_{1}^{(1)}), \tag{10}\]  
Figure 1.0  
where \((\cdot)\) denotes the dot product of the elements. Figure 1.1 Structure design of the SuperFormer Block, including the Intra-SuperFormer and Inter-SuperFormer with different structures. The difference between the two modules lies in the structure of FFN module in transformer. The Intra-Transformer uses a TCN layer to learn the intra -block data correlation of speech, and the Inter-Transformer uses an RNN network to learn the inter -block data correlation of speech. * Intra-Transformer and Inter-Transformer  
The main difference between Intra-SuperFormer and Inter-SuperFormer lies in the Feed Forward Network (FFN) in Intra-TransFormer and Inter-Transformer. A 1-D convolution and time convolution (TCN) module are designed in the Intra-TransFormer to extract the autocorrelation features in the block. The internal structure of the TCN module is illustrated in Figure 1.2 In Inter-TransFormer, an 1-D convolution and Bi-directional Long Short-Term Memory (Bi-LSTM) are resorted to extracting long-distance global features. Figure 1.3 Structural design of the TCN module, which is designed for features extraction of intra-block speech. Figure 1.4 The Forward Adaptive Module structure is designed to enhance the adaptability of the model to features. \(e^{(1)}\) is input into the Intra-SuperFormer module for channel autocorrelation calculation. Through the Forward Adaptation Module, the residual connection method is adopted.