## 3 Materials and Methods
### Chrono Block  
The Chrono-ECAPA-TDNN framework is an improvement upon the ECAPA-TDNN model. The key difference lies in the use of the Chrono module instead of the single-branch SE-Res2 Block module in ECAPA-TDNN to capture both local and global speaker features. It consists of two parallel branches and a merging module, with one branch dedicated to capturing global features through self-attention, while the other branch focuses on extracting local features using the SE-Res2 Block module. To simultaneously capture both local features and global dependency features, the design of the Chrono Block module fully considers the core requirements of speaker representation learning. Local features, such as pitch, intonation style, and pronunciation patterns, provide individualized speech feature information, while global dependency features, such as long-range correlations in variable-length speech, capture the overall contextual relationships of the speech signal. The structure of the Chrono Block module is shown in Figure 2, consisting of two parallel branches and a feature fusion module. The parallel branches include the left branch with a Bi-LSTM module and a multi-head attention module. The Bi-LSTM module captures the global temporal dependencies of the speech signal through forward and backward LSTM layers, further enhancing the model's ability to model long-range context. In the multi-head attention mechanism, a scaled dot-product attention calculation method commonly used in Transformers is applied, combined with a position encoding strategy, improving the model's adaptability and robustness to variable-length speech. The right branch consists of a Squeeze-and-Excitation (SE) [5] mechanism and residual network connections, forming the SE-Res2 Net module, which focuses on extracting multi-scale local features. Additionally, each layer of the Chrono Block module is equipped with LayerNorm normalization layers to stabilize the training process and enhance the model's feature representation capability. The feature fusion module integrates the outputs of the two branches through weighted fusion, achieving a unified representation of local and global features and providing a rich information foundation for downstream speaker embedding generation. The computation process of the Chrono Block module consists of multiple progressive steps, gradually extracting and fusing multi-scale local features and global contextual information from the speech signal. First, the Fbank features are passed through the convolutional layer to obtain a dimensionality-reduced feature representation, which is then sent to the Chrono module for further feature extraction. The Chrono module consists of two parallel branches, each capturing local and global features of the speech signal. For the left branch of the Chrono module, the input features are denoted as \(h_{m-1}\) and the output features as \(h_{m}^{2}\); for the right branch, the input features are \(h_{n-1}\) and the output features are \(h_{n}^{2}\). The computation of the left branch is detailed as follows, as shown in Equations (8)-(10):  
\[h_{m}=h_{m-1}+LayerNorm(h_{m-1}), \tag{8}\]  
\[h_{m}^{1}=h_{m}+BiLSTM(h_{m}), \tag{9}\]  
\[h_{m}^{2}=h_{m}^{1}+MHSA(h_{m}^{1}), \tag{10}\]  
where \(h_{m-1},h_{m},h_{m}^{1},h_{m}^{2}\in R^{C\times T}\), \(m=1,2,\cdots,L\) (\(L\) is maximum 3), \(C\) represents the convolutional channels in the Chrono module, and \(T\) represents the number of time frames. _LayerNorm_ refers to layer normalization, _BiLSTM_ refers to the bidirectional Long Short-Term Memory network, and _MHSA_ refers to the Multi-Head Self-Attention mechanism. The right branch focuses on local feature extraction, with input features as \(h_{n-1}\) and output features as \(h_{n}^{2}\).