## 4 Experiment, Results and Analysis
### Ablation Studies  
The Branchformer block differs from the Transformer block in many aspects, especially its dual-branch structure and merging module, and the inclusion of the Maclaurin style of FFN before and after each block. Here, we investigate the impact of the different modules introduced on model performance by transforming the Branchformer block into the Transformer block. Table 2 displays the effects of each reduction on the Branchformer block. Among all the differences, the cgMLP module, which models local context dependencies, is the most important. Next, is the appropriate merging method, which enables the model to effectively model global and local dependencies. Lastly, the FFN module is able to refine pointwise information after temporal features are aggregated. We also investigated the impact of using different fusion methods to integrate local and global information on model performance. The experimental results are shown in Table 3. From Table 3, it is evident that for short-duration speech (3 s), overall, regardless of the fusion method used, there is a positive effect on improving model performance. This is mainly because short-duration speech contains insufficient information, and introducing additional local context-dependent information can promote model performance. However, for long-duration speech for some fusion methods, there is a slight decrease in model performance. This is mainly because long-duration speech already contains sufficient information, and introducing additional information may introduce some irrelevant information, affecting model performance. Therefore, choosing the appropriate fusion method has a significant impact on model performance. We proposed six different fusion methods, and from the experimental results in Table 3, it can be seen that fusion methods based on attention and deep convolution show comprehensive performance improvement. Among them, the fusion module based on deep convolution exhibits the best performance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**3 s**} & \multicolumn{2}{c}{**10 s**} & \multicolumn{2}{c}{**30 s**} \\ \cline{2-7}  & \(EER\) & \(C_{avg}\) & \(EER\) & \(C_{avg}\) & \(EER\) & \(C_{avg}\) \\ \hline X-vector [7] & 11.79 & 11.59 & 7.81 & 7.48 & 6.84 & 6.54 \\ XSA-LID [44] & 10.71 & 10.04 & 4.89 & 4.32 & 3.71 & 3.29 \\ CNN-trans [13] (our baseline) & 7.89 & 7.10 & 3.89 & 3.46 & 2.91 & 2.62 \\ conformer [29] & 7.78 & 6.95 & 3.80 & 3.42 & 2.92 & 2.57 \\ B-transformer (ours) & 7.40 & 6.34 & 3.67 & 3.16 & 2.55 & 2.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The NIST LRE 2017 MLS14 set was evaluated using EER (%) and Cavg (%) over 3 s, 10 s, and 30 s durations of test speech. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**3 s**} & \multicolumn{2}{c}{**10 s**} & \multicolumn{2}{c}{**30 s**} \\ \cline{2-7}  & \(EER\) & \(C_{avg}\) & \(EER\) & \(C_{avg}\) & \(EER\) & \(C_{avg}\) \\ \hline B-transformer & 7.40 & 6.34 & 3.67 & 3.16 & 2.55 & 2.32 \\ w/o FFN & 7.46 & 6.57 & 3.68 & 3.22 & 2.60 & 2.39 \\ w/o Dconv & 7.67 & 6.84 & 3.77 & 3.31 & 2.75 & 2.46 \\ w/o cgMLP & 7.89 & 7.10 & 3.89 & 3.46 & 2.91 & 2.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The ablation study results of using different fusion methods while keeping other parameters unchanged. The convolutional kernel size plays a critical role in convolutional neural networks, directly affecting the model's performance and computational efficiency. As the convolutional kernel size increases, the model can capture a larger feature range, which helps extract more comprehensive global features. However, this also increases the number of model parameters and computational complexity, potentially leading to overfitting. Moreover, excessively large convolutional kernels can greatly increase computation, impacting model depth increase and computational performance.