# Weighted Cluster-Range Loss and Criticality-Enhancement Loss for Speaker Recognition
## 4 Experiments and Results
### Results
Besides, we found that such an operation did not bring extra perceptible computational burden owing to our dual-path architecture, i.e., the attention maps of both branches are calculated concurrently. By applying the idea of weighting, the proposed WCRL achieves significant improvement over the standard CRL and further improves the top-1 accuracy by 2.0% and the top-5 accuracy by 1.3% absolutely. Finally, our best results surpass the baseline (Res-SA + CRL) by 2.9% on the top-1 accuracy and 1.8% on the top-5 accuracy. When it comes to CEL, the result of using SA is slightly better than that of using DA, improving the top-1 accuracy by 1.7% and the top-5 accuracy by 1.2% compared with the baseline. Figure 7 depicts the accuracy curves of our proposed approaches and the baseline Res-SA + CRL. Obviously, the curves of our proposed methods lie totally above that of the baseline, which proves the effectiveness of our methods. The best result given in [8] achieved a top-1 accuracy of 90.8%, while our best model further improves on their best performance by 1.2%. The comparison between our results and other models is shown in Table 8.  
Furthermore, we also tested the cases where the weighting factor \(\omega_{2}\) is not one. The results of this part are presented in Table 9. Note that \(\omega_{1}\) is imposed on \(h^{n}\) and \(s_{a,n}\), and \(\omega_{2}\) is imposed on \(h^{p}\) and \(s_{a,p}\). Keeping \(\omega_{1}=1\), no matter \(\omega_{2}>1\) or \(\omega_{2}<1\), the results are worse than the version of \(\omega_{1}>1\) and \(\omega_{2}=1\). When we set \(\omega_{1}<1\), the result is also unsatisfactory. Besides, we also evaluate the \begin{table}
\begin{tabular}{l c c} \hline \hline
**Accuracy** & **Top-1\%** & **Top-5\%** \\ \hline i-vector + SVM [16] & 49.0 & 56.6 \\ i-vector/PLDA + SVM [16] & 60.8 & 75.6 \\ VGG-like CNN [16] & 80.5 & 92.1 \\ Res-SA [9] & 85.5 & 93.9 \\ VGG-like CNN + SA [8] & 88.2 & 93.8 \\ VGG-like CNN + CL [17] & 89.5 & 97.0 \\ ResNet-34 + LDE [18] & 89.9 & 95.7 \\ ResNet-18 + SA [8] & 90.8 & 96.5 \\ \hline Res-SA + CRL[9] & 89.1 & 95.8 \\ Res-CBAM + CRL (ours) & 89.5 & 96.0 \\ Res-DA + CRL (ours) & 90.0 & 96.3 \\ Res-DA + CRL + CEL (ours) & 90.2 & 96.7 \\ Res-SA + CRL + CEL (ours) & 90.8 & 97.0 \\ Res-SA + WCRL (ours) & 91.8 & 97.5 \\ Res-DA + WCRL (ours) & 92.0 & 97.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Speaker identification results on the VoxCeleb1 dataset (higher is better). Figure 7: ACC curves of different configurations. CEL, Criticality-Enhancement Loss. situation where \(\omega_{1}>1\) and \(\omega_{2}<1\), and it turns out that the identification accuracy is similar to other suboptimal situations mentioned above. The CN-Celeb dataset was employed to further evaluate our methods, and the results of this part are shown in Table 10. The method in [9] (Res-SA + CRL) was first tested, and a top-1 accuracy of 81.3% and a top-5 accuracy of 90.8% are obtained. The use of dual-attention increases the Top-1 accuracy to 82.6%. Let \(\omega_{1}\) in WCRL be 1.0002 with \(\omega_{2}\) being one; a top-1 accuracy of 83.6% is obtained. Finally, by replacing the WCRL with CRL+CEL, a top-1 accuracy of 84.3% is reached. The results of speaker verification are presented in Table 11 and will be compared with the baselines listed in Table 12. When trained on VoxCeleb1, the best result was reached by the scheme of Res-DA + CRL + CEL, and it achieved an EER of 5.1%. To further evaluate the performance of the model on other datasets, the training set was replaced with VoxCeleb2, and the EER was further reduced to 3.5%. Compared with the methods using the i-vector or x-vector, our proposed approaches are very competitive. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Accuracy** & **Top-1\%** & **Top-5\%** \\ \hline Res-DA + CRL + CEL & 84.3 & 92.1 \\ Res-DA + WCRL(\(\omega_{1}=1.0002\)) & 83.6 & 91.5 \\ Res-DA + CRL & 82.6 & 91.4 \\ Res-SA + CRL & 81.3 & 90.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Speaker identification results on the CN-Celeb dataset.