## 5 Experiments and Result
### Results  
We compared the performance of the experiments conducted in this paper with various recently reported studies and display the results in Table 3. The baseline system is a RawNet2-based model with several modifications, and reported improved performances based on the equal error rate (EER) compared to the original RawNet2. Moreover, the result of the proposed model exhibited further enhanced performance compared to the baseline system used as the encoder. This result indicates that the supervised MT framework proposed in this study can improve the generalization of SV system. In addition, the proposed system demonstrates superior performance compared to each model that feeds various input features, including the raw waveforms. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Loss**} & **Vox1-O** & **Vox1-E** & **Vox1-H** \\ \cline{3-5}  & & & **EER (\%)** & **EER (\%)** & **EER (\%)** \\ \hline ResNet-50 [9] & \multirow{2}{*}{Spectrogram} & Softmax+C & 3.95 & 4.42 & 7.33 \\ Thin ResNet-34 [42] & & Softmax & 2.87 & 2.95 & 4.93 \\ \hline \multirow{2}{*}{Stats-vector [43]} & \multirow{2}{*}{MFCC} & Softmax & 3.29 & 3.39 & 5.94 \\ ResNet-34-SE [44] & & AS-softmax & 3.10 & 3.38 & 5.93 \\ \hline RawNet2 [32] & \multirow{4}{*}{Raw} & Softmax & 2.48 & 2.57 & 4.89 \\ Y-vector [45] & & AM-softmax & 2.72 & 2.38 & 3.87 \\ Our baseline & & Softmax & 2.24 & 2.18 & 4.08 \\ Our proposed & & GE2E-H+Softmax & 1.98 & 1.88 & 3.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison results with other speaker verification systems with various models and input features. C: contrastive. To analyze the effectiveness of the proposed framework's components, we performed comparison and ablation experiments. Table 4 presents the performance according to the modification from the existing MT framework to the proposed method. All systems presented in Table 4 use a 1920 batch size and exploit the CCE loss function for classification training, along with their respective consistency loss functions. In the first row, NP refers to using negative pairs, BC indicates batch configurations, S represents using the same minibatch with added noise as the conventional MT, and D refers to the minibatch comprising different utterances from each speaker. In addition, in the LT column, which represents the learning target of the student network, P and E refer to the prediction and embedding of the MT network, respectively. System #1, which reflects the original MT framework training scheme, exhibited a noticeable performance decline compared to the baseline (2.24% vs. 4.98% on Vox1-O). Therefore, we modified the original MT framework (System #1) to be suitable for supervised SV tasks. System #2 encourages the student network to learn embeddings of the MT, not predictions, considering the characteristics of the SV task. In Systems #3 and #4, we exploited the minibatch comprising different utterance pairs for each speaker and let the student network learn to maximize the distance between negative pairs to fully employ all labels. When comparing Systems #1 and #4, it is effective to consider the negative pairs and learn the speaker embeddings of the MT with minibatches of different utterances. However, it did not exceed the baseline performance. The comparison of Systems #4 to #7 demonstrated that cosine similarity-based metric learning could improve the performance of SV. Finally, System #7, the proposed method, reported an EER of 1.98% on the Vox-O trial, with a relative error reduction of 11.61% compared with the baseline. Table 5 displays the comparison results according to the batch size of the baseline system and proposed method. For the proposed method, the batch size is the product of the number of speakers and number of utterances per speaker included in a single minibatch.