## 4 Results and Comparison
### PNR-TDNN Experiments
#### 4.2.2 Discussion of Clusters and Compressed Models  
Table 5 presents the experimental results of various PNR-TDNNs. We found that an increased number of MFCC clusters corresponding to pseudo-labels within the pre-trained model lead to enhanced effectiveness in the back-end recognition model. When the number of clusters exceeds 100, HuBERT experiences gradient overflow within the first three epochs. In this case, the corresponding PNR-TDNN exhibits significantly weak recognition performance. Therefore, the optimal strategy is to select a maximum number of clusters that ensures the convergence of the pre-trained model, balancing the model's capacity with its ability to learn effectively. In addition, recognition performance is at its peak when the cluster number is set to 80. Based on the methodology described in Section 2.4.2, which involves Canopy and Mini Batch k-means++, it is determined that for the specific application scenario, when the values of \(T_{1}\) and \(T_{2}\) are set at 400 and 180, respectively, the optimal number of clusters is obtained. In the case of noise-only interference, the EER difference between Hu + EC(80) and Wa + EC(80) is negligible, whereas the difference in MinDCF is notable. Hu + EC(80) exhibits superior performance in both metrics under conditions of combined noise and reverberation. Our study suggests that the ambiguity introduced by full-channel reverberation makes use of gated relative position bias that is inappropriate for PNR-TDNN. Additionally, the results for Hu + CA(80) consistently demonstrate lower performance compared to Hu + EC(80) across all evaluated metrics and computational factors. Consequently, Hu + EC(80) is designated as the reference implementation for PNR-TDNNs in subsequent experiments. Another key issue is that Hu + EC occupies 400 M, which is a very large amount that is unacceptable and cannot be deployed for smart microphone devices. As shown in Table 6, we reduced the parameters for HuBERT's Transformer encoder and feed forward net. The minimized HuBERT + EC (T-HuBERT + EC) is only 90 M, which is in the same order of magnitude as ECAPA-TDNN and CAM++. In subsequent experiments, small \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Methodology**} & \multicolumn{2}{c}{**Dataset A**} & \multicolumn{2}{c}{**Dataset B**} & \multicolumn{2}{c}{**Dataset C**} & \multicolumn{2}{c}{**Params**} & \multicolumn{2}{c}{**Computational Efficiency**} \\  & **EER** **(\%)** & **MinDCF** & **EER** **(\%)** & **MinDCF** & **EER** **(\%)** & **MinDCF** & **Model** **(M)** & **Flops** **(G)** & **RTF (\(1\times 10^{-3}\))** \\ \hline TDNN & 7.52 & 0.201 & 9.47 & 0.192 & 7.35 & 0.155 & **11.3** & 0.318 & 0.47 \\ Resnet-SE & 8.40 & 0.184 & 8.72 & **0.188** & 9.73 & 0.159 & 56.1 & 3.719 & 11.56 \\ Res2 net & 10.26 & 0.204 & 10.77 & 0.195 & 9.78 & 0.169 & 111.6 & 1.002 & 2.97 \\ Eres2 net & 7.61 & 0.196 & 7.89 & 0.189 & 6.65 & 0.160 & 27.4 & 2.428 & 7.18 \\ \hline
**ECAPA-TDNN**[20] & 7.18 & 0.188 & 8.44 & 0.190 & 6.77 & 0.154 & 33.9 & 0.973 & 1.23 \\
**CAM++[39]** & **5.97** & **0.178** & **7.81** & 0.191 & **6.35** & 0.159 & 28.7 & 0.813 & 4.63 \\ MFA-Conformer [58] & 7.98 & 0.198 & 8.78 & 0.189 & 7.40 & 0.160 & 77.0 & 0.994 & 2.48 \\ Wespeaker [59] & 10.88 & 0.206 & 12.12 & 0.197 & 10.22 & 0.174 & 0.96 & **0.006** & **0.19** \\ RedimNet [60] & 6.59 & 0.197 & 8.19 & 0.192 & 7.45 & 0.166 & 21.1 & 1.290 & 8.79 \\ Gemini [61] & 7.78 & 0.201 & 8.43 & 0.190 & 8.12 & 0.163 & 26.7 & 3.834 & 26.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Baseline model’s best EER and MinDCF.