# Employing Huber and TAP Losses to Improve Inter-SubNet in Speech Enhancement
## 5 Experimental Results and Discussion  
In Table 1, we can observe the SE metric scores of Inter-SubNet using three different loss functions. The results show that replacing MSE loss with Huber loss for clRM estimation leads to a significant improvement in all six metrics, demonstrating the effectiveness of Huber loss in enhancing the Inter-SubNet performance. On the other hand, replacing MSE loss (for clRM) with TAP loss (for time-domain signals) improves COVL and CSIG scores but worsens the remaining SE metrics (WB-PESQ, NB-PESQ, STOI, and SI-SDR). This suggests that solely minimizing TAP loss does not effectively optimize the clRM used in Inter-SubNet, a masking-based SE framework. Next, we incorporated TAP loss into the original MSE loss of Inter-SubNet. The corresponding results are displayed in Table 2. From the table, the following observations can be made:  
1. TAP loss fine-tunes Inter-SubNet to enhance its performance. The combination of MSE and TAP losses leads to better results in almost all SE metrics (except SI-SDR) compared to when individual losses are used alone. 2. When the weight \(\lambda_{1}\) for TAP loss is set within the range of \([0.02,0.03]\), similar good performance is achieved. However, increasing \(\lambda_{1}\) to 0.04 degrades some metrics. 3. The introduction of TAP loss does not lead to an improvement in the SI-SDR metric. This may be due to the fact that SI-SDR is more concerned with physical distortion rather than the perceptual interference that TAP loss addresses. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Loss** & **WB-PESQ** & **NB-PESQ** & **STOI** & **SI-SDR** & **COVL** & **CSIG** \\ \hline \(\mathcal{L}_{clRM,MSE}\) (baseline) & 2.843 & 3.588 & 0.943 & 18.427 & 3.419 & 4.000 \\ \hline \(\mathcal{L}_{lRM,Huber}\) & **2.900** & **3.620** & **0.946** & **18.811** & **3.493** & **4.078** \\ \hline \(\mathcal{L}_{TAP}\) & 2.746 & 3.478 & 0.939 & 17.338 & 3.442 & 4.127 \\ \hline \end{tabular}
\end{table} 
Table 1: The various SE performance scores of Inter-SubNet trained with different loss functions: \(\mathcal{L}_{clRM,MSE}\) as in Equation (6), \(\mathcal{L}_{clRM,Huber}\) as in Equation (13), and \(\mathcal{L}_{TAP}\) as in Equation (11). In addition, we compared the revised Inter-SubNet (incorporating Huber and TAP losses) with several prominent speech enhancement frameworks, SEGAN [24], CMGAN [45], and MP-SENet [46], which primarily utilize generative adversarial networks (GANs), along with MANNER [47] and SE-Conformer [48], which mainly employ attention mechanisms. This evaluation, detailed in Table 5, is based on their experimental results for the NB-PESQ and STOI metrics obtained from the VoiceBank-DEMAND dataset, as reported in the literature. From the table, it is evident that the revised Inter-SubNet achieves a superior NB-PESQ score compared to all other methods evaluated. In contrast, nearly all methods (with the exception of SEGAN) yield very similar STOI scores. These findings confirm that the proposed method performs better than or at least on par with state-of-the-art speech \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Loss** & **WB-PESQ** & **NB-PESQ** & **STOI** & **SI-SDR** & **COVL** & **CSIG** \\ \hline \(\mathcal{L}_{clRM,Huber}+\lambda_{2}\mathcal{L}_{TAP}\) & **2.955** & 3.609 & **0.946** & 18.287 & **3.584** & **4.197** \\ \hline \(\mathcal{L}_{clRM,Huber}\) & 2.900 & **3.620** & **0.946** & **18.811** & 3.493 & 4.078 \\ \hline \(\mathcal{L}_{TAP}\) & 2.746 & 3.478 & 0.939 & 17.338 & 3.442 & 4.127 \\ \hline \(\mathcal{L}_{cIRM,MSE}\) (baseline) & 2.843 & 3.588 & 0.943 & 18.427 & 3.419 & 4.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The ablation study, summarizing the influence of Huber loss and TAP loss on the performance of Inter-SubNet.