## 3 Results and Discussion
### Comparison with the Forward Approach  
Table 4 compares our approach with existing methods. The improved 1-max CNN of [38] is used in combination with a DNN learning frequency domain filter bank to pre-process time-frequency image features. VGG-FE [39] utilizes multi-cone spectroscopy, a typical migration learning approach. SleepEEGNet [40] proposes a CNN-BIRNN network architecture along with a loss function to tackle the issue of class imbalance within EEG datasets. CCRSleepNet [41] uses hybrid relational induced bias to optimize the network and uses multiple convolutional blocks to extract complex features. AttnSleep [42] utilizes small-core and wide-core dual-branch CNN to extract features of different frequencies and use a multi-head attention (MHA) mechanism to capture time dependencies between features. Furthermore, [43] used migration learning with SeqSleepNet+ and DeepSleepNet+ based on a sequence-to-sequence sleep staging framework to overcome the problem of small datasets and insufficient data in sleep studies. IITNet [44] utilizes ResNet and LSTM to learn the time context within and between epochs of learning. TinySleepNet [45] simplifies the DeepSleepNet model structure and incorporates data augmentation. Overall, our method is relatively novel and achieves better performance because the shared convolutional structure allows the TCN to process long sequences in parallel, so the TCN is more memory efficient than the recurrent network, thus, the training time is shorter, with a total cross-validation time of 5.1 h for 20 folds, which is significantly better than [42] (about 7 h).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Overall Performance**} & \multicolumn{3}{c}{**Per-Class Performance**} \\  & **Acc** & **MF1** & **\(\kappa\)** & **W** & **N1** & **N2** & **N3** & **REM** \\ \hline
1-max CNN [38] & 79.8 & 72.0 & 0.720 & - & - & - & - & - \\ \hline VGG-FT [39] & 80.3 & - & - & - & - & - & - & - \\ \hline SleepEEGNet [40] & 84.26 & 79.66 & 0.79 & 89.19 & 52.19 & 86.77 & 85.13 & 85.02 \\ \hline CCRSleepNet [41] & 84.29 & 79.81 & 0.78 & 89.01 & 51.73 & 87.25 & 88.20 & 82.86 \\ \hline AttnSleep [42] & 84.3 & 77.7 & 0.776 & 85.4 & 50.9 & 88.8 & 86.4 & 86.5 \\ \hline FT DeepSleepNet+ [43] & 84.4 & 78.8 & 0.781 & - & - & - & - & - \\ \hline IITNet [44] & 84.6 & 79.0 & 0.782 & 81.0 & 50.5 & 88.2 & 86.9 & 87.2 \\ \hline FT SeqSleepNet+ [43] & 85.2 & 79.6 & 0.789 & - & - & - & - & - \\ \hline TinySleepNet [45] & 85.4 & 80.5 & 0.80 & 90.1 & 51.4 & 88.5 & 88.3 & 84.3 \\ proposed Method & 86.2 & 79.8 & 0.808 & 92.0 & 45.5 & 89.4 & 88.6 & 83.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of NAMRTNet with other methods.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Predicted**} & \multicolumn{3}{c}{**Per-Class Metrics**} \\  & **W** & **N1** & **N2** & **N3** & **REM** & **PR** & **RE** & **F1** \\ \hline W & 7497 & 393 & 153 & 24 & 123 & 92.6 & 91.5 & 92.0 \\ N1 & 442 & 1122 & 683 & 15 & 640 & 55.2 & 38.7 & 45.5 \\ N2 & 77 & 223 & 16,416 & 625 & 804 & 88.4 & 90.5 & 89.4 \\ N3 & 8 & 0 & 609 & 5009 & 0 & 88.1 & 89.0 & 88.6 \\ REM & 76 & 295 & 711 & 12 & 6749 & 81.2 & 86.1 & 83.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Confusion matrix obtained from 20-pass cross-validation on the Fpz-cz channel of the sleep-EDF dataset.