# Weakly Supervised U-Net with Limited Upsampling for Sound Event Detection
## 4 Experiments
### Original Synthetic Policy
The next 3 rows show the precision, recall, and F1 scores obtained by the proposed LUU-Net with 3 different types of global pooling methods. The LUU-Net with GWRP showed improved F1 scores of 64.1 and 50.7, when compared to 62.0 and 49.2 with the conventional U-Net. The number of steps per second was 28.99, 3.23-times faster than U-Net. We also compared the pooling method GWRP with AlphaMEX [6] and MEX [37]. The F1 score of the AT task was 64.0 with AlphaMEX, which was similar compared to the 64.1 with GWRP. However, the F1 score of the SED was 40.7 with AlphaMEX, which was much lower than the 50.7 with GWRP. The F1 scores with MEX were 64.1 and 51.5, which were the best among the conventional 3 pooling methods, GWRP, AlphaMEX, and MEX. The final 3 rows combine the proposed LUU-Net with the proposed GTAP pooling. For hyperparameters \(\alpha=\{0.2,0,-0.4\}\), the F1 scores for the AT task were \((64.5,64.4,68.8)\), respectively. By setting \(\alpha=-0.4\), the highest F1 score for the AT task was obtained. The F1 scores for the SED task were \((52.5,53.1,50.0)\), respectively. For \(\alpha=-0.4\), the F1 score was much lower than the others. The highest SED score was obtained by setting \(\alpha=0\). However, \(\alpha=0.2\) gave a slightly better AT F1 score, so it is also a well-balanced \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\alpha\) & \(m\mathbf{F1}_{AT}\) & \(m\mathbf{F1}_{SED}\) & **Average** & **Rank** \\ \hline
1.0 & 65.26 & 50.67 & 57.96 & 7 \\
0.8 & 66.44 & 52.81 & 59.62 & 5 \\
0.6 & 65.77 & 53.51 & 59.64 & 4 \\
0.4 & 66.34 & 52.50 & 59.42 & 6 \\
0.2 & 65.64 & 53.93 & 59.78 & 3 \\
0.0 & 65.33 & 54.36 & 59.85 & 2 \\ \(-0.2\) & 64.27 & 50.35 & 57.31 & 8 \\ \(-0.4\) & 69.66 & 51.02 & 60.34 & 1 \\ \(-0.6\) & 65.72 & 47.03 & 56.37 & 9 \\ \(-0.8\) & 63.80 & 45.26 & 54.53 & 11 \\ \(-1.0\) & 64.07 & 45.38 & 54.72 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Grid search results on the dataset generated by the original policy. The model is the proposed LUU-Net. Classwise mean F1 scores of audio tagging (\(mF1_{AT}\)) and sound event detection (\(mF1_{SED}\)) tasks were computed, and their average was used to rank the hyperparameter \(\alpha\) values. The top 3 were \(\{0.2,0.,-0.4\}\). hyperparameter value. According to Equations (5) and (7), the smaller value of \(\alpha\) produced a lower threshold, so more units from the segmentation map were chosen in the average pooling. Hence, it was more advantageous in finding a single audio event label, i.e., the audio tagging task. However, more units in the boundary region having weak activations were included in the average pooling, and the SED performance, therefore, degraded. When \(\alpha=0\), the cut-threshold became the simple average of the whole segmentation map and provided well-balanced performance in both the AT and SED task. There were no meaningful differences in the computation time by varying \(\alpha\), so the average number of steps per second is given in the rightmost column of Table 9. The number of steps per second of GTAP was higher than all the other methods due to the reduced number of segmentation units in the average pooling. Figure 8 shows the sound event detection results with various models and various global pooling methods. The models in (c-e) were trained by the CNN, U-Net, and LUU-Net, respectively, and GWRP was adopted. In (c), event labels predicted by the CNN, the first event was almost missing, and many falsely detected units were seen and scattered in the upper part of the figure. In (d), U-Net prediction, the first event was detected, and much fewer false prediction units were observed. In (e), by the proposed LUU-Net, the event labels were more clearly detected, and a very small amount of false predictions were observed. To show the differences of the global pooling methods, event prediction examples are shown in (f-h), whose models were configured with AlphaMEX, MEX, and the proposed GTAP, respectively.