# Weakly Supervised U-Net with Limited Upsampling for Sound Event Detection
## 4 Experiments
### Original Synthetic Policy  
The sound event detection experiments were carried out on the generated dataset according to the original synthetic policy [16]. As shown in Table 1, the maximum event length was set to be 2.0 s, and the mean and standard deviation of the event length were 1.7 and 0.51 s, respectively. To determine the value of the hyperparameter \(\alpha\) in Equation (7), we performed a grid search. \(\alpha\) was varied from \(-1.0\) to \(1.0\) with 0.2 displacement, a total of 10 cases for the grid search. The result is shown in Table 8. There was 90% of the generated training dataset used to train the proposed LUU-Net with the pooling method G TAP, and the remaining 10% was used as a validation set. The classwise mean F1 scores of the audio tagging (AT) and sound event detection (SED) tasks were computed, and their average values were used to rank different \(\alpha\) values. We selected \(\alpha\in\{0.2,0.0,-0.4\}\) according to the average of \(m{{{\it{F1}}}_{{\it{AT}}}}\) and \(m{{{\it{FI1}}}_{{\it{SED}}}}\) and used them in the subsequent experiments. Table 9 shows the AT and SED performances with various model configurations. The baseline line CNN does not have any downsampling layers. Therefore, there was no reduction in the output map sizes along the forward path, requiring huge convolutional operations. The number of iterations per unit second, at the last column, was 3.69 and \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{**Ground Truth**} \\ \cline{3-4}  & & **T** & **F** \\ \hline \multirow{2}{*}{predicted} & T & TP & FP \\ \cline{2-4}  & F & FN & TN \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Classification of prediction results by being compared with ground truth labels. Ground truth labels are given, and predicted labels are the output of the binary classifiers. Symbols T, F, TP, FP, FN, and TN are true, false, true positive, false negative, and true negative, respectively. relatively small when compared to the other models. When GTAP was applied, the number of iterations per unit second was 4.54, meaning that a 23% faster training speed was obtained. However, both the AT and SED performances degraded greatly in terms of the mF1. Because there was no reduction in the output map sizes across the convolutional layers, as shown in Table 4, the sound event information was distributed in the final segmentation mask. According to Equations (4) and (5), the proposed GTAP does not use inactive or little active outputs, so it is not suited to CNNs. The second part shows the performance with the conventional U-Net. Significant improvements were gained in terms of computational overhead, as well as AT and SED performances by replacing the CNN with U-Net, with the help of the recursive shortcut paths from the previous layers. For both of the AT and SED tasks, the precision, recall, and F1 scores all increased by about 10%. F1 scores of 53.1 and 39.5 were obtained by the CNN and 62.9 and 49.2 by U-Net. The number of training steps per second was 8.97, which was 2.43-times faster than the CNN. Further improvements were obtained by GTAP. The number of steps per unit second was 13.11, 68% faster than GWRP. In the AT tasks, the mean F1 scores were 58.9 and 58.0 with \(\text{GTAP}_{\alpha}=0.2\) and \(\text{GTAP}_{\alpha=0}\), which were lower than 62.9 with GWRP. However, \(\text{GTAP}_{\alpha=-0.4}\) showed 68.0, which was the largest among all the U-Net results. In the SED tasks, \(\text{GTAP}_{\alpha}=0.2\) and \(\text{GTAP}_{\alpha=0}\) were better than GWRP, but \(\text{GTAP}_{\alpha=-0.4}\) was worse. With lower \(\alpha\), a smaller threshold is obtained by Equation (7), and more components in the segmentation map are used, so higher precision was obtained in the AT task. However, segment-based metrics were used in the SED task, and more false positive segments were included by the lower threshold in GTAP, resulting in very low precision (38.8).