# Weakly Supervised U-Net with Limited Upsampling for Sound Event Detection
## 4 Experiments
### Model Configurations  
We compared the proposed U-Net model with the basic CNN and conventional U-Net in terms of SED performances. The basic building blocks of the models are listed in Tables 2 and 3. We generally stacked \(3\times 3\) convolutional layers (\(Conv(3,K)\)) and used \(1\times 1\) convolutions (\(Conv(1,K)\)) to resize the number of output maps if necessary. One deconvolutional layer, denoted by \(DeConv22(3,K)\), has stride \((2,2)\), and is used to uncompress the \(x\)- and \(y\)-axes by a factor of \(2\). Another deconvolutional layer \(DeConv21(3,K)\) has stride \((2,1)\) and uncompresses the \(x\)-axis only, so it doubles the output map size along the time axis, but not along the frequency axis. \(DeConv21(3,K)\) was adopted in the proposed method only. In all the convolutional layer types, the number of output channels is given by a parameter \(K\), and the number of inputs is determined automatically according to the previous output layers. At all the outputs of the convolutional and deconvolutional layers, we performed batch normalization and applied the rectified linear unit activation function (BN-ReLU) [34; 35], as shown in Table 2. Two types of average pooling layers are used. In Table 3, \(AvgPool(2,2)\) uses a \(2\times 2\) pooling window with the same stride size in both the time and frequency axes, so the size of the output map is reduced to half of the original in both axes. \(AvgPool(1,s)\) uses a \(1\times s\) pooling window with moving \(s\) samples along the time axis and \(1\) bin along the frequency axis, so the size of the output map decreases along the time axis only. \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Onset Times** & **Max Clip** & **Mean** & **Std** \\ \hline original & 0.5, 3.0, 5.5 & 2.0 & 1.7 & 0.51 \\ longer clipping & 0.5, 3.0, 5.5 & 5.0 & 3.14 & 1.67 \\ random onset & uniformly random in \([0.5,6.5)\) & 2.0 & 1.7 & 0.51 \\ mixed & uniformly random in \([0.5,6.5)\) & 5.0 & 3.13 & 1.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Audio synthetic polices. All numbers are in seconds. The column names mean: onset times are the beginning of the events; max clip is the maximum clipping length; mean and std are the average and standard deviation of the clipping lengths. The row names: original is the policy suggested by the DCASE Challenge; longer clipping uses a longer maximum clipping length; random onset is varying the onset times randomly; mixed is the mixed policy of random onset and longer clipping. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Name** & **Kernel Size** & **Strides** & **Output Channels** & **Post Processing** \\ \hline \(Conv(3,K)\) & \(3\times 3\) & \((1,1)\) & & \\ \(Conv(1,K)\) & \(1\times 1\) & \((1,1)\) & & \\ \hline \(DeConv2(3,K)\) & \(3\times 3\) & \((2,2)\) & & \\ \(DeConv21(3,K)\) & \(3\times 3\) & \((2,1)\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Basic convolutional blocks used in SED model construction. There are two types of convolutional layers, \(Conv(3,K)\) and \(Conv(1,K)\), with \(3\times 3\) and \(1\times 1\) kernel sizes, respectively. There are also two types of deconvolutional layers. \(DeConv22(3,K)\) and \(DeConv21(3,K)\) have strides \((2,2)\) and \((2,1)\), respectively. BN-ReLU is batch normalization and rectified linear unit activation at the output. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Name** & **Description** & **Input Size** & **Output Size** \\ \hline \(AvgPool(2,2)\) & \(2\times 2\) average pooling, stride \((2,2)\) & \((w,h,K)\) & \((\frac{w}{2},\frac{h}{2},K)\) \\ \(AvgPool(1,s)\) & \(1\times s\) average pooling, stride \((1,s)\) & \((w,\frac{h}{2},K)\) \\ \hline \(Dropout(p)\) & dropout with probability \(p\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pooling blocks and dropout layer used in SED model construction. The layer \(AvgPool(2,2)\) reduces the sizes by half in both the \(x\)- and \(y\)-axes, but \(AvgPool(1,f)\) reduces the \(y\)-axis by a factor of \(f\), resizing the frequency axis, but not the time axis.