## 4 Evaluation  
### Evaluation Settings  
In order to evaluate the ensemble-guided model for the model-complexilty-limited task, evaluations with development data from DCASE 2021 Task 1A [20] were performed. The audio data of the task consisted of recordings from 12 cities in 10 acoustic scene classes with 4 recording devices, and synthetic data from 11 mobile devices [27]. Details of the recording devices and environments can be found in [4]. Figure 3: Schematic diagram of the mean-teacher model for semi-supervised learning. Each audio clip was 10 s long with a sampling frequency of 44.1 kHz, and it was transformed into a 256-bin mel-frequency spectrum with a 2048-sample Hanning window and a 50% overlap. The input features, which were fed to the models, consisted of three channels of the log mel spectrum and its delta and delta-delta values. In recent studies, most ASC models have been developed based on CNN families, e.g., ResNet [15], Inception [16], and their modifications. Most of the models submitted to DCASE 2020 Task 1 and DCASE 2021 Task 1A, which are competitions in the ASC, consisted of ResNet and Inception, and variants of ResNet such as BC-ResNet [28] and SE-ResNet [29]. Therefore, we constructed the CNN-based architecture for the ASC. Especially, we constructed multi-path structrue, which divided the features into multiple frequency groups, inspired by the Trident model [12], which showed the best performance in DCASE 2020 Task 1A. However, the Trident model was significantly large, so we applied canonical polyadic (CP) ResNet [22], which showed good performance with small-sized model in DCASE 2020 Task 1B, to the multi-path structure. The student model was a dual-path structure consisting of two subnetworks responsible for the low (from 1 st to 128 th bins) and high (from 129 th to 256 th bins) frequency components, as shown in Table 1. In Table 1, CNN (\(a\times b\), \(c\)) means a convolutional layer with an \((a\times b)\)-sized kernel and \(c\) output channels, and Residual Block (\(a\)) \(\times\)\(b\) means a residual block with \(a\) output channels and \(b\) depthwise repetition. The dual-path structure was inspired by the Trident structure [12]. The residual block consisted of the ResNet block [15] with complexity reduction by canonical polyadic (CP) decomposition [22] and parameter sharing [30], as shown in Figure 4. The model weights were quantized to a 16-bit floating point after training, so the model size became 125.8 KB and satisfied the complexity limit of DCASE 2021 Task 1A, which is 128 KB. As mentioned earlier, the objective function consists of the classification and the consistency cost functions. The classification cost function was defined as the categorical cross-entropy between the prediction results of the student model and the class labels, and the consistency cost function was defined as the mean squared error between the prediction results of the student and teacher models. The tapering parameter \(\alpha\) was set to 0.99, and the consistency cost weight \(\beta\) was set to 2.5. Stochastic gradient descent [31] was used as the optimization algorithm, and the learning rate was controlled by a cosine annealing scheduler with restart epochs of \([2,7,15,30,60,90,120,150,180,210,240]\) and has an initial value of 0.05 and a minimum value of \(10^{-5}\), as shown in Figure 5. The maximum