## 2 Related Work  
DNN-based open-set speaker verification: The majority of the early work on DNN-based SV usually trained a model for the speaker classification task on a training dataset, using classification-based objective functions, such as softmax [11; 12]. The last output layer of the trained model was omitted, and the output of the final hidden layer was exploited as a speaker embedding. However, open-set SV requires a discriminative embedding space for unseen speakers rather than an accurate classification on training datasets. Therefore, several studies have employed variants of the softmax loss function applying an additional angular margin to reduce the variance within a class [13; 14]. In contrast, open-set SV can essentially be treated as a metric learning problem [2; 8]. Thus, many recent studies have improved the generalization performance by optimizing metric-learning-based cost functions rather than classification-based cost functions [15; 16]. They trained the model to decrease the distances between speaker embeddings extracted from the same speaker utterances and increase the distances between speaker embeddings of different speakers. In addition to these loss functions, the prior studies have investigated diverse methods, such as data augmentation [17; 18], network architectures [19; 20], and system frameworks [21; 22].  
Temporal averaging and mean teacher: Loss values oscillating or bouncing without convergence during DNN training are a common training failure indicator [23]. To alleviate this issue, [PERSON] et al. [4] proposed a temporal averaging method that combines the weights collected until the end of the training. In the loss landscape, temporal averaging brings it closer to the bottom of the valley by averaging the weights of the points that oscillate back and forth [24]. Therefore, this method can be used to improve the convergence of an optimization algorithm [25] or further enhance the generalization performance of the model during the evaluation phase [26].  
Furthermore, the MT network, a temporal averaging model, was also used as a teacher model in semi-supervised image classification tasks [5]. Concretely, the MT network pro vides relatively accurate pseudo labels of unlabeled data for training the student network. The architectures of the student and MT networks are identical. The weight set of the MT network, \(\xi\), is updated through the EMA of student weights, \(\theta\), formulated as follows:  
\[\xi_{t}=\alpha\xi_{t-1}+(1-\alpha)\theta_{t}, \tag{1}\]  
where \(t\) indicates the training step, and \(\alpha\) is a smoothing coefficient hyperparameter. However, the parameter set of the student network is trained via the backpropagation algorithm. The loss function of the student network is a linear combination of classification and consistency costs. The classification cost is only applied to labeled data and adopts a categorical cross-entropy (CCE) function. For all data, including unlabeled data, the consistency loss function (e.g., MSE) is constrained to reduce the Euclidean distance between the prediction of the student and MT networks.  
The critical point of this method is to form an MT network that progressively aggregates information from the student network in an EMA fashion. Consequently, the MT network is expected to produce more reliable probability predictions that serve as a high-quality representation to guide the student network training.