# Weighted Cluster-Range Loss and Criticality-Enhancement Loss for Speaker Recognition
## 1 Introduction  
Generally, there are two subtasks in the field of speaker recognition, i.e., Speaker Identification (SI) and Speaker Verification (SV). SI aims to classify the identity of a given speaker's utterance into the corresponding one among a group of enrolled speakers [1]. Therefore, SI could be treated as a 1:N process. Differing from SI, SV aims to verify whether the identity of the current test speaker is the same as the given enrolled speaker, i.e., it could be treated as a 1:1 process. The concept of speaker recognition can be further divided into two types: text-dependent and text-independent. In this work, the latter one will be explored, which is rather more practical, but is however more difficult to deal with. For speaker recognition, there have been numerous methods that have been successfully applied to this field. Traditional methods include Vector Quantization (VQ) [2], Gaussian Mixture Models (GMMs) [3, 4], and its variant Gaussian Mixture Model-Universal Background Models (GMM-UBMs) [5]. a method with Support Vector Machine (SVM) was also explored [6]. What has dominated the field of speaker recognition are the hybrid models with the i-vector [7, 8, 9]. However, it was reported in [10] that the i-vector based approaches are sensitive to the speech duration and may not perform well when dealing with short utterances. Recently, due to the rapid development of deep learning, there has been active research on applying deep learning methods to speaker recognition. Deep Neural Networks (DNNs) are usually utilized to extract frame-level features, followed by an utterance-level feature generating operation like the temporal average. The speaker representations generated by the DNNs are referred to as the d-vector [11]. Based on DNN, the x-vector proposed in [12] employs an isolated PLDA backend to compare the embedding pairs. Actually, employingdeep neural networks to learn the representation for speaker recognition has long been reported [13]. Throughout the recent papers working on speaker recognition, deep neural networks such as Visual Geometry Group Network (VGG-Net) [14] and Residual Network (ResNet) [15] have been frequently utilized. To name only a few, in [8; 16; 17], VGG-like CNNs were adopted, while ResNet-like networks were also explored in some literature [9; 18; 19]. Along with the deep neural networks, attention mechanisms have also appealed to many researchers. Various attention mechanisms have been applied in many hot research fields, including Natural Language Processing (NLP) [20; 21; 22], speech recognition [8; 9; 23], and Computer Vision (CV) [24; 25; 26; 27]. Self-Attention (SA) is a commonly used attention mechanism and has been successfully integrated into CNNs, especially ResNet [8; 9]. Variants of self-attention are also emerging [28; 29; 30]. Furthermore, those attention mechanisms considering the spatial and channel dimension are also widely employed especially in the field of CV. [PERSON] et al. [25] proposed a residual attention network where the trunk-and-mask attention module employs a encoder-decoder style. Squeeze and Excitation blocks (SEs) [31] is a channel attention mechanism, where the global spatial information is squeezed by a global average pooling and then the channel-wise dependencies are obtained with fully-connected layers and the sigmoid function. Both in the Convolutional Block Attention Module (CBAM) [26] and Bottleneck Attention Module (BAM) [27], 3D attention map inferences are decomposed into channel and spatial. The channel attention in CBAM achieves better performance than SEs, and to further push the performance, spatial attention is also exploited. In BAM, the 3D attention map is computed along the channel and spatial axis at the same time, while in CBAM, the attention map along these two axes is computed sequentially. [PERSON] et al. [30] proposed a Dual Attention Network (DANet), which contains a position attention module and a channel attention module and also captures global dependencies in the spatial and channel dimensions, respectively.