## 1 Introduction  
Recently, deep convolutional neural networks have made great achievements in many aspects of computer vision tasks. Image classification [1] is a fundamental task and full of challenges, thanks to the large number of labeled training data, supervised learning has reached a level beyond human beings. The current convolutional neural network training process for image classification is shown in Figure 1, which includes several modules of feature extraction, feature representation, category prediction, and loss calculation. Figure 1: Traditional training process for classification tasks and new scaled Batch Normalization (BN) layer. As shown in Figure 1, given a training sample, features of the input sample are extracted through a series of convolution and pooling layers. Then, some linear layers and Softmax classifier are used to determine the prediction probability that the input image belongs to each category. Finally, the loss at this epoch is obtained by calculating the cross-entropy loss, the network's parameter is optimized by back propagation algorithm to minimize the loss of network output. With the deepening of research, many well-designed network structures have been proposed to improve the accuracy in image classification task, such as VGG (Visual Geometry Group)[2], ResNet [1], ResNeXt [3], DenseNet [4]. Their contribution mainly based on the network structure's improvement, the method of multi-layer feature concatenation has solved the problem of overfitting and gradient vanishing which have puzzled the researchers for a long time to some extent. In addition to the optimization of network structure, the optimization of loss function has also gained much attention in recent years. As a classical classification problem loss function, Softmax+cross-entropy loss has made great achievements, and its calculation method is as follows:  
\[L(y,\hat{y})=-\frac{1}{N}\sum_{i=1}^{N}y_{i}^{T}log(\hat{y}_{i})=-\frac{1}{N} \sum_{i=1}^{N}log\Big{(}\hat{y}_{i\hat{y}}\Big{)} \tag{1}\]  
where \(y_{i}\in\{0,1\}^{k}\) represents the label of the \(i^{th}\) sample in one-hot encoded representation and \(\hat{y}_{i}\in[0,1]^{k}\) is the predicted probabilities with Softmax. \(\hat{y}_{i\hat{y}}\) represents the predicted probability of the ground-truth class for the \(i^{th}\) sample. Therefore, the network parameters can achieve \(\hat{\theta}=argmin_{\theta}L(y,\hat{y})\) by training the cross-entropy loss function, where \(\hat{y}=h_{\theta}(x)\), \(h_{\theta}\) is the network's parameter and \(x\) is the training sample. Although the Softmax+cross-entropy loss function has achieved great success in many computer vision fields as a norm of neural network, some improvements have been made by researchers to let the features learned by the convolutional neural network more distinctive between classes. Loss functions such as center-loss [5], L-Softmax [6], A-Softmax [7], AM-Softmax (Additive Margin) [8], PEDCC-loss (Pre-defined Evenly-Distributed Class Centroids) [9], etc. can improve the final accuracy of models when trained for face classification and validation. Although the accuracy of the convolutional neural network for classification and recognition is constantly improving through the improvement of model structure and the optimization of loss function, there are still some unsolved problems. At present, various improved loss functions are proposed from the perspective of the output feature of convolutional neural network, that is, how to make the features extracted by the neural network have smaller intra-class distance and larger inter-class distance. The PEDCC-loss which is recently proposed achieves the best performance in these optimization methods, which are normally motivated from the perspective of face recognition to improve the accuracy of network classification. The problem is not considered from the point of view of solving the gradient vanishing problem and they did not test on the datasets which requires good generalization ability.