Learning the discriminative features of different faces is an important task in face recognition. By extracting face features in neural networks, it becomes easy to measure the similarity of different face images, which makes face recognition possible. To enhance the neural network's face feature separability, incorporating an angular margin during training is common practice. State-of-the-art loss functions CosFace and ArcFace apply fixed margins between weights of classes to enhance the inter-class separation of face features. Since the distribution of samples in the training set is imbalanced, similarities between different identities are unequal. Therefore, using an inappropriately fixed angular margin may lead to the problem that the model is difficult to converge or the face features are not discriminative enough. It is more in line with our intuition that the margins are angular adaptive, which could increase with the angles between classes growing. In this paper, we propose a new angular margin loss named X2-Softmax. X2-Softmax loss has adaptive angular margins, which provide the margin that increases with the angle between different classes growing. The angular adaptive margin ensures model flexibility and effectively improves the effect of face recognition. We have trained the neural network with X2-Softmax loss on the MS1Mv3 dataset and tested it on several evaluation benchmarks to demonstrate the effectiveness and superiority of our loss function.
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