SphereFace: Deep Hypersphere Embedding for Face Recognition This paper proposes a novel deep learning approach for face recognition under open-set conditions, where the goal is to learn face features that have smaller maximal intra-class distances than minimal inter-class distances under a suitable metric space. The proposed method, Angular Softmax (A-Softmax) loss, enables convolutional neural networks (CNNs) to learn angularly discriminative features. Geometrically, A-Softmax loss can be viewed as imposing discriminative constraints on a hypersphere manifold, which aligns with the prior that faces lie on a manifold. The size of the angular margin can be adjusted by a parameter m, and the method is shown to be effective on benchmark datasets such as LFW, YTF, and MegaFace Challenge. The A-Softmax loss is derived from the softmax loss by introducing an integer m to control the decision boundary. This loss function is designed to enhance the discriminative power of features by focusing on angular margins rather than Euclidean margins. The method is shown to outperform existing approaches in terms of performance on open-set face recognition tasks. The code for SphereFace is publicly available. The paper also discusses the geometric interpretation of A-Softmax loss, which constrains learned features to be discriminative on a hypersphere manifold. This interpretation aligns with the prior that faces lie on a manifold, making the learned features particularly suitable for open-set face recognition. The method is shown to be effective in both binary and multi-class scenarios, with the parameter m used to control the angular margin. Experiments on various datasets demonstrate the effectiveness of SphereFace in face recognition tasks. The method achieves competitive results on several benchmarks, including LFW, YTF, and MegaFace Challenge. The results show that SphereFace outperforms other methods in terms of accuracy and robustness, particularly in open-set scenarios. The paper also discusses the properties of A-Softmax loss, including its ability to adjust the difficulty of the learning task and its effectiveness in reducing the intra-class angular distance compared to the inter-class angular distance.SphereFace: Deep Hypersphere Embedding for Face Recognition This paper proposes a novel deep learning approach for face recognition under open-set conditions, where the goal is to learn face features that have smaller maximal intra-class distances than minimal inter-class distances under a suitable metric space. The proposed method, Angular Softmax (A-Softmax) loss, enables convolutional neural networks (CNNs) to learn angularly discriminative features. Geometrically, A-Softmax loss can be viewed as imposing discriminative constraints on a hypersphere manifold, which aligns with the prior that faces lie on a manifold. The size of the angular margin can be adjusted by a parameter m, and the method is shown to be effective on benchmark datasets such as LFW, YTF, and MegaFace Challenge. The A-Softmax loss is derived from the softmax loss by introducing an integer m to control the decision boundary. This loss function is designed to enhance the discriminative power of features by focusing on angular margins rather than Euclidean margins. The method is shown to outperform existing approaches in terms of performance on open-set face recognition tasks. The code for SphereFace is publicly available. The paper also discusses the geometric interpretation of A-Softmax loss, which constrains learned features to be discriminative on a hypersphere manifold. This interpretation aligns with the prior that faces lie on a manifold, making the learned features particularly suitable for open-set face recognition. The method is shown to be effective in both binary and multi-class scenarios, with the parameter m used to control the angular margin. Experiments on various datasets demonstrate the effectiveness of SphereFace in face recognition tasks. The method achieves competitive results on several benchmarks, including LFW, YTF, and MegaFace Challenge. The results show that SphereFace outperforms other methods in terms of accuracy and robustness, particularly in open-set scenarios. The paper also discusses the properties of A-Softmax loss, including its ability to adjust the difficulty of the learning task and its effectiveness in reducing the intra-class angular distance compared to the inter-class angular distance.