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This paper addresses deep face recognition (FR) problem under open-set protocol, where ideal face features are expected to have smaller maximal intra-class distance than minimal inter-class distance under a suitably chosen metric space. However, few existing algorithms can effectively achieve this criterion. To this end, we propose the angular softmax (A-Softmax) loss that 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 intrinsically matches the prior that faces also lie on a manifold. Moreover, the size of angular margin can be quantitatively adjusted by a parameter m. We further derive specific m to approximate the ideal feature criterion. Extensive analysis and experiments on Labeled Face in the Wild (LFW), Youtube Faces (YTF) and MegaFace Challenge show the superiority of A-Softmax loss in FR tasks. The code has also been made publicly available 1 .

Convolutional neural networks have achieved great improvement on face recognition in recent years because of its extraordinary ability in learning discriminative features of people with different identities. To train such a welldesigned deep network, tremendous amounts of data is indispensable. Long tail distribution specifically refers to the fact that a small number of generic entities appear frequently while other objects far less existing. Considering the existence of long tail distribution of the real world data, large but uniform distributed data are usually hard to retrieve. Empirical experiences and analysis show that classes with more samples will pose greater impact on the feature learning process [37,19] and inversely cripple the whole models feature extracting ability on tail part data. Contrary to most of the existing works that alleviate this problem by simply cutting the tailed data for uniform distributions across the classes, this paper proposes a new loss function called range loss to effectively utilize the whole long tailed data in training process. More specifically, range loss is designed to reduce overall intrapersonal variations while enlarging inter-personal differences within one mini-batch simultaneously when facing even extremely unbalanced data. The optimization objective of range loss is the k greatest range's harmonic mean values in one class and the shortest inter-class distance within one batch. Extensive experiments on two famous and challenging face recognition benchmarks (Labeled Faces in the Wild (LFW) [12] and YouTube Faces (YTF) [31]) not only demonstrate the effectiveness of the proposed approach in overcoming the long tail effect but also show the good generalization ability of the proposed approach.

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