# Double Additive Margin Softmax Loss for Face Recognition
## 1 Introduction  
Face recogniton problems are ubiquitous in the computer vision domain. In the past few years, Deep Convolutional Neural Networks (DCNNs) have set the community of face recognition (FR) on fire [1]. Due to effectively layered end-to-end learning network frameworks and carefully deep feature extracting techniques from local to global, which are the most important ingredients for their success, DCNNs has immensely improved the state of the art in real-world face recognition scenarios. Numerous layered network architectures for face recognition tasks such as AlexNet [2], VGG [3], InceptionNet [4], ResNet [5], and DenseNet [6], have been proposed. Among them, the most representative one is AlexNet, originally proposed by [PERSON] et al. AlexNet has become a pioneered architecture developed for image classification and was the winner of the ImageNet Large Scale Challenge in 2012. It is well known that the effective feature representation for face images plays an important role in FR. Over the recent years, a hot research trend towards DCNNs has been devoted to learning with more discriminative deep features. Intuitively, the learnt deep features for FR are desired if the maximal within-class variance is less than the minimal between-class variance. However, learning deep features satisfying this condition is generally not easy owing to the inherently large intra-class variation and high inter-class similarity [7] in many FR applications. Despite the softmax function with the cross-entropy loss (called softmax loss) is popularly used in the training of a DCNN, recent studies [8; 9] made it clear that the current softmax loss is insufficient to encourage the desired deep features meeting the above condition. To boost the discriminative ability of DCNNs and inspired by the previous idea, the center loss [10], pairwise loss [11] and triplet loss [12] were proposed. They unanimously proposed the enhancement of discrimination power of deep features by minimizing winth-class variance and maximizing between-class variance in the Euclidean space of features. While these methods issuperior to the traditional softmax loss over classification performance, they usually suffer from some drawbacks. The center loss only explicitly enhanced the intra-class compactness while disregarding the inter-class separability. For the pairwise loss and triplet loss, They require the careful mining of pairs or triplets of samples, which is highly time-consuming. Due to the fact that few existing softmax losses can effectively achieve the discriminative condition that the maximal within-class variance is less than the minimal between-class variance under the conventional Euclidean metric space, more recently, approaches have been proposed to address this problem by transforming the original Euclidean space of features to an corresponding angular space [10; 13; 14; 15]. Specifically, both Large-Margin Softmax Loss [13] and A-Softmax Loss [14] are an angular softmax loss that enables DCNNs to learn angular deep features by imposing an angular margin constraint for larger inter-class variance. Compared to the Euclidean margin suggested by [2; 16], the learnt angular features is more discriminative with the angular margin because the angular metric with cosine similarity is intrinsically more suitable to the softmax loss. During training of A-Softmax Loss, the orginal Softmax loss must be combined to ensure the convergence. To overcome the optimisation problem of A-Softmax Loss, the Additive Margin Softmax loass (AM-Softmax) [15] is proposed. The loss integrates a angular margin to the softmax loss in an additve manner. Its implementation and optimisation are much easier than A-Softmax Loss since A-Softmax Loss integrates the angular margin in a multiplicative way. AM-Softmax is easily reproducible and achieves state-of-the-art performance. Motivated by AM-Softmax loss, This paper propose a new additive angular margin Loss, namely double additive margin softmax loss (DAM-Softmax).