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.

本文提出了一种叫做 A-Softmax 的损失函数来训练卷积神经网络，以学习面部图像特征，使得最大内类距离小于最小类间距离，从而解决开放集（open-set）协议下的人脸识别问题。与之前的算法相比，该方法在 LFW、YTF 和 MegaFace Challenge 数据集上取得了更好的结果。