  Face recognition has made extraordinary progress owing to the advancement of
deep convolutional neural networks (CNNs). The central task of face
recognition, including face verification and identification, involves face
feature discrimination. However, the traditional softmax loss of deep CNNs
usually lacks the power of discrimination. To address this problem, recently
several loss functions such as center loss, large margin softmax loss, and
angular softmax loss have been proposed. All these improved losses share the
same idea: maximizing inter-class variance and minimizing intra-class variance.
In this paper, we propose a novel loss function, namely large margin cosine
loss (LMCL), to realize this idea from a different perspective. More
specifically, we reformulate the softmax loss as a cosine loss by $L_2$
normalizing both features and weight vectors to remove radial variations, based
on which a cosine margin term is introduced to further maximize the decision
margin in the angular space. As a result, minimum intra-class variance and
maximum inter-class variance are achieved by virtue of normalization and cosine
decision margin maximization. We refer to our model trained with LMCL as
CosFace. Extensive experimental evaluations are conducted on the most popular
public-domain face recognition datasets such as MegaFace Challenge, Youtube
Faces (YTF) and Labeled Face in the Wild (LFW). We achieve the state-of-the-art
performance on these benchmarks, which confirms the effectiveness of our
proposed approach.
