  This paper addresses the deep face recognition problem under an 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. To this end, hyperspherical face recognition, as a promising line
of research, has attracted increasing attention and gradually become a major
focus in face recognition research. As one of the earliest works in
hyperspherical face recognition, SphereFace explicitly proposed to learn face
embeddings with large inter-class angular margin. However, SphereFace still
suffers from severe training instability which limits its application in
practice. In order to address this problem, we introduce a unified framework to
understand large angular margin in hyperspherical face recognition. Under this
framework, we extend the study of SphereFace and propose an improved variant
with substantially better training stability -- SphereFace-R. Specifically, we
propose two novel ways to implement the multiplicative margin, and study
SphereFace-R under three different feature normalization schemes (no feature
normalization, hard feature normalization and soft feature normalization). We
also propose an implementation strategy -- "characteristic gradient detachment"
-- to stabilize training. Extensive experiments on SphereFace-R show that it is
consistently better than or competitive with state-of-the-art methods.
