  Deep metric learning has attracted much attention in recent years, due to
seamlessly combining the distance metric learning and deep neural network. Many
endeavors are devoted to design different pair-based angular loss functions,
which decouple the magnitude and direction information for embedding vectors
and ensure the training and testing measure consistency. However, these
traditional angular losses cannot guarantee that all the sample embeddings are
on the surface of the same hypersphere during the training stage, which would
result in unstable gradient in batch optimization and may influence the quick
convergence of the embedding learning. In this paper, we first investigate the
effect of the embedding norm for deep metric learning with angular distance,
and then propose a spherical embedding constraint (SEC) to regularize the
distribution of the norms. SEC adaptively adjusts the embeddings to fall on the
same hypersphere and performs more balanced direction update. Extensive
experiments on deep metric learning, face recognition, and contrastive
self-supervised learning show that the SEC-based angular space learning
strategy significantly improves the performance of the state-of-the-art.
