SphereFace

SphereFace is a loss function and training approach for face recognition that aims to produce highly discriminative embeddings by enforcing large angular margins between identities on a hypersphere. It builds on the idea of normalizing feature vectors and class weights to unit length, shifting the comparison from Euclidean distance to angular similarity.

The core idea is to treat each identity as a weight vector on the hypersphere and to measure the angle θ between a given feature x and the correct class weight W_y. SphereFace introduces a multiplicative angular margin by using cos(mθ) for the logit corresponding to the ground-truth class, where m > 1. The final probability for the true class is computed using a softmax over logits that include cos(mθ) for the correct class and cos θ for the others. To maintain stable training, a carefully designed function is used to approximate cos(mθ) on the relevant angular range, ensuring smooth gradients and monotonicity.

Implementation typically involves normalizing the feature representation and the classifier weights, applying a scaling factor s to control the magnitude of the logits, and optimizing the resulting loss with standard stochastic gradient descent methods. The combination of normalization, angular margins, and a scalable logit helps tighten intra-class dispersion while expanding inter-class separability on the hypersphere.

Impact and context: SphereFace was one of the early methods to demonstrate the effectiveness of angular margin losses for face recognition. It contributed to a shift toward margin-based losses on unit-hypersphere embeddings and influenced subsequent approaches such as CosFace and ArcFace, which refined margin formulations. SphereFace reported improvements on benchmark datasets and helped establish angular-margin concepts as a central technique in modern face recognition systems.