Additive angular margin gives a constant geodesic margin on the hypersphere

Deng et al. replace SphereFace's multiplicative angular margin with an additive one, cos(theta_yi + m), and give a unified formula covering SphereFace, ArcFace, and CosFace margins as special cases [deng-etal-2019-arcface] Because features are L2-normalized onto a hypersphere of radius s (a geometry imposed by construction), adding directly to the angle yields a constant linear margin with exact correspondence to geodesic distance, unlike SphereFace's nonlinear margin [deng-etal-2019-arcface] A matched ResNet50/CASIA-WebFace ablation shows ArcFace (m=0.5) beating SphereFace and CosFace (LFW 99.53% vs 99.11%/99.51%; AgeDB 95.15% vs 91.70%/94.56%), with m=0.5 optimal [deng-etal-2019-arcface] Scaled to ResNet100, the citable arXiv version reports MegaFace 98.35%/98.48% and IJB-C TAR@FAR=1e-4 of 95.6%; the higher 98.51/98.74 and 97.27 figures come from the later TPAMI/MS1MV3 revision [deng-etal-2019-arcface]