CosFace

CosFace, also known as Large Margin Cosine Loss, is a loss function used in deep face recognition to improve the discriminative power of learned features. It operates on the cosine similarity between normalized feature vectors and class weight vectors and introduces an additive margin to the logit of the ground-truth class. By normalizing both the input features and the final classifier weights to unit length, the logits reflect cos theta, where theta is the angle between the feature and the class center. The true class logit is modified by subtracting a margin, encouraging a larger angular separation between classes.

In training, a scale parameter is applied to the logits to control the softness of the probability distribution. A common formulation replaces the ground-truth logit with cos(theta_y) - m and computes the probability with softmax as exp(s (cos theta_y - m)) divided by the sum over all classes of exp(s cos theta_j). The loss is the cross-entropy between the predicted distribution and the true labels. Typical hyperparameters include a margin m roughly in the 0.3–0.5 range and a scale s in the 30–64 range, though values vary by dataset and backbone.

CosFace is part of a family of margin-based loss functions for face recognition aimed at increasing intra-class compactness and inter-class dispersion in angular space. It is distinguished from related approaches such as ArcFace, which applies an angular margin in a different formulation, and SphereFace, which uses a multiplicative angular margin. It has been evaluated on standard benchmarks and is applicable to other recognition tasks that benefit from discriminative, cosine-based representations.