# ArcFace: Additive Angular Margin Loss for Deep Face Recognition

### Introduction

• Centre loss penalises the distance between the deep features and their corresponding class centers in Euclidean space to achieve intra-class compactness.
• SphereFace assumes the linear transformation matrix in the last fully connected layer can be used as a representation of the class centers in an angular space and pensalises the angles between the deep features and their corresponding weights in a multiplicative way.
• ArcFace is an additive angular margin loss.

### Architecture

Softmax Loss

• Softmax loss doesn’t enforce higher similarity for intra-class samples and diversity for inter-class samples. (See figure below)

ArcFace Loss

•  We change W.x as W x cos\theta and set bias as 0.
•  If we normalize W as a unit vector, then W becomes 1.
• We also normalize x and scale it to s.