# [Paper Reading] SphereFace: Deep Hypersphere Embedding for Face Recognition
[by Weiyang Liu, Yandong Wen, Zhiding Yu, Ming Li, Bhiksha Raj, Le Song
Apr 2017](https://arxiv.org/abs/1704.08063)
## Problem
Open-set FR is essentially a metric learning problem. Using contrastive loss or triplet loss one can get SOTA results; however, these methods require carefully designed pair/triplet mining procedure, which is both time-consuming and performance-sensitive.

Comparison between Softmax Losses:

Decision boundaies
Modified Softmax : |x| * (cos(θ1)−cos(θ2))= 0
A-softmax : |x| * (cos(mθ1)−cos(θ2)) = 0 for class1

The authors propose the angular softmax (A-Softmax) loss that enables convolutional neural networks (CNNs) to learn angularly discriminative features.
## Deep Hypersphere Embedding
* In binary class case, lower bound of m to seperate data points is 2+sprt(3).
* In multiclass case, lower bound of m is 3.
* Experiments show that m=4 will usually suffice.
## Experiments
A-softmax is really powerful. Setting a right cost function is important since neural netowrk only knows about the cost function but not the task.
A-softmax is a large margin cost function, so it is suitable for seperation problem.