InterFace Adjustable Angular Margin Inter-class Loss for Deep Face Recognition Meng Sang12 Jiaxuan Chen23 Mengzhen Li12Pan Tan12 Anning Pan12 Shan Zhao12 Yang Yang12

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InterFace: Adjustable Angular Margin Inter-class Loss for Deep Face

Recognition

Meng Sang1,2, Jiaxuan Chen2,3, Mengzhen Li1,2,Pan Tan1,2, Anning Pan1,2, Shan Zhao1,2, Yang Yang1,2

1Yunnan Normal University, 650500, Kunming, China

2Laboratory of Pattern Recognition and Artiﬁcial Intelligence, 650500, Kunming, China

3Zhejiang University, 310058, Hangzhou, China

Emails: sangmeng.one@gmail.com, yyang ynu@163.com

Abstract— In the ﬁeld of face recognition, it is always a hot

research topic to improve the loss solution to make the face

features extracted by the network have greater discriminative

power. Research works in recent years has improved the

discriminative power of the face model by normalizing softmax

to the cosine space step by step and then adding a ﬁxed

penalty margin to reduce the intra-class distance to increase

the inter-class distance. Although a great deal of previous work

has been done to optimize the boundary penalty to improve

the discriminative power of the model, adding a ﬁxed margin

penalty to the depth feature and the corresponding weight is

not consistent with the pattern of data in the real scenario.

To address this issue, in this paper, we propose a novel loss

function, InterFace, releasing the constraint of adding a margin

penalty only between the depth feature and the corresponding

weight to push the separability of classes by adding corre-

sponding margin penalties between the depth features and all

weights. To illustrate the advantages of InterFace over a ﬁxed

penalty margin, we explained geometrically and comparisons

on a set of mainstream benchmarks. From a wider perspective,

our InterFace has advanced the state-of-the-art face recognition

performance on ﬁve out of thirteen mainstream benchmarks.

All training codes, pre-trained models, and training logs, are

publicly released. 1.

I. INTRODUCTION

With the development of face recognition technology, it

has been applied to various ﬁelds in life, such as ﬁnance,

security, and enterprises. The face recognition system con-

sists of the process of image acquisition, face detection,

face alignment, feature extraction, and feature matching. In

the process of face matching, the vectors generated in the

feature extraction are required to measure the similarity with

all the faces. Knowing that it is intuitive that the model

should have small intra-class distances for samples of the

same identity and large inter-class distances for samples

of different identities. Hence, in the face system, we are

required to make the right decision boundary, even if the

picture of the face changes dramatically under the same

identity, and also to reject the imposter under a different

identity.

Although the accuracy of face recognition has improved

greatly, it has not yet achieved the expected results [13].

Most of the recent related studies [20], [22], [4], [16], [15],

[24], [5], [10], [11], [6], [18], [2] have focused on improving

1https ://github.com/iamsangmeng/InterF ace

the loss function. The content of our work focuses on the

problem of ﬁxed margin penalty existing in the direction of

Classiﬁcation Task I-.0.b and we propose our our solution

based on ArcFace [5]. Next, we will sort out the related

work and problems in previous loss studies and summarize

them in two directions for metric learning and classiﬁcation

tasks as follows.

a) Deep Learning: In the direction of metric learning,

the design of losses [20], [22], [4] is based on triplet. Facenet

[20] directly learns a mapping from face images to a compact

Euclidean space where distances directly correspond to a

measure of face similarity. N-pair [22] proposed objective

function ﬁrstly generalizes triplet loss by allowing joint

comparison among more than one negative examples – more

speciﬁcally, N−1negative examples – and secondly reduces

the computational burden of evaluating deep embedding

vectors via an efﬁcient batch construction strategy using only

Npairs of examples, instead of (N+ 1)N. Contrastive [4]

losses learn a function that maps input patterns into a target

space such that the L1norm in the target space approximates

the ”semantic” distance in the input space. However, the

number of triplets explodes during the training period as the

number of samples in the training dataset increases.

b) Classiﬁcation Task: In the direction of the classiﬁ-

cation task, subsequent losses [16], [15], [24], [5], [10], [11],

[6], [18], [2] are designed on the basis of softmax losses. Liu

et al. [16] proposed a large-margin softmax (L-Softmax) by

introducing penalty margin ideas for softmax to encourage

intra-class compactness and inter-class separability between

learned features. SphereFace [15] extends previous work

on L-Softmax by further constraining the weights of fully

connected layers to impose discriminative constraints on

a hypersphere manifold, which intrinsically matches the

prior that faces also lie on a manifold. SphereFace deploys

a multiplicative angular penalty margin between the deep

features and their corresponding weights. In CosFace [24],

it is proposed to add a cosine angle between depth features

and weights. CosFace ﬁxes the norm value of the depth

feature and the corresponding weight and proposes to scale

the norm of the depth feature to a constant s. ArcFace

[5] proposed additive angular margin by deploying angular

penalty margin on the angle between the deep features and

their corresponding weights. The great success of softmax

arXiv:2210.02018v2 [cs.CV] 9 Oct 2022

loss with penalty margin motivated several works to pro-

pose a novel variant of softmax loss. All these solutions

achieved notable accuracies on mainstream benchmarks for

face recognition. Huang et al. [10] propose an Adaptive

Curriculum Learning loss (CurricularFace) that embeds the

idea of curriculum learning into the loss function to achieve

a novel training strategy for deep face recognition, which

mainly addresses easy samples in the early training stage

and hard ones in the later stage. In Dyn-ArcFace [11], the

traditional ﬁxed additive angular margin is developed into

a dynamic one, which can reduce the degree of overﬁtting

caused by the ﬁxed additive angular margin. Duan et al. [6]

propose Learning Deep Equidistributed Representation for

Face Recognition that imposes an equidistributed constraint

by uniformly spreading the class centers on the manifold.

Meng et al. [18] propose A Universal Representation for

Face Recognition and Quality Assessment called MagFace

that learns a general embedding feature whose dimension

measures the quality of the given image. In this way, the

embedded features of the face can be regularly distributed

around the class center according to their dimensions. In

Boutros1’s work, ElasticFace [2] refuted the assumption

of uniform distribution of class centers made by ArcFace

and CosFace, and proposed an elastic margin loss for deep

face recognition called ElasticFace. However, adding a ﬁxed

margin penalty to the depth feature and the corresponding

weight creates a ﬁxed decision boundary between the depth

feature to the other weights. This is not consistent with the

data patterns in real scenarios.

To address the issues mentioned in the Classiﬁcation

Task direction I-.0.b, in this work, we propose InterFace

loss. InterFace ﬁrst introduces the idea of adding different

penalty margins to different class centers for a single sample

to solve the problem of adding a ﬁxed margin penalty to

different class centers for a single sample. On this basis,

there are the sample-to-class center distance and inter-class

distance of corresponding class centers to other class centers

ratios(SIR) are introduced to generate a penalty margin for

different class centers by a speciﬁed function. To demonstrate

the geometric space advantage of our method, we provide

a geometric interpretation of the decision boundary and

provide a toy example of a simple network we customize

to implement a simple 8-classiﬁcation problem. At the same

time to illustrate the effectiveness of our InterFace loss on

face recognition accuracy, we will report on 13 benchmarks.

We will compare and analyze the effect achieved by the

whole method with the recent state-of-the-art. In a more

detailed comparison, with prior work and recent state-of-

the-art, our InterFace continuously extends state-of-the-art

face recognition performance on ﬁve benchmarks. Especially

the age-related datasets [19], [30] such as AgeDB-30 and

CALFW have better performance.

We summarize the contributions as follows:

•We redeﬁne ArcFace loss by decision boundary equiv-

alence and propose a novel InterFace loss to improve

the discriminative power of the network.

•We experimentally demonstrate that the redeﬁned Ar-

cFace and the original ArcFace losses are equivalent.

We do extensive ablation and toy example of geometric

interpretation to illustrate the superiority of InterFace.

•We have done a lot of ablation experiments in the ﬁeld

of face recognition, and in the ﬁnal face veriﬁcation

benchmark, 5 benchmarks have been extended and

the others are very close to the top state-of-the-art

performance.

II. INTERFACE LOSS

We propose in this work a novel learning loss stragegy,

InterFace loss, aiming at imporving the accuracy of face

recognition by optimizing spatial distribution between and

within classes. Different from previous work that constrain a

same margin value from the deep feature to the correspond-

ing weight, our proposed InterFace loss introduce SIR to

constrain the margin values from the deep feature to the other

weights. The margin values are generated by SIR through a

convex function.

a) Softmax Loss: Softmax is a normalized exponential

function that is used for the output of the last fully-connected

layer and is often used with the cross entropy function as

the most widely used classiﬁcation loss function. Softmax is

deﬁned as follows:

Lsoftmax(xi, yi) = −1

i=1

log efyi

j=1 efj

=−1

i=1

log exiWT

yi+byi

j=1 exiWT

J+bj

(1)

where xi∈Rdis the depth feature extracted by Deep

Convolutional Neural Networks(DCNNs) of sample ziand

belongs to yiclass (ziinteger in the range [1, n]and yi

integer in the range [1, c]). Given that nis the number of

samples and cis number of classes. The embedding feature

dimension d is set 512 by this paper following [5], [24],

[2]. Wyirepresents yicolumn of weights W∈Rd

cand byi

represents the corresponding bias offset. The batch size is

represented by n.

In a simple binary class classiﬁcation, assuming that input

zibelongs to class 1, the model will correctly classify ziif

1xi+b1> W T

2xi+b2and ziwill be classiﬁed as class 2

if WT

2xi+b2> W T

1xi+b1. Therefore the decision boundary

of softmax loss is x(WT

1−WT

2)+b1−b2=0. However, the

softmax loss function cannot explicitly optimize the embed-

ded features to minimize intra-class distance and maximize

inter-class distance. To address the limitations of softmax,

the idea of decision boundary introduces softmax and then

a series of optimization works based on angular margin

penalty. This idea has always guided our improvement in loss

and is also the most popular loss function for face recognition

model training.

b) Angular Margin Penalty-based Loss: Following

[16], [15], [24], the bias offset, for simplicity, can be ﬁxed to

byi= 0. In the above case, the function fyi can be simpliﬁed

as xiWT

yi=kxik kWyikcos(θyi), where θyiis the angle

between the yicolumn of the weights of the last fully-

connected layer Wand the embedding feature xi. By ﬁxing

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InterFace:AdjustableAngularMarginInter-classLossforDeepFaceRecognitionMengSang1;2,JiaxuanChen2;3,MengzhenLi1;2,PanTan1;2,AnningPan1;2,ShanZhao1;2,YangYang1;21YunnanNormalUniversity,650500,Kunming,China2LaboratoryofPatternRecognitionandArticialIntelligence,650500,Kunming,China3ZhejiangUniversity,310...

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InterFace Adjustable Angular Margin Inter-class Loss for Deep Face Recognition Meng Sang12 Jiaxuan Chen23 Mengzhen Li12Pan Tan12 Anning Pan12 Shan Zhao12 Yang Yang12

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