Enhanced Face Recognition using Intra-class Incoherence Constraint
Authors: Yuanqing Huang
Yinggui Wang
Le Yang
Lei Wang
Venue: ICLR 2024 spotlight (2024)
Keywords: Representation learning
Computer vision
Face recognition
Intra-class incoherence Constraint
Primary area: representation learning for computer vision, audio, language, and other modalities

Abstract: The current face recognition (FR) algorithms has achieved a high level of accuracy, making further improvements increasingly challenging. While existing FR algorithms primarily focus on optimizing margins and loss functions, limited attention has been given to exploring the feature representation space. Therefore, this paper endeavors to improve FR performance in the view of feature representation space. Firstly, we consider two FR models that exhibit distinct performance discrepancies, where one model exhibits superior recognition accuracy compared to the other. We implement orthogonal decomposition on the features from the superior model along those from the inferior model and obtain two sub-features. Surprisingly, we find the sub-feature perpendicular to the inferior still possesses a certain level of face distinguishability. We adjust the modulus of the sub-features and recombine them through vector addition. Experiments demonstrate this recombination is likely to contribute to an improved facial feature representation, even better than features from the original superior model. Motivated by this discovery, we further consider how to improve FR accuracy when there is only one FR model available. Inspired by knowledge distillation, we incorporate the intra-class incoherence constraint (IIC) to solve the problem. Experiments on various FR benchmarks show the existing state-of-the-art method with IIC can be further improved, highlighting its potential to further enhance FR performance.

Published as a conference paper at ICLR 2024
ENHANCED FACE RECOGNITION USING INTRA-CLASS INCOHERENCE
Yuanging Huang!* Yinggui Wang
Le Yang² Lei Wang!
Ant Group' University of Canterbury?
(huangyuanqing.hhg hyq. ringgui.wyg shensi.wl] @ antgroup.cco
lraan@@anterbury.ac.om
ABSTRACT
The current face recognition (FR) algorithms has achieved high level of accu- racy, making further improvements increasingly challenging. While existing FR algorithms primarily focus on optimizing margins and loss functions, limited at- tention has been given to exploring the feature representation space. Therefore, this paper endeavors to improve FR performance in the view of feature represen- tation space. Firstly, consider two FR models that exhibit distinct performance discrepancies, where one model exhibits superior recognition accuracy compared the other. We implement orthogonal decomposition superior model along those from the inferior model and obtain two sub-features. Surprisingly, we find the sub-feature orthogonal to the inferior still possesses certain level of face distinguishability. We adjust the modulus of the sub-fcatures and recombine them through vector addition. Experiments demonstrate this re- combination is likely to contribute to an improved facial feature representation, even better than features from the original superior model. Motivated by this dis- covery, we further consider how to improve FR accuracy when there is only one FR model available. Inspired by knowledge distillation, we incorporate the intra- class incoherence constraint (IIC) to solve the problem. Experiments on various FR benchmarks show the existing state-of-the-art method with IIC can be further improved, highlighting its potential to further enhance FR performance.
the features from the
INTRODUCTION
Face recognition (FR) has been receiving increasing attention in the field of machine learning. With the development of deep learning and the availability of large-scale face datasets, the accuracy of face recognition tasks is steadily improving. Many FR algorithms are devoted to optimizing margins and loss functions. Margin-
methods such as SphereFace (Liu al. 2017). CosFace (Wang et al. (0188) and ArcFace (Deng et al.) 2019) introduce different forms of margin functions. Adap- tive loss functions- based methods such as Curricularface (Huang et al. 2020b). MagFace (Meng et al. 2021) and AdaFace (Kim et al.) 2022) include adaptiveness in the training objective for min- ing hard samples (Lin et 2017), scheduling difficulty during training (Huang et al.) 2020b), and finding optimal hyperparameters (Zhang et al. 2019). Nevertheless, the exploration of the feature representation space in face recogmition has been somchow overlooked. From the perspective of feature representation, advanced FR model makes the features of face images increasingly distin- guishable and attempts to search the optimal feature space with the most representational capability for recognition.
Therefore, we are absorbed in interpreting the performace of FR from the view of the feature space and further considering how enhance the performance of an existing face recognition model. Firstly, we compare two FR models that exhibit distinct performance discrepancies. As shown in Fig. [[a), for the clarity of presentation, we use two-dimensional vectors illustrate the feature representations space of different FR models at the feature level, and choose ArcFace (Deng et al., 2019) and CosFace (Wang et al., 2018b) as examples. Here, d represents an optimal but unknown feature representation space for FR. and b represent the feature space of ArcFace and CosPace.
"These authors contributed equally to this work. "ooresponniig author.

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aeew
(ArcFace)
(Existing model)
(CosFace)
(Optimal) (Improved model)
(Inovvation)
(Pr feature)
Y
(Optimal)
0
a'
(a) and b represent the features from two face recognition models (such ArcFace and CosFace). an optimal unknown facial feature. We ob- tain two sub-features с and p (innovation and pro- feature) from by orthogonal decomposition. p parallel to b, and is orthogonal b.
(b) For an existing model feature a, innovation (i.c. is able to be learned, the improved model feature a new can be obtained by combining inno- vation and
Figure I: Orthogonal decomposition in the feature space of face recognition models.
Table 1: The recognition accuracy of features from ArcFace, CasFace, innovation and pro-feature decomposed by ArcFace, respectively.
Dateset
CosFace
ArcFace
Innovation
Pro-fcature
LFW
99.22
99.15
99.17
86.32
CFP
93.87
95.69
95.86
79.66
AgeDB
92.55
94.35
92.97
79.73
CALFW
92.77
93.05
92.58
80.98
CPLFW
87.57
88.20
88.00
76.17
VGG2
91.94
92.66
91.98
77.66
AVG (Averagy accuracy)
92,99
93.85
93,19
80.09
Since it is generally believed that ArcFace perform better than CosFace, a should be closer d, compared with b (i.e. La < <B). We perform orthogonal decomposition on the feature obtained from ArcFace and get two sub-features. where one of the sub-features p parallel to b (we call the sub-feature pro-feature). The other sub-feature is orthogonal to b (we call it innovation).
In T we evaluate FR performance over features from ArcFace, CosFace, innovation and pro- feature decomposed by ArcFace, respectively (depicted as in Fig. I(a)p. The results show that Ar- cFace has the best performance in most cases, while innovation exhibits certain capabilities in dis- tinguishing faces since its average accuracy outperforms CosFace. Unexpectedly, the accuracy of pro-feature far lower than that CosFace. The reasons behind this may be explained as follows. The angle between the feature from ArcFace and the feature from CosFace may be less than 90 degrees in some cases and more than 90 degrees in other cases. When is less than 90 degrees, the direction of the pro-feature is exactly aligned with that from CosFace, and the recognition accuracy thus similar. While it is greater than 90 degrees, the direction of the pro-feature would become opposite the direction features from CosFace, rendering poor recognition accuracy and degrad- ing the average FR performance. However, it does not influence the accuracy of innovation since innovation is always orthogonal features from CosFace. Such discovery can lead to a conclusion that the nigh-precision model (AreFace) performs better than the low- www-precssinn model (CosFace) be- cause the former contains innovations that are irrelevant the feature from the low- low-precision model, while these innovations do have promoting effect on face recognition. In other words, we can op- timize the features extracted from an available FR model by incorporating appropriate innovations to enhance its performance.
With the above analysis in mind, innovation motivates us to improve FR accuracy in the scenario where only single FR model is available, shown in Fig. [(b) We attempt to utilize intra-class irrelevance on the feature from an existing state-of-the-art model such that its innovation can be learned (denoted by a' in Fig, l(b),, properly scaled, and added to its original feature to get improved feature representation space(denoted by a newr in Fig. [(b)]. Consequently, the improved feature representation would be further closer to the optimal feature d.
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In general, the contributions of this work are as follows:
The concept of innovation in FR is put forward for the first time. Considering two FR models, perform orthogonal decomposition with higher recognition accuracy. The sub-feature parallel to the features from the inferior model is pro-feature, and the other sub-feature orthogonal features from the inferior model is innovation. Experiments show that innovation still has a high level of face distin- guishability.
the features from the superior model
Morcover, innovation inherently has a positive impact on face recognition. We adjust the modulus of innovation, and then synthesize new features by recombining the modified innovation and pro-feature. Experiments indicate this synthesized features are likely to have better representational capability for recognition than the original feature.
Furthermore, we consider how to enhance FR performance when there only one FR model available. Inspired by knowledge distillation, we adopt a framework incorporat- ing the intra-class irrelevance constraint. In our framework, an existing -ftt-off-hheart FR model serves the teacher network and the student has the same architecture as the teacher. However, the student network not only possesses the capability for recognition but also learns dissimilar feature representation space. Experiments show that the perfor- mance of the student network outperforms the teacher network by incorporating intra-class irrelevance.
2
RELATED WORK
2.1 FACE RECOGNITION
Face recognition algorithms are generally divided into methods with neeric-lcamnnng-busee loss functions, methods with adaptive loss functions and those with uncertainty modeling. Early meth- ods with metric learning include contrastive loss (Liu et al. 2021]. triplet loss (Schroff et al. 2015), pair loss (Sohn 2016) and angular loss (Wang et al. [017]. Then, in this category, some algorithms with higher accuracy have been proposed, which include SphereFace (Liu et al. |017], AM-softmax Wang et al. 2018a), SV-AM-Softmax (Wang et al. 2018c), CosPace (Wang al. 2018b), ArcFace
Deng et al. 2019).
Methods with adaptive loss functions introduce an element of adaptiveness in the training objec- tive for either hard sample mining (Lin et al. 2017), finding optimal hyperparameters (Zhang et al.) 2019), or brings the idea of curriculum learning into the loss function (Huang et al., 2020b). In this category, MagFace (Meng et al.) 2021 and AdaFace (Kim et al., (022) are algorithms with higher accuracy. MagFace explores the idea of applying different margins based on recognizability. It applies large angular margins to high-norm features on the premise that high-norm features are easily recognizable. Adalaace develops a new loss function that emphasizes samples of different difficulties based on their image quality, and it achieves this in the form of an adaptive margin func- tion by approximating the image quality with feature norms, Algorithms with uncertainty modeling include probabilistic face embeddings (PFE (Shi & Jain 2019)). sphere confidence face (SCF (Li et al. 2021)), and data uncertainty learning in FR (DUL (Chang et al. (020).. PFE is the first work consider data uncertainty in FR, and it estimates Gaussian distribution, instead of fixed point, in the latent space. While being effective, PFE is limited in that it does not learn the embedded feature (mean) but only the uncertainty. DUL applies data uncertainty learning (DUL) to face recog- nition such that feature (mean) and uncertainty (variance) are learned simultaneously. Besides, SCF theoretically and empirically identifies two main failures PFE when it is applied to spherical deter- ministic embeddings aforementioned. To address these issues, SCF develop a novel framework for face confidence learning in spherical space, and extend the von Mises Fisher density to its r-radius counterpart and derive new optimization objective in closed form.
Terhörst et al. 2020 introduced a seemingly similar concept, called "negative face representation". However, this method was primarily focused privacy protection, as its "negative face representa- tion" solely influenced the face verification stage and did not impact the embedding mapping process where facial features accuracy of the FR model. In contrast, our method directly influences the face-to-embee -eeeet-d-mbeddigg map- ping process, leading to improvement in the recognition accuracy of the final model.
extracted. Furthermore, it did not contribute improving the recognition
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2.2 KNOWLEDGE DISTILLATION
The method in this paper uses the framework of knowledge distillation. The general methods of knowledge distillation and the methods used in face recognition knowledge distillation are briefly introduced below.
Knowledge distillation has been actively investigated and widely used in many computer vision tasks. The basic idea proposed by Hinnon et al. (2015) minimizes the KL divergence of softened class probabilities between the teacher and the student. Later variants of distillation strategies are proposed to utilize diverse information from the teacher model, which can be divided into two types, i.e., logit distillation and feature distillation. As for the feature distillation, typical algorithms include FitNet (Romero et al. 2014), Shrink TeaNet (Duong et al. 2019), TripleDDistillationn (Feng et al.) 2020), and methods, logit distillation does not require the student to mimic the teacher's representation space, but rather to preserve the high semantic consistency with the teacher. The classical methods include the Kullback-Leibler
(Svitov & Alyamkin 2020). Different from fcature-based distillation
iivergence-basel algorithm (Hinton et al.. 2013), the mutual learning based algorithm (Zhang et al. (2018), and DKD (Zhao et al., (022), which firstly decouple the classical KD Loss into target class knowledge distillation and non-target class knowledge distillation.
The typical methods used in face recognition knowledge distillation include evaluation-oriente knowledge distillation for FR (EKD) (Huang et al., 2022), and improved FR via distribution dis- tillation loss (DDL) (Huang et al. 2020a). EKD introduces the evaluation- optimizes the student model's critical relations that cause the TPR and FPR difference between the teacher and student models. DDL uses the distillation loss to minimize the gap between easy and hard sample features. recent research [Shin et al. (2022) introduced attention similarity by knowledge distillation framework where both the student and teacher networks are of the same size. However, it still follows a traditional paradigm of knowledge distillation, attempting the student net- work to learn knowledge that is similar to the teacher network. In contrast, our proposed method aims for the student network to learn different knowledge from the teacher network.
method that
3 PROPOSED APPROACH
The fundamental goal of FR algorithms is to learn the optimal feature space with the most represen- tational capability for recognition. this paper, we suppose the feature representation space change reflects in the accuracy improvement. Firstly, provide a detailed analysis of the feature space by feature decomposition and recombination in Section 3.T Experimental results show that such recombination is likely to contribute an improved facial feature space. However, it is challenge to find innovation in a scenario where there is only one single model available. To solve the problem, adopt framework inspired by knowledge distillation in Section 3.1 We utilize intra-class inco- herence constraint (IIC) to learn innovation and finally obtain a better facial feature representation from an existing model.
3.1 FEATURE DECOMPOSITION AND RECOMBINATION
Firstly, we review the feature decomposition in Introduction, and compare two FR models that exhibit distinct performance discrepancies. We perform orthogonal decomposition on the feature from the superior model and obtain two sub-features, pro-feature and innovation. The fro-feature is parallel to the feature from the inferior model, and innovation is orthogonal to the feature from the inferior model. Let be the feature extracted from the superior model, the feature obtained by the inferior model, and e be innovation. According to the Gram-Schmin Orthogonalization, we have
(a, b)
b,
(1)
||||a||||
where (a, denotes the inner product operation of and b, || represents the L2-norm.
Table indicates that innovation also has a certain level of face distinguishability. This indicates that the feature indeed contains useful information irrelevant to the feature b. In other words, with the help of innovation, the feature a gets closer to the optimal direction d. Since the optimal feature direction is not known, is natural to investigate whether can change the modulus of innovation,
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a
d
a
at
a
(ArcFace)
d
c
a
(CosFace)
(Innovation)
(Optimal)
b
b
(a)
(b)
Figure 2: The schematic diagrams of synthesizing new features under different innovation modulus settings. (a) and b are different sides of d and (b) and are the same side of d. ct and e represent the increase and decrease of e's modulus. at and a denote the feature representation newly synthesized based ct and c
and synthesize new feature nnew using modified innovation and pro-feature, with the hope that nnew (depicted in Fig. l(b) would be closer to the optimal direction than a.
for synthesizing features. In the first case, as shown in Fig. aa), and are on different sides of d. In this case, it is necessary to reduce the modulus of innovation (or increase the modulus of pro-feature), so that new can be closer to the direction d. However, excessive reduction of the modulus of innovation (or increase the modulus of pro-feature too much) will lead the angle between new (a or a+) and being greater than that between and d, which will eventually impact the recognition accuracy. In the second case, as shown in Fig. 2(b), a and b are on the same sides of of innovation (or reduce the modulus of pro-feature), so that neww may be closer to the direction d. Similarly, extra care required when increasing the modulus. We take an example where ArcFace servers and CosFace servers b, and show the performance of the above recombinations in Table 2 We can observe that this recombination is likely to contribute to an improved facial feature representation,
According Fig. 2 there are
this case, it is necessary to increase the modulus
better than features from ArcFace.
Motivated by this discovery, we further investigate a more practical scenario where only a single model available (like in Fig. [bb), but its improved model (anew in Fig. [(b)) and innovation (a- Fig. ((b) are unknown. We need to search for innovation from the existing feature space and
properly scale it to synthesize better feature. Through the aforementioned analysis, identify two key characteristics of innovation. Firstly, the innovation is orthogonal to a. Secondly, facilitates an improvement recognition accuracy.
Table 2: The recognition accuracy of recombined features under different innovation modulus set- tings. Innovation and pro-feature are sub-fcatures ArcFace. A novel feature can be obtained by combing them with Iexonvvationn + Pro-feature', where is the coefficient. This table shows the performance of various features under different coefficients (the feature exactly represents ArcFace when 1).
Dateset LFW
ArcFace
0.1
0.5
0.8
0.9
1.1
1.2
2.0
5.0
99.15
98.82
99.20
99.12
99.13
99.15
99.15
99.17
99.17
CFP
95.69
94.77
95.61
95.67
95.61
95.69
95.73
95.73
95.70
AgeDB
94.35
92.97
94.05
94.37
94.35
94.37
94.37
94.13
94.13
CALFW
93.05
92.58
93.03
93.00
94.03
93.05
93.03
92.88
92.88
CPLFW
88.20
88.00
88.45
88.27
88.22
88.47
88.43
88,22
88.23
VGG2
92.66
91.98
92.74
92.66
92.68
92.66
92.66
92.66
92.62
AVG
93.85
93.19
93.85
93.85
94,00
93.90
93.90
93.80
93.79
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3.2 FR WITH INTRA-CLASS INCOHERENCE
Our purpose is to learn the superior feature containing innovation from an existing model feature. Based the aforementioned observations and analysises, propose novel FR training paradigm incorporating intra-class incoherence.
Specifically, first consider utilizzng the knowledge distillation(KD)) framework to implement intra-class incoherence. For traditional KD, the teacher network is model trained with the face recognition algorithm with better performance. The student network is network that needs to be trained. The teacher network supervises the student network at the feature and logit levels. However, due the different network structures the teacher and student networks, the feature dimensions are different, and the supervision on the feature level sometimes is optional.
Backbone
Block
Margin measurement
000
Head
Discimlartty
Dissimilrity
000
Dissimilarity Loss
Probabilty
Ground Truth
Classification Loss
000
Ref. Embedding
Ref. Backbone(Pre-trained])
Figure 3: Schematic diagram of imposing intra-class irrelevant constraints (IIC) output features of different layers the feature extraction network.
Nevertheless, different from the traditional knowledge distillation methods, the student network in framework keeps the same size the teacher to avoid impairing the ability of recognition. As shown in Fig the two models are the same in architecture, and we expect the to-be-trained model (the student network) perform better than the pre-trained model (the teacher network), Another noteworthy difference is that the general KD is to learn the relevant knowledge of teacher network, while our method obtains the irrelevant information teacher network with intra-class irrelevant constraints (i.e. feature dissimilarity).
Therefore, the loss function Ls for student network training is composed of the face recognition loss function Len and the intra-class incoherence cost Lidissim-
Ls LFR + Ldissim.
where 7 is the weight, Ldissim is the cosine similarity of fr and fs, and fr and fs the feature embeddings of the same face image obtained through the teacher and student networks. The term LFR preserve the capability for face recognition and Liiissim
impose IIC.
To introduce innovation of different levels when training, we take such a strategy: in addition to the final feature embeddings of the feature extraction network, the proposed intra-class irrelevance is also applied to different intermediate feature levels. Specifically, we take IR-SE-50 as the fea- ture extraction network for experiments. As shown in Fig. 3 IR-SE-50 also has four blocks. We investigate updating the four blocks' outputs using intra-class incoherence via
Ls LFR + Li (i= 1,.,,,.,,
(3)
where " is the weight, Ldissim, is the cosine similarity between fr; and fs., fr. and fs, the features of the same face image obtained through the ith block of the teacher network and student network, N denotes the number of blocks in the feature extraction network.
We also consider the case where the intra-class incoherence is applied to the outputs the four modules and the final output embedding of the feature extraction network in the following hybrid

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way:
N+1
Ls = L + Σ
where N 1 denotes the number of blocks and the output layer in the feature extraction network. By controlling whether "i is zero, can examine the effect of intra-class incoherence constraints over an arbitrary combination of different output layers on FR accuracy. See Section 4.3 for detailed ablation studies and hyper- parameter preference.
EXPERIMENTS
4.1 DATASETS AND IMPLEMENTATION DETAILS
We use CASIA Yi et al. 2014) and MS ISIM-ArcFace (also known as MSIMV2) Guo et al. 2016) as the training datasets. 7 common benchmarks including LFW (Zhang Deng 2016 CFP-FP
(Sengupta et al. 2016). CPLFW/R (Zhang & Deng 2016), AgeDB (Moschoglou et al. 2017). CALFW
(Zhang & Deng 2016), Vggface2 (Cao et al. 2018), and IJB-C (Maze al.) 2018) are used to evaluate the performance of different algorithms following the standard evaluation protocols. For
these test sets, the images show variations lighting, pose, or age.
We train the model with ResNet50 and ResNet100 (He al., 2016) as the backbone and batch size of 512 using the metric and loss functions similar to the specified definition their original text. The head of the baseline model is: BackBone- Fltoon-FFatte--F--B with embedding dimensions of 512 and the dropout probability 0.4 to output the embedding feature. Unless specified otherwise, models trained for 50 epochs using the SGD optimizer with momentum of 0.9, and weight decay of 0.0001. The model is trained with SGD with an initial learning rate 0.1 and step scheduling at 10, 20, 30 and 40 epochs. For the scale parameters, we it 64, following the suggestion of Wang et al. (2018)).
4.2 COMPARISON WITH SOTA METHODS AND ANALYSIS
In this experiment, we adopt some common baseline models such as ArcFace (Deng et al. 2019) and CasFace (Wang et al., 2018)). Besides, some recent state-of-the-art methods such as MagFace (Meng et al. 2021) and AdaFace (Kim al. 2022) also serve as the baseline models for compar- ison, and this paper adopts the training paradigm with IIC in manner consistent with the original literature. Since the proposed method is based on a pre-trained model, the parameters of the teacher network are downloaded from their official offered checkpoints if available.
Firstly, we train relatively small network with ResNet50 (He et al. 2016) as the backbone on CASIA et al., 2014). The experimental results shown in Table
Table 3: Comparison of face recognition accuracy among some common and recent FR algorithms.
All the models are trained with ResNet50 (He al. 2016) as the backbone on CASIA.
Benchmarks($$)
Method
Average
LFW
CFP-FP
AgeDB-33
CALFW
CPLFW
VGGFace2
CosFace
99.22
93.87
92.55
92.77
87.57
91.94
92.99
CosFace+IIC
99.17
94.40
92.48
92.53
88.22
91.94
93.12
ArcFaace
99.15
95.69
94.35
93.05
88.20
92.66
93.85
ArcFace+IIC
99.43
96.03
94.12
93.05
89.45
93.36
94.24
MagFaace
99.27
95.27
93.77
93.33
87.90
92.10
93.61
MagFace+IIC
99.25
95.70
93.58
92.95
88.08
92.58
93.69
AdaFace
99.42
96.41
94.38
93.23
89.97
93,08
94.42
AdaFace+1IC
99.18
96.94
94.10
93.37
90.17
93.74
94.58
We observe that IIC proposed this paper has significant improvements on all face recognition algorithms. Even the recognition accuracy of the SoTA method AdaFace is also improved. By comparing the results of Table and Table (results of AreFace), is evident that the improvement curious about
in recognition accuracy achieved by IIC surpasses that listed in Table 2 Then

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the performance of IIC some large-scale datasets and more complex networks. Therefore, train a ResNet100 network as the backbone using MSIMV2 as the training dataset and show the results in Table
Table 4: Comparison of face recognition accuracy among state-of-the-at FR algorithms. All the models trained with ResNet100 as the backbone MSIMV2.
Benchmarks($8
Method
Average
LFW
CFP-FP
AgeDB-33
CALFW
CPLFW
VGGFace2
CosFace
99.78
98.12
98.11
95.76
92.18
95.24
96.53
CosFace+IIC
99.80
98.24
98.16
95.68
92.26
95.34
96.58
ArcFace
99.78
98.10
98.20
95.87
92.62
95.74
96.72
ArcFace+IIC
99.78
98.19
98.25
96.05
93.02
95.30
96.76
MagFaae
99.83
98.46
98.17
96.15
92.87
95.40
MagFace+IIC
99.82
98. 14
98.12
96.17
92.88
95.40
96.76
AdaFaace
99.82
98.49
98.05
96.08
93.53
95.70
96.94
AdaFace+IIC
99.78
98.41
98.12
96.18
93.48
95.80
96.96
Table 5: Comparison the face recognition aceuracy for the ArcFace and AdaFace algorithms before and after using IIC. The training dataset is MSIM. and the test dataset is IJB-C.
UB-C UB-C(TPR FPR)
Method (Backbone)
le-06
le-05
le-04
1e-03
le-02
1e-01
ArcFace(R50)
85.64
92.88
95.92
97.45
98.44
99.21
ArcFace+IIC(R50)
89.50
94.53
96.28
97.52
98.48
99.23
MagFace(R550)
81.70
88.95
93.34
95.91
97.70
99.01
MagFace+IIC(RRS)
85.88
92.37
95.16
96.94
98.15
99.06
AdaFace(R50)
87.70
93.61
96.27
97.62
98.29
99.10
AdaFace++IC(R550)
87.87
94.06
96.33
97.64
98.38
99.12
MagFaco(R110))
89.26
93.67
95.81
97.26
98.27
99.10
MagFacc+IIC(RLo0)
89.38
93.95
95.89
97.28
98.27
99.12
AdaFace (R100)
89.74
94.87
96.89
97.89
98.47
99.18
AdaFace+IIC (R100)
89.99
94.88
96.89
97.89
98.51
99.17
To provide a comprehensive evaluation. we present the performance of shate-of-the-ae (SoTA) meth- ods on the IJB-C benchmark in Table In this setting, utilize the MSIMV2 dataset for training. From the results in Table 55] is evident that our method outperforms the baseline models in most cases, particularly when low false positive rate (FPR) is required. Notably, when the FPR is set le-6, the models trained with the intra-class incoherence constraint (IIC) significantly outperform all baseline methods.
However, comparing the results in Tab and Tab 3 we find that IIC plays a more effective role in relatively smaller dataset. This observation motivates us investigate the underlying reasons. Through careful analysis of the experimental results, we associate it with the technique of data aug- mentation. Data augmentation
technique of artificially increasing the training set by creating modified copies of dataset using existing data. It introduces perturbations to the data, making it challenging for the model to simply recognize them. Although data augmentation may seemingly increase the training difficulty, it actually enables the model to better learn the underlying feature representations. Furthermore, data augmentation has been shown to effectively enhance the perfor- mance of models when dealing with limited data. These explanations proposed method encourages the FR model to explore different feature space and learn a better fea- ture representation. Therefore, hypothesize that IIC serves form of "feature augmentation". To validate this hypothesis, we conduct an ablation study in Sec 4.3
also be applied to IIC. Our
4.3 ABLATION STUDY AND
PREFERENCE
In this section, if not specified, we use the CASIA dataset to train the model which ArcFace serves the basic face recognition algorithm.
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Published as a conference paper at ICLR 2024
Firstly, investigate the impact of different weights the performance of Eq. The detailed results are shown in Appendix 6 We find that the average precision on all test sets is improved. For different weights in Table 6 the performance gap is marginal. For convenience, the previous experiments also have a similar treatment. In the absence of special instructions, the default weight is 1.0.
Besides, we examine the impact of the different initialization methods for student networks on recog- nition accuracy, namely, random initialization and initialization with the teacher network's weight. We provide the results in Appendix Table 7 It is obvious that the recognition accuracy of initial- ization with the teacher network's weight is the best. Unless otherwise specified, the weight of the teacher network is used for initialization by default. We also investigate the case where the student network has no intra-class irrelevant constraints, that is, only the weight of the teacher network loaded for initialization and the model is trained solely by FR loss. It can be seen from Table that the absence of intra-class irrelevant constraints does not improve the performance, but the perfor- mance will decline slightly. We suppose it is because that the data are reused and the model training may be overfitting.
Then, we investigate the constraint of intra-class irrelevant on the outputs of four blocks, the output of the last layer of the feature extraction network, and all five outputs, respectively. The results are shown in Appendix Table [8] We find that the average accuracy is improved by adding the IIC to the output of each module. However, when all the features are imposed on IIC at the same time, the performance is degraded. The possible reason is that imposing too many restrictions would affect the capability of recognition. Since the performance of applying IIC to the outputs of the four modules and the last layer has little difference, prefer more convenient way. If not specified, the following experiment applies IIC to the last layer output of the feature extraction network.
To further verify the accuracy gained brought by innovation, we also perform orthogonal decompo- sition on the features learned from the model with IIC to investigate the ability of face recognition of innovation. We provide the experimental results in Appendix Table 9 shows that the learned innovation does have certain facial feature representation abilities. Combined with Tab 3 we can infer that the feature representation space obtained by IIC plays a role performance improvement.
Finally, we validate the supposition mentioned in the Section 4.2 1/10) of MSIMV2 to train a ResNet50 as the backbone, with AdaFace serving as the basic face recognition algorithm. We provide the results in Appendix Table 10 It confirms our hypothesis that our proposed method can be regarded as a form of "feature augmentation".
We use small portion (i.e.
LIMITATION
The method proposed in this paper is to find a more expressive feature representation space based on pre-trained model. However, the method is currently applicable face recognition tasks, and we think it has the potential to be extended to more general tasks and more general datasets. Though the improvement of recognition accuracy by IIC is greater than that listed in Table [ it is not ruled out that a better feature expression space can be found by a suitable optimization algorithm.
6 CONCLUSIONS
Generally, traditional face recognition algorithms are to enhance FR performance by increasing intra-class correlation and inter-class incoherence. This paper does the opposite, and the proposed method further improves the accuracy of the face recognition algorithm by adding intra-class inco- herence, Firstly, this paper analyzes the reasons for the improvement of face recognition accuracy from the feature representation level for different face recognition algorithms. Based detailed analysis, we adopt the knowledge distillation framework to introduce innovation by adding intra- class irrelevant constraints (IIC), attempting to obtain more representative feature space. Experi- ments show that the existing state-of-thed the method with IIC can be further improved, highlighting its potential further enhance FR performance.

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Published as a conference paper at ICLR 2024
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APPENDIX
Table 6: Comparison recognition accuracy when weight y of the intra-class uncorrelated constraint in Eq is taken as 0.1, 0.5, 1.0, 5.0 and 10.0, respectively.
Dateset
ArcFace
>=0.1
2=0.5
y=1.0
y=5.0
>=10,0
LFW
99.15
99.43
99.33
99.50
99.43
99.40
CFP
95.69
96.16
96.23
96.03
96.06
96.31
AgeDB
94.35
94.37
94.47
94.30
94.28
94.25
CALFW
93.05
93.40
93.38
93.33
93.42
93.48
CPLFW
88.20
89.10
89.15
89.45
88.92
89.37
VGG2
92.66
93.60
93.22
93.36
93.56
93.26
AVG
93.85
94.34
94.30
94.33
94.28
94.35
Table 7: Comparison of face recognition accuracy when the student network initialization mode is random initialization and teacher network weight initialization respectively, and the student network
initialized with the teacher networks' weight does not using IIC, i.e., y=0 Eq 2
Dateset
ArcFace
Random Init.
Teacher weight Init.
w/o IIC
LFW
99.15
99.37
99.50
99.22
CFP
95.69
95.57
96.03
94.84
AgeDB
94.35
93.68
94.30
93.62
CALFW
93.05
93.33
93.33
92.63
CPLFW
88.20
89.22
89.45
87.80
VGG2
92.66
93.02
93.36
92.38
AVG
93.85
94.03
94.33
93.42
Table 8: Comparison of face recognition accuracy when IIC is applied to the outputs of four blocks, the output of the last layer (represented by 'F" of the feature extraction network respectively, the output of block 1 (represented by 'B.1') and the output of the last layer, the output of block (represented by 'B.2") and the output of the last layer, and all five outputs (represented by 'overall '). In this setting, 2=0.5.
Dateset LFW
ArcFace
B.
B.2
B.3
B.4
B.I+F
B.2+F
overall
99.15
99.40
99.43
99.45
99.40
99.33
99.40
99.36
99.22
CFP
95.69
96.57
96.31
96.03
96.07
96.23
96.43
95.69
95.20
AgeDB
94.35
94.18
94.25
94.13
94.12
94.47
94.35
93.87
93.73
CALFW
93.05
93.25
93.38
93.38
93.37
93.38
93.30
92.68
92.58
CPLFW
88.22
89.53
89.57
89.47
89.37
89.15
89.20
88.75
88.63
VGG2
92.66
93.30
93.32
93.34
93.26
93.22
93.36
92.94
92.44
AVG
93.85
94.37
94.38
94.30
94.26
94.30
94.34
93.88
93.63
13

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Published as a conference paper at ICLR 2024
Table 9: Comparison of face recognition accuracy of innovation obtained from CosFace+IIC, Arc- Face+IIC, MagFace+IIC, AdaFace+IIC, and AdaFace" +IIC in the table. represents the results of model training using the dataset MSIMV2.
Dateset
CosFace
ArcFace
MagFace
AdaFace
AdaFace
LFW
97.02
96.60
98.40
98.92
99.63
CFP
85.16
86.06
91.39
94.56
95.24
AgeDB
83.38
81.73
90.27
92.70
97.07
CALFW
86.47
84.87
91.27
92.28
95.60
CPLFW
80.48
80.53
84.08
87.00
90.35
VGG2
83.30
84.98
88.20
92.60
93.68
AVG
85,97
85,80
90.60
93.01
95.26
Table 10: Comparison of face recognition accuracy among some common and recent FR algorithms. All the models are trained with ResNet50 (He al. 2016) the backbone CASIA.
Benchmarks($))
Method
Average
LFW
CFP-FP
AgeDB-30
CALFW
CPLFW
VGGFace2
AdaFace
99.40
92.86
94.92
94.67
88.73
92.64
93.87
AdaFace+IIC
99.48
93.57
94.98
94.40
88.73
93.22
94.07
14


Reviews:
[{"review_id": "sAemMgWWIg", "reviewer": "Reviewer_V2zT", "summary": "In this paper, authors present a novel method that can improve existing face recognition (FR) methods by imposing a constraint of dissimilarity with learned embeddings.  \n\nThe paper starts with a framework that decomposes the feature space of a superior model into two sub features, with one along that of a inferior model (pro-feature) and the other being orthogonal (innovation feature). Experiments show that the innovation part (orthogonal features)  has a high level of face distinguishability, which can be useful to learn from. Thus authors propose to use the dissimilarity with learning embedding as an auxiliary task in addition to the main face recognition tasks, under the knowledge distillation framework. \n\nExperiments showed that this method can consistently improve existing methods (ArcFace, CosFace, MagFace, AdaFace) across 6 FR benchmarks. It's observed that the proposed method has a larger benefit on smaller datasets. Author hypothesized that the proposed method works as an feature augmentation mechanism.", "questions": "It would be interesting if authors can conduct experiments on some more challenging classification tasks.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "The paper is well written and easy to follow.  The paper uses multiple sections to explain the main idea step by step. It starts with the introduction of feature decomposition and uses experiments to demonstrate the usefulness of the orthogonal subfeature; Then experiments show that moving the feature along the direction of the orthogonal subfeature can improve model performance; finally, authors  propose the idea to encourage the model to move towards the direction that dissimilar to learned embeddings.  The idea is implemented within the knowledge distillation framework.   \n\nThe proposed method is novel and effective. Existing knowledge distillation methods generally impose a similarity objective to help the student model better mimic the teacher model. The proposed method is on the opposite direction - it leans dissimilarity.  Authors has provided a detailed analysis to justify this novel learning objective.\n\nThe experiments are extensive and the results are solid. Multiple classic face recognization models are used as baselines and studied on several common benchmarks. The improvements look consistent. Ablation studies provides good insights for understanding the proposed method.", "weaknesses": "The ablation of the proposed method can be further enhanced.  Authors has hypothesized the proposed method works as a feature augmentation mechanism. It will be insightful if other feature augmentation or regularization methods can be compared, for example, injecting noise to the activations. \n\nThe method is only studied on face recognition. In theory, this method can be applied to other classification tasks (especially fine-grained classification). Existing face recognition benchmarks already have high accuracy, so the improvement doesn't look too significant.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "dNUb27Yvsb", "reviewer": "Reviewer_JUcW", "summary": "This paper starts with the hypothesis that when considering two face recognition (FR) models, the better-performing model can be further improved by combining features orthogonal to the worse-performing model. Authors propose the use of intra-class incoherence constraint (IIC) as a way of accomplishing this when a single FR model is available. Accuracy results on multiple face image datasets indicate that the proposed approach shows slightly better performance over other relevant approaches.", "questions": "1. Please clarify in the paper how the feature vector diagrams in Figs. 1 and 2 generalize to higher dimensions?\n\n2. On Page 2, it is stated that \"...innovation is always independent of features from CosFace\". Independence and orthogonality are different concepts. Do you mean orthogonality or independence here? If later, please provide a justification for why orthogonality implies independence.\n\n3. Manuscript suffers from language deficiencies. For example, \"orthogonal\" is a better choice for \"perpendicular\". Please revise the manuscript carefully to improve the language quality.\n\n4. In Section 3.1, it is stated that \"In the first case, as shown in Fig. 2(a), a and b are on different sides of d.\" In 2-D, it is clear what we mean by different sides. How are different sides defined in higher dimensional spaces?\n\n5. In Eq. (3), should there be a summation over i on the RHS? If not, how come there is no dependence on i on the LHS?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "One strength of the paper is the observation that incorporating the features orthogonal to the inferior model can improve the performance of a superior model. I am still not convinced of this as there is no theoretical proof of this, but numerical results are reasonably convincing.\n\nAnother strength of the paper is the collection of experimental results. Authors show accuracy results on multiple face image datasets and show comparisons with the state of the art FR methods. Also, ablation studies included seem to support authors' hypothesis.", "weaknesses": "One major weakness of the paper is the most of the concepts and associated discussion seem to be based on the 2-D spaces in Figs. 1 and 2 whereas the feature vectors are in a much higher dimensional space. One problem with over-relying on the figures is that authors speak as if there is one perpendicular component to the inferior model in Fig. 1. For a given model in n-dimensional space, there is a (n-1)-dimensional space orthogonal to it. How do we choose the innovation feature from this space?\n\nAnother major weakness is that there are no theoretical proofs or justifications for the suggested improvements.  If a superior model can be further improved by combining it with something orthogonal to an inferior model, doesn't that imply that the \"superior\" model may not have been trained sufficiently? Also, why should we stop with combining the innovation from just one inferior model? Why not consider multiple inferior models and extract and use features orthogonal to these multiple models?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "WyXi7bnFRs", "reviewer": "Reviewer_GUup", "summary": "This paper proposes a face representation learning method considering the intra-class dissimilarity. Experimental results on multiple datasets and baselines show the effectiveness of the proposed method.", "questions": "See weaknesses above", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "This paper is well-written and easy to follow, the findings about pro-features and innovation features are interesting.", "weaknesses": "Here are some questions about this paper:\n1) The loss L_{dissim} should be described more detailedly, especially the relationship between the motivation describe in introduction and minimizing the cosine similary of teacher and student feature.\n2) The student network and teacher network are in the same sturcture. Will it be better if using the trained student network to be the teacher network since the goal of the method is a student network with higher performance? More analysis should be given.\n3) Sicne this method mainly focuses on feature distillation and representation learning, more comparision with the SOTA distillation methods should be given.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "oYddvH78Lj", "reviewer": "Reviewer_UpYx", "summary": "This paper proposes a method to learn a new, better representation space for facial features, from two existing, already optimal representation spaces. The analysis is based on some geometrical consideration regarding the possibility to improve a representation feature space, by interpolating other representation spaces.\nThe feature augmentation approach demonstrates very limited improvements on some identification tests. However, the proposed idea has some merits and it is worth further considerations and discussion towards the direction of adaptive techniques for feature space augmentation.", "questions": "How would you expect to enlarge the scope of the proposed techniques?\nHow could you disentangle the proposed augmentation method from the training data, and consequently the learned features?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Attempting to design a general feature space augmentation techniques interpolating already sub-optimal baseline spaces.", "weaknesses": "The reported results demonstrate a very limited improvement, maybe not justifying the efforts.\nThe designed feature augmentation model may be dependent on the training and produce different results on  different pre-trained models.\nLanguage mistakes", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (spotlight)