Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> In modern face recognition, the conventional pipeline consists of four stages: detect => align => represent => classify. We revisit both the alignment step and the representation step by employing explicit 3D face modeling in order to apply a piecewise affine transformation, and derive a face representation from a nine-layer deep neural network. This deep network involves more than 120 million parameters using several locally connected layers without weight sharing, rather than the standard convolutional layers. Thus we trained it on the largest facial dataset to-date, an identity labeled dataset of four million facial images belonging to more than 4, 000 identities. The learned representations coupling the accurate model-based alignment with the large facial database generalize remarkably well to faces in unconstrained environments, even with a simple classifier. Our method reaches an accuracy of 97.35% on the Labeled Faces in the Wild (LFW) dataset, reducing the error of the current state of the art by more than 27%, closely approaching human-level performance. <s> BIB001 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> This paper proposes to learn a set of high-level feature representations through deep learning, referred to as Deep hidden IDentity features (DeepID), for face verification. We argue that DeepID can be effectively learned through challenging multi-class face identification tasks, whilst they can be generalized to other tasks (such as verification) and new identities unseen in the training set. Moreover, the generalization capability of DeepID increases as more face classes are to be predicted at training. DeepID features are taken from the last hidden layer neuron activations of deep convolutional networks (ConvNets). When learned as classifiers to recognize about 10, 000 face identities in the training set and configured to keep reducing the neuron numbers along the feature extraction hierarchy, these deep ConvNets gradually form compact identity-related features in the top layers with only a small number of hidden neurons. The proposed features are extracted from various face regions to form complementary and over-complete representations. Any state-of-the-art classifiers can be learned based on these high-level representations for face verification. 97:45% verification accuracy on LFW is achieved with only weakly aligned faces. <s> BIB002 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> The key challenge of face recognition is to develop effective feature representations for reducing intra-personal variations while enlarging inter-personal differences. In this paper, we show that it can be well solved with deep learning and using both face identification and verification signals as supervision. The Deep IDentification-verification features (DeepID2) are learned with carefully designed deep convolutional networks. The face identification task increases the inter-personal variations by drawing DeepID2 features extracted from different identities apart, while the face verification task reduces the intra-personal variations by pulling DeepID2 features extracted from the same identity together, both of which are essential to face recognition. The learned DeepID2 features can be well generalized to new identities unseen in the training data. On the challenging LFW dataset [11], 99.15% face verification accuracy is achieved. Compared with the best previous deep learning result [20] on LFW, the error rate has been significantly reduced by 67%. <s> BIB003 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> The state-of-the-art of face recognition has been significantly advanced by the emergence of deep learning. Very deep neural networks recently achieved great success on general object recognition because of their superb learning capacity. This motivates us to investigate their effectiveness on face recognition. This paper proposes two very deep neural network architectures, referred to as DeepID3, for face recognition. These two architectures are rebuilt from stacked convolution and inception layers proposed in VGG net and GoogLeNet to make them suitable to face recognition. Joint face identification-verification supervisory signals are added to both intermediate and final feature extraction layers during training. An ensemble of the proposed two architectures achieves 99.53% LFW face verification accuracy and 96.0% LFW rank-1 face identification accuracy, respectively. A further discussion of LFW face verification result is given in the end. <s> BIB004 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Despite significant recent advances in the field of face recognition [10, 14, 15, 17], implementing face verification and recognition efficiently at scale presents serious challenges to current approaches. In this paper we present a system, called FaceNet, that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure of face similarity. Once this space has been produced, tasks such as face recognition, verification and clustering can be easily implemented using standard techniques with FaceNet embeddings as feature vectors. <s> BIB005 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> The goal of this paper is face recognition – from either a single photograph or from a set of faces tracked in a video. Recent progress in this area has been due to two factors: (i) end to end learning for the task using a convolutional neural network (CNN), and (ii) the availability of very large scale training datasets. We make two contributions: first, we show how a very large scale dataset (2.6M images, over 2.6K people) can be assembled by a combination of automation and human in the loop, and discuss the trade off between data purity and time; second, we traverse through the complexities of deep network training and face recognition to present methods and procedures to achieve comparable state of the art results on the standard LFW and YTF face benchmarks. <s> BIB006 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Cross-entropy loss together with softmax is arguably one of the most common used supervision components in convolutional neural networks (CNNs). Despite its simplicity, popularity and excellent performance, the component does not explicitly encourage discriminative learning of features. In this paper, we propose a generalized large-margin softmax (L-Softmax) loss which explicitly encourages intra-class compactness and inter-class separability between learned features. Moreover, L-Softmax not only can adjust the desired margin but also can avoid overfitting. We also show that the L-Softmax loss can be optimized by typical stochastic gradient descent. Extensive experiments on four benchmark datasets demonstrate that the deeply-learned features with L-softmax loss become more discriminative, hence significantly boosting the performance on a variety of visual classification and verification tasks. <s> BIB007 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Convolutional neural networks (CNNs) have been widely used in computer vision community, significantly improving the state-of-the-art. In most of the available CNNs, the softmax loss function is used as the supervision signal to train the deep model. In order to enhance the discriminative power of the deeply learned features, this paper proposes a new supervision signal, called center loss, for face recognition task. Specifically, the center loss simultaneously learns a center for deep features of each class and penalizes the distances between the deep features and their corresponding class centers. More importantly, we prove that the proposed center loss function is trainable and easy to optimize in the CNNs. With the joint supervision of softmax loss and center loss, we can train a robust CNNs to obtain the deep features with the two key learning objectives, inter-class dispension and intra-class compactness as much as possible, which are very essential to face recognition. It is encouraging to see that our CNNs (with such joint supervision) achieve the state-of-the-art accuracy on several important face recognition benchmarks, Labeled Faces in the Wild (LFW), YouTube Faces (YTF), and MegaFace Challenge. Especially, our new approach achieves the best results on MegaFace (the largest public domain face benchmark) under the protocol of small training set (contains under 500000 images and under 20000 persons), significantly improving the previous results and setting new state-of-the-art for both face recognition and face verification tasks. <s> BIB008 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> This paper proposes to learn high-performance deep ConvNets with sparse neural connections, referred to as sparse ConvNets, for face recognition. The sparse ConvNets are learned in an iterative way, each time one additional layer is sparsified and the entire model is re-trained given the initial weights learned in previous iterations. One important finding is that directly training the sparse ConvNet from scratch failed to find good solutions for face recognition, while using a previously learned denser model to properly initialize a sparser model is critical to continue learning effective features for face recognition. This paper also proposes a new neural correlation-based weight selection criterion and empirically verifies its effectiveness in selecting informative connections from previously learned models in each iteration. When taking a moderately sparse structure (26%-76% of weights in the dense model), the proposed sparse ConvNet model significantly improves the face recognition performance of the previous state-of-theart DeepID2+ models given the same training data, while it keeps the performance of the baseline model with only 12% of the original parameters. <s> BIB009 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Convolutional neural networks have achieved great improvement on face recognition in recent years because of its extraordinary ability in learning discriminative features of people with different identities. To train such a well-designed deep network, tremendous amounts of data is indispensable. Long tail distribution specifically refers to the fact that a small number of generic entities appear frequently while other objects far less existing. Considering the existence of long tail distribution of the real world data, large but uniform distributed data are usually hard to retrieve. Empirical experiences and analysis show that classes with more samples will pose greater impact on the feature learning process and inversely cripple the whole models feature extracting ability on tail part data. Contrary to most of the existing works that alleviate this problem by simply cutting the tailed data for uniform distributions across the classes, this paper proposes a new loss function called range loss to effectively utilize the whole long tailed data in training process. More specifically, range loss is designed to reduce overall intra-personal variations while enlarging inter-personal differences within one mini-batch simultaneously when facing even extremely unbalanced data. The optimization objective of range loss is the $k$ greatest range's harmonic mean values in one class and the shortest inter-class distance within one batch. Extensive experiments on two famous and challenging face recognition benchmarks (Labeled Faces in the Wild (LFW) and YouTube Faces (YTF) not only demonstrate the effectiveness of the proposed approach in overcoming the long tail effect but also show the good generalization ability of the proposed approach. <s> BIB010 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> In recent years, the performance of face verification systems has significantly improved using deep convolutional neural networks (DCNNs). A typical pipeline for face verification includes training a deep network for subject classification with softmax loss, using the penultimate layer output as the feature descriptor, and generating a cosine similarity score given a pair of face images. The softmax loss function does not optimize the features to have higher similarity score for positive pairs and lower similarity score for negative pairs, which leads to a performance gap. In this paper, we add an L2-constraint to the feature descriptors which restricts them to lie on a hypersphere of a fixed radius. This module can be easily implemented using existing deep learning frameworks. We show that integrating this simple step in the training pipeline significantly boosts the performance of face verification. Specifically, we achieve state-of-the-art results on the challenging IJB-A dataset, achieving True Accept Rate of 0.909 at False Accept Rate 0.0001 on the face verification protocol. Additionally, we achieve state-of-the-art performance on LFW dataset with an accuracy of 99.78%, and competing performance on YTF dataset with accuracy of 96.08%. <s> BIB011 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Feature matters. How to train a deep network to acquire discriminative features across categories and polymerized features within classes has always been at the core of many computer vision tasks, specially for large-scale recognition systems where test identities are unseen during training and the number of classes could be at million scale. In this paper, we address this problem based on the simple intuition that the cosine distance of features in high-dimensional space should be close enough within one class and far away across categories. To this end, we proposed the congenerous cosine (COCO) algorithm to simultaneously optimize the cosine similarity among data. It inherits the softmax property to make inter-class features discriminative as well as shares the idea of class centroid in metric learning. Unlike previous work where the center is a temporal, statistical variable within one mini-batch during training, the formulated centroid is responsible for clustering inner-class features to enforce them polymerized around the network truncus. COCO is bundled with discriminative training and learned end-to-end with stable convergence. Experiments on five benchmarks have been extensively conducted to verify the effectiveness of our approach on both small-scale classification task and large-scale human recognition problem. <s> BIB012 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> This paper addresses deep face recognition (FR) problem under open-set protocol, where ideal face features are expected to have smaller maximal intra-class distance than minimal inter-class distance under a suitably chosen metric space. However, few existing algorithms can effectively achieve this criterion. To this end, we propose the angular softmax (A-Softmax) loss that enables convolutional neural networks (CNNs) to learn angularly discriminative features. Geometrically, A-Softmax loss can be viewed as imposing discriminative constraints on a hypersphere manifold, which intrinsically matches the prior that faces also lie on a manifold. Moreover, the size of angular margin can be quantitatively adjusted by a parameter m. We further derive specific $m$ to approximate the ideal feature criterion. Extensive analysis and experiments on Labeled Face in the Wild (LFW), Youtube Faces (YTF) and MegaFace Challenge 1 show the superiority of A-Softmax loss in FR tasks. <s> BIB013 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> We describe a new training methodology for generative adversarial networks. The key idea is to grow both the generator and discriminator progressively: starting from a low resolution, we add new layers that model increasingly fine details as training progresses. This both speeds the training up and greatly stabilizes it, allowing us to produce images of unprecedented quality, e.g., CelebA images at 1024^2. We also propose a simple way to increase the variation in generated images, and achieve a record inception score of 8.80 in unsupervised CIFAR10. Additionally, we describe several implementation details that are important for discouraging unhealthy competition between the generator and discriminator. Finally, we suggest a new metric for evaluating GAN results, both in terms of image quality and variation. As an additional contribution, we construct a higher-quality version of the CelebA dataset. <s> BIB014 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> In this letter, we propose a conceptually simple and intuitive learning objective function, i.e., additive margin softmax, for face verification. In general, face verification tasks can be viewed as metric learning problems, even though lots of face verification models are trained in classification schemes. It is possible when a large-margin strategy is introduced into the classification model to encourage intraclass variance minimization. As one alternative, angular softmax has been proposed to incorporate the margin. In this letter, we introduce another kind of margin to the softmax loss function, which is more intuitive and interpretable. Experiments on LFW and MegaFace show that our algorithm performs better when the evaluation criteria are designed for very low false alarm rate. <s> BIB015 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Face recognition has achieved revolutionary advancement owing to the advancement of the deep convolutional neural network (CNN). The central task of face recognition, including face verification and identification, involves face feature discrimination. However, traditional softmax loss of deep CNN usually lacks the power of discrimination. To address this problem, recently several loss functions such as central loss \cite{centerloss}, large margin softmax loss \cite{lsoftmax}, and angular softmax loss \cite{sphereface} have been proposed. All these improvement algorithms share the same idea: maximizing inter-class variance and minimizing intra-class variance. In this paper, we design a novel loss function, namely large margin cosine loss (LMCL), to realize this idea from a different perspective. More specifically, we reformulate the softmax loss as cosine loss by L2 normalizing both features and weight vectors to remove radial variation, based on which a cosine margin term \emph{$m$} is introduced to further maximize decision margin in angular space. As a result, minimum intra-class variance and maximum inter-class variance are achieved by normalization and cosine decision margin maximization. We refer to our model trained with LMCL as CosFace. To test our approach, extensive experimental evaluations are conducted on the most popular public-domain face recognition datasets such as MegaFace Challenge, Youtube Faces (YTF) and Labeled Face in the Wild (LFW). We achieve the state-of-the-art performance on these benchmark experiments, which confirms the effectiveness of our approach. <s> BIB016 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> We motivate and present Ring loss, a simple and elegant feature normalization approach for deep networks designed to augment standard loss functions such as Softmax. We argue that deep feature normalization is an important aspect of supervised classification problems where we require the model to represent each class in a multi-class problem equally well. The direct approach to feature normalization through the hard normalization operation results in a non-convex formulation. Instead, Ring loss applies soft normalization, where it gradually learns to constrain the norm to the scaled unit circle while preserving convexity leading to more robust features. We apply Ring loss to large-scale face recognition problems and present results on LFW, the challenging protocols of IJB-A Janus, Janus CS3 (a superset of IJB-A Janus), Celebrity Frontal-Profile (CFP) and MegaFace with 1 million distractors. Ring loss outperforms strong baselines, matches state-of-the-art performance on IJB-A Janus and outperforms all other results on the challenging Janus CS3 thereby achieving state-of-the-art. We also outperform strong baselines in handling extremely low resolution face matching. <s> BIB017 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Deep learning applies multiple processing layers to learn representations of data with multiple levels of feature extraction. This emerging technique has reshaped the research landscape of face recognition since 2014, launched by the breakthroughs of Deepface and DeepID methods. Since then, deep face recognition (FR) technique, which leverages the hierarchical architecture to learn discriminative face representation, has dramatically improved the state-of-the-art performance and fostered numerous successful real-world applications. In this paper, we provide a comprehensive survey of the recent developments on deep FR, covering the broad topics on algorithms, data, and scenes. First, we summarize different network architectures and loss functions proposed in the rapid evolution of the deep FR methods. Second, the related face processing methods are categorized into two classes: `one-to-many augmentation' and `many-to-one normalization'. Then, we summarize and compare the commonly used databases for both model training and evaluation. Third, we review miscellaneous scenes in deep FR, such as cross-factor, heterogenous, multiple-media and industry scenes. Finally, potential deficiencies of the current methods and several future directions are highlighted. <s> BIB018 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> One of the main challenges in feature learning using Deep Convolutional Neural Networks (DCNNs) for large-scale face recognition is the design of appropriate loss functions that can enhance the discriminative power. Centre loss penalises the distance between deep features and their corresponding class centres in the Euclidean space to achieve intra-class compactness. SphereFace assumes that the linear transformation matrix in the last fully connected layer can be used as a representation of the class centres in the angular space and therefore penalises the angles between deep features and their corresponding weights in a multiplicative way. Recently, a popular line of research is to incorporate margins in well-established loss functions in order to maximise face class separability. In this paper, we propose an Additive Angular Margin Loss (ArcFace) to obtain highly discriminative features for face recognition. The proposed ArcFace has a clear geometric interpretation due to its exact correspondence to geodesic distance on a hypersphere. We present arguably the most extensive experimental evaluation against all recent state-of-the-art face recognition methods on ten face recognition benchmarks which includes a new large-scale image database with trillions of pairs and a large-scale video dataset. We show that ArcFace consistently outperforms the state of the art and can be easily implemented with negligible computational overhead. To facilitate future research, the code has been made available. <s> BIB019 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> The cosine-based softmax losses and their variants achieve great success in deep learning based face recognition. However, hyperparameter settings in these losses have significant influences on the optimization path as well as the final recognition performance. Manually tuning those hyperparameters heavily relies on user experience and requires many training tricks. In this paper, we investigate in depth the effects of two important hyperparameters of cosine-based softmax losses, the scale parameter and angular margin parameter, by analyzing how they modulate the predicted classification probability. Based on these analysis, we propose a novel cosine-based softmax loss, AdaCos, which is hyperparameter-free and leverages an adaptive scale parameter to automatically strengthen the training supervisions during the training process. We apply the proposed AdaCos loss to large-scale face verification and identification datasets, including LFW, MegaFace, and IJB-C 1:1 Verification. Our results show that training deep neural networks with the AdaCos loss is stable and able to achieve high face recognition accuracy. Our method outperforms state-of-the-art softmax losses on all the three datasets. <s> BIB020 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Cosine-based softmax losses significantly improve the performance of deep face recognition networks. However, these losses always include sensitive hyper-parameters which can make training process unstable, and it is very tricky to set suitable hyper parameters for a specific dataset. This paper addresses this challenge by directly designing the gradients for training in an adaptive manner. We first investigate and unify previous cosine softmax losses from the perspective of gradients. This unified view inspires us to propose a novel gradient called P2SGrad (Probability-to-Similarity Gradient), which leverages a cosine similarity instead of classification probability to control the gradients for updating neural network parameters. P2SGrad is adaptive and hyper-parameter free, which makes training process more efficient and faster. We evaluate our P2SGrad on three face recognition benchmarks, LFW, MegaFace, and IJB-C. The results show that P2SGrad is stable in training, robust to noise, and achieves state-of-the-art performance on all the three benchmarks. <s> BIB021 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> In this paper, we propose a new supervision objective named uniform loss to learn deep equidistributed representations for face recognition. Most existing methods aim to learn discriminative face features, encouraging large inter-class distances and small intra-class variations. However, they ignore the distribution of faces in the holistic feature space, which may lead to severe locality and unbalance. With the prior that faces lie on a hypersphere manifold, we impose an equidistributed constraint by uniformly spreading the class centers on the manifold, so that the minimum distance between class centers can be maximized through complete exploitation of the feature space. To this end, we consider the class centers as like charges on the surface of hypersphere with inter-class repulsion, and minimize the total electric potential energy as the uniform loss. Extensive experimental results on the MegaFace Challenge I, IARPA Janus Benchmark A (IJB-A), Youtube Faces (YTF) and Labeled Faces in the Wild (LFW) datasets show the effectiveness of the proposed uniform loss. <s> BIB022 </s> Biometric Recognition Using Deep Learning: A Survey <s> Deep Learning Works on Face Recognition <s> Training large-scale unbalanced data is the central topic in face recognition. In the past two years, face recognition has achieved remarkable improvements due to the introduction of margin based Softmax loss. However, these methods have an implicit assumption that all the classes possess sufficient samples to describe its distribution, so that a manually set margin is enough to equally squeeze each intra-class variations. However, real face datasets are highly unbalanced, which means the classes have tremendously different numbers of samples. In this paper, we argue that the margin should be adapted to different classes. We propose the Adaptive Margin Softmax to adjust the margins for different classes adaptively. In addition to the unbalance challenge, face data always consists of large-scale classes and samples. Smartly selecting valuable classes and samples to participate in the training makes the training more effective and efficient. To this end, we also make the sampling process adaptive in two folds: Firstly, we propose the Hard Prototype Mining to adaptively select a small number of hard classes to participate in classification. Secondly, for data sampling, we introduce the Adaptive Data Sampling to find valuable samples for training adaptively. We combine these three parts together as AdaptiveFace. Extensive analysis and experiments on LFW, LFW BLUFR and MegaFace show that our method performs better than state-of-the-art methods using the same network architecture and training dataset. Code is available at https://github.com/haoliu1994/AdaptiveFace. <s> BIB023
There are countless number of works using deep learning for face recognition. In this survey, we provide an overview of some of the most promising works developed for face verification and/or identification. In 2014, Taigman and colleagues proposed one of the earliest deep learning work for face recognition in a paper called DeepFace BIB001 , and achieved the state-of-theart accuracy on the LFW benchmark [85], approaching human performance on the unconstrained condition for the first time ever (DeepFace: 97.35% vs. Human: 97.53%). DeepFace was trained on 4 million facial images. This work was a milestone on face recognition, and after that several researchers started using deep learning for face recognition. In another promising work in the same year, Sun et al. proposed DeepID (Deep hidden IDentity features) BIB002 , for face verification. DeepID features were taken from the last hidden layer of a deep convolutional network, which is trained to recognize about 10,000 face identities in the training set. In a follow up work, Sun et al. extended DeepID for joint face identification and verification called DeepID2 BIB003 . By training the model for joint identification and verification, they showed that the face identification task increases the inter-personal variations by drawing DeepID2 features extracted from different identities apart, while the face verification task reduces the intra-personal variations by pulling DeepID2 features extracted from the same identity together. For identification, cross-entropy is used as the loss function (as defined in the Equation 4), while for verification they proposed to use the loss function of Equation 5 to reduce the intra-class distances on the features and increase the inter-class distances. As an extension of DeepID2, in DeepID3 BIB004 Sun et al proposed a new model which has higher dimensional hidden representation, and deploys VGGNet and GoogleNet as the main architectures. In 2015, FaceNet BIB005 trained a GoogLeNet model on a large private dataset. This work tried to learn a mapping from face images to a compact Euclidean space where distances directly corresponds to a measure of face similarity. It adopted a triplet loss function based on triplets of roughly aligned matching/non-matching face patches generated by a novel online triplet mining method and achieved good performance on LFW dataset (99.63%). Given features for a given sample f (x a i ), a positive sample f (x p i ) (matching x a i ), and a negative sample f (x n i ), the triplet loss for a given margin α is defined as Equation 6 : In the same year, Parkhi et al. proposed a model called VGGface BIB006 (trained on a large-scale dataset collected from the Internet). It trained the VGGNet on this dataset and fine-tuned the networks via a triplet loss function, Similar to FaceNet. VGGface obtained a very high accuracy rate of 98.95%. In 2016, Liu and colleagues developed a "Large-Margin Softmax Loss" for CNNs BIB007 , and showed its promise on multiple computer vision datasets, including LFW. They claimed that, cross-entropy does not explicitly encourage discriminative learning of features, and proposed a generalized large-margin softmax loss, which explicitly encourages intra-class compactness and inter-class separability between learned features. In the same year, Wen et al. proposed a new supervision signal, called "center loss", for face recognition task BIB008 . The center loss simultaneously learns a center for deep features of each class and penalizes the distances between the deep features and their corresponding class centers. With the joint supervision of softmax loss and center loss, they trained a CNN to obtain the deep features with the two key learning objectives, inter-class dispension and intra-class compactness as much as possible. In another work in 2016, Sun et al. proposed a face recognition model using a convolutional network with sparse neural connections BIB009 . This sparse ConvNet is learned in an iterative fashion, where each time one additional layer is sparsified and the entire model is re-trained given the initial weights learned in previous iterations (they found out training the sparse ConvNet from scratch usually fails to find good solutions for face recognition). In 2017, in BIB010 , Zhang and colleagues developed a range loss to reduce the overall intra-personal variations while increasing inter-personal differences simultaneously. In the same year, Ranjan and colleagues de-veloped an "L2-constraint softmax loss function" and used it for face verification BIB011 . This loss function restricts the feature descriptors to lie on a hyper-sphere of a fixed radius. This work achieved state-of-the-art performance on LFW dataset with an accuracy of 99.78% at the time. In BIB012 , Liu and colleagues developed a face recognition model based on the intuition that the cosine distance of face features in high-dimensional space should be close enough within one class and far away across categories. They proposed the congenerous cosine (COCO) algorithm to simultaneously optimize the cosine similarity among data. In the same year, Liu et al. developed SphereFace BIB013 , a deep hypersphere embedding for face recognition. They proposed an angular softmax (A-Softmax) loss function that enables CNNs to learn angular discriminative features. Geometrically, A-Softmax loss can be viewed as imposing discriminative constraints on a hypersphere manifold, which intrinsically matches the prior that faces also lie on a manifold. They showed promising face recognition accuracy on LFW, MegaFace, and Youtube Face databases. In 2018, in BIB015 Wang et al. developed a simple and geometrically interpretable objective function, called additive margin Softmax (AM-Softmax), for deep face verification. This work is heavily inspired by two previous works, Large-margin Softmax BIB007 , and Angular Softmax in BIB013 . CosFace BIB016 and ArcFace BIB019 are two other promising face recognition works developed in 2018. In BIB016 , Wang et al. proposed a novel loss function, namely large margin cosine loss (LM-CL). More specifically, they reformulate the softmax loss as a cosine loss by L2 normalizing both features and weight vectors to remove radial variations, based on which a cosine margin term is introduced to further maximize the decision margin in the angular space. As a result, minimum intra-class variance and maximum inter-class variance are achieved by virtue of normalization and cosine decision margin maximization. Ring-Loss BIB017 is another work focused on designing a new loss function, which applies soft normalization, where it gradually learns to constrain the norm to the scaled unit circle while preserving convexity leading to more robust features. The comparison of learned features by regular softmax and the Ring-loss function is shown in Figure 10 . AdaCos BIB020 , P2SGrad BIB021 , UniformFace BIB022 , and AdaptiveFace BIB023 are among the most promising works proposed in 2019. In AdaCos BIB020 , Zhang et al. proposed a novel cosine-based softmax loss, AdaCos, which is hyperparameter-free and leverages an adaptive scale parameter to automatically strengthen the train- ing supervisions during the training process. In BIB021 , Zhang et al. claimed that cosine based losses always include sensitive hyper-parameters which can make training process unstable, and it is very tricky to set suitable hyperparameters for a specific dataset. They addressed this challenge by directly designing the gradients for training in an adaptive manner. P2SGrad was able to achieves state-of-the-art performance on all three face recognition benchmarks, LFW, MegaFace, and IJB-C. There are several other works proposed for face recognition. For more detailed overview of deep learning-based face recognition, we refer the readers to BIB018 . There have also been several works on using generative models for face image generation. To show the results of one promising model, in Progressive-GAN BIB014 , Karras et al developed a framework to grow both the generator and discriminator of GAN progressively, which can learn to generate high-resolution realistic images. Figure 11 shows 8 sample face images generated by this Progressive-GAN model trained on CELEB-A dataset. . Figure 12 illustrates the timeline of popular face recognition models since 2012. The listed models after 2014 are all deep learning based models. DeepFace and DeepID mark the beginning of deep learning based face recognition. As we can see many of the models after 2017 have focused on developing new loss functions for more discriminative feature learning.