The classification loss functions used in deep neural network classifiers can be grouped into two categories based on maximizing the margin in either Euclidean or angular spaces. Euclidean distances between sample vectors are used during classification for the methods maximizing the margin in Euclidean spaces whereas the Cosine similarity distance is used during the testing stage for the methods maximizing margin in the angular spaces. This paper introduces a novel classification loss that maximizes the margin in both the Euclidean and angular spaces at the same time. This way, the Euclidean and Cosine distances will produce similar and consistent results and complement each other, which will in turn improve the accuracies. The proposed loss function enforces the samples of classes to cluster around the centers that represent them. The centers approximating classes are chosen from the boundary of a hypersphere, and the pairwise distances between class centers are always equivalent. This restriction corresponds to choosing centers from the vertices of a regular simplex. There is not any hyperparameter that must be set by the user in the proposed loss function, therefore the use of the proposed method is extremely easy for classical classification problems. Moreover, since the class samples are compactly clustered around their corresponding means, the proposed classifier is also very suitable for open set recognition problems where test samples can come from the unknown classes that are not seen in the training phase. Experimental studies show that the proposed method achieves the state-of-the-art accuracies on open set recognition despite its simplicity.

Face recognition has made extraordinary progress owing to the advancement of deep convolutional neural networks (CNNs). The central task of face recognition, including face verification and identification, involves face feature discrimination. However, the traditional softmax loss of deep CNNs usually lacks the power of discrimination. To address this problem, recently several loss functions such as center loss, large margin softmax loss, and angular softmax loss have been proposed. All these improved losses share the same idea: maximizing inter-class variance and minimizing intra-class variance. In this paper, we propose 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 a cosine loss by L 2 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. We refer to our model trained with LMCL as CosFace. 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 benchmarks, which confirms the effectiveness of our proposed approach.

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 show the superiority of A-Softmax loss in FR tasks. The code has also been made publicly available 1 .

径向基函数神经网络（RBF）是用于模式分类和回归的主要候选者，并且已在经典的机器学习应用中广泛使用。但是，由于缺乏现代体系结构的适应性，RBF尚未使用常规卷积神经网络（CNN）纳入当代深度学习研究和计算机视觉。在本文中，我们通过修改训练过程并引入新的激活功能来训练现代视觉体系结构端到端以端对端进行图像分类，从而将RBF网络作为分类器将作为分类器。 RBF的特定架构使学习相似性距离度量可以比较和查找相似和不同的图像。此外，我们证明，在任何CNN体系结构上使用RBF分类器都提供了有关模型决策过程的新的人性化洞察力。最后，我们成功地将RBF应用于一系列CNN体系结构，并在基准计算机视觉数据集上评估结果。

在这项工作中，我们提出了一种新的损失，以提高特征可怜和分类性能。通过自适应余弦/相干估计（ACE）的动机，我们的提出方法包括由人工神经网络本质学学习的角度信息。我们的学习ACE（蕾丝）将数据转换为新的“白细胞”空间，可提高级别的间可分离性和级别的紧凑性。我们将我们的蕾丝与基于艺术艺术品的替代最终的和功能正则化方法进行比较。我们的研究结果表明，该方法可以作为交叉熵和角度软墨水方法的可行替代方案。我们的代码是公开的：https://github.com/gatorsense/lace。

基于软马克斯的损失函数及其变体（例如，界面，圆顶和弧形）可显着改善野生无约束场景中的面部识别性能。这些算法的一种常见实践是对嵌入特征和线性转换矩阵之间的乘法进行优化。但是，在大多数情况下，基于传统的设计经验给出了嵌入功能的尺寸，并且在给出固定尺寸时，使用该功能本身提高性能的研究较少。为了应对这一挑战，本文提出了一种称为subface的软关系近似方法，该方法采用了子空间功能来促进面部识别的性能。具体而言，我们在训练过程中动态选择每个批次中的非重叠子空间特征，然后使用子空间特征在基于软磁性的损失之间近似完整功能，因此，深层模型的可区分性可以显着增强，以增强面部识别。在基准数据集上进行的综合实验表明，我们的方法可以显着提高香草CNN基线的性能，这强烈证明了基于利润率的损失的子空间策略的有效性。

Recently, a popular line of research in face recognition is adopting margins in the well-established softmax loss function to maximize class separability. In this paper, we first introduce an Additive Angular Margin Loss (ArcFace), which not only has a clear geometric interpretation but also significantly enhances the discriminative power. Since ArcFace is susceptible to the massive label noise, we further propose sub-center ArcFace, in which each class contains K sub-centers and training samples only need to be close to any of the K positive sub-centers. Sub-center ArcFace encourages one dominant sub-class that contains the majority of clean faces and non-dominant sub-classes that include hard or noisy faces. Based on this self-propelled isolation, we boost the performance through automatically purifying raw web faces under massive real-world noise. Besides discriminative feature embedding, we also explore the inverse problem, mapping feature vectors to face images. Without training any additional generator or discriminator, the pre-trained ArcFace model can generate identity-preserved face images for both subjects inside and outside the training data only by using the network gradient and Batch Normalization (BN) priors. Extensive experiments demonstrate that ArcFace can enhance the discriminative feature embedding as well as strengthen the generative face synthesis.

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax [10] and Angular Softmax [9] have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available 1 .

Recent years witnessed the breakthrough of face recognition with deep convolutional neural networks. Dozens of papers in the field of FR are published every year. Some of them were applied in the industrial community and played an important role in human life such as device unlock, mobile payment, and so on. This paper provides an introduction to face recognition, including its history, pipeline, algorithms based on conventional manually designed features or deep learning, mainstream training, evaluation datasets, and related applications. We have analyzed and compared state-of-the-art works as many as possible, and also carefully designed a set of experiments to find the effect of backbone size and data distribution. This survey is a material of the tutorial named The Practical Face Recognition Technology in the Industrial World in the FG2023.

学习歧视性面部特征在建立高性能面部识别模型方面发挥着重要作用。最近的最先进的面部识别解决方案，提出了一种在常用的分类损失函数，Softmax损失中纳入固定的惩罚率，通过最大限度地减少级别的变化来增加面部识别模型的辨别力并最大化级别的帧间变化。边缘惩罚Softmax损失，如arcFace和Cosface，假设可以使用固定的惩罚余量同样地学习不同身份之间的测地距。然而，这种学习目标对于具有不一致的间帧内变化的真实数据并不是现实的，这可能限制了面部识别模型的判别和概括性。在本文中，我们通过提出弹性罚款损失（弹性面）来放松固定的罚款边缘约束，这允许在推动阶级可分离性中灵活性。主要思想是利用从每个训练迭代中的正常分布中汲取的随机保证金值。这旨在提供决策边界机会，以提取和缩回，以允许灵活的类别可分离学习的空间。我们展示了在大量主流基准上使用相同的几何变换，展示了我们的弹性面损失和COSFace损失的优势。从更广泛的角度来看，我们的弹性面在九个主流基准中提出了最先进的面部识别性能。

机器学习模型通常会遇到与训练分布不同的样本。无法识别分布（OOD）样本，因此将该样本分配给课堂标签会显着损害模​​型的可靠性。由于其对在开放世界中的安全部署模型的重要性，该问题引起了重大关注。由于对所有可能的未知分布进行建模的棘手性，检测OOD样品是具有挑战性的。迄今为止，一些研究领域解决了检测陌生样本的问题，包括异常检测，新颖性检测，一级学习，开放式识别识别和分布外检测。尽管有相似和共同的概念，但分别分布，开放式检测和异常检测已被独立研究。因此，这些研究途径尚未交叉授粉，创造了研究障碍。尽管某些调查打算概述这些方法，但它们似乎仅关注特定领域，而无需检查不同领域之间的关系。这项调查旨在在确定其共同点的同时，对各个领域的众多著名作品进行跨域和全面的审查。研究人员可以从不同领域的研究进展概述中受益，并协同发展未来的方法。此外，据我们所知，虽然进行异常检测或单级学习进行了调查，但没有关于分布外检测的全面或最新的调查，我们的调查可广泛涵盖。最后，有了统一的跨域视角，我们讨论并阐明了未来的研究线，打算将这些领域更加紧密地融为一体。

卷积神经网络（CNNS）在监督环境中的影响提供了巨大的性能。从CNN中学到的表示，在高度球形歧管上运作，导致了面部识别，面部识别和其他受监督任务的富有魅力结果。具有广泛的激活功能，具有间直觉，在欧几里德空间中执行优于Softmax。这项研究的主要动力是提供见解。首先，暗示立体图投影以将数据从欧几里德空间（$ \ mathbb {r} ^ {n} $）转换为高度球形歧管（$ \ mathbb {s} ^ {n} $）来分析角度边缘损失的性能。其次，从理论上证明了使用立体投影在极度上构建的决策边界义务授权了神经网络的学习。实验已经证明，在现有的最先进的角度边缘目标功能上应用立体摄影改善了标准图像分类数据集的性能（CIFAR-10,100）。此外，我们在疟疾薄血涂片图像上运行了我们的实验，导致有效的结果。该代码可公开可用：https：//github.com/barulalithb/stereo -angular-margin。

在本文中，我们提出了一种学习内部特征表示模型的新方法，该模型是\ Textit {兼容}与先前学识的。兼容功能可用于直接比较旧和新的学习功能，允许它们随时间互换使用。这消除了在顺序升级表示模型时，可以对视觉搜索系统提取用于在画廊集中的所有先前看到的图像的新功能。在非常大的画廊集和/或实时系统（即面部识别系统，社交网络，终身系统，终身系统，机器人和监测系统）的情况下，提取新功能通常是非常昂贵或不可行的。我们的方法是通过实质性（核心）称为兼容表示，通过鼓励自身定义到学习的表示模型来实现兼容性，而无需依赖以前学习的模型。实用性允许功能在随时间偏移下不改变的统计属性，以便当前学习的功能与旧版本相互操作。我们评估了种植大规模训练数据集中的单一和连续的多模型升级，我们表明我们的方法通过大幅度实现了实现兼容特征来提高现有技术。特别是，通过从Casia-Webface培训和在野外（LFW）中的标记面上评估的培训数据升级十次，我们获得了49 \％的测量倍数达到兼容的平均次数，这是544 \％对先前最先进的相对改善。

Model bias triggered by long-tailed data has been widely studied. However, measure based on the number of samples cannot explicate three phenomena simultaneously: (1) Given enough data, the classification performance gain is marginal with additional samples. (2) Classification performance decays precipitously as the number of training samples decreases when there is insufficient data. (3) Model trained on sample-balanced datasets still has different biases for different classes. In this work, we define and quantify the semantic scale of classes, which is used to measure the feature diversity of classes. It is exciting to find experimentally that there is a marginal effect of semantic scale, which perfectly describes the first two phenomena. Further, the quantitative measurement of semantic scale imbalance is proposed, which can accurately reflect model bias on multiple datasets, even on sample-balanced data, revealing a novel perspective for the study of class imbalance. Due to the prevalence of semantic scale imbalance, we propose semantic-scale-balanced learning, including a general loss improvement scheme and a dynamic re-weighting training framework that overcomes the challenge of calculating semantic scales in real-time during iterations. Comprehensive experiments show that dynamic semantic-scale-balanced learning consistently enables the model to perform superiorly on large-scale long-tailed and non-long-tailed natural and medical datasets, which is a good starting point for mitigating the prevalent but unnoticed model bias.

模式识别中的一个挑战是开放式识别。与封闭式识别相比，开放式识别不仅需要减少经验风险，也需要降低开放空间风险，并且对这两个风险的减少对应于分别分配已知类别并分别识别未知类。如何降低开放空间风险是开放式识别的关键。本文通过分析已知和未知类功能的分布来探讨开放空间风险的起源。在此基础上，提出了空间位置约束原型丢失功能，以同时减少两个风险。在多个基准数据集和许多可视化结果上的广泛实验表明我们的方法优于最多现有的方法。

开放式识别使深度神经网络（DNN）能够识别未知类别的样本，同时在已知类别的样本上保持高分类精度。基于自动编码器（AE）和原型学习的现有方法在处理这项具有挑战性的任务方面具有巨大的潜力。在这项研究中，我们提出了一种新的方法，称为类别特定的语义重建（CSSR），该方法整合了AE和原型学习的力量。具体而言，CSSR用特定于类的AE表示的歧管替代了原型点。与传统的基于原型的方法不同，CSSR在单个AE歧管上的每个已知类模型，并通过AE的重建误差来测量类归属感。特定于类的AE被插入DNN主链的顶部，并重建DNN而不是原始图像所学的语义表示。通过端到端的学习，DNN和AES互相促进，以学习歧视性和代表性信息。在多个数据集上进行的实验结果表明，所提出的方法在封闭式和开放式识别中都达到了出色的性能，并且非常简单且灵活地将其纳入现有框架中。

在开放式识别（OSR）中，分类器应能够拒绝不知名的样本，同时保持高闭合分类的精度。为了有效解决OSR问题，先前的研究试图通过离线分析（例如，基于距离的特征分析或复杂的网络体系结构）限制有限空间外部的潜在特征空间并拒绝位于有限空间之外的数据。为了通过标准分类器体系结构中的简单推理过程（无脱机分析）进行OSR，我们使用基于距离的分类器代替常规的软具有距离分类器。之后，我们设计了一种背景级正则化策略，该策略在训练阶段使用背景级数据作为不知名级的替代物。具体而言，我们制定了适合基于距离的分类器的新型正则化损失，该损失可为已知类别和强制背景类样品远离有限的空间提供足够大的类别的潜在特征空间。通过我们的广泛实验，我们表明所提出的方法可提供强大的OSR结果，同时保持高闭合分类的精度。

Metric learning aims to learn distances from the data, which enhances the performance of similarity-based algorithms. An author style detection task is a metric learning problem, where learning style features with small intra-class variations and larger inter-class differences is of great importance to achieve better performance. Recently, metric learning based on softmax loss has been used successfully for style detection. While softmax loss can produce separable representations, its discriminative power is relatively poor. In this work, we propose NBC-Softmax, a contrastive loss based clustering technique for softmax loss, which is more intuitive and able to achieve superior performance. Our technique meets the criterion for larger number of samples, thus achieving block contrastiveness, which is proven to outperform pair-wise losses. It uses mini-batch sampling effectively and is scalable. Experiments on 4 darkweb social forums, with NBCSAuthor that uses the proposed NBC-Softmax for author and sybil detection, shows that our negative block contrastive approach constantly outperforms state-of-the-art methods using the same network architecture. Our code is publicly available at : https://github.com/gayanku/NBC-Softmax

本文解决了对象识别的问题，给出了一组图像作为输入（例如，多个相机源和视频帧）。基于卷积神经网络（CNN）的框架不会有效地利用这些集合，处理如观察到的模式，而不是捕获基础特征分布，因为它不考虑集合中的图像的方差。为了解决这个问题，我们提出了基于基于CNNS的CNNS作为分类器的NN层，作为分类器的NN层，可以更有效地处理图像，并且可以以端到端的方式训练。图像集由低维输入子空间表示;并且此输入子空间与参考子空间匹配，通过其规范角度的相似性，可解释和易于计算度量。 G-LMSM的关键思想是参考子空间被学习为基层歧管的点，用黎曼随机梯度下降而优化。这种学习是稳定，高效，理论上的接地。我们展示了我们提出的方法在手工形状识别，面部识别和面部情感识别方面的有效性。

最大化类之间的分离构成了机器学习中众所周知的归纳偏见和许多传统算法的支柱。默认情况下，深网不配备这种电感偏差，因此通过差异优化提出了许多替代解决方案。当前的方法倾向于共同优化分类和分离：将输入与类向量对齐，并角度分离载体。本文提出了一个简单的替代方法：通过在计算SoftMax激活之前添加一个固定的矩阵乘法，将最大分离作为网络中的电感偏差编码。我们方法背后的主要观察结果是，分离不需要优化，可以在训练之前以封闭形式解决并插入网络。我们概述了一种递归方法，以获取由任何数量类别的最大可分离矢量组成的矩阵，可以通过可忽略的工程工作和计算开销添加。尽管它的性质很简单，但这个矩阵乘法提供了真正的影响。我们表明，我们的建议直接提高分类，长尾识别，分布式检测和开放式识别，从CIFAR到Imagenet。我们从经验上发现，最大分离最有效地作为固定偏见。使矩阵可学习不会增加表现。在GitHub上，封闭形式的实现和代码是在GitHub上。