CN112766422B - Privacy protection method based on lightweight face recognition model - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及一种基于轻量级人脸识别模型的隐私保护方法,属于图像处理、隐私安全保护技术领域。The invention relates to a privacy protection method based on a lightweight face recognition model, and belongs to the technical fields of image processing and privacy security protection.
技术背景technical background
科学的飞速发展使得如今的社会产生了翻天覆地的变化。智能手机、云处理器等产品能够满足社会的物质与精神需求是需要依托大量数据分析与处理的,应用该类数据的产品企业却并没有对个人用户信息进行合理的保护与规范。而在这一类数据保护的问题上,亟待解决的就是与人工智能、深度学习等技术相关的部分。深度学习下的隐私保护通常就是针对模型本身或者训练机制来做改变,包括网络结构的设计、训练方法的调整等。The rapid development of science has brought about earth-shaking changes in today's society. Smartphones, cloud processors and other products can meet the material and spiritual needs of the society relying on the analysis and processing of a large amount of data. However, product companies that use such data have not properly protected and regulated personal user information. As for this type of data protection issues, what needs to be solved urgently is the part related to artificial intelligence, deep learning and other technologies. Privacy protection under deep learning usually involves making changes to the model itself or the training mechanism, including the design of the network structure and the adjustment of the training method.
在隐私保护技术的初期阶段,主要是使用较为直接的保护方法,比如加密、遮盖等,即通过遮挡敏感信息实现保护或者通过加密解密等方法防止第三方访问,例如RSA加密技术便可以实现使用固定长度的公钥来进行加密以保护数据。而随着技术的发展,对于大量的图像或者视频数据的需求越来越多,使用简单的加解密方法保护数据复杂度较高,并且在深度学习的算法上较难实现。于是相继出了许多新的算法,差分隐私就是其中之一。该技术最早的提出是用于保护差分攻击的,所谓差分攻击就是攻击者使用有限次的查询以获得数据不公开部分信息的攻击方式,而差分隐私就是在数据集中使用特定的算法来达到增加概率性的目的以保护训练数据。后来随着该算法的完善,其也应用在其他许多隐私保护问题上。In the initial stage of privacy protection technology, relatively direct protection methods are mainly used, such as encryption, masking, etc., that is, to protect sensitive information by blocking it or to prevent third-party access by encryption and decryption, such as RSA encryption technology. length of the public key to encrypt to protect the data. With the development of technology, there is an increasing demand for a large amount of image or video data. Using simple encryption and decryption methods to protect data is more complex and difficult to implement in deep learning algorithms. As a result, many new algorithms have been developed one after another, and differential privacy is one of them. The earliest proposal of this technology is to protect the differential attack. The so-called differential attack is an attack method in which the attacker uses a limited number of queries to obtain the undisclosed part of the data. Differential privacy is to use a specific algorithm in the data set to increase the probability. Sexual purpose to protect the training data. Later, with the improvement of the algorithm, it was also applied to many other privacy protection issues.
在现有的视觉隐私保护技术中,常见的任务便是对人脸的保护与检测,因为在视觉数据这类特殊样本下,人脸具有唯一识别个体的特性,且人脸识别的应用范围最广泛。而深度学习下的人脸识别更是实际应用的重点,主要应用场景是在家庭场景的监控安防或者智能应用系统下的视觉数据保护,因为该数据涉及到每个人、每个家庭的隐私,私密性的需求高,而且各大公司针对智能家居等产品的发展较为重视,智能家居能够广泛应用便需要建立在数据分析的基础之上,所以该类场景下的人脸识别算法研究具有非常大的实际应用价值。In the existing visual privacy protection technology, the common task is to protect and detect human faces, because in special samples such as visual data, human faces have the characteristics of uniquely identifying individuals, and the application range of face recognition is the widest. widely. Face recognition under deep learning is the focus of practical applications. The main application scenarios are the monitoring and security of home scenes or the protection of visual data under intelligent application systems, because the data involves the privacy of everyone and every family. In addition, major companies pay more attention to the development of smart home and other products. The wide application of smart home needs to be based on data analysis. Therefore, the research on face recognition algorithms in this type of scene has a very large potential. practical application value.
发明内容Contents of the invention
传统的人脸识别算法网络具有参数量大、不容易被移植与广泛使用等缺点,且在使用私密数据集训练时存在数据泄漏的风险。本发明针对此问题提出了一种基于人脸识别网络的隐私保护方法,该方法设计的网络模型具有参数量少,易于收敛,运行速度快等优点,改善了网络的移植程度,方便被大规模的使用,且使用差分隐私的训练机制有效的保护了训练数据。The traditional face recognition algorithm network has the disadvantages of a large number of parameters, not easy to be transplanted and widely used, and there is a risk of data leakage when using private data sets for training. Aiming at this problem, the present invention proposes a privacy protection method based on face recognition network. The network model designed by this method has the advantages of less parameters, easy convergence, and fast operation speed, which improves the degree of network transplantation and is convenient for large-scale , and the training mechanism using differential privacy effectively protects the training data.
本发明采用的技术方案是:The technical scheme adopted in the present invention is:
一种基于轻量级人脸识别模型的隐私保护方法,该方法使用部分线性映射的方法减少运算复杂度,使用多层级联的轻量级网络来对人脸数据集进行特征的提取;加入“教师-学生”融合架构,训练多个教师模型并加入拉普拉斯噪声、引入投票机制来得出标注到学生模型的标签,以增加数据的概率性;把新得到的标注好的非隐私数据集放入学生模型进行训练,最后使用得到的学生模型作为最终的网络模型,具体步骤包括:A privacy protection method based on a lightweight face recognition model, which uses a partial linear mapping method to reduce computational complexity, and uses a multi-layer cascaded lightweight network to extract features from a face dataset; add " Teacher-student" fusion architecture, train multiple teacher models and add Laplacian noise, introduce a voting mechanism to obtain the labels marked to the student model, so as to increase the probability of data; the newly obtained marked non-private data set Put in the student model for training, and finally use the obtained student model as the final network model. The specific steps include:
步骤(1):准备用于训练网络的敏感数据集LFW,然后把训练集图片和验证集图片都划分成为n份,把其中的n-1份数据看作敏感数据,另一份作为非敏感数据;Step (1): Prepare the sensitive data set LFW for training the network, then divide the training set pictures and the verification set pictures into n parts, and regard n-1 parts of the data as sensitive data, and the other part as non-sensitive data;
步骤(2):生成n-1个经过改进的轻量级网络,把n-1份敏感数据中的训练集分别放入各个网络中进行训练,训练时轻量级网络分为四个子模块,分别进行特征的提取与融合,每一个子模块把原始的特征分成两部分,一部分使用卷积操作生成关键的特征图,另一部分使用线性变换把生成的特征图进行简单的映射操作,生成其他的辅助特征图,然后把两部分进行融合得到最后的特征;通过整个网络得到输出计算损失函数并进行反向求导,最终得到训练完成的n-1个教师模型;Step (2): Generate n-1 improved lightweight networks, put n-1 training sets in sensitive data into each network for training, and the lightweight network is divided into four sub-modules during training, Feature extraction and fusion are carried out separately. Each sub-module divides the original features into two parts, one part uses convolution operation to generate key feature maps, and the other part uses linear transformation to perform simple mapping operations on the generated feature maps to generate other Auxiliary feature map, and then fuse the two parts to get the final feature; get the output through the entire network to calculate the loss function and perform reverse derivation, and finally get n-1 teacher models that have been trained;
步骤(3):使用划分好的n-1个验证集进行验证,观察教师模型验证集上的准确率是否符合识别要求;Step (3): Use the divided n-1 verification sets for verification, and observe whether the accuracy rate on the verification set of the teacher model meets the recognition requirements;
步骤(4):准备剩下的一份非敏感数据作为所有的n-1个教师模型的输入,将每一个样本依次放入教师模型得到预测结果,通过softmax函数找到投票数量最多的样本类别并加入拉普拉斯噪声,将概率最大的作为每一个样本的数据标签;Step (4): Prepare the remaining non-sensitive data as the input of all n-1 teacher models, put each sample into the teacher model in turn to get the prediction result, find the sample category with the largest number of votes through the softmax function and Add Laplace noise, and use the highest probability as the data label of each sample;
步骤(5):准备得到的非敏感数据和标签作为新的训练数据集,再重新生成步骤(2)中的轻量级网络,将非敏感数据作为该网络的训练集重新训练,提取特征并融合,最终得到学生模型;Step (5): Prepare the obtained non-sensitive data and labels as a new training data set, and then regenerate the lightweight network in step (2), retrain the non-sensitive data as the training set of the network, extract features and Fusion, finally get the student model;
步骤(6):加入人脸检测模型,获取人脸坐标,然后将学生模型投入实际的使用。Step (6): Join the face detection model, obtain the face coordinates, and then put the student model into practical use.
特别地,在步骤(2)中的轻量级网络的卷积操作部分和线性变换部分所占比例如下所示:In particular, the proportion of the convolution operation part and the linear transformation part of the lightweight network in step (2) is as follows:
其中,m为轻量级网络输入的通道数,s为折叠比率,n为输出的通道数,通过折叠比率选择线性组合的占比来控制模型的运算复杂度。Among them, m is the number of channels input by the lightweight network, s is the folding ratio, and n is the number of output channels. The calculation complexity of the model is controlled by selecting the ratio of the linear combination through the folding ratio.
特别地,在步骤(4)中,使用的投票公式如下所示:In particular, in step (4), the voting formula used is as follows:
nj(x)=|{i:i∈[n],fi(x)=j}|n j (x)=|{i:i∈[n],f i (x)=j}|
在公式中,nj代表被划分到j类的概率,该完整公式的含义为教师模型投票最多的样本的类别,接下来再加入拉普拉斯噪声,In the formula, n j represents the probability of being classified into class j. The meaning of the complete formula is the category of the sample with the most votes from the teacher model, and then adding Laplacian noise,
最后完整的投票机制如下所示:The final complete voting mechanism is as follows:
其中,代表加入参数为γ的拉普拉斯噪声后被划分到j类的概率,而完整公式含义为加入拉普拉斯噪声后概率最大时j所对应的类别。in, Represents the probability of being classified into class j after adding Laplacian noise with a parameter of γ, and the meaning of the complete formula is the category corresponding to j when the probability is the largest after adding Laplacian noise.
从上述方案中可以看出,该方法相对于其他隐私保护技术的思路相差较大,并且有以下几点优势。首先,在n-1个教师模型中,数据的选择要使用互斥的数据,使用互斥的数据来保护模型虽然数据的利用率降低,但是更少的使用数据会有效的保护降低被暴露的风险。其次,使用教师模型进行的投票标记预测实际上属于半监督训练模型,这种类型模型保护的实现不是在教师模型的训练阶段,而是在形成非敏感数据集的融合阶段,该阶段使用投票的方式有效的隔离了真实数据与攻击者,使两者相对独立,无法进行隐私攻击。It can be seen from the above scheme that this method is quite different from other privacy protection technologies in terms of ideas, and has the following advantages. First of all, in the n-1 teacher model, the data selection should use mutually exclusive data, and use mutually exclusive data to protect the model. Although the utilization rate of the data is reduced, the less used data will effectively protect and reduce the exposure. risk. Second, the voting mark prediction using the teacher model actually belongs to the semi-supervised training model, and the realization of this type of model protection is not in the training stage of the teacher model, but in the fusion stage of forming a non-sensitive data set, which uses the voting The method effectively isolates the real data and the attacker, making the two relatively independent and unable to conduct privacy attacks.
综上所述,该方法有效得解决了算法运算程度较复杂并且训练数据难以保护的问题,增加了网络的推理速度,减少了模型的参数量,保证了模型的安全性。To sum up, this method effectively solves the problem of complex algorithm calculation and difficult protection of training data, increases the inference speed of the network, reduces the number of parameters of the model, and ensures the security of the model.
附图说明Description of drawings
图1是本发明的方法流程图;Fig. 1 is method flowchart of the present invention;
图2是本发明的轻量级网络结构图;Fig. 2 is a lightweight network structure diagram of the present invention;
图3是本发明的训练机制图。Fig. 3 is a diagram of the training mechanism of the present invention.
具体实施方式Detailed ways
本发明提出一种基于轻量级人脸识别模型的隐私保护方法。在传统的人脸识别模型基础上,加入了轻量级网络模块,以线性映射的方式来代替部分传统卷积网络操作,在减少运算复杂度的同时,保证了对特征的融合,具有减少网络参数量,增加推理阶段的运行速度的优点,使得模型实用性更强。其次在人脸识别模型的算法中应用“教师-学生”融合架构,使用特定的拉普拉斯噪声和投票机制生成非敏感数据的标签。最后,将生成的新数据集作为学生模型的训练集,实现切断测试集和训练集之间的关联的目的。图1中明确表示了本发明所述方法的流程图,具体实施步骤如下:The invention proposes a privacy protection method based on a lightweight face recognition model. On the basis of the traditional face recognition model, a lightweight network module is added to replace part of the traditional convolutional network operations in the form of linear mapping. While reducing the computational complexity, it ensures the fusion of features and reduces the network complexity. The number of parameters increases the running speed of the inference stage, making the model more practical. Secondly, the "teacher-student" fusion architecture is applied in the algorithm of the face recognition model, using specific Laplacian noise and voting mechanism to generate labels for non-sensitive data. Finally, the generated new data set is used as the training set of the student model to achieve the purpose of cutting off the connection between the test set and the training set. The flowchart of the method of the present invention has been clearly shown in Fig. 1, and the specific implementation steps are as follows:
(1)将敏感数据集划分成n份;(1) Divide the sensitive data set into n parts;
(2)分别生成n个神经网络作为教师模型,每个教师模型使用轻量级网络进行卷积和线性变换,在不增加算法复杂度的基础上提取深层次的特征,具体过程如下:(2) Generating n neural networks as teacher models, each teacher model uses a lightweight network for convolution and linear transformation, and extracts deep-level features without increasing the complexity of the algorithm. The specific process is as follows:
如图2所示,对每一个轻量级网络模块,首先使用卷积的操作,将原始的输入通道数进行特征提取,并且转换为m个通道数的特征,然后再将m个通道数的特征进行算法复杂度较低的线性变换,生成m(s-1)个辅助特征图,然后将两部分的特征进行叠加最后得到n个特征结果,即为ms。As shown in Figure 2, for each lightweight network module, the convolution operation is first used to extract features from the original number of input channels and convert them into features of m channels, and then the features of m channels The features are linearly transformed with low algorithm complexity to generate m(s-1) auxiliary feature maps, and then the features of the two parts are superimposed to obtain n feature results, which is ms.
从图2中可以看出,传统的提取特征结构为普通的卷积操作,运算复杂度较高,而且生成的特征图冗余度较高,有许多的重复性。而通过轻量级网络模块,将传统的卷积网络操作先提取较为关键的主要特征,然后将主要特征进行线性变换,这样的替换会使算法复杂度降低。然后再使用这种变换构造出来的轻量级网络搭建网络模型,实现最后的模型结构。模型共分为四个部分,每一个部分使用不同数量的轻量级网络来提取特征,再加以池化、激活函数等操作以进一步的实现降低冗余度并拟合数据分布的目的。It can be seen from Figure 2 that the traditional feature extraction structure is a common convolution operation, which has high computational complexity, and the generated feature maps have high redundancy and many repetitions. Through the lightweight network module, the traditional convolutional network operation first extracts the more critical main features, and then performs linear transformation on the main features. Such a replacement will reduce the complexity of the algorithm. Then use the lightweight network constructed by this transformation to build a network model to realize the final model structure. The model is divided into four parts. Each part uses a different number of lightweight networks to extract features, and then performs operations such as pooling and activation functions to further achieve the purpose of reducing redundancy and fitting data distribution.
(3)在输出特征的阶段使用arcface作为常见的损失函数。该函数是人脸识别常用的损失函数,并且是由softmax函数改进而来。softmax函数具体表达式如下所示:(3) Use arcface as a common loss function in the stage of outputting features. This function is a commonly used loss function for face recognition and is improved from the softmax function. The specific expression of the softmax function is as follows:
首先将该公式中的内积由模表达式表示,其次分别对权重和输入进行L2正则化处理并乘以缩放系数s得到具体的公式如下所示:Firstly, the inner product in the formula is converted from the modulo expression Indicates that, secondly, L2 regularization is performed on the weight and input respectively and multiplied by the scaling factor s to obtain the specific formula as follows:
对于一般的二分类,通常希望因此,可以由内积表达式得到||W1||||x||cosθ1>||W2||||x||cosθ2。所以为了进一步约束函数,引入了常数m作为严格约束得到||W1||||x||cos(θ1+m)>||W2||||x||cos(θ2+m)。最后,通过函数的变换可以得到arcface的表达式如下所示:For general binary classification, it is usually desirable Therefore, ||W 1 ||||x||cosθ 1 >||W 2 ||||x||cosθ 2 can be obtained from the inner product expression. So in order to further constrain the function, a constant m is introduced as a strict constraint to get ||W 1 ||||x||cos(θ 1 +m)>||W 2 ||||x||cos(θ 2 +m ). Finally, through the transformation of the function, the expression of arcface can be obtained as follows:
(4)通过输出的结果加上损失函数进行反向传递,多次迭代训练m个网络,生成最后的教师模型;(4) Through the output result plus the loss function for reverse transmission, multiple iterations to train m networks, and generate the final teacher model;
(5)使用基于差分隐私的算法来对网络模型进行训练,对非敏感数据集进行样本的标签标注,使用教师模型进行的投票标记预测实际上属于半监督的训练模型,这种类型的模型保护实现不是在教师模型的训练阶段,而是在形成非敏感数据集的融合阶段,该阶段使用投票的方式有效的隔离了真实数据与攻击者,使两者相对独立,无法进行隐私攻击。具体的投票方式如下所示:(5) Use a differential privacy-based algorithm to train the network model, label the samples of the non-sensitive data set, and use the teacher model to predict the voting mark. In fact, it belongs to the semi-supervised training model. This type of model protection The implementation is not in the training stage of the teacher model, but in the fusion stage of forming a non-sensitive data set. In this stage, the voting method is used to effectively isolate the real data and the attacker, making the two relatively independent and unable to conduct privacy attacks. The specific voting method is as follows:
nj(x)=|{i:i∈[n],fi(x)=j}|n j (x)=|{i:i∈[n],f i (x)=j}|
在公式中nj(x)代表输入被划分到第j类的概率,n代表总共的教师模型,fi(x)为第i个教师模型作出的预测。接下来再加入拉普拉斯噪声。In the formula, n j (x) represents the probability that the input is classified into the j-th class, n represents the total teacher models, and f i (x) is the prediction made by the i-th teacher model. Then add Laplace noise.
因此,通过加入噪声得到最后完整的投票机制如下所示:Therefore, the final complete voting mechanism obtained by adding noise is as follows:
f(x)的公式含义为票数最多的标签所占类别,其通过加入拉普拉斯噪声或者高斯噪声等增加干扰,以便提高安全性。The meaning of the formula of f(x) is the category of the label with the most votes, which increases interference by adding Laplacian noise or Gaussian noise to improve security.
(6)使用得到的完整非敏感数据集进行训练,多次迭代得到最后的学生模型;(6) Use the obtained complete non-sensitive data set for training, and obtain the final student model through multiple iterations;
(7)在投入实际的家庭场景应用时,无论是学生模型还是教师模型,都是已经检测或者切割完成的人脸,而网络实际应用学生模型时,因为是完整的自然图像,所以还需要进行人脸检测。通过检测得到准确的人脸坐标才能够进行识别。在人脸检测部分,本方法的设计分为四个阶段,分别是图像的尺寸调整阶段,人脸检测候选框生成阶段,候选框过滤选择阶段,和最终边界确定阶段。(7) When put into the actual family scene application, whether it is a student model or a teacher model, it is a face that has been detected or cut, and when the network actually applies the student model, because it is a complete natural image, it needs to be processed. Face Detection. Accurate face coordinates can only be recognized through detection. In the face detection part, the design of this method is divided into four stages, which are the image size adjustment stage, the face detection candidate frame generation stage, the candidate frame filter selection stage, and the final boundary determination stage.
首先,在图像的尺寸调整阶段,网络通过设定最小的人脸尺寸、最小的检测尺寸和放大因子等因素,将一幅图像缩小和剪裁为不同的检测基准框,便于针对不同的人脸大小进行合理的检测。First, in the image size adjustment stage, the network reduces and crops an image into different detection reference frames by setting the minimum face size, the minimum detection size, and the magnification factor, which is convenient for different face sizes. Do reasonable testing.
其次,将已经选好的不同尺寸的图像放入检测框生成网络。经过几层卷积操作提取特征后生成判断人脸分支、面部关键点定位分支和边界框回归分支。该网络输出的数据作为面部检测框的初步选定。Second, put the selected images of different sizes into the detection frame generation network. After several layers of convolution operations to extract features, the face judgment branch, facial key point location branch and bounding box regression branch are generated. The data output by the network is used as the initial selection of the face detection frame.
然后,将检测框生成网络输出的结果进一步通过一个复杂的网络,在该网络中对候选框进行细致的筛选,过滤掉效果差的预测框后,对留下的预测候选框做边界回归和去重操作,以此输入得到的候选框结果效果更好并且能够保留更多的特征。Then, the output result of the detection frame generation network is further passed through a complex network, and the candidate frames are carefully screened in the network. After filtering out the poorly effective prediction frames, boundary regression and removal are performed on the remaining prediction candidate frames. Re-operation, the candidate box obtained by this input is better and can retain more features.
最后,通过边界框确定网络结构。该网络结构更为复杂,其目的是使较多的监督来对面部特征点进行更好地回归。在保留较多的特征的基础上,能够确定检测框的坐标和面部关键点等信息。Finally, the network structure is determined by bounding boxes. The network structure is more complex, and its purpose is to enable more supervision to perform better regression on facial feature points. On the basis of retaining more features, information such as the coordinates of the detection frame and facial key points can be determined.
这样,通过三个不同功能的网络结构分开进行边界回归、特征点定位等操作得到了准确的人脸检测坐标。In this way, accurate face detection coordinates are obtained by performing operations such as boundary regression and feature point positioning separately through three network structures with different functions.
(8)通过人脸的检测得到坐标后,使用学生模型的轻量级网络再进行人脸识别,便能够实现在准确率不变的基础上,保证了数据隐私的安全性。(8) After the coordinates are obtained through the detection of the face, the lightweight network of the student model is used to perform face recognition, which can ensure the security of data privacy without changing the accuracy rate.
本申请使用的训练数据集是CASIA-WebFace,该数据集共有10575个主题和494414张图片,是目前业界较大的人脸识别数据集。在测试集LFW中,数据提供者已经给出了匹配人脸对的样本与标签,所以可以直接测试准确率。在实验训练中,将训练数据集划分为n=4,6,8,10....多个模型的数据。选取其中的一份数据看作非敏感数据,即作为测试集。通过在教师模型中的投票机制来获取该类数据的标签,以便作为学生模型进行学习。同样在LFW的测试集中也将数据进行对应的划分。而在隐私噪声参数ε的选取上,方法使用的参数包括0.6,2.04,5.04,8.03等。隐私成本代表加入噪声后对原始数据训练的影响的大小,所以ε的选择越大,对数据的保护性便越好,同样也使数据的可用性也就越差。而在参数δ的选取上,使用的是10-5。表1从参数量和速度两个方面对人脸识别模型算法进行比较,本申请在识别率几乎没有变化的情况下,参数量和速度大大降低。表2从不同教师模型的个数和噪声参数大小的角度来分析衡量识别率。发现当数据量达到一定要求时,随着教师模型的数量增加,噪声的影响逐渐减小。The training data set used in this application is CASIA-WebFace, which has 10,575 subjects and 494,414 pictures in total, and is currently the largest face recognition data set in the industry. In the test set LFW, the data provider has given samples and labels of matching face pairs, so the accuracy can be tested directly. In the experimental training, the training data set is divided into n=4, 6, 8, 10... data of multiple models. One of the data is selected as non-sensitive data, that is, as a test set. The label of this type of data is obtained through the voting mechanism in the teacher model, so as to learn as a student model. Also in the test set of LFW, the data is also divided correspondingly. In the selection of the privacy noise parameter ε, the parameters used in the method include 0.6, 2.04, 5.04, 8.03, etc. The privacy cost represents the impact of adding noise on the original data training, so the larger the choice of ε, the better the protection of the data, but also the worse the availability of the data. In the selection of the parameter δ, 10 -5 is used. Table 1 compares face recognition model algorithms from two aspects of parameter quantity and speed. In this application, the parameter quantity and speed are greatly reduced when the recognition rate hardly changes. Table 2 analyzes and measures the recognition rate from the perspective of the number of different teacher models and the size of noise parameters. It is found that when the amount of data reaches a certain requirement, as the number of teacher models increases, the influence of noise gradually decreases.
表1Table 1
表2Table 2
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