summaries: The paper's motivation is based on protecting private data and preventing its being scraped and used to train models. Even though motivation is clear and very important, the problem is the same as the works in crafting adversarial samples (i.e., the ones under data poisoning and adversarial attacks parts of the related work). The key difference is to apply Projected Gradient Descent (Mandry et al. 2018) in the reverse direction iteratively to *minimize* the loss function.  Furthermore, the performance evaluation will be the margin between models trained on completely clean data and sample-wise/class-wise adversarially corrupted data (in contrast to fooling a pretrained network in adversarial attack benchmarks).  The authors proposed the idea of using invisible noise to make personal data unusable to authorized deep learning models. To achieve this goal, the authors proposed the idea of error-minimizing noise crafted by a min-min optimization method. The error-minimizing noise is then added to training examples to make them unlearnable to deep learning models. The idea is very well motivated and explained. The experiments not only confirm the exceptional effectiveness of the proposed method but also show its flexibility. The authors studied the problem of data protection from a new perspective. They proposed one kind of error-minimizing noise to make the data (added noise) unlearnable. The noise is imperceptible to human eyes, and thus does not affect normal data utility. The idea is very interesting and inspiring. The authors conducted a series of solid experiments to validate the effectiveness of the proposed noise, and tested it on a real world task of face recognition. 
abstractText: The volume of “free” data on the internet has been key to the current success of deep learning. However, it also raises privacy concerns about the unauthorized exploitation of personal data for training commercial models. It is thus crucial to develop methods to prevent unauthorized data exploitation. This paper raises the question: can data be made unlearnable for deep learning models? We present a type of error-minimizing noise that can indeed make training examples unlearnable. Error-minimizing noise is intentionally generated to reduce the error of one or more of the training example(s) close to zero, which can trick the model into believing there is “nothing” to learn from these example(s). The noise is restricted to be imperceptible to human eyes, and thus does not affect normal data utility. We empirically verify the effectiveness of error-minimizing noise in both sample-wise and class-wise forms. We also demonstrate its flexibility under extensive experimental settings and practicability in a case study of face recognition. Our work establishes an important first step towards making personal data unexploitable to deep learning models. Code is available at https://github.com/HanxunH/Unlearnable-Examples.
authors.name: Hanxun Huang
authors.name: Xingjun Ma
authors.name: Sarah Monazam Erfani
authors.name: James Bailey
authors.name: Yisen Wang
references.authors: Martin Abadi Andy Chu Ian Goodfellow H Brendan McMahan Ilya Mironov Kunal Talwar Li Zhang
references.title: Deep learning with differential privacy
references.venue: SIGSAC,
references.authors: Yang Bai Yuyuan Zeng Yong Jiang Yisen Wang Shu-Tao Xia Weiwei Guo
references.title: Improving query efficiency of black-box adversarial attack
references.venue: In ECCV,
references.authors: Mauro Barni Kassem Kallas Benedetta Tondi
references.title: A new backdoor attack in cnns by training set corruption without label poisoning
references.venue: In ICIP
references.authors: Battista Biggio Blaine Nelson Pavel Laskov
references.title: Poisoning attacks against support vector machines
references.venue: arXiv preprint arXiv:1206.6389,
references.authors: Nicholas Carlini David Wagner
references.title: Towards evaluating the robustness of neural networks
references.venue: In SP,
references.authors: Xinyun Chen Chang Liu Bo Li Kimberly Lu Dawn Song
references.title: Targeted backdoor attacks on deep learning systems using data poisoning
references.venue: arXiv preprint arXiv:1712.05526,
references.authors: Francesco Croce Matthias Hein
references.title: Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks
references.venue: In ICML,
references.authors: Jiankang Deng Jia Guo Niannan Xue Stefanos Zafeiriou
references.title: Arcface: Additive angular margin loss for deep face recognition
references.authors: Jacob Devlin Ming-Wei Chang Kenton Lee Kristina Toutanova. Bert
references.title: Pre-training of deep bidirectional transformers for language understanding
references.venue: arXiv preprint arXiv:1810.04805,
references.authors: Terrance DeVries Graham W Taylor
references.title: Improved regularization of convolutional neural networks with cutout
references.venue: arXiv preprint arXiv:1708.04552,
references.authors: Ranjie Duan Xingjun Ma Yisen Wang James Bailey A Kai Qin Yun Yang
references.title: Adversarial camouflage: Hiding physical-world attacks with natural styles
references.authors: Alhussein Fawzi Seyed-Mohsen Moosavi-Dezfooli Pascal Frossard
references.title: Robustness of classifiers: from adversarial to random noise
references.venue: In NeurIPS,
references.authors: Ian J Goodfellow Jonathon Shlens Christian Szegedy
references.title: Explaining and harnessing adversarial examples
references.venue: arXiv preprint arXiv:1412.6572,
references.authors: Kaiming He Xiangyu Zhang Shaoqing Ren Jian Sun
references.title: Deep residual learning for image recognition
references.authors: Kashmir Hill
references.title: The secretive company that might end privacy as we know it, 2020
references.authors: Gao Huang Zhuang Liu Laurens Van Der Maaten Kilian Q Weinberger
references.title: Densely connected convolutional networks
references.authors: Gary B Huang Marwan Mattar Tamara Berg Eric Learned-Miller
references.title: Labeled faces in the wild: A database forstudying face recognition in unconstrained environments
references.authors: Andrew Ilyas Shibani Santurkar Dimitris Tsipras Logan Engstrom Brandon Tran Aleksander Madry
references.title: Adversarial examples are not bugs, they are features
references.venue: NeurIPS,
references.authors: Linxi Jiang Xingjun Ma Shaoxiang Chen James Bailey Yu-Gang Jiang
references.title: Black-box adversarial attacks on video recognition models
references.venue: In ACMMM,
references.authors: Diederik P Kingma Jimmy Ba
references.title: Adam: A method for stochastic optimization
references.venue: In ICLR,
references.authors: Pang Wei Koh Percy Liang
references.title: Understanding black-box predictions via influence functions
references.venue: In ICML,
references.authors: Alex Krizhevsky
references.title: Learning multiple layers of features from tiny images
references.authors: Alexey Kurakin Ian Goodfellow Samy Bengio
references.title: Adversarial examples in the physical world
references.venue: arXiv preprint arXiv:1607.02533,
references.authors: Yann LeCun Léon Bottou Yoshua Bengio Patrick Haffner
references.title: Gradient-based learning applied to document recognition
references.venue: Proceedings of the IEEE,
references.authors: Yunfei Liu Xingjun Ma James Bailey Feng Lu
references.title: Reflection backdoor: A natural backdoor attack on deep neural networks
references.venue: In ECCV,
references.authors: Ziwei Liu Ping Luo Xiaogang Wang Xiaoou Tang
references.title: Deep learning face attributes in the wild
references.venue: In ICCV,
references.authors: Ilya Loshchilov Frank Hutter
references.title: SGDR: stochastic gradient descent with warm restarts
references.venue: In ICLR,
references.authors: Xingjun Ma Bo Li Yisen Wang Sarah M Erfani Sudanthi Wijewickrema Grant Schoenebeck Dawn Song Michael E Houle James Bailey
references.title: Characterizing adversarial subspaces using local intrinsic dimensionality
references.venue: In ICLR,
references.authors: Xingjun Ma Yuhao Niu Lin Gu Yisen Wang Yitian Zhao James Bailey Feng Lu
references.title: Understanding adversarial attacks on deep learning based medical image analysis systems
references.venue: Pattern Recognition,
references.authors: Aleksander Madry Aleksandar Makelov Ludwig Schmidt Dimitris Tsipras Adrian Vladu
references.title: Towards deep learning models resistant to adversarial attacks
references.venue: In ICLR,
references.authors: Seyed-Mohsen Moosavi-Dezfooli Alhussein Fawzi Omar Fawzi Pascal Frossard
references.title: Universal adversarial perturbations
references.venue: In CVPR,
references.authors: Luis Muñoz-González Battista Biggio Ambra Demontis Andrea Paudice Vasin Wongrassamee Emil C Lupu Fabio Roli
references.title: Towards poisoning of deep learning algorithms with back-gradient optimization
references.venue: AISec,
references.authors: Yuval Netzer Tao Wang Adam Coates Alessandro Bissacco Bo Wu Andrew Y Ng
references.title: Reading digits in natural images with unsupervised feature learning
references.authors: NhatHai Phan Yue Wang Xintao Wu Dejing Dou
references.title: Differential privacy preservation for deep auto-encoders: an application of human behavior prediction
references.venue: In AAAI,
references.authors: NhatHai Phan Xintao Wu Han Hu Dejing Dou
references.title: Adaptive laplace mechanism: Differential privacy preservation in deep learning
references.venue: In ICDM,
references.authors: Vinay Uday Prabhu Abeba Birhane
references.title: Large image datasets: A pyrrhic win for computer vision
references.venue: arXiv preprint arXiv:2006.16923,
references.authors: Olga Russakovsky Jia Deng Hao Su Jonathan Krause Sanjeev Satheesh Sean Ma Zhiheng Huang Andrej Karpathy Aditya Khosla Michael Bernstein Alexander C. Berg Li Fei-Fei
references.title: ImageNet Large Scale Visual Recognition Challenge
references.venue: International Journal of Computer Vision,
references.authors: Ali Shafahi W Ronny Huang Mahyar Najibi Octavian Suciu Christoph Studer Tudor Dumitras Tom Goldstein
references.title: Poison frogs! targeted clean-label poisoning attacks on neural networks
references.venue: NeurIPS,
references.authors: Shawn Shan Emily Wenger Jiayun Zhang Huiying Li Haitao Zheng Ben Y Zhao
references.title: Fawkes: Protecting personal privacy against unauthorized deep learning models
references.venue: USENIX-Security,
references.authors: Reza Shokri Vitaly Shmatikov
references.title: Privacy-preserving deep learning
references.venue: In SIGSAC,
references.authors: Reza Shokri Marco Stronati Congzheng Song Vitaly Shmatikov
references.title: Membership inference attacks against machine learning models
references.venue: In SP,
references.authors: Karen Simonyan Andrew Zisserman
references.title: Very deep convolutional networks for large-scale image recognition
references.venue: arXiv preprint arXiv:1409.1556,
references.authors: Christian Szegedy Wojciech Zaremba Ilya Sutskever Joan Bruna Dumitru Erhan Ian Goodfellow Rob Fergus
references.title: Intriguing properties of neural networks
references.venue: arXiv preprint arXiv:1312.6199,
references.authors: Christian Szegedy Sergey Ioffe Vincent Vanhoucke Alex Alemi
references.title: Inception-v4, inception-resnet and the impact of residual connections on learning
references.venue: arXiv preprint arXiv:1602.07261,
references.authors: Yaniv Taigman Ming Yang Marc’Aurelio Ranzato Lior Wolf
references.title: Deepface: Closing the gap to human-level performance in face verification
references.venue: In CVPR,
references.authors: Haohan Wang Xindi Wu Zeyi Huang Eric P Xing
references.title: High-frequency component helps explain the generalization of convolutional neural networks
references.venue: In CVPR,
references.authors: Xin Wang Jie Ren Shuyun Lin Xiangming Zhu Yisen Wang Quanshi Zhang
references.title: A unified approach to interpreting and boosting adversarial transferability
references.venue: arXiv preprint arXiv:2010.04055,
references.authors: Yisen Wang Xingjun Ma James Bailey Jinfeng Yi Bowen Zhou Quanquan Gu
references.title: On the convergence and robustness of adversarial training
references.authors: Yisen Wang Difan Zou Jinfeng Yi James Bailey Xingjun Ma Quanquan Gu
references.title: Improving adversarial robustness requires revisiting misclassified examples
references.venue: In ICLR,
references.authors: Dongxian Wu Yisen Wang Shu-Tao Xia James Bailey Xingjun Ma
references.title: Skip connections matter: On the transferability of adversarial examples generated with resnets
references.venue: In ICLR,
references.authors: Dongxian Wu Shu-Tao Xia Yisen Wang
references.title: Adversarial weight perturbation helps robust generalization
references.venue: NeurIPS,
references.authors: Chaofei Yang Qing Wu Hai Li Yiran Chen
references.title: Generative poisoning attack method against neural networks
references.venue: arXiv preprint arXiv:1703.01340,
references.authors: Dong Yi Zhen Lei Shengcai Liao Stan Z Li
references.title: Learning face representation from scratch
references.venue: arXiv preprint arXiv:1411.7923,
references.authors: Sangdoo Yun Dongyoon Han Seong Joon Oh Sanghyuk Chun Junsuk Choe Youngjoon Yoo
references.title: Cutmix: Regularization strategy to train strong classifiers with localizable features
references.authors: Hongyang Zhang Yaodong Yu Jiantao Jiao Eric Xing Laurent El Ghaoui Michael Jordan
references.title: Theoretically principled trade-off between robustness and accuracy
references.authors: Hongyi Zhang Moustapha Cisse Yann N Dauphin David Lopez-Paz
references.title: mixup: Beyond empirical risk minimization
references.venue: In ICLR,
references.authors: Sheng Zhang Xiaodong Liu Jingjing Liu Jianfeng Gao Kevin Duh Benjamin Van Durme
references.title: Record: Bridging the gap between human and machine commonsense reading comprehension
references.venue: arXiv preprint arXiv:1810.12885,
references.authors: Shihao Zhao Xingjun Ma Xiang Zheng James Bailey Jingjing Chen Yu-Gang Jiang
references.title: Cleanlabel backdoor attacks on video recognition models
references.authors: Dc → Du
references.title: The stop condition error rate is λ = 0.1 for ∆c and λ = 0.01 for ∆s. For SVHN and CIFAR-10, we set the M = 10 for CIFAR-10, M = 20 for CIFAR-100 and M = 100 for ImageNet in the mini-setting. For all models and experiments, we use the Stochastic Gradient Descent (SGD) (LeCun et al., 1998) optimizer with momentum 0.9, initial learning rate 0.025 and cosine scheduler (Loshchilov
references.authors: Zhao
references.title: 2020). I DIFFERENT GENERALIZATION METHODS FOR ERROR-MINIMIZATION NOISE The proposed error-minimizing noise is generated using PGD. Specifically, PGD is applied to solve the inner minimization problem in Equation 2. Since it is a typical constrained optimization problem, it can also be solved by other optimization (attack) methods such as FGSM
references.venue: (Goodfellow et al.,
references.authors: L-BFGS (Szegedy et al W (Carlini Wagner
references.title: 2017). However, the objective needs to be reformulated to apply some of these attacks. Here, we take L-BFGS (Szegedy et al., 2013) as an example to reformulate and solve the inner minimization problem in Equation 2
references.venue: In (Szegedy et al.,
references.authors: Adam (Kingma Ba
references.title: 2015) optimizer and generate sample-wise noise ∆s on CIFAR-10. The number of optimization steps for Equation 5 is set to T = 200, while the number of optimization
sections.heading: 1 INTRODUCTION
sections.text: In recent years, deep learning has had groundbreaking successes in several fields, such as computer vision (He et al., 2016) and natural language processing (Devlin et al., 2018). This is partly attributed to the availability of large-scale datasets crawled freely from the Internet such as ImageNet (Russakovsky et al., 2015) and ReCoRD (Zhang et al., 2018b). Whilst these datasets provide a playground for developing deep learning models, a concerning fact is that some datasets were collected without mutual consent (Prabhu & Birhane, 2020). Personal data has also been unconsciously collected from the Internet and used for training commercial models (Hill, 2020). This has raised public concerns about the “free” exploration of personal data for unauthorized or even illegal purposes.
  In this paper, we address this concern by introducing unlearnable examples, which aims at making training examples unusable for Deep Neural Networks (DNNs). In other words, DNNs trained on unlearnable examples will have a performance equivalent to random guessing on normal test examples. Compared with preserving an individual’s privacy by obfuscating information from the dataset, what we aim to achieve here is different but more challenging. First, making an example unlearnable should not affect its quality for normal usage. For instance, an unlearnable “selfie” photo should be free from obvious visual defects so it can be used as a social profile picture. Ideally, this can be achieved by using imperceptible noise. In our setting, the noise can only be added to training examples on a single occasion (when the data is uploaded to the internet) prior to model training. However, DNNs are known to be robust to small noise either random (Fawzi et al., 2016) or adversarial (Szegedy et al., 2013; Goodfellow et al., 2014; Ma et al., 2018). It is still not clear whether small, imperceptible noise can stop the training of high-performance DNNs.
  The development of unlearnable examples should take full advantage of the unique characteristics, and more importantly, the weaknesses of DNNs. One well-studied characteristic of DNNs is that they tend to capture more of the high-frequency components of the data (Wang et al., 2020a). Surprisingly, by exploiting this characteristic, we find that small random noise when applied in a class-wise †Correspondence to: Xingjun Ma (daniel.ma@deakin.edu.au), Yisen Wang (yisen.wang@pku.edu.cn)
  manner to the training data can easily fool DNNs to overfit to such noise (shown in Section 4). However, early stopping can effectively counteract this type of noise. DNNs are also known to be vulnerable to adversarial (or error-maximizing) noise, which are small perturbations crafted to maximize the model’s error at the test time (Szegedy et al., 2013; Goodfellow et al., 2014). We find that error-maximizing noise cannot stop DNN learning when applied in a sample-wise manner to the training examples. This motivates us to explore the opposite direction to error-maximizing noise. Specifically, we propose a type of error-minimizing noise that can prevent the model from being penalized by the objective function during training, and thus can trick the model into believing there is “nothing” to learn from the example(s). We refer to an example that contains the errorminimizing noise as an unlearnable example. Error-minimizing noise can be generated in different forms: sample-wise and class-wise. Class-wise error-minimizing noise is superior to random noise and cannot be circumvented by early stopping. Sample-wise error-minimizing noise is the only effective noise that can make training examples unlearnable compared to random (Fawzi et al., 2016) or error-maximizing noise (Muñoz-González et al., 2017). Our main contributions are:
  • We present a type of error-minimizing noise that can create unlearnable examples to prevent personal data from being freely exploited by deep learning models. The noise is small, imperceptible to human eyes, thus it does not reduce general data utility. • We propose a bi-level optimization process to effectively generate different forms of error-
  minimizing noise: sample-wise and class-wise. • We empirically verify the effectiveness and flexibility of error-minimizing noise for cre-
  ating unlearnable examples. We also demonstrate the practical application of unlearnable examples in real-world scenarios via a case study on face recognition.
sections.heading: 2 RELATED WORK
sections.text: In this section, we briefly review most relevant works in data privacy, data poisoning, adversarial attacks against deep learning models.
  Data Privacy. Privacy issues have been extensively studied in the field of privacy-preserving machine learning (Shokri & Shmatikov, 2015; Abadi et al., 2016; Phan et al., 2016; 2017; Shokri et al., 2017). While these works have made significant progress towards protecting data privacy, they are developed based on the assumption that the model can freely explore the training data and turn to protect the model from leaking sensitive information about the training data. In this paper, we consider a more challenging scenario where the goal of the defender is to make personal data completely unusable by unauthorized deep learning models. Fawkes (Shan et al., 2020) has made the first attempt towards this type of strict situation. By leveraging the targeted adversarial attack, Fawkes prevents unauthorized face tracker from tracking a person’s identity. This work is similar to ours as we share a common objective that prevents unauthorized data usage. In contrast to the targeted adversarial attack, we propose a novel error-minimizing noise to produce unlearnable examples which can be used as a generic framework for a wide range of data protection tasks.
  Data Poisoning. Data poisoning attacks aim to degrade the model’s performance on clean examples by modifying the training examples. Previous work has demonstrated a poisoning attack on SVM (Biggio et al., 2012). Koh & Liang (2017) proposed to poison the most influential training examples using adversarial (error-maximizing) noise against DNNs, which has also been integrated into an endto-end framework (Muñoz-González et al., 2017). Although data poisoning attacks can potentially prevent free data exploitation, these approaches are quite limited against DNNs and hard to operate in real-world scenarios. For example, poisoned examples can only slightly decrease DNNs’ performance (Muñoz-González et al., 2017), and often appear distinguishable to clean examples (Yang et al., 2017) which will reduce normal data utility. The backdoor attack is another type of attack that poisons training data with a stealthy trigger pattern (Chen et al., 2017; Liu et al., 2020). However, the backdoor attack does not harm the model’s performance on clean data (Chen et al., 2017; Shafahi et al., 2018; Barni et al., 2019; Liu et al., 2020; Zhao et al., 2020). Thus, it is not a valid method for data protection. Different from these works, we generate unlearnable examples with invisible noise to “bypass” the training of DNNs.
  Adversarial Attack. It has been found that adversarial examples (or attacks) can fool DNNs at the test time (Szegedy et al., 2013; Goodfellow et al., 2014; Kurakin et al., 2016; Carlini & Wagner, 2017; Madry et al., 2018; Jiang et al., 2019; Wu et al., 2020a; Bai et al., 2020; Croce & Hein, 2020; Wang
  et al., 2020b; Duan et al., 2020; Ma et al., 2020). The adversary finds an error-maximizing noise that maximizes the model’s prediction error, and the noise can be crafted universally for the entire test set (Moosavi-Dezfooli et al., 2017). Adversarial training has been shown to be the most robust training strategy against error-maximizing noise (Madry et al., 2018; Zhang et al., 2019; Wang et al., 2019; Wu et al., 2020b; Wang et al., 2020c). Adversarial training can be formulated as a min-max optimization problem. In this paper, we explore the opposite direction of error-maximizing noise, i.e., finding small noise that minimizes the model’s error via a min-min optimization process.
sections.heading: 3 UNLEARNABLE EXAMPLES AND ERROR-MINIMIZING NOISE
sections.heading: 3.1 PROBLEM STATEMENT
sections.text: Assumptions on Defender’s Capability. We assume the defender has full access to the portion of data which they want to make unlearnable. However, the defender cannot interfere with the training process and does not have access to the full training dataset. In other words, the defender can only transform their portion of data into unlearnable examples. Moreover, the defender cannot further modify their data once the unlearnable examples are created.
  Objectives. We formulate the problem in the context of image classification with DNNs. Given a typical K-class classification task, we denote the clean training and test datasets as Dc and Dt respectively, and the classification DNN trained on Dc as fθ where θ are the parameters of the network∗. Our goal is to transform the training data Dc into unlearnable dataset Du such that DNNs trained on the Du will perform poorly on the test set Dt. Suppose the clean training dataset consists of n clean examples, that is, Dc = {(xi, yi)}ni=1 with x ∈ X ⊂ Rd are the inputs and y ∈ Y = {1, · · · ,K} are the labels and K is the total number of classes. We denote its unlearnable version by Du = {(x′i, yi)}ni=1, where x′ = x + δ is the unlearnable version of training example x ∈ Dc and δ ∈ ∆ ⊂ Rd is the “invisible” noise that makes x unlearnable. The noise δ is bounded by ‖δ‖p ≤ with ‖ · ‖p is the Lp norm, and is set to be small such that it does not affect the normal utility of the example.
  In the typical case, the DNN model will be trained onDc to learn the mapping from the input space to the label space: f : X → Y . Our goal is to trick the model into learning a strong correlation between the noise and the labels: f : ∆→ Y,∆ 6= X , when trained on Du:
  arg min θ
  E(x′,y)∼DuL(f(x ′), y) (1)
  where, L is the classification loss such as the commonly used cross entropy loss. Noise Form. We propose two forms of noise: sample-wise and class-wise. For sample-wise noise, x′i = xi + δi, δi ∈ ∆s = {δ1, · · · , δn}, while for class-wise noise, x′i = xi + δyi , δyi ∈ ∆c = {δ1, · · · , δK}. Sample-wise noise needs to generate noise separately for each example. This may have more limited practicality. In contrast to sample-wise noise, a class of examples can be made unlearnable by the addition of class-wise noise, where all examples in the same class have the same noise added. As such, class-wise noise can be generated more efficiently and more flexibly in practical usage. However, we will see that class-wise noise may get more easily exposed.
sections.heading: 3.2 GENERATING ERROR-MINIMIZING NOISE
sections.text: Ideally, the noise should be generated on an additional dataset that is different from Dc. This will involve a class-matching process to find the most appropriate class from the additional dataset for each class to protect in Dc. For simplicity, here we define the noise generation process on Dc and will verify the effectiveness of using an additional dataset in the experiments. Given a clean example x, we propose to generate the error-minimizing noise δ for training input x by solving the following bi-level optimization problem:
  arg min θ E(x,y)∼Dc [ min δ L(f ′(x+ δ), y) ] s.t. ‖δ‖p ≤ (2)
  where, f ′ denotes the source model used for noise generation. Note that this is a min-min bi-level optimization problem: the inner minimization is a constrained optimization problem that finds the ∗We omit the θ notation from fθ without ambiguity in the rest of this paper.
  Lp-norm bounded noise δ that minimizes the model’s classification loss, while the outer minimization problem finds the parameters θ that also minimize the model’s classification loss.
  Note that the above bi-level optimization has two components that optimize the same objective. In order to find effective noise δ and unlearnable examples, the optimization steps for θ should be limited, compared to standard or adversarial training. Specifically, we optimize δ over Dc after every M steps of optimization of θ. The entire bi-level optimization process is terminated once the error rate is lower than λ. The detailed training pipeline is described in Algorithm 1 in the Appendix.
  Sample-wise Generation. We adopt the first-order optimization method PGD (Madry et al., 2018) to solve the constrained inner minimization problem as follows:
  x′t+1 = Π ( x′t − α · sign(∇xL(f ′(x′t), y)) ) (3)
  where, t is the current perturbation step (T steps in total), ∇xL(f(x′t), y) is the gradient of the loss with respect to the input, Π is a projection function that clips the noise back to the -ball around the original example x when it goes beyond, and α is the step size. The perturbation is iteratively applied for T steps after each M step of model training as we explained earlier. The final output is a unlearnable example x′ and the generated error-minimizing noise is δ = x′ − x. Class-wise Generation. Class-wise noise ∆c can be obtained by a cumulative perturbation on all examples in a given class. For each example in class k at step t, it applies δk to the original example x and follows Equation 3 to produce x′t+1. The δk accumulates over every example for the corresponding class k in the entire bi-level optimization process.
sections.heading: 4 EXPERIMENTS
sections.text: In this section, we first demonstrate the effectiveness in creating unlearnable examples using random noise, error-maximizing noise and our proposed error-minimizing noise in both sample-wise and class-wise forms. We further empirically verify the effectiveness of error-minimizing noise on 4 benchmark image datasets. We then conduct a set of stability and transferability analyses of the noise. Finally, we show effectiveness in real-world scenarios via a case study on face recognition. More analyses regarding the effectiveness of error-minimizing noise on small patches or a mixture of class-wise noise can be found in Appendix F.
  According to previous studies in adversarial research, small L∞-bounded noise within ‖δ‖∞ < = 8/255 on images are imperceptible to human observers. We consider the same constraint for all types and forms of the noise in our experiments, unless otherwise explicitly stated.
  Experimental Setting for Error-Minimizing Noise. We apply error-minimizing noise to the training set of 4 commonly used image datasets: SVHN (Netzer et al., 2011), CIFAR-10, CIFAR-100 (Krizhevsky, 2009), and ImageNet subset (the first 100 classes) (Russakovsky et al., 2015). The experiments on the ImageNet subset are to confirm the effectiveness of high-resolution images. For all experiments, the ResNet-18 (RN-18) (He et al., 2016) is used as the source model f ′ to generate the noise. We use 20% of the training dataset to generate the class-wise noise and the entire training dataset for the sample-wise noise except for ImageNet †. We transform the entire training dataset into the unlearnable datasets for experiments in section 4.1 and section 4.2. Different percentages of unlearnable examples are used for experiments in section 4.3. We train four different DNNs on the unlearnable training sets: VGG-11 (Simonyan & Zisserman, 2014), ResNet-18 (RN-18), ResNet-50 (RN-50) and DenseNet-121 (DN-121) (Huang et al., 2017). We also use clean training sets as a comparison. Detailed training configurations settings can be found in Appendix B. We evaluate the effectiveness of unlearnable examples by examining the model’s accuracy on clean test examples, i.e., the lower the clean test accuracy the better the effectiveness.
  Experimental Setting for Random and Error-Maximizing Noise. For random noise, we randomly sample the noise from [− , ] independently for each training example (eg. sample-wise) or each class (eg. class-wise). For error-maximizing (adversarial) noise, we generate the noise using PGD-20 attack (Madry et al., 2018) using a pre-trained ResNet-18 model on the training set. We generate sample-wise error-maximizing noise for each training example, and the class-wise noise based on 20% of the training set following the universal attack procedure in (Moosavi-Dezfooli et al., 2017).
  †We use 20% of the first 100 class subset as the entire training set (due to the efficiency)
  Both the random and error-maximizing noise are applied to the same amount of training examples as our error-minimizing noise.
sections.heading: 4.1 COMPARISONS OF RANDOM, ERROR-MAXIMIZING AND ERROR-MINIMIZING NOISE
sections.text: First, we examine an extreme case that applies different types of noise to the entire training set. Figure 1 illustrates the effectiveness of both sample-wise and class-wise noise. In the sample-wise case, the network is robust to random or error-maximizing noise. This is understandable since DNNs are known to be robust to small random (Fawzi et al., 2016) and error-maximizing noise (Muñoz-González et al., 2017; Madry et al., 2018; Wang et al., 2019). Surprisingly, when applied in a class-wise manner, both types of noise can prevent the network from learning useful information from the data, especially after the 15-th epoch. This reveals that DNNs are remarkably vulnerable to class-wise noise. While effective in the middle and later training stages, class-wise random noise can still be circumvented by early stopping (eg. at epoch 15). This is also the case for error-maximizing noise, although not as easy as random noise since the highest clean test accuracy under error-maximizing noise is only 50%. From the perspective of making data unexploitable, both random and error-maximizing noise are only partially effective. In comparison, our error-minimizing noise is more flexible. As shown in Figure 1, the error-minimizing noise can reduce the model’s clean test accuracy to below 23% in both settings. Moreover, it remains effective across the entire training process.
  The class-wise and sample-wise noises work in different ways. Class-wise noise has an explicit correlation with the label. Learning such correlation can effectively reduce the training error. Consequently, when there is class-wise noise, the model is tricked to learn the noise rather than the real content, reducing its generalization performance on clean data. The existence of class-wise noise only in the training data also breaks the i.i.d. assumption between the training and test data distribution. This also indicates that noises that can break the i.i.d. assumption might be effective techniques for data protection. However, in the sample-wise case, every sample has a different noise, and there is no explicit correlation between the noise and the label. In this case, only low-error samples can be ignored by the model, and normal and high-error examples have more positive impact on model learning than low-error examples. This makes error-minimizing noise more generic and effective in making data unlearnable.
sections.heading: 4.2 EFFECTIVENESS OF ERROR-MINIMIZING NOISE ON DIFFERENT DATASETS
sections.text: Table 1 reports the effectiveness of both the sample-wise (eg. ∆s) and the class-wise (eg. ∆c) errorminimizing noise on datasets SVHN, CIFAR-10, CIFAR-100 and ImageNet subset. As shown in the table, our proposed method can reliably create unlearnable examples in both forms on all 4 datasets with images of different resolutions. Moreover, the noise generated on RN-18 works remarkably well to protect the data from other types of models. Compared to sample-wise noise, class-wise noise is particularly more effective, which can reduce the model’s performance to a level that is close to random guessing. These results clearly show that error-minimizing noise is a promising technique for preventing unauthorized data exploration.
sections.heading: 4.3 STABILITY ANALYSIS
sections.text: We run a set of experiments to analyze the stability of error-minimizing noise in creating unlearnable examples, and answer two key questions regarding its practical usage: 1) Is the noise still effective if only applied to a certain proportion or class of the data? and 2) Can the noise be removed by data augmentation or adversarial training? Experiments are conducted on CIFAR-10 with RN-18.
  Different Unlearnable Percentages. In practical scenarios, it is very likely that not all the training data need to be made unlearnable. For example, only a certain number of web users have decided to use this technique but not all users, or only a specific class of medical data should be kept unexploited. This motivates us to examine the effectiveness of error-minimizing noise when applied only on a proportion of randomly selected training examples. In other words, we make a certain percentage of the training data unlearnable while keeping the rest of the data clean. We train the model on this partially unlearnable and partially clean training set Du +Dc. As a comparison, we also train the model on only the clean proportion, which is denoted by Dc. A quick glance at the Du +Dc results in Table 2 tells us that the effectiveness drops quickly when the data are not made 100% unlearnable. This is the case for both sample-wise and class-wise noise. The unlearnable effect is almost negligible even when the noise is applied to 40% of the data. Such a limitation against DNNs has also been identified in previous work for protecting face images using error-maximizing noise (Shan et al., 2020).
  To better understand the above limitation, we take 80% as an example and plot the learning curves of the RN-18 model trained on 1) only the 20% clean proportion, 2) only the 80% unlearnable proportion, or 3) both. The results are shown in Figure 2 (a-b). Interestingly, we find that the 80% data with the error-minimizing noise are still unlearnable to the model, whereas the rest of the 20% clean data are sufficient for the model to achieve a good performance. In other words, models trained only on Dc demonstrate a similar performance as models trained on Du +Dc. This phenomenon is consistent across different unlearnable percentages. This indicates that the high performance of the model on < 100% unlearnable dataset may not be a failure of the error-minimizing noise. We further verify this by investigating the scenario where only one class is made unlearnable.
  One Single Unlearnable Class. We take the ‘bird’ class of CIFAR-10 as an example, and apply the error-minimizing noise (either sample-wise or class-wise) to all training images in the bird class. We train RN-18 on each of the unlearnable training set, and plot the prediction confusion matrix of the model on the clean test set in Figure 2 (c-d). The ‘bird’ class is indeed unlearnable when either the sample-wise or the class-wise error-minimizing noise is added to the class. Compared to sample-wise noise, class-wise noise is more effective with almost all the test ‘bird’ images being misclassified into other classes. Interestingly, this customized unlearnable class does not seem to influence much of the learning on other classes. Only the images from the unlearnable class are incorrectly predicted into other classes, not the other way around. This not only confirms that the unlearnable group of data
  is indeed unlearnable to the model and it suggests that our error-minimizing noise can be flexibly applied to suit different protection tasks. A similar result can also be demonstrated on more than one unlearnable class (see Appendix C). In summary, if an individual can only apply the noise to portion of his/her data, these data will not contribute to model training. If an individual can apply the noise to all his/her data, the model will fail to recognize this particular class of data. In other words, our method is effective for the defender to protect his/her own data.
  Under Noise Filtering Techniques. The resistance of our error-minimizing noise to 4 types of data augmentation techniques and adversarial training is analyzed in Appendix D. The noise is fairly robust to all 4 data augmentation techniques, and the highest accuracy that can achieve using data augmentation is 58.51% on CIFAR-10. Comparing with data augmentation, the error-minimizing noise is less resistant to adversarial training. With slightly increased on CIFAR-10, the noise can only compromise the model’s clean test accuracy to 79%. Since adversarial training forces the model to learn only robust features (Ilyas et al., 2019), we believe our method can be improved by crafting the noise based on the robust features, which can be extracted from an adversarially pre-trained model on the clean data (Ilyas et al., 2019). We leave further explorations of these techniques as future work.
sections.heading: 4.4 TRANSFERABILITY ANALYSIS
sections.text: Another important question we haven’t explored so far is that Can error-minimizing noise be generated on a different dataset? This is also important as a positive answer to the question increases the practicability of using unlearnable examples to protect millions of web users. We examine this capability for both sample-wise noise and class-wise error-minimizing noise.
  Sample-wise Noise. For ∆s, we generate the noise and create unlearnable ‘ship’ class examples on CIFAR-10 and add the unlearnable ‘ship’ class to CIFAR-100. For testing, we also include the clean test set of ‘ship’ class to the test set of CIFAR-100. Note the main difference of this experiment to the previous singe unlearnable class experiment is the unlearnable examples are generated on a different dataset. The class-wise and the overall accuracy on the clean test set are shown in Figure 3a. We
  find that the ‘ship’ class is indeed unlearnable to the model at the end, despite a small amount (60% clean test accuracy) of information being learned in the early stage. We suspect this is because the ‘ship’ class shares some common features with other classes in CIFAR-100. Overall, the generated unlearnable examples can transfer to a different dataset. Note that this experiment simulates the scenario where a user uses a different dataset (eg. CIFAR-10) to generate the sample-wise noise to make his/her personal images unlearnable before uploading them to the Internet, and these images are then collected into a large CIFAR-100 dataset.
  Class-wise Noise. For ∆c, we use the entire ImageNet as the source dataset to generate the noise using RN-18, then apply the noise to CIFAR-10. All ImageNet images are resized to 32×32. For each CIFAR-10 class, we determine its corresponding class in ImageNet based on the visual similarities between the classes. The detailed class mapping can be found in Table 4 in the Appendix. We train RN-18, RN-50 and DN-121 on the unlearnable CIFAR-10 created with the ImageNet transferred noise, and show their learning curves in Figure 3b. As can be observed, the transferred class-wise noise works reasonably well on CIFAR-10 with the clean test accuracy of all three models being reduced to around 10%. Compared to the noise directly generated on CIFAR-10 (see Figure 1), here the models can still capture some useful features in the first epoch. We conjecture this is because CIFAR-10 classes are more generic than ImageNet classes, and noise that minimizes the error of fine-grained classes can become less effective on generic classes. We also conduct an experiment on the ImageNet transferred noise to make 4 classes unlearnable of CIFAR-10. We plot the prediction confusion matrix of the RN-18 trained on the 4-class unlearnable CIFAR-10 in Figure 3c. It shows that the 4 classes are indeed unlearnable, and the model’s performance on the other 6 classes is not affected. This confirms that transferred noise can also be used in customized scenarios.
sections.heading: 4.5 REAL-WORLD SCENARIO: A CASE STUDY ON FACE RECOGNITION
sections.text: Here, we conduct a case study to apply error-minimizing noise to personal face images, which is arguably one most important real-world scenarios. In this scenario, the defender wants to prevent his/her face images from being exploited to train face recognition or verification systems. The setting is illustrated in Figure 4a. We assume the user has access to a small dataset of facial images and will use this small dataset to generate and apply the error-minimizing noise to his/her own face images before sharing them on online social media platforms. After this, the unlearnable version of face images on social media gets collected to train a DNN based facial recognition or verification system. The system will then be used to recognize one of the user’s clean face image captured somewhere by a camera. The goal is to prevent the DNN from learning the defender’s face images and make it perform poorly on his/her clean face images.
  We conduct the experiments under two different settings: 1) partially unlearnable where a small subset of identities in the training set are unlearnable; or 2) fully unlearnable where the entire training set is unlearnable. We test our error-minimizing noise against both face recognition and verification models. Face recognition model classifies the identity (class) of a face image, while face verification model verifies whether two face images belong to the same identity. In the face verification problem, two face images are determined to be of the same identity if the cosine similarity between the features (extracted from a recognition model) of the two images is below a certain threshold.
  Experimental Settings. We randomly split the WebFace dataset (Yi et al., 2014) into 80% for training and 20% for testing, according to each identity. In the partially unlearnable setting, we randomly select 50 identities from the training set of WebFace into a subset WebFace-50 as the users who want to hide their identities. We also randomly select 100 identities from CelebA (Liu
  et al., 2015) into a subset CelebA-100 as the small dataset used to generate the unlearnable images for WebFace-50. The clean WebFace-50 part of the WebFace training data will be replaced by its unlearnable version for model training. This partially unlearnable version of WebFace training set consists of 10,525 clean identities and 50 unlearnable identities. In the fully unlearnable setting, the entire WebFace is made unlearnable. In both settings, the error-minimizing noises are generated using RN-18 and CelebA-100, following the procedure described in Section 4. We train Inception-ResNet models (Szegedy et al., 2016) following a standard training procedure (Taigman et al., 2014; Parkhi et al., 2015).
  Effectiveness Against Face Recognition. Here, we adopt the partially unlearnable setting. The accuracy of the Inception-ResNet model on the clean WebFace test set is reported in the Figure 4b, separately for the 50 unlearnable identities and the 10,525 clean identities. The result confirms that the 50 identities with the error-minimizing noise are indeed unlearnable and the recognition accuracy of their clean face images is only 16%, a much lower than the rest of the identities (86%).
  Effectiveness Against Face Verification. Here, we adopt both the partially and the fully unlearnable settings. In the partially unlearnable setting, we evaluate the model performance on 6000 (3000 positives and 3000 negatives) face image pairs randomly sampled from the clean test set of WebFace. The pair is labeled as positive if the two face images are of the same identity, negative otherwise. In the fully unlearnable setting, we independently train a second Inception-ResNet model on the fully unlearnable WebFace. To further eliminate possible (dis)similarities shared across the images from the same dataset (e.g., WebFace), we follow the standard face verification evaluation protocol (Deng et al., 2019) and use the 6000 face pairs from LFW (Huang et al., 2008) for testing.
  Figure 7 in Appendix G shows the Receiver Operating Characteristic (ROC) performance of the models trained in both settings. The model trained in the partially unlearnable setting still has a good verification performance on unlearnable identities, although the Area Under the Curve (AUC) is lower than the clean identities. This is because a small subset of unlearnable examples is not powerful enough to stop the learning of a feature extractor. In fact, 2,622 (approximately equal to 25% of WebFace) clean identities are sufficient to train a high-quality facial feature extractor (Parkhi et al., 2015). This indicates that, while it is easy to make data unlearnable to classification models, it is much more challenging to stop the learning of a feature extractor. Nevertheless, the proposed error-minimizing noise is still effective in the fully unlearnable setting, reducing the AUC to 0.5321 (the clean setting AUC is 0.9975). Whilst there are still many unexplored factors, we believe our proposed error-minimization noise introduces a new practical tool for protecting personal data from unauthorized exploitation.
sections.heading: 5 CONCLUSION
sections.text: In this paper, we have explored the possibility of using invisible noise to prevent data from being freely exploited by deep learning. Different from existing works, our method makes data unlearnable to deep learning models. The effectiveness of this approach could have a broad impact for both the public and the deep learning community. We propose a type of error-minimizing noise and empirically demonstrate its effectiveness in creating unlearnable examples. The noise is effective in different forms (eg. sample-wise or class-wise), sizes (eg. full image or small patch), and is resistant to common data filtering methods. It can also be customized for a certain proportion of the data, one single class or for multiple classes. Furthermore, the noise can be easily transferred from existing public datasets to make private datasets unlearnable. Finally, we verify the usefulness for real-world scenarios via a case study on face recognition. Our work opens up a new direction of preventing free exploitation of data. Although there are still many practical obstacles for a large-scale application of the error-minimizing noise, we believe this study establishes an important first step towards preventing personal data being freely exploited by deep learning.
sections.heading: ACKNOWLEDGEMENT
sections.text: Yisen Wang is partially supported by the National Natural Science Foundation of China under Grant 62006153, and CCF-Baidu Open Fund (OF2020002). This research was undertaken using the LIEF HPC-GPGPU Facility hosted at the University of Melbourne, which was established with the assistance of LIEF Grant LE170100200.
sections.heading: A ALGORITHM OF ERROR-MINIMIZATION GENERATION
sections.text: Algorithm 1 Error-minimizing Perturbations 1: Input: Source Model θ, Perturbations δ, Lp , (x, y) ∈ Dc, Stop Error λ, Optimization steps M 2: Output: δ 3: repeat 4: for m in 1 · · ·M do 5: i,xi, yi = Next(x, y) 6: if sample-wise then 7: δ = δi 8: else if class-wise then 9: δ = δyi 10: end if 11: Optimize(xi + δ, yi, θ) 12: end for 13: for xj , yj in x, y do 14: δ = Perturbation(xi, yi, θ, δ) . Follow Equation 3 15: Cilp(δ,− , ) 16: end for 17: error = Eval(x, y, δ, θ) 18: until error < λ
sections.heading: B MORE EXPERIMENT SETTING
sections.text: For all experiments, we use Lp-norm with to regularize the imperceptibility, = 8/255 for CIFAR and SVHN, = 16/255 for ImageNet, different is used in Appendix D for additional understandings. The iterative steps T for Equation 3 is set to 20 steps for sample-wise noise and 1 for class-wise, α is set to /10. Since the class-wise noise is generated universally for each class, small iterative steps avoid overfitting to the specific example. For the class-wise experiments, we only use 20% of the training data Dc to generate the noise δ and apply to entire training dataset Dc → Du. The stop condition error rate is λ = 0.1 for ∆c and λ = 0.01 for ∆s. For SVHN and CIFAR-10, we set the M = 10 for CIFAR-10, M = 20 for CIFAR-100 and M = 100 for ImageNet in the mini-setting. For all models and experiments, we use the Stochastic Gradient Descent (SGD) (LeCun et al., 1998) optimizer with momentum 0.9, initial learning rate 0.025 and cosine scheduler (Loshchilov & Hutter, 2017) without the restart. We train all DNN models for 30 epochs on SVHN, 60 epochs on CIFAR-10, 100 epochs on CIFAR-100 and ImageNet. To generated fully unlearnable setting CIFAR-10 dataset, the computational cost is roughly 10% of the standard model training time for class-wise noise and 60% of standard model training time for sample-wise noise. Overall, the cost of generating unlearnable examples is far less than training a model on the data to be protected.
sections.heading: C STABILITY ANALYSIS
sections.heading: D RESISTANCE TO DATA AUGMENTATION AND ADVERSARIAL TRAINING
sections.text: Resistance to Data Augmentation. Another important property of the unlearnable examples created by error-minimizing noise is its resistance to data augmentations. Since standard data augmentation techniques like random shift, crop, flip and rotation have already been applied in previous experiments, here we consider 4 more advanced data augmentation techniques: Cutout (DeVries & Taylor, 2017), Mixup (Zhang et al., 2018a), Cutmix (Yun et al., 2019) and Fast Au-
  toaugment (FA) (Lim et al., 2019). For Cutout, we set the cutout length to 16 pixels. For Mixup, we apply linear mixup of random pairs of training examples and their labels during the standard training process. For Cutmix, we apply linear mixup on the cutout region. For FA, we use the fixed augmentation policy, which consists of change contrast, brightness, sharpness, rotations and cutout. It is observed that advanced data augmentation techniques including Cutout, Mixup, Cutmix and FA can indeed remove the sample-wise noise to some extent, but far less effective on class-wise noise.
  Adversarial Training. We also consider the Adversarial Training (AdvTrain), which is an augmentation based defence method against error-maximizing noise (Goodfellow et al., 2014; Madry et al., 2018). AdvTrain has been shown can effectively remove the non-robust features from the input and force the model to learn only the robust features (Ilyas et al., 2019). Compared to data augmentation techniques, adversarial training as a type of robust training technique is indeed more effective against both sample-wise and class-wise noise. However, adversarial training is known to suffer from a trade-off between robustness and accuracy (Zhang et al., 2019). For example, adversarial training only achieved 85% accuracy on the unlearnable CIFAR-10, there is still a roughly 10% (94.95% vs 85%) performance drop compared to standard training on the clean CIFAR-10. Moreover, due to the difficulty of min-max optimization, current adversarial training methods are still limited to small error-maximizing noise. To test this, we fix the maximum adversarial perturbation used by adversarial training to 8/255, while increasing the perturbation of error-minimizing noise to = 24/255. Note that adversarial training with perturbation 16/255 or 24/255 still suffers from convergence issues, even on small datasets like CIFAR-10. The results are shown in Figure 6. As can be confirmed, the clean test accuracy will drop to 79% on = 24/255 error-minimizing noise.
  The above results indicate that 1) error-minimizing noise is resistant to standard data filtering especially the class-wise noise; 2) although it is less resistant to adversarial training, the model’s performance can still be significantly compromised by our error-minimizing noise noise. In future works, it is possible to develop more advanced unlearnable examples that can further decrease the performance of adversarial training. We believe our method can be improved by crafting the noise based on only the robust features, since adversarial training forces the model to learn only robust features (Ilyas et al., 2019).
sections.heading: E CLASS-WISE NOISE TRANSFER FROM IMAGENET TO CIFAR-10
sections.heading: F FLEXIBILITY ANALYSIS OF ERROR-MINIMIZING NOISE
sections.text: Here, we focus on the class-wise error-minimizing noise and further explore its flexibility from two perspectives: 1) effectiveness when applied to smaller patches rather than the entire image; and 2) effectiveness of two sets of mixed class-wise noise. These experiments are also conducted with RN-18 on the CIFAR-10 dataset. For all the error-minimizing noise, we fix the maximum perturbation to = 8/255.
  Effectiveness on Smaller Patches. The unlearnable example can be very flexible and hard to be detected if the noise remains effective on smaller patches. To test this, we set the patch size to 32×32, 24× 24, 16× 16 and 8× 8 (CIFAR-10 image size is 32× 32). During the noise generation process when solving equation Equation 2, a random patch is selected and perturbed in each perturbation step and for each training example. Once a class-wise patch noise is generated, it then attached to a randomly selected location of a training example. The effectiveness of small patch noise is reported in Table 5. The effectiveness is still very high for patch size as small as 16× 16, although it is indeed decreased on smaller patches. An interesting observation is that the FA augmentation becomes less effective on 16× 16 noise than 24× 24 noise. We suspect this is because smaller patch noise can more easily escape the augmentation operations and stays unchanged after the augmentation.
  Effectiveness of Mixed Noises. We conduct this mix noise to simulate two possible real-world scenarios: 1) different users apply different noise apply to their own data; or 2) one set of noise is exposed and upgraded to a new set of noise. In this experiment, we apply the noise on the full image. We repeat the class-wise noise generation twice and generate two sets of noise: ∆c1 and ∆c2. For each CIFAR-10 training example, we randomly apply one of the above two class-wise noise to create unlearnable example. We note this mixture by ∆c1 ∨∆c2. Note that the class-wise mixture will eventually become the sample-wise noise if we keep mixing more class-wise noise sets. We also perform another mixture between ∆c1 and a random noise ∆u sampled from [− , ] mixed by element-wise addition. We denote this mixture by ∆c1 + ∆u. The effectiveness of mixed noise is also reported in Table 5. For both mixtures, the proposed error-minimizing noise remains highly effective, although there is a slight decrease. Surprisingly, the mixture of one class-wise noise with random noise is even more effective than the mixture of two class-wise noise, especially against the FA data augmentation. This makes the error-minimizing noise even more flexible in practical usage.
sections.heading: G RESULTS ON FACE VERIFICATION
sections.heading: H CLASS-WISE NOISE VS. BACKDOOR ATTACK
sections.text: Here, we test if class-wise noise can be used as a trigger for the backdoor attack. Figure 8 shows the backdoor attack success rate when different types of class-wise noises are applied as the backdoor trigger. At the training time, we train RN-18 models on CIFAR-10 with 0%-100% of the training samples were made unlearnable by three types of class-wise noise: random noise, error-minimizing and our error-maximizing noise. At the test (attack) time, we compute the attack success rate as follows. There are 6 models for each type of class-wise corresponding the 6 unlearnable percentages. For each type of class-wise noise and each RN-18 model, we iteratively take a clean test image from the CIFAR-10 test set, then randomly select a target class (which is different from the true class of the test image). Then, we attach the target class class-wise noise to the clean test image. If the new test image is predicted by the model as the target class, then the attack is successful.
  As shown in Figure 8, the class-wise error-maximizing (adversarial) noise is a highly effective trigger for backdoor attack, yet neither random nor our error-minimizing noise can be considered to be effective. The error-maximizing can achieve more than 75% attack success rate when only applied to 20% the training data. To achieve a similar level of attack success rate, both random and our error-minimizing noise should be added to at least 80% of the training data. This indicates that our method is different from backdoor attacks. The high attack success rate of adversarial noise may due to the fact that adversarial examples are hard (high error) examples, which force the model to pay more attention to the examples and remember more of the adversarial noise. Note that adversarial perturbations have also been used in backdoor research to enhance backdoor triggers (Turner et al., 2018; Zhao et al., 2020).
sections.heading: I DIFFERENT GENERALIZATION METHODS FOR ERROR-MINIMIZATION NOISE
sections.text: The proposed error-minimizing noise is generated using PGD. Specifically, PGD is applied to solve the inner minimization problem in Equation 2. Since it is a typical constrained optimization problem, it can also be solved by other optimization (attack) methods such as FGSM (Goodfellow et al., 2014), L-BFGS (Szegedy et al., 2013) and C&W (Carlini & Wagner, 2017). However, the objective needs to be reformulated to apply some of these attacks. Here, we take L-BFGS (Szegedy et al., 2013) as an example to reformulate and solve the inner minimization problem in Equation 2. In (Szegedy et al., 2013), the adversarial attack problem is formulated as:
  minimize c ‖δ‖p + L(x+ δ, y ′) y′ 6= y (4)
  where c is a hyperparameter and the L is the objective function (e.g. the cross entropy adversarial loss). This form has been extended to other objective functions in C&W (Carlini & Wagner, 2017). The main objective of adversarial attack is to find small Lp (i.e. ‖·‖p) bounded noise δ that can trick the model to output a wrong label y′ 6= y. For unlearnable examples, we want to trick the model to predict the correct label y with the highest confidence (i.e. lowest error). Following Equation 4, the inner minimization problem in Equation 2 can be reformulated as:
  minimize c ‖δ‖22 + L(x+ δ, y). (5)
  We set c = 1.0 and use the cross entropy loss for L. We apply L-BFGS to solve Equation 5 using Adam (Kingma & Ba, 2015) optimizer and generate sample-wise noise ∆s on CIFAR-10. The number of optimization steps for Equation 5 is set to T = 200, while the number of optimization steps for the outer minimization in Equation 2 is set to M = 100 (see more details about T and M in Section 3.2). As shown in Figure 9, error-minimizing noise can also be generated using L-BFGS, and the noise is very effective in making the training examples unlearnable. However, compared to PGD, L-BFGS is slightly less effective.
title: UNLEARNABLE EXAMPLES: MAKING PERSONAL DATA UNEXPLOITABLE