Federated learning is an emerging data-private distributed learning framework, which, however, is vulnerable to adversarial attacks. Although several heuristic defenses are proposed to enhance the robustness of federated learning, they do not provide certifiable robustness guarantees. In this paper, we incorporate randomized smoothing techniques into federated adversarial training to enable data-private distributed learning with certifiable robustness to test-time adversarial perturbations. Our experiments show that such an advanced federated adversarial learning framework can deliver models as robust as those trained by the centralized training. Further, this enables provably-robust classifiers to $\ell_2$-bounded adversarial perturbations in a distributed setup. We also show that one-point gradient estimation based training approach is $2-3\times$ faster than popular stochastic estimator based approach without any noticeable certified robustness differences.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Zhejiang University（浙江大学）；IBM Research（IBM研究院）
Federated Learning (FL) as a distributed learning paradigm that aggregates information from diverse clients to train a shared global model, has demonstrated great success. However, malicious clients can perform poisoning attacks and model replacement to introduce backdoors into the trained global model. Although there have been intensive studies designing robust aggregation methods and empirical robust federated training protocols against backdoors, existing approaches lack robustness certification. This paper provides the first general framework, Certifiably Robust Federated Learning (CRFL), …
Tulane University（杜兰大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；IBM Research（IBM研究院）
Predictions of certifiably robust classifiers remain constant in a neighborhood of a point, making them resilient to test-time attacks with a guarantee. In this work, we present a previously unrecognized threat to robust machine learning models that highlights the importance of training-data quality in achieving high certified adversarial robustness. Specifically, we propose a novel bilevel optimization-based data poisoning attack that degrades the robustness guarantees of certifiably robust classifiers. Unlike other poisoning attacks that reduce the accuracy of the poisoned models on a small …
Carnegie Mellon University（卡内基梅隆大学）；Bosch Center for AI（博世人工智能中心）
Machine learning algorithms are known to be susceptible to data poisoning attacks, where an adversary manipulates the training data to degrade performance of the resulting classifier. In this work, we present a unifying view of randomized smoothing over arbitrary functions, and we leverage this novel characterization to propose a new strategy for building classifiers that are pointwise-certifiably robust to general data poisoning attacks. As a specific instantiation, we utilize our framework to build linear classifiers that are robust to a strong variant of label flipping, where each test exam…
Tsinghua University（清华大学）；Harvard University（哈佛大学）；University of California, Berkeley（加州大学伯克利分校）；Huazhong University of Science and Technology（华中科技大学）；Virginia Tech（弗吉尼亚理工大学）
Deep learning techniques have achieved remarkable performance in wide-ranging tasks. However, when trained on privacy-sensitive datasets, the model parameters may expose private information in training data. Prior attempts for differentially private training, although offering rigorous privacy guarantees, lead to much lower model performance than the non-private ones. Besides, different runs of the same training algorithm produce models with large performance variance. To address these issues, we propose DPlis--Differentially Private Learning wIth Smoothing. The core idea of DPlis is to constr…
Provable Robustness against Backdoor Attacks via the Primal-Dual Perspective on Differential Privacy
Department of Computer Science, Technical University of Munich（慕尼黑技术大学计算机科学系）；Munich Data Science Institute（慕尼黑数据科学研究所）；MCML；Machine Learning Research, Morgan Stanley（摩根大通机器学习研究）
Randomized Smoothing (RS) is considered the state-of-the-art approach to obtain certifiably robust models for challenging tasks. However, current RS approaches drastically decrease standard accuracy on unperturbed data, severely limiting their real-world utility. To address this limitation, we propose a compositional architecture, ACES, which certifiably decides on a per-sample basis whether to use a smoothed model yielding predictions with guarantees or a more accurate standard model without guarantees. This, in contrast to prior approaches, enables both high standard accuracies and significa…
Huawei Moscow Research Center（华为莫斯科研究中心）；Lomonosov Moscow State University（罗蒙诺索夫莫斯科国立大学）；Nuro, Inc.（Nuro公司）
Currently the most popular method of providing robustness certificates is randomized smoothing where an input is smoothed via some probability distribution. We propose a novel approach to randomized smoothing over multiplicative parameters. Using this method we construct certifiably robust classifiers with respect to a gamma correction perturbation and compare the result with classifiers obtained via other smoothing distributions (Gaussian, Laplace, uniform). The experiments show that asymmetrical Rayleigh distribution allows to obtain better certificates for some values of perturbation parame…
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；University of Oxford（牛津大学）
Randomized smoothing is a recent technique that achieves state-of-art performance in training certifiably robust deep neural networks. While the smoothing family of distributions is often connected to the choice of the norm used for certification, the parameters of these distributions are always set as global hyper parameters independent from the input data on which a network is certified. In this work, we revisit Gaussian randomized smoothing and show that the variance of the Gaussian distribution can be optimized at each input so as to maximize the certification radius for the construction o…
Institut de Recherche Technologique SystemX（SystemX技术研究院）；Univ. Bordeaux（波尔多大学）；CNRS（法国国家科学研究中心）；Bordeaux INP（波尔多国立理工学院）；IMB（波尔多数学研究所）
Certification of neural networks is an important and challenging problem that has been attracting the attention of the machine learning community since few years. In this paper, we focus on randomized smoothing (RS) which is considered as the state-of-the-art method to obtain certifiably robust neural networks. In particular, a new data-dependent RS technique called ANCER introduced recently can be used to certify ellipses with orthogonal axis near each input data of the neural network. In this work, we remark that ANCER is not invariant under rotation of input data and propose a new rotationa…
Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing
Department of Computer Science, School of Computing, Institute of Science Tokyo, Tokyo, Japan（东京科学研究所计算机科学系）；College of Computing and Data Science, Nanyang Technological University, Singapore（南洋理工大学计算机与数据科学学院）；PSL University, Paris, France（巴黎高等师范学院）
University of Connecticut（康涅狄格大学）；Illinois Institute of Technology（伊利诺伊理工学院）
We study certified robustness of machine learning classifiers against adversarial perturbations. In particular, we propose the first universally approximated certified robustness (UniCR) framework, which can approximate the robustness certification of any input on any classifier against any $\ell_p$ perturbations with noise generated by any continuous probability distribution. Compared with the state-of-the-art certified defenses, UniCR provides many significant benefits: (1) the first universal robustness certification framework for the above 4 'any's; (2) automatic robustness certification t…
Building models that comply with the invariances inherent to different domains, such as invariance under translation or rotation, is a key aspect of applying machine learning to real world problems like molecular property prediction, medical imaging, protein folding or LiDAR classification. For the first time, we study how the invariances of a model can be leveraged to provably guarantee the robustness of its predictions. We propose a gray-box approach, enhancing the powerful black-box randomized smoothing technique with white-box knowledge about invariances. First, we develop gray-box certifi…
The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured outputs like sets, images, language, etc. We model the output space as a metric space under a distance/similarity function, such as intersection-over-union, perceptual similarity, total variation distance, etc. Such models are used in many machine learning problems like image segmentation, object detection, generative models, image/audio-to-text systems, etc. B…
Randomized smoothing is a general technique for computing sample-dependent robustness guarantees against adversarial attacks for deep classifiers. Prior works on randomized smoothing against L_1 adversarial attacks use additive smoothing noise and provide probabilistic robustness guarantees. In this work, we propose a non-additive and deterministic smoothing method, Deterministic Smoothing with Splitting Noise (DSSN). To develop DSSN, we first develop SSN, a randomized method which involves generating each noisy smoothing sample by first randomly splitting the input space and then returning a …
Randomized smoothing is the dominant standard for provable defenses against adversarial examples. Nevertheless, this method has recently been proven to suffer from important information theoretic limitations. In this paper, we argue that these limitations are not intrinsic, but merely a byproduct of current certification methods. We first show that these certificates use too little information about the classifier, and are in particular blind to the local curvature of the decision boundary. This leads to severely sub-optimal robustness guarantees as the dimension of the problem increases. We t…
Carnegie Mellon University（卡内基梅隆大学）；Bosch Center for AI（博世人工智能中心）
We show how to turn any classifier that classifies well under Gaussian noise into a new classifier that is certifiably robust to adversarial perturbations under the $\ell_2$ norm. This "randomized smoothing" technique has been proposed recently in the literature, but existing guarantees are loose. We prove a tight robustness guarantee in $\ell_2$ norm for smoothing with Gaussian noise. We use randomized smoothing to obtain an ImageNet classifier with e.g. a certified top-1 accuracy of 49% under adversarial perturbations with $\ell_2$ norm less than 0.5 (=127/255). No certified defense has been…
Backdoor attack is a severe security threat to deep neural networks (DNNs). We envision that, like adversarial examples, there will be a cat-and-mouse game for backdoor attacks, i.e., new empirical defenses are developed to defend against backdoor attacks but they are soon broken by strong adaptive backdoor attacks. To prevent such cat-and-mouse game, we take the first step towards certified defenses against backdoor attacks. Specifically, in this work, we study the feasibility and effectiveness of certifying robustness against backdoor attacks using a recent technique called randomized smooth…
School of Computation, Information & Technology, Technical Univ. of Munich（慕尼黑工业大学计算、信息与技术学院）；Fraunhofer Institute for Cognitive Systems IKS（弗劳恩霍夫认知系统研究所IKS）
Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothing
Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；CSIRO’s Data61（联邦科学与工业研究组织数据61部）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Simon Fraser University（西蒙菲莎大学）；University of Chicago（芝加哥大学）
Randomized smoothing (RS) is an effective and scalable technique for constructing neural network classifiers that are certifiably robust to adversarial perturbations. Most RS works focus on training a good base model that boosts the certified robustness of the smoothed model. However, existing RS techniques treat every data point the same, i.e., the variance of the Gaussian noise used to form the smoothed model is preset and universal for all training and test data. This preset and universal Gaussian noise variance is suboptimal since different data points have different margins and the local …
Randomized smoothing, a method to certify a classifier's decision on an input is invariant under adversarial noise, offers attractive advantages over other certification methods. It operates in a black-box and so certification is not constrained by the size of the classifier's architecture. Here, we extend the work of Li et al. \cite{li2018second}, studying how the choice of divergence between smoothing measures affects the final robustness guarantee, and how the choice of smoothing measure itself can lead to guarantees in differing threat models. To this end, we develop a method to certify ro…
Recent advances in machine learning (ML) algorithms, especially deep neural networks (DNNs), have demonstrated remarkable success (sometimes exceeding human-level performance) on several tasks, including face and speech recognition. However, ML algorithms are vulnerable to \emph{adversarial attacks}, such test-time, training-time, and backdoor attacks. In test-time attacks an adversary crafts adversarial examples, which are specially crafted perturbations imperceptible to humans which, when added to an input example, force a machine learning model to misclassify the given input example. Advers…
Technical University of Munich（慕尼黑工业大学）；University of Maryland, College Park（马里兰大学帕克分校）
Randomized Smoothing (RS), being one of few provable defenses, has been showing great effectiveness and scalability in terms of defending against $\ell_2$-norm adversarial perturbations. However, the cost of MC sampling needed in RS for evaluation is high and computationally expensive. To address this issue, we investigate the possibility of performing randomized smoothing and establishing the robust certification in the latent space of a network, so that the overall dimensionality of tensors involved in computation could be drastically reduced. To this end, we propose Latent Space Randomized …
We present a new certification method for image and point cloud segmentation based on randomized smoothing. The method leverages a novel scalable algorithm for prediction and certification that correctly accounts for multiple testing, necessary for ensuring statistical guarantees. The key to our approach is reliance on established multiple-testing correction mechanisms as well as the ability to abstain from classifying single pixels or points while still robustly segmenting the overall input. Our experimental evaluation on synthetic data and challenging datasets, such as Pascal Context, Citysc…
Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks. Many works have devised new randomized smoothing schemes for other metrics, such as $\ell_1$ or $\ell_\infty$; however, substantial effort was needed to derive such new guarantees. This begs the question: can we find a general theory for randomized smoothing? We propose a novel framework for devising and analyzing randomized smoothing schemes, and validate its effectiveness in practice. Our theoretical contributions are: (1) we show that for an appropriate notion of "opti…
Laplace-Bridged Randomized Smoothing for Fast Certified Robustness
Department of Computer Science, Old Dominion University, Norfolk, VA, USA（旧 Dominion 大学计算机科学系）；Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, USA（德克萨斯理工大学数学科学系）；School of Cybersecurity, Old Dominion University, Norfolk, VA, USA（旧 Dominion 大学网络安全学院）
Randomized smoothing is a recent and celebrated solution to certify the robustness of any classifier. While it indeed provides a theoretical robustness against adversarial attacks, the dimensionality of current classifiers necessarily imposes Monte Carlo approaches for its application in practice. This paper questions the effectiveness of randomized smoothing as a defense, against state of the art black-box attacks. This is a novel perspective, as previous research works considered the certification as an unquestionable guarantee. We first formally highlight the mismatch between a theoretical …
School of Computation, Information & Technology, Technical Univ. of Munich（慕尼黑工业大学计算、信息与技术学院）；Fraunhofer Institute for Cognitive Systems IKS（弗劳恩霍夫认知系统研究所IKS）
Randomized smoothing is a popular way of providing robustness guarantees against adversarial attacks: randomly-smoothed functions have a universal Lipschitz-like bound, allowing for robustness certificates to be easily computed. In this work, we show that there also exists a universal curvature-like bound for Gaussian random smoothing: given the exact value and gradient of a smoothed function, we compute a lower bound on the distance of a point to its closest adversarial example, called the Second-order Smoothing (SoS) robustness certificate. In addition to proving the correctness of this nove…
Randomized smoothing has been shown to provide good certified-robustness guarantees for high-dimensional classification problems. It uses the probabilities of predicting the top two most-likely classes around an input point under a smoothing distribution to generate a certified radius for a classifier's prediction. However, most smoothing methods do not give us any information about the confidence with which the underlying classifier (e.g., deep neural network) makes a prediction. In this work, we propose a method to generate certified radii for the prediction confidence of the smoothed classi…
MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
The fragility of modern machine learning models has drawn a considerable amount of attention from both academia and the public. While immense interests were in either crafting adversarial attacks as a way to measure the robustness of neural networks or devising worst-case analytical robustness verification with guarantees, few methods could enjoy both scalability and robustness guarantees at the same time. As an alternative to these attempts, randomized smoothing adopts a different prediction rule that enables statistical robustness arguments which easily scale to large networks. However, in t…
National Technical University of Athens（希腊雅典国家技术大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CSX-AI（CSX-AI公司）；Carl von Ossietzky University of Oldenburg（奥尔登堡卡尔·冯·奥西特齐大学）；Chalmers University of Technology（查尔姆斯理工大学）
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Peking University（北京大学）
Neural networks (NNs) are known to be vulnerable against adversarial perturbations, and thus there is a line of work aiming to provide robustness certification for NNs, such as randomized smoothing, which samples smoothing noises from a certain distribution to certify the robustness for a smoothed classifier. However, as shown by previous work, the certified robust radius in randomized smoothing suffers from scaling to large datasets ("curse of dimensionality"). To overcome this hurdle, we propose a Double Sampling Randomized Smoothing (DSRS) framework, which exploits the sampled probability f…
Randomized smoothing, using just a simple isotropic Gaussian distribution, has been shown to produce good robustness guarantees against $\ell_2$-norm bounded adversaries. In this work, we show that extending the smoothing technique to defend against other attack models can be challenging, especially in the high-dimensional regime. In particular, for a vast class of i.i.d.~smoothing distributions, we prove that the largest $\ell_p$-radius that can be certified decreases as $O(1/d^{\frac{1}{2} - \frac{1}{p}})$ with dimension $d$ for $p > 2$. Notably, for $p \geq 2$, this dependence on $d$ is no …
Mila（米拉）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；Peking University（北京大学）
Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing noise and only work for $\ell_2$ perturbation. We propose a general framework of adversarial certification with non-Gaussian noise and for more general types of attacks, from a unified functional optimization perspective. Our new framework allows us to identify a key trade-off between accuracy and robustness via designing smoothing distributions, helping to design new families of n…
We extend randomized smoothing to cover parameterized transformations (e.g., rotations, translations) and certify robustness in the parameter space (e.g., rotation angle). This is particularly challenging as interpolation and rounding effects mean that image transformations do not compose, in turn preventing direct certification of the perturbed image (unlike certification with $\ell^p$ norms). We address this challenge by introducing three different kinds of defenses, each with a different guarantee (heuristic, distributional and individual) stemming from the method used to bound the interpol…
