Top-k predictions are used in many real-world applications such as machine learning as a service, recommender systems, and web searches. $\ell_0$-norm adversarial perturbation characterizes an attack that arbitrarily modifies some features of an input such that a classifier makes an incorrect prediction for the perturbed input. $\ell_0$-norm adversarial perturbation is easy to interpret and can be implemented in the physical world. Therefore, certifying robustness of top-$k$ predictions against $\ell_0$-norm adversarial perturbation is important. However, existing studies either focused on certifying $\ell_0$-norm robustness of top-$1$ predictions or $\ell_2$-norm robustness of top-$k$ predictions. In this work, we aim to bridge the gap. Our approach is based on randomized smoothing, which builds a provably robust classifier from an arbitrary classifier via randomizing an input. Our major theoretical contribution is an almost tight $\ell_0$-norm certified robustness guarantee for top-$k$ predictions. We empirically evaluate our method on CIFAR10 and ImageNet. For instance, our method can build a classifier that achieves a certified top-3 accuracy of 69.2\% on ImageNet when an attacker can arbitrarily perturb 5 pixels of a testing image.
Google（谷歌）；Carnegie Mellon University（卡内基梅隆大学）；Bosch Center for AI（博世人工智能中心）
In this paper we show how to achieve state-of-the-art certified adversarial robustness to 2-norm bounded perturbations by relying exclusively on off-the-shelf pretrained models. To do so, we instantiate the denoised smoothing approach of Salman et al. 2020 by combining a pretrained denoising diffusion probabilistic model and a standard high-accuracy classifier. This allows us to certify 71% accuracy on ImageNet under adversarial perturbations constrained to be within an 2-norm of 0.5, an improvement of 14 percentage points over the prior certified SoTA using any approach, or an improvement of …
Adversarial training instances can severely distort a model's behavior. This work investigates certified regression defenses, which provide guaranteed limits on how much a regressor's prediction may change under a poisoning attack. Our key insight is that certified regression reduces to voting-based certified classification when using median as a model's primary decision function. Coupling our reduction with existing certified classifiers, we propose six new regressors provably-robust to poisoning attacks. To the extent of our knowledge, this is the first work that certifies the robustness of …
In a \emph{data poisoning attack}, an attacker modifies, deletes, and/or inserts some training examples to corrupt the learnt machine learning model. \emph{Bootstrap Aggregating (bagging)} is a well-known ensemble learning method, which trains multiple base models on random subsamples of a training dataset using a base learning algorithm and uses majority vote to predict labels of testing examples. We prove the intrinsic certified robustness of bagging against data poisoning attacks. Specifically, we show that bagging with an arbitrary base learning algorithm provably predicts the same label f…
Shanghai JiaoTong University（上海交通大学）；The Hong Kong Polytechnic University（香港理工大学）
Neural network classifiers are vulnerable to data poisoning attacks, as attackers can degrade or even manipulate their predictions thorough poisoning only a few training samples. However, the robustness of heuristic defenses is hard to measure. Random selection based defenses can achieve certified robustness by averaging the classifiers' predictions on the sub-datasets sampled from the training set. This paper proposes a framework of random selection based certified defenses against data poisoning attacks. Specifically, we prove that the random selection schemes that satisfy certain conditions…
It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to top-1 predictions. In many real-world applications, top-$k$ predictions are more relevant. In this work, we aim to derive certified robustness for top-$k$ predictions. In particular, our certified robustness is based on randomized smoothing, which turns any classifier to a new classifier via adding noise to an input example. We adopt randomized smoothing because…
Shanghai Jiao Tong University（上海交通大学）；Hong Kong University of Science and Technology（香港科技大学）
The robustness of deep neural networks (DNNs) against adversarial example attacks has raised wide attention. For smoothed classifiers, we propose the worst-case adversarial loss over input distributions as a robustness certificate. Compared with previous certificates, our certificate better describes the empirical performance of the smoothed classifiers. By exploiting duality and the smoothness property, we provide an easy-to-compute upper bound as a surrogate for the certificate. We adopt a noisy adversarial learning procedure to minimize the surrogate loss to improve model robustness. We sho…
University of Southern California（南加州大学）；Emory University（埃默里大学）；Xidian University（西安电子科技大学）
Adversarial data examples have drawn significant attention from the machine learning and security communities. A line of work on tackling adversarial examples is certified robustness via randomized smoothing that can provide a theoretical robustness guarantee. However, such a mechanism usually uses floating-point arithmetic for calculations in inference and requires large memory footprints and daunting computational costs. These defensive models cannot run efficiently on edge devices nor be deployed on integer-only logical units such as Turing Tensor Cores or integer-only ARM processors. To ov…
In this paper, we aim to develop a scalable algorithm to preserve differential privacy (DP) in adversarial learning for deep neural networks (DNNs), with certified robustness to adversarial examples. By leveraging the sequential composition theory in DP, we randomize both input and latent spaces to strengthen our certified robustness bounds. To address the trade-off among model utility, privacy loss, and robustness, we design an original adversarial objective function, based on the post-processing property in DP, to tighten the sensitivity of our model. A new stochastic batch training is propo…
Graph neural networks (GNNs) have recently gained much attention for node and graph classification tasks on graph-structured data. However, multiple recent works showed that an attacker can easily make GNNs predict incorrectly via perturbing the graph structure, i.e., adding or deleting edges in the graph. We aim to defend against such attacks via developing certifiably robust GNNs. Specifically, we prove the certified robustness guarantee of any GNN for both node and graph classifications against structural perturbation. Moreover, we show that our certified robustness guarantee is tight. Our …
Adversarial examples that fool machine learning models, particularly deep neural networks, have been a topic of intense research interest, with attacks and defenses being developed in a tight back-and-forth. Most past defenses are best effort and have been shown to be vulnerable to sophisticated attacks. Recently a set of certified defenses have been introduced, which provide guarantees of robustness to norm-bounded attacks, but they either do not scale to large datasets or are limited in the types of models they can support. This paper presents the first certified defense that both scales to …
Community detection plays a key role in understanding graph structure. However, several recent studies showed that community detection is vulnerable to adversarial structural perturbation. In particular, via adding or removing a small number of carefully selected edges in a graph, an attacker can manipulate the detected communities. However, to the best of our knowledge, there are no studies on certifying robustness of community detection against such adversarial structural perturbation. In this work, we aim to bridge this gap. Specifically, we develop the first certified robustness guarantee …
Center for Data Science, Peking University（北京大学数据科学中心）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；National School of Development, Peking University（北京大学国家发展研究院）；Beijing International Center for Mathematical Research（北京国际数学研究中心）；Institute for Artificial Inteligence, Peking University（北京大学人工智能研究所）
Randomized smoothing has achieved state-of-the-art certified robustness against $l_2$-norm adversarial attacks. However, it is not wholly resolved on how to find the optimal base classifier for randomized smoothing. In this work, we employ a Smoothed WEighted ENsembling (SWEEN) scheme to improve the performance of randomized smoothed classifiers. We show the ensembling generality that SWEEN can help achieve optimal certified robustness. Furthermore, theoretical analysis proves that the optimal SWEEN model can be obtained from training under mild assumptions. We also develop an adaptive predict…
Duke University（杜克大学）；University at Buffalo, SUNY（纽约州立大学布法罗分校）
The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning algorithm. Although a significant body of work on developing defensive models has been considered, most such models are heuristic and are often vulnerable to adaptive attacks. Defensive methods that provide theoretical robustness guarantees have been studied intensively, yet most fail to obtain non-trivial robustness when a large-scale model and data are prese…
Institute of Information Science, Academia Sinica（中央研究院资讯科学研究所）
Randomized smoothing has established state-of-the-art provable robustness against $\ell_2$ norm adversarial attacks with high probability. However, the introduced Gaussian data augmentation causes a severe decrease in natural accuracy. We come up with a question, "Is it possible to construct a smoothed classifier without randomization while maintaining natural accuracy?". We find the answer is definitely yes. We study how to transform any classifier into a certified robust classifier based on a popular and elegant mathematical tool, Bernstein polynomial. Our method provides a deterministic alg…
In recent years, researchers have extensively studied adversarial robustness in a variety of threat models, including L_0, L_1, L_2, and L_infinity-norm bounded adversarial attacks. However, attacks bounded by fractional L_p "norms" (quasi-norms defined by the L_p distance with 0<p<1) have yet to be thoroughly considered. We proactively propose a defense with several desirable properties: it provides provable (certified) robustness, scales to ImageNet, and yields deterministic (rather than high-probability) certified guarantees when applied to quantized data (e.g., images). Our technique for f…
Tsinghua University（清华大学）；RealAI（瑞莱智慧）；Peng Cheng Laboratory（鹏城实验室）；Tsinghua University-China Mobile Communications Group Co., Ltd. Joint Institute（清华大学-中国移动通信集团有限公司联合研究院）；Research Institute of Tsinghua University in Shenzhen（深圳清华大学研究院）
Certified defenses such as randomized smoothing have shown promise towards building reliable machine learning systems against $\ell_p$-norm bounded attacks. However, existing methods are insufficient or unable to provably defend against semantic transformations, especially those without closed-form expressions (such as defocus blur and pixelate), which are more common in practice and often unrestricted. To fill up this gap, we propose generalized randomized smoothing (GSmooth), a unified theoretical framework for certifying robustness against general semantic transformations via a novel dimens…
Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race between defenders who attempt to train robust networks and attackers who try to construct adversarial examples. One promise of ending the arms race is developing certified defenses, ones which are provably robust against all attackers in some family. These certified defenses are based on convex relaxations which construct an upper bound on the worst case loss over…
University of California, Los Angeles（加州大学洛杉矶分校）；IBM Research（IBM研究院）；Massachusetts Institute of Technology（麻省理工学院）
Finding minimum distortion of adversarial examples and thus certifying robustness in neural network classifiers for given data points is known to be a challenging problem. Nevertheless, recently it has been shown to be possible to give a non-trivial certified lower bound of minimum adversarial distortion, and some recent progress has been made towards this direction by exploiting the piece-wise linear nature of ReLU activations. However, a generic robustness certification for general activation functions still remains largely unexplored. To address this issue, in this paper we introduce CROWN,…
Peking University（北京大学）；Princeton University（普林斯顿大学）；Zhongguancun Haihua Institute for Frontier Information Technology（中关村海华前沿信息技术研究院）；Microsoft Research（微软研究院）
It is well-known that standard neural networks, even with a high classification accuracy, are vulnerable to small $\ell_\infty$-norm bounded adversarial perturbations. Although many attempts have been made, most previous works either can only provide empirical verification of the defense to a particular attack method, or can only develop a certified guarantee of the model robustness in limited scenarios. In this paper, we seek for a new approach to develop a theoretically principled neural network that inherently resists $\ell_\infty$ perturbations. In particular, we design a novel neuron that…
DSSmoothing: Toward Certified Dataset Ownership Verification for Pre-trained Language Models via Dual-Space Smoothing
North China Electric Power University（华北电力大学）；Research Institute, China Unicom（中国联合研究院）；Wuhan University（武汉大学）；Beihang University（北京航空航天大学）；Nanyang Technological University（南洋理工大学）
