Local robustness ensures that a model classifies all inputs within an $\ell_2$-ball consistently, which precludes various forms of adversarial inputs. In this paper, we present a fast procedure for checking local robustness in feed-forward neural networks with piecewise-linear activation functions. Such networks partition the input space into a set of convex polyhedral regions in which the network's behavior is linear; hence, a systematic search for decision boundaries within the regions around a given input is sufficient for assessing robustness. Crucially, we show how the regions around a point can be analyzed using simple geometric projections, thus admitting an efficient, highly-parallel GPU implementation that excels particularly for the $\ell_2$ norm, where previous work has been less effective. Empirically we find this approach to be far more precise than many approximate verification approaches, while at the same time performing multiple orders of magnitude faster than complete verifiers, and scaling to much deeper networks.
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,…
Certified defenses against small-norm adversarial examples have received growing attention in recent years; though certified accuracies of state-of-the-art methods remain far below their non-robust counterparts, despite the fact that benchmark datasets have been shown to be well-separated at far larger radii than the literature generally attempts to certify. In this work, we offer insights that identify potential factors in this performance gap. Specifically, our analysis reveals that piecewise linearity imposes fundamental limitations on the tightness of leading certification techniques. Thes…
Northwestern University（西北大学）；University of Liverpool（利物浦大学）
The robustness of deep neural networks has received significant interest recently, especially when being deployed in safety-critical systems, as it is important to analyze how sensitive the model output is under input perturbations. While most previous works focused on the local robustness property around an input sample, the studies of the global robustness property, which bounds the maximum output change under perturbations over the entire input space, are still lacking. In this work, we formulate the global robustness certification for neural networks with ReLU activation functions as a mix…
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab, IBM Research（IBM研究院MIT-IBM沃森人工智能实验室）
Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial distortion of neural networks (with ReLU activations) has been shown to be an NP-complete problem, obtaining a non-trivial lower bound of minimum distortion as a provable robustness guarantee is possible. However, most previous works only focused on simple fully-connected layers (multilayer perceptrons) and were limited to ReLU activations. This motivates us…
Cornell University（康奈尔大学）；Alibaba Group Inc.（阿里巴巴集团）
Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded adversarial perturbations. However, how to train a good base classifier that is accurate and robust when smoothed has not been fully investigated. In this work, we derive a new regularized risk, in which the regularizer can adaptively encourage the accuracy and robustness of the smoothed counterpart when training the base classifier. It is computationally efficient a…
Northwestern University（西北大学）；Boston University（波士顿大学）；University of Liverpool（利物浦大学）
With the increment of interest in leveraging machine learning technology in safety-critical systems, the robustness of neural networks under external disturbance receives more and more concerns. Global robustness is a robustness property defined on the entire input domain. And a certified globally robust network can ensure its robustness on any possible network input. However, the state-of-the-art global robustness certification algorithm can only certify networks with at most several thousand neurons. In this paper, we propose the GPU-supported global robustness certification framework GROCET…
University of California, Berkeley（加州大学伯克利分校）；Tsinghua-Berkeley Shenzhen Institute（清华-伯克利深圳学院）
In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and control systems. Certification techniques using convex optimization have been proposed, but they often suffer from relaxation errors that void the certificate. Our work exploits the structure of ReLU networks to improve relaxation errors through a novel partition-based certification procedure. The proposed method is proven to tighten existing linear programmi…
ETH Zurich（苏黎世联邦理工学院）；UIUC（伊利诺伊大学厄巴纳-香槟分校）；VMware Research（威睿研究部）
Formal verification of neural networks is critical for their safe adoption in real-world applications. However, designing a precise and scalable verifier which can handle different activation functions, realistic network architectures and relevant specifications remains an open and difficult challenge. In this paper, we take a major step forward in addressing this challenge and present a new verification framework, called PRIMA. PRIMA is both (i) general: it handles any non-linear activation function, and (ii) precise: it computes precise convex abstractions involving multiple neurons via nove…
Selective Risk Certification for LLM Outputs via Information-Lift Statistics: PAC-Bayes, Robustness, and Skeleton Design
Department of Computer Science Iowa State University（计算机科学系爱荷华州立大学）；Department of Civil, Construction and Environmental Engineering Iowa State University（土木、建设与环境工程系爱荷华州立大学）
In this discussion paper, we survey recent research surrounding robustness of machine learning models. As learning algorithms become increasingly more popular in data-driven control systems, their robustness to data uncertainty must be ensured in order to maintain reliable safety-critical operations. We begin by reviewing common formalisms for such robustness, and then move on to discuss popular and state-of-the-art techniques for training robust machine learning models as well as methods for provably certifying such robustness. From this unification of robust machine learning, we identify and…
University of Illinois（伊利诺伊大学）；ETH Zürich（苏黎世联邦理工学院）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Peking University（北京大学）
As machine learning (ML) systems become pervasive, safeguarding their security is critical. However, recently it has been demonstrated that motivated adversaries are able to mislead ML systems by perturbing test data using semantic transformations. While there exists a rich body of research providing provable robustness guarantees for ML models against $\ell_p$ norm bounded adversarial perturbations, guarantees against semantic perturbations remain largely underexplored. In this paper, we provide TSS -- a unified framework for certifying ML robustness against general adversarial semantic trans…
Generative neural networks can be used to specify continuous transformations between images via latent-space interpolation. However, certifying that all images captured by the resulting path in the image manifold satisfy a given property can be very challenging. This is because this set is highly non-convex, thwarting existing scalable robustness analysis methods, which are often based on convex relaxations. We present ApproxLine, a scalable certification method that successfully verifies non-trivial specifications involving generative models and classifiers. ApproxLine can provide both sound …
Recent work has exposed the vulnerability of computer vision models to vector field attacks. Due to the widespread usage of such models in safety-critical applications, it is crucial to quantify their robustness against such spatial transformations. However, existing work only provides empirical robustness quantification against vector field deformations via adversarial attacks, which lack provable guarantees. In this work, we propose novel convex relaxations, enabling us, for the first time, to provide a certificate of robustness against vector field transformations. Our relaxations are model…
There has been a rapid development and interest in adversarial training and defenses in the machine learning community in the recent years. One line of research focuses on improving the performance and efficiency of adversarial robustness certificates for neural networks \cite{gowal:19, wong_zico:18, raghunathan:18, WengTowardsFC:18, wong:scalable:18, singh:convex_barrier:19, Huang_etal:19, single-neuron-relax:20, Zhang2020TowardsSA}. While each providing a certification to lower (or upper) bound the true distortion under adversarial attacks via relaxation, less studied was the tightness of re…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial or worst-case inputs, but researchers have recently shown a need for methods that consider random input noise. In this paper, we examine the setting where inputs are subject to random noise coming from an arbitrary probability distribution. We propose a robustness certification method that lower-bounds the probability that network outputs are safe. This bound is cast as a chance-constrained opt…
The existence of adversarial examples poses a real danger when deep neural networks are deployed in the real world. The go-to strategy to quantify this vulnerability is to evaluate the model against specific attack algorithms. This approach is however inherently limited, as it says little about the robustness of the model against more powerful attacks not included in the evaluation. We develop a unified mathematical framework to describe relaxation-based robustness certification methods, which go beyond adversary-specific robustness evaluation and instead provide provable robustness guarantees…
Defence Science and Technology Group（国防科学技术集团）；University of Melbourne（墨尔本大学）
In response to subtle adversarial examples flipping classifications of neural network models, recent research has promoted certified robustness as a solution. There, invariance of predictions to all norm-bounded attacks is achieved through randomised smoothing of network inputs. Today's state-of-the-art certifications make optimal use of the class output scores at the input instance under test: no better radius of certification (under the $L_2$ norm) is possible given only these score. However, it is an open question as to whether such lower bounds can be improved using local information aroun…
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…
Carnegie Mellon University（卡内基梅隆大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
A vast literature shows that the learning-based visual perception model is sensitive to adversarial noises, but few works consider the robustness of robotic perception models under widely-existing camera motion perturbations. To this end, we study the robustness of the visual perception model under camera motion perturbations to investigate the influence of camera motion on robotic perception. Specifically, we propose a motion smoothing technique for arbitrary image classification models, whose robustness under camera motion perturbations could be certified. The proposed robustness certificati…
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…
University of Manchester（曼彻斯特大学）；University of Utah（犹他大学）
Graph Laplacian (GL)-based semi-supervised learning is one of the most used approaches for classifying nodes in a graph. Understanding and certifying the adversarial robustness of machine learning (ML) algorithms has attracted large amounts of attention from different research communities due to its crucial importance in many security-critical applied domains. There is great interest in the theoretical certification of adversarial robustness for popular ML algorithms. In this paper, we provide the first adversarial robust certification for the GL classifier. More precisely we quantitatively bo…
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…
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…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Carnegie Mellon University（卡内基梅隆大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Amazon AWS AI（亚马逊AWS人工智能部门）
As reinforcement learning (RL) has achieved near human-level performance in a variety of tasks, its robustness has raised great attention. While a vast body of research has explored test-time (evasion) attacks in RL and corresponding defenses, its robustness against training-time (poisoning) attacks remains largely unanswered. In this work, we focus on certifying the robustness of offline RL in the presence of poisoning attacks, where a subset of training trajectories could be arbitrarily manipulated. We propose the first certification framework, COPA, to certify the number of poisoning trajec…
CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）；ETH Zurich（苏黎世联邦理工学院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；VMware Research（VMware研究院）
The use of deep 3D point cloud models in safety-critical applications, such as autonomous driving, dictates the need to certify the robustness of these models to real-world transformations. This is technically challenging, as it requires a scalable verifier tailored to point cloud models that handles a wide range of semantic 3D transformations. In this work, we address this challenge and introduce 3DCertify, the first verifier able to certify the robustness of point cloud models. 3DCertify is based on two key insights: (i) a generic relaxation based on first-order Taylor approximations, applic…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Washington University in St. Louis（圣路易斯华盛顿大学）；Carnegie Mellon University（卡内基梅隆大学）
As reinforcement learning (RL) has achieved great success and been even adopted in safety-critical domains such as autonomous vehicles, a range of empirical studies have been conducted to improve its robustness against adversarial attacks. However, how to certify its robustness with theoretical guarantees still remains challenging. In this paper, we present the first unified framework CROP (Certifying Robust Policies for RL) to provide robustness certification on both action and reward levels. In particular, we propose two robustness certification criteria: robustness of per-state actions and …
University of Göttingen（哥廷根大学）；neurocat GmbH（neurocat有限公司）
Machine learning image classifiers are susceptible to adversarial and corruption perturbations. Adding imperceptible noise to images can lead to severe misclassifications of the machine learning model. Using $L_p$-norms for measuring the size of the noise fails to capture human similarity perception, which is why optimal transport based distance measures like the Wasserstein metric are increasingly being used in the field of adversarial robustness. Verifying the robustness of classifiers using the Wasserstein metric can be achieved by proving the absence of adversarial examples (certification)…
High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior certification work requires strong assumptions on network structures and massive computational costs, and thus the range of their applications was limited. From the relationship between the Lipschitz constants and prediction margins, we present a computationally efficient calculation technique to lower-bound the size of adversarial perturbations that can deceiv…
Cooperative multi-agent reinforcement learning (c-MARL) is widely applied in safety-critical scenarios, thus the analysis of robustness for c-MARL models is profoundly important. However, robustness certification for c-MARLs has not yet been explored in the community. In this paper, we propose a novel certification method, which is the first work to leverage a scalable approach for c-MARLs to determine actions with guaranteed certified bounds. c-MARL certification poses two key challenges compared with single-agent systems: (i) the accumulated uncertainty as the number of agents increases; (ii…
