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Register a new userRandom Projections for Improved Adversarial Robustness
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Ginevra Carbone
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We propose two training techniques for improving the robustness of Neural Networks to adversarial attacks, i.e. manipulations of the inputs that are maliciously crafted to fool networks into incorrect predictions. Both methods are independent of the chosen attack and leverage random projections of the original inputs, with the purpose of exploiting both dimensionality reduction and some characteristic geometrical properties of adversarial perturbations. The first technique is called RP-Ensemble and consists of an ensemble of networks trained on multiple project
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Whilst adversarial attack detection has received considerable attention, it remains a fundamentally challenging problem from two perspectives. First, while threat models can be well-defined, attacker strategies may still vary widely within those constraints. Therefore, detection should be considered as an open-set problem, standing in contrast to most current detection strategies. These methods take a closed-set view and train binary detectors, thus biasing detection toward attacks seen during detector training. Second, information is limited at test time and confounded by nuisance factors including the label and underlying content of the image. Many of the current high-performing techniques use training sets for dealing with some of these issues, but can be limited by the overall size and diversity of those sets during the detection step. We address these challenges via a novel strategy based on random subspace analysis. We present a technique that makes use of special properties of random projections, whereby we can characterize the behavior of clean and adversarial examples across a diverse set of subspaces. We then leverage the self-consistency (or inconsistency) of model activations to discern clean from adversarial examples. Performance evaluation demonstrates that our technique outperforms ($>0.92$ AUC) competing state of the art (SOTA) attack strategies, while remaining truly agnostic to the attack method itself. It also requires significantly less training data, composed only of clean examples, when compared to competing SOTA methods, which achieve only chance performance, when evaluated in a more rigorous testing scenario.
Adversarial training is one of the most effective approaches defending against adversarial examples for deep learning models. Unlike other defense strategies, adversarial training aims to promote the robustness of models intrinsically. During the last few years, adversarial training has been studied and discussed from various aspects. A variety of improvements and developments of adversarial training are proposed, which were, however, neglected in existing surveys. For the first time in this survey, we systematically review the recent progress on adversarial training for adversarial robustness with a novel taxonomy. Then we discuss the generalization problems in adversarial training from three perspectives. Finally, we highlight the challenges which are not fully tackled and present potential future directions.
While great progress has been made at making neural networks effective across a wide range of visual tasks, most models are surprisingly vulnerable. This frailness takes the form of small, carefully chosen perturbations of their input, known as adversarial examples, which represent a security threat for learned vision models in the wild -- a threat which should be responsibly defended against in safety-critical applications of computer vision. In this paper, we advocate for and experimentally investigate the use of a family of logit regularization techniques as an adversarial defense, which can be used in conjunction with other methods for creating adversarial robustness at little to no marginal cost. We also demonstrate that much of the effectiveness of one recent adversarial defense mechanism can in fact be attributed to logit regularization, and show how to improve its defense against both white-box and black-box attacks, in the process creating a stronger black-box attack against PGD-based models. We validate our methods on three datasets and include results on both gradient-free attacks and strong gradient-based iterative attacks with as many as 1,000 steps.
Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are relatively robust to random noise. In this paper, we propose to study a textit{semi-random} noise regime that generalizes both the random and worst-case noise regimes. We propose the first quantitative analysis of the robustness of nonlinear classifiers in this general noise regime. We establish precise theoretical bounds on the robustness of classifiers in this general regime, which depend on the curvature of the classifiers decision boundary. Our bounds confirm and quantify the empirical observations that classifiers satisfying curvature constraints are robust to random noise. Moreover, we quantify the robustness of classifiers in terms of the subspace dimension in the semi-random noise regime, and show that our bounds remarkably interpolate between the worst-case and random noise regimes. We perform experiments and show that the derived bounds provide very accurate estimates when applied to various state-of-the-art deep neural networks and datasets. This result suggests bounds on the curvature of the classifiers decision boundaries that we support experimentally, and more generally offers important insights onto the geometry of high dimensional classification problems.
We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms~(JLT), we propose two tensorized random projection maps relying on the tensor train~(TT) and CP decomposition format, respectively. The two maps offer very low memory requirements and can be applied efficiently when the inputs are low rank tensors given in the CP or TT format. Our theoretical analysis shows that the dense Gaussian matrix in JLT can be replaced by a low-rank tensor implicitly represented in compressed form with random factors, while still approximately preserving the Euclidean distance of the projected inputs. In addition, our results reveal that the TT format is substantially superior to CP in terms of the size of the random projection needed to achieve the same distortion ratio. Experiments on synthetic data validate our theoretical analysis and demonstrate the superiority of the TT decomposition.
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