Image classification is vulnerable to adversarial attacks. This work investigates the robustness of Saak transform against adversarial attacks towards high performance image classification. We develop a complete image classification system based on multi-stage Saak transform. In the Saak transform domain, clean and adversarial images demonstrate different distributions at different spectral dimensions. Selection of the spectral dimensions at every stage can be viewed as an automatic denoising process. Motivated by this observation, we carefully design strategies of feature extraction, representation and classification that increase adversarial robustness. The performances with well-known datasets and attacks are demonstrated by extensive experimental evaluations.
Use of knowledge distillation when training networks can be used as defense against adversarial samples @cite_10 . Reinforcement of network structure by using bounded ReLU activations help in enhancing stability to adversarial perturbations @cite_3 . Pixel defend is used as an image purification process, as described in @cite_17 .
@cite_10 @cite_3 @cite_17
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Deep learning algorithms have been shown to perform extremely well on manyclassical machine learning problems. However, recent studies have shown thatdeep learning, like other machine learning techniques, is vulnerable to adversarial samples: inputs crafted to force adeep neural network (DNN) to provide adversary-selected outputs. Such attackscan seriously undermine the security of the system supported by the DNN, sometimes with devastating consequences. For example, autonomous vehicles canbe crashed, illicit or illegal content can bypass content filters, or biometricauthentication systems can be manipulated to allow improper access. In thiswork, we introduce a defensive mechanism called defensive distillationto reduce the effectiveness of adversarial samples on DNNs. We analyticallyinvestigate the generalizability and robustness properties granted by the useof defensive distillation when training DNNs. We also empirically study theeffectiveness of our defense mechanisms on two DNNs placed in adversarialsettings. The study shows that defensive distillation can reduce effectivenessof sample creation from 95 to less than 0.5 on a studied DNN. Such dramaticgains can be explained by the fact that distillation leads gradients used inadversarial sample creation to be reduced by a factor of 1030. We alsofind that distillation increases the average minimum number of features thatneed to be modified to create adversarial samples by about 800 on one of theDNNs we tested. Deep learning algorithms have been shown to perform extremely well on many classical machine learning problems. However, recent studies have shown that deep learning, like other machine learning techniques, is vulnerable to adversarial samples: inputs crafted to force a deep neural network (DNN) to provide adversary-selected outputs. Such attacks can seriously undermine the security of the system supported by the DNN, sometimes with devastating consequences. For example, autonomous vehicles can be crashed, illicit or illegal content can bypass content filters, or biometric authentication systems can be manipulated to allow improper access. In this work, we introduce a defensive mechanism called defensive distillation to reduce the effectiveness of adversarial samples on DNNs. We analytically investigate the generalizability and robustness properties granted by the use of defensive distillation when training DNNs. We also empirically study the effectiveness of our defense mechanisms on two DNNs placed in adversarial settings. The study shows that defensive distillation can reduce effectiveness of sample creation from 95 to less than 0.5 on a studied DNN. Such dramatic gains can be explained by the fact that distillation leads gradients used in adversarial sample creation to be reduced by a factor of 10^30. We also find that distillation increases the average minimum number of features that need to be modified to create adversarial samples by about 800 on one of the DNNs we tested. Adversarial perturbations of normal images are usually imperceptible to humans, but they can seriously confuse state-of-the-art machine learning models. What makes them so special in the eyes of image classifiers? In this paper, we show empirically that adversarial examples mainly lie in the low probability regions of the training distribution, regardless of attack types and targeted models. Using statistical hypothesis testing, we find that modern neural density models are surprisingly good at detecting imperceptible image perturbations. Based on this discovery, we devised PixelDefend, a new approach that purifies a maliciously perturbed image by moving it back towards the distribution seen in the training data. The purified image is then run through an unmodified classifier, making our method agnostic to both the classifier and the attacking method. As a result, PixelDefend can be used to protect already deployed models and be combined with other model-specific defenses. Experiments show that our method greatly improves resilience across a wide variety of state-of-the-art attacking methods, increasing accuracy on the strongest attack from 63 to 84 for Fashion MNIST and from 32 to 70 for CIFAR-10. The rapidly growing body of research in adversarial machine learning has demonstrated that deep neural networks (DNNs) are highly vulnerable to adversarially generated images. This underscores the urgent need for practical defense techniques that can be readily deployed to combat attacks in real-time. Observing that many attack strategies aim to perturb image pixels in ways that are visually imperceptible, we place JPEG compression at the core of our proposed SHIELD defense framework, utilizing its capability to effectively "compress away" such pixel manipulation. To immunize a DNN model from artifacts introduced by compression, SHIELD "vaccinates" the model by retraining it with compressed images, where different compression levels are applied to generate multiple vaccinated models that are ultimately used together in an ensemble defense. On top of that, SHIELD adds an additional layer of protection by employing randomization at test time that compresses different regions of an image using random compression levels, making it harder for an adversary to estimate the transformation performed. This novel combination of vaccination, ensembling, and randomization makes SHIELD a fortified multi-pronged defense. We conducted extensive, large-scale experiments using the ImageNet dataset, and show that our approaches eliminate up to 98 of gray-box attacks delivered by strong adversarial techniques such as Carlini-Wagner's L2 attack and DeepFool. Our approaches are fast and work without requiring knowledge about the model.