Understanding and evaluating the robustness of neural networks under adversarial settings is a subject of growing interest. Attacks proposed in the literature usually work with models trained to minimize cross-entropy loss and output softmax probabilities. In this work, we present interesting experimental results that suggest the importance of considering other loss functions and target representations, specifically, (1) training on mean-squared error and (2) representing targets as codewords generated from a random codebook. We evaluate the robustness of neural networks that implement these proposed modifications using existing attacks, showing an increase in accuracy against untargeted attacks of up to 98.7 and a decrease of targeted attack success rates of up to 99.8 . Our model demonstrates more robustness compared to its conventional counterpart even against attacks that are tailored to our modifications. Furthermore, we find that the parameters of our modified model have significantly smaller Lipschitz bounds, an important measure correlated with a model's sensitivity to adversarial perturbations.
Several defenses have also been proposed. To date, the most effective defense technique is adversarial training ( @cite_25 , @cite_22 , @cite_23 , @cite_16 ), where the model is trained on a mix of clean and adversarial data. This has shown to provide a regularization effect that makes models more robust towards attacks.
@cite_22 @cite_16 @cite_25 @cite_23
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Adversarial examples are perturbed inputs designed to fool machine learning models. Adversarial training injects such examples into training data to increase robustness. To scale this technique to large datasets, perturbations are crafted using fast single-step methods that maximize a linear approximation of the model's loss. We show that this form of adversarial training converges to a degenerate global minimum, wherein small curvature artifacts near the data points obfuscate a linear approximation of the loss. The model thus learns to generate weak perturbations, rather than defend against strong ones. As a result, we find that adversarial training remains vulnerable to black-box attacks, where we transfer perturbations computed on undefended models, as well as to a powerful novel single-step attack that escapes the non-smooth vicinity of the input data via a small random step. We further introduce Ensemble Adversarial Training, a technique that augments training data with perturbations transferred from other models. On ImageNet, Ensemble Adversarial Training yields models with strong robustness to black-box attacks. In particular, our most robust model won the first round of the NIPS 2017 competition on Defenses against Adversarial Attacks. Adversarial examples are malicious inputs designed to fool machine learning models. They often transfer from one model to another, allowing attackers to mount black box attacks without knowledge of the target model's parameters. Adversarial training is the process of explicitly training a model on adversarial examples, in order to make it more robust to attack or to reduce its test error on clean inputs. So far, adversarial training has primarily been applied to small problems. In this research, we apply adversarial training to ImageNet. Our contributions include: (1) recommendations for how to succesfully scale adversarial training to large models and datasets, (2) the observation that adversarial training confers robustness to single-step attack methods, (3) the finding that multi-step attack methods are somewhat less transferable than single-step attack methods, so single-step attacks are the best for mounting black-box attacks, and (4) resolution of a "label leaking" effect that causes adversarially trained models to perform better on adversarial examples than on clean examples, because the adversarial example construction process uses the true label and the model can learn to exploit regularities in the construction process. Neural networks are vulnerable to adversarial examples and researchers have proposed many heuristic attack and defense mechanisms. We address this problem through the principled lens of distributionally robust optimization, which guarantees performance under adversarial input perturbations. By considering a Lagrangian penalty formulation of perturbing the underlying data distribution in a Wasserstein ball, we provide a training procedure that augments model parameter updates with worst-case perturbations of training data. For smooth losses, our procedure provably achieves moderate levels of robustness with little computational or statistical cost relative to empirical risk minimization. Furthermore, our statistical guarantees allow us to efficiently certify robustness for the population loss. For imperceptible perturbations, our method matches or outperforms heuristic approaches.