Decoupling Direction and Norm for Efficient Gradient-Based L2 Adversarial Attacks and Defenses (1811.09600v3)

Abstract: Research on adversarial examples in computer vision tasks has shown that small, often imperceptible changes to an image can induce misclassification, which has security implications for a wide range of image processing systems. Considering $L_2$ norm distortions, the Carlini and Wagner attack is presently the most effective white-box attack in the literature. However, this method is slow since it performs a line-search for one of the optimization terms, and often requires thousands of iterations. In this paper, an efficient approach is proposed to generate gradient-based attacks that induce misclassifications with low $L_2$ norm, by decoupling the direction and the norm of the adversarial perturbation that is added to the image. Experiments conducted on the MNIST, CIFAR-10 and ImageNet datasets indicate that our attack achieves comparable results to the state-of-the-art (in terms of $L_2$ norm) with considerably fewer iterations (as few as 100 iterations), which opens the possibility of using these attacks for adversarial training. Models trained with our attack achieve state-of-the-art robustness against white-box gradient-based $L_2$ attacks on the MNIST and CIFAR-10 datasets, outperforming the Madry defense when the attacks are limited to a maximum norm.

• The paper introduces the Decoupled Direction and Norm (DDN) attack that optimizes perturbation direction and norm separately to produce effective L2 adversarial examples.
• Experimental results on MNIST, CIFAR-10, and ImageNet show that DDN achieves similar attack performance to the C&W method while drastically reducing iteration count and computational time.
• The proposed approach facilitates more efficient adversarial training and robustness evaluation, enabling quicker deployment of secure AI systems.

Decoupling Direction and Norm for Efficient Gradient-Based $L_2$ Adversarial Attacks and Defenses

The paper "Decoupling Direction and Norm for Efficient Gradient-Based $L_2$ Adversarial Attacks and Defenses" presents a novel approach to adversarial attacks in computer vision, focusing on overcoming the limitations of the Carlini and Wagner (C&W) method. The primary objective is to generate $L_2$ norm adversarial examples in fewer iterations, rendering the attack method viable for adversarial training purposes.

Key Contributions

The paper introduces the Decoupled Direction and Norm (DDN) attack, which addresses two main challenges in adversarial example generation: 1) achieving a low $L_2$ norm, and 2) ensuring the misclassification of the input data. The method proposed decouples the direction and norm of the perturbation, optimizing the cross-entropy loss and projecting perturbations onto an $L_2$-sphere centered at the original image.

Experimental Results

The DDN attack is evaluated against well-known datasets (MNIST, CIFAR-10, and ImageNet) and demonstrates performance comparable to the state-of-the-art C&W method but with significantly reduced computational resource requirements. For example, on the ImageNet dataset, DDN can successfully attack 1,000 images in less than 10 minutes, whereas C&W requires over 35 hours. In terms of numerical results, DDN achieves performance with norms close to C&W while requiring as few as 100 iterations.

Practical and Theoretical Implications

This new attack algorithm has two critical implications:

1. Efficiency in Training: By significantly reducing the iteration requirement, DDN can be effectively integrated into adversarial training frameworks, which enhances a model's robustness against white-box adversarial attacks.
2. Robustness Evaluation: The reduction in computational cost facilitates quicker evaluations of the robustness of models, making it feasible to deploy such assessments in real-time environments.

Future Directions

The introduction of DDN opens pathways for further research in adaptive adversarial training methods that harness efficient adversarial generation techniques. A possible extension could involve exploring the integration of DDN with other forms of regularization and network architectures besides convolutional neural networks. Furthermore, the principles employed in decoupling direction and norm might be expanded to other types of norm-based adversarial attacks, such as $L_1$ or $L_\infty$, providing a more comprehensive understanding of robust defenses in AI models.

Conclusion

This paper's contribution to reducing the computational burden associated with generating adversarial examples is significant, allowing robust methods to be developed and tested more efficiently. As adversarial attacks remain a vital area of paper in artificial intelligence, innovations such as the DDN facilitate advancements in defensive strategies and ensure AI systems are both reliable and secure in an increasingly complex digital landscape.