Certified Adversarial Robustness with Additive Noise

Abstract: The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning algorithm. Although a significant body of work on developing defensive models has been considered, most such models are heuristic and are often vulnerable to adaptive attacks. Defensive methods that provide theoretical robustness guarantees have been studied intensively, yet most fail to obtain non-trivial robustness when a large-scale model and data are present. To address these limitations, we introduce a framework that is scalable and provides certified bounds on the norm of the input manipulation for constructing adversarial examples. We establish a connection between robustness against adversarial perturbation and additive random noise, and propose a training strategy that can significantly improve the certified bounds. Our evaluation on MNIST, CIFAR-10 and ImageNet suggests that the proposed method is scalable to complicated models and large data sets, while providing competitive robustness to state-of-the-art provable defense methods.

• The paper introduces a certified robustness bound that quantifies permissible adversarial perturbations with theoretical rigor.
• It leverages additive Gaussian noise during training to enhance defenses while preserving high natural accuracy.
• Empirical results on MNIST, CIFAR-10, and ImageNet demonstrate scalability and improved performance over methods like TRADES and PixelDP.

Certified Adversarial Robustness with Additive Noise

This paper addresses the ongoing challenge in deep learning involving adversarial examples—subtle perturbations of inputs that can lead to incorrect model outputs. While various heuristic defense mechanisms have been proposed to withstand adversarial attacks, theoretical robustness guarantees remain difficult, especially for large-scale models and datasets. This paper presents a novel framework that provides certified bounds on permissible input perturbations, thus ensuring adversarial robustness.

Key Contributions

1. Certified Robustness Bound: The authors derive a theoretical bound for adversarial robustness applicable to general network structures and activation functions. The bound is tight for $\ell_1$ perturbations in binary classification settings.
2. Connection to Additive Noise: A pivotal insight of this work is the relationship established between adversarial robustness and additive random noise. This connection is leveraged to develop a training strategy that enhances robustness bounds.
3. Empirical Demonstration: Evaluations on datasets such as MNIST, CIFAR-10, and ImageNet demonstrate the framework's scalability and its competitive performance relative to state-of-the-art provable defense methods.

Methodology

The paper introduces a certified robustness framework that integrates the notion of additive noise into adversarial defense mechanisms. By deploying random Gaussian noise during data preprocessing, the model suppresses the impact of adversarial perturbations. Theoretical analysis rooted in R{é}nyi divergence is used to quantify the robustness, offering a tight upper bound for tolerable perturbation sizes.

Experimental Results

Empirical results underscore the efficacy of the method:

• The proposed approach significantly improves certified bounds on MNIST and CIFAR-10 datasets compared to prior certifications.
• In contrast to methods like TRADES, the framework maintains high natural accuracy while boosting robustness against substantial adversarial perturbations.
• On large-scale datasets like ImageNet, the approach outperforms prior PixelDP bounds, reinforcing its applicability to complex and large neural networks.

Implications and Future Directions

This framework bridges the gap between empirically successful defenses and theoretically certified robustness, suggesting that improving robustness to random noise could also bolster defenses against adversarial perturbations. The method's scalability with model complexity makes it appealing for real-world applications where robustness guarantees are crucial.

For future work, potential avenues include extending the framework to consider multiple noise types and exploring its application within other machine learning contexts, such as unsupervised learning and reinforcement learning. The exploration of tighter bounds and refining training strategies could further consolidate its position as a robust defense mechanism against adversarial attacks.

In conclusion, this paper contributes a scalable, theoretically justified framework for adversarial defense, promising to elevate the resilience of neural networks to adversarial perturbations while maintaining competitive accuracy.