Adversarial Weight Perturbation Helps Robust Generalization (2004.05884v2)

Abstract: The study on improving the robustness of deep neural networks against adversarial examples grows rapidly in recent years. Among them, adversarial training is the most promising one, which flattens the input loss landscape (loss change with respect to input) via training on adversarially perturbed examples. However, how the widely used weight loss landscape (loss change with respect to weight) performs in adversarial training is rarely explored. In this paper, we investigate the weight loss landscape from a new perspective, and identify a clear correlation between the flatness of weight loss landscape and robust generalization gap. Several well-recognized adversarial training improvements, such as early stopping, designing new objective functions, or leveraging unlabeled data, all implicitly flatten the weight loss landscape. Based on these observations, we propose a simple yet effective Adversarial Weight Perturbation (AWP) to explicitly regularize the flatness of weight loss landscape, forming a double-perturbation mechanism in the adversarial training framework that adversarially perturbs both inputs and weights. Extensive experiments demonstrate that AWP indeed brings flatter weight loss landscape and can be easily incorporated into various existing adversarial training methods to further boost their adversarial robustness.

An Analysis of "Adversarial Weight Perturbation Helps Robust Generalization"

The paper "Adversarial Weight Perturbation Helps Robust Generalization" by Dongxian Wu, Shu-Tao Xia, and Yisen Wang investigates the robustness of deep neural networks (DNNs) against adversarial examples. The central theme of this paper focuses on the unexplored territory of the weight loss landscape in adversarial training and proposes a novel approach, Adversarial Weight Perturbation (AWP), which contributes to robust generalization.

Adversarial training (AT) has long been recognized as a crucial method for enhancing the robustness of DNNs against adversarial examples, which are crafted to deceive models by slight, imperceptible modifications to inputs. However, the paper identifies a gap in how existing methodologies address weight perturbations, that is, the alterations in model weights in response to adversarial examples. This paper fills this gap by exploring the weight loss landscape—how weight perturbations affect loss functions—and its impact on robust generalization, which refers to maintaining model performance on adversarial inputs during testing.

Key Contributions

1. Correlation Between Weight Loss Landscape and Robust Generalization Gap: The authors establish a relationship between the flatness of the weight loss landscape and the robust generalization gap in adversarially trained models. Their analyses indicate that methods implicitly flattening the weight loss landscape, such as early stopping and certain loss function designs, correlate with improved robustness.
2. Introduction of Adversarial Weight Perturbation (AWP): AWP is proposed as a mechanism to explicitly flatten the weight loss landscape. It introduces perturbations on weights to find the worst-case scenarios over multiple training examples, offering a complementary strategy to adversarial input perturbations, which focus on individual examples. This dual-perturbation mechanism demonstrably improves robustness in several state-of-the-art adversarial training methods, such as TRADES, MART, and RST.
3. Empirical Evaluation: Extensive experiments reveal that AWP enhances the robustness of adversarial training methods across various datasets (including CIFAR-10 and CIFAR-100), model architectures, and different threat models. A notable improvement in test robustness is achieved using AWP over traditional adversarial training, indicating its efficacy across different contexts.
4. Theoretical Insights: The paper provides a theoretical justification for AWP using a PAC-Bayes bound framework, demonstrating that this approach helps in controlling the generalization gap by optimizing the weight loss landscape's flatness.

Implications and Future Directions

The implications of this research are significant for enhancing the security of machine learning models deployed in adversarial environments. By focusing on weight perturbations, the paper paves the way for more robust models capable of maintaining performance under adversarial conditions. The method's capacity to integrate with existing adversarial training techniques with minimal overhead enhances its practical utility.

The paper opens several avenues for future investigation. Researchers might explore optimizing other aspects of the deep learning architecture or formulating alternative weight perturbation strategies that further improve robustness. Additionally, the exploration of flatter weight loss landscapes could be extended to natural data variations beyond adversarial scenarios, potentially leading to advances in model generalization independent of specific adversarial attacks.

Overall, this paper contributes a substantial advancement in our understanding of adversarial resilience in DNNs by focusing on a novel and effective dimension of the weight loss landscape, with robust empirical evidence supporting its utility in real-world applications.