Bridging Mode Connectivity in Loss Landscapes and Adversarial Robustness (2005.00060v2)

Abstract: Mode connectivity provides novel geometric insights on analyzing loss landscapes and enables building high-accuracy pathways between well-trained neural networks. In this work, we propose to employ mode connectivity in loss landscapes to study the adversarial robustness of deep neural networks, and provide novel methods for improving this robustness. Our experiments cover various types of adversarial attacks applied to different network architectures and datasets. When network models are tampered with backdoor or error-injection attacks, our results demonstrate that the path connection learned using limited amount of bonafide data can effectively mitigate adversarial effects while maintaining the original accuracy on clean data. Therefore, mode connectivity provides users with the power to repair backdoored or error-injected models. We also use mode connectivity to investigate the loss landscapes of regular and robust models against evasion attacks. Experiments show that there exists a barrier in adversarial robustness loss on the path connecting regular and adversarially-trained models. A high correlation is observed between the adversarial robustness loss and the largest eigenvalue of the input Hessian matrix, for which theoretical justifications are provided. Our results suggest that mode connectivity offers a holistic tool and practical means for evaluating and improving adversarial robustness.

• The paper demonstrates that mode connectivity paths between models can effectively mitigate backdoor attacks using limited clean data.
• The study identifies a robustness loss barrier between regular and adversarially-trained models in evasion attacks, suggesting challenges in improving robustness without affecting generalization.
• A significant correlation is found between robustness loss in adversarial attacks and the largest eigenvalue of the input Hessian matrix, linking landscape curvature to attack vulnerability.

Bridging Mode Connectivity in Loss Landscapes and Adversarial Robustness

The paper "Bridging Mode Connectivity in Loss Landscapes and Adversarial Robustness" investigates the connection between mode connectivity and adversarial robustness in neural networks. The authors explore the geometric properties of loss landscapes to enhance adversarial robustness through mode connectivity, a concept that describes high-accuracy pathways between trained neural networks.

The paper evaluates various neural network architectures and datasets under different adversarial scenarios: backdoor attacks, error-injection attacks, and evasion attacks. The core claim is that mode connectivity provides an effective mechanism to mitigate these adversarial effects while preserving model accuracy on clean data, using only limited amounts of bonafide data.

Key Contributions

1. Connection Paths After Adversarial Tampering: The paper demonstrates that connecting models with tampered paths can mitigate backdoor attacks using limited clean data. For example, models on a path between two tampered models showed significant improvement in attack failure rates, nearly reaching 0% from almost 100%. This suggests that mode connectivity offers a promising approach to repairing adversarially-modified models.
2. Loss Landscape Analysis Against Evasion Attacks: The paper identifies a robustness loss barrier between regular and adversarially-trained models in evasion attacks, supporting the hypothesis that there is no free lunch in adversarial robustness. This geometric perspective indicates that enhancing adversarial robustness without affecting model generalization is challenging.
3. High Correlation Between Robustness Loss and Hessian Eigenvalue: A significant correlation is observed between the robustness loss in adversarial attacks and the largest eigenvalue of the input Hessian matrix. This insight offers a deeper understanding of the local loss landscape's curvature in the context of adversarial attacks, aligning theoretical assumptions with empirical observations.

Implications and Future Directions

• Robust Model Training:

The findings imply that mode connectivity could be utilized strategically for designing pathways that enhance model resilience to adversarial perturbations. This can be particularly helpful in areas requiring stringent security against model manipulation, such as autonomous systems and financial applications.

• Extended Applications:

While primarily focused on standard classification tasks, the framework might be applicable to diverse machine learning problems requiring robustness, such as reinforcement learning or sequence prediction.

• Expanding Geometric Analysis:

Future research may further explore different geometrical aspects of loss landscapes and their implications for model robustness. Insights gathered could drive innovations in adversarial training and robust architectural designs.

Overall, the research offers substantial evidence that mode connectivity not only enriches our understanding of loss landscapes but also serves as a practical tool for improving adversarial robustness in neural networks. This could set a foundation for developing sophisticated defense mechanisms in AI systems, showcasing both the theoretical and empirical applications of mode connectivity principles.