AUCPro: AUC-Oriented Provable Robustness Learning.

Area of Science:

• Machine Learning
• Deep Neural Networks
• Adversarial Robustness

Background:

• Traditional provable robustness methods for deep neural networks (DNNs) often assume balanced class distributions.
• Real-world applications, particularly safety-sensitive systems, frequently encounter imbalanced datasets with a long-tailed distribution.
• The Area Under the ROC Curve (AUC) is a more suitable metric for evaluating model performance on imbalanced datasets compared to accuracy.

Purpose of the Study:

• To propose the first AUC-oriented provable robustness learning framework (AUCPro) designed for long-tailed distributions.
• To theoretically analyze the certified safety region and robustness generalization of the proposed AUCPro framework.
• To investigate the performance-robustness trade-off and excess risk in the context of AUC-based robustness.

Main Methods:

• Developed AUCPro, a framework that utilizes a proxy model smoothed by isotropic Gaussian noise.
• Optimized the proxy model from an AUC-oriented learning perspective.
• Derived theoretical guarantees for a certified safety region against $\ell _{2}$ℓ2 adversarial attacks and proposed a novel standard for robustness generalization.

Main Results:

• Established a certified safety region for AUCPro, ensuring freedom from $\ell _{2}$ℓ2 adversarial attacks within this region.
• Proposed a new theoretical framework to study robustness generalization for provable robustness methods, linking it to the adversarial risk of AUC.
• Demonstrated the efficacy of AUCPro through comprehensive experiments, validating its performance and generalization capabilities.

Conclusions:

• AUCPro offers a robust solution for deep neural networks facing imbalanced data distributions.
• The study introduces a novel approach to understanding and improving robustness generalization in provable robustness learning.
• The findings are crucial for developing reliable AI systems in safety-critical domains with long-tailed data.