Data-dependent stability analysis of adversarial training.

Area of Science:

• Deep Learning
• Machine Learning Theory
• Robustness in AI

Background:

• Stability analysis is crucial for deep learning generalization.
• Adversarial training is a key defense against attacks.
• Existing generalization bounds lack data distribution information.

Purpose of the Study:

• To provide generalization bounds for adversarial training that include data distribution.
• To analyze the impact of data distribution and adversarial budget on generalization gaps.
• To improve the understanding of robust generalization in deep learning.

Main Methods:

• Utilizing on-average stability and high-order approximate Lipschitz conditions.
• Deriving generalization bounds for both convex and non-convex losses.
• Analyzing the effects of distribution shifts and adversarial budgets.

Main Results:

• Developed novel generalization bounds incorporating data distribution for adversarial training.
• Bounds are comparable or superior to existing uniform stability-based bounds.
• Demonstrated the influence of distribution shifts from data poisoning on robust generalization.

Conclusions:

• The proposed generalization bounds offer enhanced insights into adversarial training robustness.
• Data distribution significantly impacts generalization gaps in adversarial settings.
• Findings are critical for developing more resilient deep learning models against various attacks.