Training Provably Robust Models by Polyhedral Envelope Regularization

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computer Vision

Background:

• Adversarial attacks pose a significant threat to the reliability of neural networks.
• Existing methods for certifiable robustness offer limited fine-grained guarantees.
• There is a need for efficient techniques to improve provable robustness.

Purpose of the Study:

• To introduce a novel framework for achieving provable adversarial-free regions around input data.
• To develop polyhedral envelope regularization (PER) to enhance certified robustness.
• To demonstrate the effectiveness and flexibility of PER across various neural network architectures.

Main Methods:

• Utilizing a polyhedral envelope to define provable adversarial-free regions.
• Implementing polyhedral envelope regularization (PER) during model training.
• Evaluating the framework on standard benchmarks with diverse network architectures and activation functions.

Main Results:

• The proposed framework provides more fine-grained certified robustness compared to existing methods.
• PER effectively enlarges adversarial-free regions, leading to improved provable robustness.
• The approach achieves state-of-the-art robustness guarantees with negligible computational overhead.
• Maintained high accuracy on clean data across various settings.

Conclusions:

• Polyhedral envelope regularization (PER) is a flexible and effective method for enhancing certified robustness in neural networks.
• PER offers superior robustness guarantees and accuracy with minimal computational cost.
• The framework is applicable to various network architectures and activation functions, demonstrating broad utility.