Approaching Adversarial Example Classification with Chaos Theory

Area of Science:

• Deep Learning
• Chaos Theory
• Image Processing

Background:

• Adversarial examples, imperceptible input perturbations, pose a significant challenge to robust deep learning models.
• Current research focuses on developing attack/defense methods and detecting adversarial examples to mitigate risks.

Purpose of the Study:

• To investigate the application of chaos theory methods for distinguishing adversarial examples from regular images.
• To assess the robustness of Lyapunov exponents in adversarial example detection and explore complementary methods.

Main Methods:

• Utilized Lyapunov exponents, a measure of chaoticity, to analyze deep network behavior.
• Investigated the impact of image processing transformations on Lyapunov exponent robustness.
• Proposed a complementary approach combining Lyapunov exponents with image entropy for enhanced discrimination.

Main Results:

• Lyapunov exponents alone are not robust to image processing transformations altering image entropy.
• Integrating image entropy with Lyapunov exponents significantly improves the accuracy of adversarial example detection.
• The proposed method achieved 65%-100% accuracy on MNIST, Fashion-MNIST, and CIFAR 19 datasets against diverse attacks and transformations.

Conclusions:

• Chaos theory, particularly when combined with image entropy, offers a robust approach to detecting adversarial examples.
• The findings suggest a pathway to enhance classifier robustness against adversarial attacks in real-world and threatening scenarios.