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arXiv · 2011.14085

Deterministic Certification to Adversarial Attacks via Bernstein Polynomial Approximation

Ching-Chia Kao·Jhe-Bang Ko·Chun-Shien Lu
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Abstract

Randomized smoothing has established state-of-the-art provable robustness against $\ell_2$ norm adversarial attacks with high probability. However, the introduced Gaussian data augmentation causes a severe decrease in natural accuracy. We come up with a question, "Is it possible to construct a smoothed classifier without randomization while maintaining natural accuracy?". We find the answer is definitely yes. We study how to transform any classifier into a certified robust classifier based on a popular and elegant mathematical tool, Bernstein polynomial. Our method provides a deterministic algorithm for decision boundary smoothing. We also introduce a distinctive approach of norm-independent certified robustness via numerical solutions of nonlinear systems of equations. Theoretical analyses and experimental results indicate that our method is promising for classifier smoothing and robustness certification.

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Ching-Chia Kao, Jhe-Bang Ko, Chun-Shien Lu. 2020-11-28. Deterministic Certification to Adversarial Attacks via Bernstein Polynomial Approximation. https://arxiv.org/abs/2011.14085

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