# Deterministic Certification to Adversarial Attacks via Bernstein Polynomial Approximation

arXiv: https://arxiv.org/abs/2011.14085 · HTML: https://mlsanity.com/paper/2011.14085/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2020.

## Built on by (most cited first, 1 of 1)

- [Improved, Deterministic Smoothing for L_1 Certified Robustness](https://mlsanity.com/paper/2103.10834/) (2021)

## Abstract (arXiv)

Randomized smoothing has established state-of-the-art provable robustness against ℓ2 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.