论文标题
通过伯恩斯坦多项式近似对对抗性攻击的确定性认证
Deterministic Certification to Adversarial Attacks via Bernstein Polynomial Approximation
论文作者
论文摘要
随机平滑性已经建立了最先进的可证明的鲁棒性，以$ \ ell_2 $ norm vorm vormestrial攻击具有很高的概率。但是，引入的高斯数据增强导致自然精度严重降低。我们提出了一个问题：“是否可以在保持自然准确性的同时构建平滑的分类器而无需随机分类？”。我们发现答案绝对是。我们研究了如何根据流行而优雅的数学工具Bernstein多项式将任何分类器转换为认证的鲁棒分类器。我们的方法为决策边界平滑提供了确定性算法。我们还通过非线性方程系统的数值解决方案引入了独立于规范的认证鲁棒性的独特方法。理论分析和实验结果表明，我们的方法对于分类器的平滑和鲁棒性认证有希望。
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.
