Randomized Smoothing (RS) is currently a scalable certified defense method
providing robustness certification against adversarial examples. Although
significant progress has been achieved in providing defenses against $\ell_p$
adversaries, the interaction between the smoothing distribution and the
robustness certification still remains vague. In this work, we comprehensively
study the effect of two families of distributions, named Exponential Standard
Gaussian (ESG) and Exponential General Gaussian (EGG) distributions, on
Randomized Smoothing and Double Sampling Randomized Smoothing (DSRS). We derive
an analytic formula for ESG's certified radius, which converges to the origin
formula of RS as the dimension $d$ increases. Additionally, we prove that EGG
can provide tighter constant factors than DSRS in providing $\Omega(\sqrt{d})$
lower bounds of $\ell_2$ certified radius, and thus further addresses the curse
of dimensionality in RS. Our experiments on real-world datasets confirm our
theoretical analysis of the ESG distributions, that they provide almost the
same certification under different exponents $\eta$ for both RS and DSRS. In
addition, EGG

随机平滑是一种可扩展的认证防御方法，提供对抗样本的稳健认证。研究重点在于探讨指数标准高斯分布和指数通用高斯分布对随机平滑和双抽样随机平滑的影响，以解决维度诅咒问题。实验结果验证了指数标准高斯分布在不同指数下对随机平滑和双抽样随机平滑的相同认证效果。