KAN-Robust-Bench：用于评估柯尔莫哥洛夫-阿诺德网络（Kolmogorov-Arnold Networks，KAN）鲁棒性的基准

中文摘要 AI 辅助

尽管机器学习模型在诸多领域展现出强劲性能，但面对对抗性威胁时存在显著脆弱性。对抗性攻击分为多种类别，研究中最突出的是规避攻击：攻击者生成人类肉眼无法察觉的样本扰动版本，这类样本通常能以高置信度欺骗机器学习模型，对模型安全性构成重大威胁。本文研究各类柯尔莫哥洛夫-阿诺德网络（KAN）架构在强规避攻击下的可验证鲁棒性与经验鲁棒性。首先，给出随机平滑（randomized smoothing）和区间边界传播（interval bound propagation）的数学基础，报告随机平滑下模型的$\boldsymbol{\textit{l}}_2$可验证鲁棒性；随后，系统评估各类带防御与无防御的KAN模型在FGSM、PGD、C&W攻击下的鲁棒性，以探寻最优防御策略与架构。

英文摘要

While machine learning models have demonstrated strong performance in many domains, these models have shown profound vulnerabilities when they are exposed to adversarial threats. While adversarial attacks fall into various categories, the most prominent category in research studies is evasion. In evasion attacks, the adversary generates perturbed versions of samples, which might not be observable by human eyes. These samples generally fool the machine learning models with high confidence. This phenomenon poses a significant security violation against machine learning models. In this paper, we investigate the certified and empirical robustness of various Kolmogorov-Arnold network architectures against strong evasion attacks. At first, we provide the mathematical foundations for randomized smoothing and interval bound propagation, and report the $\ell_2$-certified robustness of the models under randomized smoothing. After that, we systematically evaluate the robustness of various defended and undefended KAN models under FGSM, PGD, and C&W attacks in order to find out the optimal defense strategies and architectures.

发表机构

• University of New Brunswick（新不伦瑞克大学）

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