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arXiv 2602.03415cs.LG

大多数卷积网络受到小对抗扰动的困扰

Most Convolutional Networks Suffer from Small Adversarial Perturbations

The Hebrew University(海法大学)

Amit Daniely, Idan Mehalel

AI总结:

本文证明了在随机CNN中存在小对抗扰动,并展示了如何通过梯度下降一步找到这些扰动。

摘要:

对抗示例的存在对于随机全连接神经网络而言相对了解,但对于卷积神经网络(CNNs)则了解较少。最近的工作[Daniely, 2025]确立了在CNN中可以找到对抗示例,且在输入的非最优距离下。我们扩展了这项工作,并证明在随机CNN中,输入维度为d的情况下,可以在ℓ₂距离为顺序‖x‖/√d的范围内找到对抗示例,这基本上是最近的可能。我们还展示了可以使用梯度下降的一次步骤找到这样的对抗小扰动。为了推导我们的结果,我们使用傅里叶分解来高效地界随机线性卷积算子的奇异值,这是一层CNN的主要成分。这个界限可能有独立的兴趣。

英文摘要:

The existence of adversarial examples is relatively understood for random fully connected neural networks, but much less so for convolutional neural networks (CNNs). The recent work [Daniely, 2025] establishes that adversarial examples can be found in CNNs, in some non-optimal distance from the input. We extend over this work and prove that adversarial examples in random CNNs with input dimension $d$ can be found already in $\ell_2$-distance of order $\lVert x \rVert /\sqrt{d}$ from the input $x$, which is essentially the nearest possible. We also show that such adversarial small perturbations can be found using a single step of gradient descent. To derive our results we use Fourier decomposition to efficiently bound the singular values of a random linear convolutional operator, which is the main ingredient of a CNN layer. This bound might be of independent interest.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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