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arXiv 2602.00822stat.MLcs.LG
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安全与有效性权衡:对抗数据污染的鲁棒性

Safety-Efficacy Trade Off: Robustness against Data-Poisoning

Mathematical Institute, University of Oxford, UK(牛津大学数学研究所)

Diego Granziol

AI总结:

本文研究了数据污染攻击在输入空间中的鲁棒性问题,通过核岭回归模型揭示了攻击有效性与频谱可见性之间的权衡关系,并提出通过正则化和数据增强抑制污染的方法。

摘要:

后门和数据污染攻击可以在逃避现有频谱和优化防御的同时实现高攻击成功率。我们证明这种行为并非偶然,而是源于输入空间中的基本几何机制。使用核岭回归作为宽神经网络的精确模型,我们证明聚类的污损标签污染会在输入Hessian中引起一个秩一尖峰,其幅度与攻击有效性平方成正比。关键的是,对于非线性核,我们识别出一个近克隆区域,在此区域中,污染有效性保持为一阶,而诱导的输入曲率消失,使攻击在频谱上不可检测。我们进一步证明输入梯度正则化在梯度流下会收缩与污染对齐的Fisher和Hessian特征模式,从而通过减少数据拟合能力产生显式且不可避免的安全有效性权衡。对于指数核,这种防御可以被精确解释为一种各向异性高通滤波器,它增加了有效长度尺度并抑制近克隆污染。在MNIST和CIFAR 10和CIFAR 100上的线性模型和深度卷积网络的广泛实验验证了理论,展示了攻击成功率与频谱可见性之间的一致滞后,并显示正则化和数据增强共同抑制污染。我们的结果确立了当后门本质上不可见时的条件,并提供了首次端到端的污染、可检测性和防御通过输入空间曲率的特征描述。

英文摘要:

Backdoor and data poisoning attacks can achieve high attack success while evading existing spectral and optimisation based defences. We show that this behaviour is not incidental, but arises from a fundamental geometric mechanism in input space. Using kernel ridge regression as an exact model of wide neural networks, we prove that clustered dirty label poisons induce a rank one spike in the input Hessian whose magnitude scales quadratically with attack efficacy. Crucially, for nonlinear kernels we identify a near clone regime in which poison efficacy remains order one while the induced input curvature vanishes, making the attack provably spectrally undetectable. We further show that input gradient regularisation contracts poison aligned Fisher and Hessian eigenmodes under gradient flow, yielding an explicit and unavoidable safety efficacy trade off by reducing data fitting capacity. For exponential kernels, this defence admits a precise interpretation as an anisotropic high pass filter that increases the effective length scale and suppresses near clone poisons. Extensive experiments on linear models and deep convolutional networks across MNIST and CIFAR 10 and CIFAR 100 validate the theory, demonstrating consistent lags between attack success and spectral visibility, and showing that regularisation and data augmentation jointly suppress poisoning. Our results establish when backdoors are inherently invisible, and provide the first end to end characterisation of poisoning, detectability, and defence through input space curvature.

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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