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arXiv 2412.00537cs.LGcs.CR
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针对标签投毒的(图)神经网络精确认证

Exact Certification of (Graph) Neural Networks Against Label Poisoning

Technical University of Munich(慕尼黑工业大学);Munich Data Science Institute(慕尼黑数据科学研究所);Munich Center for Machine Learning(慕尼黑机器学习中心)

Mahalakshmi Sabanayagam, Lukas Gosch, Stephan Günnemann, Debarghya Ghoshdastidar

AI总结:

本文提出首个针对神经网络标签投毒攻击的精确认证方法,利用神经正切核将双层优化问题转化为混合整数线性规划,为图神经网络推导出样本级和集体级鲁棒性证书。

摘要:

机器学习模型极易受到标签翻转的攻击,即通过对抗性修改(投毒)训练标签来破坏模型性能。因此,推导鲁棒性证书对于保证测试预测不受影响以及理解最坏情况下的鲁棒性行为至关重要。然而,对于图神经网络(GNNs),认证标签翻转的问题至今尚未解决。我们通过引入一种精确认证方法改变了这一现状,推导出了样本级和集体级证书。我们的方法利用神经正切核(NTK)来捕捉宽网络的训练动态,使我们能够将表示标签翻转的双层优化问题重新表述为混合整数线性规划(MILP)。我们将该方法应用于节点分类任务中,以认证广泛的GNN架构。因此,关于标签翻转的最坏情况鲁棒性:$(i)$ 我们在不同的基准图上建立了GNN的层级关系;$(ii)$ 量化了激活函数、深度和跳跃连接等架构选择的影响;令人惊讶的是,$(iii)$ 我们发现在所有研究的数据集和架构中,中等扰动预算下鲁棒性出现停滞的新现象。虽然我们专注于GNNs,但我们的证书通过NTK通常适用于足够宽的NNs。因此,我们的工作提出了有史以来第一个为神经网络推导出的针对投毒攻击的精确证书,这可能具有独立的研究价值。代码可在 https://github.com/saper0/qpcert 获取。

英文摘要:

Machine learning models are highly vulnerable to label flipping, i.e., the adversarial modification (poisoning) of training labels to compromise performance. Thus, deriving robustness certificates is important to guarantee that test predictions remain unaffected and to understand worst-case robustness behavior. However, for Graph Neural Networks (GNNs), the problem of certifying label flipping has so far been unsolved. We change this by introducing an exact certification method, deriving both sample-wise and collective certificates. Our method leverages the Neural Tangent Kernel (NTK) to capture the training dynamics of wide networks enabling us to reformulate the bilevel optimization problem representing label flipping into a Mixed-Integer Linear Program (MILP). We apply our method to certify a broad range of GNN architectures in node classification tasks. Thereby, concerning the worst-case robustness to label flipping: $(i)$ we establish hierarchies of GNNs on different benchmark graphs; $(ii)$ quantify the effect of architectural choices such as activations, depth and skip-connections; and surprisingly, $(iii)$ uncover a novel phenomenon of the robustness plateauing for intermediate perturbation budgets across all investigated datasets and architectures. While we focus on GNNs, our certificates are applicable to sufficiently wide NNs in general through their NTK. Thus, our work presents the first exact certificate to a poisoning attack ever derived for neural networks, which could be of independent interest. The code is available at https://github.com/saper0/qpcert.

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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