为无害数据投毒生成可验证的水印，防止滥用

In recent years, data poisoning attacks have been increasingly designed to appear harmless and even beneficial, often with the intention of verifying dataset ownership or safeguarding private data from unauthorized use. However, these developments have the potential to cause misunderstandings and conflicts, as data poisoning has traditionally been regarded as a security threat to machine learning systems. To address this issue, it is imperative for harmless poisoning generators to claim ownership of their generated datasets, enabling users to identify potential poisoning to prevent misuse. In this paper, we propose the deployment of watermarking schemes as a solution to this challenge. We introduce two provable and practical watermarking approaches for data poisoning: {\em post-poisoning watermarking} and {\em poisoning-concurrent watermarking}. Our analyses demonstrate that when the watermarking length is $Θ(\sqrt{d}/ε_w)$ for post-poisoning watermarking, and falls within the range of $Θ(1/ε_w^2)$ to $O(\sqrt{d}/ε_p)$ for poisoning-concurrent watermarking, the watermarked poisoning dataset provably ensures both watermarking detectability and poisoning utility, certifying the practicality of watermarking under data poisoning attacks. We validate our theoretical findings through experiments on several attacks, models, and datasets.