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版本更新 · v3arXiv:2602.16596

Sequential Membership Inference Attacks

Thomas Michel, Debabrota Basu, Emilie Kaufmann

原文摘要

Modern AI models are not static. They go through multiple updates in their lifecycles. We propose to design Sequential Membership Inference (SeMI) attacks leading to tighter privacy audits by exploiting the sequence of models and injecting a target canary at a controlled insertion time. First, for empirical mean computation, we develop SeMI*, an optimal SeMI attack to identify the presence of a target inserted at a specific insertion step. We derive the power of SeMI* to show that accessing the model sequence yields more powerful MI attacks than scrutinising only the final model. SeMI* exhibits an isolation property. Its power depends on the statistics obtained right before and after insertion of the target. Leveraging this insight, we develop practical white-box (accessing model gradients) and black-box (accessing loss) SeMI attacks against models trained with (DP-)SGD. Across datasets and models trained with (DP-)SGD, our experiments show that SeMI attacks achieve higher power than snapshot-independent baselines, and yield tighter privacy audits thanks to (a) control over the insertion time and (b) observations across the model sequence. Code is available at https://github.com/Thomick/pysemi.

cs.LG · cs.CR · math.ST · stat.ML

新论文 · v1arXiv:2611.06364

Estimating the Volume of a Union of Convex Bodies

Eeshan Banerjee, Aranya Kumar Bal, Debabrota Basu, Sourav Chakraborty, Debarshi Chanda, Uddalok Sarkar

原文摘要

The \textit{Union Volume Estimation problem}, i.e. yielding an $(\varepsilon, δ)$-approximation of the volume of the union of convex bodies, is a classical problem in computational geometry and formal methods. In this paper, we first detect where and why the efficient union volume estimators with approximate sampling and PAC volume estimation oracles fail. Specifically, we show that having only TV-distance guarantees on the approximate sampler does not suffice, and demonstrate this bottleneck by constructing the sunflower families of convex bodies. In this context, we propose the concept of \textit{tail-controlled samplers} that can yield with high-probability almost-$\ell_{\infty}$ closeness. Secondly, we leverage this concept to propose a generic algorithmic framework \texttt{Alpona} that properly combines a PAC volume computation and approximate point sampling oracles with tail-controls to yield an $(\varepsilon, δ)$-estimate of the union volume for any collection of convex bodies. We show that \texttt{Alpona} needs only linear (in number of convex bodies) oracle calls to be $(\varepsilon, δ)$-correct. Finally, we provide a tail-controlled analysis of the Hit-and-Run sampler~\citep{lovasz2006fast}. We further provide a novel geometric analysis to improve the required walk length of Hit-and-Run. We further instantiate \texttt{Alpona}'s correctness for the sparse frequency streams of convex bodies: a special case of the union volume estimation problem where no convex body intersects more than $τ$ many other bodies.

cs.DS