{"ID":2874054,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.05865","arxiv_id":"2509.05865","title":"The Measure of Deception: An Analysis of Data Forging in Machine Unlearning","abstract":"Motivated by privacy regulations and the need to mitigate the effects of harmful data, machine unlearning seeks to modify trained models so that they effectively ``forget'' designated data. A key challenge in verifying unlearning is \\emph{forging} -- adversarially crafting data that mimics the gradient of a target point, thereby creating the appearance of unlearning without actually removing information. To capture this phenomenon, we consider the collection of data points whose gradients approximate a target gradient within tolerance $ε$ -- which we call an $ε$-forging set -- and develop a framework for its analysis. For linear regression and one-layer neural networks, we show that the Lebesgue measure of this set is small. It scales on the order of $ε$, and when $ε$ is small enough, $ε^d$. More generally, under mild regularity assumptions, we prove that the forging set measure decays as $ε^{(d-r)/2}$, where $d$ is the data dimension and $r\u003cd$ is the dimension of vector space of right singular vectors corresponding to ``small'' singular values of a variation matrix defined by the model gradients. Extensions to batch SGD and almost-everywhere smooth loss functions yield the same asymptotic scaling. In addition, we establish probability bounds showing that, under non-degenerate data distributions, the likelihood of randomly sampling a forging point is vanishingly small. These results provide evidence that adversarial forging is fundamentally limited and that false unlearning claims can, in principle, be detected.","short_abstract":"Motivated by privacy regulations and the need to mitigate the effects of harmful data, machine unlearning seeks to modify trained models so that they effectively ``forget'' designated data. A key challenge in verifying unlearning is \\emph{forging} -- adversarially crafting data that mimics the gradient of a target poin...","url_abs":"https://arxiv.org/abs/2509.05865","url_pdf":"https://arxiv.org/pdf/2509.05865v2","authors":"[\"Rishabh Dixit\",\"Yuan Hui\",\"Rayan Saab\"]","published":"2025-09-06T23:44:05Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}