[2603.03172] Less Noise, Same Certificate: Retain Sensitivity for Unlearning

Computer Science > Machine Learning arXiv:2603.03172 (cs) [Submitted on 3 Mar 2026] Title:Less Noise, Same Certificate: Retain Sensitivity for Unlearning Authors:Carolin Heinzler, Kasra Malihi, Amartya Sanyal View a PDF of the paper titled Less Noise, Same Certificate: Retain Sensitivity for Unlearning, by Carolin Heinzler and 2 other authors View PDF HTML (experimental) Abstract:Certified machine unlearning aims to provably remove the influence of a deletion set $U$ from a model trained on a dataset $S$, by producing an unlearned output that is statistically indistinguishable from retraining on the retain set $R:=S\setminus U$. Many existing certified unlearning methods adapt techniques from Differential Privacy (DP) and add noise calibrated to global sensitivity, i.e., the worst-case output change over all adjacent datasets. We show that this DP-style calibration is often overly conservative for unlearning, based on a key observation: certified unlearning, by definition, does not require protecting the privacy of the retained data $R$. Motivated by this distinction, we define retain sensitivity as the worst-case output change over deletions $U$ while keeping $R$ fixed. While insufficient for DP, retain sensitivity is exactly sufficient for unlearning, allowing for the same certificates with less noise. We validate these reductions in noise theoretically and empirically across several problems, including the weight of minimum spanning trees, PCA, and ERM. Finally, we refi...