DFMU: Data-Frugal Machine Unlearning

Privacy protection laws, such as the GDPR, grant individuals the right to request the forgetting of their personal data not only from databases but also from machine learning (ML) models trained on them. Machine unlearning has emerged as a practical means to facilitate model forgetting of data instances seen during training. Although some existing machine unlearning methods guarantee exact forgetting, they are typically costly in computational terms. On the other hand, more affordable methods do not offer forgetting guarantees and are applicable only to specific ML models. In this paper, we present \emph{efficient unlearning with privacy guarantees} (EUPG), a novel machine unlearning framework that offers formal privacy guarantees to individuals whose data are being unlearned. EUPG involves pre-training ML models on data protected using privacy models, and it enables {\em efficient unlearning with the privacy guarantees offered by the privacy models in use}. Through empirical evaluation on four heterogeneous data sets protected with $k$-anonymity and $ε$-differential privacy as privacy models, our approach demonstrates utility and forgetting effectiveness comparable to those of exact unlearning methods, while significantly reducing computational and storage costs. Our code is available at https://github.com/najeebjebreel/EUPG.

We propose PURGE, a machine unlearning algorithm built on a simple but an under-exploited observation: continual learning (CL) and machine unlearning (MU) which are fundamentally dual problems. CL tries to learn new tasks without forgetting old ones; MU tries to erase specific data without hurting retained performance representing the same underlying tension in opposite directions. PURGE leverages this duality by adapting gradient projection from A-GEM (Chaudhry et al., 2019) so that every unlearning step is constrained to not increase the retain-set loss. On top of this, it performs multi-layer representation erasure, pushing forget-set activations in intermediate layers towards the retain distribution to remove information from hidden representations rather than just suppressing it at the output. A key design choice is the retain-confusion target: rather than pushing forget outputs toward the uniform distribution, which we found to be surprisingly easy for membership inference attacks to detect, we instead target the model's natural confusion pattern on retain data. This makes the unlearned model hard to distinguish from one retrained from scratch. Two self-regulating stopping criteria (a retain-loss budget and a forget-accuracy target) let the algorithm decide on its own when to stop, removing the need for manual epoch tuning. In experiments on five datasets (CIFAR-10, MNIST, SVHN, STL10, PathMNIST) across 22 class-level forgetting tasks, PURGE consistently keeps retain accuracy above 96% while achieving MIA AUROC close to 0.5 (the ideal), outperforming gradient ascent, KL-uniform, and several published baselines on the privacy-utility frontier.

Large language models deployed in sensitive applications increasingly require the ability to unlearn specific knowledge, such as user requests, copyrighted materials, or outdated information, without retraining from scratch to ensure regulatory compliance, user privacy, and safety. This task, known as machine unlearning, aims to remove the influence of targeted data (forgetting) while maintaining performance on the remaining data (retention). A common approach is to formulate this as a multi-objective problem and reduce it to a single-objective problem via scalarization, where forgetting and retention losses are combined using a weighted sum. However, this often results in unstable training dynamics and degraded model utility due to conflicting gradient directions. To address these challenges, we propose OFMU, a penalty-based bi-level optimization framework that explicitly prioritizes forgetting while preserving retention through a hierarchical structure. Our method enforces forgetting via an inner maximization step that incorporates a similarity-aware penalty to decorrelate the gradients of the forget and retention objectives, and restores utility through an outer minimization step. To ensure scalability, we develop a two-loop algorithm with provable convergence guarantees under both convex and non-convex regimes. We further provide a rigorous theoretical analysis of convergence rates and show that our approach achieves better trade-offs between forgetting efficacy and model utility compared to prior methods. Extensive experiments across vision and language benchmarks demonstrate that OFMU consistently outperforms existing unlearning methods in both forgetting efficacy and retained utility.