Machine unlearning is essential for compliance with privacy regulations such as General Data Protection Regulation (GDPR), enabling selective removal of user data from trained models while preserving utility in sensitive applications like healthcare and finance. However, existing methods fail to account for the inherent complexity of loss landscapes and the varying stability of network layers during unlearning, leading to unstable updates, catastrophic forgetting, and poor robustness under large-scale or adversarial deletions. We introduce roughness-informed machine unlearning, a unified framework that explicitly models these challenges through geometric and statistical roughness analysis. Geometric Roughness-Informed Machine Unlearning (GRIMU) stabilizes unlearning by regularizing updates to smooth rugged loss landscapes using the Roughness Index, while Statistical Roughness-Informed Machine Unlearning (SRIMU) prioritizes adjustments in well-trained, spectrally stable layers via heavy-tailed distribution analysis. Empirical evaluations on MNIST, CIFAR-10, CIFAR-100, and UCI Adult demonstrate that GRIMU and SRIMU outperform state-of-the-art baselines including AGU, ORTR, SISA, SCRUB, AmnesiacML, SalUn, and Boundary Unlearning in test accuracy retention, privacy leakage, and KL-divergence across diverse deletion strategies (random, class-specific, and adversarial).
Partohaghighi et al. (Wed,) studied this question.