Statistical Roughness-Informed Machine Unlearning

Abstract: Machine unlearning aims to remove the influence of a designated forget set from a trained model while preserving utility on the retained data. In modern deep networks, approximate unlearning frequently fails under large or adversarial deletions due to pronounced layer-wise heterogeneity: some layers exhibit stable, well-regularized representations while others are brittle, undertrained, or overfit, so naive update allocation can trigger catastrophic forgetting or unstable dynamics. We propose Statistical-Roughness Adaptive Gradient Unlearning (SRAGU), a mechanism-first unlearning algorithm that reallocates unlearning updates using layer-wise statistical roughness operationalized via heavy-tailed spectral diagnostics of layer weight matrices. Starting from an Adaptive Gradient Unlearning (AGU) sensitivity signal computed on the forget set, SRAGU estimates a WeightWatcher-style heavy-tailed exponent for each layer, maps it to a bounded spectral stability weight, and uses this stability signal to spectrally reweight the AGU sensitivities before applying the same minibatch update form. This concentrates unlearning motion in spectrally stable layers while damping updates in unstable or overfit layers, improving stability under hard deletions. We evaluate unlearning via behavioral alignment to a gold retrained reference model trained from scratch on the retained data, using empirical prediction-divergence and KL-to-gold proxies on a forget-focused query set; we additionally report membership inference auditing as a complementary leakage signal, treating forget-set points as should-be-forgotten members during evaluation.