On the Misalignment Between Data Learnability and Forgettability in Machine Unlearning

Abstract

We report a structural mismatch between a data point’s {learnability}—how quickly it improves the loss—and its {forgettability}—how much it anchors the final parameters—an aspect ignored by prior machine unlearning frameworks such as SISA, Fisher-Forget, and influence-based fine-tuning. To make this gap measurable we introduce Unlearning Gradient Sensitivity (UGS), an influence score computable with a single Hutch++ sketch, and derive the Learnability–Forgettability Divergence (LFD), the Jensen–Shannon distance between the model’s learning and forgetting distributions. We prove that UGS dispersion decays exponentially only under explicit regularisation and that LFD converges to zero when its weight grows sub-linearly relative to the UGS term. Building on these findings, we introduce Dual-Aware Training (DAT)—a lightweight regularization method that reduces variability in how easily data points can be forgotten and aligns learning and forgetting behaviors during training. On CIFAR-10, MNIST, and IMDB, DAT maintains the original model accuracy while cutting forgettability divergence in half and significantly lowering the cost of certified unlearning, showing that it’s effective to make models forgettable from the start.