Hyperspherical Local Margin Retraction for Zero-Shot Instance-Wise Machine Unlearning

Zero-shot machine unlearning aims to remove the influence of specified training instances from a pretrained model when the retain set is unavailable. Instance-wise unlearning further operates at the level of individual instances, where a forget instance may induce instance-specific representation and margin deviations that are entangled with class-relevant local structure. However, without retain instances, separating these deviations from the structure that retraining would preserve is difficult, exposing retain-forget entanglement in representation space. We propose HLMR, a novel zero-shot instance-wise unlearning approach that formulates unlearning as local margin retraction in hyperspherical representation space. HLMR uses hyperspherical geodesic probes to construct a local reference in representation space, preserving the structure supported by this reference while unlearning instance-specific margin excess. Empirical evaluation across multiple dataset--architecture settings shows that HLMR aligns more closely with the retraining oracle in utility and membership-inference risk than state-of-the-art zero-shot baselines.