Distance Is Not Enough: Forget-Retain Alignment Gap Predicts LLM Relearning Robustness

Making large language models (LLMs) deeply forget specific knowledge and values without sacrificing general capabilities remains a central challenge in unlearning. Current methods are easily reversed by fine-tuning or few-shot prompting, suggesting their forgetting is only shallow. We identify the root cause. Existing methods target representations shared with both the retain set and the subspace recovered by a fine-tuning attacker, making unlearning both disruptive to general capabilities and easy to reverse. We propose RepSelect (Representation Selectivity), which isolates forget-set-specific representations by collapsing top principal components of weight gradients before each update, leaving general capabilities intact while limiting what fine-tuning can recover. We evaluate across two forget categories, biohazardous knowledge and abusive tendencies, and four model families spanning dense and Mixture-of-Experts architectures (Llama 3, Qwen 3.5, Gemma 4 E4B, DeepSeek V2 Lite). Compared to five popular baselines (GradDiff, NPO, SimNPO, RMU, UNDIAL), RepSelect achieves a 4-50x larger reduction in post-relearning answer accuracy than the strongest baseline, and is near-perfectly robust to few-shot prompting attacks. Targeting selective representations is thus an important step towards deep and robust LLM forgetting.

Large Language Model (LLM) unlearning is often evaluated primarily by target suppression and clean retain utility. These metrics can miss a local failure mode: a model may perform well on standard retain prompts, yet degrade on benign reasoning when prompts lie near the forgotten domain. This phenomenon is termed forget-adjacent utility loss. A fundamental question is: where should forget representations go after they leave the removed behavior? Successful unlearning depends not only on whether forget-conditioned representations depart from the harmful computation, but also on the direction in which they are redirected afterward. We propose RA$^2$ (Retain-Anchored Attraction), a latent-space unlearning method that redirects forget-token states toward nearby retain-supported representations while preserving higher-layer behavior on retain data. On WMDP and MUSE, RA$^2$ yields higher forget-adjacent utility than strong unlearning baselines at similar broad-utility levels. These results show that the migration direction of forget representations materially affects benign behavior near the forget boundary. Our code is available at https://github.com/ZacLing/retain_anchored_attraction.

Unlearning aims to remove selected knowledge from large language models to mitigate privacy and safety risks while preserving useful capabilities. For models that continue to be fine-tuned after release, this goal is insufficient: they must also resist relearning the deleted knowledge while preserving plasticity, the ability to learn new tasks. Existing defenses train against simulated relearning while trying to preserve useful capabilities, but low relearning alone cannot distinguish selective resistance from a general loss of plasticity. Evaluating preservation after an update requires deciding what the updated model should remain close to. A pre-update reference penalizes useful changes induced by the update simply because they depart from earlier outputs. We therefore formulate the reference-timing hypothesis that, at comparable target suppression, an update-matched reference better preserves plasticity than a pre-update one. To test and address this hypothesis, we propose Update-Matched Unlearning (UMU), which applies the same simulated relearning update to the defended model and to an undefended reference initialized from the same unlearned model, and uses new-task learning to guide model selection. Extensive experiments on TOFU and FaithUn with Llama and Qwen models show that UMU improves both relearning resistance and plasticity across all three base unlearning methods, lowering harmful and benign relearning by 30.4 and 9.9 points on average while raising new-task accuracy by 3.5 points. When the reference does not receive the update, relearning remains similarly low but new-task accuracy falls below the base method, supporting the reference-timing hypothesis and showing that robust unlearning should prevent recovery selectively without suppressing learning itself.