Robust LLM Unlearning Against Relearning Attacks: The Minor Components in Representations Matter

Large language model (LLM) unlearning aims to remove specific data influences from pre-trained model without costly retraining, addressing privacy, copyright, and safety concerns. However, recent studies reveal a critical vulnerability: unlearned models rapidly recover "forgotten" knowledge through relearning attacks. This fragility raises serious security concerns, especially for open-weight models. In this work, we investigate the fundamental mechanism underlying this fragility from a representation geometry perspective. We discover that existing unlearning methods predominantly optimize along dominant components, leaving minor components largely unchanged. Critically, during relearning attacks, the modifications in these dominant components are easily reversed, enabling rapid knowledge recovery, whereas minor components exhibit stronger resistance to such reversal. We further provide a theoretical analysis that explains both observations from the spectral structure of representations. Building on this insight, we propose Minor Component Unlearning (MCU), a novel unlearning approach that explicitly targets minor components in representations. By concentrating unlearning effects in these inherently robust directions, our method achieves substantially improved resistance to relearning attacks. Extensive experiments on three datasets validate our approach, demonstrating significant improvements over state-of-the-art methods including sharpness-aware minimization.