Decoupling Knowledge and Privacy: Post-Task Self-Distillation Replay for LLM Continual Learning
Privacy-preserving continual learning (PPCL) must reduce the reproduction of sensitive content while retaining useful knowledge across sequential tasks. Formal privacy guarantees characterize randomized mechanisms, whereas operational output control concerns whether a trained model selectively reduces the likelihood of sensitive content in its outputs. In this work, we investigate the latter together with continual-learning utility under realistic task evolution. Retention and privacy correction operate at different granularities: task acquisition requires broad preservation of current- and old-task behavior, whereas privacy correction targets sparse annotated positions. Joint optimization leaves the current-task preservation target continually changing. We propose SPARK, a retention-correction decomposition that first freezes the learned post-task distribution and then applies selective correction around this stable reference. Self-Distillation Replay learns the current task while distilling behavior from previous tasks, and Post-Task Privacy Correction reduces annotated-PII likelihood while anchoring current- and old-task non-PII behavior to the resulting checkpoint. Extensive evaluations demonstrate that SPARK achieves effective selective PII suppression while preserving strong continual-learning utility and knowledge retention across diverse settings. Code and data will be released upon publication.