Learning with Unlearning: Synaptic Role Partitioning for Simultaneous Continual Learning and Machine Unlearning

Continual Learning (CL) asks a model to acquire new knowledge without forgetting what it already knows. Machine Unlearning (MU) asks it to destroy specific knowledge without damaging the rest. The challenge is having them in the same system simultaneously; the two objectives pull on the same weights, and an edit made for one harms the other. To address this, we propose Learning with Unlearning (LwU), a unified framework that resolves the conflict at the level where it occurs, the individual synapse. LwU scores every weight twice, once against the data to keep and once against the data to delete, and partitions the network into four zones with separate update rules. Weights that only require retention are frozen. Weights that only require deletion are cleared and returned to the network as free capacity. Contested weights take a gradient-ascent step projected orthogonally to the retention gradient. The remaining capacity learns the incoming task by a privileged teacher via self-distillation. Deletion is served post hoc, and no retraining is required. Across both CL and MU jobs, LwU outperforms or matches the strongest baseline. Its real-world practicality has been demonstrated on the Physical Artificial Intelligence (PAI) dataset we conducted. Additionally, in the image generation task and in removing dangerous content, it outperformed the closest baseline, as shown in Fig.1.