Sleep renormalizes learning-perturbed cortical dynamics to stabilize memory

The brain must preserve learning-induced circuit changes without destabilizing the network dynamics required for future learning. We show that sleep addresses this tension through perturbation-dependent renormalization of cortical dynamics. Using high-density electroencephalography in humans following declarative learning and a matched non-learning control, we found that learning displaced cortical population dynamics during wakefulness, followed by an opposing reorganization during non-rapid eye movement (NREM) sleep. The preceding waking perturbation constrained this sleep response across time, cortical space, and individuals: NREM activity evolved along the wake-defined state-space direction, regions with larger waking perturbations showed stronger opposing responses, and larger perturbations predicted stronger restorative trajectories. This cross-state geometry generalized to held-out participants and predicted sleep-specific memory benefit beyond either state alone or their simple difference. Neural stability is therefore achieved by regulating trajectories rather than returning to a fixed baseline, with plasticity-induced perturbations specifying how cortical state space is reorganized to preserve learned structure while enabling further change.