Hippocampal indexing alters the stability landscape of synaptic weight space allowing life-long learning.

Systems-level consolidation holds that the hippocampus rapidly encodes new information during wakefulness, and that coordinated cortico-hippocampal replay during subsequent sleep transfers and stabilizes those traces in cortex. This idea captures key learning principles, but exactly how replay reshapes the synaptic-weight landscape - creating new representations while preserving old ones - remains unclear. To address this, we used a biophysically realistic network model to probe the effects of slow-wave sleep (SWS) on synaptic-weight space. We show that previously learned memories are stable attractors in that space, and that hippocampus-driven interactions between sharp-wave ripples and cortical slow waves push the system into new attractor states that jointly encode old and new memories. As a result, replay allows recently acquired information to be incorporated without degrading prior memories. Our results offer a novel mechanistic - and conveniently "geometric" - framework for understanding how sleep-driven replay sculpts synaptic weights during consolidation.