Can your Attractors Adapt? : Persistent Read and Write in Associative Memory

Associative memory networks recover stored information by evolving incomplete cues towards learned attractors. Most existing formulations assue a fixed memory bank and therefore leave a central problem unsolved : How can memories be added without unpredictable damaging the landscape that supports future recall? Persistence has the properly of changing the dynamics of all future memories during ingestion. For this reason, we introduce **Attractor Lifecycle Control ( ALC )**, a framework for persistent read and write operations over a versioned energy landscape and reading as controlled navigation through it. During recall, a transient query lens reshapes the geometry seen by the dynamics without altering the persistent base landscape. During writing, candidate updates are evaluated for their effects on memory separation, attractor stability and perviously stored content before they can modify the system. To produce effective read and write proposals, ALC uses a recurrent **Proposal Flow Model ( PFM )** trained through continuous-conditional flow matching. PFM iteratively refines schedules and candidate write transformations using the current landscape, operation constraints and its previous predictions. Its outputs remain proposals : the dynamical system executes them, observes their consequences, and accepts only outcomes that satisfy the corresponding geometric and stability checks. ALC achieves **82.1% Recall@1** on LongMemEval-S and reaches an exactly certified stored core on **91.8%** of queries. On controlled synthetic tasks derived from approximately 770,000 arXiv abstracts, ReadPFM improves certified retrieval success by **25%**, while WritePFM enables exact writes for **28.1%** of initially uncertifiable cases. Cost-fitted physical descent reduces NFE by **72.2%** during inference without changing terminal outcomes.