What should we forget? A computational model of memory consolidation

Neural and immune memory rely on different biological mechanisms but face the same computational problem: future situations rarely repeat past ones exactly. Memory must retain distinctions that alter future responses while discarding irrelevant variation. We formulate this problem as scaffold-flow memory: fast, state-dependent responses constitute the flow, whereas slowly changing physical variables form a scaffold that constrains future dynamics. Consolidation writes a predictive coarse-graining of experience into that scaffold. A useful coarse-graining must preserve future-relevant distinctions, generalize to novel experiences, support approximately autonomous coarse dynamics, and provide enough future benefit to justify its physical cost. We quantify failures of coarse autonomy through a leakage measure, relate leakage to excess future error, and identify persistent memory classes with slow dynamical modes. We further show that when experience does not self-average, storage is necessary rather than efficient. In a Willshaw associative memory, a metastable neural attractor, and a stochastic affinity-maturation model, future risk is minimized at an intermediate granularity: overly fine representations waste capacity and generalize poorly, whereas overly coarse ones merge situations requiring different responses. These results support a common computational principle: memory consolidation selects a predictive, dynamically usable, and affordable representation of the past.