AI RESEARCH
Consolidation-Expansion Operator Mechanics:A Unified Framework for Adaptive Learning
arXiv CS.LG
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ArXi:2605.09968v1 Announce Type: new Every adaptive learning system must alternate between two operations: consolidating what it already knows and expanding into new evidence. We propose \emph{Consolidation-Expansion Operator Mechanics} (OpMech), a framework that makes this structure precise. The central object is the \emph{order-gap} $\Ogap(\theta; e)$, the degree to which a consolidation operator~$Q$ and an expansion operator~$P_e$ fail to commute at a given knowledge state.