Mastery Equilibrium Theory (MET)

Mastery Equilibrium Theory (MET) proposes a unified framework for understanding how conceptual knowledge is maintained, transformed, or lost over time within learning agents—human or artificial. Contrary to traditional assessment paradigms that treat mastery as a static outcome verified by momentary performance, MET frames mastery as a dynamic equilibrium: a sustained alignment between an internal representation and a normative target concept under continuous perturbations. Perturbations arise from representational compression, contextual interference, inconsistent feedback, generalization shortcuts, and gradual shifts in the distribution of exemplars encountered during subsequent use. The central claim of MET is that correctness on surface tasks is necessary but not sufficient for conceptual fidelity; durable mastery requires stabilizing forces whose cumulative effect balances or exceeds the tendency to drift. At its core MET posits three minimal primitives that together support both conceptual description and empirical measurement. First, a representation space captures internal encodings of concepts along with a task-relevant distance metric that quantifies deviation from a target. Second, drift operators model systematic perturbations acting on representations over time; they encode how inference shortcuts, contextual weighting, or abstraction processes distort concept structure. Third, stabilizing operators represent corrective interventions—feedback, explicit constraints, varied exemplars, and pedagogical scaffolding—whose aggregate magnitude constrains or reverses drift. The interaction of these primitives produces an equilibrium condition: when stabilizing force exceeds perturbation pressure, fidelity is preserved; when it does not, conceptual drift accumulates. From these primitives MET derives operational outputs designed for empirical validation. A drift rate metric estimates how rapidly representational fidelity declines in longitudinal probes; a stabilizing capacity index quantifies the expected corrective effect of an intervention schedule; and a masking predictor estimates the probability that surface task performance remains intact despite underlying conceptual deformation. These outputs enable concrete, falsifiable claims—for example, that curricula emphasizing relational invariants and high-variance exemplars will yield lower drift rates than curricula that prioritize repetitive rote practice, or that infrequent but targeted corrective feedback can provide disproportionate stabilizing benefit compared to dense but shallow practice. MET emphasizes measurement strategies compatible with existing tools: longitudinal probing, representation similarity analysis, targeted diagnostic items, and perturbation experiments that intentionally vary contextual cues. The theory articulates testable hypotheses about curriculum sequencing and model maintenance. In classrooms, MET predicts that instruction designed to expose structural invariants and varied contexts will preserve conceptual fidelity longer; in deployed AI systems, MET predicts that regular targeted probing and corrective fine-tuning focused on invariant features will reduce representational drift that otherwise accumulates during continual learning or domain shift. Importantly, MET is intentionally presentation-agnostic: the abstract formulation requires only a conceptual representation space and observable probes of fidelity, enabling interdisciplinary adoption across cognitive science, educational measurement, and machine learning. While minimal mathematical formalization is helpful for deriving thresholds and precise predictions, the conceptual scaffold itself yields immediate utility for practitioners designing assessments, interventions, and lifecycle maintenance regimes. Empirical agendas include controlled longitudinal studies in classrooms and synthetic experiments with neural models: controlled cohorts receiving variant feedback schedules, curricula emphasizing invariants versus exemplars, and adversarial contextual shifts. Expected outcomes include measurable differences in drift rates, differing resource requirements for stabilization, and diagnostic signatures distinguishing transient performance from preserved conceptual structure. Practically, MET reframes evaluation from single-point verification to continuous stewardship, providing a principled basis for interventions aimed at durable conceptual mastery.