Structural Decoupling: A Scaffold-Flow Theory of Generalization and Alignment

arXiv:2506.20699v2 Announce Type: replace Abstract: Learning in non-stationary and multi-context environments requires more than ordinary within-task generalization. A system must also discover which contexts exist, route inputs to the correct context, preserve old contexts, and revise the context library when the environment changes. This paper presents Structural Learning Theory (StrLT) as a framework of filling this missing structural gap. StrLT complements Vapnik's Statistical Learning Theory (SLT): SLT governs the \emph{funnel}, prediction or control within a fixed regime; while StrLT governs the \emph{trap}, the discovery and maintenance of structural regimes. The core StrLT object is \emph{width}, the minimum number of locally feasible contexts needed to cover a problem. We summarize three basic results: width is incomparable with VC dimension; learning exhibits a phase transition at the true width; and width can be estimated by a contractive-similarity (CS) operator that converts task-induced non-contractivity into spectral separation. Under the StrLT framework, we explain how fixed-class structural learnability leads to a \emph{structural decoupling principle}: the mechanisms that maintain the structural scaffold should not be trained by the same gradients that optimize within-context flow. This principle motivates a scaffold-flow model in which alignment and generalization separate architecturally. Finally, we argue that several safety failures, including hallucination, reward-model boundary errors, and deceptive alignment, can be interpreted as scaffold-resolution or scaffold-preservation failures rather than merely output-level prediction errors.