Hierarchy Shift: Learning with Changing Semantic Structure

Hierarchical learning usually assumes that the semantic structure used to judge a prediction is fixed. We study the case in which that structure changes at deployment, possibly while the ordinary data law does not. We call this setting hierarchy shift. The resulting excess Bayes risk decomposes exactly into a value recoverable from observed context and a residual hierarchy-information gap. We characterize when this gap is zero and show that it is operational: with a finite action space and bounded risks, an empirical incompatibility statistic from $m$ conditionally iid plausible hierarchies converges to the gap at rate $O(\sqrt{\log |\text{A}|/m})$, without uniqueness, margin, metric, or binary-hierarchy assumptions. Plug-in and kernel-robust versions cover estimated risks and hierarchy posteriors. We then relate residual risk to the Bayes error of identifying the active hierarchy from context. The resulting regime law is simple: hierarchy conditioning can help only when plausible hierarchies favor different decisions and context identifies the relevant semantic state. Controlled experiments recover the exact decomposition, and learned gains track the oracle recoverable value ($r=0.964$). On locked Visual-WSD, the average MRR gain is small but rises to $0.023$ on positive-signal queries; shuffling posterior-to-branch alignment reverses this advantage. A low-conflict CIFAR-100 audit yields only a small gain, as predicted.