Structure-adaptive probe bound in high dimensions

Establish a structure-adaptive probe-complexity bound for Wand that tightens the worst-case high-dimensional witness-cone bound beyond the dependence p_tau = Theta((tau/sqrt(d))^(d-1)).

Background

Wand’s output-sensitive theorem guarantees anomaly coverage using uniformly sampled directions, but its worst-case probe requirement deteriorates rapidly with dimension because the lower bound on witness-cone measure scales as (tau/sqrt(d))^d-1. Experiments suggest that empirical witness cones are substantially wider than this adversarial bound, even in dimensions approaching 1,555. The paper therefore identifies the derivation of a structure-adaptive bound as an unresolved problem for high-dimensional settings.