Definition. Localized and distributed degradation [ftip-00AP]
Definition. Localized and distributed degradation [ftip-00AP]
Fix pairwise disjoint evaluated slices \(C_1,\ldots ,C_J\) and a declared degradation threshold \(\kappa >0\). Define the set of materially degraded slices
\[ \mathcal H_\kappa (P_1,P_0) =\left \{j:\Delta _{\rm suc}(C_j;P_1,P_0)\leq -\kappa \right \}. \]Degradation is localized relative to this slice family and threshold when \(|\mathcal H_\kappa |=1\). It is distributed when \(|\mathcal H_\kappa |\geq 2\).
These terms depend on the chosen partition, threshold, and evaluation budget. They do not turn a finite benchmark vector into a statement about all capabilities.