The architectural mirage: capacity ratios fail as a safeguard against harmful knowledge distillation in cross-domain pill retrieval

Compact models on edge devices need knowledge distillation (KD) to close their cross-domain accuracy gap, but the choice of teacher decides whether distillation helps or harms. We characterise that failure at a scale that tests selection rules rather than illustrates them: 180 teacher–student pairings on ePillID over three training seeds, and 180 more on an independently derived CURE benchmark. Harmful transfer is common (21.8% and 27.3% of pairings) and concentrates in compact transformer students on both benchmarks (45.0% versus 8.6% for CNN students on ePillID; 55.0% versus 11.4% on CURE; single-seed labels). The capacity ratio, the safeguard much of the literature relies on and this study originally proposed, fails three ways: it discriminates weakly (screening AUC 0.66); its fitted threshold does not transfer between benchmarks (17.1 and 24.0, neither of them the asserted 12); and at 12 it admits no teacher for the two smallest students, forbidding distillation where it is most needed. Of the replacements we test, one result is modestly positive and the rest are negative. No training-free signal we evaluate, including four similarity metrics, their fusions, and five external transferability estimators, ranks teachers better than taking the strongest teacher by its own benchmark accuracy, by more than the measured noise floor. For the easier question of whether a pairing will harm at all, a correspondence-aware manifold divergence leads on ePillID; its AUC margin over the capacity ratio is unresolved at eleven student clusters, but at a threshold fitted out of sample, and on the nine students where both rules give a decision, it admits 3 harmful pairings against that rule’s 9 while discarding 24 beneficial ones against 39, it still leads when the rule is given its own fitted threshold, and it is defined for every student. The screen does not transfer visibly to CURE, where no signal we test separates harm from safety, in a design with power only against strong screens.