How Many Categories Are Enough? Distribution-Free Certification Limits for Few-Shot Anomaly Thresholds

Gia Huy Thai, Nguyen Thai Anh

Few-shot anomaly detectors are judged by ranking metrics, yet deployment requires an alarm threshold with a controlled false-alarm rate (FAR). We ask how much normal evidence, in images or category units, is needed to certify such a threshold for an unseen category. Using a frozen DINOv2 principal component analysis (PCA) residual ranker on 15 MVTec and 12 VisA categories under four corruption types, we show that target-only leave-one-image-out (LOIO) calibration is resolution-limited and shift-fragile: rank values cannot fall below $1/(k+1)$, and at the attainable level $α=0.20$, empirical FAR reaches 0.341 on Gaussian-corrupted MVTec at $k=4$, 1.7 times the nominal level. A category-count feasibility calculus is then derived: even with all-zero category losses and no multiplicity charged, any deterministic, uniformly valid, distribution-free 95% upper confidence bound (UCB) requires at least 14, 29, and 59 independent and identically distributed (iid) category draws at $α=0.20$, $0.10$, and $0.05$; these counts are necessary but not sufficient. The Cross-category Reliability Estimation with Source Support (CRESS) protocol splits source categories into disjoint reference,…