Self-Poisoning in Adaptive Out-of-Distribution Detection: A Sharp-Threshold Theory and Certified Label-Free Calibration

The paper models memory-bank contamination in test-time adaptive OOD detectors as a generalized Pólya urn. It proves almost-sure convergence to a mean-field equilibrium, with an admission-kernel slope acting as a reproduction number: below one, impurity remains controlled; above one, the bank becomes fully poisoned and detection collapses. Across 96 settings, the predicted threshold reportedly matches empirical collapse, while ungated dictionaries lose up to 0.163 AUROC. The paper also proposes a certified gate using only a frozen reserve, a label-free drift-calibration method called CDC, and an impossibility theorem showing that drift and contamination cannot be fully distinguished without labels.