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This research establishes a provable dynamical law for test-time adaptive out-of-distribution detection, demonstrating that unlabelled memory banks inevitably collapse into impurity unless governed by specific near-critical thresholds. The authors introduce certified admission gates and static calibration methods to sever feedback loops and restore performance under adversarial contamination or data drift without requiring labels. These findings define the fundamental possibility and impossibility boundaries for robust, label-free adaptive detection in dynamic environments.
Self-Poisoning in Adaptive Out-of-Distribution Detection: A Sharp-Threshold Theory and Certified Label-Free Calibration
arXiv:2607.21673v1 Announce Type: cross Abstract: Test-time adaptive out-of-distribution (OOD) detectors update a memory bank from the unlabelled stream. We show this adaptation obeys a provable dynamical law. Modelling bank impurity as a generalized P\'olya urn, we prove almost-sure convergence to a mean-field equilibrium whose slope acts as a reproduction number. Below one, impurity stays benign. Above one, the bank is fully poisoned and the detector collapses. The measured admission kernel is affine ($R^2 \ge 0.996$) with slope just below one in every encoder family (a protocol signature), so this detector class is near-critical by design, and across 96 settings the predicted threshold matches the empirical collapse, where ungated dictionaries lose up to $0.163$ AUROC. We then prove that a certified admission gate, reading only a frozen reserve, severs the feedback loop and removes the transition at every contamination rate, even adversarially, while controlling false positives label-free. For the complementary static-calibration failure under drift we give CDC, which restores nominal FPR label-free on all tested drift-affected cells. Finally we prove a two-world impossibility theorem. Drift and contamination are indistinguishable without labels, forcing a closed-form power ceiling our procedure approaches. Together these give a complete possibility/impossibility characterization of label-free adaptive OOD detection.
Abstract:Test-time adaptive out-of-distribution (OOD) detectors update a memory bank from the unlabelled stream. We show this adaptation obeys a provable dynamical law. Modelling bank impurity as a generalized Pólya urn, we prove almost-sure convergence to a mean-field equilibrium whose slope acts as a reproduction number. Below one, impurity stays benign. Above one, the bank is fully poisoned and the detector collapses. The measured admission kernel is affine ($R^2 \ge 0.996$) with slope just below one in every encoder family (a protocol signature), so this detector class is near-critical by design, and across 96 settings the predicted threshold matches the empirical collapse, where ungated dictionaries lose up to $0.163$ AUROC. We then prove that a certified admission gate, reading only a frozen reserve, severs the feedback loop and removes the transition at every contamination rate, even adversarially, while controlling false positives label-free. For the complementary static-calibration failure under drift we give CDC, which restores nominal FPR label-free on all tested drift-affected cells. Finally we prove a two-world impossibility theorem. Drift and contamination are indistinguishable without labels, forcing a closed-form power ceiling our procedure approaches. Together these give a complete possibility/impossibility characterization of label-free adaptive OOD detection.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Cryptography and Security (cs.CR); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (stat.ML)
arXiv:2607.21673 [cs.LG]
(or arXiv:2607.21673v1 [cs.LG] for this version)
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