Self-Poisoning in Adaptive Out-of-Distribution Detection: A Sharp-Threshold Theory and Certified Label-Free Calibration
Vishnu Bindu Balachandran
cs.LG, cs.AI, cs.CR, cs.CV, stat.ML
Submitted: 2026-07-23
Comments: 28 Pages, 5 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: Test-time adaptive out-of-distribution (OOD) detectors update a memory bank from the unlabelled stream.
Terminology
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 squared 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.
Sources
- Robust Conformal Outlier Detection under Contaminated Reference Data
- On the Stability of Iterative Retraining of Generative Models on their own Data
- Noisy Test-Time Adaptation in Vision-Language Models
- Strong Model Collapse
- How Does Unlabeled Data Provably Help Out-of-Distribution Detection?
- Is Out-of-Distribution Detection Learnable?
- Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data
- Training OOD Detectors in their Natural Habitats
- Selection from Hierarchical Data with Conformal e-values
- RDumb: A simple approach that questions our progress in continual test-time adaptation
- Generalized Polya urns via stochastic approximation
- On the Adversarial Risk of Test Time Adaptation: An Investigation into Realistic Test-Time Data Poisoning
- Out-of-Distribution Detection with Deep Nearest Neighbors
- When Does Trimming Help Conformal Prediction? A Retained-Law Diagnostic under Calibration Contamination
- Anytime-valid FDR control with the stopped e-BH procedure
- OODD: Test-time Out-of-Distribution Detection with Dynamic Dictionary
- Test-time Recalibration of Conformal Predictors Under Distribution Shift Based on Unlabeled Examples
- OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection
- Model-free Test Time Adaptation for Out-Of-Distribution Detection
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