自适应分布外检测中的自中毒：尖锐阈值理论与无标签认证校准
Self-Poisoning in Adaptive Out-of-Distribution Detection: A Sharp-Threshold Theory and Certified Label-Free Calibration
AI总结：
研究自适应分布外检测中的自中毒问题，通过将内存库杂质建模为广义波利亚瓮证明相关动态规律，给出认证准入门等方法，证明双世界不可能性定理，完整刻画了无标签自适应OOD检测的可能性与不可能性。
AI中文摘要：
测试时自适应分布外（OOD）检测器会根据未标记流更新内存库。我们证明这种自适应遵循可证明的动态规律。将内存库杂质建模为广义波利亚瓮，我们证明其几乎必然收敛到一个平均场平衡，其斜率充当繁殖数。低于1时，杂质保持良性；高于1时，内存库完全中毒，检测器崩溃。所测准入核是仿射的（\(R^2 \ge 0.996\)），在每个编码器族中斜率略低于1（一种协议特征），所以这类检测器在设计上接近临界，在96种设置下预测阈值与经验崩溃匹配，无门控字典的AUROC损失高达0.163。然后我们证明一个认证准入门，仅读取冻结储备，切断反馈回路并消除每个污染率下的转变，即使是对抗性的，同时无标签控制误报。对于漂移下的互补静态校准失败，我们给出CDC，它在所有测试的受漂移影响的单元上无标签恢复标称FPR。最后我们证明了一个双世界不可能性定理。没有标签时，漂移和污染无法区分，迫使我们的过程接近一个封闭形式的功率上限。这些共同给出了无标签自适应OOD检测的完整可能性/不可能性特征。
英文摘要：
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.
