发表机构
Université Paris-Saclay; CNRS; CentraleSupélec; LISN UMR 9015; Laboratoire Interdisciplinaire des Sciences du Numérique（巴黎-萨克雷大学; 法国国家科学研究中心; 中央理工-高等电力学院; 数字科学跨学科实验室; 数字科学跨学科实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对固定目标神经异常检测器在收敛时残差信号消失的坍缩问题，提出核锚定正则化器（KAR），通过惩罚预测与核加权目标偏差保持局部性，在ADBench上缓解坍缩并提升AUROC。
AI 中文摘要
一类表格异常检测器在平方误差损失下将神经映射训练至固定目标，并通过测试时残差对异常进行评分；收缩匹配、单步整流流和重建自编码器均符合此模板。我们刻画了一种收敛坍缩：更好的优化使检测器性能更差。在收敛时，学习到的映射即使在分布外也跟踪目标，因此残差信号在异常和正常数据上均消失。这些检测器因此依赖隐式非收敛（早停、容量限制）来保留信号。我们认为这是结构性的：有效的异常检测需要局部性约束以阻止无约束的外推。经典检测器（kNN、KDE、孤立森林、LOF）显式施加局部性；固定目标神经检测器则不然。我们通过证明固定目标检测器的核回归类比是有限带宽的Nadaraya-Watson平滑器（称为核收缩匹配，KCM）来形式化这一联系。KCM是闭式、免训练且CPU高效的，但在ADBench上匹配已建立的神经基线。基于此桥梁，我们引入核锚定正则化器（KAR），它惩罚神经预测与训练目标核加权平均值的偏差。在易坍缩的ADBench数据集和三个骨干网络上，KAR缓解了坍缩并在长时间训练下提高了AUROC。
英文摘要
A family of tabular anomaly detectors trains a neural map toward a fixed target under squared-error loss and scores anomalies by the test-time residual; contraction matching, one-step rectified flow, and reconstruction autoencoders all fit this template. We characterize a convergence collapse: better optimization makes the detector worse. At convergence, the learned map tracks the target even off-distribution, so the residual signal vanishes on anomalies as well as on normal data. These detectors therefore rely on implicit non-convergence (early stopping, capacity caps) to retain signal. We argue this is structural: effective anomaly detection requires a locality constraint that blocks unconstrained extrapolation. Classical detectors (kNN, KDE, isolation forests, LOF) enforce locality explicitly; fixed-target neural detectors do not. We formalize the connection by showing that the kernel-regression analog of a fixed-target detector is a finite-bandwidth Nadaraya-Watson smoother, which we call Kernel Contraction Matching (KCM). KCM is closed-form, training-free, and CPU-efficient, yet matches established neural baselines on ADBench. Building on this bridge, we introduce the Kernel-Anchored Regularizer (KAR), which penalizes deviation of the neural prediction from a kernel-weighted average of training targets. Across collapse-prone ADBench datasets and three backbones, KAR mitigates collapse and improves AUROC under prolonged training.
CommentsAccepted at CIKM 2026 (oral). 11 pages
