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.