Fixed-target anomaly detectors improved by kernel-based locality penalty
Mitigating Convergence Collapse in Fixed-Target Anomaly Detectors via Kernel-Anchored Locality Regularization
Machine Learning
Summary
Some anomaly detection methods using neural networks struggle because they learn to mimic a fixed target too well, losing the ability to spot unusual data. The authors show this happens because these methods don’t limit how much they generalize beyond the training data, causing anomalies to look normal. They connect these neural methods to classical techniques that explicitly keep predictions local. Using that insight, they introduce a new penalty that keeps neural predictions close to local averages, helping the detectors avoid this problem and detect anomalies better over longer training.
What this means in practice
- •For data security teams: Improve anomaly detection systems by adding a locality-based regularizer to maintain detection quality during extended training.
- •For financial fraud analysts: Enhance fraud detection algorithms by reducing false negatives caused by overfitting in fixed-target neural detectors.
Authors
José Lucas De Melo Costa, Fabrice Popineau, Arpad Rimmel, Bich-Liên Doan
Abstract
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.