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This research addresses a critical structural flaw in fixed-target neural anomaly detectors where optimal convergence inadvertently eliminates the residual signal needed for detection. By introducing a kernel-anchored locality regularizer, the authors demonstrate that enforcing neighborhood constraints prevents this collapse and restores robustness without sacrificing performance on standard benchmarks. The work bridges classical non-parametric methods with modern neural architectures to provide a more reliable foundation for unsupervised learning systems.
Mitigating Convergence Collapse in Fixed-Target Anomaly Detectors via Kernel-Anchored Locality Regularization
arXiv:2610.02345v1 Announce Type: new 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.
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.
Accepted at CIKM 2026 (oral). 11 pages
Machine Learning (cs.LG)
arXiv:2610.02345 [cs.LG]
(or arXiv:2610.02345v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.02345 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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