# Mitigating Convergence Collapse in Fixed-Target Anomaly Detectors via Kernel-Anchored Locality Regularization

arXiv: https://arxiv.org/abs/2610.02345 · HTML: https://mlsanity.com/paper/2610.02345/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 21 of 21)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [Unsupervised Representation Learning by Predicting Random Distances](https://mlsanity.com/paper/1912.12186/) (2019)
- [Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach](https://mlsanity.com/paper/2310.18677/) (2023)
- [Simple and Effective Prevention of Mode Collapse in Deep One-Class Classification](https://mlsanity.com/paper/2001.08873/) (2020)
- [Beyond Individual Input for Deep Anomaly Detection on Tabular Data](https://mlsanity.com/paper/2305.15121/) (2023)
- [Scalable, Explainable and Provably Robust Anomaly Detection with One-Step Flow Matching](https://mlsanity.com/paper/2510.18328/) (2025)
- [REFLECT: Rectified Flows for Efficient Brain Anomaly Correction Transport](https://mlsanity.com/paper/2508.02889/) (2025)
- [EntropyStop: Unsupervised Deep Outlier Detection with Loss Entropy](https://mlsanity.com/paper/2405.12502/) (2024)
- [Deep Learning for Network Anomaly Detection under Data Contamination: Evaluating Robustness and Mitigating Performance Degradation](https://mlsanity.com/paper/2407.08838/) (2024)
- [Diffusion-Scheduled Denoising Autoencoders for Anomaly Detection in Tabular Data](https://mlsanity.com/paper/2508.00758/) (2025)
- [Interpretable Tabular Foundation Models via In-Context Kernel Regression](https://mlsanity.com/paper/2602.02162/) (2026)
- [GradStop: Exploring Training Dynamics in Unsupervised Outlier Detection through Gradient](https://mlsanity.com/paper/2412.08501/) (2024)
- [Targeted collapse regularized autoencoder for anomaly detection: black hole at the center](https://mlsanity.com/paper/2306.12627/) (2023)
- [Time-reversed Flow Matching with Worst Transport in High-dimensional Latent Space for Image Anomaly Detection](https://mlsanity.com/paper/2508.05461/) (2025)

## Abstract (arXiv)

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.