Just Repair: A Minimal Denoising Network for Time Series Anomaly Detection

Kadir-Kaan Özer; René Ebeling; Markus Enzweiler

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Just Repair: A Minimal Denoising Network for Time Series Anomaly Detection

Kadir-Kaan Özer, René Ebeling, Markus Enzweiler

arXiv:2604.17388v3Apr 19, 2026cs.LGcs.AI

TL;DR

The paper asks whether complex time-series anomaly detectors need their additional machinery to outperform a minimal repair baseline. It evaluates JURE, a single-block denoising detector with fixed structural scoring, and finds second-place rankings on both standardized benchmarks, alongside substantial efficiency and methodological tradeoffs.

Problem
The paper asks whether the complexity added by modern time-series anomaly detectors yields genuine detection gains over a principled repair baseline.
Method
JURE trains a single depthwise-separable residual block to repair Gaussian-corrupted, channel-masked normal windows and scores repaired-test discrepancies with fixed structural weights.
Results
JURE ranks second on TSB-AD-M with AUC-PR 0.404 and on UCR with AUC-PR 0.201, leading neural methods on UCR while running roughly 20× faster than AxonAD on TSB-AD-M.
Takeaways & Limitations
A minimal denoising objective and network can remain competitive with substantially more complex systems under the evaluated benchmark settings.
Takeaways & Limitations
The synthetic geometric validation uses a linear subspace, while nonlinear manifolds and small-displacement robustness remain untested.

Abstract

from arXiv · show

Time series anomaly detectors have grown steadily more complex, incorporating attention mechanisms, adversarial training, and stochastic latent variables. Yet, it is unclear how much of this machinery detection actually requires. We test this question with JuRe (Just Repair), a deliberately minimal detector: a single depthwise-separable convolutional residual block trained to repair Gaussian-corrupted, channel-masked windows, scored at inference by a fixed structural discrepancy function with no learned parameters. JuRe ranks second on the TSB-AD multivariate benchmark (AUC-PR 0.404 over 180 series) and second on the UCR univariate archive (AUC-PR 0.201 over 250 series), where it leads all neural baselines. On TSB-AD, JuRe runs roughly $20\times$ faster than AxonAD, one of the top-ranked methods on that benchmark. Full-benchmark ablations show that removing Gaussian corruption reduces AUC-PR by 0.046, whereas AUC-PR across the evaluated architecture variants spans at most 0.017. A synthetic linear-manifold experiment provides partial evidence for this geometric interpretation: anomaly scores correlate with true off-manifold distance (Pearson $r=0.725$), and repair directions align increasingly with the true projection as anomaly magnitude grows. Wilcoxon signed-rank tests with Holm correction find significant differences against 20 of 25 baselines, although dependence among series limits dataset-level interpretation. Code is available at https://github.com/iis-esslingen/JuRe.

I. INTRODUCTION

JURE tests whether a minimal denoising repair baseline can remain competitive with increasingly complex anomaly detectors. It achieves strong benchmark rankings while exposing efficiency and evaluation tradeoffs.

Modern anomaly detectors add attention, predictive dynamics, variational encoders, stochastic states, and adversarial training, increasing learned machinery.
Standardized benchmarks had not systematically tested whether this complexity improves detection over a principled repair baseline.
JURE trains one depthwise-separable residual block to repair Gaussian-noised, channel-masked normal windows and uses a fixed structural discrepancy score without learned scoring weights.
JURE ranks second on both TSB-AD-M and UCR, leads neural methods on UCR, and runs roughly 20× faster than AxonAD on TSB-AD-M.
The paper positions JURE alongside denoising autoencoders, score-based methods, structured-discrepancy detectors, and classical approaches such as MatrixProfile.
The benchmark comparisons establish relative detection and efficiency tradeoffs, while the ablations characterize evaluated design choices rather than universal causal ordering.

III. JUST REPAIR (JURE)

JURE defines anomaly detection as repairing corrupted normal windows and measuring how test windows differ from the repair. Gaussian corruption is central to the denoising interpretation and prevents trivial identity reconstruction.

JURE models repair by learning fθ(˜x) ≈ x from inputs corrupted with Gaussian noise and channel masking.The stated corruption settings are σ = 0.1 and masking probability p = 0.05.
Gaussian denoising is motivated by the Bayes-optimal correction toward higher-density regions of the Gaussian-smoothed normal-data distribution.This interpretation does not guarantee projection behavior for arbitrary inputs.
Input corruption prevents the identity function from minimizing reconstruction loss and encourages nontrivial denoising corrections.
The training loss combines amplitude and first-difference reconstruction, with λ_Δ = 0.25 encouraging temporal-structure preservation.

B. Architecture

JURE uses a deliberately small convolutional architecture tailored to local temporal repair and cross-channel mixing. Its residual design starts as the identity and adds only one depthwise-separable block.

Architecture: The architecture uses a 1×1 input projection, one depthwise-separable residual block, a 1×1 output projection, and a global skip connection.The output projection is zero-initialized, so fθ(x) = x at initialization.
Architecture: With hidden width H = 128, JURE has 17,665 parameters for univariate input.
Architecture: Convolution supplies a translation-equivariant local operation suited to repairing local temporal neighborhoods.
Architecture: Depthwise separability separates temporal filtering from cross-channel mixing and reduces parameters from O(H^2K) to O(HK + H^2).The decomposition mirrors temporal Gaussian noise and masked-channel corruption.
Architecture: One residual block suffices on the evaluated benchmarks, while added depth yields no measurable improvement.
Architecture: GELU supports the small-correction regime, and zero-initialization makes the network learn corrections from the identity.

C. Structural Scoring and Inference

At inference, JURE compares each test window with its repaired output using fixed amplitude and structural discrepancies. Overlapping window scores are standardized and averaged back onto the time axis.

Raw amplitude residuals can miss structural anomalies, so JURE evaluates amplitude, differences, trends, and cross-channel correlations.The evaluated anomaly examples include amplitude spikes, trend shifts, gradient noise, and correlation breaks.
The fixed score combines amplitude, first-difference, trend, and correlation discrepancies as s(x) = s_amp + w_diff s_diff + w_trend s_trend + w_corr s_corr.The weights are w_diff = 0.5, w_trend = 0.5, and w_corr = 0.25.
The correlation term compares changes in the upper-triangular channel-correlation matrix and is set to zero for univariate series.
Inference extracts stride-1 overlapping windows, computes scores, robustly standardizes them using training medians and IQRs, and averages overlaps on the time axis.
The anomaly-typology figure contrasts normalized scores from three models across four anomaly classes using a dashed 95th-percentile threshold.

IV. EXPERIMENTAL SETUP

The evaluation uses standardized multivariate and univariate anomaly-detection archives, with fixed global settings and held-out benchmark testing. Results are accompanied by workflow descriptions and a caution that series dependence limits inferential interpretation.

The study evaluates TSB-AD with 180 multivariate series and the UCR archive with 250 univariate series.
Training repairs corrupted windows against clean targets, whereas inference scores uncorrupted test windows using structural discrepancy.
JURE uses one globally fixed configuration, with hyperparameters selected on 20 development series excluded from the 180-series evaluation set.The post-hoc full-benchmark sweeps do not affect model selection.
Dependence among series from the same dataset may make nominal per-series Wilcoxon p-values anticonservative.The tests are therefore treated as descriptive evidence across evaluated series rather than confirmatory evidence of generalization across independent datasets.

V. RESULTS

JURE is highly competitive across both benchmark settings, ranking second on the multivariate archive and second on the univariate archive while leading neural methods on UCR. Pairwise significance results support broad but qualified advantages over many baselines.

A. TSB-AD Multivariate: AUC-PR 0.404 places JURE second on the 180-series TSB-AD benchmark, behind AxonAD at 0.437.Every other listed baseline falls below the single-block repair network.
A. TSB-AD Multivariate: JURE significantly outperforms 20 of 25 baselines under Holm–Bonferroni correction, while AxonAD significantly outperforms JURE.The comparison uses pairwise Wilcoxon signed-rank tests on per-series AUC-PR.
B. UCR Univariate: AUC-PR 0.201 places JURE second on UCR behind MatrixProfile at 0.292 and first among neural methods.JURE also ranks first among neural methods on VUS-PR.
B. UCR Univariate: UCR-Score ranks three neural baselines above JURE, illustrating that archive-level rankings can differ across evaluation measures.UCR-Score rewards only the single highest-scored point and can diverge from continuous ranking quality.

C. Efficiency

JURE occupies a favorable efficiency point: it is substantially faster than AxonAD with a modest AUC-PR difference, while the ablations indicate that Gaussian corruption matters more than the evaluated architecture choices.

C. Efficiency: 9,870 scores/s for JURE versus 497 scores/s for AxonAD yields roughly 20× higher throughput at a cost of 0.033 AUC-PR.Throughput includes network inference and score computation on a single NVIDIA A100 GPU.
C. Efficiency: Neither small nor large parameter budgets predict AUC-PR across the compared TSB-AD methods.
A. Effect of the Training Objective: Removing Gaussian noise corruption reduces AUC-PR by 0.046, the largest drop among the evaluated training and scoring choices.This comparison retains channel masking and therefore shows the evaluated contribution of Gaussian corruption under those conditions.
A. Effect of the Training Objective: Removing channel masking costs 0.024 AUC-PR, whereas removing the auxiliary difference loss changes aggregate AUC-PR by 0.001.
A. Effect of the Training Objective: Amplitude-only scoring drops to 0.388, and removing the correlation term alone costs 0.023.Excessive correlation weighting, wcorr ≥1.0, degrades performance across the evaluated sensitivity sweep.

B. Model Capacity

JuRe’s performance saturates across the evaluated moderate-capacity settings, while noise corruption is substantially more consequential than the tested capacity choices.

Capacity sweep: AUC-PR is 0.357 at H = 8, versus 0.405 at H = 64 and 0.404 at H = 128.The H = 64 and H = 128 difference is not significant: W = 7149, p = 0.155.
Hyperparameter sensitivity: Removing Gaussian noise causes a severe performance drop, whereas the evaluated diff-loss and structural-score weights are robust across their tested ranges.Excessive correlation weighting, wcorr ≥1.0, degrades performance.
Capacity sweep: H = 128 wins 104 of 180 series against 76 for H = 64, without a significant aggregate difference.The paper retains H = 128 as a pre-specified default rather than a theoretically derived capacity threshold.
Capacity sweep: A second residual block yields AUC-PR 0.401, supporting saturation across the evaluated moderate-width and depth settings.These observations do not establish a general capacity threshold.

C. Architecture and Inductive Bias

Across the full benchmark, the tested architecture variants differ little compared with the effect of Gaussian corruption, while depthwise-separable convolution and Huber loss provide modest advantages.

Architecture variants: Depthwise-separable convolution leads standard convolution by +0.016 AUC-PR and the linear MLP by +0.010.Its advantage was visible on the 180-series benchmark but not on the 20-series tuning subset.
Activation function: Replacing GELU with ReLU trades −0.006 AUC-PR for +0.003 AUC-ROC.The comparison reports a performance-efficiency tradeoff between the two activation choices.
Architecture variants: The total spread across evaluated architecture variants is at most 0.017 AUC-PR, compared with a 0.046 reduction when Gaussian corruption is removed.This is descriptive because exact parameter comparability among variants is not established.
Loss function: Huber loss reaches AUC-PR 0.404, versus 0.400 for MSE and 0.371 for MAE.This ordering differed on smaller subsets.

W AUC-PR AUC-ROC

The window-size sweep shows a tradeoff: larger windows capture longer-range structure for AUC-ROC, while tighter windows favor AUC-PR; W = 100 balances both.

Window-size sensitivity: W = 100 achieves the highest AUC-PR among the evaluated window sizes.Performance degrades gracefully on either side of W = 100.
Window-size sensitivity: AUC-ROC continues rising at larger windows because they capture longer-range structure, whereas AUC-PR favors tighter localization.The default W = 100 balances the two metrics without per-dataset tuning.

E. Synthetic Validation of the Manifold Interpretation

A controlled linear-manifold experiment offers partial support for JuRe’s geometric interpretation: scores track off-manifold distance, and repair directions align more closely with projection at larger anomalies. The evidence is limited to the tested linear setting and does not establish general projection behavior.

Controlled setup: The synthetic experiment embeds a d = 4 subspace in R^W×C with W = 100 and C = 10, using 5,000 noisy training windows.Test anomalies are planted at seven orthogonal distances from δ = 0 to δ = 3.0.
Score–distance relation: JuRe’s anomaly score correlates with true orthogonal distance at Pearson r = 0.725 ± 0.004 and Spearman ρ = 0.611 ± 0.009.The gap between the correlations indicates mild nonlinearity in the score–distance relationship.
Repair alignment: Repair-direction cosine similarity rises from 0.06 at δ = 0.1 to 0.85 at δ = 3.0.Intermediate values are 0.18 at δ = 0.3 and 0.50 at δ = 1.0.
Scope and limitations: The experiment provides only partial geometric support because alignment is noise-sensitive near the manifold and general manifolds or real anomalies were not tested.The broader benchmark experiments also do not establish a general causal ordering between objective and architecture.