Generalist Representation, Specialist Detection: TS-Router for Time-Series Anomaly Detection
Organizations: Department of Industrial Engineering Tsinghua University · Huawei · Datadog AI Research Paris, France
Abstract
Time-series anomaly detection (TSAD) is difficult to generalize across datasets because heterogeneous temporal dynamics imply different notions of normality and favor different detection criteria. While time-series foundation models provide transferable representations, coupling them with a fixed anomaly-scoring mechanism can overlook this variation. This motivates a different perspective on foundation-model-based TSAD: using foundation models to coordinate specialized anomaly criteria rather than directly imposing a universal one. Based on this view, we propose \textbf{TS-Router}, a generalist-representation, specialist-detection framework that estimates the relative competence of heterogeneous anomaly detectors from pretrained temporal representations and selects suitable specialists for each target series. To avoid relying on specialist-performance labels from real tasks, we derive soft competence supervision from specialists' relative performance on labeled simulated tasks. At deployment, routing requires no target anomaly labels, and only the selected specialists are fitted unsupervisedly on the target series. We bound Top- set-competence regret under representation coverage and conditional competence stability. Across 16 real-world benchmarks and four complementary evaluation metrics, TS-Router achieves the best overall average rank. Controlled ablations with multiple frozen TSFM encoders further support the use of pretrained representations for competence estimation and adaptive specialist selection. The code is available at https://anonymous.4open.science/r/TS-Router-D8FF.
Figures & tables
| Method | VUS-PR | Aff.-F1 | F1 T | Std.-F1 | Overall Rank | #Top-1 | #Top-2 | ||||
| Score | Rank | Score | Rank | Score | Rank | Score | Rank | ||||
| Foundation-guided specialist routing | |||||||||||
| TS-Router | 49.59 | 2.44 | 86.87 | 2.44 | 47.37 | 3.00 | 45.34 | 2.75 | 2.66 | 26 | 39 |
| Direct zero-shot models | |||||||||||
| TimeRCD | 37.00 | 3.88 | 83.94 | 3.69 | 40.88 | 3.62 | 37.03 | 4.19 | 3.84 | 14 | 26 |
| DADA | 30.16 | 5.62 | 81.41 | 4.88 | 37.29 | 5.84 | 32.60 | 6.31 | 5.66 | 5 | 10 |
| Variant | Detection performance | Routing quality | ||||
|---|---|---|---|---|---|---|
| VUS-PR | Aff.-F1 | F1 T | Std.-F1 | NDCG@ | Hit@ | |
| Selection and fusion strategy | ||||||
| Best Fixed | 39.68 | 84.34 | 41.01 | 36.43 | 0.607 | 0.207 |
| Full Ensemble | 49.54 | 85.55 | 46.22 | 43.48 | – | – |
| Best Fixed Top-3 | 47.44 | 86.56 | 47.56 | 43.42 | 0.625 | 0.532 |
| Router Top-1 | 49.00 | 86.80 | 43.47 | 41.41 | – | – |
Appendix figures & tables13 assets
Supplementary material from the paper’s appendix.
Appendix
| Name | Domain | #TS | Avg. Length | AR (%) |
|---|---|---|---|---|
| UCR | Misc. | 228 | 67818.7 | 0.6 |
| NAB | Mixed | 28 | 5099.7 | 10.6 |
| YAHOO | Web | 259 | 1560.2 | 0.6 |
| IOPS | Operations | 17 | 72792.3 | 1.3 |
| MGAB | Synthetic | 9 | 97777.8 | 0.2 |
| SED | Medical | 3 | 23332.3 | 4.1 |
| Name | Domain | #TS | Avg. Length | AR (%) |
|---|---|---|---|---|
| MSL | Space | 16 | 3119.4 | 5.1 |
| PSM | Sensor | 1 | 217624.0 | 11.2 |
| SMAP | Space | 27 | 7855.9 | 2.9 |
| SMD | Server | 22 | 25466.4 | 3.8 |
| SWaT | ICS | 2 | 207457.5 | 12.7 |
| Specialist | Primary inductive bias |
|---|---|
| PCA | Low-dimensional subspace reconstruction; anomalies produce large reconstruction residuals. |
| Sub-PCA | Windowed PCA on subsequences; anomalies produce large reconstruction residuals relative to local temporal structure. |
| Sub-HBOS | Marginal density modeling through histogram-based statistics; low-density observations receive larger anomaly scores. |
| POLY | Smooth temporal structure modeled by polynomial fitting; deviations from the fitted temporal trend indicate anomalies. |
| Sub-KNN | Neighborhood-distance structure; observations far from their nearest neighbors are considered anomalous. |
| Sub-LOF | Relative local density; anomalies exhibit substantially lower local density than their surrounding neighborhoods. |
| Specialist | Hyperparameters |
|---|---|
| PCA | Period rank ; all principal components. |
| Sub-PCA | Period rank ; all principal components. |
| Sub-HBOS | Period rank ; histogram bins. |
| POLY | Period rank ; polynomial degree . |
| Sub-KNN | Period rank ; neighbors. |
| Sub-LOF | Period rank ; neighbors. |
| Metric | Model | Univariate datasets | Multivariate datasets | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| IOPS | MGAB | NAB | NEK | Power | SED | Stock | TODS | UCR | WSD | YAHOO | MSL | PSM | SMAP | SMD | SWaT | ||
| VUS-PR | TS-Router | 41.49 | 43.09 | 51.97 | 76.92 | 22.40 | 65.42 | 73.18 | 71.65 | 39.60 | 56.91 | 77.32 | 20.86 | 19.55 | 38.12 | 52.24 | 42.75 |
| TimeRCD | 20.23 | 1.05 | 24.32 | 27.88 | 21.25 | 80.75 | 77.28 | 93.46 | 23.09 | 21.77 | 84.41 | 20.45 | 18.69 | 22.68 | 37.03 | 17.58 | |
| DADA | 24.97 | 0.57 | 24.73 | 46.85 | 10.61 | 6.42 | 99.51 | 64.83 | 2.94 | 33.42 | 70.74 | 12.74 | 17.17 | 20.02 | 25.98 | 21.13 | |
| Chronos | 19.00 | 0.60 | 23.76 | 31.80 | 10.95 | 8.65 | 97.49 | 70.66 | 6.56 | 18.81 | 83.54 | 8.25 | 14.61 | 5.18 | 10.22 | 16.44 | |
| MOMENT | 37.35 | 0.56 | 45.38 | 67.74 | 10.50 | 4.31 | 76.97 | 56.45 | 6.17 | 55.26 | 30.81 | 9.32 | 16.48 | 8.97 | 15.96 | 14.90 | |
| Metric | Representation | Univariate datasets | Avg. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| IOPS | MGAB | NAB | NEK | Power | SED | Stock | TODS | UCR | WSD | YAHOO | |||
| VUS-PR | TimeRCD | 41.49 | 43.09 | 51.97 | 76.92 | 22.40 | 65.42 | 73.18 | 71.65 | 39.60 | 56.91 | 77.32 | 56.36 |
| Chronos | 38.63 | 33.44 | 49.34 | 50.10 | 15.99 | 94.18 | 71.64 | 78.81 | 33.17 | 53.83 | 66.87 | 53.27 | |
| MOMENT | 40.73 | 33.44 | 46.83 | 33.93 | 20.56 | 94.18 | 87.24 | 76.35 | 38.09 | 57.55 | 63.87 | 53.89 | |
| Catch22 | 44.58 | 9.46 | 42.75 | 38.31 | 22.27 | 94.18 | 76.57 | 84.05 | 34.11 | 48.86 | 54.39 | 49.96 | |
| TSFresh | 36.98 | 35.44 | 35.53 | 50.10 | 17.54 | 37.17 | 88.43 | 73.84 | 33.18 | 51.50 | 79.40 | 49.01 | |
| Metric | Method | Univariate datasets | Avg. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| IOPS | MGAB | NAB | NEK | Power | SED | Stock | TODS | UCR | WSD | YAHOO | |||
| VUS-PR | TS-Router | 41.49 | 43.09 | 51.97 | 76.92 | 22.40 | 65.42 | 73.18 | 71.65 | 39.60 | 56.91 | 77.32 | 56.36 |
| PCA | 23.21 | 0.60 | 45.77 | 78.45 | 10.49 | 3.77 | 80.92 | 54.01 | 13.40 | 16.95 | 21.15 | 31.70 | |
| Sub-PCA | 20.35 | 0.66 | 49.82 | 83.68 | 10.49 | 4.00 | 77.81 | 52.82 | 13.53 | 14.09 | 19.41 | 31.51 | |
| Sub-HBOS | 4.97 | 0.50 | 33.26 | 19.43 | 15.69 | 63.09 | 64.60 | 64.54 | 15.07 | 2.21 | 12.08 | 26.86 | |
| POLY | 27.51 | 0.70 | 46.91 | 55.64 | 9.30 | 7.88 | 79.01 | 57.39 | 15.80 | 35.24 | 27.89 | 33.02 | |
| Routing head | VUS-PR | VUS-ROC | F1 T | Std.-F1 | Aff.-F1 |
|---|---|---|---|---|---|
| VUS-PR | 56.36 | 88.30 | 49.62 | 47.73 | 88.11 |
| Affiliation-F1 | 56.27 | 89.24 | 49.17 | 46.83 | 88.49 |
| F1 T | 58.24 | 89.29 | 53.03 | 49.96 | 89.17 |
| Standard-F1 | 55.28 | 87.81 | 50.00 | 47.77 | 87.83 |
| Metric | Selector | Univariate datasets | Avg. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| IOPS | MGAB | NAB | NEK | Power | SED | Stock | TODS | UCR | WSD | YAHOO | |||
| VUS-PR | TS-Router | 41.49 | 43.09 | 51.97 | 76.92 | 22.40 | 65.42 | 73.18 | 71.65 | 39.60 | 56.91 | 77.32 | 56.36 |
| SATzilla | 41.77 | 33.44 | 41.71 | 53.12 | 22.40 | 74.65 | 70.43 | 72.73 | 41.82 | 58.30 | 59.20 | 51.78 | |
| ARGOSMART | 44.02 | 9.46 | 44.73 | 31.94 | 22.36 | 11.94 | 82.21 | 70.71 | 34.24 | 54.88 | 53.37 | 41.81 | |
| MetaOD | 42.21 | 33.44 | 40.23 | 57.82 | 22.40 | 33.96 | 70.20 | 72.73 | 41.82 | 56.72 | 57.89 | 48.13 | |
| ISAC | 43.02 | 33.44 | 41.84 | 39.78 | 22.40 | 74.65 | 76.03 | 72.72 | 40.42 | 58.08 | 57.09 | 50.86 | |
| Metric | Method | Univariate datasets | Avg. | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| IOPS | MGAB | NAB | NEK | SED | Stock | TODS | UCR | WSD | YAHOO | |||
| VUS-PR | TS-Router | 28.72 | 45.61 | 57.45 | 94.24 | 63.78 | 52.84 | 87.54 | 29.67 | 45.05 | 69.09 | 57.40 |
| SATzilla | 20.45 | 48.52 | 43.74 | 76.40 | 77.57 | 90.36 | 73.87 | 38.32 | 35.01 | 45.81 | 55.00 | |
| ARGOSMART | 23.07 | 48.52 | 42.86 | 41.35 | 77.57 | 94.57 | 78.03 | 25.53 | 38.48 | 49.53 | 51.95 | |
| MetaOD | 19.58 | 48.52 | 39.00 | 76.40 | 77.57 | 90.36 | 77.94 | 39.62 | 35.01 | 55.13 | 55.91 | |
| ISAC | 18.96 | 42.10 | 42.93 | 36.70 | 36.09 | 52.00 | 64.30 | 31.10 | 33.26 | 19.34 | 37.68 | |
| Metric | Method | Held-out target dataset | Avg. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| IOPS | MGAB | NAB | NEK | Power | SED | Stock | TODS | UCR | WSD | YAHOO | |||
| VUS-PR | TS-Router | 41.49 | 43.09 | 51.97 | 76.92 | 22.40 | 65.42 | 73.18 | 71.65 | 39.60 | 56.91 | 77.32 | 56.36 |
| SATzilla | 29.32 | 0.97 | 38.66 | 39.31 | 24.97 | 7.88 | 77.81 | 62.13 | 20.21 | 43.48 | 29.34 | 34.01 | |
| ARGOSMART | 27.68 | 24.70 | 32.40 | 52.31 | 9.30 | 24.70 | 76.93 | 57.39 | 20.83 | 44.15 | 36.26 | 36.97 | |
| MetaOD | 27.79 | 0.97 | 40.12 | 39.31 | 24.97 | 7.88 | 77.81 | 63.46 | 20.43 | 44.46 | 29.37 | 34.23 | |
| ISAC | 31.77 | 24.70 | 41.41 | 41.83 | 37.05 | 7.88 | 78.19 | 64.33 | 25.04 | 40.10 | 30.47 | 38.43 | |