Distilling Multi-Teacher Scoring Principles for Unsupervised Time Series Anomaly Detection
Organizations: Industrial AI Lab, SimPlatform Co. Ltd. Affiliate Research Institute
Abstract
Time series anomalies take diverse forms, and individual detectors encode different anomaly scoring principles that rarely cover all anomaly types. Recent unsupervised time-series anomaly detectors provide complementary scoring signals, yet deploying them as an ensemble preserves the inference and maintenance cost of every individual detector. We study whether heterogeneous teacher detectors can be distilled into a single lightweight detector in the unsupervised setting, where no anomaly labels are available to define a shared target. AnoMix addresses this by extracting weak pairwise supervision from the training-set anomaly scores of frozen teachers. It normalizes each teacher score sequence independently and trains the student with CoRank, a multi-teacher ranking-distillation objective that converts teacher score gaps into pairwise supervision through teacher consensus. Across seven benchmark datasets, AnoMix successfully integrates complementary teacher scoring principles into a single deployable model, improving over individual detectors and static score ensembles while using a compact student with under 80k parameters on the benchmark settings. A zero-shot variant further shows that the distilled ranking signal transfers to unseen datasets and can outperform large pretrained time-series foundation models for anomaly detection.
Figures & tables
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | Avg Rank | |||||||
| V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | ||
| Omni [ 3 ] | 51.59 | 22.52 | 59.42 | 27.32 | 99.98 | 99.75 | 95.40 | 69.98 | 49.93 | 27.68 | 78.60 | 18.38 | 92.06 | 91.16 | 6.18 |
| USAD [ 9 ] | 52.15 | 22.73 | 68.92 | 33.39 | 99.97 | 99.63 | 95.98 | 71.97 | 49.80 | 27.58 | 76.95 | 17.15 | 89.80 | 88.60 | 6.36 |
| A.T [ 15 ] | 53.76 | 23.13 | 56.63 | 23.55 | 37.70 | 24.88 | 44.03 | 11.80 | 40.56 | 22.30 | 46.28 | 10.33 | 86.33 | 81.07 | 10.29 |
| TranAD [ 10 ] | 55.90 | 22.25 | 77.06 | 37.86 | 99.50 | 93.88 | 86.51 | 52.05 | 71.96 | 37.06 | 76.71 | 17.98 | 92.02 | 86.48 | 6.93 |
| TimesNet [ 11 ] | 57.91 | 24.32 | 59.29 | 24.35 | 98.61 | 85.33 | 93.96 | 53.06 | 59.22 | 23.90 | 90.25 | 33.97 | 93.87 | 88.77 | 6.71 |
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | Avg Rank | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | ||
| Mean | 67.00 | 31.23 | 63.80 | 27.07 | 99.65 | 95.82 | 97.55 | 74.23 | 53.50 | 34.87 | 91.64 | 38.10 | 93.96 | 91.54 | 4.00 |
| Max | 66.81 | 31.20 | 59.77 | 25.78 | 99.45 | 93.49 | 96.46 | 68.26 | 53.02 | 35.59 | 89.35 | 31.59 | 93.98 | 91.30 | 5.21 |
| Median | 61.93 | 27.28 | 65.66 | 28.21 | 99.83 | 97.78 | 96.50 | 72.13 | 66.88 | 32.59 | 90.24 | 38.85 | 92.81 | 89.47 | 4.57 |
| Rank Fusion | 64.90 | 27.81 | 65.08 | 28.57 | 99.97 | 99.74 | 97.72 | 83.70 | 70.26 | 37.86 | 92.71 | 46.11 | 93.88 | 91.69 | 2.93 |
| RRF [ 44 ] | 67.37 | 31.69 | 65.28 | 28.55 | 99.47 | 94.59 | 97.73 | 79.13 | 71.84 | 39.62 | 91.32 | 36.18 | 94.24 | 91.59 | 3.00 |
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | Avg Rank | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | ||
| LOO-1 | 48.10 | 22.32 | 43.48 | 25.09 | 80.05 | 81.58 | 59.08 | 48.49 | 56.59 | 56.58 | 75.65 | 30.98 | 90.81 | 84.37 | 7.00 |
| LOO-2 | 69.91 | 42.22 | 73.28 | 38.72 | 99.99 | 99.96 | 98.92 | 89.48 | 98.37 | 97.65 | 94.01 | 51.50 | 92.45 | 90.77 | 4.61 |
| LOO-3 | 69.04 | 42.64 | 76.82 | 43.37 | 99.99 | 99.96 | 98.87 | 89.37 | 98.40 | 97.72 | 94.12 | 51.96 | 93.75 | 91.76 | 3.61 |
| LOO-4 | 67.55 | 35.17 | 80.98 | 44.59 | 99.99 | 99.96 | 98.90 | 89.37 | 98.41 | 97.75 | 94.10 | 51.94 | 93.60 | 91.52 | 3.68 |
| LOO-5 | 67.64 | 34.40 | 75.49 | 41.28 | 99.99 | 99.96 | 98.90 | 89.39 | 98.42 | 97.77 | 94.15 | 52.25 | 93.43 | 91.28 | 3.68 |
| Method | Params | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | Avg Rank | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | |||
| MOMENT [ 42 ] | 110M | 41.87 | 16.66 | 54.62 | 20.17 | 99.66 | 97.18 | 58.22 | 10.38 | 56.03 | 28.31 | 91.49 | 34.49 | 92.06 | 86.29 | 5.57 |
| TimesFM [ 45 ] | 200M | 53.99 | 20.14 | 49.45 | 19.22 | 99.19 | 96.64 | 59.04 | 16.19 | 94.65 | 88.93 | 89.97 | 34.79 | 93.79 | 87.66 | 4.50 |
| Chronos [ 46 ] | 710M | 52.46 | 18.68 | 63.11 | 23.33 | 87.54 | 61.15 | 89.06 | 34.67 | 70.54 | 30.97 | 90.53 | 33.50 | 93.02 | 88.11 | 4.71 |
| MOIRAI [ 47 ] | 14M | 54.02 | 19.47 | 55.17 | 20.49 | 91.52 | 66.86 | 60.99 | 10.37 | 57.98 | 21.12 | 91.07 | 34.11 | 92.64 | 83.72 | 5.43 |
| Lag-Llama [ 48 ] | 10M | 54.63 | 20.45 | 47.96 | 18.56 | 89.08 | 58.11 | 83.10 | 33.47 | 80.29 | 39.28 | 92.04 | 38.24 | 93.11 | 87.86 | 4.43 |
Appendix figures & tables20 assets
Supplementary material from the paper’s appendix.
Appendix
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | |
| Omni | 22.52 | 21.43 | 24.07 | 27.32 | 24.03 | 32.12 | 99.75 | 98.88 | 99.96 | 69.98 | 71.68 | 75.18 | 27.68 | 26.97 | 28.08 | 18.38 | 16.97 | 19.25 | 91.16 | 54.34 | 91.51 |
| USAD ’20 | 22.73 | 22.52 | 24.35 | 33.39 | 29.60 | 38.56 | 99.63 | 98.47 | 99.93 | 71.97 | 72.42 | 77.36 | 27.58 | 26.86 | 27.98 | 17.15 | 15.24 | 18.31 | 88.60 | 49.50 | 87.86 |
| A.T | 23.13 | 21.95 | 23.18 | 23.55 | 20.94 | 26.87 | 24.88 | 24.59 | 25.28 | 11.80 | 9.74 | 13.74 | 22.30 | 21.35 | 22.90 | 10.33 | 9.40 | 11.35 | 81.07 | 36.05 | 85.01 |
| TranAD ’22 | 22.25 | 21.27 | 22.61 | 37.86 | 31.38 | 43.86 | 93.88 | 93.35 | 93.97 | 52.05 | 46.92 | 45.51 | 37.06 | 35.94 | 37.54 | 17.98 | 16.48 | 19.29 | 86.48 | 41.25 | 86.87 |
| TimesNet ’23 | 24.32 | 20.33 | 26.19 | 24.35 | 20.87 | 28.20 | 85.33 | 81.74 | 88.15 | 53.06 | 44.41 | 56.79 | 23.90 | 22.80 | 24.62 | 33.97 | 31.01 | 36.82 | 88.77 | 43.48 | 90.36 |
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | VUS | AUC | R-AUC | |
| Omni | 51.59 | 59.49 | 52.74 | 59.42 | 59.91 | 63.64 | 99.98 | 99.91 | 100.00 | 95.40 | 95.17 | 96.34 | 49.93 | 48.90 | 50.83 | 78.60 | 79.20 | 79.01 | 92.06 | 63.19 | 86.54 |
| USAD ’20 | 52.15 | 58.18 | 52.52 | 68.92 | 70.88 | 72.92 | 99.97 | 99.88 | 99.99 | 95.98 | 95.40 | 96.88 | 49.80 | 48.77 | 50.70 | 76.95 | 76.13 | 78.18 | 89.80 | 56.15 | 81.06 |
| A.T | 53.76 | 54.64 | 44.00 | 56.63 | 54.36 | 59.22 | 37.70 | 37.13 | 38.35 | 44.03 | 42.04 | 44.83 | 40.56 | 39.73 | 41.49 | 46.28 | 44.92 | 47.59 | 86.33 | 50.95 | 78.38 |
| TranAD ’22 | 55.90 | 55.14 | 48.22 | 77.06 | 72.97 | 81.54 | 99.50 | 99.47 | 99.50 | 86.51 | 82.75 | 81.84 | 71.96 | 70.85 | 72.81 | 76.71 | 73.04 | 79.00 | 92.02 | 52.60 | 81.50 |
| TimesNet ’23 | 57.91 | 53.22 | 57.87 | 59.29 | 53.56 | 64.78 | 98.61 | 98.24 | 98.88 | 93.96 | 90.60 | 92.45 | 59.22 | 58.06 | 60.13 | 90.25 | 88.98 | 91.30 | 93.87 | 56.52 | 86.33 |
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| F1 | Event | Aff | F1 | Event | Aff | F1 | Event | Aff | F1 | Event | Aff | F1 | Event | Aff | F1 | Event | Aff | F1 | Event | Aff | |
| Omni | 32.33 | 33.23 | 71.17 | 36.08 | 42.27 | 71.63 | 98.90 | 100.00 | 99.92 | 65.77 | 73.18 | 83.23 | 40.81 | 100.00 | 94.05 | 31.66 | 33.39 | 86.13 | 49.72 | 49.17 | 71.05 |
| USAD ’20 | 31.42 | 32.11 | 71.52 | 45.84 | 44.86 | 74.07 | 98.70 | 99.85 | 99.91 | 64.51 | 66.15 | 83.88 | 40.81 | 100.00 | 94.05 | 30.87 | 31.11 | 85.85 | 49.17 | 49.17 | 71.05 |
| A.T | 30.13 | 28.58 | 66.79 | 32.80 | 42.83 | 70.23 | 29.57 | 78.63 | 87.28 | 15.07 | 35.43 | 64.33 | 30.92 | 57.50 | 77.16 | 16.68 | 46.50 | 79.35 | 49.17 | 32.23 | 53.48 |
| TranAD ’22 | 29.30 | 29.20 | 69.43 | 48.65 | 33.39 | 71.64 | 97.62 | 100.00 | 99.11 | 52.64 | 76.91 | 91.88 | 63.20 | 100.00 | 93.14 | 29.36 | 61.49 | 88.35 | 49.17 | 49.17 | 71.05 |
| TimesNet ’23 | 29.20 | 29.20 | 69.43 | 30.39 | 30.26 | 71.63 | 90.08 | 94.00 | 97.45 | 51.94 | 67.34 | 86.40 | 40.20 | 100.00 | 92.58 | 40.48 | 58.10 | 82.44 | 49.17 | 49.17 | 71.05 |
| Dataset | Subset | Domain | Train | Validation | Test | Anomaly (%) | Events | |
|---|---|---|---|---|---|---|---|---|
| PSM | – | Server monitoring | 25 | 67,500 | 7,500 | 142,624 | 11.2 | 72 |
| SWaT | – | Cyber-physical control | 66 | 3,374 | 375 | 11,247 | 13.2 | 6 |
| Exathlon | id22 | Distributed stream processing | 31 | 9,689 | 1,077 | 32,300 | 12.6 | 3 |
| SMD | id6 | Internet-company server | 38 | 6,462 | 718 | 21,542 | 6.1 | 10 |
| SMAP | id1 | Satellite telemetry | 25 | 1,846 | 206 | 6,157 | 13.7 | 1 |
| Daphnet | – | Wearable accelerometer | 9 | 8,723 | 970 | 29,081 | 5.9 | 6 |
| Model | Window | Learning rate | Stopping rule |
|---|---|---|---|
| OmniAnomaly | 100 | Early stopping | |
| USAD | 100 | Early stopping | |
| Anomaly Transformer | 50 | Early stopping | |
| TranAD | 10 | Early stopping | |
| TimesNet | 96 | Early stopping | |
| SARAD | 100 | Early stopping |
| Rank | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN |
|---|---|---|---|---|---|---|---|
| 1 | SARAD | CrossAD | CrossAD | SARAD | CrossAD | CrossAD | SARAD |
| 2 | CrossAD | SARAD | SARAD | OracleAD | SARAD | SARAD | CrossAD |
| 3 | CATCH | CATCH | CATCH | CrossAD | CATCH | USAD | OracleAD |
| 4 | USAD | OracleAD | OracleAD | CATCH | USAD | Omni | CATCH |
| 5 | OracleAD | Omni | USAD | TranAD | Omni | OracleAD | USAD |
| 6 | Omni | USAD | Omni | USAD | OracleAD | CATCH | Omni |
| Teacher set | Mean Spearman | Pair support | AnoMix VUS-PR | vs. best teacher | vs. mean ensemble |
|---|---|---|---|---|---|
| Sel-3 | 0.463 | 36.8% | |||
| HML-3 | 0.248 | 27.1% | |||
| Mid-3 | 0.607 | 33.9% | |||
| Bottom-3 | 0.024 | 3.9% | |||
| Corr-3 | 0.844 | 27.3% |
| Dataset | Learning Rate | Window Size | Batch Size |
|---|---|---|---|
| PSM | 127 | 64 | |
| SWaT | 127 | 64 | |
| Exathlon | 127 | 64 | |
| SMD | 64 | 64 | |
| SMAP | 127 | 64 | |
| Daphnet | 127 | 64 |
| Model | Complexity | Params | Memory (MB) | FLOPs |
|---|---|---|---|---|
| SARAD | 9.66M | 58.04 | 2.03G | |
| CrossAD | 2.64M | 178.49 | 8.81G | |
| OracleAD | 211.72M | 893.94 | 21.21G | |
| CATCH | 13.52M | 86.17 | 1.18G | |
| Omni | 314k | 27.55 | 31.64M | |
| USAD | 1.00M | 13.82 | 1.60M |
| Component | Configuration |
|---|---|
| CPU | Intel Core Ultra 7 265K, 20 cores |
| GPU | NVIDIA GeForce RTX 5090, 32 GB memory |
| System memory | 96 GB RAM |
| Operating system | Ubuntu 24.04.4 LTS, Linux 6.14 |
| NVIDIA driver | 570.153.02 |
| Software stack | Python 3.13, PyTorch 2.7.0+cu128, CUDA runtime 12.8 |
| Dataset | |||||
|---|---|---|---|---|---|
| PSM | 0.04 | 0.09 | 0.08 | 0.40 | 99.39 |
| SWaT | 4.06 | 5.16 | 7.36 | 11.65 | 71.76 |
| Exathlon | 0.01 | 0.02 | 0.02 | 0.05 | 99.91 |
| SMD | 3.72 | 4.52 | 6.14 | 9.85 | 75.77 |
| SMAP | 2.30 | 2.02 | 2.71 | 5.61 | 87.36 |
| Daphnet | 0.40 | 0.58 | 0.83 | 2.22 | 95.96 |
| Training confidence range | VUS-ROC | VUS-PR |
|---|---|---|
| (Full) | ||
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | |
| Omni [ 3 ] | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| USAD [ 9 ] | 0.89 | 0.57 | 1.31 | 0.75 | 0.00 | 0.04 | 0.34 | 1.31 | 0.00 | 0.00 | 0.84 | 0.38 | 0.20 | 0.29 |
| A.T [ 15 ] | 4.04 | 2.59 | 10.16 | 6.40 | 6.57 | 6.97 | 2.63 | 1.03 | 7.06 | 4.02 | 7.63 | 1.77 | 3.05 | 0.96 |
| TranAD [ 10 ] | 0.59 | 0.19 | 1.25 | 0.78 | 0.01 | 0.36 | 0.15 | 0.17 | 11.31 | 3.95 | 0.34 | 0.25 | 0.18 | 0.28 |
| TimesNet [ 11 ] | 0.69 | 0.58 | 1.01 | 0.89 | 0.11 | 0.84 | 0.65 | 2.05 | 4.50 | 1.85 | 0.15 | 0.59 | 0.46 | 0.90 |
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | |
| Mean | 2.66 | 1.59 | 3.54 | 1.29 | 0.13 | 1.76 | 0.28 | 1.24 | 0.58 | 0.14 | 0.88 | 3.92 | 0.32 | 0.30 |
| Max | 3.91 | 2.46 | 6.60 | 2.80 | 0.18 | 2.74 | 0.49 | 1.42 | 0.41 | 0.08 | 1.46 | 3.67 | 0.52 | 0.14 |
| Median | 2.01 | 0.86 | 0.68 | 0.31 | 0.21 | 2.49 | 0.34 | 1.38 | 0.82 | 0.41 | 0.38 | 1.38 | 0.89 | 1.85 |
| Rank Fusion | 1.28 | 0.86 | 2.47 | 1.14 | 0.01 | 0.08 | 0.50 | 2.13 | 0.93 | 1.04 | 0.44 | 2.14 | 0.19 | 0.34 |
| RRF [ 44 ] | 1.33 | 1.45 | 2.48 | 1.30 | 0.12 | 1.17 | 0.15 | 1.32 | 1.55 | 1.51 | 0.77 | 2.82 | 0.37 | 0.91 |
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | |
| LOO-1 | 6.07 | 4.27 | 22.60 | 10.70 | 39.37 | 36.16 | 34.56 | 33.08 | 39.45 | 36.99 | 29.93 | 13.42 | 3.05 | 5.10 |
| LOO-2 | 2.41 | 3.93 | 2.14 | 2.02 | 0.01 | 0.03 | 0.42 | 0.76 | 0.06 | 0.06 | 0.28 | 1.76 | 0.18 | 0.33 |
| LOO-3 | 6.25 | 5.11 | 3.10 | 4.75 | 0.01 | 0.04 | 0.42 | 1.29 | 0.04 | 0.05 | 0.38 | 2.01 | 0.51 | 0.67 |
| LOO-4 | 3.11 | 2.55 | 3.16 | 3.35 | 0.00 | 0.02 | 0.38 | 0.99 | 0.04 | 0.04 | 0.38 | 1.99 | 0.43 | 0.80 |
| LOO-5 | 3.86 | 2.53 | 7.15 | 5.06 | 0.01 | 0.04 | 0.38 | 0.99 | 0.04 | 0.04 | 0.38 | 2.01 | 0.27 | 0.84 |
| Method | PSM | SWaT | Exathlon | SMD | SMAP | Daphnet | SWAN | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | V-ROC | V-PR | |
| AnoMix-ZS | 1.45 | 1.45 | 1.46 | 2.17 | 0.08 | 1.38 | 0.47 | 4.72 | 0.75 | 2.30 | 1.00 | 4.63 | 0.25 | 0.53 |
Unsupervised Anomaly Detection
Unsupervised anomaly detection finds unusual patterns without labeled examples of faults, attacks, defects, or other rare events.
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