TimeRadar: A Domain-Rotatable Foundation Model for Time Series Anomaly Detection
Authors: Hui He, Hezhe Qiao, Yutong Chen, Kun Yi, Guansong Pang
Organizations: School of Computing and Information Systems, Singapore Management University, Singapore · Chongqing Institute of Green and Intelligent Technology, University of Chinese Academy of Sciences, Chongqing, China · State Information Center, Beijing, China
Current time series foundation models (TSFMs) primarily focus on learning prevalent and regular patterns within a predefined time or frequency domain to enable supervised downstream tasks (e.g., forecasting). Consequently, they are often ineffective for inherently unsupervised downstream tasks-such as time series anomaly detection (TSAD), which aims to identify rare, irregular patterns. This limitation arises because such abnormal patterns can closely resemble the regular patterns when presented in the same time/frequency domain. To address this issue, we introduce TimeRadar, an innovative TSFM built in a fractional time-frequency domain to support generalist TSAD across diverse unseen datasets. Our key insight is that rotating a time series into a data-dependent fractional time-frequency representation can adaptively differentiate the normal and abnormal signals across different datasets. To this end, a novel component, namely Fractionally modulated Time-Frequency Reconstruction (FTFRecon), is proposed in TimeRadar to leverage a learnable fractional order to rotate the time series to the most pronounced angle between a continuous time and frequency domain for accurate data reconstruction. This provides adaptive data reconstruction in an optimal time-frequency domain for each data input, enabling effective differentiation of the unbounded abnormal patterns from the regular ones across datasets, including unseen datasets. To allow TimeRadar to model local abnormality that is not captured by the global data reconstruction, we further introduce a Contextual Deviation Learning (CDL) component to model the local deviation of the input relative to its contextual time series data in the rotatable domain.
Figures & tables
Figure 1. Normal patterns vs. three types of anomaly patterns (trend, shapelet, and seasonal anomalies, highlighted by the colored shadows) across three domains on synthetic data. (a) In the time domain , trend and seasonal anomalies exhibit changes that are highly similar to normal variations, whereas shapelet anomalies are more identifiable. (b) In the frequency domain , shapelet anomalies exhibit changes that are highly similar to normal variations whereas trend and seasonal anomalies produce clearer deviations from the normal patterns. (c) In our proposed rotatable time–frequency domain , all three anomaly types exhibit pronounced deviations from the normal time series.
Figure 2. Overview of TimeRadar. Given a time series X , its FTFRecon module firstly ① learns an input-dependent adaptive rotation angle α and accordingly transforms X into a flexible and expressive fractional time–frequency domain. After ② patching and complementary masking, the complex-valued time series patches are fed into the ③ fractionally modulated encoder and a reconstruction head. To complement the data reconstruction with local abnormality modeling, the ④ CDL module models the deviation of each patch relative to its contextual patches in the time–frequency hidden space via a margin learning loss. During pre-training, TimeRadar is jointly optimized with the reconstruction loss Lrec and the margin loss Lcdl .
Dataset
Setting
Method
SMD
MSL
PSM
SWaT
SMAP
CICIDS
SWAN
Creditcard
Avg.
AUC-R
Full-shot
TFMAE
29.37
45.19
33.35
56.04
58.49
50.41
40.21
47.68
45.09
Anomaly Transformer
36.74
49.06
49.99
39.69
49.60
51.23
50.86
52.66
47.48
DCdetector
47.99
50.19
49.44
49.86
49.97
54.48
50.34
44.47
49.59
D3R
72.01
45.77
58.46
30.01
46.93
61.82
55.63
92.39
57.88
ModernTCN
70.21
63.04
58.91
24.04
43.42
70.22
52.63
83.54
58.25
CATCH
73.59
65.36
64.68
23.49
47.26
78.20
49.26
95.41
62.16
Table 1. Quantitative results for TimeRadar ( Ours ) in eight real-world datasets. The best ones are in bold, and the second ones are underlined. Avg. denotes the average performance.
Figure 3. Few-shot performance of TimeRadar and DADA using different amount of training data in a target dataset.
Design
MSL
SMAP
SWaT
PSM
CICIDS
SWAN
Aff-F1
AUC-R
AUC-P
Aff-F1
AUC-R
AUC-P
Aff-F1
AUC-R
AUC-P
Aff-F1
AUC-R
AUC-P
Aff-F1
AUC-R
AUC-P
Aff-F1
AUC-R
AUC-P
TimeRadar
79.44
76.02
24.38
75.41
59.85
16.42
76.73
83.31
70.33
82.03
67.72
44.44
73.51
82.76
00.38
71.06
81.13
76.02
A.1 Frequency domain + CDL
76.69
72.61
22.57
73.74
58.52
15.10
73.46
80.23
69.33
79.20
63.98
38.99
69.48
78.64
00.24
68.37
77.39
72.22
A.2 Time domain + CDL
70.03
73.06
21.49
70.67
51.32
12.31
70.52
82.27
69.72
71.79
65.45
44.29
67.96
73.30
00.20
70.38
79.39
69.04
B BottleneckCNN Encoder
77.66
75.08
23.84
73.27
58.26
14.96
74.63
80.46
69.38
80.12
64.96
40.73
70.12
79.20
00.25
69.41
76.92
72.21
C TimeRadar(w/o CDL)
77.33
75.40
23.86
74.03
58.81
15.73
74.51
80.39
69.60
79.47
62.02
38.72
69.26
80.73
00.27
68.19
78.43
73.74
Table 2. Ablation study results. The higher values indicate better performance. The best ones are in bold.
Figure 4. Comparison of TimeRadar (learnable rotation angle) to its variants with manually searched rotation angles.
Figure 5. Visualization of anomaly scores.
Figure 6. Efficiency comparison on PSM.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Dataset
Domain
Frequency
Length
Aus. E.D.
Energy
Half Hourly
1,155,264
Wind
Energy
4 Seconds
7,397,147
Wind Farms
Energy
Minutely
172,178,060
Solar Power
Energy
4 Seconds
7,397,223
Solar
Energy
10 Minutes
7,200,857
London Smart M.
Energy
Half Hourly
166,527,216
Appendix
Table 3. Multi-domain time series datasets from the Monash Prediction Library ( Godahewa et al., 2021 ) .
Dataset
Domain
Dimension
Training
Validation
Test(labeled)
AR(%)
MSL
Spacecraft
1
46,653
11,664
73,729
10.5
PSM
Server Machine
25
105,984
26,497
87,841
27.8
SMAP
Spacecraft
1
108,146
27,037
427,617
12.8
SMD
Server Machine
38
566,724
141,681
708,420
4.2
SWaT
Water treatment
31
396,000
99,000
449,919
12.1
Creditcard
Finance
29
113,922
28,481
142,404
0.17
Appendix
Table 4. The datasets used for evaluation, where AR represents the anomaly ratio.
Method
TimeRadar
DADA
SEMPO
Time-MoE
Chronos-Bolt
TimesFM
Architecture
Encoder-only
Encoder-decoder
Encoder-only
Decoder-only
Encoder-decoder
Decoder-only
Model Size
1.6M
1.8M
6.5M
200M
205M
500M
Model version
-
-
Small
Large
Base
v2.0
Input Token
Patch
Patch
Patch
Point
Point
Patch
Dataset Scale
408M
473M
83M
309B
84B
100B
Context Length
100
100
512
≤ 4096
≤ 512
≤ 512
Appendix
Table 5. Comparison between pre-trained FMs on time series.
Dataset
Method
Aff-P
Aff-R
Aff-F1
AUC-R
AUC-P
R-A-R
R-A-P
V-R
V-P
SMD
Anomaly Transformer
54.08
97.07
66.42
36.74
03.87
51.22
07.09
51.17
07.96
D3R
64.87
97.93
78.02
72.01
14.18
62.89
11.20
61.69
11.01
ModernTCN
74.07
94.79
83.16
70.21
14.95
77.54
16.28
77.07
15.96
GPT4TS
73.33
95.97
83.13
74.15
15.85
77.27
17.68
76.79
17.45
TimesFM
61.44
88.47
72.52
62.80
07.37
69.72
12.08
74.58
12.69
Chronos-Bolt
52.69
97.21
68.34
63.40
07.64
70.41
12.45
75.19
13.13
Appendix
Table 6. Multi-metrics results in the three real-world datasets. The higher values for all metrics represent better performance. The best ones are in bold, and the second ones are underlined.
Dataset
SMD
MSL
SMAP
SWaT
PSM
Metric
Aff-P
Aff-R
Aff-F1
Aff-P
Aff-R
Aff-F1
Aff-P
Aff-R
Aff-F1
Aff-P
Aff-R
Aff-F1
Aff-P
Aff-R
Aff-F1
OCSVM
66.98
82.03
73.75
50.26
99.86
66.87
41.05
69.37
51.58
56.8
98.72
72.11
57.51
58.11
57.81
PCA
64.92
86.06
74.01
52.69
98.33
68.61
50.62
98.48
66.87
62.32
82.96
71.18
77.44
63.68
69.89
HBOS
60.34
64.11
62.17
59.25
83.32
69.25
41.54
66.17
51.04
54.49
91.35
68.26
78.45
29.82
43.21
LOF
57.69
99.10
72.92
49.89
72.18
29.00
47.92
82.86
60.72
53.20
96.73
68.65
53.90
99.91
70.02
IForest
71.94
94.27
81.61
53.87
94.58
68.65
41.12
68.91
51.51
53.03
99.95
69.30
69.66
88.79
78.07
Appendix
Table 7. Quantitative results for TimeRadar ( Ours ) in five real-world datasets. The Aff-P, Aff-R and Aff-F1 represent the Affiliation Precision, Recall and F1 (as %) respectively. The best ones are in bold, and the second ones are underlined.
Figure 7. Results on UCR benchmark.
Figure 8. Sensitivity analysis w.r.t window size T , contextual deviation margin γ , and weight parameter λ .
Figure 9. Visualization of the shapelet anomaly in Fig. 1 under the rotatable time–frequency domain with different rotation angles α .
Figure 10. Contextual deviation differences: (a) before training and (b) after training.
Time series anomaly detection is a crucial task in various domains, including finance, healthcare, and industry. However, existing methods often struggle to generalize across different datasets, especially when anomalies are subtle or context-dependent. To solve this issue, we introduce ChronosAD, a novel architecture for anomaly detection that uses a time series foundation model as a feature extractor. Specifically, it employs a two-stage pipeline: first, it uses the foundation model to extract embeddings for each time series in a zero-shot manner. Then, a custom-developed Temporal Block, composed of Bidirectional Long Short-Term Memory (BiLSTM) and Multi-Head Attention, refines these embeddings to capture temporal dependencies and highlight salient patterns. Unlike previous approaches, our model requires minimal task-specific tuning and demonstrates robust generalization across a wide range of domains, including industrial, medical, cyber-physical, and automotive systems. Extensive experiments on 11 benchmarks show that ChronosAD outperforms existing methods by 4.72% in AUC and 6.60% in AP on average. The source code is available at https://github.com/intelligolabs/ChronosAD.
Uzair Khan, Luigi Capogrosso, Francesco Biondani +4
University of Verona · Interdisciplinary Transformation University of Austria · ETH Zurich
Time Series Foundation Models (TSFMs) achieve strong generalization by learning to reconstruct or forecast broad temporal patterns from large-scale time series during pre-training. Yet this strength can become a weakness for anomaly detection: TSFMs may model rare anomalous patterns as effectively as normal ones, allowing anomalies to be accurately reconstructed or forecasted and thus diminishing their reconstruction/forecasting error-based anomaly scores. This paper proposes \underline{\textbf{N}}$$\textbf{ormality}\underline{\textbf{C}}$$\textbf{onstraint}\underline{\textbf{L}}$$\textbf{earning} (NCL), a lightweight plug-and-play framework that adapts pre-trained TSFMs for accurate anomaly detection without modifying their pre-trained parameters. Our key insight is to constrain the broad pattern space of TSFMs to the normal structure of a target time series, preventing their broad modeling capability from obscuring abnormal deviations. Specifically, NCL constructs a compact normality subspace from a few normal patch features and adaptively steers each patch feature toward normality within this subspace, guided by contrastive constraints that form compact and discriminative normality manifolds. The calibrated features are aggregated to reinforce normal components and fused with the original TSFM output, amplifying the discrepancy between normal and abnormal observations for the reconstruction/forecasting error-based anomaly scoring. Extensive experiments across diverse TSFM families and benchmarks show that NCL consistently improves anomaly detection performance, providing a generalizable framework for adapting TSFMs to anomaly detection.
Xiaohui Zhou, Yijie Wang, Hongzuo Xu +2
National Key Laboratory of Parallel and Distributed Computing · College of Computer Science and Technology, National University of Defense Technology · Intelligent Game and Decision Lab (IGDL) +1
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 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-k 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.
Tian Lan, Yifei Gao, Yimeng Lu +6
Department of Industrial Engineering Tsinghua University · Huawei · Datadog AI Research Paris, France