TimeRadar: A Domain-Rotatable Foundation Model for Time Series Anomaly Detection

Hui He; Hezhe Qiao; Yutong Chen; Kun Yi; Guansong Pang

cs.LGFeb 22, 2026

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

Abstract

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 $\alpha$ 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 $\mathcal{L}_{rec}$ and the margin loss $\mathcal{L}_{cdl}$ .

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
Design	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.

Panel of Figure 4 — 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	$\leq$ 4096	$\leq$ 512	$\leq$ 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.

Panel of Figure 8 — Figure 8. Sensitivity analysis w.r.t window size $T$ , contextual deviation margin $\gamma$ , and weight parameter $\lambda$ .

Figure 9. Visualization of the shapelet anomaly in Fig. 1 under the rotatable time–frequency domain with different rotation angles

\alpha

Panel of Figure 10 — Figure 10. Contextual deviation differences: (a) before training and (b) after training.

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