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

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.

• The paper introduces TimeRadar, a 1.6M-parameter foundation model that learns input-specific fractional time-frequency rotations and combines reconstruction with contextual deviation learning to detect diverse anomalies.
• TimeRadar achieves 76.97 AUC-ROC, 32.67 AUC-PR, and 76.92 affiliation F1 in zero-shot evaluation across eight benchmarks, improving over DADA by 10.5% and 29.4% on AUC-ROC and AUC-PR.
• The results show that adaptive domain rotation outperforms fixed time- or frequency-domain modeling, though reliance on synthetic anomalies and uncertain out-of-distribution robustness remain important limitations.

Motivation and problem setting

TimeRadar addresses a mismatch between existing time series foundation models (TSFMs) and the requirements of time series anomaly detection (TSAD). Most TSFMs are pre-trained to capture prevalent, regular patterns for supervised tasks such as forecasting, whereas TSAD is inherently unsupervised and targets rare, irregular patterns that are unbounded in form. The authors further argue that operating in a single, predefined domain—time or frequency—is insufficient: trend and seasonal anomalies can closely resemble normal temporal variations in the time domain, while shapelet anomalies show only minor spectral deviations in the frequency domain. Prior anomaly-specific foundation models such as DADA operate exclusively in the time domain and inherit this limitation.

The paper's central claim is that anomalies become more discriminative when the input is rotated into a data-dependent fractional time–frequency domain. Using the Fractional Fourier Transform (FRFT), which performs a continuous rotation of order $r$ between the time and frequency axes, TimeRadar learns an input-specific rotation angle $\alpha = r\pi/2$ with $r = \mathrm{Sigmoid}(\mathrm{MLP}(X))$, so that normal signals align along a dominant time–frequency trajectory while anomalous signals remain misaligned and disperse their energy.

Architecture

TimeRadar is an encoder-only model built from two components:

FTFRecon (Fractionally modulated Time-Frequency Reconstruction) applies instance normalization followed by FRFT conversion with the learnable fractional order; patches the complex-valued representation into non-overlapping patches projected by linear layers on real and imaginary parts separately; applies complementary masking shared across both parts to preserve phase consistency; and processes the masked representations through stacked FracBlocks. Each FracBlock performs modulation–convolution–demodulation: a quadratic-phase chirp rotates phase without altering amplitude, a bottlenecked dilated Conv1D operates on concatenated real/imaginary parts (DownNet → Conv1D → UpNet), and the conjugate chirp removes the rotation. A complex-valued MLP reconstruction head followed by inverse FRFT and amplitude projection yields the reconstructed series, trained with an $\ell_2$ reconstruction loss $\mathcal{L}_{rec}$.

CDL (Contextual Deviation Learning) models local abnormalities missed by global reconstruction. It computes each patch's contextual deviation as the average cosine dissimilarity of amplitudes against its context patches within the window, then enforces a margin loss requiring average deviation of abnormal patches to exceed that of normal patches by at least $\gamma$. Deviations are tracked via exponential moving averages during optimization. The joint pre-training objective is $\mathcal{L}_{rec} + \lambda \mathcal{L}_{cdl}$ with $\lambda = 0.1$ and $\gamma = 2$.

At inference, the anomaly score combines the variance across the $W$ complementary reconstructions with the squared error to their mean, exploiting the observation that anomalous inputs yield less stable reconstructions. Thresholding uses SPOT (extreme value theory). Few-shot adaptation is restricted to head probing, keeping the backbone frozen. Multivariate inputs are handled via channel independence.

Experimental results

Pre-training uses approximately 408 million time points drawn from the Monash$\alpha = r\pi/2$0 collection (anomaly-injected Monash data), with none of the evaluation datasets included. Evaluation covers eight benchmarks—SMD, MSL, PSM, SWaT, SMAP, CICIDS, SWAN, and Creditcard—plus UCR in the appendix, using AUC-ROC (AUC-R), AUC-PR (AUC-P), and affiliation F1 (Aff-F1), deliberately excluding point adjustment due to its documented flaws.

The headline zero-shot results:

Metric	Best full-shot baseline	DADA (zero-shot)	TimeRadar (zero-shot)
AUC-R	62.16 (CATCH)	69.15	76.97
AUC-P	18.57 (CATCH)	24.86	32.67
Aff-F1	71.59 (CATCH)	76.56	76.92

Relative to DADA, this corresponds to average gains of 10.5% in AUC-R and 29.4% in AUC-P. Notably, these gains come from a model with only 1.6M parameters—smaller than DADA (1.8M), SEMPO (6.5M), Time-MoE (200M), Chronos-Bolt (205M), or TimesFM (500M)—and pre-trained in three hours on two GPUs. Forecasting-oriented TSFMs (TimesFM, Chronos-Bolt, Time-MoE, SEMPO) perform poorly, supporting the claim that forecasting objectives do not transfer to anomaly detection. Generalist TSAD models also surpass conventional full-shot baselines trained per-dataset, indicating that large-scale multi-domain pretraining yields more transferable notions of normality than single-dataset training.

In few-shot experiments on MSL and PSM, head-probed TimeRadar consistently outperforms DADA across training-data fractions and exceeds the strongest full-shot baseline CATCH, indicating that the pretrained initialization provides strong inductive biases under data scarcity.

Ablations and analysis

The ablation study isolates each design choice. Replacing the FRFT with pure frequency-domain modeling plus CDL (variant A.1) or pure time-domain modeling plus CDL (A.2) degrades performance relative to the full model—for example, on PSM, AUC-R drops from 67.72 to 63.98 and 65.45 respectively—supporting the claim that the continuous, rotatable time–frequency space, rather than either fixed domain, drives the discriminative power. Removing CDL consistently lowers all metrics, confirming its role in enlarging normal–abnormal separation beyond what reconstruction alone achieves. Removing fractional modulation within FracBlocks also hurts performance, attributing part of the gain to local phase alignment enabling convolutional weight sharing.

Comparisons against grid-searched fixed rotation angles (step size 9°) show two things: the optimal angle varies substantially across datasets, and the learned input-dependent angle matches the best grid-searched angle closely. This validates the adaptive rotation mechanism as the source of cross-dataset generalization rather than a fortunate fixed choice. Anomaly-score visualizations further show that TimeRadar correctly identifies challenging subsequence anomalies (shapelet, trend, seasonal) where time-domain variants produce overly sharp or overly smooth responses and frequency-domain variants miss contextual point anomalies.

On efficiency, TimeRadar offers faster inference than DADA, Chronos-Bolt, and TimesFM despite its small footprint, though it remains slower and larger than conventional detectors such as CATCH and Anomaly Transformer—the authors position this as a favorable effectiveness–efficiency trade-off rather than dominance on both axes.

Limitations and open questions

Several caveats bear directly on the reported results. First, pre-training relies on synthetically injected anomalies (following DADA's injection protocol over Monash data), so the learned notion of abnormality may not fully cover naturally occurring anomaly distributions; the degree to which synthetic injection biases detection on real anomalies is not quantified. Second, the CDL margin loss requires patch-level labels during pre-training, using a coarse assignment where any patch containing an anomalous point is labeled abnormal—an assumption whose sensitivity to label noise is unexamined. Third, although the learned rotation angle matches grid-search optima on the four datasets tested, whether the Sigmoid-parameterized order generalizes to domains far outside the pre-training distribution remains open. Fourth, hyperparameter analysis shows performance declines for overly strict margins $\alpha = r\pi/2$1 and large $\alpha = r\pi/2$2, indicating the method depends on careful regularization balance. Finally, the inference score couples reconstruction error with cross-view variance; the individual contribution of each term to the reported gains is not decomposed.

Conclusion

TimeRadar demonstrates that rotating time series into a learnable, input-dependent fractional time–frequency domain improves the discriminability of diverse anomaly types for foundation-model-based TSAD. Combined with contextual deviation learning, this design achieves state-of-the-art zero-shot results on eight benchmarks—with average improvements of 10.5% AUC-R and 29.4% AUC-P over the prior generalist detector DADA—at a parameter budget of only 1.6M. The evidence supports adaptive domain selection as a viable alternative to fixed time- or frequency-domain modeling for generalist anomaly detection, while leaving open questions about reliance on synthetic anomaly injection and out-of-distribution robustness of the learned rotation.