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

TL;DR

TimeRadar introduces a domain-rotatable, time–frequency foundation model for time series anomaly detection by learning a data-dependent fractional rotation of signals in the continuous time–frequency space. Its core components, FTFRecon and CDL, enable adaptive reconstruction in an optimal fractional domain and capture local deviations from contextual patches, respectively. Pretrained on large multi-domain data and evaluated under zero-shot and few-shot settings, TimeRadar consistently surpasses strong TSAD baselines and other TSFMs across diverse datasets. The approach demonstrates robust cross-domain generalization with practical efficiency, offering a new paradigm for unsupervised TSAD in real-world deployments.

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 (10)

• 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 $\mathcal{L}_{cdl}$.
• Figure 3: Few-shot performance of TimeRadar and DADA using different amount of training data in a target dataset.
• Figure 4: Comparison of TimeRadar (learnable rotation angle) to its variants with manually searched rotation angles.
• Figure 5: Visualization of anomaly scores.