Contextual and Seasonal LSTMs for Time Series Anomaly Detection
Lingpei Zhang, Qingming Li, Yong Yang, Jiahao Chen, Rui Zeng, Chenyang Lyu, Shouling Ji

TL;DR
This paper introduces CS-LSTMs, a novel prediction-based framework that combines contextual and seasonal information with noise decomposition to improve detection of subtle anomalies in univariate time series.
Contribution
The paper presents a new prediction-based approach, CS-LSTMs, that effectively captures seasonal and contextual dependencies for anomaly detection in time series.
Findings
CS-LSTMs outperform existing methods on benchmark datasets.
The approach effectively detects subtle and slowly rising anomalies.
Integration of time and frequency domain representations enhances modeling accuracy.
Abstract
Univariate time series (UTS), where each timestamp records a single variable, serve as crucial indicators in web systems and cloud servers. Anomaly detection in UTS plays an essential role in both data mining and system reliability management. However, existing reconstruction-based and prediction-based methods struggle to capture certain subtle anomalies, particularly small point anomalies and slowly rising anomalies. To address these challenges, we propose a novel prediction-based framework named Contextual and Seasonal LSTMs (CS-LSTMs). CS-LSTMs are built upon a noise decomposition strategy and jointly leverage contextual dependencies and seasonal patterns, thereby strengthening the detection of subtle anomalies. By integrating both time-domain and frequency-domain representations, CS-LSTMs achieve more accurate modeling of periodic trends and anomaly localization. Extensive…
Peer Reviews
Decision·ICLR 2026 Poster
- **Systematic analysis of detection failures in existing methods.** The paper identifies why current approaches fail on small point anomalies and slowly rising segment anomalies, attributing this to inadequate integration of local trends with periodic variations. - **Principled noise decomposition strategy.** The wavelet-based approach effectively filters noise while preserving trend and seasonal components, enabling robust learning of normal patterns despite unlabeled anomalies in training dat
- Equation 6 appears to rely on the function or definition presented later in Equation 7. For clarity and logical coherence, the authors should introduce Equation 7 before Equation 6. - The paper lacks critical implementation details including specific hyperparameters such as batch size, number of training epochs,window sizes, decomposition Level L. - The paper provides limited explanation for why LSTMs are better over other recent architectures (Transformers, state-space models) that have also
- The separation of seasonal and contextual learning provides complementary modeling of periodic and local behaviors, enabling precise detection of small or slowly evolving anomalies. - The use of wavelet-based decomposition allows simultaneous handling of non-stationarity and noise suppression, improving interpretability and robustness compared with pure time-domain models. - Demonstrates consistent superiority over SOTA baselines across several datasets, supported by transferability and ablati
- Key mechanisms—especially the noise-decomposition pipeline, fusion process, and masked loss formulation—lack detailed mathematical description and ablation justification. - The paper does not analyze how the method scales to multivariate time series or handles cross-variable dependencies. - Efficiency metrics are presented in relative terms without absolute computational cost (e.g., GPU time, memory).
- **Clear problem framing**. This paper is, to my knowledge, the first to explicitly explain the two challenges of *small point anomalies* and *slowly rising anomalies* in UTS, and to analyze why popular reconstruction- and prediction-based baselines struggle with them. - **Probabilistic predictions**. Instead of deterministic outputs, the model predicts $\mu$ and $\sigma$, allowing $\sigma$ to act as a data-driven tolerance band and enabling a principled anomaly score. - **Architectural novelty
- **Generalization beyond the targeted anomaly types.** The evaluation focuses on cases where the two targeted anomaly types are present. It remains unclear how the model behaves when anomalies fall outside these categories (e.g., regime shifts without seasonality, changes in variance, or adversarial bursts). - **Scope limited to univariate data.** Many real-world series are multivariate. It is not apparent how this UTS-specific design would extend to multivariate settings. - **Hyperparameter se
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Taxonomy
TopicsTime Series Analysis and Forecasting · Anomaly Detection Techniques and Applications · Software System Performance and Reliability
