When Will It Fail?: Anomaly to Prompt for Forecasting Future Anomalies in Time Series

Thank you for giving us meaningful feedback!

More Datasets and Baselines

• TimeSeAD |Model|Exathlon-Avg.F1|SMD-Avg.F1| |:-:|:-:|:-:| |P-TST+AT|14.76|30.58| |A2P(Ours)|15.28|39.72|

• TranAD, BeatGAN, TimeMixer, DiffusionAD |F model|AD model|Avg.F1| |:-:|:-:|:-:| |P-TST|TranAD|42.63| ||BeatGAN|43.08| ||DiffusionAD|30.08| |MICN|TranAD|41.22| ||BeatGAN|45.04| ||DiffusionAD|31.04| |GPT2|TranAD|43.40| ||BeatGAN|38.40| ||DiffusionAD|29.89| |iTransformer|TranAD|43.97| ||BeatGAN|43.29| ||DiffusionAD|30.45| |FITS|TranAD|42.57| ||BeatGAN|40.17| ||DiffusionAD|27.09| |TimeMixer|AT|42.72| ||DC|34.40| ||CAD|17.16| ||TranAD|41.85| ||BeatGAN|43.55| ||DiffusionAD|26.10| |A2P(Ours)||46.84|

Our method outperforms all existing baselines across widely used benchmark datasets, demonstrating its effectiveness and generalizability.

Numerical Modesty of Results

AP is challenging as it requires predicting rare anomalies. Even small metric gains are meaningful. Table 1 shows our method consistently outperforms baselines, proving its effectiveness.

Dataset Splitting

Following prior works [1], we used non-overlapping windows for AP.

[1] Xu et al. “Anomaly transformer: Time series anomaly detection with association discrepancy.” ICLR 2022.

Dataset Statistics

The visualized sample in Fig. 8 typically contains a single anomaly pattern, but our method also handles subtle anomalies effectively, as shown in the table.

Trajectory Modeling

AP focuses on forecasting rare anomalies, while trajectory modeling predicts paths under normal conditions [1,2]. Some works [3] focus on anomaly detection, not future predictions, so AP remains underexplored in this context. A2P’s core idea could be explored in trajectory modeling in future research.

[1] Tang et al. “HPNet: Dynamic Trajectory Forecasting with Historical Prediction Attention.” CVPR 2024.

[2] Phan-Minh et al. “CoverNet: Multimodal Behavior Prediction using Trajectory Sets.” CVPR 2020.

[3] D'amicantonio et al. “uTRAND: Unsupervised Anomaly Detection in Traffic Trajectories.” CVPR 2024.

Cross-attention

While the cross-attention design may seem intuitive, the core contribution of AAF lies not in the architecture itself but in the idea of learning the inherent patterns of prior and posterior signals to predict future anomalies. By modeling the relationship between these signals, AAF captures temporal dependencies that are critical for AP, going beyond traditional forecasting or anomaly detection approaches.

Loss terms and Hyperparameters

Our method introduces two unique loss terms, $L_{AAF}$ and $L_{D}$, with others extended from traditional time series loss functions. A2P shows strong robustness across hyperparameter settings,as shown in Section E of the supplementary material. This suggests that they do not significantly complicate the tuning process.

Anomaly Threshold

The anomaly threshold follows the widely accepted protocol from [1], adjusting for a percentage of anomalies in the test data. This approach ensures consistency with established standards for anomaly detection tasks.

[1] Shen et al. "Timeseries anomaly detection using temporal hierarchical one-class network." NeurIPS 2020.

Trainable Parameters

In the pre-training stage, only AAFN and APP parameters are trainable. In the main training phase, only the backbone parameters are trained.

Simultaneous Training

We experimented with training all components simultaneously and found it suboptimal as shown in the table. This may be due to the Anomaly Probability output from the Anomaly-Aware Forecasting Network, which, when not fully trained, hinders proper forecasting. By using a two-stage training strategy, we ensure that the anomaly probability is learned first, allowing it to enhance future time series prediction during the main training phase, leading to better performance.

[CLS] Token

The [cls] token is a learnable embedding used to capture global representations, similar to its role in BERT [1]. It helps select the most relevant anomaly prompt in A2P, enabling effective abnormal signal synthesis.

[1] Devlin et al. "Bert: Pre-training of deep bidirectional transformers for language understanding." NAACL 2019.

We greatly appreciate your helpful comments, and we will be sure to include the above-mentioned details in our revision. This will provide a more thorough explanation and address the points you raised in a comprehensive manner, enhancing the overall quality of the paper.

We are sincerely grateful for giving us positive comments and acknowledging the contribution of our proposed method A2P for tackling the challenges of AP.

Initialization and Optimization Details

All additional parameters introduced for APP are initialized using a standard uniform initialization method in the PyTorch library. We will include this detail in the revision.

Computational Complexity

• To investigate the impact of additional computational complexity of our proposed methods, we measured GFLOPs per iteration (including both pre-training and main training) and the total number of parameters of the baseline (combination of PatchTST and AnomalyTransformer) and our proposed A2P. As shown in the figure (URL:https://ifh.cc/v-SRor7L), A2P does require additional computation compared to the baseline. However, since our model unifies both forecasting and anomaly detection within a single framework, it significantly reduces the overall parameter footprint. More importantly, this additional cost is only incurred during training, with no extra overhead at inference time. Despite the modest increase in training complexity, A2P achieved an average 10% improvement in performance over the baseline, demonstrating a favorable trade-off between cost and accuracy. Moreover, the train time consumed is utmost 1 hour in WADI dataset, which is negligible and is not really a heavy burden for A2P to be applied in real-world scenarios.
• Regarding scalability, the four datasets in Table 1 cover various ranges of dataset scales, as well as dynamic environments. To further validate A2P’s effectiveness, we conducted additional experiments on the KPI dataset (representing large-scale data) and the NeurIPS-TS dataset (characterized by highly dynamic anomaly patterns across all five anomaly types specified in [1]). A2P achieved state-of-the-art F1-score on both datasets, highlighting its robustness and scalability in large and dynamic settings.

[1] Lai et al. "Revisiting time series outlier detection: Definitions and benchmarks." NeurIPS 2021.

Existing Method for AP

To the best of our knowledge, there are currently no existing methods specifically designed for the AP task. However, a related study [1] conducted AP experiments using existing forecasting models, though these approaches do not directly address the unique challenges of AP. For a fair comparison, we constructed baselines by systematically combining established forecasting and anomaly detection models. This setup allows us to benchmark our method against the most relevant alternatives and highlights its distinct advantages.

[1] You et al. "Anomaly Prediction: A Novel Approach with Explicit Delay and Horizon." ICCP 2024.

Precursor Detection

Our proposed model A2P can detect precursors of impending anomalies. Since there are no labels indicating ‘precursor of anomalies’ in the dataset, we cannot measure the numeric performance of detection of precursors explicitly. Instead, we visualized the attention map of the cross attention in Anomaly-Aware Forecasting Network, to investigate if the model can relate specific parts of the prior signals when identifying future anomalies, as shown in the figure (URL:https://ifh.cc/v-cQD6Ka). When identifying the future anomalies (red-shaded area), which is the main purpose of AP, the model focuses on specific area of prior signals (circled area). While not perfect, our proposed model can provide a further explainable information to infer which prior time steps contribute to predicting future anomalies. This approach can be effective in many real-world scenarios, for example, medical doctors can scrutinize the normal data of patients to give them appropriate instructions to prevent possible diseases.

We will incorporate the additional details such as initialization and computational costs in the revision, and thank you again for your careful attention.

We appreciate your meaningful feedback, and your insights are invaluable as we continue to improve our work!

Computational Complexity

Please refer to the Computational Complexity section in Reviewer ADJk.

AP Task

The only prior work on Anomaly Prediction in time series is [1], which only formulates the problem without proposing concrete solutions. In contrast, our work is the first to introduce practical methods for AP, specifically through SAP and AAF, which directly address the core challenges and advance the field.

[1] You et al. "Anomaly Prediction: A Novel Approach with Explicit Delay and Horizon." ICCP 2024.

Underspecified Metrics

The conventional point adjustment for evaluation, as discussed in [1], has known limitations. Since the goal is to predict anomalies within a reasonable time window rather than at exact points, using raw prediction outputs is not ideal. For instance, medical doctors are more concerned with detecting abnormal symptoms over a time window, rather than at specific seconds or minutes. To address this, we use the F1-score with tolerance, a modified version of the traditional F1 with point adjustment, which allows error tolerance with a set time window around predicted anomalies, offering a more realistic evaluation, as shown in the figure (URL: https://ifh.cc/v-ZLV6Kf).

[1] Kim et al. "Towards a rigorous evaluation of time-series anomaly detection." AAAI 2022.

Data Augmentation

We compared A2P with data augmentation methods from [1]. While these methods improve prediction to some extent, they are limited by fixed anomaly injection rules. A2P, with context-aware prompts, generates more realistic anomalies, yielding better performance.

[1] Goswami et al. “Unsupervised model selection for time series anomaly detection.” ICLR 2023.

Unified Framework

Additional references on unified and multi-task frameworks, like [1] and [2], will be discussed. However, these models are unsuitable for AP. [2] only focuses on forecasting and simply combining forecasting and anomaly detection modules-such as in foundation models that handle each task independently-performs poorly, as shown in Table 1 baselines. AP requires forecasting anomalies and learning temporal patterns, which existing models lack. In contrast, A2P is specifically built for AP, integrating AAF with a learnable prompt pool to extend unified modeling trends into proactive anomaly handling.

[1] Gao et al. “UniTS: A unified multi-task time series model.” NeurIPS 2024.

[2] Woo et al. “Unified training of universal time series forecasting transformers.” ICML 2024.

Method Flow

Our two methods—SAP and AAF—work together in the A2P framework to bridge anomaly detection and forecasting. SAP addresses the challenge of limited abnormal signals in training data by using trainable anomaly prompts to create realistic synthetic anomalies, enhancing the model's anomaly recognition. AAF, in contrast, forecasts anomalies directly, improving predictions in abnormal conditions. Together, SAP and AAF complement each other—SAP enriches training data, while AAF uses this enriched data to enhance forecasting signals with anomalies. This synergy allows A2P to effectively detect and predict anomalies.

SAP Explanation

To clarify the SAP module, we include a figure (URL: https://ifh.cc/v-3dyYJd) that illustrates its mechanism. The Anomaly Prompt transforms normal features into anomalies, and the loss function $L_D$ guides the prompt pool to generate meaningful anomalies.

Grammatical Errors

We will carefully proofread the manuscript to correct any minor grammatical errors, e.g., “we formulate called Anomaly Prediction” or “are jointly pre-train”, and inconsistencies in punctuation, ensuring a more polished and professional presentation.

Hyperparameter Sensitivity

Please refer to the Loss terms and Hyperparameters section in Reviewer Xvbm.

Extra Anomaly Scenarios

We evaluated A2P on five univariate NeurIPS-TS datasets, covering various anomaly types, as outlined in [1]. A2P outperformed the baseline in F1-score, especially on contextual anomalies. However, it struggles with point anomalies due to their short duration. Future work could explore adding context or using multi-step forecasting to better detect point anomalies.

[1] Lai et al. "Revisiting time series outlier detection: Definitions and benchmarks." NeurIPS 2021.

Code Provision

We provide the reproducible code in anonymous repository https://anonymous.4open.science/r/A2P-E2FC.