Title: Multivariate Time Series Anomaly Detection with Idempotent Reconstruction
Venue: NeurIPS 2025
Accepted: yes
Keywords: multivariate time series

anomaly detection

idempotent generative network
Abstract: Reconstruction-based methods are competitive choices for multivariate time series anomaly detection (MTS AD). However, one challenge these methods may suffer is over generalization, where abnormal inputs are also well reconstructed. In addition, balancing robustness and sensitivity is also important for final performance, as robustness ensures accurate detection in potentially noisy data, while sensitivity enables early detection of subtle anomalies. To address these problems, inspired by idempotent generative network, we take the view from the manifold and propose a novel module named **I**dempotent **G**eneration for **A**nomaly **D**etection (IGAD) which can be flexibly combined with a reconstruction-based method without introducing additional trainable parameters. We modify the manifold to make sure that normal time points can be mapped onto it while tightening it to drop out abnormal time points simultaneously. Regarding the latest findings of AD metrics, we evaluated IGAD on various methods with four real-world datasets, and they achieve visible improvements in VUS-PR than their predecessors, demonstrating the effective potential of IGAD for further improvements in MTS AD tasks. Our instructions on integrating IGAD into customized models and example codes are available at https://github.com/ProEcho1/Idempotent-Generation-for-Anomaly-Detection-IGAD.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors propose a new framework to enhance general reconstruction-based time series anomaly detection methods. The main idea is to complement the training objective with an idempotent loss term and a tightness loss term. The former aims to avoid the model of being too affected by noisy normal data in the training phase, while the latter focus on tightening the learned manifold to mitigate the model capability of reconstructing abnormal instances. The proposal is evaluated with 15 models from the literature on 4 datasets. Most results indicate gains (sometimes by a large margin) when using the new strategy when compared to not using it.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper is well organized and written, with each component of the IGAD framework detailed both visually and textually. The experiments are comprehensive, covering several recent models from the literature and presenting strong results when the proposed approach is included. Moreover, the fact that IGAD can used to enhance very distinct reconstruction-based methods is very interesting. The robustness and sensitivity analysis further highlight the advantages of IGAD. The ablation section is very detailed and justifies the methodological choices. I also praise the authors for the provided code and supplementary material, with several additional results.\n\nDespite not presenting serious weaknesses, it would be of interest to further explore the intuition behind the importance of the idempotent loss term. In practice, does it prevent the cases illustrated in Fig. 1? Perhaps some toy examples could be used to emphasize this point. Moreover, in the light of the work by Liu and Paparrizos, 2024 [31], which praises simpler models, it would be useful to verify how IDAG behaves with models such as standard AEs and VAEs.\n\nThe need of tuning the five hyperparameters in the IGAD objective could hinder its use in practice. Tab. 4 indicates that it would be difficult to fix default values across distinct datasets. Nevertheless, the authors argue that this choice may be reduced to three hyperparameters (the ones introduced by IGAD) and indicate good search intervals, which can be informed to standard optimization tools, such as Optuna.\n\nQUESTIONS:\n- Section 3.3.2: When explaining the idempotent objective, there is no obvious reason to pursue the frequency domain reconstruction path. Could, for instance, you elaborate on that? Is just a way to avoid the inclusion of trainable parameters? Could time-domain PCA be considered? This discussion could be a valuable inclusion to the text.\n\n- Section 3.3.3: The \"Inverse Effect\" is the main idea behind the tightness objective. However, it is not straightforward to link the accident expansion of the learned manifold and this operation. This section can be enhanced with a more thorough discussion on this.\n\n- Fig. 1: Can you make the font size slightly bigger?\n\n- Some references indicate the arXiv version, instead of the published version: [19, 27, 57, 69].\n\nLIMITATIONS:\nThe authors state the limitations of their work.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces the use of a idempotent generative network framework for multivariate time series anomaly detection in order to address the over generalization problem of reconstruction based time series anomaly detection methods, i.e., reconstruction models that rely on the assumption that abnormal time series would be poorly reconstructed by a generative model that has only seen normal data, may not in practice be the case. Two hypotheses are provided for this behaviour: 1) there is contaminated data in the normal training samples that are impractical to remove, and 2) reconstruction models that have good regularization/generalization properties could generalize well to anomalies. The proposed solution, IGAD, adds an idempotent loss and a tightness loss to ensure a tight mapping of normal samples to the target manifold. Improvements shown over many base reconstruction models and ablation studies demonstrate the effectiveness of this approach.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- Novel solution to the problem of over-generalization problem in reconstruction-based MTS AD methods\n- Theoretical analysis of how regularization leads to over-generalization and good reconstruction of anomalies (undesired)\n- Framework is compatible with almost every existing reconstruction-based MTS AD models, with no additional trainable parameters required\n- Consistent positive improvements of the framework over the original backbones.\n- A larger-than-average number of baselines is compared\n- Figure 5, Table 2, and Table 3 are impressive results\n- Robust protocol that includes optimizing the hyperparameters of baselines\n\nWeaknesses\n- Framework is almost the same as [45], although the application in MTS AD is novel\n- Proof of convergence is the same as [45]\n- Does not mention other work in the contaminated data in MTS AD, e.g., [Ref 1], and there are more in the general context of Anomaly detection. Note that the original IGN was tested on MNIST, so it is expected to cover contaminated AD in the non-TS field as well.\n- Does not achieve state-of-the-art results compared to [63]\n- Limited number of datasets (only 4, and they are small datasets). It would be more convincing to follow [63] and include SWaT, NIPS-TS, and UCR. More datasets would be favoured over a large number of baselines.\n- The delta_model percentage should be w/IGAD minus w/oIGAD as opposed to w/IGAD divided by w/oIGAD\n- Justify why VUS-PR is favoured over the other evaluation metrics. Can also report reconstruction error on abnormal data to be meaningful. \n- Figure 4b) is not very impressive looking compared to Figure 4a)\n\n[Ref 1] Contaminated Multivariate Time-Series Anomaly Detection with Spatio-Temporal Graph Conditional Diffusion Models\n\n\nMinor weaknesses:\n- Inconsistent use of the terms \"over generalization\" and \"over generation\"\n- The distinction between x and z is not clear in the introduction, but becomes clearer later.\n- Please clarify if a sliding window is used\n\nQUESTIONS:\n- Since the original IGN was tested on MNIST, can the proposed framework be applied to image data?\n- What is the justification for doing reconstruction on x and IGAD on z, why not use z for reconstruction, or use both x and z for IGAD?\n- How do we know that the tightness objective implicitly excludes anomalies from the manifold, when we don't have knowledge of the nature of the anomalies?\n- Are f and f' two separate networks of different weights? By the definition of idempotent, shouldn't f and f' be the same function? Is it the same network but in different points of time? Please clarify. It would also clear up how Eq (9) wouldn't cancel out.\n- The MAE over MSE experiment is interesting. Since 0.1684 VUS-PR is the performance of no IGAD with MSE, is it possible that the 0.2080 VUS-PR is attributed to the MAE loss instead of IGAD - this is potentially a weakness.\n\nLIMITATIONS:\nSome limitations have been discussed.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-27"}

comments: SUMMARY:
This paper proposes a novel module named IGAD to address the risk of over generalization in reconstruction-based methods for multivariate time series anomaly detection. IGAD draws on the ideas of idempotent generative networks and makes reasonable improvements for the task. And this paper presents sufficient theoretical analyses and experimental results.

STRENGTHS AND WEAKNESSES:
Strengths:  
S1: The paper has reasonable motivation.   
S2: The paper is easy to follow and well-written.    
S3: The paper has sufficient and detailed theoretical analysis.   

Weaknesses:   
W1: The number of datasets is slightly small.    
W2: The increased training time caused by IGAD limits its practicality, especially the more complex the base methods and datasets used with IGAD, the greater the additional time overhead introduced by IGAD.  
W3: The method in the paper is based on idempotent generative networks, which limits its innovativeness.

QUESTIONS:
Q1: In some datasets and for certain models, the use of IGAD has instead led to performance degradation. Considering that these are results after hyperparameter search, is this related to the compatibility between IGAD and some methods? For example, CAE-M shows limited improvement on the PSM and SMAP datasets and even performance degradation on the SMD dataset; ModernTCN exhibits significant performance drops on both the PSM and SMAP datasets.  
Q2: Why does the method with IGAD perform worse when the noise weight is smaller in Figure 4(b)?  
Q3: The models marked with * are concentrated on the MSL dataset. Is this related to the characteristics of the dataset?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-01

comments: SUMMARY:
This paper proposes a plug-and-play module named Idempotent Generation for Anomaly Detection (IGAD), which can be flexibly combined with a reconstruction-based method without introducing additional trainable parameters.  This method helps to release over-generalization and balance between robustness and sensitivity from a manifold perspective. Experiments on four datasets demonstrate its effectiveness.

STRENGTHS AND WEAKNESSES:
Strengths:
1. Figure 1 clearly illustrates the motivation of this paper.
2. In the experiments, 15 reconstruction-based multivariate time series anomaly detection methods are utilized as backbone models. Experimental results are sufficient.
3. Representation is clear and fluent.

Weakness: 
1. The lower part of Figure 2 should be improved with clear information flow, as well as its caption.
2. There are lots of hyperparameters of losses in Eq.11. There is not sufficient analysis about how these hyperparameters influence the model performance. Do those hyperparameters need to be carefully fine-tuned?
3. Is the method implemented on the pretrained backbone models or trained from initialization?
4. The proposed model performs as an additional module based on the backbone model. Thus, it is important to analyze the increased complexity and inference time, compared to the backbones.

QUESTIONS:
1. Are all the experimental results listed in Table 1reimplemented or directly from the original paper? Clear marks should be added.

LIMITATIONS:
Not mentioned.
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-03