Title: ScatterAD: Temporal-Topological Scattering Mechanism for Time Series Anomaly Detection
Venue: NeurIPS 2025
Accepted: yes
Keywords: Time series anomaly detection

representation learning

mutual information

graph attention network
Abstract: One main challenge in time series anomaly detection for industrial IoT lies in the complex spatio-temporal couplings within multivariate data. However, as traditional anomaly detection methods focus on modeling spatial or temporal dependencies independently, resulting in suboptimal representation learning and limited sensitivity to anomalous dispersion in high-dimensional spaces. In this work, we conduct an empirical analysis showing that both normal and anomalous samples tend to scatter in high-dimensional space, especially anomalous samples are markedly more dispersed. We formalize this dispersion phenomenon as scattering, quantified by the mean pairwise distance among sample representations, and leverage it as an inductive signal to enhance spatio-temporal anomaly detection. Technically, we propose ScatterAD to model representation scattering across temporal and topological dimensions. ScatterAD incorporates a topological encoder for capturing graph-structured scattering and a temporal encoder for constraining over-scattering through mean squared error minimization between neighboring time steps. We introduce a contrastive fusion mechanism to ensure the complementarity of the learned temporal and topological representations. Additionally, we theoretically show that maximizing the conditional mutual information between temporal and topological views improves cross-view consistency and enhances more discriminative representations. Extensive experiments on multiple public benchmarks show that ScatterAD achieves state-of-the-art performance on multivariate time series anomaly detection.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel anomaly detection framework, ScatterAD, which jointly enhances  feature discriminability and temporal consistency by using a temporal-topological scattering mechanism. Specifically, ScatterAD employs a dual-encoder architecture, consisting of an online encoder and a target encoder, where the online encoder is updated via backpropagation and the target encoder is updated using an exponential moving average (EMA) of the online encoder's parameters. The online encoder enforces temporal consistency across adjacent time steps, while the target encoder captures compact and consistent scattering representations in a projected hypersphere space. Moreover, a contrastive fusion mechanism is employed to align temporal and topological representations through a cross-view contrastive loss. The effectiveness of the paper is validated through extensive experiments.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\nThe paper formalize the dispersion phenomenon of normal and anomalous samples in high-dimensional space as scattering, quantified by the mean pairwise distance among sample representations. The authors further leverage this insight as an inductive signal to enhance spatio-temporal anomaly detection and propose a novel anomaly detection framework, ScatterAD, providing  valuable insights for multivariate time series anomaly detection. The overall paper is well-structured and easy to follow. The motivation of each component in the proposed framework is well explained. The effectiveness of the proposed framework is validated through both  theoretical analysis and extensive experiments across diverse datasets.\n\nWeakness:\nWhile the paper provides empirical observations that the scattering of anomalous samples tend to be more pronounced in high-dimensional space, it remains unclear whether such a phenomenon generalizes well across datasets with different types of anomalies or varying noise levels. The paper could benefit from systematically examining the scattering phenomenon across more datasets. Additionally, the experimental results should report the mean and standard deviation, with multiple repetitions to ensure statistical reliability.\n\nQUESTIONS:\n(a) Could the authors provide further justification or quantitative analysis to confirm that the observed scattering behavior is consistent and not occasional?\n\n(b) Could the authors clarify whether the reported experimental results are based on a single run or averaged over multiple runs?\n\n(c) The global scattering center c in the paper is randomly initialized inside the unit ball. Could the authors clarify whether this random initialization significantly affects the model performance or stability? Have you ever considered using alternative strategies?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-17"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors insightfully propose ScatterAD, a spatiotemporal anomaly detection framework for industrial IoT, introducing representation dispersion as an inductive bias to model the scattered nature of anomalies in high-dimensional space. ScatterAD combines a topological encoder and a temporal encoder to extract complementary features, and detects anomalies via scattering deviation and temporal inconsistency. The authors also prove that maximizing conditional mutual information is equivalent to a contrastive loss objective. Experiments on six benchmarks confirm its effectiveness through strong performance, visual analysis, and ablation studies.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe strengths of the work can be summarized as follows: \n\n1. Well written and clear. The paper introduces representation scattering as a novel perspective for high-dimensional anomaly detection, with a logical flow from dispersion to feature separation and detection.\n2. The paper presents a novel MTSAD approach inspired by the scattering phenomenon in industrial data, demonstrating clear insight.\n3. The effectiveness of the method is demonstrated on multiple MTSAD benchmarks with comprehensive evaluations.\n4. The authors’ theory unifies contrastive learning and conditional mutual information to enhance spatiotemporal representation complementarity.\n5. The authors provide the code implementation in the supplementary materials, which facilitates reproducibility.\n\nWeaknesses:\n\n1. A potential weakness lies in the initialization of the scattering center 𝑐 in Equation (6), which is randomly sampled within the unit sphere. This strategy may lead to suboptimal local minima and instability during training. For instance, poor initialization is a well-documented problem in machine learning, often causing slower convergence or trapping the model in unfavorable local optima, which degrades performance[1, 2].\n2. The scattering mechanism fundamentally depends on cosine similarity between samples and a reference center. However, the manuscript does not discuss the well-documented limitations of cosine similarity in high-dimensional settings, which may affect the robustness of the method. \n\n[1] Glorot, Xavier, and Yoshua Bengio. \"Understanding the difficulty of training deep feedforward neural networks.\" Proceedings of the thirteenth international conference on artificial intelligence and statistics. JMLR Workshop and Conference Proceedings, 2010.\n\n[2] Sutskever, Ilya, et al. \"On the importance of initialization and momentum in deep learning.\" International conference on machine learning. PMLR, 2013.\n\nQUESTIONS:\nPlease see weakness.\n\nLIMITATIONS:\nThe authors have sufficiently addressed the limitations of their study. I have no additional comments.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes ScatterAD, a novel approach for multivariate time series anomaly detection that leverages temporal-topological scattering mechanisms. The method combines a temporal encoder and a topological encoder with contrastive fusion to learn complementary spatio-temporal representations. The core insight is that anomalous samples exhibit more pronounced scattering patterns in high-dimensional space compared to normal samples. The authors provide theoretical justification using information bottleneck theory and demonstrate state-of-the-art performance across six real-world datasets.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n(1) The paper introduces conditional mutual information maximization based on information bottleneck theory into multivariate time series anomaly detection, providing theoretical proof that maximizing  $I(Z_T; Z_G \\mid G) $ can effectively enhance cross-view consistency and improve representation discriminability.\n\n(2) The method jointly considers temporal features and topological features, significantly enhancing the model's ability to capture complex spatio-temporal dependencies and anomaly patterns.\n\n(3)The paper employs multiple optimization objectives including scattering loss $L_{scatter}$, temporal consistency loss $L_{time}$, and contrastive fusion loss $L_{contrast}$. The contrastive fuse learning design can effectively prevent over-scattering of representations while maintaining temporal structural consistency, simultaneously improving feature discriminability and representation stability.\n\n**Weaknesses**\n\n(1) The paper states that $h_i$  \"represent the input feature vectors\" in equation (2), but subsequent text indicates that these symbols denote different data representations $h_i = h'_i + h^{(l)}$ while using identical notation. This creates ambiguity regarding what specific data each variable represents.\n\n(2) Section 3.1 introduces the online encoder $f_θ (∙)$ and target encoder $f_ϕ (∙)$ without providing concrete model architecture details. The paper lacks a clear explanation of how $h_{online,t}$ and $h_{target,t}$ are obtained, making it difficult to understand the specific implementation and reproduce the results.\n\n(3) Numerous formulas contain unexplained parameters, including $τ$ in Section 3.2, $l,k$ in equation (1), and ξ in equation (8). Additionally, critical parameter values such as the range or default value of $l,τ$ are not specified.\n\n(4) Section 3.2 states \"the node features are aggregated with topological features and temporal features, yielding $h_i = h'_i + h^{(l)}$\". \nThis description lacks clarity regarding how many values are being aggregated and what specific representations correspond to \"node features,\" \"topological features,\" and \"temporal features,\" respectively.\n\n(5) Section 3.3 \"Temporal Topological Scattering Representation Learning\" presents $c = \\text{Randn}(\\cdot), c = \\frac{c}{\\|c\\|} \\cdot \\epsilon$, what appears to be two equations without clearly describing their sequential relationship or dependencies.\n\n(6) The experimental comparison could benefit from including more classic and recent methods such as ModernTCN [Ref1], iTransformer [Ref2], and DCDetector [Ref3].\n\n- [Ref1] Moderntcn: A modern pure convolution structure for general time series analysis, ICLR. 2024.\n\n- [Ref2] Itransformer: Inverted transformers are effective for time series forecasting, ICLR 2023.\n\n- [Ref3]Dcdetector: Dual attention contrastive representation learning for time series anomaly detection, KDD. 2023.\n\nQUESTIONS:\n(1) Could you provide detailed architectural specifications for the online encoder $f_θ(·)$ and target encoder $f_ϕ(·)$? Additionally, please clarify how h_online and h_target are obtained from these encoders - are they direct outputs or derived through additional processing steps?\n\n(2) Many critical parameters lack proper definition, including $l, k$ in Section 3.2, $τ$ in equation (1), and ξ in equation (8). Could you provide precise definitions of these parameters and their typical value ranges? Furthermore, what are the specific values of parameters such as $l$ you used in your experiments?\n\n(3) How does the theoretical result $I(Z_T; Z_G | G)$ connect to your actual implementation? What specific graph structure $G$ is used in practice, and how does it relate to the conditional mutual information maximization in your theoretical framework?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents ScatterAD, a novel anomaly detection framework for multivariate time series in industrial IoT, which links representation learning to the information bottleneck principle, proving that maximizing conditional mutual information between temporal and topological views improves anomaly discrimination. ScatterAD jointly models temporal dynamics and topological techniques via the scattering loss, temporal constraint, and contrastive fusion. Extensive experiments on six benchmarks show state-of-the-art results of ScatterAD.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: This paper addresses a critical gap in spatio-temporal anomaly detection by unifying temporal consistency and topological dispersion. Achieves impressive results across diverse datasets. It is novel to formalize scattering as a learning signal and integrate information bottleneck theory into multivariate time series anomaly detection. The paper is well-structured, with clear method descriptions and precise theoretical proofs in the Appendix. \nAuthors provide a technically rigorous study with thorough ablation studies, sensitivity analysis, and visualizations. The proposed scattering mechanism is empirically validated via feature space analysis and training dynamics.\n\nWeaknesses: While inference speed is competitive, the need for careful hyperparameter tuning may hinder plug-and-play adoption in other testing domains. The mutual information bound relies on strong independence assumptions, which may not hold if the graph structure correlates with anomalies. Assuming a static graph structure, it seems to limit its applicability to systems with evolutionary dependencies.\n\nQUESTIONS:\n1. The temporal graph is fixed during training/inference. I  wonder how the performance of ScatterAD would be if the topology were to change suddenly.\n2. Using mean pairwise Euclidean distance instead of dispersion metrics like Mahalanobis distance or others needs clarification.  Does this choice affect sensitivity to feature scaling?\n3. PA-F of the method was high, but the AF-F in NIPS-TS-SWAN dropped sharply, although the authors stated the possible reasons in Sec. 4.2. More analysis could reveal method limitations. Or does scattering fail for bursty patterns?\n\nLIMITATIONS:\n1. Although the authors acknowledge static topology and lack of causality modeling in Appendix H. However, these aspects need more expansion.\n2. More testing of the proposed method for Real-world noisy data will help explore the robustness.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}