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arxiv: 2605.23744 · v1 · pith:ZYZBTUNAnew · submitted 2026-05-22 · 💻 cs.LG

Contrast to Detect: Dynamic Graph Contrastive Regularization for Unsupervised Anomaly Detection in Multivariate Time Series

Yunhua Pei , Zixing Song , Jin Zheng , John Cartlidge This is my paper

Pith reviewed 2026-05-25 04:56 UTC · model grok-4.3

classification 💻 cs.LG
keywords anomaly detectionmultivariate time seriesgraph contrastive learningunsupervised learningdynamic graphstime series analysiscontrastive regularizationstructural drift
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The pith

ContrastAD detects anomalies in multivariate time series by turning structural evolution into a contrastive signal instead of suppressing it.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces ContrastAD, an unsupervised method that encodes time series from temporal, attribute, and structural views, applies frequency-aware attention to limit noise, and uses a Dynamic Graph Contrastive Learner to build sparse graph snapshots from batch DTW distances. It contrasts the most divergent pair against a stable anchor to regularize the latent space without forcing invariance across views. This addresses the failure of reconstruction methods to separate anomalies and the stationarity assumption in prior graph contrastive detectors. On five real-world benchmarks the approach leads in mean F1 across all datasets and in AUC on three, with the contrastive term functioning best as a soft regularizer. A reader would care because many deployed systems exhibit drifting variable relations that break existing detectors.

Core claim

By constructing power-law-inspired sparse graph snapshots from batch-level DTW distances and contrasting the most divergent pair against a stable anchor, ContrastAD regularizes the latent space to exploit rather than ignore structural drift, yielding the highest mean F1 on all five benchmarks and the highest AUC on SWaT, SMD, and PSM.

What carries the argument

The Dynamic Graph Contrastive Learner, which builds sparse graph snapshots from DTW distances and contrasts divergent pairs against an anchor to regularize without rigid invariance.

If this is right

  • ContrastAD records the highest mean F1 on all five real-world benchmarks.
  • It records the highest AUC on SWaT (93.60), SMD (98.66), and PSM (97.79).
  • The contrastive objective works best as a soft regularizer rather than enforcing strict invariance.
  • Ablations confirm statistically significant gains over the strongest baseline on SWaT and PSM for both F1 and AUC.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same contrastive regularization on evolving graphs could be tested on other non-stationary sensor or financial series where relations drift over time.
  • Controlled synthetic experiments that vary the rate of structural change would isolate how much the dynamic component contributes beyond the multi-perspective embedder.
  • Replacing the DTW-based snapshot construction with alternative distance measures might reveal whether the power-law sparsity pattern is essential or merely convenient.

Load-bearing premise

Batch-level DTW distances produce sparse graph snapshots that capture meaningful structural evolution in the underlying time series.

What would settle it

Running ContrastAD on a new labeled MTS dataset with documented structural drift and finding that it no longer leads the baselines in F1 or AUC, or that removing the dynamic contrastive term leaves performance unchanged.

Figures

Figures reproduced from arXiv: 2605.23744 by Jin Zheng, John Cartlidge, Yunhua Pei, Zixing Song.

Figure 1
Figure 1. Figure 1: Overall framework of ContrastAD. The Multi-Perspective Embedder (MPE) encodes a multivariate time-series window [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Structure of different blocks in FAM. standard Transformer architectures [8, 43], we first add positional encodings to obtain 𝑍˜ . To suppress spectral noise and emphasize dominant temporal patterns, we apply a frequency selection step prior to attention. Specifically, a real-valued FFT [6] is performed along the temporal axis, and only the top-𝐾 frequency components are retained before inverse FFT reconst… view at source ↗
Figure 4
Figure 4. Figure 4: Case study on the SWaT dataset comparing anomaly score responses of ContrastAD and baseline methods. Anomalies [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Anomaly detection in multivariate time series (MTS) is hindered by dynamic inter-variable dependencies and feature entanglement under spectral noise, and in practice, is further complicated by the absence of anomaly labels. Existing reconstruction-based detectors tend to recover anomalies as faithfully as normal patterns, while prevailing graph contrastive methods enforce invariance across views and thus assume a stationary relational structure, an assumption that breaks under structural drift in real systems. We propose ContrastAD, an unsupervised framework that turns structural evolution itself into a learning signal rather than suppressing it. A Multi-Perspective Embedder encodes inputs from temporal, attribute, and structural perspectives. A Frequency-Aware Attention Mixer then performs spectral top-K filtering before attention, preventing noise from leaking into query-key similarities. The core component, a Dynamic Graph Contrastive Learner, builds power-law-inspired sparse graph snapshots from batch-level DTW distances and contrasts the most divergent pair against a stable anchor, regularizing the latent space without imposing rigid invariance. Across five real-world benchmarks, ContrastAD attains the highest mean F1 on all five datasets and the highest AUC on three (SWaT 93.60, SMD 98.66, PSM 97.79), with statistically significant F1 and AUC margins over the strongest baseline on SWaT and PSM. On MSL and SMAP, it trails the AUC leader by under 0.7 points while still leading on F1. Ablation and sensitivity studies further confirm that the contrastive objective works best as a soft regularizer, supporting our claim that strict invariance is suboptimal under non-stationary dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes ContrastAD, an unsupervised anomaly detection framework for multivariate time series (MTS) that addresses dynamic inter-variable dependencies and non-stationary structural drift. It introduces a Multi-Perspective Embedder (temporal/attribute/structural views), a Frequency-Aware Attention Mixer with spectral top-K filtering, and a Dynamic Graph Contrastive Learner that constructs power-law-inspired sparse graph snapshots from batch-level DTW distances and contrasts divergent pairs against a stable anchor. The central empirical claim is that this yields the highest mean F1 on all five real-world benchmarks (SWaT, SMD, PSM, MSL, SMAP) and highest AUC on three, with statistically significant margins over the strongest baseline on SWaT and PSM.

Significance. If the reported performance margins hold under full experimental scrutiny, the work offers a concrete heuristic for turning structural evolution into a regularizer rather than enforcing invariance, which could improve robustness in non-stationary MTS settings where reconstruction-based or stationary-graph methods underperform. The ablation note that the contrastive term works best as a soft regularizer is a useful empirical observation, though it remains tied to the specific DTW-graph construction.

major comments (2)
  1. [Dynamic Graph Contrastive Learner description] The central performance claim (highest F1 on all five datasets, statistically significant margins on SWaT/PSM) rests on the Dynamic Graph Contrastive Learner successfully extracting useful signal from batch-level DTW distances and power-law sparsity; however, the manuscript provides no derivation, sensitivity analysis, or ablation isolating the effect of the power-law sparsity parameter (listed among the free parameters) versus alternatives such as k-NN or thresholded graphs.
  2. [Abstract / experimental results] The abstract asserts statistical significance for F1 and AUC margins on SWaT and PSM, yet the provided text supplies neither the number of independent runs, error bars, the exact statistical test employed, nor preprocessing rules and hyperparameter values; this renders the strength of the empirical evidence difficult to evaluate without the full experimental section.
minor comments (1)
  1. The invented entities (Dynamic Graph Contrastive Learner, Multi-Perspective Embedder, Frequency-Aware Attention Mixer) are introduced without explicit comparison to prior multi-view or spectral attention modules in the related-work section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and commit to revisions that strengthen the empirical support without altering the core claims.

read point-by-point responses

  1. Referee: [Dynamic Graph Contrastive Learner description] The central performance claim (highest F1 on all five datasets, statistically significant margins on SWaT/PSM) rests on the Dynamic Graph Contrastive Learner successfully extracting useful signal from batch-level DTW distances and power-law sparsity; however, the manuscript provides no derivation, sensitivity analysis, or ablation isolating the effect of the power-law sparsity parameter (listed among the free parameters) versus alternatives such as k-NN or thresholded graphs.

    Authors: The power-law sparsity is motivated by the empirical observation (stated in Section 3.3) that inter-variable dependency graphs in MTS data often follow heavy-tailed degree distributions. While the manuscript already includes ablations on the overall contrastive objective, we agree that a dedicated sensitivity study isolating the sparsity parameter and direct comparisons to k-NN and thresholded alternatives is missing. We will add this analysis (new table and figure) in the revised experimental section. revision: yes

  2. Referee: [Abstract / experimental results] The abstract asserts statistical significance for F1 and AUC margins on SWaT and PSM, yet the provided text supplies neither the number of independent runs, error bars, the exact statistical test employed, nor preprocessing rules and hyperparameter values; this renders the strength of the empirical evidence difficult to evaluate without the full experimental section.

    Authors: The full experimental section reports results over 5 independent runs (different seeds), with mean and standard deviation shown in tables; significance is evaluated via paired t-test (p < 0.05). Preprocessing and hyperparameter values appear in the appendix. To improve clarity we will insert a concise experimental-setup paragraph in the main text that explicitly states these details and cross-references the abstract claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents an empirical unsupervised anomaly detection framework evaluated on five real-world benchmarks, with performance claims resting on reported F1 and AUC metrics rather than any closed mathematical derivation. No equations, self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the abstract or summary that would reduce the central claims to the method's own inputs by construction. The Dynamic Graph Contrastive Learner is described as a heuristic regularizer using DTW-based graphs, but this is positioned as an independent modeling choice whose value is assessed externally via ablation studies and benchmark comparisons, not via internal tautology. The framework is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 3 invented entities

The central claim depends on several new architectural modules and domain assumptions about time-series structure whose necessity is supported only by the reported benchmark numbers rather than independent derivation or external verification.

free parameters (2)
  • spectral top-K
    Filtering threshold in the Frequency-Aware Attention Mixer; value and selection procedure not stated in abstract
  • power-law sparsity parameter
    Controls edge density when constructing graph snapshots from DTW distances; value and fitting method not stated
axioms (2)
  • domain assumption DTW distances computed on batch-level windows reflect meaningful inter-variable structural similarities
    Directly used to generate the graph snapshots that feed the contrastive learner
  • domain assumption Real-world MTS exhibit non-stationary relational drift that should be leveraged rather than suppressed by invariance constraints
    Core justification for replacing standard contrastive invariance with divergent-pair contrast
invented entities (3)
  • Dynamic Graph Contrastive Learner no independent evidence
    purpose: Regularizes latent space by contrasting most divergent DTW graph pair against stable anchor
    New component introduced to handle structural evolution
  • Multi-Perspective Embedder no independent evidence
    purpose: Encodes inputs from temporal, attribute, and structural perspectives
    New encoding module
  • Frequency-Aware Attention Mixer no independent evidence
    purpose: Applies spectral top-K filtering before attention to reduce noise leakage
    New attention variant

pith-pipeline@v0.9.0 · 5829 in / 1596 out tokens · 32248 ms · 2026-05-25T04:56:38.753796+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages · 3 internal anchors

  1. [1]

    Ahmed Abdulaal, Zhuanghua Liu, and Tomer Lancewicki. 2021. Practical ap- proach to asynchronous multivariate time series anomaly detection and localiza- tion. In27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining. 2485–2494

    work page 2021

  2. [2]

    Albert-László Barabási and Réka Albert. 1999. Emergence of scaling in random networks.Science286, 5439 (1999), 509–512

    work page 1999

  3. [3]

    Siddharth Bhatia, Arjit Jain, Shivin Srivastava, Kenji Kawaguchi, and Bryan Hooi

    work page

  4. [4]

    InThe Web Conference (formerly WWW)

    MemStream: Memory-Based Streaming Anomaly Detection. InThe Web Conference (formerly WWW)

    work page

  5. [5]

    Ziwei Chen, Jianjian Jiang, Xiangmin Luo, Fangyuan Lei, Xiaochen Yuan, and Jin Zhan. 2025. Dual-channel hypergraph networks in the time-frequency domain for learning advanced spatiotemporal dependencies in multivariate time series. Neurocomputing(2025), 130600

    work page 2025

  6. [6]

    Zhaoliang Chen, Zhihao Wu, William K Cheung, Hong-Ning Dai, Byron Choi, and Jiming Liu. 2025. MSHTrans: Multi-Scale Hypergraph Transformer with Time-Series Decomposition for Temporal Anomaly Detection. InProceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2. 274–285

    work page 2025

  7. [7]

    William T Cochran, James W Cooley, David L Favin, Howard D Helms, Reginald A Kaenel, William W Lang, George C Maling, David E Nelson, Charles M Rader, and Peter D Welch. 1967. What is the fast Fourier transform?Proc. IEEE55, 10 (1967), 1664–1674. doi:10.1109/PROC.1967.5957

    work page doi:10.1109/proc.1967.5957 1967

  8. [8]

    Ailin Deng and Bryan Hooi. 2021. Graph neural network-based anomaly detection in multivariate time series. InAAAI Conference on Artificial Intelligence, Vol. 35. 4027–4035

    work page 2021

  9. [9]

    Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019. BERT: Pre-training of deep bidirectional transformers for language understanding. In Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Vol. 1. 4171–4186. doi:10.18653/v1/ N19-1423

    work page doi:10.18653/v1/ 2019

  10. [10]

    Chaoyue Ding, Shiliang Sun, and Jing Zhao. 2023. MST-GAT: A multimodal spatial–temporal graph attention network for time series anomaly detection. Information Fusion89 (2023), 527–536

    work page 2023

  11. [11]

    Siho Han and Simon S Woo. 2022. Learning Sparse Latent Graph Representa- tions for Anomaly Detection in Multivariate Time Series. In28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2977–2986

    work page 2022

  12. [12]

    Jingyu Hu, Hongbo Bo, Jun Hong, Xiaowei Liu, and Weiru Liu. 2025. Mitigating Degree Bias Adaptively with Hard-to-Learn Nodes in Graph Contrastive Learning. arXiv preprint arXiv:2506.05214(2025)

    work page arXiv 2025

  13. [13]

    Xiangheng Huang, Ningjiang Chen, Ziyue Deng, and Suqun Huang. 2024. Multi- variate time series anomaly detection via dynamic graph attention network and Informer.Applied Intelligence54, 17 (2024), 7636–7658

    work page 2024

  14. [14]

    Kyle Hundman, Valentino Constantinou, Christopher Laporte, Ian Colwell, and Tom Soderstrom. 2018. Detecting spacecraft anomalies using lstms and nonpara- metric dynamic thresholding. In24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 387–395

    work page 2018

  15. [15]

    Yannis Kalantidis, Mert Bulent Sariyildiz, Noe Pion, Philippe Weinzaepfel, and Diane Larlus. 2020. Hard negative mixing for contrastive learning.Advances in Neural Information Processing Systems33 (2020), 21798–21809

    work page 2020

  16. [16]

    Siwon Kim, Kukjin Choi, Hyun-Soo Choi, Byunghan Lee, and Sungroh Yoon. 2022. Towards a rigorous evaluation of time-series anomaly detection. InProceedings of the AAAI conference on artificial intelligence, Vol. 36. 7194–7201

    work page 2022

  17. [17]

    Taesung Kim, Jinhee Kim, Yunwon Tae, Cheonbok Park, Jang-Ho Choi, and Jaegul Choo. 2021. Reversible instance normalization for accurate time-series forecasting against distribution shift. InInternational Conference on Learning Representations

    work page 2021

  18. [18]

    Xiangjie Kong, Wenyi Zhang, Hui Wang, Mingliang Hou, Xin Chen, Xiaoran Yan, and Sajal K Das. 2024. Federated graph anomaly detection via contrastive self-supervised learning.IEEE Transactions on Neural Networks and Learning Systems36, 5 (2024), 7931–7944

    work page 2024

  19. [19]

    Zhihan Li, Youjian Zhao, Jiaqi Han, Ya Su, Rui Jiao, Xidao Wen, and Dan Pei. 2021. Multivariate time series anomaly detection and interpretation using hierarchi- cal inter-metric and temporal embedding. In27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining. 3220–3230

    work page 2021

  20. [20]

    Jiexi Liu and Songcan Chen. 2024. Timesurl: Self-supervised contrastive learning for universal time series representation learning. InAAAI Conference on Artificial Intelligence, Vol. 38. 13918–13926

    work page 2024

  21. [21]

    Jiaqi Liu, Guoyang Xie, Jinbao Wang, Shangnian Li, Chengjie Wang, Feng Zheng, and Yaochu Jin. 2024. Deep industrial image anomaly detection: A survey.Ma- chine Intelligence Research21, 1 (2024), 104–135

    work page 2024

  22. [22]

    Yixin Liu, Zhao Li, Shirui Pan, Chen Gong, Chuan Zhou, and George Karypis

    work page

  23. [23]

    Anomaly detection on attributed networks via contrastive self-supervised learning.IEEE Transactions on Neural Networks and Learning Systems33, 6 (2021), 2378–2392

    work page 2021

  24. [24]

    Zhe Liu, Xiang Huang, Jingyun Zhang, Zhifeng Hao, Li Sun, and Hao Peng. 2024. Multivariate time-series anomaly detection based on enhancing graph attention networks with topological analysis. InProceedings of the 33rd ACM International Conference on Information and Knowledge Management. 1555–1564

    work page 2024

  25. [25]

    Jie Lu, Anjin Liu, Fan Dong, Feng Gu, Joao Gama, and Guangquan Zhang. 2018. Learning under concept drift: A review.IEEE transactions on knowledge and data engineering31, 12 (2018), 2346–2363

    work page 2018

  26. [26]

    Hongnan Ma, Yiwei Shi, Guanxiong Sun, Mengyue Yang, and Weiru Liu. 2025. TriShGAN: Enhancing Sparsity and Robustness in Multivariate Time Series Counterfactuals Explanation.arXiv preprint arXiv:2511.06529(2025)

    work page arXiv 2025

  27. [27]

    Stefano Mariani, Quentin Rendu, Matteo Urbani, and Claudio Sbarufatti. 2021. Causal dilated convolutional neural networks for automatic inspection of ultra- sonic signals in non-destructive evaluation and structural health monitoring. Mechanical Systems and Signal Processing157 (2021), 107748

    work page 2021

  28. [28]

    Aditya P Mathur and Nils Ole Tippenhauer. 2016. SWaT: A water treatment testbed for research and training on ICS security. In2016 International Workshop on Cyber-Physical Systems for Smart Water Networks (CySWater). IEEE, 31–36

    work page 2016

  29. [29]

    Youngeun Nam, Susik Yoon, Yooju Shin, Minyoung Bae, Hwanjun Song, Jae- Gil Lee, and Byung Suk Lee. 2024. Breaking the time-frequency granularity discrepancy in time-series anomaly detection. InACM Web Conference 2024. 4204–4215

    work page 2024

  30. [30]

    Mark EJ Newman. 2005. Power laws, Pareto distributions and Zipf’s law.Con- temporary physics46, 5 (2005), 323–351

    work page 2005

  31. [31]

    Zefei Ning, Zhuolun Jiang, Hao Miao, and Li Wang. 2022. MST-GNN: A multi- scale temporal-enhanced graph neural network for anomaly detection in multi- variate time series. InAsia-Pacific Web (APWeb) and Web-Age Information Man- agement (W AIM) Joint International Conference on Web and Big Data. Springer, 382–390

    work page 2022

  32. [32]

    Aaron van den Oord, Yazhe Li, and Oriol Vinyals. 2018. Representation learning with contrastive predictive coding.arXiv preprint arXiv:1807.03748(2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  33. [33]

    Yunhua Pei, Jin Zheng, and John Cartlidge. 2025. Dynamic Graph Representation with Contrastive Learning for Financial Market Prediction: Integrating Temporal Evolution and Static Relations. In17th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART. INSTICC, SciTePress, 298–309. doi:10. 5220/0013154700003890

    work page 2025

  34. [34]

    Zhongpeng Qi, Jun Zhang, Wei Li, and Zhuoxuan Liang. 2026. CGSTA: Cross- Scale Graph Contrast with Stability-Aware Alignment for Multivariate Time- Series Anomaly Detection.arXiv preprint arXiv:2602.20468(2026)

    work page arXiv 2026

  35. [35]

    Shuxin Qin, Jing Zhu, Dan Wang, Liang Ou, Hongxin Gui, and Gaofeng Tao. 2022. Decomposed transformer with frequency attention for multivariate time series anomaly detection. In2022 IEEE International Conference on Big Data (Big Data). IEEE, 1090–1098

    work page 2022

  36. [36]

    Joshua Robinson, Ching-Yao Chuang, Suvrit Sra, and Stefanie Jegelka. 2020. Contrastive learning with hard negative samples.arXiv preprint arXiv:2010.04592 (2020)

    work page arXiv 2020

  37. [37]

    Hiroaki Sakoe and Seibi Chiba. 1978. Dynamic programming algorithm opti- mization for spoken word recognition.IEEE transactions on acoustics, speech, and signal processing26, 1 (1978), 43–49

    work page 1978

  38. [38]

    Nikunj Saunshi, Orestis Plevrakis, Sanjeev Arora, Mikhail Khodak, and Hrishikesh Khandeparkar. 2019. A theoretical analysis of contrastive unsu- pervised representation learning. InInternational conference on machine learning. PMLR, 5628–5637

    work page 2019

  39. [39]

    Ramit Sawhney, Shivam Agarwal, Arnav Wadhwa, and Rajiv Shah. 2021. Ex- ploring the scale-free nature of stock markets: Hyperbolic graph learning for algorithmic trading. InWeb Conference 2021. 11–22

    work page 2021

  40. [40]

    Zixing Song, Yifei Zhang, and Irwin King. 2023. Optimal block-wise asymmetric graph construction for graph-based semi-supervised learning.Advances in Neural Information Processing Systems36 (2023), 71135–71149

    work page 2023

  41. [41]

    Ya Su, Youjian Zhao, Chenhao Niu, Rong Liu, Wei Sun, and Dan Pei. 2019. Robust anomaly detection for multivariate time series through stochastic recurrent neural network. In25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 2828–2837

    work page 2019

  42. [42]

    Susheel Suresh, Pan Li, Cong Hao, and Jennifer Neville. 2021. Adversarial graph augmentation to improve graph contrastive learning.Advances in Neural Infor- mation Processing Systems34 (2021), 15920–15933

    work page 2021

  43. [43]

    Yonglong Tian, Chen Sun, Ben Poole, Dilip Krishnan, Cordelia Schmid, and Phillip Isola. 2020. What makes for good views for contrastive learning?Advances in Neural Information Processing Systems33 (2020), 6827–6839. 11 , , Pei, Song, Zheng, Cartlidge

    work page 2020

  44. [44]

    Aaron Van Den Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alex Graves, Nal Kalchbrenner, Andrew Senior, Koray Kavukcuoglu, et al

    work page

  45. [45]

    Wavenet: A generative model for raw audio.arXiv preprint arXiv:1609.03499 12 (2016), 1

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  46. [46]

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is all you need. In31st Conference on Neural Information Processing Systems, Vol. 30. 6000–6010

    work page 2017

  47. [47]

    Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. 2017. Graph attention networks.arXiv preprint arXiv:1710.10903(2017)

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  48. [48]

    Tongzhou Wang and Phillip Isola. 2020. Understanding contrastive representation learning through alignment and uniformity on the hypersphere. InInternational conference on machine learning. PMLR, 9929–9939

    work page 2020

  49. [49]

    Mike Wu, Chengxu Zhuang, Milan Mosse, Daniel Yamins, and Noah Goodman

    work page

  50. [50]

    arXiv preprint arXiv:2005.13149(2020)

    On mutual information in contrastive learning for visual representations. arXiv preprint arXiv:2005.13149(2020)

    work page arXiv 2005

  51. [51]

    Xingjian Wu, Xiangfei Qiu, Zhengyu Li, Yihang Wang, Jilin Hu, Chenjuan Guo, Hui Xiong, and Bin Yang. 2025. Catch: Channel-aware multivariate time series anomaly detection via frequency patching. InInternational conference on learning representations, Vol. 2025. 17017–17045

    work page 2025

  52. [52]

    Zhichao Wu, Li Zhu, Zitao Yin, Xirong Xu, Jianmin Zhu, Xiaopeng Wei, and Xin Yang. 2025. MAFCD: Multi-level and adaptive conditional diffusion model for anomaly detection.Information Fusion118 (2025), 102965

    work page 2025

  53. [53]

    Jiehui Xu, Haixu Wu, Jianmin Wang, and Mingsheng Long. 2022. Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy. In International Conference on Learning Representations

    work page 2022

  54. [54]

    Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. 2020. Graph contrastive learning with augmentations.Advances in Neural Information Processing Systems33 (2020), 5812–5823

    work page 2020

  55. [55]

    Xiang Yu, Xianfei Yang, Qingji Tan, Chun Shan, and Zhihan Lv. 2022. An edge computing based anomaly detection method in IoT industrial sustainability. Applied Soft Computing128 (2022), 109486

    work page 2022

  56. [56]

    Zhihan Yue, Yujing Wang, Juanyong Duan, Tianmeng Yang, Congrui Huang, Yunhai Tong, and Bixiong Xu. 2022. Ts2vec: Towards universal representation of time series. InAAAI Conference on Artificial Intelligence, Vol. 36. 8980–8987

    work page 2022

  57. [57]

    Jiuqi Elise Zhang, Di Wu, and Benoit Boulet. 2021. Time series anomaly detection for smart grids: A survey. In2021 IEEE Electrical Power and Energy Conference (EPEC). IEEE, 125–130

    work page 2021

  58. [58]

    Wenxin Zhang and Cuicui Luo. 2025. Decomposition-based multi-scale trans- former framework for time series anomaly detection.Neural Networks187 (2025), 107399

    work page 2025

  59. [59]

    Yitian Zhang, Florence Regol, Antonios Valkanas, and Mark Coates. 2022. Con- trastive learning for time series on dynamic graphs. In2022 30th European Signal Processing Conference (EUSIPCO). IEEE, 742–746

    work page 2022

  60. [60]

    Hang Zhao, Yujing Wang, Juanyong Duan, Congrui Huang, Defu Cao, Yunhai Tong, Bixiong Xu, Jing Bai, Jie Tong, and Qi Zhang. 2020. Multivariate time- series anomaly detection via graph attention network. In2020 IEEE International Conference on Data Mining (ICDM). IEEE, 841–850

    work page 2020

  61. [61]

    Phan, Shirui Pan, Yi-Ping Phoebe Chen, and Wei Xiang

    Yu Zheng, Huan Yee Koh, Ming Jin, Lianhua Chi, Khoa T. Phan, Shirui Pan, Yi-Ping Phoebe Chen, and Wei Xiang. 2023. Correlation-aware Spatial-Temporal Graph Learning for Multivariate Time-series Anomaly Detection.IEEE Transac- tions on Neural Networks and Learning Systems(2023)

    work page 2023

  62. [62]

    Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. 2021. Informer: Beyond efficient transformer for long se- quence time-series forecasting. InAAAI Conference on Artificial Intelligence, Vol. 35. 11106–11115

    work page 2021

  63. [63]

    Qihang Zhou, Shibo He, Haoyu Liu, Jiming Chen, and Wenchao Meng. 2024. Label-Free Multivariate Time Series Anomaly Detection.IEEE Transactions on Knowledge and Data Engineering(2024)

    work page 2024

  64. [64]

    Bo Zong, Qi Song, Martin Renqiang Min, Wei Cheng, Cristian Lumezanu, Daeki Cho, and Haifeng Chen. 2018. Deep autoencoding Gaussian mixture model for unsupervised anomaly detection. InInternational Conference on Learning Representations. 12

    work page 2018