Title: CrossAD: Time Series Anomaly Detection with Cross-scale Associations and Cross-window Modeling
Venue: NeurIPS 2025
Accepted: yes
Keywords: time series; anomaly detection
Abstract: Time series anomaly detection plays a crucial role in a wide range of real-world applications. Given that time series data can exhibit different patterns at different sampling granularities, multi-scale modeling has proven beneficial for uncovering latent anomaly patterns that may not be apparent at a single scale. However, existing methods often model multi-scale information independently or rely on simple feature fusion strategies, neglecting the dynamic changes in cross-scale associations that occur during anomalies. Moreover, most approaches perform multi-scale modeling based on fixed sliding windows, which limits their ability to capture comprehensive contextual information. In this work, we propose CrossAD, a novel framework for time series Anomaly Detection that takes Cross-scale associations and Cross-window modeling into account. We propose a cross-scale reconstruction that reconstructs fine-grained series from coarser series, explicitly capturing cross-scale associations. Furthermore, we design a query library and incorporate global multi-scale context to overcome the limitations imposed by fixed window sizes. Extensive experiments conducted on seven real-world datasets using nine evaluation metrics validate the effectiveness of CrossAD, demonstrating state-of-the-art performance in anomaly detection.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes CrossAD, a novel framework for time series anomaly detection that improves upon prior methods by modeling two key aspects: cross-scale associations and cross-window context. Instead of treating different temporal scales independently, CrossAD reconstructs fine-grained time series from coarser scales to explicitly capture anomalies as disruptions in multi-scale consistency. It also introduces a global multi-scale context and a query library to flexibly model sub-series across different time windows, overcoming limitations of fixed-size sliding windows. Extensive experiments show that CrossAD achieves state-of-the-art performance across a wide range of metrics, validating the effectiveness of its design.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1. CrossAD introduces a novel cross-scale reconstruction mechanism that explicitly captures hierarchical relationships between time series at different granularities, improving anomaly detection sensitivity.\n2. It effectively overcomes the fixed sliding window limitation by using a global multi-scale context and query library, enabling better modeling of long-range dependencies.\n3. Extensive evaluations show consistently superior performance across diverse metrics, demonstrating strong generalizability.\n\n**Weaknesses:** See my detailed comments in the Question section.\n\nQUESTIONS:\nI only have a main concern: \n\n1. Please provide the number of parameters, and the runtime of the proposed method and the baseline methods associated with the reported results. In my understanding, the multi-scale anomaly detection approach 'copy' the given time series, so tend to consume more time to run. Additionally, the architecture of CrossAD seems be computational intensive. \n\nA few other questions: \n\n2. How robust is the Fourier-based period-aware router to non-stationary or noisy time series? Since the query selection mechanism relies on selecting top-k frequency components via the Fourier transform, it's unclear how sensitive the approach is to time series with transient anomalies or irregular patterns. Have the authors conducted any ablation or robustness analysis on this component?\n\n3. Does the cross-scale reconstruction introduce any training imbalance or representation collapse across scales? Since finer-scale series are reconstructed from coarser ones, does the model tend to overfit to coarse-grained patterns at the expense of fine-grained anomaly features? Have the authors observed any issues with convergence or representational bias?\n\nLIMITATIONS:\nThe paper has a limitation discussion in Section G.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper identifies the challenges of lack of cross-scale association modelling and fixed window sizes in time series anomaly detection. \n\nTo address the first challenge, the authors propose a new cross-scale reconstruction (interpolation) task and CrossAD, an encoder-decoder Transformer architecture for solving the task. To address the second, the authors propose a learnable query library and an adaptive key-value vector repository (global multi-scale context) that decoder could use to retrieve global (historical) context for next-scale interpolation.\n\nEvaluation with range-based metrics demonstrates that CrossAD achieves new SOTA on seven detection benchmarks.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n1. The proposed cross-scale reconstruction (interpolation) task is novel and appropriate for anomaly detection. Many reconstruction-based methods face the challenge of “identity shortcut” and may replicate the unmasked input instead of modelling the data distributions. The input for CrossAD, the “mutli-scale series” $ \\{ \\boldsymbol{X}_{i} \\} $ are effectively downsampled from the original $\\boldsymbol{X}_m$ and prevent the model from replicating the input.\n2. The proposed global context repository could mitigate the limitations that come with the fixed sliding window size.\nFigures in the paper are highly illustrative, e.g., Fig.2.(2) and (3) visualise the scale-dependent masking and up-interpolation processes clearly.\n3. Evaluation on detection benchmarks are overall comprehensive.\n\n**Weaknesses:**\n1. One of the main motivations (lines 35-45) is neither logically coherent nor very convincing to me, i.e., \"existing multi-scale methods overlook the association among different scales\".\n\nIn providing Fig.1 as an example of cross-scale association, the authors suggest that the two normal sub-series (in blue) are similar at Scale 3 and Scales 1,2. However, it is not clear why the similarity between the two are relevant to cross-scale associations. The authors further suggest that the association among the anomalous subseries (in red)  are different from the normal subseries. Here, the authors suggest that the anomalous subseries are different across scales. The similarity comparison is changed from **between subseries at the same scale** to **the same subseries across different scales**.\n\nThe authors also suggest that the dissimilarity of the anomalous subseries across scales is due to the anomalies and such a discrepancy is indicative of abnormal behaviour. The claim is questionable on several grounds. 1) The anomalous subseries at Scales 1,2, 3 are all effectively downsampled from the original. While they appear visually different, they should be similar in correlation metrics like Pearson. In what way are they dissimilar to each other? 2) Should all the normal seasonal peaks simulate the anomalous subseries (in red), would that not make all the normal peaks anomalous? If not, why would cross-scale association discrepancy be a good indicator for anomalies? 3) From CrossAD, the cross-scale association is not visualised in this paper. Does the detection benchmark show any discrepancy in cross-scale association on anomalous subseries?\n\n2. There is a lack of justifications for design choices of CrossAD throughout the paper. Many parts also lack clarity.\n- 1. Scale-dependent encoding seems very inefficient. In scale-dependent encoding, a block diagonal matrix $M_1$ is used for masking. Considering the quadratic cost of attention, would it not be more efficient to encode each scale independently?\n- 2. In subseries representation, it is not clear whether the query library is learnable or not. If so, how is each vector in the query library $q_t$ initialised? \n- 3. Next-scale generation (Line 184) uses a Transformer encoder (attention layers) but there is a lack of justification for it. Why is Transformer chosen here instead of other networks such as MLP?\n- 4. Missing ablation study on the query library. In global multi-scale context, the vector prototypes are randomly initialised and adapted to form clusters of historical cross-scale representations $\\boldsymbol{R}^t$. Would it not be possible to remove the query library and make $G$ directly trainable? The ablation study Row4 only considers a dynamic update of $G$ based on encoder output but not a fully trainable $G$.\n- 5. Missing explanation for using only the first continuous dimension (Lines 255-256) in MSL and SMAP.\n\n3. Up-interpolation should be either upsampling or interpolation. There is no down-interpolation.\n4. Lines 264-265 incorrectly state that TimeMixer and TimesNet are SOTA detection methods. They are mainly forecasting models with detection capabilities. They often do not achieve SOTA performance on detection benchmarks.\n5. On multi-metrics, CrossAD is compared against ModernTCN, TimeMixer, and TimesNet. All of them were not specifically designed for anomaly detection.\n6. Quite a few grammatical errors stand out throughout the paper, e.g., scale “independent” encoding (Line 59), “Specifically” (Line 139).\n7. The words “generation”, “(down/up)-sampling”, and “interpolation” are used interchangeably throughout the paper. Sometimes, they are used inappropriately when referring to another. For instance, multi-scale generation is in fact down-sampling.\n8. Multi-scale generation may not conform to the periods of time series. It has pooling sizes of {2, 4, 8, 16, 32} but some datasets are sampled daily or hourly.\n9. Different datasets use different window sizes and there is no explanation for that.\n\nOverall, the paper is technically solid with novel ideas and could be valuable to the NeurIPS conference. I am willing to increase my rating should the authors clarify their main motivations (Weakness1), define clearly the cross-scale association, and answer my questions in W1.\n\nQUESTIONS:\n**Please refer to weaknesses.**\n\n1. The assumption and limitation of channel independence is not addressed. Why is the assumption needed for CrossAD? How are anomaly scores calculated for multivariate time series? Is the final score an average of scores across channels (data dimensions)?\n2. There are many anomalies in SWaT and other benchmarks which affect multiple channels at the same time. Is CrossAD capable of detecting those attacks with the channel independence assumption? Is there a delay compared to multivariate detection methods?\n3. In multi-scale generation, the relationship between $T_i$ and $P_i$ is not clear. How is patching done (“following [26]” need to be explained)?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper addresses the problem of time series anomaly detection by proposing a novel framework, CrossAD, which emphasizes multi-scale modeling. The key insight is that time series often contain patterns that manifest at different temporal resolutions, and that anomalies may disrupt relationships across these scales. CrossAD introduces a cross-scale reconstruction mechanism, where fine-grained time series are reconstructed from coarser versions, thereby enabling better modeling of associations across resolutions. Additionally, the model incorporates cross-window modeling through the use of a \"query library\", allowing it to overcome the limitations of fixed-size windows. The authors conduct extensive experiments on seven real-world datasets (6 only in the main paper and one in the appendix) using several evaluation metrics and claim state-of-the-art performance across the board.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper is built on an important idea: leveraging multi-scale representations to enhance anomaly detection in time series, which is especially relevant in domains with complex temporal dynamics. The notion of reconstructing from coarse to fine resolutions is well-motivated, and the framework appears to be well-designed. The experimental setup demonstrates strong efforts, with appropriate baselines, appropriate metrics, and a wide range of of datasets. I also appreciate the attention paid to runtime analysis, at least in the appendix (even though I believe that it should be integrated in the main paper).\n\nThat said, I have several concerns that temper my confidence in the contribution. The core idea of coarse-to-fine reconstruction is not entirely novel and has already been explored in prior work, including recent efforts such as [ref1]. While the authors rightly argue that many prior works either fuse or treat resolutions independently, I find the distinction between CrossAD and existing fusion-based approaches somewhat underdeveloped. I might have missed or misunderstood some very important part in the paper that would make the difference and the contribution obvious. Therefore, I believe that emphasizing more on this aspect could benefit the paper.\n\nFrom an empirical standpoint, the choice of datasets could be more comprehensive. While seven datasets are included, one mentioned in Section 4.1 is not actually used in the main experiments. Notably, the UCR archive, one of the most diverse and well-established benchmarks, is not included in Table 1. Similarly, larger benchmarks such as TSB-AD-M and TSB-AD-U [ref2] would provide stronger validation. Lastly, although many models and datasets are included, there is no statistical test to assess whether performance differences are significant.\n\n**References**\n\n[ref1] Qingning, L., Wenzhong, L., Chuanze, Z., Yizhou, C., Yinke, W., Zhijie, Z., Linshan, S, Sanglu, L. (2023). Multi-Scale Anomaly Detection for Time Series with Attention-based Recurrent Autoencoders. Proceedings of The 14th Asian Conference on Machine\n Learning, in Proceedings of Machine Learning Research 189:674-689\n\n[ref2] Qinghua Liu and John Paparrizos. 2025. The elephant in the room: towards a reliable time-series anomaly detection benchmark. In Proceedings of the 38th International Conference on Neural Information Processing Systems (NIPS '24), Vol. 37. Curran Associates Inc., Red Hook, NY, USA, Article 3437, 108231–108261.\n\nQUESTIONS:\nHere is a list of suggestions:\n\n**Clarify the Novelty**: Please clarify more precisely what differentiates your method from existing work.\n\n**Dataset Usage**: Several datasets mentioned in Section 4.1 are not used in the main experiments. In particular, the UCR is highly diverse and widely used; its inclusion would greatly strengthen the empirical evaluation.\n\n**Benchmark Coverage**: Consider including larger benchmarks such as TSB-AD-M and TSB-AD-U, which offer broader application domains. In addition, as the UCR is mentioned in the considered datasets (in Section 4.1), I suggest that the authors integrate it in Table 1.\n\n**Statistical Significance Testing**: I recommend performing a Wilcoxon signed-rank test and visualizing the results with a critical difference diagram. The eaon package offers utilities for this.\n\n**Ablation Study**: The ablation on the cross-scale module is conducted on only a subset of the datasets. Given that this is a central contribution, the ablation should be extended to cover all datasets or larger benchmarks to robustly validate its impact.\n\n**Execution Time Analysis**: The runtime analysis in the appendix is interesting, but this is an important aspect that should be more visible in the main paper. I suggest that the authors include more discussion on this, such as adding a 2D scatter plot comparing execution time versus accuracy across methods.\n\n**Scalability Evaluation**: Given that training time appears high (Table 9), a scalability analysis as a function of series length and dimensionality would be useful. A theoretical complexity analysis could also help practitioners understand practical limitations to their specific use cases.\n\nLIMITATIONS:\nYes, in the Appendix.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

comments: SUMMARY:
This paper proposes a time series anomaly detection algorithm that looks for anomalies at different sampling granularities and within the relationships between these scales. The authors claim that their innovation is to explicitly model cross-scale associations and detect anomalies at each of the scales considered.

STRENGTHS AND WEAKNESSES:
Strengths:
1. The experimental results are quite thorough and seem to show good results.

Weaknesses:
1. While figure 2 is helpful, please put pseudocode of the full algorithm to explicitly show how the different steps of the algorithm are connected. This will be useful for reproducibility.
2. All functions, such as LayerNorm, Attention, and FeedForward, need to have explicit definitions in the text.
3. While the experimental results are thorough, I think the authors should also experiment with adding anomalies synthetically to varying extents (different levels of anomalies at each scale, varying number of scales) to test the limits of the algorithm and compare these limits to the baselines.

Some additional questions:
3. On page 6, how is $S$ calculated, and how does it relate to other variables like $P$ and $T$?
4. On pages 14-15, do you have a good way to choose $K$?
5. Associated with table 9, what is the order of growth of the training time as the training set size increases?

QUESTIONS:
The key questions/clarification requests that I have are:
1. While figure 2 is helpful, please put pseudocode of the full algorithm to explicitly show how the different steps of the algorithm are connected. This will be useful for reproducibility.
2. All functions, such as LayerNorm, Attention, and FeedForward, need to have explicit definitions in the text.

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