CrossAD: Time Series Anomaly Detection with Cross-scale Associations and Cross-window Modeling
Authors: Beibu Li
Qichao Shentu
Yang Shu
Hui Zhang
Ming Li
Ning Jin
Bin Yang
Chenjuan Guo
Venue: NeurIPS 2025 poster ()
Keywords: time series; anomaly detection
Primary area: deep_learning
TL;DR: We propose CrossAD, a novel framework for time series Anomaly Detection that takes Cross-scale associations and Cross-window multi-scale modeling into account.

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.

CrossAD: Time Series Anomaly Detection with Cross-scale Associations and Cross-window Modeling
Beibu Li Qichao Shentu's : Yang Shu', Hui Zhang', Ming Li?, Ning Jin?
Bin Yang', Chenjuan Guo 1
1 East China Normal University, *Shandong Inspur Database Technology Co., Ltd. ecnu. edu. cn, (yshu, cjguo, byang) waageeddaeeeeeeeee ecnu. edu. cn, {zhanghui, liming2017,
com
Abstract
Time series anomaly detection plays crucial role in 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 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 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 multiple wal-world datasets using nine evaluation metrics validate the effectiveness of CrossAD, demonstrating state-of-the--ue performance in anomaly detection. The code is made available http::/gghhh...ooomccccoomllllns
rely
Introduction
As society becomes increasingly digitized, time series analysis assuming progressively more important function [13] From fluctuations in financial markets to changes in meteorological data, time series data ubiquitous 447). Timely detection of anomalies in time series data is crucial for identifying potential issues and taking action before they escalate into severe crises [8. For example, early identification of anomalous patterns in the financial sector enables timely corrective measures, preventing significant economic losses. In manufacturing, anomaly detection can significantly reduce costs by minimizing downtime and optimizing maintenance schedules.
Anomalies in various time series exhibit significant differences in both duration and characteristics, such as the difference between sudden spike in temperature readings and gradual drift in voltage levels that indicates equipment failure [9]. These differences motivate the need for multi-scale modeling [10] that effectively detects anomalies across different temporal granularities. Specifically, fine-ge fin-ggrined modeling facilitates the identification of point anomalies, where individual or few time points significantly deviate from expected patterns; whereas coarse-grand -rarined series modeling is more suitable for revealing sub-series anomalies, where continuous segment of data collectively behaves inconsistently with normal patterns.
'Equal contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Normal ussociation
Normal series
Abmormal association
Abnormal sub-series
BPMM
Value
Scale
WAMAN
Scale
Time
Scale
Figure I: Example of cross-scale associations. Scales 1, 2, and represent three series obtained by downsampling from the same original series, ranging from fine to coarse. The blue arrows indicate the associations between coarse- goareeer and fine- line-grained series under normal conditions, while the red arrows highlight the associations that are disrupted during anomaly occurrences.
However, existing multi-scale modeling methods for anomaly detection still face two major challenges: (I) Existing multi-scale methods overlook the association among different scales. Coarse-grained series highlight overall trends in time series data and serve as the foundation for fine-grained series, while the fine-grained series offer richer local details and represent further refinement of the coarse-grained series. Fine-grained series can be reconstructed from coarse- gunsse-rained series through mapping process. We refer to this multi-scale mapping relationship cross-scale association, as shown in Figure [ where the cross-scale association of normal sub-series (blue part) differs from that of abnormal sub-series (red part). We learn to model the normal associations. When anomaly occurs, the abnormal sub-series at the coarse coarse-grained (scale 3) cannot reconstruct the corresponding anomalous seb-series at the fine- mne-grained (scales 1, 2) via the normal association, thereby enabling anomaly detection. Existing multi-scale methods often independently model each scale [TT [2] or apply feature fusion strategies integrate multi-scale information
[3] 14, but overlook this important cross-scale mapping relationships for anomaly detection. (2) ) The limitation of window size hinders existing methods from capturing multi-scale information. Existing methods typically perform multi-scale modeling either by downsampling [10] or by dividing the series into patches of varying sizes 15] Regardless of the method used, they both employ sliding window segment the series. However, due to the fixed size of sliding windows, data sampling cannot exceed the boundaries of the sliding windows, leading to limited sampling that fails to obtain global information. These methods essentially make the series of each window independent of the overall time series. Although it can efficiently model the information within the window, cannot flexibly associate the multi-scale information of the current window with the global context of the time series, which weakens the detection performance.
To address these challenges, we propose CrossAD, novel framework for time series Anomaly Detection that takes Cross-scale associations and Cross-window modeling into account. For the first challenge, we innovatively propose the cross-scale reconstruction to explicitly model the association across different scales, which consists of three stages: multi-scale generation and embedding, scale- independent encoding, and next-scale generation. In the first two stages, multi-scale series are generated from the original time series, and temporal association within each scale independently modeled through a ocale-independennc masking mechanism. The third stage, next-scale generation, reconstructs fine-grained series based on coarser information with a Cross-scale Mask, thereby explicitly learning cross-scale association. For the second challenge, we introduce novel cross- window modeling. We innovatively construct a query library help model various sub-series patterns that can be shared across different sliding windows. We use sub-series queries in the query library to flexibly extract the sub-series representations from multi-scale information. During training, sub-series representations dynamically update to global multi-scale context. In the decoding stage, the global multi-scale context is incorporated into the next-scale generation process of cross- scale reconstruction, enabling the model to transcend individual window boundaries and facilitate global context sharing across windows to enhance our model's detection performance. Our main contributions are summarized as follows:
We propose the cross-scale reconstruction, which innovatively detects time series anomalies from the perspective of cross-scale association. It explicitly models the association among multiple scales by reconstructing fine-grained series from coarser series.

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We innovatively propose the cross-window modeling, which models sub-series from multi- scale information using sub-series queries in the query library. The window size limitation is transcended by integrating global multi-scale information during the decoding.
Our method achieves consistently superior performance multiple metrics of various datasets compared with state-of-the-an models.
Related work
Unsupervised time series anomaly detection Recently, unsupervised time series anomaly detec- tion has been widely explored [1] Traditional unsupervised methods can be categorized into clustering-basee based and censity-estimatinn
methods. Among these, clustering -based methods include LOF [22] COF 233,, and DAGMM [24]. while censity-estimation methods include SVDD [2 and
THOC 26 Unsupervised time series anomaly detection methods based on deep learning can gener- ally be divided into three categories: forecasting-bast
[27], reconstruction-based [8]
28] 29 and
contrastive- based approaches [30]. Forecasting-base based methods, like GDN [27] predict current value using historical series and use the prediction error the anomaly criterion. Reconstruction- based methods encode the input data into compressed representation and then decode it back to reconstruct the original series, with the reconstruction error serving the anomaly criterion [31]. Classic methods include (29 34]. Contrastive- based methods aim to capture the intrinsic differ- ences between normal and anomalous series. For instance, Anomaly Transformer (35 simultaneously models prior associations and series associations to highlight association discrepancies, while DCde- tector (30) learns permutation inrmmutttionnivvriannt invariant representation that enhances the representational differences between normal points and anomalies.
Multi-scale modeling for time series analysis In the real world, time series exhibit varied changes and fluctuations at different time scales, making multi-scale modeling essential for accurately cap- turing these characteristics [T0 36 371. TimesNet [14] divides time series into multiple 2D
tensors based on the varying sizes of their periods. Pyraformer 38 introduces pyramid attention to capture feature attention at different scales. Pathformer [15 selects different patch sizes based on seasonality and trend decomposition. TimeMixer [10 proposes a novel perspective of multi-scale mixing. MODEM [39] integrates multi-scale series using diffusion model and frequency-enhancer decomposable network to adeptly navigate the intricacies of non-stationarity. MAD-TS [40] captures different scales through its various model layers. These methods fuse information from different scales or use separate models to handle each scale independently. Different from previous methods, CrossAD performs time series anomaly detection by explicitly modeling the cross-scale associations and detects anomalies at each scale to detect anomalies different granularities.
3 Method
Given multivariate time series X (I1, .2..... IT) E RT'C containing T successive observations, where C' the data dimensions. Time series anomaly detection can be defined as given input time series sequence X, for another unknown test time series Nest of length 7" with the same modality as the training sequence, aim to output Deest (y1, 1/2 -.., yr Here y: (0, 1} denotes whether the observation x, at time f in the test time series is an anomaly or not.
3.1 Overall architecture
The overall architecture of CrossAD shown in Figure 2
We first generate multiple series of different scales by Multi-scale Generation. The generated series then undergoes Patch Embedding. Subsequently, these series fed into the encoder with Scale- Indeeeeenden Mask, which performs independent encoding on series of each scale. After the output of the encoder goes through an Interpolation, it then input into the decoder with Cross- Cross-scale Mask to generate finer- fineregrained series. During the inference stage, after obtaining the reconstruction scores for each scale, we aggregate the final anomaly score through Anomaly Score Interpolation. Additionally, we introduce the cross- window modeling. The Period-aware Router selects appropriate Sub-series Queries in Query Library for the current window, and these queries are then fused with the multi-scale information of the current window through cross cross-attenten attention. The Global Multi-scale Context is dynamically updated
3

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Period-aware Rouler
Crosa- Attention
updaato
mondaiion(X. - /(.........))011
org 1N- -.- & Ni:.1...
Query library
Glubaal Mulivactic
Encoder
V
Decoder
Pruch Emrieaing
W
und bossang 2019
Input X
Mask Matrix
Mask Matrix
MaltiSeale
Scalo-Indoeedeent
Up-interpalation
Anomaly Interpalation
X
H
2 DE o ge 2 1
44 45
&
Miekk
2
Mask
Th By
Figure The architecture of CrossAD, which takes scale number m=3 as an example.
based on the sub-series representation and integrates global multi- information into the next-scale generation process of the decoder. CrossAD is trained using a channel-independer method that has been widely adopted in the time series domain
3.2 Cross-scale reconstruction
As mentioned before, we emphasize the importance modeling the cross-scale association, and therefore, we innovatively define the cross-scale reconstruction from this perspective. During training, the model captures the cross-scale associations from normal time series by reconstructing finer-grained series from coarser series. When anomalies occur during inference, the cross-scale association is disrupted because of the differing sensitivities of coarse- -rrsine- and tnn-grained series to local and global variations. This leads to failure in reconstructing the fine-grat fine-grained series, which enables us to detect anomalies successfully through reconstruction error.
To ease our description, we denote the original series X as Xm, from which we generate m multi- scale series (Xg. "I. Xm- We use X, R to denote the i-th scale series of X. where T < Ti+1 indicating the temporal granularity becomes finer. We reconstruct each scale's 's series to model the associations among different scales, which facilitates the detection of anomalies across different temporal granularities. Specifically, given any series X; and its corresponding coarser series (X,,Xc X,, X,- the training process aims to minimize the reconstruction error of X,- We calculate the reconstruction error across all scales, and the overall optimization objective of the parameter f for the cross-scale reconstruction model f(: can be formalized as:
8" arg min
X; f ((Xo. .x,1); 0).
To implement the cross-scale reconstruction model, we design three stages and elaborate blow: multi-scale generation and embedding, scale-independent encoding, and next-scale generation.
Multi-scale generation and embedding This stage aims to generate multi-scale time series data with different temporal resolutions and obtain their embedded representations. As shown in Figure @ given the original series Xm. we first apply average pooling with m different size pooling kernels downsample Xm generating multi-scale series (Xo, XI.... Xm-1). }. where each series X; E R and the length T; satisfies T; < T:+1- Subsequently, we individually perform the patch embedding operation each series X, following [33], which divides X; into total of P; patches and maps them into a representation space dimensionality d using a Multi-Layer Perceptron (MLP). Positional encodings are also added to preserve temporal information. We denote the embedding of the i-th series as h. PP.x xd. The embeddings of all m series are then concatenated along the

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patch dimension to form the input to the encoder, denoted as H (b). ... .h E RPd, where P -m P: and superseript 0 indicates the number of layers passed through the encoder.
Scale-independent encoding This stage aims to explore the temporal dependencies at each scale. In implementation. employ a Transformer encoder to model the temporal patterns. We define the mask-attention mechanism as follows:
(QW (KW)) + +M] (vW.),
MaskAttn(.... K, V, M) softmax
(2)
Vd
where M denotes the mask matrix. To fully capture the temporal dependencies within each individual scale while avoiding interference among different scales, we introduce a scale-independen mask matrix, denoted M1 E IR PxP (see Figure 2 (). In M1, all off-diagonal elements set to -oo, representing masked positions. The diagonal blocks are defined as B, xp.PP: which are zero matrices of size P. x Ps, indicating the unmasked regions corresponding to each scale. Then, for the representation H' E IR Pxd the I-th layer, the modeling process of the 1-th layer of Encoder can be expressed as:
H'S LayerNorm (H MaskAttm (H' HH 1H'1,M,)
H' LayerNorm(( (H' + Feedforward((")),
where the scale-independent mask M1 ensures only attention scores within the same scale are retained. We represent the output of the L-layer Encoder as H = (ho, h E Pxd, where h E R.P: xd is the representation of i-th multi-scale series.
Next-scale generation the decoder stage, we model the cross-scale associations by performing reconstruction on fine-grained series using coarser series information. As shown in Figure P & we first use interpolation to match the representation h R R2xd of each scale in the encoder output with its next scale representation h E RP+ixd xd in the patch dimension. This process can be formalized as follows:
interpolation, (herpollation(hh),, i= 0, "...-..-------
where z E R2++xxd superscript indicates the number of layers passed through the decoder, and subscript i indicates the scale number. Subsequently, we decode the multi-scale representation z = = -. Take the reconstruction of the i-th scale series as an example. We take coarser series representations {z]. ... . } as the reconstruction condition. As shown in Figure 4 we achieve this by designing cross-scale mask M2, whose diagonal elements B, Op... x P.++ are zero matrices of size P.+1 x P.+1. and its lower triangular elements are all zero. Cross-scale mask ensures that each scale be reconstructed can only focus on its coarser series.
Additionally, to overcome the limitations imposed by the local window size, we integrate the global multi-scale context G' with the information from the current window. More implementation details about G' will be introduced in Section 3.3 The process of decoding can be summarized as:
t LayerNorm Z MaskAttn (7. Zz z M2)).
Z' LayerNorm(Z' + Attention 'Z' G',G"),.
Z LayerNorm + FeedForward(Z').
Finally, the model maps the output of the decoder back to the original input space through linear layer, generating the reconstruction results Xx,,,,,.., _,,).
3.3 Cross-window modeling
Multi-scale modeling within local windows is insufficient due to the limitation of sliding window size, which results in the model's 's failure to fully capture the complete context across different windows. We attempt to share information across different windows and propose query library and global multi-scale context for long-range multi-scal. association modeling. Sub-series queries in the query library are used to flexibly extract the sub-series representations, which are then updated to the global multi-scale context. For a clear description, we add a window identifier 1, which will be used in the following sections. For example, we denote X multi-scale representation generated by the encoder.
m as the series X,, at the 1-th window, and L. its
5

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Sub-series representation The sliding window restricts the model accessing only the series within the current window, preventing it from accessing external context. However, as shown F the sub-series within a window possess com- plete context, and sub-series across different windows exhibit a certain degree of contextual similarity, e.g., sub-series of the same color. Based this observation, propose to model these sub-series that can more effectively capture the temporal dependencies in time series data. Therefore, innovatively build a query library, denoted as Q= (q1..... qu contains sub-series queries q: E TR Sxd, which randomly initialized and learnable, and S denotes the length of the sub-series query. To establish the correspondence between the time series X m and the sub-series queries, we design period-aware router. The period-aware router first maps the input series X into the frequency domain via the Fourier transform, and retains only the l largest amplitude components to suppress noise. Then, the periodic pattern reconstructed back in the time domain through the [22] This process can be formulated as:
91
92
Un
W
Sub-series
Sliding window
Figure Sub-series of the same color have similar contexts.
inverse Fourier transform F
Xperiod = F FF (Aiop-k +);
where A k is the matrix of the top-k largest amplitude components from the Fourier spectrum, and & represents the phase spectrum. Subsequently, we input X X into an MLP to generate routing decision vector E R", The Gumbel-Sootnaa gating mechanism is then employed to dynamically activate the sub-series queries q' for the current window. Given the independently sampled gumbel noise y: (0mbel 1) and temperature coefficient this process can be formulated as:
exp ((u, + 9:)/T)
qº Σ
j==1 exp (u, 9;)/T) qi u MLP (Ppppri)))
(8)
Naturally, since different sub-series need to focus on different scale information over the entire window, we extract multi-scale information from the encoder output representation H to construct a cross-scale sub-series representation RR E S that can be shared across windows:
R = Cross-Attention(g H. H
(9)
Global multi-scale context To utilize these representations across windows, we construct global multi-scale context G = .g...... gg 1, consisting of K randomly initialized prototypes g: E Sxd By continuously updating the prototypes in G with sub-series representations during training, the context is able to capture global multi-scale information across windows. Specifically, we first compute the distances between R and the K prototypes in G, getting a distance vector d' [d',,... ,dk] E R Then, the cross-scale sub-series representation RR is assigned to the nearest prototype, and the corresponding prototype updated using an exponential moving average (EMA):
dc distance ,g), i= 1, K
(10)
g: EMA(g, R), argmin[d;, dxl
(11)
where distance(-) is the function for computing the Euclidean distance. The corresponding pseu- docode of EMA is summarized in Algorithm in Appendix [A] We concatenate the prototype in to obtain G' E TR s)xd and then incorporate G' into the next-scale generation process to transcend the limitations imposed by window size, as shown in Eq. 6
3.4 Anomaly criterion
We the reconstruction error the anomaly score for each scale. To detect anomalies different granularities, as shown in Figure 2 s, we aggregate the anomaly scores from all different scale series into a final anomaly score through interpolation. The final anomaly score of origin series X,, can be denoted as:
m
AnomalyScore(X...)
interpolate ((X, - (.,
(x.)13;0))²) ((X.........)::00))
(12)
m

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where X; denotes the time series at scales i, and AnomalyScore(X (m.) RTT Interpolation is applied to align the anomaly scores of varying lengths from all scales unified length Tm. Following
existing works 31 32 43 after obtaining the anomaly score, we run SPOT [44] to automatically
compute the threshold 6, and a point is marked as an anomaly if its anomaly score is larger than
4 Experiments
4.1 Experimental settings
Datasets We evaluate our model on various datasets. Here is the description of these datasets: (1) SMD (Server Machine Dataset) captures resource utilization data from computer clusters belonging to Internet company 43 (2) MSL (Mars Science Laboratory Dataset), collected by NASA, includes telemetry data that reflects the operational status of sensors and actuators on the Martian rover 45 (3) SMAP (Soil Moisture Active Passive Dataset), also gathered by NASA, provides soil moisture data obtained from spacecraft monitoring systems 45 (4) SWaT (Secure Water Treatment) contains sensor data from continuously operating water treatment infrastructure [46]. (5) PSM (Pooled Server Metrics Dataset) is sourced from eBay server machines, capturing metrics related to their performance [47]. (6) NeurIPS-TS (NeurIPS 2021 Time Series Benchmark) is dataset introduced by 488, and we utilize the sub-datasets GECCO and SWAN, which encompass a variety of anomaly scenarios. For the MSL and SMAP datasets, only the first continuous dimension is retained [1] as discrete variables inherently lack the smooth and structured latent space required for effective reconstruction. The statistical details about the datasets are available in Appendix B
Baselines We extensively compare CrossAD against 18 baselines, including the latest state-of- the-art (SOTA) anomaly detection models. These baselines include the linear transformation-
based methods: OCSVM [49], PCA [50]: the outlier-based methods: IForest [5T] LODA [52];
the density estimation based methods: HBOS [53]. LOF [54]; the neural network-based meth-
ods: AutoEncoder (AE) (55), DAGMM (24), LSTM [45). CAE-Ensemble (CAE) [29], Omni-
Anomaly (Omni) 43), Anomaly Transformer (AT) 35), DCdetector (DC) 130, ModernTCN (56).
GPT4TS (57), MtsCID I.. TimeMixer [00, TimesNet [4] Among them, MtsCID, TimeMixer,
and TimesNet are SOTA time series anomaly detection methods that employ multi-scale strategy.
Metrics Recent works have shown that even random methods using point adjustment, which is widely used in time series anomaly detection [30 35), can achieve statc-of-the-art results. To address this limitation, some methods have adopted Affiliation-FI (58). which considers the average directed distance between predicted anomaly events and ground truth events for precision, well as the average directed distance between ground truth events and predicted anomaly events to determine recall. The latest research, TSB-AD [59]. demonstrates through case studies and quantitative analyses that VUS-PR [60) the most robust (insensitive to lag), accurate (unbiased and effective across scenarios), and fair (consistent in similar situations) evaluation metric, while other metrics have inevitable defects. Therefore, our main results, we compare detection results using VUS-PR and VUS-ROC metrics. Meanwhile, to ensure comprehensive comparison, we also utilize commonly employed metrics such as AUC-ROC, AUC-PR, Standard-F1, Affiliation-FI, Range-AUC-Re and Range-AUC-PR (60). Implement details are shown in Appendix C
4.2 Detection results
Main results We extensively evaluate our model on seven real-world datasets with 18 competitive baselines as shown in Table It can be seen that our proposed method, CrossAD, achieves superior performance under the VUS-PR PR and VUS-AUC metrics across all datasets, indicating that it can effectively distinguish between normal and abnormal samples and maintain high detection accuracy and stability even under various pre-selected thresholds, which is important for real-world applications. These results substantiate the effectiveness of our proposed cross-scale reconstruction and cross- window modeling, which offer new perspectives for time series anomaly detection by effectively modeling association across different scales and taking time series cross sliding windows into account. The Affiliation metric results available in Table 9 in Appendix E.]
7

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Table 1: Results in the seven real-world datasets. The V-R and V-P are the VUS-ROC and VUS-PR,
that higher indicate better performance. The best ones are in bold, and the second ones are underlined.
Dataset
SMD
MSL.
SMAP
SWaT
PSM
GECCO
SWAN
Metrie
V-R
V-P
V-R
V-P
V-R
V-P
V-R
V-P
V-R
V-P
V-R
V-P
V-R
V.P
OCSVM
0.6451
0.1131
0.5798
0.1753
0.4185
0.1133
0.5903
0.4396
0.5903
0.4252
0.7533
0.1207
0.9088
0,9000
0.7174
0.1529
0.1889
0.4090
0.1144
0.6149
0.4459
0.6351
0.4706
0.5366
0,0443
0,9290
0.9123
IForest
0.7224
0.1304
0.1631
0.4960
0.1315
0.3677
0.1011
0.6009
0.3964
0.7083
0.0943
0.8835
0.8793
LODA
0.6745
0.1213
0.5375
0,1689
0.3973
0.1017
0.6358
0.3531
0.6089
0.4423
0.5749
0.0339
0,9170
0.9107
HBOS
0.6670
0.1102
0.6265
0.1790
0.5620
0.1388
0. 7.7044
0.4602
0.70%6
0.5061
0.5440
0.0453
0.9056
0.8894
LOF
0,6893
0.1076
0.6081
0.1715
0.5673
0.1409
0.6667
0.4187
0.6628
0.4615
0.7817
0.0919
0.9095
0.9007
AE
0.7560
0.1542
0.6047
0,1890
0,4687
0.1366
0,5903
0.4141
0.6359
0.1190
0.6124
0,0418
0,6982
0.0201
DAGMM
0.6988
0.149
0.1803
0.5599
0.1349
0.5745
0.4731
D.550K
0,4522
0.8051
0.8697
LSTM
0.2001
0.1395
0.1681
0.5329
0.1399
0.5482
0.2200
0.5571
0.4592
0.0668
0,9082
0.8862
CAK
0.7174
0.1376
0.5382
0,1639
0.4212
0.1140
0.5939
0,4104
0.6113
0,4395
0,5524
0.0528
0,9042
0,9022
Omni
0,2080
0.1340
0.5490
0.1973
0.4743
0.1239
0.6187
0.4475
0.6340
0.4472
0,5386
0.0517
0.9041
0.9022
AT
0.5117
0.0796
0.3890
0.1041
0.4571
0.1239
0.5561
0.2679
0.5186
0.3309
0.4751
0.0278
0,8046
0,7943
DC
0.5148
0:08:14
0.3900
0.0948
0.4444
0.1149
0.5191
0,1498
0.5235
0.3366
0.5454
0.0361
0.8429
0.8338
GPT4TS
0.7679
0.1745
0.7697
0,2769
0,5149
0.1289
0,2537
0,0816
0.6166
0.1599
0.9776
0.1181
0,9340
0,8921
MCN
0.7707
0.1596
0.7747
0.3010
0.5470
0.1395
0,2735
0.0941
0.6480
0,4668
0.4819
0.9027
0.8962
MIsCID
0,5162
0:0815
014666
0.1181
0.4260
0.1177
0.5021
0.1283
0.5194
0.5296
0.5315
0.0381
0.8128
0.8375
TimeMiser
0.7711
0.1391
0.7858
0.2461
0.5552
0.1371
0.2673
0.0918
0.5974
0.3807
0.9899
0.4606
0,9290
0.8721
TimeeNett
0.8420
0,2040
0.7880
0.2731
0,5495
0.1352
0.2974
0.1158
0.6344
0.4373
0.98334
0.4578
0,9515
0.9160
CrossAD
0,8580
11,2344
0.8091
0.3144
0.5779
0,1443
0,7865
0.4767
0.7302
0.5896
01.9948
0.6211
0.9499
0.9171
Table 2: Multi-metrics results in the three
datasets. The higher values for all metrics represent better performance. The best ones are in bold, and the second ones are underlined.
Dataset
Method
Ace
Std-FI
AFF-FT
AUC-R
AUC-P
R-A-R
R-A-P
V-R
V.P
ModernTTN
0.9074
0.1967
0.8316
0.7021
0.1401
0.7754
0.1628
0.7707
0.1596
TimeMixer
0,9091
0.1772
0,8408
0.6795
0,1215
0.7549
0.1580
0.7711
0.1390
SMD
TemesNet
0.9066
0.2146
0,8397
0.7603
0.1627
0.8300
0.2320
0.8420
0,2040
CrossAD
0.9095
0,2412
0.8531
0,7823
0.1864
0.8421
0.2589
0,8580
0.2344
TCN
0,3016
0,4345
0,7959
0,5846
0,3843
0.6550
0.4748
0,6480
0,4689
TimeMixer
0,2774
0,4341
0.7499
0.5522
0.3447
0.6140
0.4089
0,5974
0,3807
PSM
TimesNet
0,2773
0.4342
0.7970
0.5755
0.3701
0.6617
0.4827
0.6344
0.4373
CrossAD
0.6847
0.4974
0,8603
0.6810
0,4906
0.7564
0.6032
0.7302
0.5596
MOdernTCN
0,9882
0.5510
0,9018
0.9595
0.4325
0.9733
0.5036
0,9694
0.4819
TimeMixer
0.9832
0,4806
0,8989
0.9620
0.3559
0.9803
0.5106
0.9899
0.4106
GECCO
NimesNet
0.9860
0.4618
0.8906
0.9173
0,3431
0.9327
0,3593
0,9834
0.4578
CrossAD
0.9883
0.5700
0.9226
0.9867
0,5514
0,9889
0.6386
0.9948
0.6211
Multi-metrics For a comprehensive comparison, we also evaluate our proposed method, CrossAD, using more metrics. To ensure a comprehensive comparison, we evaluate the models on the Accuracy (Acc), Standard F1 (Std-F1), Affiliation-F1 (Aff-FI), AUC-ROC (AUC-R), AUC-PR (AUC-P), Range- AUC-ROC (R-A-R), Range-AUC-PR AUC-PR (R-A-P), VUS-ROC (V-R), and VUS-PR (V-P). Specifically, we compare CrossAD with three recognized advanced methods: ModernTCN, TimeMixer, and TimesNet. It is shown that CrosSAD achieves consistently superior results across multiple metries, demonstrating its excellent anomaly detection capabilities.
4.3 Model analysis
Abaltion studies As shown in Table 3 to evaluate the property of our proposed CrossAD, we conduct detailed ablations. Row 2 introduces multi-scale reconstruction based on Row and reconstructs each scale by itself. Compared to Row 1, Row 2's average VUS-PR increases 8.1%, indicating the importance of multi-scale modeling for time series anomaly detection. Based on Row 2, Row 3 further employs cross- cross-scale reconstruction, where coarser series are used to reconstruct their corresponding fine- -reiindd series and calculate the reconstruction error for each scale. It brings 2.47% and 9.18% improvements on VUS-ROC and VUS-PR, which highlights the importance of modeling the associations between multi-scale series. Row has a global multi-scale context compared with Row 3. Different from Row 6 (CrossAD), the update of the global multi-scale context in Row 4 is directly based on the multi-scale representation generated by the encoder instead of the sub-series representation. The results show that introducing the global multi-scale context helps the model
8

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Table 3: Ablation studies for CrossAD. The V-R and V-P are the VUS-ROC and VUS-PR, that higher indicate better performance. The best ones are in bold.
Dataset
PSM
MSL
GECCO
Avg.
Malti-Scale
Cross-ccal
Sub-series
Global
V-R
Modeling
Reconstraction
Representation
Context
X
X
K
X
0,6783
0.4467
0.7388
0.2385
0.9944
0.4145
0.78388
0,3665
x
X
X
0,6889
0.2479
0,3962
X
X
0.7125
0.2984
0.4376
v
/
X
0.3000
X
X
0.2869
V
0.3144
break through the limitation window size, thereby further improving the performance of anomaly detection. Additionally, the result of Row 4 shows decline compared to Row 6 (CrossAD), It indicates the importance of cross-scale sub-series representation, rather than directly using multi- scale representations with limited context. The results in Row 5 further illustrate the importance of global multi-scale context and cross-scale sub-series representation, which brings 3.18% and 10.4% improvements on VUS-ROC and VUS-PR.
Model efficiency We provide a comparison of various time series anomaly detection methods, including transformer-basee method (AnomalyTrame Transfooran,,,,mer)) MLP--ased method (TimeMixer), and CNN-based methods (ModerTTNN, TimesNet), in terms of efficiency on the GECCO dataset. As shown in Table the CNN-based method MCdernTCN and the MLP-based method TimeMixer are more efficient than the transformer-based method, which is determined by the nature of the models themselves. Compared with the Transformer-bate based method AnomalyTramme Tramallraasformer, CrossAD has advantages in inference time because we perform downsampling and patching the input series. CrossAD employs the continuous update of global multi-scale context throughout the training process to ensure the comprehensiveness of contextual information, and this optimization for performance entails a corresponding time cost in training.
Table 4: Comparison of various methods with respect to training time, inference time, total parameters, and VUS-PR metric result. Training time represents the time cost train the model for 5 epochs with the same batch size 128, while inference time indicates the duration required to process the entire test dataset. Total params represents the total number of trainable parameters of the model.
Method
Training Time (s)
Inference Time (s)
Total Params (M)
VUS-PR
ModernTCNN
22.75
0.57
0.05
0,4819
TimesNet
342.79
1.68
4.68
0.4578
TimeMixer
57.20
0.87
0.10
0.4606
CnomalyTransfomee
270.49
15.05
4.74
0.0278
CrossAD
270.75
0,80
0.93
0.6211
Visualization We conduct a comparative visualization analysis of the cross-scale reconstruction criterion and the traditional reconstruction criterion demonstrate the effectiveness of cross-scale reconstruction. As shown in Figure we select five different types of anomalies and display the anomaly scores produced by both criteria boxes. The results show that while both criteria exhibit similar sensitivity to point anomaly, and can effectively detect simple anomaly patterns. The traditional reconstruction criterion demonstrates significant instability when faced with more complex anomaly patterns, such shapelet, scasonal, and trend. This instability leads to higher incidence of false positives and false negatives. In contrast, due to its ability to model cross-scale associations, the cross-scale reconstruction criterion accurately identifies anomalous series across various complex anomaly patterns, achieving superior anomaly detection performance.
figure, with successful detection highlighted by green
To further illustrate effectiveness results across different scales GECCO. As shown in Figure the blue line is the input time series, the orange lines are reconstructed series each scale, and the green lines are the corresponding anomaly scores. Figure 5(t) presents the final anomaly score, with red regions marking the actual
cross-scale reconstruction, we visualize the reconstruction

---

Globall Prinet
Contectial Point
Shagelet
Seauunal
Tread
Reoominrden Crlterion
//1 MUNAAAn
Mww 1MAM
14
Time
Time
Time
Time
Time
Figure 4: Visualization of the traditional reconstruction criterion and cross-scale reconstruction criterion across five anomaly patterns. The first row shows the original series. The second and third rows display anomaly scores based on the traditional reconstruction criterion and cross-scale reconstruction criterion, respectively. Red areas indicate anomalies.
anomaly events. By reconstructing fine- fine-grained series from coarser ones, model captures the association between different scales. As illustrated the figure, when an anomaly occurs, the cross-scale associations are disrupted, leading to reconstruction failures across multiple scales. We observe that for the subtle pattern anomalies shown in the figure, combining anomaly scores across multiple scales yields better detection performance than relying any single scale alone.
4.3
0.3
0.00
(8) Scale
0.5
-.00
4.0
0.28
Timee
Anumaly
Figure 5: Visualization of cross-scale reconstruction results. (a)-(e) represent the five scales ranging from coarse to fine, where the blue line indicates the input series, the orange lines depict the reconstructed series each scale, and the green lines show the corresponding anomaly scores. (f) illustrates the final anomaly score obtained by fusing the anomaly scores from all five scales, with red regions marking the actual anomaly events.
Conclusion
This paper studies the multi-scale modeling problem in time series anomaly detection. Unlike previous works, we consider anomaly detection from the perspective of cross-scale association and propose cross-scale reconstruction. We explicitly model the association among multi-scales by reconstructing fine-gre fine-grained series from coarser series. We also take time series cross sliding windows into account and propose global multi-scale context to model the context of similar sub-series with multi-scale information. The window size limitation is transcended by integrating the global multi-scale context during the next-scale generation process. Extensive experiments prove that CrossAD achieves superior results compared with state-of-the models on multiple metrics.
10

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Acknowledgments
This work was supported by National Natural Science Foundation of China (62372179, 62406112).
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A
Algorithm
We present the procedures for updating the global multi-scale context in Algorithm I
Algorithm 1 Global Multi-scale Context Update
Input: Sub-series representation R for window t
Hyperparameters: Number of prototypes K, decay rate a 0.95
1: Initialize: (G.) ~ (0.
D Random initialization G; E Sxd
2: for each window do
3: Compute distances: [di,..., dx] + [D(R', G.)l
We use the Euclidean distance
4: Find index: -- arg min dj
D Nearest prototype selection
5: Update prototype: G, + aG, + R
6: end for
7: return Updated global prototypes { 1k
B
Datasets
To validate the effectiveness our model, we conducted extensive experiments on multiple publicly available datasets, including SMD (Server Machine Dataset) 43), MSL (Mars Science Laboratory Dataset) 45). SMAP (Soil Moisture Active Passive Dataset) 455) SWaT (Secure Water Treat- ment) 44), PSM (Pooled Server Metries Dataset), GECCO and SWAN from NeurIPS-TS (NeurIPS 2021 Time Series Benchmark) [48), and UCR [61]. These datasets are chosen for their diversity in terms of data characteristics and anomaly types, offering comprehensive evaluation framework. More statistical details are in T
Table 5: Statistics of the datasets. AR (anomaly ratio) represents the abnormal proportion of the
whole dataset.
Dataset
Domain
Dimension
Window
Training
Validation
Test (labeled)
(%)
MSL.
Spacecraft
96
46,653
11,664
73,729
10.5
PSM
Server Machine
25
192
105,984
26,497
87,841
27.8
SMAP
Spacecraft
1
192
108,146
27,037
427,617
12.8
SMD
Server Machine
38
192
566,724
141,681
708,420
4.2
SWaT
Water treatment
31
192
396,000
99,000
449,919
12.1
GECCO
Water treatment
9
128
55,408
13,852
69,261
1.25
SWAN
Space Weather
38
192
48,000
12,000
60,000
23.8
UCR
Natural
1,790,680
447,670
6,143,541
0.6
C Implement details
In our experiments, we set the dimension of hidden states 128, the dimension of attention as 32, the number of attention heads as 4, the dropout as 0.1, the encoder layer as 2, the decoder layer as 2, the number sub-series queries window to process the series and conduct the anomaly detection using -verlapppg windows. The various window sizes for different datasets can be seen Table The average pooling kernel sizes for multi-scale generation are selected from [32, 16, 8, 4, 2). We use the Adam optimizer with an initial learning rate of 10-4 and set the batch size to 128. To ensure fair comparison, we do not use a drop last trick in the inference stage [62] After obtaining the anomaly scores, we use the widely adopted SPOT 44 method to determine the threshold [3 We conduct our experiments
5, and the size global multi-scale context as 32. We run a sliding
using Pytorch with an NVIDIA Fes0a-A800-80GB GPU.
21

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D Parameter sensitive
The hyperparameter that significantly affects the anomaly detection performance are the patch size, the window size, and the hidden state dimension. The hyperparameters that may affect the performance of CrossAD are the multi-scale series numbers, the sub-series query numbers, and the size of global multi-scale contexts. To analyze their influence on anomaly detection, based on the main results Table we analyze the performance of the model under different parameters through extensive experiments.
Figure 6 shows the model performance under different patch sizes, different window sizes, and different hidden state dimensions. It shows that CrossAD is insensitive to these hyperparameters. Patch size is very important parameter for time series analysis. In time series, a single point does not contain any information, so the performance declines significantly when the patch size is set to 1.
patch size
window size
model
0.69
0.67
0.67
0.61
0.63
0.63
0.53
0.59
0.59
0.45
0.55
0.55
1
2
4
8
96
128
160
192
224
128
192
256
320
Figure 6: Results the parameter sensitivity analysis for the patch size, the window size, and the hidden state dimension dynodel the GECCO dataset. The dark line represents the mean of experiments, and the light area represents the range.
Analysis of the number of scales. The cross-scale reconstruction helps uncover the association between different scales. In Table 6 we present the model's performance under different scale numbers m and observe that increasing the number of scales generally leads improved model performance. After having a certain number of scales, the performance improvement of the model tends to be stable.
Table 6: Parameter sensitive analysis on scale numbers m. The V-R and V-P are the VUS-ROC and VUS-PR, that higher indicate better performance. The best ones in Bold.
Dataset
MSL.
PSM
SMAP
GECCO
SWAN
Metries
V-R
V-P
V-R
V-P
V-R
V-P
V-R
V-P
V-R
V.P
m
0,8052
0.3044
0.6677
0.4764
0,5608
0.1388
0.9893
0,6089
0,9408
0.8906
m
0.8088
0.3103
0,4748
0.5695
0.1433
0.9842
0.6050
0.9490
0.9047
mm 3
0.8111
0,3133
0.6947
0,5163
0.5779
0.1443
0.9946
0.6113
0.9501
0.9076
m 0.8091
0,3144
0.7147
0.5409
0.5739
0.1435
0.9948
0.6211
0.9506
0.9094
=
0,8102
0.3137
0.7302
0,5596
0.5748
0.1441
0.9942
0.6174
0.9499
0.9171
Analysis of the number of sub-series queries. In Table 7 present the performance of models with different numbers of sub-series queries in query library. The results show that as the number of queries increases, the model performance gradually improves. After reaching a certain threshold, however, further improvements become difficult, and there may even be a decline in performance. This indicates that increasing the number of queries can help uncover richer sub-series patterns within the data, thereby enhancing the effectiveness of anomaly detection. Mcanwhile, it also suggests that the sub-series patterns covered by the data are limited; many queries might introduce noise, which could degrade the model's performance.
Analysis of the number of prototypes in global multi-scale context. The global multi-scale context contains K prototypes, with each prototype corresponding to specific sub-series pattern with multi-scale information. damostBees the model's performance for the global multi-scale context having varying numbers of prototypes. The results in the table indicate that the best number
22

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Table 7: Parameter sensitive analysis on the number n of sub-series queries. The V-R and V-P are the VUS-ROC and VUS-PR, that higher indicate better performance. The best ones are in Bold.
Dataset
MSL.
PSM
SMAP
GECCO
SWAN
Metries
V-P
V-R
V-R
V-P
V-R
V-P
V-P
n
0.7854
0.2748
0.7016
0.5128
0.5604
0.1331
0.9840
0.6022
0.9301
0.9177
n 2
0.7890
0.2735
0.7017
0,5155
0,5669
0,1411
0.9914
0.6031
0.9474
0,9171
3 0.7986
0.2933
0.7181
0.5443
0.5673
0.1426
0.9938
0.6136
0,9458
0,9170
= 5
0.8091
0.3144
0.7302
0.5596
0.5779
0.1443
0.9948
0.6211
0.9499
0,9171
n=7 0.8090
0.3141
0.7325
0.5614
0.5756
0.1446
0.9980
0.6218
0,9427
0.9165
of prototype in global multi-scale context differs for each dataset. A number that is too small leads to suboptimal model performance, while a number that is too large will introduce unnecessary noise and cause side effects.
Table 8: Parameter sensitive analysis on the size K of global multi-scale context. The V-R and V-P are the VUS-ROC and VUS-PR, that higher indicate better performance. The best ones are in Bold.
Dataset
MSL.
PSM
SMAP
GECCO
SWAN
Metries
V-R
V-P
V-R
V-P
V-R
V-P
V-R
V-P
V-R
V-P
= 8
0.7889
0.2934
0.7027
0.5287
0.5729
0.1408
0.9894
0.6108
0.9405
0,9184
K 16
0.8066
0.3224
0.7188
0,5412
0.5779
0.1435
0.9980
0.6215
0,9502
0.9177
32
0.8091
0.3144
0.7302
0.5596
0.5779
0.1443
0.9948
0.6211
0.9499
0,9171
K 64
0.8093
0.3144
0.7266
0.5551
0.5797
0.1450
0.9941
0.6119
0,9400
0.9102
E
Additional experiments
E.
Affiliation metric results
Table 9: Affiliation metric results in the five real-world datasets. We use the widely adopted SPOT 44
method to determine the threshold 31 43 All results are in %. The best ones are in bold and the second ones are underlined.
Datasel
SMD
MSL
SMAP
SWaT
PSM
Metrie
Aff-P
AfE-R
AfT-F1
Atf-P
Aff-R
Aff-F1
Aff-P
AIf-R
Aff-F1
AIT-P
AfT-R
Aff-F1
AfF-P
AfT-R
Aff-FI
OCSVM
66.98
82.03
73.75
50.26
99. 86
66.87
41.05
69.37
51.55
56,80
98.72
72. 11
57.51
58.1 58.11
57.81
PCA
64.92
86.06
74.01
52.69
98.33
68.61
50.62
98.48
66.87
62.32
82.96
71.18
77.44
63.68
69.89
IFonest
71.94
94.27
81.61
53.87
94.58
68.65
41.12
68.91
$1.51
53.03
99.95
69.
69.66
38.77 79
78.07
LODA
66.09
74.12
57.79
72.05
100.00
56.30
70.34
87.
72.69
HBOS
60.34
64.11
62.17
66.17
$4.49
91.3 35
LOF
57.69
99.10
72.92
49.89
72.
59.00
47.92
82.86
60.72
53,20
96.73
68. 65
53,90
99.91
70.02
AE
69.22
98.48
$1.30
55.75
96.66
70.72
39.42
70.31
50.52
54.92
98.20
70.45
60.67
98. 24
75.01
DAGMM
63.57
70.83
67.00
51.07
92.11
68.14
50.75
96.38
66. 66.19
59.12
92.36
72.32
68.22
70.50
69.34
1STM
60:12
84.77
70.35
58.82
14. 68
23.49
55.25
27.70
36.00
49.99
82.11
62. 155
$7.06
95.99 92
71.55
CAE
73.05
83.61
77.97
54.99
93.93
69.37
62.32
64.72
63.
62.10
82.90
71.01
73.17
73.66
73.42
Omni
79.09
75.77
77.44
51.23
99.40
67.61
52.74
98.51
68.
62.76
82.82
71.41
69.20
80.79
74.55
A.T.
51.08
97.07
69.16
51.01
95.36
66.19
56.91
96.69
71.65
53.63
98.27
69.39
51.26
82.18
65.37
DC
50.93
97.57
66.45
55.90
95.53
70.56
53.12
98.37
68
53.25
VM. 12
54.73
66.99
GPT4TS
73.33
95.97
83.14
95.43
77.23
90.56
74.67
56.84
70.11
73.61
91.13
$1.44
ModemTCN
74.07
94.79
83.16
65.94
93.00
77.17
65.15
67.41
59.11
89.22
71.13
73.17
79.59
MtsCID
67.96
78.10
72.68
56.45
94.41
70.65
98.65
71.03
$3.13
08
08.96
52.79
82.13
64.27
TimeMiser
74.94
95.75
$4.08
74.24
75.41
74,82
64.57
77.02
70.25
60.56
89.72
72.31
60.31
99.09
74.98
TomesNNi
72,73
94.16
82.07
67.47
90.40
77.27
65.74
89.39
75.77
73,82
75.10
74. 16.46
66.41
99 66
79.70
CresAD
75.70
97.71
85,31
67.65
90.44
77.40
66.20
90.35
76.41
65.33
90.99
76.05
77.43
96.77
86.03
To make the result more persuasive, we present results using the affiliation F1 (Aff-F1) metric [58] in Table Table/Jacros, across all baselines. This metric takes into account the average directed distance between predicted anomalies and ground truth anomaly events to calculate affiliation precision (Aff-P) and recall (Aff-R). Since the precision and recall are significantly influenced by thresholds, focusing solely on one of them fails to provide comprehensive evaluation of the model, and thus, we pay more attention the Fl score, which is the harmonic mean of precision and recall and has gained
23

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Random query
Learnable sub-series query
0.6
0.2
0.2
1.0
0.0
0.6
0.0
0.6
0.4
y
0.4
V
0.6
1.0
0.0
1.0
Query
Query ID2
Query ID3
Quxry ID4
Quary ID5
Figure The I-SNE visualization sub-series representation of the PSM dataset using (left) random queries and (right) learnable sub-series queries respectively.
is evident that another multi-scale method, TimesNet, achieves great detection performance. However, CrossAD benefits from cross-scale reconstruction and the construction of global multi-scale context, outperforms TimesNet across all datasets.
widespread adoption recently 32)
E.2 Visualization of sub-series representations
We perform t-SNE visualization on sub-series representations. Specifically, in Figure (right), sub-series representations extracted by learnable sub-series queries show a distinct clustering trend, indicating that this method can effectively capture the internal structure of the sub-series and generate discriminatory feature representations. For comparison, we perform the same random initialization for the queries in the sub-series library. The corresponding visualization result is shown in Figure 7 (left), presenting a relatively mixed distribution state, and the boundaries between various samples became blurred. This discovery provides us with new research ideas and practical basis for applying this model more complex time series applications the future, that is, further enhance model's s ability to capture key features and generalization performance by optimizing the query mechanism.
E.3
TSB benchmark
TSB-AD benchmark [59] comprises 40 diverse, publicly available datasets. We provide comparison with the state-of-the tfe-the-art methods from TSB-AD. In Table TO we present a comparison of the accuracy between CrossAD and other detection algorithms
TSB-AD-U and TSB-AD-B Additionally. in Figure g we provide the critical diagram and the score distribution for VUS-PR. From the results, can be found that CrosSAD demonstrates excellent detection performance across all metries, whether TSB-AD-U or TSB-AD-M. More details about the baselines and metrics can be seen in TSB-AD benchmark.
E.4
UCR benchmark
UCR Dataset, compiled by 61]. consists of 250 sub-datasets. Fach sub-dataset contains one- dimensional data with a single anomaly segment. We evaluate CrossAD on the UCR Anomaly Archive, where the task is to find the position of an anomaly within the test set. To achieve this, we compute the anomaly scores for each time step in the test set and subsequently rank them in descending order. Following the approach of Timer [63] and DADA [3I] if the time step with the quantile hits the labeled anomaly interval the test set, the anomaly detection is accomplished. Digure/9Jpeeeents which the model successfully detects anomalies quantile levels of 3% and 10%; a higher count indicates stronger detection capability of the model. The right figure shows the quantile distribution and the average quantile across all UCR datasets. CrossAD has a lower average quantile compared to Timer and DADA, which indicates better performance of anomaly detection. In addition, shown
Figure 9 presents the results of our evaluation. The left figure displays the number of datasets in

---

we also visualize the detection results of CrossAD to further illustrate its powerful anomaly detection capability.
in Figure to Figure 14
F Broader impacts
Time series anomaly detection plays a critical role in real-world applications. Early detection of anomalies helps prevent potential risks and reduce economic losses. However, since existing anomaly detection methods cannot achieve 100% precision and recall, false positives may lead to unnecessary costs in terms of both human effort and resources, while false negatives could result in hidden dangers. Improving the performance of time series anomaly detection models is therefore an important direction for future research, which is a goal that current approaches are actively striving toward.
G Limitations
In this work, we propose CrossAD, a novel framework for time series Anomaly Detection that takes Cross-scale associations and Cross- modeling into account. We propose the cross-scale reconstruction to model cross-scale associations to capture more complex anomaly patterns and build a global multi-scale context overcome the limitations of window size. Our experiments show that the optimal number of sub-series queries and prototypes in the global multi-scale context varies across datasets. Currently, we use unified set of parameters across all datasets. If these parameters could be automatically adjusted based on the characteristies of each dataset, it would further improve detection performance. We will address this as part of our future work.
Table 10: Comparison of results on TSB-AD-U and TSB-AD-M under different metrics. The best ones are in bold and the second ones underlined.
Meshod
AUC-PR
AUC-RIX:
VUS-PR VUS-ROC
Staddad-FF1
PA-FI
Event-busol-Fi
R-busod-F1
Atfiliation-H1
CrossAD
01.4
0.78
0.45
0.54
0.47
[I8]]
1.68
0.41
0,89
Sub-PCA
0.37
0.71
0.42
0.76
0.42
0.56
0.49
0.41
0.85
SullShupeAD
0.74
[T40
0.76
11:00
0.58
(1.6
[A0
DX31
POLY
0.31
0.73
0.39
0.76
0.37
0.53
0.45
0.35
Series2Gmphh (PT)
0.50
(ZS)
KMaansAD
0.32
0.74
0.76
0.37
0.44
0.82
USAD
0.32
0.66
0.36
0.7
0.37
0.50
0.43
0.40
0.84
Sub- KNN
0.27
0.76
0.35
0.79
0.34
0.61
0.43
0.22
0.84
MarrixProfile
0.26
0.73
0.76
0.33
0.63
0.44
0.32
TSB-AD-4
SAND
0.73
76
0.47
ISTMAD
0.31
0.68
SR
0.32
0.74
0.32
0.8
0.38
0.87
0.67
0.35
0.39
TimesPM
0.28
0.67
0.30
1174
0.34
1134
066
0.34
0.30
[Forest
0.29
0.71
0.30
0.75
0.35
0.73
0.56
0.30
0.1
OmniAnomaly
0.27
0.65
0.29
0.72
0.31
0.50
0.46
0.29
Lag-Liama
0.65
0.77
0.59
0.31
TimeaNict
AutoEncoder
0.63
0.26
0.69
0.25
0.54
0.36
0.28
0.82
TranAD)
0.30
0.57
0.26
0.68
0.25
0.5K
0141
0.25
DX1
FITS
0.17
0.61
0.26
0.75
0.23
0.65
0.42
0.20
0.86
Sal-LOP
0.16
0.68
D.25
0.75
0.24
0.57
0.33
0.25
0.82
OFA
0.59
0.71
0.22
0.67
0.15
0.20
3.56
0.67
Sub-HBOS
Sub- Sub-OCSVM
0.16
0.65
0.21
0.75
0.22
0.55
0.32
0.23
0.79
Sub-IForest
0.16
0.63
0.22
0.72
0.22
0.63
0.34
0.23
0.80
Donut
0.14
0.56
0.20
0.68
0.20
0.57
0.38
0.20
0.82
LOF
0.14
0.58
0.17
0.68
0.21
0.62
0141
(1.2
0.79
Anomaly Tranffomer
0.08
0.50
0.12
0.56
0.12
0.53
0.31
0.11
0.77
CrossAD
0:50
0.23
(mmminnomaly
PCA
0.31
0.70
0.31
0.74
0.37
0.79
0.59
0.29
0.35
LSTMAD
0.31
0.70
0.31
0.74
0.36
0.79
0.64
0.38
0,87
USAD
0.26
0.64
0.30
0.68
D.31
0.33
0.40
0.37
0.80
AutoEncoder
0.30
0.67
0.30
0.69
0.34
0.60
0.44
0.28
3.00
KMicusAD
0.31
0.49
82
ISB-AD-M
MCD
0.65
OCSVM
0.23
0.61
0.26
0.67
0.28
0.48
0.11
0.30
0.50
Donut
0.30
01.64
0.26
0.1
0.28
0L52
0.36
0.21
088
RobustPCA
0.21
0.58
0.21
0.61
0.29
0.60
0.12
0.33
0.8]
PITS
0.15
0.58
0.1
0.66
0.22
0.72
0.32
0.16
0.81
0.55
0.5
0.21
0.72
0.11
0.17
COPOD
0.65
IForest
0.19
0.66
0.20
0.69
0.26
0.68
0.41
0.24
0.30
HROS
0.11
0.63
0.19
0.7
0.24
0.67
(1400
0124
0.00
TemesNet
0.13
0.56
0.19
0.61
0.20
0.68
0.32
0.17
0.82
KNN
0.14
0.51
D.18
0.50
0.19
0.69
0145
0121
0.79
TramAD
0.14
0.59
0.18
0.65
0.21
0.68
0.10
0.21
0.79
0.53
0.32
Asomaly Transoener
25

---

VUS
0.
Crosdd
Matrir SAN
LSTHIng
Timefti
CroGoA
CNN
Omnikno mollyy
PCA
LSTM60
US4D
Autafinoie
CILOT
MCD
Donut
Rob POOSSPAA
ITTS
COPOD
Foond
HROS
Timestee
Thank
LOF
POMME MOMEENT
S
(a) TSB-AD-U
(b) TSB-AD-M
Figure 8: The critical diagram and the score distribution for VUS-PR on TSB-AD-U and TSB-AD-M. For the score distribution plot, the dashed line represents the mean, and the solid line represents the median.
Detovets Count [Acompiishel]
250
100%
220
Quantill Quanttll Distribution
Timer Aug. 12.5%
80%
200
186
166
172
DADA Aug: 7.60%
40%
CrossAD
0%
39%
10%
Figure 9: Anomaly detection results for UCR benchmark. The left figure displays the number of
datasets in which the model successfully detects anomalies at quantile levels of 3% and 10%, and higher count indicates a stronger detection capability. The right figure shows the quantile distribution and the average quantile across all UCR datasets, and lower average quantile indicates stronger detection capability.
26

---

series arom scom
aromely Intenval
Anutral
22500
13000
Figure 10: Visualization of OOI_UCR A DiSTORYYDSSOORREECOOOOOOOO
10000 11800 11800_12100.0xx 12100.txt.
1.0
6.8
-02
1..0
5.00
1000
1500
2590
3020
Figure 11: Visualization of 0U0 2ttpiiionn__000_2_22222222 22700000000000505999909990
sedles
ontriiy score anterialy
4.2
-15-
5.0
3000
15900
Figure 12: Visualization of 071 LOT1_CCC_AAooetaeet Lo_.CCRAooonnDDSSTTTTDDSassssssa 0400:///AA__20002222202222282000
aerics srom score
aromely Intevval
14
0.2
2500
7503
10000
12500
15000
17503
22000
Figure 13: Visualization of 119_UCR Awn.nalyooCCriaa
scricc
-10
+0.2
+0.0
soco
10003
15000
22000
22000
Figure 14: Visualization of 145 RSSSUCR_00 UCR_Anomaay LatimmalyyLaa0Cmm011111121 1 11
27


Reviews:
[{"review_id": "dRX7dUU8rr", "reviewer": "Reviewer_sbi4", "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.", "questions": "The key questions/clarification requests that I have are:\n1. 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.\n2. All functions, such as LayerNorm, Attention, and FeedForward, need to have explicit definitions in the text.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The experimental results are quite thorough and seem to show good results.\n\nWeaknesses:\n1. 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.\n2. All functions, such as LayerNorm, Attention, and FeedForward, need to have explicit definitions in the text.\n3. 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.\n\nSome additional questions:\n3. On page 6, how is $S$ calculated, and how does it relate to other variables like $P$ and $T$?\n4. On pages 14-15, do you have a good way to choose $K$?\n5. Associated with table 9, what is the order of growth of the training time as the training set size increases?", "was_revised": true, "final_justification": "I have raised my decision to \"accept\" based on the way that the authors addressed my questions and those of the other reviewers.", "rebuttal": "We sincerely thank Reviewer sbi4 for the valuable comments and constructive suggestions, which have helped us improve our work. We appreciate your recognition of our novel contributions and will address each concern point-by-point.\n\n### W1 & Q1: The pseudocode of the full algorithm\nWe sincerely thank the reviewer for the valuable suggestion. To enhance the clarity and reproducibility of our work, we will include complete pseudocode in the revised manuscript, which will clearly illustrate the logical flow of each step in the algorithm, enabling readers to easily reproduce our methodology.\n\n### W2 & Q2: Supplement to the function definitions\nWe will provide clear and detailed definitions of these functions, such as LayerNorm, Attention, and FeedForward, in the corresponding section of the methodology to help readers gain a deeper understanding of every technical aspect of our research.\n\n### W3: Synthetic Anomalies\nThank you very much for your suggestion. Our method is comprehensively validated across multiple real-world datasets containing diverse anomalies, where it significantly outperforms baseline approaches. Furthermore, as evidenced by the detection results in Fig. 4 in the main text, our method effectively handles various synthetic anomalies.\n\nTo better test the limits of CrossAD, we add an additional 40 anomalies of different degrees to the test dataset. These anomalies affect each scale to varying degrees. We divided these anomalies into 4 groups according to the degree of impact, with 10 in each group. From the following results, it can be found that our method detects a total of 33 synthetic anomalies, which is more than the 26 of the baseline method, TimeNets.\n\n|Group|hard|medium|easy+|easy|Total|\n|-|-|-|-|-|-|\n|TimeNets|2|5|9|10|26|\n|CrossAD|5|8|10|10|33|\n\n### Q3 & Q4 in weakness: Variable Calculation and Parameter Selection\nWe sincerely apologize for the confusion. S denotes the length of the learnable query, P represents the patch length, and T stands for the length of the input series to the model. S is a hyperparameter of the model. The learnable query is employed to extract sub-sequence representations from the input sequence; hence, S is smaller than T. We will elaborate on this in the corresponding parts of the paper.\n\nK indicates the number of prototypes in the global multi-scale context. We performed a grid search on two validation datasets to select a better-performing K and used this K value for all the test datasets. Selecting K is quite open-ended. Here are some of our thoughts:\n\n+ We can assess the dataset complexity to determine a suitable K. For simple and small-scale datasets, a small K suffices.\n+ Dynamic prototypes can be considered. Instead of being fixed, the number of prototypes dynamically adjusts during data processing to determine the optimal K value for retaining relevant information.\n+ Neural architecture search techniques can be used to find the optimal K.\n\n### Q5 in weakness: The Relationship between Training Time and Training Set Size\nThank you for your care about computational resource consumption. When the sliding window size is fixed, the training time per epoch mainly depends on the number of window sequences (i.e., samples) in the training set. Under this condition, the training time grows roughly linearly with the size of the training set. The following result is the time cost required for training 5 epochs on training data sets with varying numbers of time points, which increases linearly.\n\n| Training Set Size (time points) | 498672 | 997344 | 1496016 |\n| --- | --- | --- | --- |\n| Training Time (5 epochs) | 270.75s | 535.44s | 820.25s |"}, {"review_id": "a8j05XQDqw", "reviewer": "Reviewer_WTgi", "summary": "The 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.", "questions": "Here 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.", "limitations": "Yes, in the Appendix.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The 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.", "was_revised": true, "final_justification": "Most of my comments and suggestions have been addressed by the authors in the discussion phase. I am therefore raising my score to \"accept\". Nonetheless, the contents of the discussion should be included in the paper.", "rebuttal": "We sincerely thank Reviewer WTgi for the valuable comments and constructive suggestions, which have helped us improve our work. We appreciate your recognition of our novel contributions and will address each concern point-by-point.\n\n### Q1: Clarify the Novelty\nWe are grateful to the reviewer for bringing this relevant work to our attention. In the revised manuscript, we will add a discussion of [Ref1] in the Related Work section and highlight the key distinctions.\n\nIn [Ref1], a hierarchical RNN processes the raw time series to generate multi-scale representations, with each scale reconstructed independently. To improve reconstruction at the current scale, the method fuses coarser-level features into the current scale's representation. As a result, the reconstruction in [Ref1] is fundamentally **reconstruction-based**: it relies on the current scale's own features, enhanced by higher-level contextual information, mainly focusing on the modeling of temporal dependencies and ignoring cross-scale associations. \n\nIn contrast, CrossAD adopts a **prediction-like** mechanism. Instead of depending on the current scale, our method reconstructs (predicts) the fine-grained series solely from coarser-grained representations. By the next-scale reconstruction, the model captures the cross-scale associations. This design shift—from _refining_ the current scale using multi-scale fusion, to _generating_ it from higher-level abstractions—reflects a fundamental difference in modeling philosophy.\n\nIn addition, the number of scales in [Ref1] is strictly determined by the number of model layers, whereas in CrossAD， **it can be set adaptively with flexible numbers of scales**. This demonstrates that CrossAD has a more flexible and general architecture.\n\nThe novelty of CrossAD compared to fusion-based methods such as [Ref1] can be highlighted in the following aspects: (1) \n**Modeling objective is novel**. Fusion-based methods aim to enhance the modeling of temporal dependencies within each scale by integrating multi-scale features. In contrast, CrossAD not only captures temporal dependencies but also explicitly models the associations across scales. (2) **Modeling methodology is novel**. To achieve the objective, we novelly reconstruct fine-grained series exclusively from coarse-grained inputs, without relying on the current scale, which is a design principle that has not been explored in existing fusion-based approaches. (3) **The criterion is novel**. Our method explicitly models the cross-scale associations and, in a novel way, leverages these associations as an anomaly criterion for anomaly detection.\n\n### Q2: Dataset usage\nThank you very much for your suggestion. Due to considerations of evaluation methodology and paper length, we have not included the UCR dataset in the main text, but have provided a detailed discussion in Appendix E.5. Unlike other datasets, UCR consists of 250 distinct univariate sub-datasets, each containing only one continuous anomalous sequence. Importantly, the UCR dataset focuses on whether a model can successfully detect anomalies in each individual sub-dataset. Therefore, we follow the evaluation protocol used by Timer [ref3] and DADA [ref4]. As shown in Figure 7 of Appendix E.5, when alpha quantile = 3%, CrossAD successfully detects anomalies in 186 sub-datasets, outperforming Timer with 110 and DADA with 166. Moreover, CrossAD achieves a lower average quantile of 4.40% across all sub-datasets, compared to 12.5% for Timer and 7.60% for DADA. These results demonstrate the superior performance of CrossAD. We have also included visualization results for several sub-datasets.\n\nWe will strengthen the empirical evaluation by including additional benchmarks in Figure 7, and we will move this analysis to a more prominent location in the main text. Additionally, **since the TSB-AD benchmark is more comprehensive and includes the UCR datasets**, we will include the TSB-AD results in Table 1.\n\n### Q3: Benchmark coverage\nThank you for your suggestion. The TSB-AD benchmark is a collection of multiple open-source datasets after preprocessing and integration. We add experimental results on TSB-AD-U and TSB-AD-M and provide a comparison with the state-of-the-art methods from TSB-AD [Ref2]. CrossAD achieves excellent detection performance on this benchmark. Further comparative results can be found in Table 5 of [Ref2].\n\n|TSB-AD-U|AUC-PR|AUC-ROC|VUS-PR|VUS-ROC|Standard-F1|PA-F1|Event-based-F1|R-based-F1|Affiliation-F1|\n|-|-|-|-|-|-|-|-|-|-|\n|SOTA (TSB-AD-U)|0.37|0.71|0.42|0.76|0.42|0.56|0.49|**0.41**|0.85|\n|CrossAD|**0.44**|**0.78**|**0.45**|**0.84**|**0.47**|**0.81**|**0.68**|**0.41**|**0.89**|\n\n\n|TSB-AD-M|AUC-PR|AUC-ROC|VUS-PR|VUS-ROC|Standard-F1|PA-F1|Event-based-F1|R-based-F1|Affiliation-F1|\n|-|-|-|-|-|-|-|-|-|-|\n|SOTA (TSB-AD-M)|0.32|0.73|0.31|0.76|0.37|0.78|**0.65**|**0.37**|**0.87**|\n|CrossAD|**0.34**|**0.74**|**0.33**|**0.77**|**0.38**|**0.82**|0.64|**0.37**|0.86|\n\n### Q4: Statistical significance testing\nThank you for the suggestion. We conduct the Wilcoxon signed-rank test on the VUS-PR results in TSB-AD-U (in Q3), which has 350 sub-datasets. CrossAD achieves the highest average rank among all models, which is 9.54. \n\nWe include the p-values between CrossAD and other baseline models, indicating that the performance improvement of CrossAD over other models is statistically significant and not due to random chance.\n\n| Models | Average Rank | p value(vs CrossAD) |\n| --- | --- | --- |\n| CrossAD | 9.54 | 1.0 |\n| POLY | 12.51 | 0.00032 |\n| Series2Graph | 13.62 | 1.34E-05 |\n| Sub-PCA | 13.788 | 0.006579 |\n| CNN | 13.91 | 7.59E-25 |\n| MOMENT(FT) | 13.89 | 4.45E-05 |\n| Sub-KNN | 14.85 | 3.72E-06 |\n| KShapeAD | 14.90 | 0.008831 |\n| KMeansAD | 14.95 | 3.17E-05 |\n| MatrixProfile | 15.06 | 1.34E-05 |\n\n**As visualizations are not permitted in the rebuttal**, we will include the critical difference diagram in the revised version of the paper.\n\n### Q5: Ablation study\nThank you very much for your suggestion. We include additional datasets as follows. Due to time constraints, we will include results on a larger benchmark in the final version of the paper.\n\n|Dataset|MSL||SMAP||PSM||GECCO||SWAN||Avg.||\n|-|-|-|-|-|-|-|-|-|-|-|-|-|\n|method|V-R|V-P|V-R|V-P|V-R|V-P|V-R|V-P|V-R|V-P|V-R|V-P|\n|Row1|0.7388|0.2383|0.4729|0.1173|0.6783|0.4467|0.9344|0.4145|0.8638|0.8322|0.7376|0.4098|\n|Row2|0.7513|0.2479|0.5423|0.1288|0.6889|0.4739|0.9542|0.4668|0.9143|0.9051|0.7702|0.4445|\n|Row3|0.7782|0.2984|0.5673|0.1424|0.7125|0.4874|0.9628|0.5121|0.9385|0.9142|0.7919|0.4709|\n|Row4|0.7790|0.3000|0.5734|0.1402|0.7211|0.5491|0.9581|0.5299|0.9421|0.9159|0.7947|0.4870|\n|Row5|0.7696|0.2869|0.5619|0.1333|0.6991|0.4600|0.9577|0.4679|0.9382|0.9099|0.7853|0.4516|\n|Row6|0.8091|0.3144|0.5779|0.1443|0.7302|0.5596|0.9948|0.6211|0.9499|0.9171|0.8124|0.5113|\n\n### Q6: Execution time analysis\nWe sincerely thank you for your valuable suggestion. We will include further discussion along the following directions:\n\n1. The effect of varying sequence length and dimensionality on inference time (in Q7).\n2. A 2D scatter plot comparing execution time versus accuracy across different methods.\n\nWe will place this analysis in a more visible location in the revised manuscript to better highlight it.\n\n### Q7: Scalability evaluation\n**(1) About series length.** \n\nWe provide a theoretical complexity analysis of how sequence length affects computational cost. Let the length of the original sequence be _N_. After _m_ downsampling steps, the total length of multi-scale sequences becomes: \n\n$\\frac{N}{2} + \\frac{N}{4} + ... + \\frac{N}{2^m}<N$\n\nFor the encoder, the attention computation cost is based on these sequences. \n$ O((\\frac{N}{2}+ ...+ \\frac{N}{2^m})^2)<O(N^2)$\n\nSince the length S of the sub-series queries and context prototypes is smaller than _N_, the overall complexity of the model remains $O(N^2)$. This quadratic complexity is consistent with most transformer-based methods. \n\nExperimental results on GECCO (5 epochs) demonstrate that the model scales efficiently, with computational time growing acceptably as sequence length increases.\n\n| Series length | Training time(s) |\n| --- | --- |\n| 96 | 231.21 |\n| 128 | 270.75 |\n| 192 | 304.84 |\n\n**(2) About data dimension.**\n\nDue to its channel-independent design, the theoretical complexity scales linearly with dimensionality. For $ c $ channels, the complexity becomes $ O(cN^2) $, aligning with existing channel-independent approaches.\n\n**Reference**\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 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 NeurIPS, 2024.\n\n[ref3] Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, and Mingsheng Long. Timer: Transformers for time series analysis at scale. In ICML, 2024.\n\n[ref4] Qichao Shentu, Beibu Li, Kai Zhao, Yang Shu, Zhongwen Rao, Lujia Pan, Bin Yang, and Chenjuan Guo. Towards a general time series anomaly detector with adaptive bottlenecks and dual adversarial decoders. In ICLR, 2024."}, {"review_id": "N4R390Tx7O", "reviewer": "Reviewer_fJUJ", "summary": "The 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.", "questions": "**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)?", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**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.", "was_revised": true, "final_justification": "Resolved issues:\n- Weakness 1: Cross-scale association (mapping) has now been clearly defined and forms a fundamental motivation to this work (**significant weight**).\n- W2: Most design choices have been justified in discussions (medium weight) except perhaps for W2(5) which is only minor and follows previous work.\n- W3-W9 and Question1-Q3 have been clarified (minor weight).\n\nIn summary, the paper is technically solid, presents novel ideas for anomaly detection, and has improved clarity (especially on motivation of using cross-scale mapping for anomaly detection) after author-reviewer discussions. I have raised my score since the discussions.", "rebuttal": "We sincerely thank Reviewer fjUj for the valuable comments and constructive suggestions, which have helped us improve our work. We appreciate your recognition of our novel contributions and will address each concern point-by-point.\n### W1: Our motivation for cross-scale association\nWe sincerely apologize for the misunderstanding, and we will refine the logical flow in the introduction. The cross-scale association emphasizes the **mapping relationship across different scales of the same subseries**. \n\nWe use mathematical functions to further clarify. Consider three subseries: $A$, $B$, and $C$, where $A$ and $B$ are normal (blue parts in Fig. 1), and $C$ is anomalous (red part). Take scale 2 and scale 3 as examples, we denote $f$ as the cross-scale association of normal series. \n\nWe construct the model to learns the cross-scale association $f$. During training, we learn the normal cross-scale association patterns $f$ by reconstructing the fine-grained series from the coarse-grained series, e.g., $\\hat A_{scale2}=f(A_{scale3})$, $\\hat B_{scale2}=f(B_{scale3})$, and minimizing between $A_{scale2}$ and $\\hat A_{scale2}$, and between $B_{scale2}$ and $\\hat B_{scale2}$. \nHowever, during inference, when an anomalous series $C$ is encountered, the model reconstructs $\\hat C_{scale2}=f(C_{scale3})$ using the cross-scale association $f$ and expects $\\hat C_{scale2}=C_{scale2}$. As the associations are different between normal and abnormal series, the cross-scale association $f$ can only reconstruct normal subseries, leading to $C_{scale2} \\neq \\hat C_{scale2}$. This discrepancy enables effective anomaly detection (corresponding to lines 40–42: \"when anomalies occur .. in the normal state\").\n\n**Three questions in W1:**\n\n(1) In line 42, we say, \"This discrepancy...abnormal behavior\". \nThe \"discrepancy\" refers to the different associations between normal and abnormal series, as we defined above. We do not detect anomalies by comparing the similarity among scales 1, 2, and 3.\n\n(2) If all the normal peaks simulate the anomalies in the training data, the model will capture such associations and can't detect the peaks as anomalies in the test. If these peaks only appear in test data, it can be detected as the model does not learn this in the normal association.\n\nThe cross-scale association discrepancy enables the detection of anomalies by learning mappings across different scales and allows for more precise localization of the specific scale at which an anomaly occurs. Moreover, as shown in Fig. 4, we find that the cross-scale association discrepancy is more effective, particularly in identifying complex anomalies like shapelet or seasonal. From an experimental perspective, the results in Tables 1, 2, and 3 demonstrate that the next-scale reconstruction approach indeed achieves better detection performance.\n\n(3) We can visualize the reconstruction results at each scale for both normal and abnormal subseries to illustrate the differences between normal and abnormal associations. As shown in Fig. 6 (Appendix E.3), when an anomaly occurs, the cross-scale association deviates from the normal pattern, leading to reconstruction failure across all scales. This observation is consistent with our original motivation.\n\nIf there are any parts that we have not explained clearly or if you have any questions, please feel free to let us know. We would be more than happy to provide further clarification and engage in deeper discussion.\n### W2:  Justifications for design choices\n(1) Scale-independent encoding: While the two implementations are functionally equivalent, we agree that your approach is indeed more computationally efficient. When we wrote the paper, we chose to concatenate the multi-scale representations before the encoder to simplify the illustration in Fig. 2, since these representations are later used for cross-attention. In practice, your suggested approach is more efficient and can be adopted during actual implementation.\n\n(2) The query library is randomly initialized and learnable. We will include this clarification in the revised version of the paper.\n\n(3) About the Next-scale generation: Since the output of the encoder needs to query a more relevant context from the global multi-scale context, attention mechanisms have a natural advantage in computing similarity.\n\n(4) Ablation study on the query library: Thank you for the valuable suggestion. We add experiments that directly use a trainable context, and the results further support our design choices.\n\n||PSM(V_R/V_P)|MSL(V_R/V_P)|GECCO(V_R/V_P)|Avg. (V_R/V_P)|\n|-|-|-|-|-|\n|Direct trainable context|0.7129/0.5076|0.7794/0.3012|0.9621/0.5274|0.8181/0.4454|\n|CrossAD|0.7302/0.5596|0.8091/0.3144|0.9948/0.6211|0.8447/0.4984|\n\n(5) About dataset MSL and SMAP: As a next-scale reconstruction-based approach, our model relies on learning continuous latent representations through autoencoding. Discrete variables inherently lack the smooth and structured latent space required for effective reconstruction.\n### W3: About \"Up-interpolation\"\nWe correct the \"up-interpolation\" to \"interpolation\" in the revised version of the paper.\n### W4 & W5: SOTA detection methods\nWe included TimesNet and TimeMixer as they are multi-scale methods, and they show great detection performance in our experiments. We add the anomaly detection models D3R[ref1] and the latest SOTA model Catch[ref2].\n\n||Method|F1|Aff-F1|AUC_R|AUC_P|R_AUC_R|R_AUC_P|V_ROC|V_PR|\n|-|-|-|-|-|-|-|-|-|-|\n|SMD|D3R|0.117|0.780|0.533|0.128|0.628|0.148|0.661|0.175|\n||Catch|0.237|0.847|0.811|0.172|0.800|0.159|0.797|0.159|\n||Ours|0.241|0.853|0.782|0.186|0.842|0.258|0.858|0.234|\n|PSM|D3R|0.386|0.802|0.502|0.308|0.529|0.396|0.521|0.393|\n||Catch|0.116|0.859|0.652|0.434|0.640|0.435|0.639|0.436|\n||Ours|0.497|0.850|0.681|0.490|0.756|0.603|0.730|0.559|\n\n### W6: Grammatical errors\nWe have fixed the error.\n### W7: About the words \"generation\", \"(down/up)-sampling\", and \"interpolation\"\nFrom the perspective of module naming, we use the term \"generation\" to refer to the process of creating multi-scale series. In practice, we implement this via \"downsampling\". Thank you for your suggestion. We will review the entire paper and unify the term consistently.\n### W8: About the pooling size and period of time series\nTo enhance the model's generality, we use a fixed pooling size across all datasets. If prior knowledge is available, finer adjustments can be made. Adaptively selecting the pooling size based on each dataset is indeed a valuable direction for multi-scale methods, and we would like to leave it as a direction for future research and discussion.\n### W9: About the window size\nSince CrossAD is not highly sensitive to the window size parameter, we selected a window size that achieves relatively good performance. We include results for various window sizes (96, 128, 192) for completeness. From the results, CrossAD demonstrates great detection performance across various window sizes. \n\n||SMD|||MSL|||SMAP|SWAT|PSM|\n|-|-|-|-|-|-|-|-|-|-|\n||96|128|192|96|128|192|96|128|192|96|128|192|96|128|192|\n|TimesNet|0.8492|0.8383|0.842|0.7838|0.7838|0.7747|0.5541|0.5617|0.5765|0.2635|0.2742|0.2875|0.645|0.6469|0.6433|\n|TimeMixer|0.7802|0.7792|0.7814|0.7899|0.8001|0.7754|0.5512|0.5586|0.5666|0.26|0.2646|0.2712|0.6194|0.6326|0.6253|\n|CrossAD|0.8521|0.8546|0.858|0.8091|0.8082|0.8075|0.5621|0.5699|0.5779|0.787|0.7818|0.7865|0.7227|0.7356|0.7302|\n\n### Q1: About channel-independent\nIn our method, the query library and global multi-scale context store global information. Extending to multi-channel sub-series and global context would introduce additional complexity, making it more challenging to extract meaningful patterns. Therefore, modeling multi-channel series requires further specialized optimization. As the current work focuses on temporal dependency modeling, we leave the exploration of channel-wise correlations as future work.\n\nThe final anomaly score is calculated as the average of the scores from all channels.\n### Q2: About the correlation among multiple channels\nAlthough CrossAD does not explicitly model inter-channel dependencies, it demonstrates strong capability in capturing temporal modeling. We conduct a visualization analysis of the anomaly scores on the SWAT dataset, and the results show that CrossAD is able to detect most of the anomalies without noticeable delay because we promptly detect the anomalies in each channel. We will include these visualization results in the revised manuscript.\n\nAdditionally, we add experimental results of Catch, an anomaly detection model that captures inter-channel correlations (The results are in W4&W5). However, in practice, Catch does not show a significant performance advantage. The primary reason is that CrossAD's strong capability in modeling temporal dependencies compensates for the lack of channel correlation modeling.\n### Q3: About patch embedding\nGiven a time series of length $T_i$, it can be divided into $P_i$ patches by splitting the sequence into $P_i$ non-overlapping segments of equal length. Each patch has a length of $T_i/P_i$. We will include additional explanations regarding the patch embedding in the revised manuscript. \n\n[ref1] Chengsen Wang, Zirui Zhuang, Qi Qi, et.al. Drift doesn’t matter: Dynamic decomposition with diffusion reconstruction for unstable multivariate time series anomaly detection. In NeurIPS, 2023.\n\n[ref2] Wu Xingjian, Qiu Xiangfei, Li Zhengyu, et.al. Catch: Channel-aware multivariate time series anomaly detection via frequency patching. In ICLR, 2025."}, {"review_id": "nP3oy8SR8W", "reviewer": "Reviewer_bwo6", "summary": "The 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.", "questions": "I 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?", "limitations": "The paper has a limitation discussion in Section G.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**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.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank Reviewer bwo6 for the valuable comments and constructive suggestions, which have helped us improve our work. We appreciate your recognition of our novel contributions and will address each concern point-by-point.\n\n### Q1: Computational Efficiency and Parameter Analysis\nThank you for raising this important question. The design of CrossAD has been carefully considered from multiple perspectives to ensure computational efficiency:\n\n1. Instead of 'copy', we use downsampling to obtain multi-scale sequences. Each downsampling step results in a sequence that is half the length of the previous one. Let the length of the original sequence be _N_. After _m_ downsampling steps, the total length of multi-scale sequences is: $\\frac{N}{2} + \\frac{N}{4} + ... + \\frac{N}{2^m}<N$. For the encoder, the attention computation cost is based on multi-scale sequences. The overall complexity of the model remains $O(N^2)$. This quadratic complexity is consistent with most transformer-based methods. \n2. For cross-window modeling, we employ a prototype compression mechanism that compresses the global context into a fixed number of prototypes, effectively avoiding the storage of a massive number of sub-series. Moreover, during inference, we only need to use the pre-trained global multi-scale context to generate the next-scale output, without having to compute sub-series representations.\n3. Detailed information on runtime and parameter count is provided in Appendix E.2. As shown in Table 9, CrossAD achieves great performance with 0.93M parameters. On the GECCO dataset, its inference time (0.8 seconds) outperforms multi-scale methods like TimesNet and transformer-based approaches such as AnomalyTransformer.\n\nWe will include these details in Appendix E.2 to provide readers with a clearer understanding of our method's efficiency.\n\n### Q2: About the period-aware router\nThe period-aware routing mechanism filters out high-frequency noise by retaining only the top-k magnitude components and then reconstructs the time-domain patterns through the inverse Fourier transform to enhance stability. Additionally, the Gumbel-Softmax gating further improves robustness to noise by injecting stochastic noise. Consequently, the Fourier-based period-aware router is robust when handling non-stationary or noisy time series. This capability is validated on non-stationary datasets like SMD and SWaT[ref1] in Table 1, where CrossAD achieves superior detection performance.\n\nThe core design objective of the top-k Router is to extract long-term periodic patterns from time-series data, enabling appropriate selection of sub-series queries for constructing a global multi-scale context. Crucially, during detection, it does not filter the multi-scale series input to the Encoder and Decoder. Therefore, the selection of top-k in the router does not directly impact the method's sensitivity to time series containing transient anomalies or irregular patterns. As seen in Fig. 4, CrossAD effectively detects both global and contextual anomaly points, confirming its sensitivity to transient anomalies.\n\n### Q3: Training imbalance or representation collapse\nWe employ scale-independent encoding to ensure that features at different scales are not dominated by coarser granularities, and use a masking mechanism (Scale Independent Mask M1 in Fig.2(2)) to isolate cross-scale interference. The decoder operates in a staged manner: it first independently upsamples each scale and then reconstructs the signal under the guidance of a cross-scale mask (Cross Scale Mask M2 in Fig.2(4)) to control the reconstruction conditions.\n\nAt the same time, we dynamically update the global multi-scale context, enabling the model to effectively integrate information across scales and prevent the loss of fine-grained features. As shown in the detection results in Fig. 6, the model maintains a strong detection capability for fine-grained global point anomalies.\n\nThe training curves show that the MSE errors across all scales decrease synchronously, validating the balanced optimization process. No representation collapse is observed during training.\n\n### Formatting Concerns\nWe sincerely thank the reviewer for the valuable suggestions. We carefully review and revise the formatting. Modifications include, but are not limited to, the following:\n\n1. Standardized the fonts in Figure 2 (Arial for text and Times New Roman for equations).\n2. Corrected the operator notation in equations.\n3. Fixed vertical spacing issues and symbol errors.\n4. Streamlined the description of the standard architecture for clarity and conciseness.\n\n[ref1] Chengsen Wang, Zirui Zhuang, Qi Qi, et.al. Drift doesn't matter: Dynamic decomposition with diffusion reconstruction for unstable multivariate time series anomaly detection. In NeurIPS, 2023."}]

Author rebuttal:

Meta-review: This paper provided a novel architecture for time-series anomaly detection which exploits both cross-scale and cross-window information. Previous deep learning approaches were predominantly limited to single window and were less explicit in integrating cross-scale information. The evaluation seems quite extensive and avoided using point adjustment, a major pitfall in TSAD evaluation. All reviewers were enthusiastic about accepting the paper. The AC concurs.
Decision: Accept (poster)