CATCH: Channel-Aware Multivariate Time Series Anomaly Detection via Frequency Patching
Authors: Xingjian Wu
Xiangfei Qiu
Zhengyu Li
Yihang Wang
Jilin Hu
Chenjuan Guo
Hui Xiong
Bin Yang
Venue: ICLR 2025 Poster (2025)
Keywords: Multivariate Time Series
Anomaly Detection
Primary area: learning on time series and dynamical systems

Abstract: Anomaly detection in multivariate time series is challenging as heterogeneous subsequence anomalies may occur. Reconstruction-based methods, which focus on learning normal patterns in the frequency domain to detect diverse abnormal subsequences, achieve promising results, while still falling short on capturing fine-grained frequency characteristics and channel correlations. To contend with the limitations, we introduce CATCH, a framework based on frequency patching. We propose to patchify the frequency domain into frequency bands, which enhances its ability to capture fine-grained frequency characteristics. To perceive appropriate channel correlations, we propose a Channel Fusion Module (CFM), which features a patch-wise mask generator and a masked-attention mechanism. Driven by a bi-level multi-objective optimization algorithm, the CFM is encouraged to iteratively discover appropriate patch-wise channel correlations, and to cluster relevant channels while isolating adverse effects from irrelevant channels. Extensive experiments on 10 real-world datasets and 12 synthetic datasets demonstrate that CATCH achieves state-of-the-art performance. We make our code and datasets available at https://github.com/decisionintelligence/CATCH.

Published as a conference paper at ICLR 2025
CATCH: CHANNEL-AWARE MULTIVARIATE TIME SERIES ANOMALY DETECTION VIA FREQUENCY PATCHING
Xingjian Wu', Xiangfei Qiu', Zhengyu Li', Yihang Wang', Jilin Hu', Chenjuan Guo",
Hui Xiong", Bin Yang!*
EEst China Normal University
"The Hong Kong University of Science and Technology (Guangzhou)
(x jwu, xfqiu, 1i zizengyu,, yhwang) @stu. ecnu edu. en, (ilhu, c jquo, byang) | @dase. ecnu. edu. en, xi xionghui@ust. .kk
ABSTRACT
Anomaly detection in multivariate time series is challenging heterogeneous subsequence anomalies may occur. Reconstruction-bast methods, which focus learning normal patterns in the frequency domain detect diverse abnormal subsequences, achieve promising results, while still falling short on capturing fine- grained frequency characteristics and channel correlations. To contend with the limitations, we introduce CATCH, a framework based on frequency patching. We propose patchify the frequency domain into frequency bands, which enhances its ability to capture fine-grained frequency characteristics. To perceive appro- priate channel correlations, we propose Channel Fusion Module (CFM), which features patch-wise mask generator and a masked-attention mechanism. Driven by a bi-level multi-objective optimization algorithm, the CFM is encouraged to iteratively discover appropriate patch-wiss channel correlations, and to cluster rel- evant channels while isolating adverse effects from irrelevant channels. Extensive experiments 12 real-world datasets and 12 synthetic datasets demonstrate that CATCH achieves state-of of-the-art performance. We make our code and datasets available http://ggghbbboommeeeessnnnlllne
INTRODUCTION
Modern cyber physical systems are often monitored by multiple sensors, which produce sucessive
multivariate time series data (Wang et al. 2024f Dai et al.) 2024 Sun et al. 2025 Tian al. 2025
Guo et al. 2014). In recent years, there has been significant progress in multivariate time series
analysis, with key tasks such as forecasting (Qiu et al. 2025c Yu et 2023 Wu al. 2024b
Liu et al. 2024a Huang et al. 2024 Chen et al. (024). classification Yao et al. 2024b] Campos
al. 2023), and imputation (Gao et al. 2024 Wang et al., 2024c b). among others (Huang et al.,
2023
Yao et al. 2024a| Liu et al. 2025), gaining attention. Among these, Multivariate Time Series
Anomaly Detection (MTSAD), which focuses on identifying abnormal data multivariate time series, stands out critical studied task. It is applied widely including but not limited to financial fraud detection, medical disease identification, and cybersecurity threat detection (Wen et al. 2022
Yang et al. 2023a Kieu al. 2018 2019 Wu et al. 2024c Shentu et al. 2024 Yang et al. 202
Time series anomalies are typically classified into point anomalies and subsequence anomalies. The point anomalies can be further classified as contextual or global anomalies (Lai et al., 2021). Re- cent reconstruction-bass methods show strong capability of detecting point anomalies, which are characterized by specific values that significantly deviate from the normal range of the probability distribution. However, subsequence anomalies consist of values that fall within the probability dis- tribution, making them much harder detect (Paparrizos et al. 2022b Nam et al.; 2024). According to the behavior-driven taxonomy LLa et al. 2021), )) the subsequence anomalies can be further divided
"Corresoonding author

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into seasonal, shapelet, and trend anomalies-see see Figure la A promising approach is to transform the time series into the frequency domain to better derive the subsequence anomalies.
When transformed into the frequency domain, distinct subsequence anomalies also show promi- nent differences against the normal series in different frequency bands (Figure Tap. In this case, shapelet anomalies mainly affect the third frequency band while seasonal anomalies affect the first two frequency bands. However, the frequency domain features a long-tailed distribution that most information centralizes in the low frequency bands. Coarse-grained reconstruction- based methods may neglect the details in the high frequency bands (Guo et al.) 2023] Piao jt al. 2024] Park & Kim 2022; Wang et al., (022). thus failing to detect correspond anomalies, which calls for fine- tieeggraned modeling in each frequency band to precisely reconstruct the nor- mal patterns, so that heterogeneous subsequence anomalies can be detected. Moreover, consid- ering the relationships among channels also promotes better reconstruction for normal patterns. Figure [b] shows multivariate time series with three channels, and we observe the vary- ing channel associations in different frequency bands, where Channel 1 and Channel 2 are sim- ilar in the third band but dissimilar to Channel 3. and all channels are similar in the fourth band but show dissimilarity in the fifth. However, the commonly-used Channel-Independee and
Time doman
Frequency domain
M
Mhy M
(CI) (CD) strategies exhibit polarization effects, rendering them inadequate for this task. CI uses the same model across dif- ferent channels and overlooks potential channel correlations, which offers robustness (Nie et al. 2023 Qiu et al. 2025a) but lacks generalizabil- ity and capacity. CD considers all channels si- multancously with larger capacity, but may be
mwwh www m
(a) Different subsequence anomalies.
Fow lera
susceptible to noise from irrelevant channels, thus lacking robustness (Han et al.] [202]] Qiu et al.) 2025a). This calls for flexibly adapting the distinct channel interrelationships in differ- ent frequency bands.
(b) Varying correlations among channels.
Figure 1: The frequency domain is partitioned into five frequency bands with the high-frequency bands zoomed in for clarity. mal time series and its variations after being in- jected seasonal, shapelet, trend and mixture sub- sequence anomalies. In the time domain, anoma- lies are highlighted in red, while the affected fre- quency bands in the frequency domain are em- phasized in gray. (b) Shows the frequency bands of a multivariate time series with three channels. These channels exhibit varying correlations across different frequency bands, where Channels I and 2 exhibit similar behavior in the third frequency band and are therefore marked in red, while Channel 3 exhibits distinct characteristics and is marked in yellow. In the fourth frequency band, all channels behave similarly and are marked in green, while in the fifth band, they exhibit distinct characteristics and are marked in different colors.
(a) Shows a nor-
Inspired by the above observations, we propose CATCH, a Chamnel-Aware MTSAD frame- work via frequency patching. Technically, we utilize Fourier Transformation to stretch across time and frequency domains to facilitate the de- tection of both point and subsequence anoma- lies, of which the latter can be improved by patching in the frequency domain for fine- grained modeling. To flexibly utilize the chan- nel correlations in frequency bands, we propose Channel Fusion Module (CFM) that incorpo- rates a Channel Correlation Discovering mech- anism and utilizes masked attention through bi-level multi-objective optimization process. Specifically, we utilize patch-wise mask gen- erator to adaptively discover channel correla-
tion for each frequency band. The discovered channel correlation is between CI and CD, providing both the capacity and robustness by clustering relevant channels while isolating the adverse effects from irrelevant channels. The contributions are summarized as follows:
We propose a general framework called CATCH, which enables simultaneous detection of het- erogeneous point and subsequence anomalies via frequency patch learning. The framework enhances subsequence anomaly detection through domman patching and integrates fine-grained adaptive channel correlations across frequency bands.
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We design the CFM fully utilize the fine- channel correlations. Driven by a bi-level multi-objective optimization algorithm, the CFM is able to iteratively discover appropriate chan- nel correlations and facilitate the isolation of irrelevant channels and the clustering of relevant channels, which provides both the capacity and robustness.
We conduct extensive experiments on 24 multivariate datasets. The results show that CATCH outperforms state-of-the-ar baselines.
2 RELATED WORK
2.1 MULTIVARIATE TIME- SEERESEREES ANOMALY DETECTION
Traditional MTSAD methods can be classified into non-learning (Breunig et al., 2000:
Goldstein
& Dengel 2012 Yeh et al.) 2016) Li et al., (024a) and machine learning (Liu et al.
2008 Ra-
maswamy al. 2000). Recently, deep learning has made impressive progress natural language
processing (He et al.
2025b; Wang et al. 2024e| Wu et al., 2024a 2025a). computer vision (Wu 2025a b Yu et al. 2024b), and other aspects (Yi et al. 2025 He et al. 2025a
ct al.) 2025b Li et al.
Li et al. (023). 3. Studies have shown that learned features may perform better than human-designed Yu et al. 2025 2024a). Therefore, many deep learning- based MTSAD methods have been
features
proposed and have received substantial extensive attention (Liu et al. 2024b Liu & Paparrizos, 2024 Hu et al., 2024, Wang et al. 2023] Li et al., 2021] Wang et al. 2222a They can be clas-
sified into forecasting-batt based, reconstruction-best bbsed and contrastive-basee methods. GDN (Deng & Hooi 2021) is a forecasting-basee model that uses a graph structure to learn topology and graph attention network encode input series, with anomaly detection based on the maximum forecast error among channel variables. Anomaly Transformer is reconstructive approach that combines series and prior association to make anomalies distinctive (Xu al., 202T). DCdetector uses con- trastive learning in anomaly detection to create an embedding space where normal data samples are close together and anomalies are farther apart (Yang al. 2023b).
2.2 CHANNEL STRATEGIES IN MTSAD
A channel refers to variable in MTSAD, while channel strategy refers to how these channel cor- relations are effectively considered during the modeling process. CATCH employs reconstruction- based MTSAD algorithm, using reconstruction error the anomaly score, making reconstruction quality crucial for anomaly detection accuracy. Since the channels multivariate time series often exhibit complex dependencies, explicitly modeling these correlations enables more comprehen- sive capture of global features, thereby improving reconstruction capabilities and anomaly detection performance. There are mainly two existing approaches that consider relationships among channels. (CI) based methods such as: PatchTST (Nie et al., 2023) and Sparse'TSF (Lin) et al. 2024) impose the constraint of using the same model across different channels. While offers robustness, it overlooks potential interactions among channels and can be limited in generalizability and capacity for unseen channels (Han et al., 2024). Previous studies have shown that correlation discovery in data is crucial for time series anomaly detection (Song et al. 2018). Channel-Dependen (CD) based methods such as: MSCRED (Zhag et al.] 2019) uses a convolutional--LTT. network with attention and a loss function to reconstruct correlation matrices among channels in multivariate time series input. MTAD-GAT (Zhao et al.] 2020) treats each univariate time series as a feature and uses two parallel graph attention layers to capture dependencies across both temporal and chan- nel dimensions. The existing methods could not adequately extract interrelationship, they may be susceptible to noise from irrelevant channels, reducing the model's robustness.
2.3 FREQUENCY DOMAIN ANALYSIS FOR TSAD
Frequency domain analysis can un- cover subsequence anomalies that are
Table 1: Comparison of existing TSAD methods.
challenging to detect in the time do- main, such as anomalies in periodic fluctuations or oscillation patterns, significantly enhancing detection ac- curacy (Zhang et al., 2022). Conse-
Proporty
Munalisuriate time satic usmnly detection
Tenc-frqpeccy guaulaiit digunent
high fragaaayy information
Capture clanne
cuncitionn
TEAD
Dial-TF
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Channel Carrelation
Mask
Module
Tranfornue
Channel Masked
Asal
IFFT
demals
Time
www
Disowering (OCH)
FankFarwann
Flarten & Lincar Head
X E E
Clistiingoos:
Balnnca
Addl
Channel Fusion Medule
ITRM
E ER Freg-Res
Mait NumuMMM
E 3
BegubeLosc
Sultras
g Aflle
Madked
MG
CMT
CPM
postivic pain Mani aa
Projection
Projection
Polebiily Mass
Alction
FFT & Patching
Freq
Real
p N
demaln
Tmag
C CR
Wg
Micie Stakk Marte MG
Pocittongil Muss
Instance Norm
X X
Forward Module
Channel
Time Frequency Recesstruction Module
Figure 2: CATCH architecture. (I) Forward Module normalizes the input data, patchifies the fre- quency domain, and then projects it into the hidden space. (2) Channel Fusion Module captures channel interrelationships in each frequency band with Channel-Masked Transformer (CMT) Layer, where the mask matrix (channel correlation) is generated by Mask Generator (MG). Dur- ing training, MG and CMT are optimized by Channel Correlation Discovering (CCD) for more appropriate channel correlations. (3) Time-Free FreneeFFrenccyy Reconstruction Module obtains the frequency reconstruction through Flatten & Linear Head Layer, and obtains the time reconstruction after iFFT.
quently, frequency- -based time series anomaly detection models have garnered widespread attention in recent years. SR-CNN (Ren et al., 2019), the first method to leverage the frequency domain for TSAD, employs frequency-basets approach to generate saliency maps for identifying anomalies, and PFT (Zhang et al.) 2022) built on this foundation by introducing partial Fourier transform to achieve substantial acceleration. However, both methods are confined to univariate time series and fail to address the complexities of multivariate scenarios. TFAD (Zhang et al.] 2022) emerges as the first approach integrate time-domain and frequency-domain analyses for MTSAD, yet it lacks fime-frequnncy granularity alignment. Dual-TF (Nam et al., 2024). the most recent algorithm for MTSAD using freeuunuyy analysis, partially addresses the time-frequency granularity align- ment issue but lacks a tailored backbone, instead relying directly on the Anomaly Transformer (Xu al. 202T). While TFAD and Dual-TF represent progress in this area, they still exhibit the fol- lowing limitations: i) Frequency-domain modeling methods have inherent biases, often overlooking high-frequency information; 2) Insufficient exploration and utilization of channel correlations in multivariate time series.
CATCH
In the context time series anomaly detection, X NxT denotes time series with N channels and length T. For clear delineation, we separate dimensions with commas and use this format throughout this paper. For example, we denote X,, as the i-th channel the j-th timestamp. X,,: E FT. as the time series of n-th channel, where 1,2,-.. ... The multivariate time series anomaly detection problem is to determine whether X is anomaly or not.
3.1 STRUCTURE OVERVIEW
Figure 2 shows the overall architecture of the CATCH, which consists of three main modules: 1) the Forward Module, 2) the Channel Fusion Module (CFM), and 3) the Time-Frequency Reconstruction Module (TFRM). Specifically, the input multivariate time series is firstly processed via the Forward Module, consisting of the Instance Norm Layer, FFT& & Patching Layer, and Projection Layer.
The Instance Norm Layer is firstly mitigate the distributional shifts between the training and testing data caused by varying statistical properties, enhancing the model's generalization in recon- structing the testing data. Then, the FFT Patching Layer is perform fine-gra fine-grained modeling in each frequency band (patch). Specifically, we utilize the efficient FFT (Brigham & Morrow] 1967) to transform time series into orthogonal trigonometric signals in the frequency domain, where keep
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both the real and imaginary parts through X X FFT(X) for maximum information retention, where X, X' E RNT"" Next, we apply the frequency patching operation to create fine-gre gggaine frequency bands (patches), which can be formalized as follows.
(p p ,.... ,...,, 3P
Patching (X"), "), (P"1 pl,,... pln Patching(X')
where PR, pl. N denote the i-th patch of X and X [ pl/s + is the total patch number, where p is the patch size and is the patch stride.
We then concat each pair of P.. and p4: into P E B-Nx2,, as the i-th frequency patch. After patch- ing in the frequency domain, the frequency patches are then projected into the high-dimensional hidden space through the Projection Layer: P Projection(P').
After the Forward Module, the processed time series is fed into the Channel Fusion Module (CFM) to dynamically model the channel correlations in each fine-gre grained frequency band.
(P_ . p = CFM((P") pp? ...,,P'')),
(2)
where pri pi RNxdd N is the number of channels and d is the hidden dimension in attention blocks. The CFM parallels in a patch-wise way to model the frequency patches simultaneously. We further introduce the details of CFM in Section
Next, we utilize the Time-Frequent Frequency Reconstruction Module (TFRM) to reconstruct all frequency spectrums for real and imaginary patches and simultaneously obtain their temporal reconstruction:
X', R x" = TFRM( p .... PR.J, , , ,,'')), where X' is the temporal reconstruction, and X R. x" E RNT are the frequency reconstruction.
Finally, we integrate the reconstruction error in both time and frequency domains anomaly score.
3.2 CHANNEL FUSION MODULE
The Channel Fusion Module (CFM) contains the following three components: 1) the Mask Gen- erator (MG). 2) the Channel-Masked Transformer Layer (CMT), and 3) the Channel Correlation Discovering (CCD) mechanism. Specifically, the MG is to perceive and generate the mask matrices (channel correlations) in different frequency bands and guide the masked attention in CMT. The CMT aims model the appropriate patch-wise channel correlations. And the CCD is to guide the MG and CMT to explore better channel correlations during optimization.
Mask Generator. Inspired by Selective State Space Models such as Mamba (Dao & Gu 2024), which utilizes Linear projections to flexibly update the hidden states based on the current data for larger capacity, the patch-wise channel associations can also be treated strongly associated with the current patch. Therefore, we devise Linear-based mask generator to perceive the suitable channel associations for each frequency band by generating binary mask matrices to isolate the adverse effects from irrelevant channels. Note that the binary mask is an intermediate state between CI (identity matrix) and CD (all-ones matrix) strategies. We take the i-th frequency patch as an example:
changing hidden state
Dí (Lincar(PP")) M² Resample(D'),
where pr E Nxd, D' E NNN, and M NNN are the hidden representation, the probability matrix, and the binary mask matrix of i-th patch, respectively. a projects the values to probabilities.
Since our goal is to filter out the adverse effects of irrelevant channels, we further perform Bernoulli resampling on the probability matrices to obtain binary mask matrix M with the same shape. Higher probability Di.m results in Mi,.. closer 1, indicating relationship between channel ( and channel m. And we manually keep the diagonal items to 1. To ensure the propagation of gra- dients, we use the Gumbel Softmax reparameterization trick (Jang et al. 2017) during Bernoulli resampling.
Channel-Masked Transformer Layer. After the Mask Generator outputs the mask matrices for frequency bands, we utilize the transformer layer to further capture the fine- tnn-grained channel correla- tions. The Layer Normalization is applied before each attention block mitigate the over-focusing
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phenomenon frequency components with larger amplitudes (Piao et al.
2024
pa Layerrorm(P")) (P") = (Pr Mean (P n, Var - (Pr R.)):
(5)
where pr R Vxd and p* E Nxd are the hidden representation and the normalized representa- tion of i-th patch, respectively. Empirically, we utilize the masked attention mechanism further model the fine-graines interrelationships among relevant channels and integrate the mask matrix in a calculated way to keep the propagation of gradients:
Q'= pr W V = p WV, T'= Q'K''KK'''' T M + M (-
(6)
(7)
MaskedScores S /v, p Softmax (MaskedScores') V
(8)
where W W WV E Rdxd M E RNXN T E RNN,, NNN, and P Nx are the binary mask matrix, the attention matrix, the masked attention matrix, and the hidden representation processed by CMT of i-th patch, respectively.
We utilize the same Forward networks and skip connections as the classical transform- (Vaswani al.) 2017). We also apply multi-head mechanism to jointly attend to information from different representational subspaces and the CMT can be stacked multiple times.
Channel Correlation Discovering. From an optimization perspective, it is essential de- sign appropriate optimization objectives to enhance the effectiveness of generated masks. A direct motivation is to explicitly enhance the attention scores between relevant channels de- fined by the mask, thus aligning the attention mechanism with the currently discovered opti- mal channel correlation, which helps isloate the adverse effects from irrelevant channels and provides robustness for the attention mechanism. Then we iteratively optimize the Mask Generator to refine the channel correlations, tuning the capacity of attention mechanism in the Channel-Masked Transformer Layer to fully capture the interrelationships between chan- nels. Intuitively, we devise two loss functions to guide the Mask Generator exploring the space of channel correlations (from CI to CD). The proposed loss functions formalized
Em expl(Sk Smmm/ Σ exp(TE,)/T
Σ log ClusteringLoss = N
1 -MMMM (10) N
(9) Regularl.oss
where is the temperature coefficient, N is the number of channels, T is the identity matrix, and ||. ||| is the Frobenius norm. T E RNNN St c XN, and M E R are the attention
matrix, the masked attention matrix, and the binary mask matrix for i-th patch, respectively.
The ClusteringLoss is similar to the InfoNCE (He et al. 2020 in form but does not fix the number of "positive" pairs. In contrast, changes its "positive" pairs for different patches based on the current discovered channel correlation M Theoretically, the similarities between "positive" or "negative" pairs are also calculated through inner product, so we share the calculating results of S and T from the attention mechanism to save the computational cost. As shown in Figure 2 we exhibit the "positive" and "negative" pairs in the attention matrix T and masked attention matrix S. Specifically, it sets the Query and Key views of relevant channels in a frequency band (Mi,.. 1) as the "positive" pairs, otherwise (M = 0) "negative" pairs, thus encouraging the w and WK to cluster the patch-wise relevant channels in the hidden spaces and lead to higher attention scores. However, only a single ClusteringLoss may cause some adverse effects by urging the Mask Generator to output constant ones matrix, so that we add a RegularLoss to mitigate this risk by restricting the number of relevant channels. Equipped with the two optimization objectives, the Mask Generator is encouraged to discover appropriate patch-wise channel correlations between CI and CD, and the attention mechanism is also enchanced by optimizing the WQ and WK to learn fine-grained channel representations in the hidden spaces.
3.3 TIME FREQUENCY RECONSTRUCTION MODULE
The Time- Freee-FFruency Reconstruction Module (TFRM) contains the following two components: 1) the Flatten & Linear Head Layer and 2) the iFFT Layer. Specifically, after the CFM fully extract

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the fine- fine-grained channel correlations, utilize the TFRM flatten the patch-wise representations and reconstruct all frequency spectrums with MLP projections separately for real and imaginary patches, and obtain temporal reconstruction through iFFT:
x Projection (FlattenHead *F ((PR) (PR,,, ,p,R, .p...... (. D)),
(11)
X Projection (FlattenHead (P p/.,....,Pp
(12)
X iFFT(X" ,
(13)
where X X" and X' E BNXT We then adopt the reconstruction loss functions both in time and frequency domains to separately enhance the ability of point-to-point and subse- quence modeling. The reconstruction functions in time and frequency domains are formalized as:
RecLoss time || - 1
(14) RecLoss = ||x x + || X
(15)
We utilize 2-norm in the time domain and 1-norm in the frequency domain due the distinct nu- merical characteristics time and frequency domains (Wang et al. 2024d).
3.4 JOINT BI-LEVEL OPTIMIZ.ATION
We then design a novel joint bi-level training process to enhance the model's ability to detect both point anomalies and subsequence anomalies. Our TotalLoss L mainly consists of reconstruction loss functions in the time (RecLoss and frequency (RecLoss/reg) domains, ClusteringLoss and RegularLoss from the Channel Correlation Discovering mechanism. The reconstruction loss functions are used to enhance model's ability in both time and frequency domains to detect point and subsequence anomlies. The ClusteringLoss and RegularLoss are used guide the discovering for fine- tine-grained channel correlations. Specifically, we weightsum these four optimization objectives:
L = RecLoss time + X RecLoss + A2 ClusteringLooss + X RegularLoss,, (16)
where A1, A2, and A are empircal coefficients. We then utilize a bi-level optimization Algorithm to iteratively update the Mask Generator and other model parameters. Intuitively, the process optimizes model parameters for current channel correlations and then discovers better channel correlations for the optimized model parameters, which facilitates the refinement of channel correlations continuous way.
3.5 ANOMALY SCORING
When calculating the anomaly score, the convention to obey the point-to-point man- anomaly score for each timestamp. thus mainly reflecting the point anomlies in the time domain. To better quantify subsequence anomalies, existing methods often consider coarse coarse-grained window-grame grrnuuarrtt scoring, which adds a fre- quency anomaly score to each point in the whole input window (Ren et al. 2019 Park al. 2021 Zhang al. 2022). However, they fail to know the actual boundaries of sub- sequence anomalies, thus causing misjudgment or omission. During scoring, we perform the patching operation in the input window with the stride length equal to 1. In Figure the shadow the Time Series indicates a series of subse- quence anomalies. Take the calculation of the anomaly score for the red time point in the Time Series as an example, we first calculate the time do- main reconstruction error (RecLoss" fime) between its reconstructed value in the time domain and the true value using Equation 14, and denote the result as the time domain anomaly score (time-score). At the same time, we collect all patches containing the red time point, transform these patches into the frequency domain, and compute the frequency reconstruction error (RecLoss between the reconstructed value and the true frequency-domal value using Equation [3] The average frequency reconstruction error of all patches is then taken as the frequency domain anomaly score (freq-score)
ner by assigning
Time Series
Frequency
Patch Scan
Reconstruction
0900900908
average
frequscor
time-score
Anomaly
Score
Time
Figure 3: Anomaly Scoring.

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for this red time point, as the average performs better than the minimum maximum value (Schmidl (et al. (022). Finally, we weightsum the time-score and freq-score point-to-pone to obtain the final anomaly score for the Time Series.
AnomalyScore = time-score + Ascore freq-score
(17)
For ease of understanding, we provide an efficient implementation version of the calculation of freq- score in Appendix[AAG. Obviously, our method can reflect the real surroundings of each point by con- sidering all possible subsequence anomalies around this point, thus achieving the point-granularity alignment and showing strong sensitivity (Nam et al. 2024).
EXPERIMENTS
Datasets We conduct experiments using 12 real-world datasets and 12 synthetic datasets (TODS datasets) to assess the performance of CATCH, more details of the benchmark datasets are included in Appendix(AA.I A.II The synthetic datasets are generated using the method reported in (Lai et al. 2021). Please refer to Appendix [A.7 for specific implementation. We report the results on 12 woaldworld MTSAD datasets, including MSL, SMAP, PSM, SMD, SWAT, CICIDS, Cal1t2, NYC, Creditcard, GECCO, Genesis, and ASD in the main text. We also report the mean results of the 6 types of synthetic anomalies. The complete results can be found in the Appendix C
Baselines We comprehensively compare our model against 15 baselines, including the latest state-
of-the-art (SOTA) models. These baselines feature the 2024 SOTA iTransformer (iTrans) (Liu
al., 2024c), ModernTCNN (Modem) (Luo & Wang] 2024), and DualTF (Nam et al. 2024). along
with the 2023 SOTA Anomaly Transformer (ATrans) (Xu et al., (021). DCdetector (DC) Yang
al. 20236). TimesNet (TsNet) (Wu al.] (023). PatchTST (Patch) (Nie al., 2023).
DLin-
ear (DLin) Zeng et al.) 2023), NLinear (NLin) (Zeng et al. 2023). TEAD (Zhang et al. 2022),
and AutoEncoder (AE) (Sakurada & Yairi (2014). Additionally, we include non-learning methods
such as One-Class -lesS SVM (OCSVM)(Schölkopl et al.] 1999), Isolation Forest (IF) et al.
2008
Principal Component Analysis (PCA) (Shyu et al. (0003). and HBOS Goldstein & Dengel
2012).
Setup To keep consistent with previous works, we adopt Label-based metric: Affiliated-F1- score (AffFF) (Huet al. 2022) and Score-based metric: Area under the Receiver Operating Characteristics Curve (ROC) (Fawcett (006) as evaluation metrics. We report the algorithm per- formance under a total of 16 evaluation metrics in the Appendix C and the details of the 16 metrics can be found in Appendix A.2 More implementation details are presented in the Appendix A.3
4.1 MAIN RESULTS
We first evaluate CATCH with 15 competitive baselines on 12 real-world multivariate and 6 types of synthetic multivariate datasets generated by the methods reported in TODS (Lai al., 202T as shown in Table 2 It can be seen that our proposed CATCH achieves SOTA results under the widely used Affiliated-FI-sena est AUC-ROC values on most datasets. It means that our model performs well in the false and true-positive rates under various pre-selected thresholds, which is important for real-world ap- plications. Since the continuous abnormal segments in SWAT exceed the look-back window sup- ported by the reconstruction model, CATCH cannot effectively capture this kind of abnormality, In summary, CATCH effectively handles both point (Contextual, Global) and subsequence (Seasonal, Shapelet, Trend, Mixture) anomalies while showing greater improvement in detecting the subse- quence anomalies.
metric in most benchmark datasets. Besides, CATCH has the high-
4.2 MODEL ANALYSIS
Ablation study To ascertain the impact of different modules within CATCH, we perform
ablation studies focusing on the following components: (I) Substitute the channel correla- tion discovering mechanism with fixed Channel Strategies, (2) Delete one of the four op- timization objectives separately. (3) Remove the patching operation during training pro-
cess. (4) Replace the Scoring technique with others. (5) Replace the bi-level optimization process with a normal process to optimize the Mask Generator and model simultaneously.
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Table 2: Average A-R (AUC-ROC) and AfI-F (Affiliated-II) accuracy measures for 12 real-world datasets and 6 synthetic datasets of different types of anomalies. The best results are highlighted in bold, and the second-best results are underlined.
Diseett
Manic
CATCH
Modem
TTm
DuaffF
ATrara
DC
Tehict
Paich
D1iin
Ni.i
AF.
Oceern
IF
PCA
FIBOS
TEAD
CIIDS
ASFFF
A-k
0.795
0.767
0.697
0.654
0098
0.708
0.605
0.692
0.578
0.560
0.636
0.964
0.657
0.733
0.716
0.650
0:151
0.589
0.601
0.669
0.679
0.243
0.387
0.693
0.604
0.787
0.601
0.619
0
0.542
0.579
0.594
Calli2
0.838
0.751
0.574
0.73
0.527
0.697
0.771
0.704
0.28
0.391
0.753
0.73
0,005
07677
0.381
0.403
0.775
0.50
0.268
0.504
67744
SWAT
0.355
0.75
0.342
0.557
0.405
0.666
01501
0.258
0.242
0317
0.677
0.345
0210
0831
0,500
Credk
ATE
A-K
0.750
0.344
0187
0.713
01954
13703
0.655
0.500
0.553
0.62
0.504
0.344
115T
0357
0.346
0.738
0.954
0.743
0.561
0.909
0951
0.714
0.634
0180
0.200
11871
0.695
1151
0.500
0.600
GECOO
ASTF
A-k
8.771
0.986
0.893
0.795
0.639
0.201
112
0.116
0.783
0.687
0.94
1994
1949
0.00
0.20
0.500
0.81
0.823
1229
0.666
0-1
0.124
0112
0.255
1121
0.006
0.627
Genenis
0.966
0.991
0.10
0556
0.00
0.776
0864
0256
0.55
0.22
0.544
0,77
0.788
0.1
0.35
MSI
A.K
0.740
0664
0.635
0.11
0.576
0.588
0.514
02292
0.507
0015
1.34
0.034
0.03
0.134
0.584
0.524
0.552
01676
0,500
NYC
AME
A-K
0.994
B336
0.760
0 0.8
01600
0.684
11015
0.356
0353
19971
0.999
1961
0354
1251
0336
0.03
0.761
036
0601
0.600
0.50
0/456
0.697
0.545
11375
11666
0.680
11546
0.675
0.600
0.913
PSM
ASTFF
A-k
0.869
8 1.
0.555
0.54
0225
199
0310
0331
0:10
0.51
0.20P
1000
0.007
0331
0019
0.020
03:1
0200
1100
8.58
0.625
0.90
A
0347
0240
0227
0,92
0224
0245
0:51
0,50
0762
0.25
0:238
0.680
022
0200
0148
110
SMAP
A
A-R
0.304
0.699
0455
0.597
0.65
04788
0,00
6311
133
1.00
0255
0248
0.907
0.33
0.45
0391
0.00
0.513
0448
0.36
1559
0.585
0.500
ASD
AFF
A-R
0.224
0752
0.692
0780
0.799
11655
0.579
0.06
00574
0.002
8.330
1900
0.760
0.730
0.703
0.706
0,000
0.331
0.704
0217
0.588
0.610
1331
11250
01856
0.009
0.033
0.630
0.502
Contestual
ASFF
0.233
0.910
0A19
11588
0.35
0600
0.881
0,00
0.66
0250
0.000
0200
0530
0.000
0.86
0255
0711
0
0521
0.67
0.775
11538
0.41
0.569
Globd
ATT.F
A-R
0,997
0.921
0.9%6
0.595
0.54
0656
01544
1010
1166
1000
0.5%
0.5
0156
0.996
0.978
0.55%
0.528
0008
0,500
0.666
Scoural
ARf-F-
A-R.
B.997
0.998
0.512
0.945
0191
0.351
0.776
0.68
0.554
D.644
0180
1192
0.55
0540
0522
0.533
0961
0.03
0927
0.940
0,505
0.129
0.978
0.915
1.437
0.516
0.66
0,502
Stapeket
Adf-P
A-R
IL9AS
0.977
0.522
0.675
0.64
(.91
0573
1000
0519
0.99
1991
8877
1915
0218
0:64
356
015
881
036
0.771
0.63
0.45
(1887
1163
0.577
8660
0,37
0684
0.563
8.916
0201
007
0684
0.65
0.97
0268
0.211
0630
0.69
0.91
0914
0.95
0641
0524
0559
0355
9.64
0374
01381
Mistue
0131
0,292
0550
0.61
0516
0351
0.453
0911
0.517
0.501
0.710
Table 3 iilustrates the unique impact
Table 3: Ablation studies for CATCH in terms of the highest AUC-ROC highlighted in bold.
of each module. We have the fol-
lowing observations: 1) Compared to
(CI) Strat- egy, considering the relationships be- tween variables using Channel De- pendent (CD) Strategy or random masking yields better results, with the random masking performing worse than the CD method. Ours out- performs the CD method, further demonstrating the effectiveness of the channel correlation discovering mechanism. 2) Removing any of the four optimization objectives leads to a decline in model performance, with the most significant drop occurring when the frequency loss is removed. This fully demonstrates the rationality and effectiveness of the four optimization objec- tives. 3) When the patching operation is removed during training and replaced with a window-base based approach to model the relationships between variables, the model performance significantly de- creases. This indicates that the patching operation captures fine-grained frequency information, which is more conducive to anomaly detection. 4) When replacing the combination of point- granularity temporal anomaly scores and wise point-aligned frequency anomaly scores with the combination of point-gramulie gramullrtyyy temporal anomaly scores and hindow-granularity frequency anomaly scores, or when using only one of them, the model performance decreases in both cases. This indicates our Scoring technique shows stronger sensitivity in detecting anomalies. 5) When using a normal optimization process, the model performance also decreases consistently, which pro- vides empircal evdience for the bi-level optimization.
the
Varfations
CICIS
Call12
GECCO
MSL.
SMD
Ang
Channel Conrelation
C1) Random
0,735
0.649
0.806
01818
0.912
0.555
0.625
0.657
0.757
0.790
0.755
0.742
0.807
0.945
0.631
0.764
0.782
w/o Roee
0.784
0.827
0.553
0.651
0.766
0.796
Oprimization Objectives
wio freLosgffen
0.663
0,825
0.96
0.508
0.745
0,760
wil Clusteringloss
0.775
0,822
0.958
01644
0.791
0.798
wro RegularL.oss
0.788
0.830
0.966
0.657
0,802
0.809
Training
Patching
0,747
0,802
0.947
0.632
0,777
0,781
Scoring Technique
woo point score
window
0.743
0.808
0,952
0.653
0.622
0.775
0,770
wio patcis sooce
0.763
0.780
0.956
0.648
0.787
bi-level optimization
0.791
00:333
0.965
0.658
0.809
0.811
CATCH (ours)
0.795
0.8338
0.970
0.664
0.811
0.816
Parameter Sensitivity We also study the parameter sensitivity of the CATCH Figure 4a shows the performance under different input window sizes. As discussed, a single point can not be taken as an instance in time series. Window segmentation is widely used in the analysis, and window size is a significant parameter. For our primary evaluation, the window size is usually set as 96 or 192. Besides, we adopt the score weight in section 3.5 to trade off the temporal score and the

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Published as a conference paper at ICLR 2025
DICCO
dieco
AUCROC
AUC-ROC
AVC-WOC
AUC-OCC
370
0.55
02
36
32
26
Window size
Score lambda
(a) Window size
(b) Ascore
(c) Training patch size
(d) Testing patch size
Figure 4: Parameter sensitivity studies of main hyper-parameters in CATCH.
frequency score-see Figure 4b
We find that score weight is mostly stable and easy to tune in the range of 0.01 to 0.1. Figure 4c and Figure eegure4dj.n 4d present that our model is stable to the Traing patch size and Testing patch size respectively over extensive datasets. Note that small patch size indicates a larger memory cost and larger patch number. Especially, only considering the performance, its relationship to the patch size can be determined by the data pattern. For example, our model performs better when the traing patch size is 8 for MSL. the testing patch size is 32 for CICIDS.
Inpus
Final TimaGFreg
Tyme
Truth
anomaly
Final
Figure 5: Visualization of dual-domain anomaly scores from CATCH for different categories of point and subsequence anomalies using the TODS dataset.
Anomaly criterion visualization We show how CATCH works by visualizing different anoma- lies in Figure 5] This figure showcases CATCH's performance across five anomaly categories (Lai al. 2021) on the TODS dataset, with temporal and frequency scores displayed in the second row, and the final anomaly scores in the third row. For point anomalies (first and second columns), the temporal scores exhibit sharp increases the true anomaly locations, dominating the total scores. In contrast, for subsequence anomalies (third, fourth, and fifth columns), frequency scores remain elevated across the entire anomaly interval, show strong sensitivity to the actual boundaries of sub- sequence anomalies and compensate for the insensitivity of the temporal scores. Consequently, each domain contributes uniquely, allowing the final anomaly scores accurately capture both point and subsequence anomalies.
5 CONCLUSION
In this paper, we propose a novel framework, CATCH, capable of simultaneously detecting both point and subsequence anomalies. sum up. patchifys the frequency domain for fine-grained insights into frequency bands, flexibly perceives and discovers appropriate channel correlations, optimizes the attention mechanism for both robustness and capacity with a bi-level optimization algorithm. These innovative mechanisms collectively empower CATCH precisely detect both point and subsequence anomalies. Comprehensive experiments on real-world and synthetic datasets demonstrate that CATCH achieves state-of-the-art performance.
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Published as a conference paper at ICLR 2025
ACKNOWLEDGEMENTS
This work was partially supported by National Natural Science Foundation of China (62472174, 62372179). Bin Yang is the corresponding author of the work.
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A EXPERIMENTAL DETAILS
A.1 DATASETS
Table 4: Statistics of multivariate datasets (AR: anomaly ratio).
Dutaset
Domalin
Dim
(%))
Avg Thtal Length
Avg Test Length
Description
MSL
Spseecratt
55
5.88
132,046
73.729
Spececr alt inciest and ancutaly data from the MSL Curiiiity rover
SMAP
Spececratt
25
9.72
562,800
427.617
Preseuus the sod sumples and telemety infocmation used the Mars tover
PSM
Server Machine
25
11:07
220.322
87.841
dassect collected from milliple application server nodos eRay
SMD
Server Machine
38
2,08
1 1116,225
705.420
Telenetry datrect collectod from 28 differmi server machines al largo Internet company
Crediicard
Finance
0.17
284,807
142.404
Credit card dataset includes subset online transactions that occurred
days
GBCCO
Water treamment
9
1.25
138.521
69.26
Water quality dataet publiched the GECCO Industial Challenge
SWATT
944.919
Ottaine from
system under comiinous operatiots fcatures utack labels
CICIDS
Web
170,231
85.116
Network traflic from Miteew
Call12
flowrate
people
buibling
daya
Genevis
Machinary
signes dataset collected syhas-pysical
NYC
Tranepori
Traneporttion provides information
nie-hailing trips New York collected large Internet compony
Applicatio
Application
TODS
Synthetic
20,000
Including 6 anomaly opes: global, coneesual. shupeler, seasonal. trend, znomalies
In order to comprehensively evaluate the performance of CATCH, we evaluate 12 world datasets and 12 synthetic datasets which cover domains. The anomaly ratio vary from 0.17% to 11.07%, the range of feature dimensions varies from 3 to 72, and the sequence length varies from 5,040 to 1,416,825. This substantial diversity of the datasets enables comprehensive studies of MTSAD methods. Table 4 lists statistics of the 24 multivariate time series.
A.2 METRICS
The metrics we support can be divided into two categories: Score-based and Label-based. Label-based metrics includes Accuracy (Acc), Precision (P), Recall (RR). Fl Fcore (F1), Range-
Precision (R-P), Range-Recall (R-R), Range-Fl-score (R-F) (Tatbul et al. 2018), Precision @k k, Prreisied-rrecision (Af--P,, Affiliated-Recal (Aff-R), and Affiliated-FT-soom (Aff-F) (Huet ct al., 2022). Score-based metrics includes the Area Under the Precision-Recal Curve (A-P) (Davis & Goadrich 2006). the Area under the Receiver Operating Characteristics Curve (A-R) (Fawcett) 2006). the Range Area Under the Precision- Recall Curve (R-A-P), the Range Area under the Re- ceiver Operating Characteristics Curve (R- (--AR) (Paparrizos al.) (022a), the Volume Under the Surface of Precision-Recall (V-PR), and the Volume Under the Surface of Receiver Operating Characteristic ( (V-ROC) (Paparrizos al. (002a)). As noted earlier, CATCH computes all metrics to provide a complete picture of each method. More implementation details are presented in the Appendix A.3
A.3 IMPLEMENTATION DETAILS
The "Drop Last" issue is reported by several researchers (Qiu et al. 2024 Li et al. 2024b Qiu et al.) 20256). That is, in some previous works evaluating the model on test set with drop- True setting may cause additional errors related to test batch size. In experiment, ensure fair comparison in the future, we set the drop last to False for all baselines to avoid this issue.
All experiments are conducted using PyTorch (Paskke et al. 2019) in Python 3.8 and execute on an NVIDIA Tesla-A800 GPU. We employ the ADAM optimizer during training. Initially, the batch size is set 32, with the option to reduce it by half (to minimum of 8) in case of an Out-Or-Memory (OOM) situation. We do not use the "Drop Last" operation during test- situation, ing. To ensure reproducibility and facilitate experimentation. datasets and code are available at: https://ahhbkoommdcccussnllllgna
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A.4 MODEL HYPERPARAMETER SETTINGS
For each baseline method, we strictly follow the hyperparameter configurations recommended in their original papers. Additionally, we conduct hyperparameter searches on multiple sets and select the optimal configurations based on these evaluations to ensure a comprehensive and fair assessment of each method's performance.
The hyperparameters for the baseline methods are set as follows:
AutoEncoder: The architecture of Autoencoder is selected from (10, 3), (25, 10, 5), (50, 20, 10).
One-Class SVM: The RBF kernel is used. The upper bound on the fraction of training errors is
be 0.5.
Isolaion Forest: The number of estimators is selected from 3, 5, 25, 50, 60, 70, 80, 90, 100,
110.
Principal Component Analysis: The number of principal components is the smaller of the number of samples and the number of features.
HBOS: The number of bins is selected from 3, 5, 10, 20, 30, 40, 50
MCdernTCN: The dimension hidden states 256. The FFN ratio is Patch size is set as 16 and patch stride is set 8.
Anomaly Transformer, DualTF: The number of layers is selected form 1, 2, 3, the channel number of hidden states dmodel is 512, and the number of heads is The loss function hyper- parameter lambda for balancing two parts is set as 3.
iTranstormer, TimesNet, DCdetector, PatchTST: The number of blocks is selected form 1, 2,
3. The dmodel selected form 8, 64, 128, 256, 512 and the number heads is 8.
DLinear, NLinear: The length of the reconstructed sequence is set 100.
TFAD: The number of layers in the TCN is selected from 5, 6, 7, 8, and the number of kernels is selected from 5,
A.5 BI-LEVEL GRADIENT DESCENT OPTIMIZATION
Algorithm Bi-level Gradient Descent Optimization
Input: Model purameters fosstat Pracks learning rate Thratel Thrakt number iterations No. Ar. loss lunction C RecLoss 43
As RocLoss free A2 Clusteringlooss Ag RegularLoss
2:
Initialize: (needt initial value, fmnk +- initial value
3: For No
4: Outer Loop: Update the mask generator parameters
5: Oank +- Graak
Voraee Li0ude, (mak))
D. Update the Mask Generator
6: For 1 No,
7: Inner Loop: Update the model parameteers
8:
Omoka Omniil Vmustet V Frnde C( C(Oratt, Owade)
D Update the model
9:
EndFfor
10:
EndFFor
Output: Optimized parameters Paocet, Bank
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A.6 IMPLEMENTATION DETAILS OF SCORING
We provide efficient implementation of Frequency-Enbaree Point-Gramularity Scoring in Sec- tion 3.5 We present the pseudo-code in Algorithm 2 Specifically, we adopt the scatter operation in Pytorch efficiently parallel the collection of patches to which each point belongs.
Algorithm Calculation of freq-score
from einops import import torch
rearrange
class Silepennc_criteriiee (torch.mn.Module))
def
_nnit_(self,, configs):
super
self) initt.
Define the frequency metric
self.metric = (onesee dim=l,
self.patch_ size
patch
self.patch_stride wtw.iig....feeeeccooottttt......
self.win_size
self.patch_nnum = (sseff.wwwwwsiile
self.
seth.ptchhssssrieeeee 1)
self.paadiing_eenghhe self self.win_size (self.patch_siza
pseif.patch 1)
self.patch_stzide)
def fsrlard outputs, batch_y):
output_patch oo oo--
sixe=sell..atootssiee stepsself.patcch_steee
b, D, G, p output_patch.shere ourput purpat_patchhoo patch rearrange pouuutut_ppttet "b (b, p.....
y_patch (d
size=self.patch size, http:ssef..aacchccc stride)
patahh rearrange "b, ".A.A.B..P.((,.... p_c()
main Batlppat______ loss = melf.matric
y-patch)
Create patches mair_part_loss = mein_part_loss. (1, self. palt.patch_size, 11
main_part_loss = (rain_aatterai
(b__))_____>__________ b-b)
Calculate the overlapped indices end_point self.patch_size
seeeffpptch_nmm - 1)
seti.patch_stride
Start_indices np.array (range (0, end_point, sel self.patch_striade self.patch_size
indices = start_indien
indices torch. (Trange (start indices(il, end indices [il) for i in range (n) 1) .usgquezze (0) .unqqueese (-1)
indices repect (b, 1, 1, ct. www.sappat_ttssttd_eeeooooooosee
Point Granularity Alignment loss zerch (b, self.win_size (aaai_maaattttttteeea
self. self.padding length, ct) (main part loss device)
mair loss seatter_/dimes index=indices, srosmain_eart_lod
non_zero_ent wow.h..conttnoooooooooooooo wwwnt_nonneeeteeeeeoooooooooo (main_loss, dim=1) lain_ losi__osss.smm? non_zere_cnt
Calculate the metric of the remained part if self
> 0:
oss melf..eerrcccouppute.
-sel pe :),
batch_yle self.padding
:))
padding_los padding wtt._llssreepe... (1, self.padding_
Cotal_loss = torch.concat ( [mminn loss, padding_lsss]] dim=1)
else:
total loss main loss
return total loss
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A.7 COMMAND USED FOR GENERATING THE SYNTHETIC DATASETS
We use the provided source code LLai et al. 2021) without alterations as demonstrated below, except for adjusting the length parameter to generate longer time series, ensure fair comparison.
Algorithm 3 TODS Synthesis
This code is based on the original implementation from the TODS project. Original author:
Lab Rice University
Source URL: tttps://githule con/ hetr/datamlllld lab/tods
Set base values and behavior types
DIM NUM 5
BERAVIOR [sine, cosine, sine, cosine, sine]
CONFIG ("freq": 0,04, "coef": 1.5, "offset": 0.C, "noise_ amp": 0.05)
VALUES [c.145, 0.128, 0.094, C.077, 0.111, 0.145, 0.179, 0.214, 0.2141
Generate training data train_data mult_varlaaeeDataGeneeaa (dim-DIM stream 120ghh2200, bensvior=BeHATTOR, behavi caaavooooooooog00015.
Generate test data test test_data - MuLtivarrarrepttaeeeeraaat (dim-DIK NUM, stream stream length-5000,
bebavior-BEHAVIOR, behavior_config-O00
Add anomalies based on the specified anomaly type
for (DTMM if anomaly_type -- sac.bbalaanomaly"
test_ best_data..pont__oooaioooott (din_no=i,, ratio=0.01 01, factor=3.5, radius-S)
elif anomaly_type == aaantexxuallanommlyyy
past_data.point_contee lotttoteeeettaattllaaaaoo fers (dim_no=i, ratio=0.01, factor=2.5, radius=5)
elif anomaly_type =-
test htt.:ooleeeeeeeegllll.o.ooooooee (din ratio-O. 01, radius-S,
aptioo= square', coef-1.5, noise_amp-0.03, level-20, freq-0.04, base-VALUES, offset-O.C)
elif anomaly_type
aatasonallanommaln
set__dtte.collleeteeeeeeeeee radius=5)
lers (din_ro=i, ratio=0.01, factor=3,
elif anomaly_type "trend aarema_ancmalyy
test_ ses__date.coolletteeeeeeeee outte ndim_no-i, ratio-0.01 01, factor-0.5, radius-5)
elif anomaly_type m subsequence lacpeuuuence_ammalylll.e
(din_neii, ratio=0, 006, radius=5, option="squaz", coef=1.5, coise_am=0.005 level-20, Eseq=0.04, base=VALUES, offset=0.C) l iers (dim_nomi, ratio-0.006, factor=3,
test
radius=5)
test_data. cesta.collectt wecelletteeeeeeeeeeeeeeeeeeeeeee tee_tveee__e_eueeeeeeeeeeee Hers (dim_no-i, ratio-0. 006, factor-0.5, radius=5)
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B ADDITIONAL CASE STUDIES
As shown Figure 6 we visualize the anomaly scores various recent SOTAs to obtain an intu- itive comparison of detecting accuracy. Our proposed CATCH shows most distinguishable anomaly scores in detecting both point and subsequence anomalies.
Seasonal
Input
18m4
Tars
DUNITF
ModenTCN
Aromaty Tandforme
Tome
Time
Tima
Tima
Input Time Series
Ground Truth
Final anomaly score
Figure 6: Visualization of anomaly scores from recent SOTAs for the TODS datasets.
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C FULL EXPERIMENTAL RESULTS
The full MTSAD results are provided in the following section due to the space limitation of the main text. Tables 6
8 9 and 10 show the (Accuracy), (AUC-ROC, R-AUC-ROC, VUS-ROC), (AUC-PR, R-AUC- C- PR. VUS-PR), (Precision, Recall, Fl-score), (Range-Recall, Range-Precision, Range-Fl-score (Affiliated Preecision,,, Affiliated- Recall, Affiliated -sssooe results, respectively.
Table Average Acc (Accuracy) measures for all datasets. The best results are highlighted in bold, and the second-best results are underlined.
Dutreet
Meinc
CATCH
Modern
iTrms
DraffT
ATrans
DC
ToNlet
Panch
D1.nn
NL.t
AE:
THAD
|Orom
IF
PCA
HIBCS
0.745
0.750
0.994
ChiliZ
0.889
0.944
0.541
0.946
0.844
0.960
0.886
Ciedt
0.911
0.847
0.766
0.951
0.991
0.347
GBCCO
0.884
0.983
0.984
0.957
0.525
0.999
0,590
Genesis
0.931
0.771
0.57
0316
0.089
SWAT
0.257
0.836
0,867
0.813
0.700
0378
0.19
0.745
SMAP
0.362
0.689
0.663
0,845
0.368
0.689
0.685
0.05
0.655
0.571
0.368
0313
0.50
0.855
0.21
ASD
0.53
0.913
0.898
0.912
0.920
0.928
0,912
0.946
0.53
0.863
0,700
Coseettal4
Aaz
0.961
0.754
0.95
0.713
0.641
0.618
0.734
0.388
09941
0,743
0.965
0.574
0.586
0.956
0.848
0.65
Coiixhel77.2
Aaz
1.960
0.721
0,937
0
0,702
0.61
0.759
0.386
0.81
0.739
6.056
0.350
0.877
0.930
0818
0.50
Globa4 8
Aac
11.99
0.8%
0.994
0.833
0.174
0.630
0.980
0.915
1.933
0.305
03500
0.376
0.563
0.977
0.688
0872
Global7.2 2
Aoc
11.75
0.849
0.72
0.336
0.232
0.665
0.987
0.944
1981
0.900
0.97%
0.355
0.915
0.570
0.644
0.43
8 8
Acc
11965
0.851
0.973
0.956
0.956
0.952
0.974
0.74
107
0.944
0.959
0.9-7
0.550
0.557
0.55
0.63
Semsnal7.7
Acc
1.979
0.792
0.964
0.894
0:928
0.925
0.93
0,60
196
03443
03935
0.915
0.597
0.559
0329
0.499
Stapelesi.9
Acc
0.969
0.820
0.966
0,942
0.950
0,946
0.957
0.53
196
01947
0.950
0.577
0.579
0.552
0.81
0.355
Stapele?7.4
Acc
0.957
0.715
0.949
0.871
0.911
0,825
0.951
0.41
1367
0.891
03922
0913
0.572
0.925
0.838
0.39
Mistines7
Acc
0.501
0.893
0.885
0.658
0:915
0.540
039
0,589
(1400
01833
0.992
0521
0.183
0.988
0113
0.190
Mistuned 9
Acc
0.888
0.849
0.22
0,818
1032
0.910
0882
03111
0156)
0108
0:300
0350
0. 0.123
01933
013
0.215
Trinkk
Asc
0888
0.873
0.891
0:946
01013
01:01
(1550)
01827
03855
0.064
0L8SS
0065
0.22
Trnd77.8
Asc
0911
0.813
0.700
0.785
00003
0.911
0.801
0:578
(.600
0,984
0.640
0.395
0.079
0.927
0.000
0.319
1d Count
7
0
9
4
0
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Table 6: Average A-R (AUC-ROC), R-A-R (R-AUC-ROC) and V-ROC (VUS-ROC) accuracy mea- sures for all datasets. The best results are highlighted in bold, and the second-best results are under- lined.
Datrset
Matric
CATCH
Modem
TTran
DuafTF
ATrara
DC
ToNe:
Paacs
D1.in
NI
ARF.
TFAD
OCeem
IF
PCA
HBOS
A-K
0.795
0:097
0,692
0.603
0.528
0,638
0.752
0.716
0.751
0.091
0.629
0.508
0.537
0.787
0.601
0.700
CICIN
R-A-R
0.259
0.637
0.584
0-454
0.392
0.692
0.661
0.650
0,692
0.609
0.574
0.888
0.681
0.739
0.478
0.720
V-ROC
0.943
0.649
0.626
0-485
0.408
0,538
0.691
0.663
0.700
0.61
0.586
0.408
0.505
0.750
0.496
0.935
A-R
8838
0.676
0.791
0.574
0.533
0.527
0.771
0.808
0.752
0.695
0.767
0.504
0.804
0.775
0.700
0.796
Call2
R.A.R
0.84
0.726
0.517
0.656
0.523
0.505
0,807
0.500
0.794
0.745
0.798
0.502
0.840
0.518
0.796
0.347
V ROC
0.848
0.716
0.509
0.630
0.517
0.505
0.796
0.824
0.761
0.728
0.789
0.501
0.828
0,302
0.756
0.331
A-R
0.952
0.9%
0.20
0,552
0.904
0.57
0.57
0.54
0:94
0.909
0.500
0.95
0.860
0.71
0.951
Credit
R-4-R
R921
0.19
0.882
0.535
0.379
0.433
0919
0918
0964
0:002
0.43
0.14
0.309
0.84
0.004
0917
0.775
0.398
0.455
0914
0911
0.908
0.897
0.400
0.905
0.818
0.305
0.895
0.970
0.558
0.78
0:587
GR000
0.25
0.501
0.510
V-ROC
0.17
0.503
0.998
0.979
0962
0.071
0.677
0.503
A.R
0.94
0.676
0.090
0.957
3942
0,659
0913
0.685
0.696
0.755
0.951
0,549
0.397
Genesis
R
0.981
0.727
0.797
0.975
15%
0,742
0.19
0.741
0.791
0.917
0.694
0,683
0.322
0.319
ROC
0.978
0.775
0.91
0,730
0.13
0.735
0,787
0.916
0.859
0,060
0:827
A-R
R6644
0.635
0.511
0.576
0.508
0.907
0.61
0.63
0.64
0,592
0.562
0.900
0.534
0.534
0.553
0.574
MSL
RAR
0.747
0.708
0.685
0.662
0.529
0.596
0.701
0.720
0,703
0.611
0.635
0.515
0.594
0.575
0.631
0.643
V
0.735
0,701
0.676
0.652
0.277
0.587
0.692
07112
0.695
0,672
0.625
0.514
0.590
0,571
0.622
0.635
A-R
R816
0.466
0.640
0.633
0.671
0.549
0.91
0.709
0.768
0.671
0.504
0.900
0.456
0.475
0.666
0-446
NYC
R-A-R
8.856
0.598
0.597
0.754
0.753
0.5%
0.55
0.722
0.762
0.706
0.636
0.509
0.612
0.632
0.74
0.545
V-ROC
R.827
0.579
0.689
0.757
0.722
0.530
1771
0.719
0,760
0.701
0.619
0.509
0.559
0.600
0.730
0.536
A
0,63
0.595
0.592
0.600
0.54
0.501
0392
0.586
0.580
0:585
0,500
0,500
0.69
0.542
0.65
0.620
PSM
RAR
0.600
0.586
0.589
0.50
0.353
0.559
0393
0.586
0.539
0:585
0187
0.999
0.500
0.45
0:54
0.722
V-ROC
0.699
0.589
0.586
0.00
0.451
0.639
0.91
0.585
0.579
0.585
0.889
0 0,699
0,512
0,542
0.585
0.375
AR
0.745
0.31
3.08
0.002
0.227
0.236
0.728
0.28
0,774
0.500
0,00
0,664
0,77
0.636
SMD
R-A-R
0.062
0.941
0.00
0.505
0.422
0.260
0.254
0002
0.79
0,679
0.597
V-RCC
0.797
0.92
0.505
0.266
0.758
0.251
0,000
0.70
0558
0,676
0.655
0.597
A-R
0:345
0.242
0.567
0.405
0.501
0.88
0.242
0.521
0.251
0817
0.346
0,331
SWAT
R.A.R
0.473
0.353
0611
0.511
0.354
0.358
0.358
0.645
0.431
0.115
V-BOC
0.462
0,348
0.344
0.608
0.434
0.511
0.32
0.345
0,350
0.638
0,424
0.744
A-R
0.504
0,455
0.409
0.473
0.11
0.522
0,53
0.438
0.397
0,434
0,222
0.500
0.391
0.487
0.396
0.585
SMAP
R-A-K
0.66
0.491
0.441
0516
0530
0537
0.50
0,483
0.455
0:466
0565
0.308
0.610
0.499
042)
0.465
V-BOC
0.543
0.489
0.439
0.515
0.520
035
0.489
0,482
0.435
0.465
0.54
0.30N
0.488
6499
0.419
0.566
A-
6834
0.092
0.759
0.579
0.066
0.500
0.05
0,700
0.739
0,090
0.704
0.500
0.588
0.18
0.065
0.600
ASD
R-A-R
8861
0.745
0.812
0.624
0508
OS85
0835
0311
0.251
0:541
0753
0.306
0612
10094
0661
0.634
V-ROC
8851
0.739
0.404
0.61
0550
0,56
0831
0.806
07544
0:035
07455
0.506
0.885
0.674
0.619
A-R
R9921
0.566
0.916
0.600
0.54
0.535
0.562
0.700
0.545
0014
0.697
0.706
0.540
0.538
D-470
Costextaab499 9
R.A.R
0889
0.386
0.551
0.5
0.96
0425
1855
0.761
0:543
0.991
02:3
0.998
0.537
03766
0.644
0:300
ROC
0.854
0.445
0.545
0.45
0.41
0,768
0.536
0.437
0.842
0.501
0,583
0.745
0.745-0
0.405
0.362
A-R
0.99
0.558
0.891
0.366
0519
0.86
0.345
0.011
0.515
0.27
0510
67/6
0,003
0.54
0.45%
Cistextra77.2
B.A.R
0.88
0.512
0361
9374
0330
1216
0.30
0.522
03300
0.466
0.20
0624
0360
0.297
VBC
0.442
0.514
0424
3.306
0,445
6319
0.36
0.367
0.409
0.797
0.472
0555
0,093
0.401
0.351
0.815
0990
0:901
0.605
0,006
0968
0,44
0720
Globoi44.8
0464
0980
0.60
0.001
0.444
V-RCC
0.952
0.533
0.402
0967
0.92
0.579
03903
A.R
0.997
0.971
0.559
0.513
0958
0.992
0.778
0,665
0.9%
0.95
0,928
0.745
0.605
Global7.2
R.A
0.993
0.945
0.955
0.303
0.385
0977
0.64
01577
0.534
0.991
0.698
0,386
0.475
RBC
0.979
0.957
0.452
0.339
0.997
0962
0.96
0.99
0.560
0972
0.700
0,378
0.512
AR
0.999
0.511
0.945
0.855
0.590
0.561
0959
0.922
0309
0.13
0.43
0.698
0.540
0.21
0.447
0.522
Semsona34.
RAR
1,000
0.613
0.929
0972
0350
0.52
0133
0.31
0.47
0.67
0395
0.528
0.549
0355
0.533
0.629
V BBC
0.999
0.59
0.929
0950
0.577
0.034
0.32
0.99
0.39
0.66
0.89
0.522
0.455
0,357
0.544
0.609
A-R
8.997
0.515
0.946
0.50
0.579
0.628
0.99
0.921
0837
0.644
0.84
0.906
0817
0.955
0-225
0.509
Scoomma77.7
R-A-ll
8.997
0.640
0.46
0.58
0.558
0,625
0143
0.31
0360
0.601
0.007
0,512
0444
0311
0.563
0:615
V-RCC
IL994
0.615
0.45
0616
0.559
0.611
8946
0.920
0851
0.680
0.155
0.537
0.913
0.546
0.602
A
0.922
0.527
0.355
0623
0532
0.627
0311
0.070
0:552
0357
0.500
0,01
0767
0
0.342
Stupetesa.
R AAR
0.996
0.508
0.883
0243
0606
0.02
0190
03551
0.214
0:42
0854
0.51
0.766
0,00
0.24
0.110
V-RCC
0.733
3.994
0.5%6
0875
0.844
01712
0.627
0.811
0710
0.794
0.60)
0
AR
0.572
0.23
0.006
0.567
0342
0.324
0.07
0.75
0.874
0.500
0600
0.728
0.545
0.352
Stapeter7.4
R
0.577
0.24
0527
0.546
0,80
0.60
0353
0146
0.700
0.667
0.512
V-KC
0.576
0.603
0518
0.537
03855
0.53
0.34
0.635
0356
01227
0.71
0.688
0.485
A-R
1996
0.559
0.524
0.400
0.577
0.700
0.550
0.02
0.645
0A522
0.98
0.400
0:443
Mistund3.7
R-A-R
0.509
0.699
0.519
0.50
0.738
0.300
0.36
0.576
0.465
V-BOC
0.59
0.63
0.463
0.522
0.992
0.745
0.722
0.385
0.510
0.311
0.577
0.455
AR
0879
0.5%
0.834
0.23
0.508
0.562
0.555
0.319
0.650
0.656
0.513
0.500
0.500
0.74
0.497
0.492
Mistuna8.
R-A-R
08877
0.706
0.565
0.630
0.500
0.552
0.871
0.557
0.713
6.728
0..05
0.517
0.476
0.76
0.463
0.545
V-BOC
0.90
0.687
0.560
0.610
0.501
0.542
0.865
0.850
0.706
0.719
0.400
0,516
0.662
0.5%
0.446
0.531
AR
R914
0,715
0.581
0.511
0,502
0,530
0.377
0.368
0.733
0.719
0.477
0,502
0.663
0.943
0.525
0.532
Trend4.8
R-A-K
R.96
0.57b
0.920
0.620
0.502
0.505
0.924
0.929
01838
0:335
0.465
0:211
0,506
0.471
0.595
V-R0C
0983
0.645
0,915
0.617
0.504
0.506
0917
0.930
0:81
0.449
0.519
0,910
0-40 0.480
0.582
T
V-BOC
R-A-R
A-R
RL977
8.940
0,582
0.821
0.574
0.527
0.572
0.884
0.578
0.616
0.542
0.530
0.537
0.501
0.504
0.502
01845
(8833
0353
0.595
0980
0.558
0.900
03635
0.780
0:539
0350
1.508
11581
0.509
0.501
-
0,500
0,488
09400
0.878
0.879
0.580
0.63
0.71
1,500
0.625
0.550
Count
63
0
0
0
0
0
0
0
0
2
23

---

Published as a conference paper at ICLR 2025
Table 7: Average A-P PRUC. R-A-P (R-AUC-PR) and V-PR (VUS-PR) accuracy measures for all datasets. The best results are highlighted in bold, and the second-best results are underlined.
Dainset
Metric
CATCH
Modern
/Tanss
DealTF
ATTras
DC
ToNeet
Ponch
11.in
NL.t
AE:
TRAD
|Oovm
IF
PCA
HBBOS
A-P
0,002
0.001
0.002
0.002
0.001
0.002
0.002
0.001
0
0.001
0.001
0
0.001
0,001
0.001
0.003
CICIDS
R-A-P
BL02
0.82
0.002
0.001
0.001
0.001
0.002
0.002
0.002
0.002
0.000
0.002
0.364
0,002
0.001
B.022
V-PR
0.002
0.002
0.002
0.001
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.389
0.003
0.001
0.002
A-P
0.114
0.04
0.106
0.057
0.045
0.005
0.073
0.116
0.90
0.054
0.084
0.000
0.085
0.080
0.033
0.000
R-A-P
0.824
000
0111
0.088
0.089
0.087
0.02
0.115
0.90
0.073
0.086
0.000
0.109
0.055
0.106
0.113
V-PR
0.821
0.00
0.10
0.082
0.085
0.063
0.090
0.115
0.055
0.072
0.067
0.011
0.109
0.001
0.10
0.108
0.107
0,088
0.042
0.007
0.002
0.091
0.061
0.057
0.040
0,012
0,063
0.074
0.029
0.173
Cledi
R.A.P
01033
0.054
0.002
0.002
0.056
0.153
0.020
0,000
0.099
0JI1
V.RR
0.51
0.051
0.024
0.011
0.002
0.002
0.053
0.051
0.020
0,039
0.012
0.076
0.447
0.013
0.306
0,032
GROC0
0.433
0.478
0,392
V-PR
0.465
0.022
0.019
0.429
0.015
0.083
D033
A.P
0.249
0.015
0.019
0
0,05%
0,010
0.036
0.031
0,055
0,005
0.011
0.029
Genesis
0.384
0.015
0.021
0.101
0,101
0,012
0.038
0.013
0.016
0.013
0,047
0,033
0.506
0.011
0.015
0.090
0.371
0.015
0.020
0,095
0,012
0.037
0.016
0.014
0,047
0,506
0,010
0.087
A.P
0.167
0.146
0.151
0.156
0,107
0.107
146
0.157
0.147
0.140
0.14K
0.106
0.15%
0.114
0.157
0.152
MSI.
R-A-P
0.260
0.234
0,222
0,230
0.165
0.157
0.251
0.243
0.225
0222
6,300
0.162
0.185
0.174
0.201
0.190
VR
0.256
0.200
0.234
0.218
0.162
0.156
0.227
0.33
0.221
0.218
0.199
0.159
0.185
0.173
0.200
0.189
A-P
0.9%
0.020
0.033
0.040
0.08
0.004
0.000
0.046
0.46
0,00
0.005
0003
0.000
0021
0.066
0019
NYC
R-A-P
0.120
0.038
0.51
0.065
0.06
0.045
0,899
0.59
0/66
0.966
0.046
80%6
0.383
0.06
0083
V-PR
14
0.037
0051
0.063
0.087
0.047
0.070
0.000
0.061
0.065
0.045
0.47
0:318
0.045
0.022
0.052
AP
0.434
0.385
0.383
0,411
0.298
0.281
0.391
0.378
0.371
0.376
0.465
0229
6418
0.334
0
0.384
PSM
RAP
V-R
0.4%
0,435
0.383
0.364
0.386
0.387
0.385
0.384
0.295
0.295
0.285
0.285
0.395
0.395
0.379
0,380
0.372
0.373
0.378
0.379
0.22
0.420
029]
1:20
0:300
1
0334
0.244
0.423
0.370
0.369
0.123
0.30
0.146
0.049
0.46
0.045
0.141
0.147
0.139
0:141
0.188
0042
0.00
0122
0128
0.145
SMD
R.A.P
01.50
0.30
0.145
0.070
0.055
0.466
0.140
0.152
0.145
0:145
0:182
0003
0100
0099
0
0088
V-PR
01
0.130
0.145
0.070
0.054
0.046
0.140
0.144
0.145
0.181
0000
0.099
0.109
0.88
0.106
0.093
0:121
0.121
0.107
0,085
0.131
0.081
0.713
0,70
0,093
0.726
0.738
SWAT
RAP
0:251
0.138
0.172
0:111
0.154
0.178
0.170
0:113
0.446
0010
0235
0.133
0333
0.59
V-PK
0.241
0.132
0.188
0.121
0,109
0.155
0.189
0.121
0.111
0.474
0.129
0.504
0.561
A.P
0.131
0.114
0.114
0.150
0.132
0.114
0.104
0.111
0.126
0.122
0.104
IL145
SMAP
R.A.P
1.155
0.129
0.141
0.155
0.149
0.151
0.118
0.126
0.142
0.344
0.135
ILI65
V-PR
0.155
0.129
0.126
0.152
0.350
0.151
0.127
0.145
0.153
1.117
0.156
0.166
A.
0.251
0.15
0.161
0,085
0,052
0,049
0.345
0.124
0.170
0,132
0,303
0051
0.143
0.195
0.144
0.133
ASD
R-A-P
0.269
0.10
0.19
0,105
0.022
0.000
0.51
0.202
0.191
0.139
0:08
0069
0.003
0.107
0.154
0.152
V-PR
0.261
0.17
0.194
0,109
0.080
0.000
0751
0,300
0.188
0.139
0:308
03991
0.005
0.197
0. 0.149
0.150
A.P
0.754
0.090
0.754
0.086
0,070
0,044
0.773
0.640
0.274
0.155
0.732
0.009
0.533
0.323
0.066
0.044
Castestua34.9
R.A.P
11585
0.050
0.585
0,075
0.55
0.055
0.614
0,322
0.135
01154
6356
0025
0.263
11255
0.054
0.047
V
0,562
0.074
0.59
0.094
0.068
0:067
0.596
0,425
0.148
0.856
0.334
0247
0242
0.250
0.058
0.057
A-P
0,770
0.006
0.256
0.087
0.09
0:006
0251
0,622
0.319
0.000
0.721
0. 0.109
0543
0324
0.105
0075
Contestial.22 2
R-A-P
0612
0.83
0.594
0.078
D00S
0:009
066
0477
0.166
0,05
0.56
0082
(1260
0.79
D007
V-PR
0.594
0.000
0.579
0.007
0004
0.004
0.5M
0469
0.163
0.000
0.588
0009
0271
0.98
0061
A-P
0.78
0,552
0.9
0.087
0.054
0:001
0.999
0,69
0927
0.09
0:811
0096
0.455
0.336
0.13
Clobal44
R-A.P
0.957
0.3
0881
0.068
0.85
04000
0918
0918
0.88
04072
0:912
0051
0.61
0110
0063
VPRR
0.901
0.361
0834
0.002
0.099
0.062
0.886
0.364
0.86
0.080
0.584
0000
0.394
0.140
0074
0.974
0.517
Q921
0.09
0.074
0.447
0960
0912
0.134
0.935
6074
0,492
0.152
0.106
Global7.2
R.P.P
0.316
0.081
0.074
0,822
0225
03334
0.106
0:48
0060
0.95
0,429
0.145
00000
VR
0,305
0.357
0818
0.101
0.009
0.800
0.576
0.796
0.122
0.899
0007
0.426
0.182
0.107
0.975
0.55
0.60
0.584
0.713
0.223
0.54
Scoomao4488
0.994
0.087
0.122
0.535
0.50
0.540
0.718
0.679
0084
V-PR
0.987
0.084
0.755
0.185
0.200
0.61
0.737
0.21
0.679
D083
AP
0,963
0.092
0.81
0,164
0.148
0.906
0.645
0.109
0,500
0.133
0.733
0.116
0.080
Seasonal7.7
RAP
0.978
0.148
080
0,139
0,192
0.260
008
0.599
0.163
0.758
0.098
0345
0.552
0.169
0.132
VRR
0.963
0.141
0,134
0.190
0.346
0.933
0.605
0.159
0,782
0.165
0.543
0.132
A.P
0.774
0.055
0633
0.134
0.066
0.142
0.683
0.49
0.363
0.53
0.659
0.102
0.883
0.283
0.994
0.043
Stspda44
R.A.P
11340
0.08)
0.564
0.199
0002
0.355
0.58
0.463
0.314
0.090
0.556
0.04
0110
0319
0.138
0.070
V-PR
11387
0.089
0.571
0.195
0.0%
0.347
0.59
0.465
0.322
0.089
0,568
0.33
0432
0311
0.135
0,071
AP
0.774
0.077
0.651
0.009
0.109
0.135
0.708
0.542
0.419
0.089
0.115
0.118
0.337
0295
0.136
0,02
Shopeler7.4
R.P
0,921
0.132
0.68
0.149
0:145
0.169
0.639
0,528
0.166
0.137
0.69
0.155
0.888
00522
0.241
0.104
V-R
0,777
0.133
0.16
0,148
0.137
0.164
0.65
0.334
0:422
0.136
0.634
0.121
0.498
03543
0.22
0.101
Mistund37
R-A.P
V-PR
A-P
11366
I1509
0.477
0.196
0.264
0.276
0.238
0.340
0.339
0.106
0.060
0.110
0,050
0.922
0.090
0.146
0.088
0.145
0.288
01853
0.252
0.369
0.273
0.356
0.173
0.197
0.204
0.160
0.104
0157
0.068
00001
0009
0.154
0000
1125
1::23
0000
11577
11591
11529
0092
0.000
0082
0.122
B051
0.125
A.P
0.355
0.18
0.311
0.091
0.091
0.135
0.355
0.298
0.19)
0.167
0.128
0091
1
0.00
0,593
0.090
0.89
Mistune.9
R-A-P
0.490
0225
0.386
0.160
0,152
0.199
0.003
0.164
0.299
01243
0.165
0165
0250
0627
0154
0.236
V-RR
0.465
0147
0.375
0.157
0.150
0.192
0.393
0.357
0.333
(1236
0.162
0.149
0246
0,119
0151
0.21
0.373
0.215
0.048
0.063
0.274
0.228
0.155
0.133
0.056
0.058
0.044
0.61
0.054
0054
Trend4.8
0/022
0.095
0.400
0.241
01223
0,060
0.589
0.5
0.516
023
0.007
0.002
0.980
0.375
0.235
0.216
0.009
0.001
0.316
0.555
Trana7.8
V
A.P
0.510
0.437
0.665
0.521
0.515
0.514
0.386
0.327
0.399
0.169
0.126
0.371
0.106
0.166
0.124
0.125
0.07%
0225
0.454
0:23
0312
0.359
0.589
0.1.5
0,003
0.15
0.005
0.157
0.150
0005
02250
0.51
0035
0133
0.240
0.250
0.082
1d1 Count
31
11
24

---

Published as a conference paper at ICLR 2025
Table 8: Average P (Precision), R (Recall) and F1 (FI-score) accuracy measures for all datasets. The best results are highlighted in bold, and the second-best results are underlined.
Dainset
Metri
CATCH
Modern
/Tanss
DeafTF
ATfras
DC
ToNNet
Potch
11lin
NL.t
AE:
TRAD
|Oromm
IF
PCA
HBBOS
P
IUN43
0.001
0,012
0.001
0.001
0.001
0.001
0.001
0,002
0.031
0.000
0.001
0.001
0.000
0.001
0.000
CICIDS
R
11739)
0.277
3.451
0.995
0.255
0.266
0.354
0.380
0.506
0.380
0.000
0.038
0.987
0.063
0.425
0.013
F1
10006
0.002
0.094
0.003
0.002
0.002
0.003
0.003
0.004
0.003
0,000
0.001
0.002
0.001
0.002
0.000
0.138
0.074
0.124
0.073
0.085
0.004
0.101
0.091
0.033
0.056
0.067
0.038
0.089
0.125
0.084
0.075
R
0.062
0.263
02200
0.176
0.065
0.162
0.108
0.311
0.264
0.344
0.027
0.81
0.378
0.14
0.291
0.257
0.140
0114
0.161
0.103
0.000
0.066
0.106
0.141
0.128
0.109
0.008
0.000
0.144
0.024
0151
0.117
IL092
0,058
3.026
0.001
0.001
0.058
0.058
1.057
0.157
0.047
0.055
6.013
0.156
0.099
0,002
Cledi
0.755
0.740
0343
0.5%6
0.139
0.238
0.740
1.736
0.744
0.135
0.901
0
0.731
0.15
0.110
0.137
3,051
0.006
0.005
0.005
0.107
0.105
0.107
0.069
0.007
0.026
0.201
0.017
0.018
0.373
0:012
0011
0.144
0014
GR000
D81K
0.779
0,12
0.518
0.504
0.010
0.516
0.000
0.27
0.116
0.015
0.065
0,055
0,015
0.119
0.055
0.013
0,047
0,066
0.077
0.017
Genesis
0.160
0.120
0,500
0,900
0.029
0.250
0.200
0.140
0.080
0.120
0,00
1,000
0,000
0,990
0.134
0.027
0.095
0.116
0,100
0,018
0.149
0,009
0.008
0.00
0,014
0.009
0.033
0.185
0.166
0.158
6,348
0.145
0.181
0.156
0.194
0.179
0.191
0:210
0.107
0.32%
0.180
0.1%)
0.129
MSI.
0.117
0.090
0.000
0.019
0.038
0.008
0.093
0.066
0.091
0.067
6.014
0365
0.325
0014
0.137
0.124
F1
0.143
0.117
0.114
0.005
0.015
0.016
0.119
0.398
0.121
0.100
6:026
0010
0.126
0025
0.133
0.127
1,000
0.000
0.344
0.111
0,395
0:350
0.000
0.000
0.00
0.000
0:089
0.000
0,022
0086
0.99
00000
NYC
R
0010
0.000
0,291
0.010
0000
0/000
0.000
02000
0100
0.00
0:001
8000
0,990
1010
0222
00000
F1
0,020
0.000
A061
0.019
0.028
0.019
0.000
0.000
0.000
0.000
0.017
00000
02445
0.017
00000
P
0.624
0.653
0.600
0,461
0.396
0.278
0.591
0,633
0.58
0.644
0.446
0282
6246
0,00
0.427
0.564
PSM
R
0.064
0.017
0.09
6,559
0.025
0.245
0.88
0,047
0025
0.847
0:110
0005
0299
0004
0.421
0.302
11
0.115
0.089
0.108
6.596
0.046
0:259
0.058
0.088
0.047
0.057
0.176
0110
0.000
0.389
0.194
0151
0162
0.091
0.112
0.042
0.176
0.185
0.197
0.201
0.006
0003
6007
05504
0117
00055
SMD
0,00
0.445
0.257
0.022
0:301
0.111
0.175
0.134
0:126
0:077
6005
0:004
11000
0,59
0.352
11237
0.148
3.198
0.037
0.009
0.178
0.179
0.153
0.155
0.014
0.009
0.099
0.176
0.145
0,195
0.119
0.053
0,105
0.107
0.329
0.110
0.089
0.151
0,25
0,20
0,128
0152
0.290
SWAT
0,056
0.058
0:013
0.015
0.044
0.074
0,302
0001
0,90
0,002
0.07
0.742
0.077
0.075
0.015
0.008
0.077
0,301
0.001
0
0.004
0.261
0.177
11.336
0.096
0.086
0.119
0.15L
0.121
0.066
0.084
0.064
0.04
0.092
SMAP
0,035
0.171
6.256
0.047
0.005
0.167
0.148
0.001
0042
0.002
0.045
0.045
0.061
0.125
0.130
0,072
0,000
0.121
0.130
0.107
0,001
0.004
0.060
0.309
0,237
0.230
0,116
0,07%
0.069
0.318
0.261
0.301
0.207
0.223
0.02
0.063
0.455
0.083
0.100
ASD
0.225
0.178
0.253
0,185
0.022
0.045
0.299
0,147
0.135
0,177
0,101
0016
0.060
0.063
0.263
0.242
0.219
0.15
0.184
0,107
0.051
0.047
0.258
0.177
0.163
0.146
0.199
6017
0.885
0.108
0115
0.131
P
0.584
0.067
0.555
0.044
0.051
0.049
0.101
0.264
0.416
0.119
0,670
0.01
0.234
0.577
0.072
0,029
Castestua34.9
R
0.733
0.340
0.696
0,235
0356
0.364
0.559
0.713
0.656
0.656
0391
0060
0.559
11393
0.174
0
F1
0.650
0.112
0.618
0.075
0.089
0:066
0.172
0.385
0.531
0.201
03225
0351
1051
0.330
0.407
0.102
0,037
P
0.264
0.995
0.548
0.085
0.00
0:067
0.577
0,382
0.373
01100
6:775
0004
0.306
0.63
0.100
0053
Contestea7.22
R
0.686
0.356
6.19
0.461
0299
0.542
0.000
07000
02117
0160
0:556
0093
0.566
1350
0.99
0064
F1
0.714
0.148
0,62
0.143
0.176
0.112
0244
0446
0:491
0:337
0.547
8000
01504
0.511
0113
DOSA
0.9%
0.27
1,000
0.011
0.88
0:04
0.90
1000
0977
0.200
0:147
0066
0:31
0226
0.00
0.86
Clobal44 8
0.921
0.72
0875
0.304
0.854
0:529
0.88
0:58
087)
0.85
0:825
0029
0120
0758
0175
0.920
0.40
0933
0.105
0.000
0.060
0.878
0.400
0.21
0.429
0.806
0/068
0,96
0.758
0.150
0.166
0.801
0.281
3.764
0,07L
0.077
0.73
1915
0.001
0.57
6000
0.34
0.134
Global7.2
0.925
0.713
0.738
0.836
0.534
0,866
0916
0372
0.902
0.008
0070
0.27
0.721
0.84
0.403
3319
0.136
0.135
0.125
0,904
0,594
0.80
0.54
0.38
0.00
0.777
0.226
0071
0.994
0.66
0.653
0.639
01944
0.600
0000
0.309
0043
Scoomo44.8
0..47
114
0,100
0.451
0.51
0311
D067
0.863
0.089
0.179
0.125
0.459
00000
0,305
0.412
0.066
0.54
0.961
0.050
1000
0,092
0
0.597
0.995
1.00
0.963
0.092
0.379
0.766
0.099
0.103
Seasonal7.7
0,852
0,765
0.150
0.107
0.69
0.041
0,057
0,078
0.144
0,176
0.105
0.685
0.523
0,664
0.006
114
0.00
0.271
0.435
09955
0:35
0.22
0.60
0,688
0.444
0.13
0.124
0.113
Stupda44
F1
R
P
0.920
11.51
I.364
0.096
0.064
0.855
0.300
0.524
0.093
0.000
0.033
0.101
0.438
0.057
0.315
0.145
0.004
0.500
0.335
0.968
0,184
0.55
0.519
0.366
0.88
0.500
0.396
0.25
0418
6338
6396
0.479
6007
6004
0003
10004000
0336
03305
02300
0211
0131
0.54
0.150
0.105
0.075
0
0.035
0.026
P
0,994
0.050
0.785
0.132
0.302
0.151
0.925
0,096
0.411
0.253
0,585
0235
0.296
0.889
0.147
00030
Shopeler7.4
R
0.418
0.222
0.423
0.132
0.01
0:289
0337
0.407
0.307
0325
0015
0353
0119
0.245
0033
P1
0.588
0.124
0.500
0,132
0/888
0:301
0.525
0.144
055
0.255
0334
0.14
0.35
0:388
0.19
0.154
0034
Mistund377
F1
R 11627
P
1l321
u.425
0.211
0.253
0.314
0.260
0.54
0.352
0.058
0.09%
0.324
0.000
0001
0.048
0.370
0.009
0.102
0.551
0.257
0.377
0.557
0.272
0.366
0.764
0.131
0071
0455
0:201
022880000
0:111
0005
0006
5000
1
2111
0093
1.329
1122
06677
0944
0.17
0062
0.707
0.001
0.274
0.200
0.29
0.089
0.855
0.552
02287
0.275
0.18
0.25
0.02
0000
0.004
0.92
0.090
Mistune59
R
0.203
0.254
3.88
0.515
0.000
0:065
0,672
0.600
0.502
01692
0235
0001
0298
0225
1,000
0.84
0.394
0216
0.406
0.140
0.08
0.110
0.80
0.390
0.195
01909
0:145
0/024
0.168
0.34
0.162
01.15
0.171
0.331
0.034
0.167
0.243
0.212
0.073
0.15%
0.048
6000
0.490
0
0.049
B.499
Trend4.8
01427
0.0%6
0/009
01346
0,988
0.304
0.224
0.22
0.346
0.015
0.040
0.299
0.255
0.083
00000
0,003
0.326
0.01
0.92
Trend7.5
0.468
0.438
I1507
0.352
0.653
0.241
0.211
0.144
0.630
0.120
0,051
00033
0.107
0001
0.049
0.003
000040000
0.664
0333
0.231
0:15
0.558
1:55
0.250
0.317
0.130
1.117
0.342
0::74-10
0.07%
0,334
6,125
00000
0.137
0000
0,005
0.07%
0394
0,344
0.640
0,641
1119
01145
1000
0.76%
0.152
0.084
1d Count
11
25

---

Published as a conference paper at ICLR 2025
Table 9: Average R-R (Range- Recall,, R-P measures for all datasets. The best results are highlighted in bold, and the second-best results are underlined.
and R-F (Range-Fi -c-sore) accuracy
Dutrect
Metric
CATCH
Modern
iTrass
DeaffF
ATrass
DCC
ToNeet
Patch
D1.nn
Ni.tt
AE
THAD
|Orom
IF
PCA
HBBCSS
0.786
0.277
0.245
0.285
0.399
0.523
0.386
0.000
0.986
0.057
0.009
CICIDS
11004
0.802
3,002
0.001
0.001
0.002
0.002
0.003
0.001
0.000
0.004
0.001
0.001
0,000
00007
0.003
3.094
0.003
0.005
0.002
0.003
0.003
0.000
0.001
0.805
0.001
0.003
0.000
0:278
0.318
0.161
0,205
0.161
0,065
0.011
0.300
0.105
0.005
0.067
0.125
0.185
0.060
0.049
0.134
01735
0.716
0,828
0.150
0.234
0.716
0.701
0.721
0,135
0.292
0.709
0.907
Ciedix
U1054
0,052
0,005
0.002
0.051
0.049
0.047
0.156
0.009
0,101
0.097
0.947
0,004
0.007
0.005
0.096
0.097
0,070
0.007
0,025
0.204
0.017
R-R
0.795
0.644
0.266
0,146
0.063
0.040
0.762
0.166
0.700
0,274
0,188
0.000
0351
0.000
0.9%
0.361
GRC00
R-P
0.065
0.086
0111
0.019
0.013
0.008
0.053
0.280
0.43
0.296
0.001
0/00
0206
0.114
0.041
0016
R-F
0.119
0.152
0.156
0.063
0.022
0,013
0.099
0,323
0.000
0.285
0,088
0015
0.011
0.52
0.079
0.531
R.R
11497
0.174
0.507
0.550
0.855
0,079
0.211
0.385
0.100
0.162
0.356
0
1,000
0.077
0.325
0.861
Genesis
R.P
0.119
0.014
0.030
0,005
0.016
0.056
0.067
0.059
0.013
0.047
0.00
0.003
0.005
0.055
0.002
RF
0.392
0.026
0.102
0.058
0,010
0:027
0.122
0.114
0.089
0.024
0,085
0.000
0.005
0.011
0.063
0.005
R-R
11.241
0.99
0182
0.049
0.150
0.126
0.224
0.176
0.20
0.162
0.110
0.13
0,202
0.112
0.232
0.199
MSI.
R-P
11.50
0.29
0125
0,267
0.145
0.179
0110
0.136
0.130
0.132
0:219
0.107
0.088
0.180
0118
0.119
R-F
ILIK5
0.155
0.148
0.084
0.146
0.346
0.164
0.153
0.158
0.140
0.146
0.120
0.135
0.153
0.149
R.R
0.208
0.000
0.223
0.208
0.208
0.308
0.000
0,000
0.000
0.000
0.208
0000
0.208
0.289
0.000
NYC
RF
1,000
0.000
0,033
0.145
0333
0.250
0.000
0,000
0.000
0.000
0.09
0000
0040
0,066
0.53
0.000
R-1
0.344
0.000
0.02
0,169
02256
0:227
0.000
0.000
0.000
0.000
0.092
00000
0.004
0.088
0.089
0.000
0.450
0.376
3,470
0,410
0,135
0:111
0.455
0.370
0.999
0.339
0:230
0/044
6133
0.139
0
0.265
PSM
11557
0.553
0.533
0.456
0.374
0.234
0.557
0.557
0.564
0.587
0444
0.85
0,802
0.459
D
0.498
0.848
0.197
0:238
0.893
0.440
0.305
0.001
0.196
0.27
0.451
0.338
0.378
0.126
0.276
0,384
0.079
0.12
0.297
SMD
11005
0.092
0.055
0,101
0.042
0.130
0.134
0.131
0.506
0.544
0.02
0.1.5
0.148
0,085
0.112
0.075
0.171
0.1%6
0.145
0.311
0.192
0.103
RR
0.184
0.200
0.20
0.220
0,205
0.305
0.201
0,190
0.204
0,200
0.173
0324
0.153
0.719
0.442
SWAT
R-P
0.124
0.072
0.066
0,122
0.115
0.120
0.140
0.079
0.233
0,072
0.151
0.358
0004
0.124
0071
0.067
R-F
0.148
0.106
0.09
0,157
0.147
0.151
0.185
0.217
0.106
0,161
0.134
0207
0.130
0.116
R-R
11.822
0.276
0.211
0.236
0.204
0.340
0.298
0.234
1.760
0.250
0.044
0.118
0.334
0.922
0.157
0.128
SMAP
R.P
1L164
0.057
0.888
0,110
0.33
0.121
0.054
0,079
01107
0.000
0384
0.35
0259
1092
0.056
0.075
R.F
0.173
0.133
0.124
0.148
0.151
0.330
0.151
0.118
1155
0.188
03066
0::0
0.000
0099
0.105
0.094
kk
0.300
0.255
0.291
0.145
0:997
0.116
0.328
0.265
0.33
0.215
0.194
0,02
0.166
0.196
0,312
0.217
ASD
R-P
0.212
0.88
0.165
0.165
0001
0:000
0218
0.183
0.20
01111
02222
0027
0267
6.066
0064
R-F
0.219
0.192
0.176
0.088
0.084
0:085
0.23
0.
0.185
0.500
01179
03388
0006
0.003
0.266
0 11146
0.111
R-R
I.733
0.341
0.677
0.232
0.47
0.361
0.556
0. 0.709
0.666
0.699
0:003
6070
0.559
0.396
0.181
Costextual4.9
R.P
11586
0.071
0.59)
0.041
0057
0/M7
0119
0267
0.440
0.125
0:670
8081
0240
0577
0.061
B025
R.F
0.651
0.118
0.620
0.069
0.097
0:065
0.222
0.345
0.536
0.200
02035
0052
0002
0.336
0,470
0.092
0.034
0.692
0.335
6.238
0.453
0.291
0:445
0.29
0,97
0.112
0.09
0.580
0/95
6.5%
0,000
0192
0.61
Cintectua7.22
0.244
0100
0.566
0.070
0.000
0.000
0222
0.51
0:775
0084
0.04
0633
0.077
0051
0.717
0.154
0.33
0.122
0.125
0.105
0.328
0.68
0.461
0.263
0.564
00000
00000
0,903
0.499
0.130
0057
0,919
0.726
0374
0.206
0.859
0:227
0.855
0,87
0.700
0.887
8076
0,799
0.733
0.178
Global4.8
0.539
0.292
0.013
0.41
0,055
0,200
1200
1978
0.202
0000
0:36
0.766
0.113
0.116
0.929
0.416
3933
0.079
0,076
0.877
0,940
0.21
0.500
0.11
0055
0.505
0.762
0.196
0.140
0.921
0716
0.81
0:500
0,813
0.640
0006
0.682
0.761
Clolol77.
01882
0.297
0.73
0,052
0,400
0000
00700
R
0.374
0.420
0824
0,997
0.117
0.902
0391
0391
0,860
0.624
0.796
0.213
0.076
R-R
0.475
0.24
0.464
0.347
0228
0.170
0.453
0.441
0443
0.554
0330
0000
0.478
0220
0.258
0.187
8 8
R.P
(.990
0.62
L000
0.977
0.864
0.500
1000
1.000
1.00
0.966
6580
0080
0.115
0610
0.065
0.041
R.F
0.644
0.099
0.634
0,350
0,373
0.254
0.634
0.11
0.604
0.329
0,387
0.00
0.583
0.102
0.067
RR
0.480
0.254
0.425
0,089
0.175
0.191
0.423
0.409
0.397
0.355
0.275
0.232
0.53
0.75
0.157
0.223
Seasonal7.7
R
0.544
0.071
1,000
0.112
0.922
0.588
0.93
0917
1,00
0.926
0.92
0.325
0.178
07666
0.03
0.149
RP
0.636
0.111
0.96
0.099
0.295
0.289
0.541
0.566
(1369
0.513
0.966
0.270
0.256
0.008
0.044
0.179
R-R
0.447
0.29
0.431
0.057
0.154
0.174
0.338
0,445
0.445
0.24
0.279
0012
1244
0234
0.116
Stspdas0
R.P
[1.64
0.065
0.670
0.104
0.455
0.582
0.064
01348
0.778
0223
0.470
0003
1152
0057
0036
R-F
I1507
0.107
0.527
0.074
0.227
0.240
0.564
0.391
0.566
0230
0.355
8018
2018
0144
1.336
0.011
B055
R
0.471
0.304
0.373
0.197
0.138
0.345
0.642
0,57
0.466
0.365
0.272
0221
0253
0315
0.996
Stopeter7.4
R-P
0.980
0.033
36600
0.125
0.309
0.153
0818
0/19
0.599
02211
0.855
0235
0118
0,699
0.14
0D42
K-F
0.66
0.100
0536
0.151
0.191
0:312
030
0,468
0.334
01268
0.395
0.26
12224
0333
0.168
0053
(.600)
0.341
3.508
0.347
0.076
0:11
0.515
0,47
0.305
0.564
0:29
0.50
0.29
0.554
0.718
Misture3.7
11455
0.091
01000
0:335
0.50
0.344
1,066
0253
0.066
0:13
0,627
0.091
0,096
0.515
0.143
3.488
0.106
0.086
0.175
0.12
0,403
0.121
0254
0.00
0.332
0,000
0.366
0.163
0.170
01293
0,057
0.145
0.599
0.558
0.3M
0.665
0.279
0.178
0.96
0.267
1,000
0.305
Misunes.9
0.516
0.148
0.000
0.445
0.111
0.217
0.092
0.00
0.704
0.000
0.116
0.551
0.296
0.119
0.005
0.910
0.492
0.562
0.025
0.062
0.474
0.625
0.538
0,280
0.26
1000
0.799
Teends
0.267
0.157
0.255
0,037
0.167
0.273
0.169
0.064
0.117
0.045
0.000
0
0.002
0.050
0,388
0.234
0.300
0.110
0.347
0,251
0.116
0.192
0,081
0.000
0,001
0.371
0.054
0.094
Trond7.8
R-R
R.P
0.529
0.361
(.680
012
0168
0.561
0.080
0,316
(116
00065
0/446
0.015
018
0,681
0,546
0.06
0063
0.315
01155
00006
6.799
6006
0.127
0.161
0.001
0.305
0.220
01641
0.000
1,000
0.064
0.763
R.
0.352
0.207
0.258
0.150
60115
0:023
0.244
0.53
0L147
0229
0.119
0.150
00002
0.327
0.004
0.117
1d Count
25
0
0
0
5
2
2
3
9
26

---

Published as a conference paper at ICLR 2025
Table 10: Average P Liffliated-Precisionn Aff-R (Affiliated -effliated-Reeal) and Aff-F (Affiliate-FF) score) accuracy measures for all datasets. The best results are highlighted in bold, and the second- best results are underlined.
Dutrect
Meiric
CATCH
Modern
iTrms
DeaffF
ATrass
DCC
ToNeet
Patch
D1in
Ni.it
AE
THAD
[
|Orom
IF
PCA
HBBCS
AIEP
1.667
0.563
3.536
0.531
0.535
0.566
0.575
0.579
0.543
0.548
0.541
0.538
CICIDS
AB-R
1,959
0.781
0.936
0.995
0.582
0.783
0.785
1.799
0.794
0.156
0.611
1,000
0.673
0.724
0.545
AEFF
0.787
0.654
3.788
0.692
0.580
0.664
0.657
0.660
0.609
0.669
0.243
0.579
0.693
0.604
0.619
0.542
0.650
0.20
0.645
0.691
0.66
0.500
0.62
0.529
0.630
0.555
0.836
0.321
0.85
0.739
0.754
0.587
0.003
0.7%6
AIE-
0.611
0.559
0.521
0.488
0.610
0.605
0.608
0.560
0.658
0.564
0.533
Cledk
AR-R
0155
0.952
0.54
0.925
0,865
0.59%
0.953
0.955
0.943
0,952
0.562
0.97
0.12
0.959
0.999
0,750
0.744
0.13
0,663
0.650
0.632
0.744
0.746
0.742
0,561
0.660
0.714
0.54
0.730
0.695
AP-P
0,52
0.888
0.755
0.635
0.600
0.567
0.810
0.531
0.80
0.791
0,836
0.526
0.490
0.647
0.646
0.630
GRC00
A6-R
0.998
0.988
0.979
0.786
0.905
0.872
0.907
0.995
0997
0.99
0.810
0.776
1,000
0.915
1000
0.277
AFEF
0.908
0.893
0.8%
0.701
0,782
0.687
0.894
0.906
0.01
0,80
0.835
0.627
0.666
0.424
0.765
0.708
A
0,835
0.734
0822
0.683
0.749
0.659
0.750
0.763
0.772
0.724
0.759
0.45
0.312
0.633
0.691
0.564
Genesis
AB
0.565
0.974
0.72
0.996
1,000
0:945
0.938
0.774
0.959
0.911
0.966
0.87
1,000
0.511
0.991
1,000
AlF F
0.396
0.833
0.99
0,800
0.856
0.776
0.854
0.356
0.856
0.829
0.854
0.335
0,677
0.788
0.814
0.721
AG-P
1.399
0.588
0,566
0.563
0.549
0.536
0.59
0.584
0.577
0.584
0:521
0.16
0,99
0.502
0.538
0.520
MSI.
AB-R
0.966
0.755
a951
0.618
0:93
0.534
0001
0.522
0.975
0,48
03781
0036
0502
0.697
0914
IL992
AIEF
I.740
0.726
0770
0.588
0.754
0.724
0.725
0.723
0.635
0.665
0.441
0.564
0.678
0.680
AEF P
1,000
0.639
0,530
0,551
0.731
0.769
0.750
0.719
0.14
0.81
0:339
0.89
1.500-000
0,881
0.516
0.525
NYC
ARR R
0.989
0.955
0.999
0.988
0998
0.580
0.81
0.533
0.863
0369
0089
1990
0989
0.997
0.966
AFF 0
0.994
0.799
0.634
0.708
0.855
0.500
0.754
0.776
0.829
0.819
0.689
0.089
0,667
0.643
0.690
0.675
AGEP
0.808
0.33
0.265
0.623
0.600
0:536
0.202
0.30
0.777
0.760
0:726
0.543
0662
0,204
0.12
0.61
PSM
AG-R
0915
0.941
0.966
0.868
0.871
0922
0.29
0.48
0,893
0.942
0:649
0744
6447
0,473
0.692
0.000
MF
0
0.25
0,710
0,682
0.812
0,531
0.845
0,007
0.62
0.511
0.630
0.658
AIEP
0.773
0.755
0.607
0.510
0,762
0.889
0.650
0.557
SMD
AG-R
0.938
0.948
0.43
0.056
0,895
0.99%
0.038
0.040
0.946
0.291
0,666
0.513
0.007
0.722
0,447
0.840
0.724
0.675
0.851
0,844
0,439
0.742
0.626
0.629
AFF
0.21
0.595
0.588
0,535
0,539
0.539
0.688
0.582
0.586
0.565
0,004
0.613
0.543
0.544
0.71
0:527
SWAT
Mf-R
0.556
0.942
0.976
0
0.981
0.962
0.918
0.883
0,972
0,949
0.77
0.99
0.35
0.932
0.447
AFFF
0.755
0.728
0.218
0,865
0.696
0.096
0.793
0,716
0.736
0.715
0,738
0.685
0.005
0.661
0. 0.206
0.650
AIEP
0.574
0.422
0.49
0.909
0,545
0.548
0.475
0.450
D.455
0:447
0.416
0.315
0.392
0.455
0.399
0.399
SMAP
AI-R
01895
0.971
0.55
0.997
0.91
03955
0.972
0,931
1.953
0.914
0.534
0529
0645
0.657
0.703
AFFF
1.699
0.635
0.557
0.674
0.505
0.701
0.634
0,605
0.616
0.601
0.463
0.615
0.512
0.505
0.509
Aff
0.69
0.659
0.600
0
0.555
0:569
0.63
0,002
0.690
01680
0,000
0.33
0,505
0.61
0.322
0.538
ASD
AB-R
D.666
0.95
0.99
0.760
0.500
0:921
0953
0954
0915
0161
0:942
0785
0310
0842
0371
0.991
AF-F
0.804
0.62
0.790
0.604
0.674
0.002
0.00
0.777
0.763
0.766
0:731
0630
0.711
0.656
0.000
AIEP
0.838
0.505
0x21
0.503
0.337
0.490
0.553
0,660
0.773
0.563
0.861
0.525
0261
0.458
0.487
Costextual4.9
AB-R
01812
0.144
0.61
0.776
0392
0/779
03837
0.883
1.006
6.99
0:074
0060
0769
0181
0.463
0.547
AF
0.925
0.623
0.50
0.611
0.025
0,002
0.606
0,761
0.789
0.695
07756
0.88
0,86
0.694
0.475
0.515
ABFP
0,907
0.58
0826
0.51
0.698
0.496
0.556
0205
0. 0.000
0.585
0:001
0.21
0,60
0877
0.56
0.476
Cintectua7.22
AG-R
0.748
0.60
488
6,995
0.85
0:055
0.00
0.51
0.41
0.83
0.647
0.50
0260
0.35
0.447
0422
AFEF
0,820
0.66
0814
0.560
0.577
0.902
0.685
0.71
0.700
00055
0.753
0.550
0.707
0.665
0.474
0.447
AIE
0,985
0,661
0.549
0.506
0.579
0,964
1,000
1.994
0.221
0:916
0,20
0213
01938
0.599
0.535
Global4.8
0.922
0.867
0:933
0:27
0.855
0,59
02775
0.807
0:912
0079
0.96
0,900
0.994
0.554
AF
0,953
0.750
0.34
0.656
0.541
0.912
0.41
0.90
0.904
0.914
0.589
0,331
0.119
0.717
0.544
AHF-P
0.854
0,687
0.906
0.003
0.440
0.750
0:018
0.721
0.950
0.572
Clolol77.2
AB-R
0.955
0.857
0.017
0.8%
0.861
0.805
0.510
ABf P
0.945
0.756
0.988
0.657
0.52
0.907
0558
0.926
0,812
0.925
0.43
1.555
0,568
0906
0.512
AGEP
1,000
0.533
1000
0.950
0044
0.002
1.000
1.000
1000
01991
0.830
0.533
0.644
0350
0.5%
0.500
8 8
AG-R
0.998
0.95
0.96
0.761
0734
0.547
01087
0387
1463
0311
63944
0.465
0996
0.991
0,893
0.944
AIEF
0.999
0.684
0.993
0.845
0.857
0.579
0.933
0394
0.954
0.911
0:905
0.525
0.590
15500
0.921
0.668
0.66]
AEE P
1.592
0.534
18000
0.628
0:570
0.582
0.998
0.855
1,00
03952
0.568
0.788
0.997
0.255
0.482
0.345
Seasonal7.7
ABR R
ABF P
0.995
0,995
0.934
0.679
0.933
0.992
0,707
0.809
0.718
0.570
0.900
0.839
0.990
0.93
0581
0563
1996
0.99
0.901
0.940
6391
0.925
0.317
0915
03300
0361
0.588
0.956
0317
0.606
0.919
0.685
ABEP
0,997
0.517
0.52
0.653
0.779
0.763
0.988
0.824
1.770
01646
0:332
0
0132
0.547
D-492
Stspdas0
AR-R
119777
0.976
0.79
0.732
0.004
0.745
018
00983
10770
0.977
0.992
0512
1688
10055
0.88
B940
AI-F
11987
0.676
0.966
0.650
0.740
0.755
0.917
0.925
1.770
0.744
0:542
0.54
0.351
01894
0.650
0.646
Aff P
0.999
0.514
0.11
0.591
0.008
0.41
0.955
0913
0914
0.636
0.227
0228
0,62
0821
0.67
0.399
Stupeter7.4
ABR
0.569
0.975
0.92
0.842
0.099
0.235
(1877
0820
0994
01963
0.885
0207
0285
0889
0.70
0.733
AP-F
0.983
0.673
0.57
0.885
0.658
0.221
0.906
0.40
0963
0.77
0.899
0314
0791
0.800
0.696
0.635
ABEP
0.863
0,628
0867
0.555
0.541
0.902
0.875
0367
0-561
0.779
0.560
0620
0.30
0,879
0.543
0.501
Misture3.7
AB-R
0.991
0.940
3920
0,910
0.711
0:737
0.20
0923
1.95)
0.80
0.992
0384
6.98
0,700
0.997
0.969
AFFF
0.923
0.75
3393
0.689
0.618
0.768
0.897
1.723
0.33
0.766
0.000
0.922
0.660
ABF
0.311
0.607
0.502
0.814
0.820
0.797
0.563
0.744
0.520
0.561
0.117
0368
0.18
0.515
Misunes.9
0.936
0:716
0.989
0.47
0.995
0716
0.763
0.897
0.877
0.682
0.906
0.678
AIE-
01861
0.812
0331
0.505
0.560
0.751
0.861
0.540
0.571
0.765
0.502
0,577
0.505
0.503
Teend4s
AI-R
11997
0.974
0954
0.817
0.746
0.505
0.929
0.991
0.994
0.995
1,000
0.942
1.000
0.996
A
0.924
0.556
0.640:00
0.776
0.893
0.724
0,865
0.667
0.562
1,52
0.909
0.671
0.665
Trand7.8
A6-R
AfFP
09966
0.002
0.766
0.97%
0.085
0.200
0.668
01009
0.637
0.655
0.722
0.981
(061
0,770
0.580
01166
07712
0,516
69601
0348
0.510
0,865
0.517
1000
0.71
0.505
AFF
0,559
0.827
0.25
0.647
0942
0:641
0.832
0.355
0.729
0.812
0.079
0.721
0085
0.681
0.663
1d Count
34
0
2
3
1
2
3
16
2
27

---

Published as a conference paper at ICLR 2025
Table 11: Average A-R (AUC-ROC) and Aff-F (Affiliate-FII) accuracy measures for 4 synthetic datasets of different types of anomalies. The best results are highlighted in bold, and the second- best results are underlined.
Model
CATCH
Modern
iTrans
DualTF
TFAD
Metric
Aft-F
A-R
Af-F
A-R
Aff-F
A-R
Aff-F
A-R
Aft-F
A-R
Low-frequency anomalies
0.998
0.996
0.811
0.873
0.850
0.929
0.744
0.662
0.700
0.538
fdidffreuuency anomalies
0.927
0.987
0.814
0,859
0.913
0.984
0.723
0.575
0.519
High-frrquence anomalies
0.915
0.987
0.738
0.864
0.927
0.462
0.602
0.513
Not distinetly frequency band
0.873
0.917
0.775
0.765
0.852
0.910
0.720
0.630
0.619
0.495
D EMPIRICAL VERIFICATION SHOWS THAT CATCH CAN PERFORM FINE-GRAINED MODELING IN EACH FREQUENCY BAND
We design a set of experiments to validate the advantages of our method in capturing fine- grained frequency characteristics. We use the synthetic dataset creation method provided by TODS (Lai et al.) 2021) to generate four synthetic datasets Figure 7 simulating scenarios with known serguunncy-speciffe anomalies: low-frequency anomalies, medium- medium-frequency anomalies, high-frequency anomalies, and anomalies that are not distinctly separated across different frequency bands. We then test CATCH and several state-of-the-ee methods on these datasets.
The experimental results in Table IT show that CATCH consistently outperforms other algorithms across all four datasets. Notably, most algorithms perform poorly when dealing with time series containing high-frequency anomalies, while CATCH demonstrates outstanding performance. More- over, even on time series where anomalies are uniformly distributed across each frequency band, CATCH still achieves outstanding results. These findings provide strong evidence that CATCH cels in capturing fine-grained frequency characteristics, significantly enhancing the performance of time series anomaly detection.
28

---

Published as a conference paper at ICLR 2025
Time domain
Frequency domain
Ampiltude
Velue
Amplluuto Ampittde
Value
Neto A
Value
Frequency
(a) Time series containing low-frequency anomalies
Time domain
Frequency domain
Amplitudie
Volue
Volue
Channe
Amplltdde Ampllhudle
Cratrel
Channel
Cratral
Volue
Wey
Time
Frequency
(b) Time series containing medium- frequency anomalies
Time domain
Frequency domain
10lc
Channel
Amplitude
C
Volue
Clernd
Amplitdde
Currdd
by
Volue
Clarnd
Amplitude
Cunrda
Whl
150
220
150
150
Time
Frequency
(c) Time series containing high-frequency anomalies
Time domain
Frequency domain
Volue
Charns
Amplltude
Chatrel
Volue
Charn''
Amolttde Amplitude
Cratrel
value
Charnel
Cratrel
Aay M
100
130
200
:10
157
Time
Frequency
(d) Anomalies that are not distinctly separated across different frequency bands
Figure 7: Four synthetic time series simulating scenarios with known frequency-spedn anomalies.
29


Reviews:
[{"review_id": "wPZrgAJIE1", "reviewer": "Reviewer_AEcB", "summary": "The paper proposed a method called CATCH \n for Multivariate Time Series Anomaly Detection.", "questions": "Please see above.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well structured.\n\n2. The architecture of CATCH is clearly articulated.\n\n3. Nice figures help to understand the proposed CATCH\n\n4. The proposed CATCH has been verified by extensive experiments.\n\n5. The code of the proposed method has been open, thus it has good reproducibility.", "weaknesses": "1. Figures are not self-explanatory sufficiently such as Fig. 1(b).\n2. Lack of parameter settings, resulting in weak reproducibility.\n3. Table 1 shows that the proposed method outperforms all baselines for all tested datasets. Does this mean that the proposed method can win in any dataset/application?\n4. The tested datasets are not the ones most commonly tested by the baselines. Why? Please test some datasets tested by your baselines.\n5. No guidance on choosing parameters for your proposed method?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "q6dpzkX6ZR", "reviewer": "Reviewer_wHnp", "summary": "This paper presents a new multivariate time series anomaly detection method that operates in the frequency domain. The proposed method introduces two main components: (1) a frequency patching mechanism that segments the frequency domain into bands for capturing fine-grained frequency characteristics, and (2) a channel fusion module that leverages patch-wise masking and masked attention to find relevant channel correlations. The approach is optimized using a bi-level multi-objective algorithm.", "questions": "Could you elaborate on how your frequency patching approach differs from existing frequency-domain analysis methods?", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.\tThe paper exhibits good presentation standards. Specifically, the quality of figures can reach the bar of ICLR. The visualizations effectively communicate complex concepts and experimental results.\n2.\tThe idea of frequency patch learning is novel in the field of time series anomaly detection, while I am not sure whether this idea is proposed in the domain of time series modeling.  \n3.\tThe authors released an anonymous GitHub repository, which improves reproducibility.", "weaknesses": "1. The foundational motivation of the paper needs stronger articulation. The authors primarily focus on the limitations of reconstruction-based methods, specifically their tendency to overlook details in high-frequency bands. However, several studies have already explored leveraging frequency information in MTSAD. The introduction section could benefit from a detailed comparison between current frequency-based methods and the proposed approach. A structured comparison that highlights the specific gaps addressed by CATCH would strengthen the paper’s positioning and clarify its contributions to the field. Consider including a table or a structured comparison in the introduction that clearly outlines how CATCH addresses specific gaps in existing frequency-based MTSAD methods, such as handling high-frequency information, computational efficiency, and the ability to capture channel correlations.\n2. The experimental evaluation would benefit from a broader comparison with relevant frequency-based methods. Although several approaches (e.g., SR-CNN, PFT, TFAD, and Dual-TF) are mentioned, they are notably absent from the experimental comparisons. To enhance this aspect, it would be constructive to include these specific methods in the experimental comparisons and to explain why comparing against these particular approaches is valuable for demonstrating CATCH’s contributions.\n3. The paper’s central claim regarding superior detection of frequency-specific anomalies requires more rigorous theoretical or empirical validation. While the method aims to better capture fine-grained frequency characteristics, there is no dedicated experimental design to verify this capability. To address this, consider adding specific experiments or analyses that can demonstrate superior detection of frequency-specific anomalies. For instance, you could create synthetic datasets with known frequency-specific anomalies or analyze performance across different frequency bands.\n4. The manuscript requires careful editorial revision to address. There are some typos like “results” in the abstract. Also, some citations should be updated to published versions instead of preprints.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "S3BJu79Exy", "reviewer": "Reviewer_aaEz", "summary": "This paper introduces CATCH, a Multivariate Time Series Anomaly Detection framework that enables the simultaneous detection of point and subsequence anomalies through frequency patching. By leveraging Fourier Transformation across time and frequency domains, CATCH enhances subsequence anomaly detection and utilizes the Channel Fusion Module (CFM) to adaptively exploit channel correlations. The CFM integrates a channel correlation discovery mechanism and a bi-level multi-objective optimization process to effectively isolate irrelevant channels and cluster relevant ones.", "questions": "1.\tIn line 53, the term \"heterogeneous subsequence anomalies\" is mentioned. Could you provide a specific definition for heterogeneous subsequence anomalies? How do they differ from or relate to regular time series anomalies?\n2.\tIn sections 2.2 and 2.3, in addition to discussing the current state of research, could you include some definitional descriptions? For instance, elaborating on the relationships between channels and frequency domain information in the MTSAD problem could enhance the clarity and structure of the article.\n3.\tIn section 3.1, the description of the framework structure provides technical details, but it lacks a clear explanation of the processes involved. The roles and relationships of the various modules don’t seem to connect well, which affects the logical flow. Adding descriptions of their functions and interrelations could improve the overall coherence.\n4.\tIn lines 230 to 245, where the mathematical principles of the framework are introduced, the abundance of symbols can be overwhelming. It would be clearer if each symbol were introduced upon its first occurrence, or if specific definitions were provided before delving into the mathematical principles and formulas.\n5.\tIn line 369, does the description suggest that contextual and global anomalies are considered as point anomalies in this paper? Similarly, does this apply to the subsequence types in parentheses? It seems that in the field of time series anomaly detection, anomalies are usually classified into various categories without clarifying their hierarchical relationships. This may need further investigation and explanation.\n6.\tIn Figure 5, when examining the temporal scores and frequency domain scores separately, both seem to serve as good anomaly detection metrics. Why does the paper choose to combine these two scores? Are there any examples where the temporal score performs poorly but can be compensated by the frequency domain score (or vice versa)? Such results could better illustrate the effectiveness of this anomaly scoring approach.\n7.\tThere are some typographic faults: The reference in line 185 needs to be enclosed in parentheses; in line 161, there is a spelling error, it should be \"modules\" instead of \"Moudles\"; in line 320, it would be better to align the text and the image on the same page.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper introduces CATCH, a novel framework that enhances the detection of both point and subsequence anomalies in multivariate time series through frequency domain patching. This approach creatively combines existing ideas with new methodologies, particularly through its Channel Fusion Module (CFM).\n2. The paper is clearly organized and well-written.\n3. CATCH addresses some limitations of existing methods. Its integration of frequency and time domain analysis holds promise for impactful applications in various fields.", "weaknesses": "1.\tThe paper presents modules in isolation, lacking a cohesive explanation of their interactions, which can confuse readers regarding the overall system functionality. A clearer narrative linking module interactions would enhance comprehension.\n2.\tKey operations like instance normalization and frequency domain patching are described without adequate context, leaving readers questioning their necessity. \n3.\tThe innovation behind the Channel Fusion Module (CFM) is not sufficiently highlighted, particularly regarding the necessity of the masking mechanism and its impact on detection performance.  \n4.\tThe goals and significance of the Time-Frequency Reconstruction Module (TFRM) are not clearly articulated, potentially leading to misunderstandings about its contributions. Clarifying the objectives of TFRM would enhance the reader's understanding of its role.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "y85XL2sKs5", "reviewer": "Reviewer_LbNG", "summary": "This paper centers on temporal anomaly detection and introduces an algorithm capable of capturing fine-grained frequency characteristics and channel interdependencies. The proposed method leverages frequency patches to discern subtle frequency details and employs channel fusion techniques to identify correlations among different channels. The experimental results indicate that the algorithm delivers state-of-the-art performance across various datasets.", "questions": "1. As the paper indicates, frequency characteristics exhibit long-tailed distributions, with the majority of information concentrated in the low-frequency band. Thus, what is the rationale behind the focus of this study on capturing details within the high-frequency band? In reality, as depicted in Figure 1(a), there are already significant differences between normal and anomalous data in the low-frequency band. \n2. Was point adjustment employed when assessing the algorithm's performance? \n3. Why does Table 2, presenting the multi-metric results, only illustrate performance on three datasets? It might be beneficial to include all results in the appendix for comprehensiveness.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The paper introduces innovative frequency patching techniques and a Channel Fusion Module (CFM) in\nthe field of multivariate time series anomaly detection, which can more finely capture frequency\ncharacteristics and channel correlations, marking a significant improvement over existing methods.\n\n2. The experimental findings demonstrate that the proposed methodology possesses commendable performance.", "weaknesses": "1. The methodological descriptions and accompanying figures are not entirely congruent, which poses challenges for readers. For instance, the structure on the left side of Figure 2 appears disorganized, obscuring the input data and its flow for the reader. Furthermore, the freq-score and time-score mentioned in Figure 3 lack corresponding textual or formulaic explanations in the relevant sections, thereby hindering readers' comprehension of the actual computation of the anomaly scores.\n\n2. While the CFM is an innovative feature, its complexity might be challenging for some readers to grasp.\nThe paper could provide more intuitive explanations or diagrams to help readers better understand how\nthe CFM operates.\n\n3. The experiments did not incorporate classic datasets such as ASD or SWaT.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)