Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
Authors: HyunGi Kim
Jisoo Mok
Dongjun Lee
Jaihyun Lew
Sungjae Kim
Sungroh Yoon
Venue: ICML 2025 poster (2025)
Keywords: Multivarite Time Series Anomaly Detection
Time Series
Contrastive Learning
Causality
One-class Classification
Primary area: applications->time_series
TL;DR: We introduce a novel multivariate time-series anomaly detection pipeline that incorporates the notion of causality into contrastive learning.

Abstract: Utilizing the complex inter-variable causal relationships within multivariate time-series provides a promising avenue toward more robust and reliable multivariate time-series anomaly detection (MTSAD) but remains an underexplored area of research. This paper proposes Causality-Aware contrastive learning for RObust multivariate Time-Series (CAROTS), a novel MTSAD pipeline that incorporates the notion of causality into contrastive learning. CAROTS employs two data augmentors to obtain causality-preserving and -disturbing samples that serve as a wide range of normal variations and synthetic anomalies, respectively. With causality-preserving and -disturbing samples as positives and negatives, CAROTS performs contrastive learning to train an encoder whose latent space separates normal and abnormal samples based on causality. Moreover, CAROTS introduces a similarity-filtered one-class contrastive loss that encourages the contrastive learning process to gradually incorporate more semantically diverse samples with common causal relationships. Extensive experiments on five real-world and two synthetic datasets validate that the integration of causal relationships endows CAROTS with improved MTSAD capabilities. The code is available at https://github.com/kimanki/CAROTS.

Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
HyunGi Kim
Jisoo Mok
Dongjun Lee?
Jaihyun Lew?
Sungjae Kim
Sungroh Yoon 124
Abstract
1. Introduction
Multivariate time-series anomaly detection (MTSAD) aims to identify anomalies in time-series collected across multi- ple interdependent variables (Li & Jung, 2023; Choi et al., 2021). Applications of MTSAD are far-reaching, span- ning from detecting network intrusion in cyber-physical systems (Nandanwar & Katarya, 2024) to monitoring pa- tient vitals in healthcare systems (Clifford et al., 2017; Ben- Moshe al., 2024). Since undetected anomalies can cause serious harm in mission-critical systems, MTSAD plays crucial role in ensuring their operational efficiency and security. Furthermore, as such systems continue to grow in size and complexity, with an increasing number of variables, understanding the intricate vater-variable relationships rises as a critical challenge in MTSAD (Kang & Kang, 2024).
Utilizing the complex inter-variable causal re- lationships within multivariate time-series pro- vides promising avenue toward more robust and reliable multivariate time-series anomaly de- tection (MTSAD) but remains an underexplored area of research. This paper proposes Causality- Aware contrastive learning for RObust multi- variate Time-Series (CAROTS), novel MT- SAD pipeline that incorporates the notion of causality into contrastive learning. CAROTS em- ploys two data augmentors to obtain causality- preserving and -disturbing samples that serve as a wide range of normal variations and syn- thetic anomalies, respectively. With causality- preserving and -disturbing samples as positives and negatives, CAROTS performs contrastive learning to train encoder whose latent space separates normal and abnormal samples based on causality. Moreover, CAROTS introduces a similarity-filtered one-class contrastive loss that encourages the contrastive learning process to gradually incorporate more semantically diverse samples with common causal relationships. Ex- tensive experiments on five real-world and two synthetic datasets validate that the integration of causal relationships endows CAROTS with im- proved MTSAD capabilities. The code is avail- able at https///ittubb.cm//maaaaiCCCCCa
Causality offers a structured approach capture the under- lying relationships within multivariate time-series (Runge et al., 2019). In multivariate time-series, the observed vari- ables are governed by causal relationships that dictate how changes in one variable affect others (Granger, 1969; Cheng et al., 2024b). For instance, the increase in temperature di- rectly causes the duration for which the air conditioner stays on to be longer. Once an anomaly arises, provoking an un- expected behavior from one more variables, these causal relationships break down (e.g., broken air conditioner will remain turned off regardless of the temperature). Except in the case of such an abnormal event, the inter-variable causal relationships generally remain consistent, and thus, a viola- tion of causal relationships can be used as a key indicator of anomalies (Liu et al., 2025; Febrinanto et al., 2023).
Understanding the complex inter-variable dynamics from the perspective of causality enables more reliable and robust MTSAD by allowing discernment of causality- preserving variations of normal instances (e.g., the air- conditioner staying on for longer than usual due to heat- waves) from true anomalies with broken causality. How- ever, current unsupervised MTSAD methods, such as reconstruction- or contrastive learning-based approaches, fo- cus instead on superficial differences in data values distri- butions and overlook inter-variabl, causal relationships (Dai et al., 2024; Xu et al., 2022; Kim et al., 2023). Failing to account for vaterlbariable causal relationships can lead to
'Department of Electrical and Computer Engineering, Scoul Na- tional University, Scoul, Republic of Korea 'Interdisciplinaryy Pro- gram in Artificial Intelligence, Seoul National University, Seoul, Republic of Korea 'Hyundai Motor Company, Gyeonggi-do, Re- public of Korea AIIS, ASRI, and INMC, Scoul National Univer- sity, Scoul, Republic of Korea. Correspondence to: Sungroh Yoon <sryoon @ krr
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
misidentifying normal variations as anomalies, resulting in false alarms and reduced detection accuracy.
We propose CAROTS, novel MTSAD pipeline that leverages
and -disturbing augmen- tors to induce causal-awareness in contrastive learning, The trained encoder successfully separates normal and abnormal samples based on causal relationships.
In this work, we propose a novel causality- MTSAD framework dubbed CAROTS, which is a shorthand for Causality-Awand ware contrastive learning for RObust MTSAD. CAROTS first extracts the causal relationships among nor- mal multivariate time-series by leveraging a forecasting- based causal discovery model. Afterward, it augments the training data with both prreariiigg and -disturbing samples. The former represents diversified set of nor- mal, suusality-preserving operations, while the latter sim- ulates anomalies that violate causal relationships. To ex- plicitly separate normal operations from anomalies based on the causal structure, CAROTS utilizes contrastive learn- ing, where
We propose a similarity-filteeed one-class contrastive loss, which enforces the latent space to respect diverse semantic patterns by progressively incorporating more dissimilar samples throughout training.
An extensive empirical verification of CAROTS on five real-world and two synthetic datasets highlights its outstanding ability to detect anomalies, especially those that previous baselines thoroughly struggle with.
and -disturbing samples serve as positive and negative examples, respectively. In the embedding space of this contrastively-train encoder, the causality- causality-preserving and -disturbing samples form their own clusters that are clearly distinguishable from each other.
2. Related Works
2.1. Multivariate Time-series Anomaly Detection
In addition, we introduce a similarity- -ilttree one-class con- trastive loss, which guides the contrastive learning process to gradually incorporate more semantically diverse samples that share common normal causal relationships. With each sample in a mini-batch as an anchor, the similarity filter excludes low-similarity positive samples, which fall below pre-set threshold, from the loss computation. Thus, the sim- ilarity filter only treats samples with highly similar patterns as positives in early iterations. As training progresses, pos- itive samples with more diverse patterns are incorporated, allowing the trained encoder to include a broader range of normal variations. Finally, CAROTS performs anomaly de- tection by ensembling two causality-awar anomaly scores; the distance between a test time-series and the centroid of normal, causality-preservingg embeddings obtained with the contrastively- -trained encoder and the forecasting error of the forecasting- based causal discovery model.
Reconstruction-basse methods. Reconstruction-based MTSAD methods train a reconstruction model exclusively on normal data (Wang et al., 2025; Dai et al., 2024). Anoma- lies are detected based on the reconstruction error of this model, under the assumption that they will yield higher re- construction errors. This line of research mostly focuses on utilizing advanced architectures. AnomalyTramm Transformer (Xu et al., 2022) introduces anomaly attention which models prior and series associations to distinguish normal and anomalous points. TimesNet (Wu et al., 2023) exploits TimesBlock that learns multi-scale temporal dependencies based on Fourier transform. Aside from studying architec- tural variants, USAD (Audibert et al., 2020) uses adversarial training to build more reliable reconstruction model. How- ever, the sole reliance on normal training samples limits their ability to fully consider the variability of normal operations or integrate insights related to potential anomalies.
We validate the effectiveness of CAROTS across five real- world MTSAD datasets, where it consistently outperforms existing MTSAD methods. On two synthetic datasets with explicit linear and non-linear causal relationships, CAROTS again significantly outperforms methods that over- look causal relationships. In particular, CAROTS success- fully detects even the most difficult synthetic anomalies, which other baselines all fail to identify; the remarkable improvement in AUROC up to 50% verifies that the integra- tion of causal knowledge endows CAROTS with the ability to reliably detect anomalies. We demonstrate that CAROTS is robust to changes in hyperparameters and encoder archi- tecture to showease its practical applicability. Lastly, the ablation study on each technical component of CAROTS verifies its individual contributions.
Contrastive learning- based methods. Contrastive learn- ing is a self-supervised learning approach that aims to learn latent representations of data by contrasting positive and neg- ative sample pairs (Chen al., 2020; He et al., 2020; Lee et al., 2024). Its usefulness in anomaly detection has been shown across various domains (Tack et al., 2020; Sehwag et al., 2021). In anomaly detection, contrastive learning is used to train an encoder that can distinguish normal and abnormal patterns in a self-supervised manner. The nega- tive samples in contrastive MTSAD allow the integration of simulated anomalies during the training phase, unlike in reconstruction--ant based methods (Darban et al., 2025; Kim et al., 2023). The efforts to advance contrastive MTSAD can be categorized into: data augmentation techniques (Ky et al., 2024; Choi et al., 2024), integration of one-class learn- ing (Kim et al., 2023; Xu et al., 2024), and self-supervised classification (Yang et al., 2023; Ngu & Lee, 2023).
We summarize our contributions as follows:
2

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
(a) Causal Discovery Model
(b) Causality-aware Contrastive Learning
N: Number of Variables B: Initial Batch Size
BGG * +GG
G. GII
GG IG.,IG,UGG--2B
0
Causality- Preserving
Causality- Disturbing
4B
Encoder
Augmentor
|.,=B
Augmentor
|G,==
|GUGG|-2B
Window
Window
Figure 1. An overall pipeline of CAROTS, (a) First, a causal discoverer is trained to learn the normal causal relationships in the training data. (b) Based on the causal discoverer, the causality-preserving and -disturbing augmentors construct a mini-batch of four groups of samples: original (G1),
augmentations (G2), causality-disturbing augmentations of C₁ (Ga), and causality- disturbing augmentations of C2 (Ga). Contrastive learning with the similarity- filleerdd one-class contrastive loss clusters positive groups (Gp == G1 U G2) while separating them from (Gx == G3 U G4) in the embedding space. N, B, and @ denotes the number of variables, initial batch size, and concatenation operation, respectively.
Our work sets itself apart from previous contrastive MTSAD by integrating the concept of causality into the data augmen- tation process. In contrastive MTSAD, data augmentation functions that reflect the traits of time-series are preferable for creating positive and negative examples that simulate normals and abnormal samples. In this vein, CL-TAD (Ngu & Lee, 2023) leverages encoder-decoder-basee reconstruc- tion with randomly masked inputs, while CTAD (Kim et al., 2023) offers guidelines for using general time-series aug- mentations for contrastive MTSAD. CARLA (Darban et al., 2025) introduces various types of synthetic anomalies, such as point, contextual, and collective anomalies, to improve anomaly detection. In contrast, our approach employs causality-preservvve and causality-distubinn augmentors, allowing the model to explicitly exploit causal relationships, an essential characteristic of multivariate time-series.
aging causal relationships to distinguish anomalies from normal operations in MTSAD remains underexplored (Qiu et al., 2012; Xing et al., 2023; Liu et al., 2025).
3. Preliminaries
3.1. Causal Discovery Model
A multivariate time-series is defined as a collection of time- series obtained from N variables {x*),N where N > 1. According to the Granger causality (Granger, 1969), x² causes x² if the past values of x² affect the future values of x'. In this case, x² is the cause of x² while ad is the effect of x². We denote a set of causes and effects of x' as Pa(x*) and Ch(z"), respectively. The objective of a causal discovery model is to search for Pa(x") and Ch(z*) for every x' and to learn the function 3 that maps the causal relationships between x' and Pa(æ"). Given Pa(r*) and f', the value of x² at time f, denoted as x/,, can be represented as o = (ar Pa(x))=)) where x²=, denotes the values of x¹ p.eceding t.
Ji=1.
2.2. Causal Discovery in Multivariate Time-series
Causal discovery uncovers causal relationships among in- terdependent variables in multivariate time-series (Assaad et al., 2022: Cheng et al., 2024b). The Granger causal- ity test (Granger, 1969) has been widely adopted to in- fer causal relationships by testing whether past values of one variable improve the prediction of another. Recently, deep learning approaches have been used for more robust causal discovery (Tank et al., 2021; Cheng et al., 2023; 2024a). NGC (Tank et al., 2021) infers non-linear causal relationships in multivariate time-series by combining struc- tured neural networks with sparsity-inducing regulariza- tion. CUTS (Cheng et al., 2023) jointly imputes missing data and constructs causal graphs, and CUTS+ (Cheng et al., 2024a) extends this by improving scalability for high-dimensional data with Coarse-to-fine Discovery tech- nique and Message- Passinn- based Graph Neural Network. Causalformer (Kong et al., 2024) integrates causal discovery into Transformer, learning sparse adjacency matrices to cap- ture temporal and causal relationships. Contrary to the ex- haustive efforts toward causal discovery in time-series, lever-
The forecasting brased causal discovery model F-) rep- resents the causal relationships with the causality ma- trix A E (0, N) and causal relationship functions ()))) The causality matrix A represents Pa(x') and Ch(x'), where A = 1 holds if and only if x E Pa(x"). To train F)) a single, contiguous multivariate time- series {a, [x is segmented with a sliding window with window size such that X, (#;-w+1:--- .. R=xN where 2; E E denotes the values of N variables at time t. Fo) is trained to minimize the forecasting Mean Squared Error (MSE) as follows:
Ô, Å argmin E [MSE (F 21) + 1111, 0.A X.
(I) where Xxx denotes values in X, preceding t. Fo.a()) ap- proximates {f)( that predicts o; based on the preced-
ing values Xxt and A. Our work utilizes CUTS+ (Cheng
3

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
al., 2024a), representative forecasting-basee causal dis- covery model, to extract meaningful causal structures.
CPA adds small Gaussian noise z NN o²) trigger variations in the causing variables. The modified causing variables are fed into F which predicts new values of E' according to the leared causal relationship. By replac- ing the original values of E with the predictions of (.), CPA obtains new causality-pesserving samples that maintain the original causal relationships as the following:
3.2. MTSAD through the Lens of Causality
Following the general assumption in time-series analy- sis (Absar & Zhang, 2021; Absar et al., 2023), we assume the causal relationships in normal multivariate time-series remain consistent over time (i.e., A and {.){,) are time-invariant. From the causal perspective, multivariate time-series anomalies can then be interpreted as values that deviate from the normal causal relationships:
(Xet)* +2 a'
(x2x)*
(Xet)' otherwise,
(Fo,) if E E
(3)
(xr))²
}et : f' Pa(x') 6.
(2)
x otherwise,
CPA(X,) Concat xx)=)=()))
In this study, we harness this causal interpretation of anoma- lies by integrating the notion of causality into contrastive MTSAD. By exploiting synthetic samples that either pre- serve normal, consistent causal relationships or violate them as in Eq. 2, we enable an explicitly causal-aware discrimi- nation of anomalies in MTSAD.
Causality-Ditturinng Augmentor (CDA) generates neg- ative samples with broken causal relationships. Causality- disturbing samples from CDA act as proxies for anomalies caused by disrupted causal relationships. Multivariate time- series can be represented in a directed graph, whose nodes are all variables and edges are formed according to A. Like in CPA, CDA first selects random set of causing variables C. Beginning from C, CDA performs depth-finst search (DFS) to generate multiple subgraphs as shown in Figure 2. Each iteration of DFS terminates with a cut-off probability of p. allowing subgraphs of varying sizes to be extracted. CDA perturbs the variables in the extracted subgraph by injecting random biases so that the original causal relation- ships no longer hold.
4. Methodology
We now introduce CAROTS, Causality-A ware contrastive learning for RObust MTSAD. Section 4.1 discusses how the causal relationships, extracted by a causal discoverer, are employed for causality-aware data augmentation. Sec- tion 4.2 elaborates how the causality-informee discrimi- native embedding space is obtained through contrastive learning with the proposed similarity-filter filtered one-class con- trastive loss. Lastly, Section 4.3 describes how the anoma- lies are scored based on the overall framework. Figure illustrates the overall pipeline of CAROTS.
4.2. Causality-aware Contrastive Learning with Similarity-fittered One-class Contrastive Loss
With samples from CDA and CPA, CAROTS performs con- trastive learning to train an encoder E-(-) that explicitly separates normal, causality-pesservigg samples from ab- normal, causality-disturbing samples. In the latent space of the resulting encoder, trained with causality-aware con- trastive learning, the embeddings of causality-preservinn and -disturbing samples appear far apart from each other.
4.1. Causality-aware Data Augmentation
The process in Section 3 yields causality matrix A, which encodes the causal interactions among variables, and a causality-integratee forecaster (-) that predicts future values given these causal relationships. Because unsuper- vised MTSAD assumes that training data are void of anoma- lies, the learned A and Fo, represent normal causal relationships. With A and (+), CAROTS generates causality preserving and -disturbing samples with respec- tive augmentors, visualized in Figure 2.
Given a mini-batch of B samples (G1), the CPA first gener- ates B additional ausality-presseving samples (G2). After- ward, the CDA is applied simultaneously to G1 and G2 to obtain causality- diitsliiy samples from both original and causality-preserving preserving augmented samples. As a result, CDA yields a total of 2B types of data Gj, G2. B causality disturbing samples from original samples (Gs), and B mqusalit-disttrbiin samples from causality- an augmented mini-batch B:
Causality- Preservt- Augmentor (CPA) generates pos- itive samples with intact causal relationships. Causality- preserving samples from CPA increase the diversity of nor- mal data that maintain causal relationships and simulate wide-ranging normal data not included in the training set. For a given input X,, CPA randomly selects a set of M < N causing variables C' such that C C [ C = M. Then, a set of variables directly affected by C. defined as E == (Ch(x²) x E C), is identified based on A.
samples. The four
augmented samples (G,)) form
B = Concat (fG), G2, G3, G43), |B = 4B. (4)
These four groups of data are used for positive and negative
4

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
(a-1) Fausality-Preserving Augmentor (CPA)
Noise Injection
New Predictoos
(b) Similarity -iettitd--- One-class Contrastive (SOC) Loss
Early Iterations
Later Iterations
Ratio of Unfiltered Samples
10
X7
Anchor
Positive Augmentation
Ratio
0.6
(a-2) Causality-Disturbii Augmentor (CDA)
Bias Injaction
Anchor
DFS
2000
Negalive Augmentattion
Itoration
G. G.G.
G G G:G
a= 0.5
Q== 0.7 0.9
Figure 2. (a-1) CPA adds Gaussian noise to randomly selected variables (Red) and uses the cousality-integradn forecaster predict and replace the values of affected variables (Blue). (a-2) CDA selects a random variable (Ycllow) and extracts a directed subgraph of a causality matrix through DFS. Random perturbations that unrelated causal relationships [Left] In early iterations, SOC loss filters out low-similarity positive samples (Dashed) based on a threshold a, ensuring that the loss applied only to high-similarity positive samples and their aousalityddisturren counterparts (Solid-colored). As training progresses, more diverse samples engage in the SOC loss computation. [Right] shows that a ratio of unfiltered samples steadily increases during training.
injected into the selected variables.
samples in contrastive learning as:
is formulated as follows:
Gp Gi G2
(5)
2B
1
exp(S log exp(S..) + Σ exp(St.t))
GN Cx= U4,
L =
2B
P
1=1
JEP.
KEN,
where Gp and GN denote set of positive and negative samples, respectively. Gp allows the encoder to effectively embed a wide variety of causality-presse preserving samples, in- cluding those not immediately available as part of the orig- inal training data. Gv enables the encoder to distinguish anomalies caused by disturbances in causal relationships. In particular, we note that G2 and its causality-disturbin counterparts G4 equip the encoder generalize to normal variations and anomalies that arise from them.
P. = Ej (1,2,..... .2. St.j 2 a/T),
N; = {j + +B | j P.}.
(6)
where Sr denotes cosine similarity between embeddings of i-th and j-th sample in B divided by temperature T. SOC encourages each anchor sample to be aggregated with se- mantically similar samples first, allowing the encoder to respect different semantic clusters within Gp. As positive embeddings are aggregated during training, the proportion of filtered positive samples decreases, gradually incorporat- ing more diverse samples sharing causal relationships.
In Gp, semantically diverse samples that share common causal relationships exist (e.g. the causal relationship be- tween the temperature and the air conditioner usage is pre- served, but diverse patterns are generated depending on the air conditioner setting, such as the wind strength). There- fore, Gp can be grouped into multiple clusters based the semantic similarity of individual samples. However, the naive one-class contrastive loss forces all samples in the Gp to collapse into a single cluster, which in turn prevents the encoder's is embedding space from encoding the semantic diversity of samples belonging to Gp.
4.3. Anomaly Score
CAROTS conducts anomaly detection by combining two causality-aware anomaly scores: the distance between test time-series and the centroid of normal, data embeddings obtained with the contrastively- encoder (Ac1.) and the forecasting error of the forecasting- based causal discovery model (ACd).
To address this pitfall, we introduce mauillrity-filtered One-class Contrastive Loss (SOC), whose overall scheme is illustrated in Figure 2. At each update step, SOC filters out positive samples in Gp whose similarity with an i-th anchor sample is lower than a pre-defined threshold a. Then, SOC applies the one-class contrastive loss only to the remaining positive and corresponding negative samples, whose indices are denoted P; and N,, respectively. The proposed SOC
To compute ACL, CAROTS relies on the latent space of the contrastively-trained encoder E-) from Section 4.2. Given this latent space, CAROTS obtains the centroid ptp of embeddings of all positive samples, including original data. Since the encoder is trained to cluster the embeddings of Gp closely while pushing them away from those of causality- disturbing GN. the distance between a test time-series and pe is indicative of how much the test time-series deviates
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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
from preeeeirigg positive samples. Consequently, larger Act. signifies that the corresponding test time-series is more likely to be anomalies.
et al., 2021), CSI (Tack et al., 2020), CTAD (Kim al., 2023), and CARLA (Darban al., 2025) - as strong base- lines for comparison with CAROTS. The MTSAD perfor- mance is evaluated using AUROC, AUPRC, and Fl scores.
CAROTS additionally incorporates ACD, the forecasting error of forecasting-bane -aseed causal discovery model (-) in Section 3.1, as an auxiliary anomaly score. F-) which is trained to predict future values based on learned normal causal relationships, struggles to forecast future values of abnormal samples that deviate from normal causal relationships. Therefore, the forecasting error of Fa,a (-) provides another crucial signal for causality-driven detection of anomalies following Eq. 2. Like ACL. test-time time- series with large ACD are considered to be anomalies.
Implementation details. We use 20% of the training data as validation data and apply standard normalization to the entire dataset using the mean and standard deviation of training data. We construct training, validation, and test sets using sliding window; windows containing at least one anomaly point are labeled as anomalies. Unless specified otherwise, we train models with a window size of 10 and a batch size of 256 for 30 epochs. We report the average value for each metric obtained over three random seeds. For contrastive learning- -hased models including CAROTS, we primarily employ an LSTM encoder (Hochreiter & Schmid- huber, 1997) following CTAD (Kim et al., 2023) and set the temperature parameter to 0. The threshold for similarity filtering is initialized to 0.5 and linearly increased to 0.9.
To ensemble the two scores, CAROTS normalizes each score to match the scales. Specifically, we calculate the mean and standard deviation of each score over the training data and apply z-normalization. The final anomaly score is obtained by summing the two z-scores as the following:
A(X,) = Aparm (X,)
morm X)):
5.2. Results on Real-world Datasets
Ac (X.) = D (E Xx),, pP):
The results in Table 1 showcase the effectiveness of CAROTS and CAROTS (without AcD) across various real- world MTSAD datasets. CAROTS consistently achieves the highest detection scores in nearly all metrics and datasets, while CAROTST comes in a close second. Both CAROTS and CAROTS surpassing other baselines underscore that Act. from causality- contrastive learning is robust MTSAD score. For instance, CAROTS already outper- forms other baselines on the particularly challenging WADI and MSL.P-15 datasets, highlighting that it is capable of identifying anomalies in complex environments. Yet, the slight superiority of CAROTS to CAROTS implies that ACD makes CAROTS even more robust. Notably, in SWaT, CAROTS, with an AUROC of 0.852, AUPRC of 0.764, and Fl score of 0.791, outperforms all competitors. We report full results including standard deviations in the Appendix.
AcD(X) (X.) = MSE (Fo (X))), x)),
where Apamm and Anorm denote the z-normalized Aci. and ACD. respectively, and D denotes distance function.
5. Experiments
5.1. Experimental Setup
Datasets. We demonstrate the effectiveness of CAROTS on five widely used real-world MTSAD datasets SWaT (Goh al., 2016), WADI (Ahmed et al., 2017), PSM (Abdu- laal et al., 2021), SMD (Su et al., 2019), and MSL (Hund- man et al., 2018)- and two synthetic datasets VAR and Lorenz96 (Karimi& & Paul, 2010). The real-world datasets are characterized by the intricate causal relationships among variables, which are critical for understanding and detecting anomalies. For example, in SWaT and WADI, the behavior of actuators, such as pumps and valves, is directly influ- enced by sensor readings such flow rates and water levels. The two synthetic datasets are generated based on explicit linear and non-linear causal relationships. Following the approach of Lai et al. (2021), test sets for these datasets are constructed by injecting four different types of synthetic anomalies, enabling evaluation of the model performance under diverse anomaly scenarios and difficulties. Detailed descriptions of each dataset are provided in the Appendix.
5.3. Results on Synthetic Datasets
In Table 2, We compare CAROTS against various models on Loren996 and VAR, synthetically designed to exhibit clear causal relationships. These datasets provide a controlled environment to evaluate how effectively models leverage causal relationships for MTSAD. On the Lorenz96 dataset, CAROTS excels detecting Point Global (PG) and Point Contextual (PC) anomalies, achieving AUROC scores of 0.998 and 0.975, respectively, significantly outperforming all other models. It also achieves the highest AUROC for Collective Global (CG) anomalies, highlighting its ability to capture both local and global causal relationships. On the VAR dataset, CAROTS is particularly effective at detecting Point Contextual (PC) and Collective Global (CG) anoma- lies with AUROC scores of 0.648 and 0.997, respectively.
Baselines and evaluation metries. We select three rep- models Anomaly Trans- former (Xu et al., 2022), TimesNet (Wu et al., 2023), and USAD (Audibert et al., 2020)- and five contrastive learning- based models SimCLR (Chen al., 2020), SSD (Sehwag
resentative reconstruction-bast
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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
Table Evaluation on widely-used real-works MTSAD datasets. AT and TN denote ChomalyTransfonne and TimsNet, respectively. CAROTS' refers to the CAROTS without ensemble scoring, which only employs contrastive learning learning-based anomaly score.
Dataset
Metric
AT
TN
USAD
SimCLR
SSD
CSI
CTAD
CARLA | CAROTS
CAROTS'
AUROC
0.501
0.808
0.812
0,528
0.486
0.540
0.820
0.807
0.852
0.861
SWaT
AUPRC
0.477
0.713
0.720
0.136
0.264
0.146
0.702
0.691
0.764
0.760
F1
0.222
0.762
0.755
0.289
0.394
0.297
0.755
0.742
0.791
0.789
AUROC
0,430
0.493
0.493
0.519
0.471
0.512
0.599
0.533
0.502
0.622
WADI
AUPRC
0.045
0,055
0,054
0.106
0.246
0.297
0.327
0.103
0.056
0.260
F1
0.116
0.140
0.133
0.183
0.130
0.141
0.374
0.175
0.143
0.391
AUROC
0.500
0.742
0.694
0.766
0.689
0.695
0.708
0.445
0.783
0.729
PSM
AUPRC
0.642
0.547
0.538
0.593
0.514
0,511
0.527
0.257
0.595
0,535
F1
0.443
0.589
0,506
0.554
0.498
0.498
0.515
0.444
0.603
0.534
AUROC
0,503
0.702
0.707
0.655
0.602
0.662
0.744
0.546
0.703
0.726
SMD.2-1
AUPRC
0.530
0.321
0.349
0.227
0.184
0.231
0.229
0.156
0.184
0.193
F1
0.103
0.353
0.390
0.240
0.207
0.242
0.254
0.202
0.260
0.299
AUROC
0.584
0.767
0.727
0.642
0.640
0.664
0.659
0.483
0.769
0.779
SMD_3-7
AUPRC
0.225
0.340
0.300
0.101
0.044
0.251
0.120
0.171
0.430
0.392
F1
0.190
0,436
0.380
0.197
0.093
0.329
0.193
0.254
0.564
0,542
AUROC
0.484
0.734
0.734
0.398
0.469
0.496
0.761
0.712
0.764
0.782
MSL.P-14
AUPRC
0.042
0.309
0.309
0,072
0.076
0.064
0.303
0.521
0.372
0,449
F1
0.064
0,502
0,502
0.182
0.115
0.104
0,406
0.639
0.545
0,599
AUROC
0.500
0.572
0.580
0.504
0.527
0.537
0.641
0.572
0.701
0.683
MSL P-15
AUPRC
0.339
0.017
0.016
0.014
0.014
0.015
0.018
0.150
0.022
0.019
Fl
0.021
0.072
0.070
0.053
0.053
0.072
0.067
0.272
0.087
0.079
Point Global
Point Contextual
Collective Trend
Similarly, CAROTS shows consistent performance across varying batch sizes, with optimal results observed in the range of B 256 to B 512. The stability across these hyperparameters implies that CAROTS can be practically and reliably applied in real-world scenarios.
AUROC 1.0
0.5
1.0
2.0
A
3.0
4.0
1.0
2.0
A
3.0
4.0
1.0
2.0
A
3.0
4.0
A Ablation studies. Table 4 studies the effect of key technical components in CAROTS. Without CPA. AUPRC noticeably drops from 0.764 to 0.721 and the F1 score declines from 0.792 0.775, which implies that observing augmented normal variations during training was crucial in CAROTS. Similarly, the absence of SOC results in a significant de- crease in AUROC from 0.852 to 0.819 and F1 score from 0.792 to 0.769. The contrastive learning-base bbsed anomaly score (Acr.) is shown to play an essential role as the pri- mary anomaly score, as its exclusion leads one of the largest performance drops, reducing AUROC from 0.852 to 0.814. When CDA is removed, all variables are selected for perturbation without performing DFS, and the results indicate that CDA, along with ensemble scoring, contributes to additional robustness. The contrastive learning- based anomaly score (Ac1.) is also essential, as excluding leads to one of the largest performance drops, reducing AUROC from 0.852 to 0.814.
Anomaly Transformer - USAD -a- SSD -0- CTAD
TimesNet + SimCLR + CSI - CAROTS
Figure 3. Anomaly detection performance measured by AUROC across different anomaly types in the Loren296 dataset, evaluated based on anomaly difficulty levels controlled by the factor A.
Figure 3 shows the MTSAD performance for three anomaly types in the Lorenz96 dataset across four difficulty levels. determines the difficulty of synthetic anomalies, where a smaller λ corresponds injecting more challenging anoma- lies. We highlight that CAROTS demonstrates successful dtection capability even for the most difficult anomalies (A=1.0), where other methods struggle.
5.4. Analysis of CAROTS
Robustness to hyperparameters. Table 3 analyzes the robustness of CAROTS to variations in the temperature hyperparameter (T) and batch size (B), both critical in contrastive learning. CAROTS shows stable performance across a wide range of 7. This suggests that CAROTS resilient to changes in how similarity scores are scaled.
Choice of encoder architecture. Table 6 presents the re- sults of CAROTS with various encoder architectures, rang- ing from representative recurrent architectures (Hochre-
7

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
Table Evaluation synthetic datasets with explicit causal relationships: Lorenz96 and VAR. We report separate and averaged AUROC
scores across four anomaly types: Point Global (PG), Point Contextual (PC), Collective Trend (CT), and Collective Global (CG).
Loren296
VAR CT
PG
PC
CT
CG
AVG.
PG
PC
CG
AVG.
AT
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.615
0.526
0.535
TimesNet
0.710
0.594
0.880
0.617
0.700
0.635
0.610
0.970
0.997
0.803
USAD
0.667
0.601
0,860
0.506
0.659
0.663
0,610
0.968
0,997
0.810
SimCLR
0.505
0.506
0,648
0.531
0.548
0.525
0.515
0.838
0.854
0.683
SSD
0,504
0.507
0.641
0.526
0,545
0,525
0.516
0.837
0.853
0.683
CSI
0,500
0.509
0.628
0.527
0,541
0.520
0.516
0.837
0.850
0.681
CTAD
0.511
0.512
0.618
0.486
0.532
0.527
0.522
0.897
0.842
0.697
CAROTS
0.998
0.975
0.874
0.788
0.909
||
0.612
0.648
0.963
0.997
0.805
Table Performance evaluation the SWaT and PSM datasets under varying temperature (7) and batch size (B). ROC and PRC represent AUROC AUPRC, respectively.
Table 5. Results how CAROTS perform under different causal discovery methods. We report the averaged AUROC for runs with three different seeds.
SWaT PRC
PSM PRC
SWaT
WADI
SMD.2-1
SMD.3-7
MSL_
ROC
F1
ROC
F1
NGC CUTS CUTS+
0.85
0.49
0.68
0.69
0.76
0.1
0.85
0.76
0.79
0.73
0.54
0.53
0.86
0.49
0.73
0.69
0.66
0.2
0.85
0.76
0.79
0.76
0.56
0.57
0.85
0.50
0.70
0.77
0.70
0.4
0.84
0.76
0.80
0.69
0.47
0.53
0.8
0.84
0.75
0.78
0.62
0.43
0.50
1.6
0.85
0.77
0.81
0.61
0.44
0.46
Table 6. Anomaly detection performance of CAROTS with differ-
B
128
0,85
0.75
0.77
0.73
0.54
0.54
ent encoder architectures on the SWaT and PSM datasets.
256
0.85
0.76
0.79
0.76
0.56
0.57
SWaT PRC
PSM PRC
512
0.86
0.78
0.80
0.74
0.55
0.54
ROC
F1
ROC
F1
1024
0.84
0.76
0.79
0.73
0.54
0.52
LSTM GRU iTransformer
0.85
0.76
0.79
0.78
0.60
0.60
0.86
0.78
0.81
0.82
0.63
0.65
0.85
0.75
0.78
0.81
0.60
0.63
Table 4. Ablation studies on the SWaT dataset, evaluating the im- pact of key components in the CAROTS framework, including CPA. CDA, similarity filtering, and score ensemble.
and CUTS+ (Cheng et al., 2024a). We find that CAROTS consistently performs well across causal discovery meth- ods, with only modest performance variation. While each method performs best different datasets (e.g., CUTS+ WADI and SMD.3-7; CUTS on SWaT and SMD.2-1; NGC on MSL. P-15), the overall performance remains ro- bust and competitive. This indicates that CAROTS does not overly depend on a particular discovery algorithm or exact causal graph structure. Instead of solely relying on the causal graph searched by causal discoverer for anomaly detection, CAROTS uses the causal graph guide for generating semantically meaningful causality poeelitt--peerrvingg disturbing augmentations for contrastive learning.
AUROC
AUPRC
F1
w/o CPA
0.850
0.721
0.775
w/o CDA
0.842
0.740
0.786
w/o similarity filtering
0.819
0.733
0.769
w/o ACL
0.814
0.722
0.769
w/o ACD
0.861
0.760
0.789
CAROTS
0.852
0.764
0.792
iter & Schmidhuber, 1997; Cho et al., 2014) to a recent Transformer-based architecture (Liu et al., 2024). While GRU achieves the highest overall performance, the differ- ence in performance from LSTM, GRU, and iTransformer is small. Such a result suggests that the strong MTSAD capa- bility of CAROTS is not contingent a specific choice of architecture, and thus, CAROTS is compatible with different temporal modeling approaches.
5.5. Qualitative Analysis with t-SNE Visualization
Figure 4 presents the t-SNE plots (Van der Maaten & Hin- ton, 2008) of learned embeddings during CAROTS training. Blue, green, and red points represent original samples, posi- tive samples from CPA, and negative samples from CDA, respectively. Prior to training, the data embeddings lie ac- cording to natural clusters based on the semantic similarity;
Choice of causal discovery model. Table 5 presents results CAROTS with different causal discovery mod- els: NGC (Tank al., 2021), CUTS (Cheng et al., 2023),
8

---

Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
Epoch
Epoch
Epoch
Validation
versity)], the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R 1B22RIA311077200
the BK21 FOUR program of the Education and the Research Program for Future ICT Pioneers, Seoul National University in 2025, Hyundai Motor Company, and a grant from Yang Young Foundation.
0022RIA577083008
Original Data
Positive Samples from CPA
Negative Samples from CDA
Figure 4. T-SNE visualizations of embeddings during training and
validation after training.
thus, they show significant overlap and appear inseparable from causal viewpoint. As training progresses, positive and negative samples begin to separate, showing that the proposed causality- contrastive learning successfully distinguishes the two. Also, the embeddings of positive samples form distinct clusters, showing that the model ef- fectively encodes information about different semantic pat- terns in the data. In final iterations, the positive samples become more integrated, focusing on shared causal rela- tionships. CPA-generated samples lie outside the original data distribution, providing diverse extrapolated information that enriches the training process and enhances the model's understanding of causal structures. The t-SNE plot from validation data again shows a clear separation positive and negative samples, confirming the encoder's ability to extend causality- aware discrimination unseen data.
Impact Statement
Effective anomaly detection in multivariate time series re- quires an understanding of the causal relationships among variables, as anomalies often disrupt these stable inter- variable dependencies rather than simply deviating from statistical norms. CAROTS pioneers a causality-aware con- trastive learning framework that leverages both causality- preserving and cousality-disturbin augmentations to better differentiate normal variations from true anomalies. This approach highlights the growing importance of causality in time-serics analysis and offers a promising direction for further research such as extending to dynamic causal structures, integrating latent confounders, or adapting to non-stationary aavitonmenns-paving the way toward more robust and reliable anomaly detection systems.
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Causality-Aware Contrastive Learning for Robust Multivariate Time-Serics Anomaly Detection
A. Dataset Description
A.1. Real-world Datasets
The datasets SWaT (Goh et al., 2016), WADI (Ahmed et al., 2017), PSM (Abdulaal ct al., 2021), MSL (Hundman et al., 2018), and SMD (Su al., 2019) are widely used time series anomaly detection research, each tailored specific domains such industrial control systems, equipment maintenance, and environmental monitoring. These datasets provide labeled multivariate time series data and designed test the effectiveness of anomaly detection methods under real-world conditions. Their diverse domains and unique characteristics make them valuable resources for developing and benchmarking -fate-of-the-art art algorithms.
The Secure Water Treatment (SWa')) dataset, developed by iTrrust at the Singapore University of Technology and Design, simulates six-stage water treatment process within an industrial control system (ICS). consists of time series data collected from sensors and actuators, featuring both normal and attack data, where attacks simulate intentional anomalies introduced to disrupt the system. The multivariate nature of the dataset, combined with its complex censor-actuaton relationships, makes it benchmark for ICS anomaly detection. Similarly, the Water Distribution (WADI) dataset, also created by iTruut, extends the scope to urban water distribution systems. It provides larger and more complex simulation of long-term water network operations, capturing anomalies within a broader and more intricate system compared to SWaT.
The Proactive System Maintenance (PSM) dataset focuses on anomaly detection in industrial equipment maintenance. Derived from real-world industrial systems, this dataset contains multivariate time series data from various sensors monitoring equipment states and processes. PSM emphasizes fault detection and proactive maintenance, where anomalies represent potential equipment failures. The strong interdependencies among sensors this dataset make it particularly useful for testing models that require context-awas anomaly detection.
In the domain of space exploration, the Mars Science Laboratory (MSL) dataset is derived from telemetry data collected by NASA's Curiosity Rover. It contains labeled normal and anomalous data based on real incidents recorded during the rover's 's operations. The dataset includes multivariate time series data from various sensors, reflecting the complexity and interconnectivity of space exploration systems.
Finally, the Server Machine Dataset (SMD) represents time series data from large-scale server systems. It includes measurements from server components such as CPU, memory, and disk, along with labeled normal and anomalous states. SMD is particularly relevant for IT infrastructure and server monitoring, it simulates realistic operational anomalies in server clusters.
Table Summary of dataset characteristics, including the number of variables, training and test sequence lengths, anomaly ratio, and stationarity assessment using Augmented Dickey-Fulle (ADF) test statistics.
Dataset
Variables
Train Steps
Test Steps
Anomaly Ratio
ADF Statistics
p-value
SWaT
51
495,000
449,919
0.121
-0.780
0.83
WADI
123
784,537
172,801
0.058
-0.347
0.92
PSM
25
132,481
87,841
0.278
-3.493
0.01
SMD 2-1
38
23,693
23,694
0.049
-13.649
0.00
SMD 3-7
38
28,705
28,705
0.015
0.128
0.97
P-14
55
2,880
6,100
0.030
-1.228
0.66
MSL.P-15
55
3,682
2,856
0.007
-0.621
0.87
Table summarizes the key characteristics of the datasets used in our experiments. The datasets vary in the number of variables, the length of training and test sequences, and the proportion of anomalies. The anomaly ratio represents the fraction of anomalous data points in the test set, highlighting the imbalance in certain datasets. Additionally, report the Augmented Dickey-Fuller (ADF) test (Dickey & Fuller, 1979) statistics and corresponding p-values to assess the stationarity of each dataset, where higher p-values indicate non-stationary time-series.
For SMD and MSL, we selected subsets that exhibit stronger non-stationarity, making them more challenging for anomaly detection. These subsets better reflect real- world scenarios where complex temporal dependencies and distribution shifts pose difficulties for standard detection methods.
13

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
A.2. Synthetic Datasets
The Lorenz96 system a chaotic dynamical system widely used for modeling time-series with complex temporal dependen- cies (Karimi & Paul, 2010). Originally designed to represent simplified atmospheric dynamics, it has become benehmark for evaluating causality-awarr models, including those based on Granger causality. The system consists of N coupled variables x evolving according to the differential equation:
dxf
xat i= 1,
(x+
(8)
di
where is an external forcing parameter controlling the level of chaos. The indices follow cyclic boundary conditions such that x; oi - x = xi"; "i = =t. From a Granger causality perspective, the Loren796 system exhibits strong directional dependencies between variables. Each variable x' is influenced by its two preceding variables (x'=1 and x=-2) and its one succeeding variable (x*+1). We F 10.0 following the values in (Cheng et al., 2024a).
The VAR dataset is generated using Vector Autoregressive model. The VAR model captures linear dependencies among multiple time-serie variables by modeling each variable function of both its past values and the past values of other variables in the system. A VAR model is defined as:
Ct
Ax + Et.
(9)
where ny E N denotes the value of N variables observed at time A is coefficient matrices that define the relationships between past and current values, and p is the lag order, determining how many past time steps are considered. C₁ ~ (N0, represents a multivariate Gaussian noise. We set A, p, and following the values in (Cheng et al., 2024a).
Following the approach of Lai et al. (2021), we constructed the synthetic datasets with anomalies by injecting four types of synthetic anomalies, each designed to evaluate different aspects of anomaly detection. The following introduces how we generated each type of synthetic anomaly: Point Global (PG), Point Contectual (PC), Collective Trend (CT), and Collective Global (CG).
For Point Global (PG) anomalies, anomalous time steps were randomly selected based on predefined anomaly ratio, and affected variables were also chosen randomly. For each selected variable æ6, the global mean and global standard deviation computed as:
Hglobal
1
Σ
Tglobal
Σ
(1)
Mglobal)
(10)
The value at the anomalous time step ta was then replaced as follows:
Lt/ = Pglobal + X Oglobal,
(11)
where the factor À controls the magnitude of deviation, allowing adjustment of anomaly difficulty.
For Point Contextual (PC) anomalies, the approach was similar, but instead using global statistics, local mean and local standard deviation were computed over surrounding window of radius 5:
+
tur Σ 2r + t=ta->
Alocal
alocal
(of 1loccl)
(12)
2r
t=ta-1
The anomaly was then injected as:
to Mlecal + Glocals
(13)
ensuring that the anomaly is context-dependent rather than an absolute deviation.
For Collective Trend (CT) anomalies, values within the selected radius r = were modified by adding a linear trend with a randomly assigned slope:
x of + sign A (t (ta - -r)), E [ta r, La + r),
(14)
14

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
Table Standard deviations for evaluation widely-used real-world MTSAD datasets. AT and TN denote Anomaly Transformer and TimsNet, respectively. CAROTS' refers to the CAROTS without ensemble scoring, which only employs contrastive learning carning-based
anomaly score.
AT
TN
USAD
SimCLR
SSD
CSI
CTAD
CARLA
CAROTS
CAROTS'
SWaT
AUROC AUPRC
0.001
0,002
0,000
0.015
0.015
0.054
0.031
0.034
0.008
0,003
0.013
0.005
0.000
0.008
0.008
0.002
0.160
0.015
0.003
0.020
FI
0.000
0.002
0.000
0.000
0,000
0.014
0.075
0.022
0.008
0.009
WADI
AUROC
0.025
0.005
0.003
0.068
0.068
0.095
0.016
0.056
0.007
0.042
AUPRC
0.002
0.000
0.000
0.022
0,022
0.019
0.033
0.047
0.001
0.021
F1
0.000
0.001
0.002
0.031
0.031
0.019
0.043
0.058
0.002
0.076
PSM
AUROC
0.000
0.021
0.015
0.060
0,060
0.015
0.089
0.041
0.008
0.018
AUPRC
0.000
0.010
0.004
0.050
0.050
0.012
0.026
0.012
0.007
0,012
Fl
0.000
0.040
0.013
0.043
0.043
0.014
0.027
0.001
0.011
0.022
SMD 2-1
AUROC
0.000
0.008
0.001
0.006
0.006
0.016
0.021
0.157
0.021
0.023
AUPRC
0.000
0.007
0.001
0.017
0.017
0.023
0.050
0.078
0.016
0.018
F1
0.000
0.005
0.002
0.026
0.026
0.027
0.055
0.087
0.025
0.026
SMD.3.7
AUROC
0.036
0.006
0.001
0.006
0.006
0.044
0.004
0.075
0.011
0.045
AUPRC
0.235
0.015
0.000
0.050
0.050
0.135
0.001
0.050
0.015
0.008
Fl
0.099
0.016
0.000
0.061
0.061
0.157
0.001
0.069
0.011
0.012
MSL
AUROC
0.031
0.000
0.000
0.204
0.204
0.294
0.195
0.165
0.000
0.028
AUPRC
0.008
0.000
0.000
0.010
0.010
0.226
0.229
0.154
0.000
0.030
F1
0.005
0.000
0.000
0.030
0.030
0.295
0.274
0.113
0.000
0.051
MSL.P-15
AUROC
0.000
0.001
0.000
0.077
0.077
0.055
0.048
0.117
0.008
0.012
AUPRC
0.289
0.000
0.000
0.007
0.007
0.005
0.004
0.115
0.001
0.002
F1
0.000
0.001
0.000
0.038
0.038
0.037
0.024
0.136
0.004
0.013
where sign is randomly chosen as +1 or -1 ensuring that the trend can either increase or decrease, introducing deviations from the expected behavior.
For Collective Global (CG) anomalies, values within predefined radius r 5 around the selected time step were replaced using a square sine wave, defined as:
= Σ + A sin (2 1)t), E [ta r, + r].
(15)
where A and f control the amplitude and frequency of the anomaly. We used A = 1.5, / - = 0.04, L = following (Lai et al., 2021). As with other anomaly types, only a subset of variables was affected.
In this experiment, synthetic datasets were generated with N 128 and a total length of 40,000 time steps, which were split into 16,000, 4,000, and 20,000 steps for the train, validation, and test sets, respectively. Following the unsupervised time-series anomaly detection setting, synthetic anomalies were injected only into the test set, with anomaly ratio of 0.01. Among the 128 variables, 10 were randomly selected, and anomalies were introduced only into these variables. The factor A was set to 2.0 by default for all anomaly types except Collective Global (CG), which does not require a factor.
B. Additional Implementation Details
Baselines. We re-implement all baseline methods for a fair comparison. For the contrastive learning- based baselines, we follow the augmentation strategies of (Kim et al., 2023).
cuusality-reesevving augmentation. For (M- = 1). Gaussian noise with standard deviation of 0.2 is applied at the last time step of X to maintain stability.
augmentation, we randomly select a single causing variable
Causality augmentation. Perturbations were introduced by adding a random bias to increase anomaly diversity and difficulty. The bias was randomly chosen from (-0.5, -0.4, -0.3, -0.2, -0.1, 0.1, 0.2, 0.3, 0.4, 0.5). creating anomalies ranging from easy to hard. To enhance augmentation diversity, perturbations were applied to 50% of randomly selected time
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Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection
Table Anomaly detection performance on the SWaT dataset for various values of the similarity filtering threshold o, with and without scheduling. In the scheduled setting, is linearly increased to 0.9 over epochs.
a scheduling
a
AUROC
AUPRC
F1
-1.0
0.820
0.733
0.770
no
-0.5
0.820
0.734
0.766
no 0.0
0.828
0.744
0.786
no 0.5
0.857
0.761
0.778
no
0.75
0.855
0.778
0.801
yes
-1.0
0.820
0.736
0.773
yes
-0.5
0.825
0.743
0.784
yes 0.0
0.845
0.759
0.779
yes
0.5
0.852
0.764
0.791
yes 0.75
0.845
0.767
0.799
steps per variable. To enhance the diversity of the extracted subgraph, a cut-off probability p of 0.1.
Model optimization and evaluation. Each model optimized using Adam optimizer (Kingma & Ba, 2015). We applied gradient clipping (Pascanu al., 2013) with maximum norm of 1.0 for training stability. The learning rate followed cosine learning rate scheduling (Loshchilov & Hutter, 2017) with warm up, starting at 0.0001 and increasing linearly over 5 epochs as a warm-up phase. A hyperparameter search was conducted over the learning rate in {0.001, 0.0003, 0.0001} and weight decay in {0.001, 0.0001, 0.0}. The model with the lowest validation loss was selected for evaluation. Training was performed on a single NVIDIA A40 GPU. Following standard evaluation protocols, we reported the best Fl-score. We excluded the point-adjusted F1 (Xu al., 2018), which considers a segment as detected if any anomaly point within identified. This is because the point-adjusted Fl overestimates anomaly detection performance (Kim et al., 2022), and robust detector should be capable of identifying arbitrary anomaly point effectively. For computational efficiency, the SWaT and WADI datasets were downsampled by factor of 5. In Lorenz96 and VAR, the window sizes were set to 2 and 4 following (Cheng et al., 2024a), respectively. L2 distance was used for anomaly scoring of ACL, except for WADI and VAR, where cosine distance provided better performance.
C. Additional Experimental Results
Standard deviations. Table 8 shows the standard deviations for experiments presented in Table 1, which is averaged for three random seeds.
Effectiveness of similarity filtering. Table 9 presents anomaly detection performance on the SWaT dataset across different values of the similarity filtering threshold a and examines the impact of a scheduling. In the non-scheduled setting, a is fixed throughout training, while in the scheduled setting, a is linearly increased up to 0.9 over epochs. The results indicate that increasing a generally improves AUROC and AUPRC, suggesting that a more relaxed similarity filtering threshold enhances anomaly detection.
Applying scheduling consistently leads to better performance, particularly in AUPRC and Fl score, highlighting its role in improving model robustness. The performance gains are more pronounced at intermediate a values, where scheduling stabilizes results and enhances the model's ability to distinguish anomalies. Overall, a moderate similarity filtering threshold combined with progressive a scheduling yields the best results. This underscores the importance of adaptively tuning a over training to balance anomaly separation and representation diversity.
Extended ablation studies. Table 10 shows the extended ablation studies of Table 4 on 7 real-world datasets and synthetic datasets, validating the effectiveness of each component of CAROTS. Table 11 presents the performance across different values of in CPA. Performance remains stable across different o's. s. indicating that the generated samples do not degrade model quality, even with higher noise levels. These results suggest that CPA is robust to the choice of a within reasonable range.
Causal relationships over time. CAROTS assumes that causal relationships among variables remain consistent over time, following existing literature on causal discovery (Tank et al., 2021; Cheng et al., 2023; 2024a). To empirically assess whether
16

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Serics Anomaly Detection
Table 10. Ablation studies real-world datasets and 2 synthetic datasets. We report the averaged AUROC for runs with three different seeds, For Lorenz96 and VAR, the reported values represent the average performance across the four different synthetic anomaly types.
SWaT
WADI
PSM
SMD 2-1
SMD 337
MSL.P-14
MSL.P-15
Lorenz96
VAR
w/o CPA
0.850
0,486
0.786
0.700
0.756
0.764
0.740
0.918
0.767
w/o CDA
0.842
0.488
0.789
0.623
0.732
0.764
0.609
0.917
0.785
w/o similarity filtering
0.819
0.493
0.706
0.758
0.719
0.764
0.719
0.923
0.765
w/o AcI.
0.814
0,494
0.778
0.602
0.701
0.768
0.694
0.943
0.732
CAROTS (w/o ACD)
0.861
0.622
0.729
0.726
0.779
0.782
0.683
0.919
0.769
CAROTS
0.852
0.502
0.783
0.703
0.769
0.764
0.701
0.909
0.805
Table 11. Performance metries across different a in CPA on SWaT datasct.
AUROC
AUPRC
F1
0.850::00011
0.798=10.001 0.761
0.05
0.003
0.762++0.00
0.797=+0.004
0.1
0.852:10.008
0.764=10003
0.791=0.000
0.2
0.849110.007
0.759110.009
0.795
0.4
0.800+00002
0.762:10.007
0.792+10.001
this statement holds in our setting, we further analyze the evolution of causal structures three benchmark datasets: SWaT, WADI, and PSM. For each dataset, we split the normal training data into four disjoint, time-ordered segments (quarters I to 4), train causal discovery model each, and compute pairwise cosine similarities between the resulting graphs. As shown in Table 12, the consistently high similarity indicates that the learned causal relationships remain stable across time segments, supporting the validity of our approach.
Computational cost. We compare the training times of the evaluated anomaly detectors in Table 13. The pre-training time of the causal discovery model is excluded to ensure a fair comparison of the anomaly detector training times. Even with causal modules, CAROTS efficient due lightweight one-layer LSTM. The train time of CAROTS is comparable to baselines and cheaper than heavier models like TimesNet, indicating that leveraging causal structure can reduce reliance on deeper architectures.
Learned causality matrix. Figure 5 presents the learned causality matrix from the causal discovery model for each dataset.
D. Limitations and Future Work
CAROTS demonstrates strong performance in MTSAD by effectively leveraging causal relationships. the same time, there remain opportunities to further enhance its robustness and applicability in more complex scenarios. First, CAROTS assumes that causal relationships in normal operations remain largely time-invariant. While this assumption holds in many stable environments, real-world systems often experience gradual or abrupt causal shifts due evolving conditions or external interventions. Adapting CAROTS to dynamically capture and adjust to non-stationary causal structures would further strengthen its applicability to real-world settings. Second, CAROTS focuses on direct causal relationships but does not explicitly model confounding variables, which can introduce hidden biases. Addressing this challenge by developing mechanisms to identify and mitigate confounding effects could improve the reliability causality-aware anomaly detection. Third, exogenous variables, which influence the system externally without being directly modeled, may impact the learned causal relationships. Incorporating external contextual factors, such domain knowledge auxiliary data sources, could expand CAROTS' effectiveness in handling more complex causal interactions. Despite these challenges, CAROTS introduces novel and pioneering approach to MTSAD by integrating causal awareness into contrastive learning. To the best of our knowledge, this is the first framework to explicitly incorporate causality into contrastive MTSAD, providing a new perspective on how anomalies can be characterized through deviations from stable causal structures.
17

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Causality-Aware Contrastive Learning for Robust Multivariate Time-Serics Anomaly Detection
Table 12, Comparison of cosine similarity of causality matrix across different quarters for SWaT, WADI, and PSM datasets.
Quarters
SWaT
WADI
PSM
vsvQ2
0.911
0.965
0.955
Q1vsQ3
0.923
0.966
0.953
Q1v+Q4
0.928
0.959
0.918
Q2vsQ3
0.978
0.973
0,952
Q2vsQ4
0.978
0.964
0.898
Q3vsQ4
0.981
0.963
0.915
Table 13. Comparison of training time for different anomaly detectors on SWaT dataset.
Method
Time (min)
CAROTS
25
AnomalyTransfome Transformer
12
TimesNet
56
USAD / SimCLR / SSD
CSI CTAD
10
SWAT
WADI
PSM
22
0.1
Cause
Cause
132
Effect
Effect
120
Effect
SMD 2-1
SMD 3-7
MSL P-14 MS1_P-14
MSL P-15
Cause
43
01
39
Effect
Effect
Effect
Effect
Figure Learned causality matrix the causal discovery model for each dataset.
18


Reviews:
[{"review_id": "MT66cL4B6h", "reviewer": "Reviewer_vFwM", "summary": "The paper proposes a way to detect anomalies from multivariate time-series data using causality. The proposed method employs two data augmentors to obtain causality-preserving and causality-disturbing samples, respectively. Afterwards, regarding those samples as positive and negative samples, contrastive learning is performed to train the encoder of the abnormal detector. Experiments on five real-world and two synthetic datasets validate the effectiveness of the proposed method.\n\n## update after rebuttal\nAuthors covered most of my concerns in the rebuttal, so I will increase my rating.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank Reviewer vFwM for constructive comments. We are encouraged that the reviewer acknowledges our work's potential to impact various domain that involves multivariate time-series. We hope our response addresses your concerns. Should the reviewer have more follow-up questions, we would be happy to answer them during the discussion period.\n\n>**Extended ablation study from Table 4**\n\nThe table below presents the extended ver. of Table 4 on 7 real datasets and 2 synthetic datasets. For Lorenz96 and VAR, the reported values represent the average performance across the four different synthetic anomaly types. In summary, the extended results are generally consistent with Table 4 in the main paper.\n\n|Config|SWaT|WADI|PSM|SMD_2-1|SMD_3-7|MSL_P-14|MSL_P-15|Lorenz96|VAR|\n|-|-|-|-|-|-|-|-|-|-|\n|w/o CPA|0.850|0.486|0.786|0.700|0.756|0.764|0.740|0.918|0.767|\n|w/o CDA|0.842|0.488|0.789|0.623|0.732|0.764|0.609|0.917|0.785|\n|w/o SOC|0.819|0.493|0.706|0.758|0.719|0.764|0.719|0.923|0.765|\n|w/o A_CL|0.814|0.494|0.778|0.602|0.701|0.768|0.694|0.943|0.732|\n|CAROTS† (w/o A_CD)|0.861|0.622|0.729|0.726|0.779|0.782|0.683|0.919|0.769|\n|CAROTS|0.852|0.502|0.783|0.703|0.769|0.764|0.701|0.909|0.805|\n\n- The setting without data augmentation and contrastive learning corresponds to using only A_CD, the causal forecasting-based anomaly score. This result, included in Table 4, is also included in the table above (w/o A_CL). While A_CD alone performs competitively, full CAROTS, which includes CPA, CDA, SOC, and A_CL, further improves the detection results.\n\n- Anomaly detection without both A_CL and A_CD is infeasible because, by definition, every detection method requires at least one anomaly score to score samples. Instead, in Table 4 and the extended table above, we report the results of using only one of the two scores (w/o A_CL and w/o A_CD) to demonstrate the efficacy of each score. CAROTS† (w/o A_CD) achieves the highest detection performance on 6 datasets, which highlights the effectiveness of the proposed causality-driven contrastive learning and A_CL. CAROTS, which additionally uses A_CD, further improves CAROTS† on 3 datasets, indicating that the auxiliary A_CD score offers complementary signals for anomaly detection.\n\n- Table 4 and the extended table demonstrate that CDA and CPA are more effective than conventional data augmentation methods because replacing either one with a conventional method (w/o CPA & w/o CDA)  results in a performance drop. More explanation on their effectiveness is detailed in the section below. \n\n>**Validation for the effectiveness of each module**\n\nWe hope our extended ablation study, which empirically evidences the effectiveness of each module, alleviates reviewer's concern about less theoretical validation. Below, we clarify the intuitive justification behind the design of each module.\n\n- Novel Data Augmentation (CPA + CDA)  \n  - CPA (Causality-Preserving Augmentor) generates causality-preserving variations by perturbing causing variables and using the causal forecaster to reconstruct affected variables, ensuring that augmented samples retain the normal causal behavior. This encourages the model to learn representations that belong to diverse yet causally consistent normal patterns.  \n  - CDA (Causality-Disturbing Augmentor) breaks causal relationships to synthesize anomalies. By injecting perturbations into randomly extracted subgraphs of the causal graph, CDA produces samples that simulate how real anomalies disrupt inter-variable dynamics—something conventional augmentations cannot replicate.  \n   - Compared to conventional time-series augmentation methods that rely on surface-level distortions (e.g., time warping, noise injection), CPA and CDA leverage the underlying causal structure from the train data to obtain more semantically meaningful and task-relevant augmentations. Together, augmentations from CPA and CDA enable the contrastive learning process to discriminate samples based on causal consistency rather than superficial similarity.\n\n- Novel SOC Loss guides contrastive learning to respect the semantic diversity within normal data by filtering out low-similarity positives early in training. In effect, it yields a more structured embedding space, grouped by semantic diversity.\n\n- Novel Anomaly Scores (A_CL and A_CD): Once contrastive learning with CPA, CDA, and SOC yields a causality-informed embedding space, A_CL detects anomalies by measuring how much a test sample deviates from the causality-preserving embedding space. In addition, A_CD utilizes the causal forecaster to obtain an auxiliary causality-driven signal for anomaly detection; if the causal forecaster yields a high forecasting error, the sample is more likely to be an anomaly.\n\n>**Ethics review flag**\n\nWe noticed that an ethical review flag was raised for our paper. To our understanding, our work does not involve any ethical concerns, but we would be grateful for any clarification to help us address this appropriately.", "claims_and_evidence": "- The use of two data augmentors to generate positive and negative examples of the contrastive learning. Also, applying the contrastive learning to train the encoder of the anomaly detector to achieve the causality-aware data anomaly detection. \n\n- Similarity-filtered one-class contrastive loss (SOC) is further proposed to incorporate hard samples during the training process.", "methods_and_evaluation_criteria": "- The method looks rather simple to involve two types of data augmentation methods and applying the existing contrastive learning on those datasets.\n- There seems less theoretical validation for the reasons to propose each module.", "theoretical_claims": "- There seems not much theoretical claim and analysis.", "experimental_designs_or_analyses": "- Ablation study in Table 4 should be more complete:\n\n(1) It should be conducted for more datasets (7 datasets) used for the entire experiments. It was originally conducted only for 1 dataset and the effect is hard to be captured. I think 1 more ablation study is essential for the same dataset as Table 2, to clearly see the effectiveness of the proposed method. \n\n(2) Also, I request authors to report the baseline performance without performing the data augmentation and contrastive learning. It might be useful to judge the effectiveness of the method if authors could show the baseline performance. \n\n(3) The reason for using two types of anomaly score is not yet clear since there is no comparison to \"w/o A_CL and A_CD\" that does not use both A_CL and A_CD.\n\nIn overall, I am not fully convinced about the effectiveness of each module, due to incomplete experimental settings yet.", "relation_to_broader_scientific_literature": "The paper has a potential to impact various domain that involves the multivariate time-series data.", "essential_references_not_discussed": "Reference looks rather complete.", "other_strengths_and_weaknesses": "I think the most critical weakness of the paper are on experimental settings: Experimental settings, especially the ablation studies, are not complete yet. Authors need to design experiments to validate the (1) effectiveness of each module on \"all\" multiple benchmarks that are used, (2) gap between baseline and proposed methods.\n\nAlso, there is less theoretical validation for the effectiveness of each module.", "other_comments_or_suggestions": "I think authors to better design experiments in the aspect of what I mentioned in previous sections. Also, authors could include more theoretical analysis on each module.", "questions_for_authors": "In Table 4, why other combinations such as \"w/o A_CL and A_CD\" are not considered yet?\nIs ablation study on SWaT can represent the tendency for other datasets? Why not conducted the ablation study on other dataset?\nWhat motivates authors to use both A_CL and A_CD are used in scoring the anomaly? \nHow and why CPA and CDA are more effective, compared to conventional data augmentation methods?", "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": {"ethical_review_flag": "Flag this paper for an ethics review."}}, {"review_id": "V1IRNyfhpw", "reviewer": "Reviewer_aXkV", "summary": "This paper firstly addresses the problem of Multi-variate Time-Series Anomaly Detection (MTSAD) by incorporating causality relationships. The authors propose novel data augmentation methods, CPA and CDA, which generate samples by leveraging causality learned from previous causality learning approaches. Furthermore, they suggest a novel loss term, Similarity-filtered One-class Contrastive loss, which enables the model to capture the semantic diversity. Finally, CAROTS calculates anomaly score based not only distance (A_CL) but also causality preservation (A_CD). The results demonstrate that the proposed methods outperform existing approaches and exhibit robustness across diverse datasets.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank Reviewer aXkV for helpful comments, which we believe will enrich the depth of our work. We are delighted that the reviewer commends that the proposed method is intuitively convincing, outperforms existing approaches, and exhibits robustness across diverse datasets. We tried our best to answer all of the questions during the initial response period, and we are happy to engage in further discussion during the author-reviewer discussion period. Also, the “results of using other causal discovery methods” will be updated later in the discussion period.\n\n>**Do causality relationships in normal multivariate time-series remain consistent over time?**\n\nWhile we do not assume strict stationarity, previous works in both classical [1,2] and deep learning-based causal discovery [3] has observed that causal structures often remain stable over time in real-world time-series.\n\nTo empirically assess whether this statement holds in our setting, we further analyze the evolution of causal structures in three benchmark datasets: SWaT, WADI, and PSM. For each dataset, we split the normal training data into four disjoint, time-ordered segments (Quarter 1 to 4), train a causal discovery model on each, and compute pairwise cosine similarities between the resulting graphs.\n\nCausality Matrix Consistency across Time Segments (Cosine Similarity by Dataset)\n|Quarters|SWaT|WADI|PSM|\n|-|-|-|-|\n|Q1vsQ2|0.911|0.965|0.955|\n|Q1vsQ3|0.923|0.966|0.953|\n|Q1vsQ4|0.928|0.959|0.918|\n|Q2vsQ3|0.978|0.973|0.952|\n|Q2vsQ4|0.978|0.964|0.898|\n|Q3vsQ4|0.981|0.963|0.915|\n\nThe consistently high similarity indicates that the learned causal relationships remain stable across time segments, supporting the validity of our approach.\n\n[1] Spirtes et al., Causation, Prediction, and Search, 2000.  \n[2] Peters et al., Elements of Causal Inference, 2017.  \n[3] Kong et al., CausalFormer:..., 2024.  \n\n>**Comparison with CARLA**\n\nAccording to the reviewer’s suggestion, we compare CAROTS with CARLA [4] under the same settings and datasets and report the mean ± std results over three seeds. The results below show that CAROTS outperforms CARLA on most datasets and metrics.\n\n|Dataset|Metric|CARLA|CAROTS|\n|-|-|-|-|\n|SWaT|AUROC|0.807±0.034|0.852±0.008|\n| |AUPRC|0.691±0.015|0.764±0.003|\n| |F1|0.742±0.022|0.791±0.008|\n|WADI|AUROC|0.533±0.056|0.622±0.042|\n| |AUPRC|0.103±0.047|0.260±0.021|\n| |F1|0.175±0.058|0.391±0.076|\n|PSM|AUROC|0.445±0.041|0.783±0.008|\n| |AUPRC|0.257±0.012|0.595±0.007|\n| |F1|0.444±0.001|0.603±0.011|\n|SMD_2-1|AUROC|0.546±0.157|0.726±0.023|\n| |AUPRC|0.156±0.078|0.193±0.018|\n| |F1|0.202±0.087|0.299±0.026|\n|SMD_3-7|AUROC|0.483±0.075|0.769±0.011|\n| |AUPRC|0.171±0.050|0.430±0.015|\n| |F1|0.254±0.069|0.564±0.011|\n|MSL_P-14|AUROC|0.712±0.165|0.782±0.028|\n| |AUPRC|0.521±0.154|0.449±0.030|\n| |F1|0.639±0.113|0.599±0.051|\n|MSL_P-15|AUROC|0.571±0.117|0.701±0.008|\n| |AUPRC|0.150±0.115|0.022±0.001|\n| |F1|0.272±0.136|0.087±0.004|\n\n[4] Darban et al., CARLA:..., 2025\n\n>**Ablation study on sigma**\n\nResults of ablation study on σ in CPA over a wide range (0 to 0.4) are presented below (SWaT dataset; mean ± std over 3 seeds):\n\n|σ|AUROC|AUPRC|F1|\n|-|-|-|-|\n|0   |0.850±0.001|0.761±0.002|0.798±0.001|\n|0.05|0.853±0.003|0.762±0.002|0.797±0.004|\n|0.1 |0.852±0.008|0.764±0.003|0.791±0.008|\n|0.2 |0.849±0.007|0.759±0.009|0.795±0.000|\n|0.4 |0.848±0.002|0.762±0.007|0.792±0.001|\n\nPerformance remains stable across different σ’s, indicating that the generated samples do not degrade model quality, even with higher noise levels. These results suggest that CPA is robust to the choice of σ within a reasonable range.\n\n>**Results of using other causal discovery methods**\n\nWe agree that studying the impact of different causal discovery methods is important for assessing the generality of CAROTS. We are currently running experiments with alternative causal discovery methods, and we will upload the results as soon as the experiments are completed.\n\n>**Explanation for the VAR results**\n\nCAROTS behaves differently on the VAR dataset because VAR has different characteristics from other datasets.\n\nVAR is synthetically generated using a linear autoregressive process, where all variable relationships are linear and stable over time. As a result, methods that rely on modeling correlations or co-occurrence patterns (like TimesNet or USAD) are naturally well-suited for this setting.\n\nIn contrast, CAROTS is designed to detect anomalies that disrupt more complex or directional causal relationships, especially in non-linear or dynamic systems. This is why it performs particularly well on datasets like Lorenz96 or SWaT, which reflect those properties.\n\nThat said, CAROTS still achieves strong results on VAR for certain anomaly types, such as Point Contextual and Collective Global, where detecting multi-variable inconsistency is important. We believe this suggests that CAROTS complements correlation-based approaches and is especially useful when anomalies reflect deeper structural disruptions.", "claims_and_evidence": "It is intuitively convincing that leveraging causality relationships to distinguish anomalies from normal operations. To concentrate on this, the authors propose new augmenters to enable the model to capture these relationships. However, it remains unclear how to ensure that causality relationships in normal multivariate time-series remain consistent over time. This is a critical and fundamental assumption of the proposed approach, but there is no theoretical or experimental support for it. I believe this is a major weakness of the paper and strongly recommend that the authors to provide some evidence or discussion to address this issue.", "methods_and_evaluation_criteria": "There are no issues regarding the evaluation criteria in this paper. As for the proposed method, it is sound convincing, but the authors need to provide additional evidence or justification to support their assertions.", "theoretical_claims": "There are no theoretical claims in this paper. Please check the comment in “Claims And Evidence”.", "experimental_designs_or_analyses": "Despite their extensive experiments, the paper lacks comparisons with state-of-the-art methods, such as CARLA [1]. For a fair evaluation, I strongly recommend considering more recent and relevant works. Additionally, an ablation study on sigma is required. If it is too large, the samples generated by CPA may become anomaly rather than representing normal data. Lastly, the performance of the proposed methods are highly dependent to causal discover methods. CAROTS used CUTS+, but there is no ablation or other causal discover methods. I am curious about that how vary the performance of CAROTS depends on the causal discover methods. \n\n[1] Darban, Zahra Zamanzadeh, et al. \"CARLA: Self-supervised contrastive representation learning for time series anomaly detection.\" Pattern Recognition 157 (2025): 110874.", "relation_to_broader_scientific_literature": "The key contribution of the paper is leveraging causality relationships to discriminate the normal and anomaly. Despite additional justifications are needed, the proposed approach is convincing.", "essential_references_not_discussed": "This paper cited the related works appropriately.", "other_strengths_and_weaknesses": "The figures in the paper are well structured and help a lot to understand the methods and process.", "other_comments_or_suggestions": "No other comments or suggestions.", "questions_for_authors": "In the experiments on VAR, although CARLOTS is competitive, other baselines achieve better performance. I believe this trend differs from the results on other datasets and is likely related to dataset characteristics. I request that the authors provide additional analysis on this point.", "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": "ZVUx7oLSqW", "reviewer": "Reviewer_Xmpv", "summary": "This paper proposes a new anomaly detection method called CAROTS, tailored for multivariate time-series data. Its central idea is to leverage stable causal relationships among variables discovered through a forecasting-based causal model. These discovered relationships guide two specialized data-augmentation “augmenters”: one generates variations that preserve the typical causal structures, while the other simulates anomalies by breaking them. A contrastive-learning framework is then trained to distinguish these “causality-preserving” and “causality-disturbing” samples, thereby learning a representation space where typical (standard) patterns and anomalous (disturbed) patterns are well separated. \n\nCAROTS combines two scores to detect anomalies at test time. First, it measures a sample’s distance from a centroid of “causality-preserving” training samples in the learned embedding space. Second, it computes a forecasting error with the original causal discovery model because true anomalies are more complex to predict under the learned causal relationships. Experiments on both real-world and synthetic datasets show consistently strong performance for CAROTS, emphasizing that explicitly modeling and preserving causal relationships can enhance the robustness and accuracy of anomaly detection.\n\n## update after rebuttal\nThe authors covered most of my concerns in the rebuttal, so I kept the original positive rating.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are grateful for Reviewer Xmpv’s detailed yet positive comments. Overall, the reviewer believes that “the paper’s claims are are supported by results on multiple datasets,” which “makes it suitable for real-world scenarios.” This response includes additional experiments and discussion to consolidate our contributions. We would love to answer further questions during the discussion period. Lastly, the “Interpretability analysis” will be updated later in the discussion period.\n\n>**How inaccuracies in the learned causal graph impact CAROTS**\n\nTo assess the robustness of CAROTS to inaccuracies in the causal graph, we study the performance of CAROTS on the SWaT dataset as diverse perturbations are introduced to the learned causal structure: \n- random init: causal edges randomly initialized\n- zero init: no causal edges (fully disconnected graph)\n- flipped: cause-effect directions reversed\n- noisy: Gaussian noise added to the causal matrix\n- original: learned causal structure without perturbation\n\nWe report AUROC (mean ± std over 3 seeds) below:\n\n||CAROTS|w/o CPA|w/o A_CD|w/o CPA,A_CD|\n|--|--|--|--|--|\n|random|0.841±0.004|0.833±0.002|0.844±0.004|0.833±0.004|\n|zero|0.848±0.005|0.826±0.016|0.835±0.030|0.616±0.121|\n|flip|0.831±0.009|0.836±0.004|0.836±0.010|0.836±0.004|\n|noisy|0.839±0.004|0.837±0.004|0.842±0.005|0.840±0.005|\n|orig|0.852±0.008|0.850±0.005|0.861±0.005|0.849±0.004|\n\nThese results show that CAROTS is robust under moderate graph perturbations. Notably, the combining CPA and A_CD helps preserve performance even when the causal structure is partially inaccurate. \n\n>**Results when partial anomalies are in the training set**\n\nTo evaluate the robustness of CAROTS in more realistic settings, we conduct additional experiments where synthetic anomalies are injected into the train set at varying ratios (0% to 20%). Synthetic anomalies are generated by injecting point-level global anomalies (same as the outlier generation synthesis process in the main paper).\n\nThe results below (AUROC, mean ± std over 3 seeds on SWaT) show that CAROTS maintains strong performance even when the train data is partially contaminated. \n\n|Ratio|AUROC|\n|--|--|\n|0%|0.861±0.003|\n|0.1%|0.856±0.006|\n|1%|0.845±0.002|\n|3%|0.852±0.003|\n|5%|0.848±0.006|\n|10%|0.856±0.001|\n|20%|0.847±0.001|\n\n>**Discussion of neural causal discovery works**\n\nWhile our method builds on recent causal discovery tools like CUTS+, we acknowledge that referencing earlier approaches like Neural Granger Causality [1] would help contextualize the development of CAROTS. We will revise the related work section to include and cite this line of research.\n\n[1] Tank et al., Neural Granger Causality, 2018\n\n>**Hyperparameter settings**\n\nThe dynamic similarity threshold (from 0.5 to 0.9) is not dataset-specific but follows a fixed schedule. This threshold schedule is kept constant across all datasets and does not undergo dataset-specific tuning. Likewise, other hyperparameters such as temperature are selected based on standard practices from prior contrastive learning literature [2] and kept fixed throughout all experiments.\n\n[2] Kim et al., Contrastive Time-series Anomaly Detection, 2024.\n\n>**Interpretability analysis**\n\nCAROTS is inherently interpretable, as it leverages explicitly learned causal graphs and performs anomaly detection by identifying violations of these relationships. We are currently conducting following interpretability analyses:\n\n- Forecasting-based attribution: identifying variables with high causal forecasting error and tracing them back to their parents in the graph to localize disrupted relationships.\n- CDA attribution: comparing real anomalies with synthetic ones generated via CDA to identify which causal subgraphs were likely disturbed.\n\n>**Other comments**\n\n- Tighter phrasing and broad statements: We will surely improve the writing of our paper and clarify broader statements in the revised version.  \n- “How inaccuracies in the learned causal graph impact CAROTS” presents results of incomplete causal graphs (in which CAROTS may underperform).\n\n>**Questions**\n\n- Handing Imperfect Causal Graphs: included in “How inaccuracies in the learned causal graph impact CAROTS.”\n- Similarity filter threshold: included in “Hyperparameter settings.”\n- Computational Overhead: Due to the character limit, we would greatly appreciate it if the reviewer could refer to “Computational cost of our method” section to Reviewer J2ZH.\n- Reusable Code: We fully agree that releasing code enhances reproducibility and transparency. We plan to make the implementation publicly available upon acceptance.", "claims_and_evidence": "Overall, the paper’s central claims—including that (i) incorporating causal discovery leads to more robust anomaly detection, (ii) contrastive learning can separate samples based on whether their causal structures are preserved or disrupted, and (iii) the combined distance-and-forecasting anomaly score outperforms standard baselines—are supported by results on multiple datasets (including both real-world and synthetic scenarios). Notably, the authors demonstrate that existing approaches struggle more than CAROTS on anomalies that stem from “broken” causal relationships, thereby lending convincing evidence to the core claim that integrating a causal model helps.\n\nThat said, a few points merit caution: the paper relies heavily on the assumption of correct (or near-correct) causal discovery in standard data. While the authors test different hyperparameters and show consistent performance, it would help to see explicit empirical checks on how inaccuracies in the learned causal graph impact final performance. Also, while they provide ablations (removing specific components and comparing results), the paper could explore real-world complications like partial anomalies in the “normal” training set in more detail. Still, these caveats do not significantly detract from the main results that the authors present.", "methods_and_evaluation_criteria": "The paper’s use of public, well-known benchmarks (SWaT, WADI, PSM, SMD, MSL) and synthetic datasets (VAR and Lorenz96) aligns well with the anomaly detection context, as each dataset is commonly used to test multivariate time-series methods. Likewise, the evaluation metrics (AUROC, AUPRC, and F1) are standard and appropriate for anomaly detection, capturing different aspects of precision, recall, and overall ranking performance. By showing strong results across these diverse benchmarks, the authors demonstrate that the approach is suitable for real-world scenarios and that the chosen evaluation pipeline genuinely assesses detection performance.", "theoretical_claims": "The paper does not formally present (or prove) any strong theoretical claims that typically require rigorous mathematical proofs (e.g., convergence guarantees or asymptotic optimality). Instead, the authors rely on conceptual justifications—particularly around the plausibility that “causality-preserving” vs. “causality-disturbing” samples guide a practical contrastive learning objective—and empirical evidence across multiple benchmark datasets. Hence, there were no formal proofs to check in the text, and all theoretical underpinnings (e.g., why preserving causal relationships should help anomaly detection) are primarily described at a high level rather than as fully proved theorems.", "experimental_designs_or_analyses": "The experimental design aligns with standard anomaly-detection practices:\n\n- **Data Splits**: The paper uses a regular portion of the training set for validation and then evaluates a test set containing anomalies.  \n- **Metrics**: AUROC, AUPRC, and F1 are all standard and appropriate.  \n- **Comparisons**: The authors test against reconstruction-based and contrastive-based methods, offering thorough performance comparisons.  \n- **Ablations**: They turn off individual components (causality-preserving or disturbing augmentations, similarity filtering) to highlight each element’s contribution.\n\nNo significant flaws stand out. While it assumes predominantly standard training data, this is common in unsupervised detection research. Overall, the experiment design and analyses appear valid and consistent with standard practice.", "relation_to_broader_scientific_literature": "They extend two critical lines of multivariate time-series anomaly detection research:\n\n1. **Contrastive Learning Approaches**: Similar to techniques (e.g., CSI, CTAD) that generate synthetic anomalies, they introduce “causality-preserving” and “causality-disturbing” samples, making their contrastive training explicitly reflect causal structures.  \n2. **Causal Discovery**: Previous works (e.g., CUTS+, causal formers) show that learning inter-variable causal graphs can improve forecasting. The authors directly embed such causal insights into anomaly detection, bridging causal discovery and self-supervised representation learning.", "essential_references_not_discussed": "The paper cites primary contrastive anomaly-detection methods (e.g., CSI, CTAD) and noteworthy causal-discovery tools (e.g., CUTS+). However, it could reference earlier neural causal discovery work—like Neural Granger Causality [1] —as an additional example that merges neural networks with causal inference to further illustrate the lineage of ideas leading to the proposed CAROTS framework.\n\n[1] Tank, Alex, et al. \"Neural granger causality.\" IEEE Transactions on Pattern Analysis and Machine Intelligence 44.8 (2021): 4267-4279.", "other_strengths_and_weaknesses": "**Other Strengths**  \n- **Originality**: Although each element (causal discovery, contrastive learning) has been studied, combining them into a coherent anomaly-detection pipeline is creative.  \n- **Application Potential**: The method’s strong performance on real industrial datasets (e.g., SWaT, WADI) hints at practical significance.  \n\n**Other Weaknesses**  \n- **Clarity in Hyperparameters**: The paper could further clarify how thresholds, temperature, or other tunings might generalize across domains.  \n- **Interpretability**: While causal relationships are central, it would be valuable to see deeper interpretability analyses linking detection results to specific causal graphs or disruptions.", "other_comments_or_suggestions": "- **Writing Style**: The manuscript reads overall, but some sections would benefit from tighter phrasing (e.g., focusing on the essential motivations and the underlying intuition of causal-based data augmentation).  \n- **Minor Edits**: The text occasionally uses broad statements like “overlook inter-variable causal relationships” without citations. Cite or clarify specific methods as examples.  \n- **Discussion of Negative Results**: Any cases where CAROTS fails or underperforms (e.g., if causal graphs are partially wrong) would further enrich the discussion.", "questions_for_authors": "1. **Handling Imperfect Causal Graphs**: How sensitive is CAROTS if the learned causal structure is partially incorrect or the training set contains mild anomalies? If it severely degrades performance, clarifying mitigation strategies (e.g., robust training or iterative graph refinement) would increase my confidence in real-world applicability.\n\n2. **Threshold Tuning**: The paper employs a dynamically adjusted similarity filter (0.5→0.9). Could you elaborate on how this threshold is chosen or adapted for different datasets? If there’s a systematic tuning procedure, it would clarify reproducibility and broader applicability.\n\n3. **Computational Overhead**: Generating causality-preserving/-disturbing augmentations repeatedly might be costly. Is there a significant runtime impact compared to simpler contrastive approaches, and have you explored approximate techniques to reduce cost?\n\n4. **Reusable code**: Could you consider making reproducible code publicly available to enhance the persuasiveness of the proposed method?", "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": "QKRnlQkDHr", "reviewer": "Reviewer_J2ZH", "summary": "This paper proposes a causality-aware contrastive learning method for time-series anomaly detection. Experiments on five real-world and two synthetic datasets validate that the integration of causal relationships  improve the anomaly detection capabilities.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank Reviewer J2ZH’s insightful and constructive comments. This response presents additional experiments and discussion to address the reviewer’s concerns, all of which will surely be integrated into the main paper. \n\n>**Time series anomalies can arise from various sources… discuss specific types of time series anomalies their method is designed to address and identify scenarios in which their approach might fail.**\n\nAs the reviewer notes, certain anomalies may result in anomalies while keeping the causal structure. CAROTS is designed to detect anomalies that violate inter-variable causal dependencies, including scenarios:\n\n- A variable behaves inconsistently with its known causal parents.\n- Structural dynamics deviate from the learned causal graph.\n- Temporal or multi-variable patterns break causal relationships.\n\nWe humbly acknowledge that CAROTS may be less sensitive to anomalies that lie within the causal structure; however, our method consistently demonstrates strong anomaly detection performance across a wide range of datasets, which suggests that CAROTS remains effective in practice.\n\n>**Computational cost of CAROTS**\n\nEven with causal modules, CAROTS is efficient due to a lightweight one-layer LSTM. We compare the total train time of the studied methods on SWaT:\n\nTrain Time (min):\n|Method|Time|\n|-|-|\n|CAROTS|25|\n|AnomalyTransformer|12|\n|TimesNet|56|\n|USAD / SimCLR / SSD|6|\n|CSI / CTAD|10|\n\nThe train time of CAROTS is comparable to baselines and cheaper than heavier models like TimesNet, indicating that leveraging causal structure can reduce reliance on deeper architectures.\n\nWe also profile the per-iteration time on MSL_P-14:\n\nPer-Iter Time (seconds):\n|Component|Time|Ratio|\n|-|-|-|\n|CPA|0.0382|78%|\n|CDA|0.0017|3%|\n|Loss|0.0017|3%|\n|Others|0.0072|15%|\n|Total|0.0488|100%|\n\nEach iteration takes less than 0.05 sec, and even the heaviest component (CPA) is lightweight.\n\n>**# of sensors included in the discovered causal mode/graph**\n\nDiscovered causal graphs include all sensors, even if they can include disjoint subgraphs and isolated nodes. Some sensors appear as isolated nodes, which is expected in complex systems with partially independent components.\n\nCPA and CDA ensure that every sensor is incorporated in training and synthetic outlier generation. CDA randomly selects a node and performs DFS over causal graph to extract a local subgraph. If the selected node is isolated, it forms a single-node subgraph, and bias is directly injected into its values. This allows us to synthesize abnormal behavior for all sensors, regardless of connectivity. As node selection is random and repeated, all variables have equal chances to be selected and perturbed during training.\n\nCPA similarly applies to all sensors, including isolated nodes. CPA perturbs parents of a selected variable and forecasts the target with the causal forecaster. For isolated nodes, we consider temporal self-dependence as the causal link. The node is perturbed through its past values, and forecasting is performed accordingly, enabling CPA to handle the absence of graph edges.\n\nWe also report # of non-trivial subgraphs (excluding isolated nodes) and isolated nodes in datasets:\n\n||#Vars|#Subgraphs|#Isolated Nodes|\n|-|-|-|-|\n|SWaT|51|1|13|\n|WADI|123|1|32|\n|PSM|25|1|2|\n|SMD_2-1|38|1|14|\n|SMD_3-7|38|2|12|\n|MSL_P-14|55|1|53|\n|MSL_P-15|55|1|47|\n|Lorenz96|128|1|0|\n|VAR|128|3|121|\n\nCAROTS’ strong performance even on datasets with a large # of isolated nodes and fragmented subgraphs indicates that it can handle complex graph structures and partially disconnected systems.\n\n>**More related works**\n\n- Related works will be updated to include discussion of [1, 2], a relevant early work connecting causality and anomaly detection.\n\n- Correlation vs. Causality: Correlation-based methods, such as [3, 4], model dependencies with co-activation patterns across variables. While these methods are effective at capturing immediate statistical associations, they may fail to distinguish true dependencies from spurious correlations, particularly under distribution shifts or external interventions. In contrast, CAROTS is grounded in the causal perspective. It explicitly models directional relationships by learning a causal graph from train data using a causal discovery method. This enables our method to simulate both causality-preserving and causality-breaking augmentations, which serve as the foundation for contrastive learning. Anomalies are then interpreted as deviations from learned causal relationships, making CAROTS more robust to superficial variations that do not reflect structural disruptions.\n\n[1] Yang et al., A Causal Approach to Detecting Multivariate Time-series Anomalies and Root Causes, 2022.  \n[2] Qiu et al., Granger Causality for Time-Series Anomaly Detection, 2012.  \n[3] Zheng et al., Correlation-aware Spatial-Temporal Graph Learning, 2023.  \n[4] Wang et al.,  Correlation-Based Anomaly Detection Method for Multi-sensor System, 2022.", "claims_and_evidence": "Most the claims in the paper are clear, except for the following concerns. \n\nTime series anomalies can arise from various sources, such as evolving underlying processes, external events, or sensor transmission errors. In many cases, while the time series may exhibit abnormal values, they can still adhere to the underlying causal relationships. For instance, external events might disrupt overall sensor readings and push them into abnormal ranges; however, the fundamental causal processes within the system may remain unchanged. I recommend that the authors discuss the specific types of time series anomalies their method is designed to address and identify scenarios in which their approach might fail.\n\nThe proposed method appears to be highly complex and likely computationally intensive. Considering that changes in causal relationships may not be the sole factor contributing to time series anomalies, I recommend that the author explore more practical and efficient methods for time series anomaly detection.", "methods_and_evaluation_criteria": "I recommend that the authors also report the number of sensors included in the discovered causal model/graph in the experiment. If not all sensors are included into the causal graph, how can abnormal behaviors  from sensors that fall outside the model's coverage be detected?", "theoretical_claims": "I didn't see any issues.", "experimental_designs_or_analyses": "I recommend that the authors also report the number of sensors included in the discovered causal model/graph in the experiment. If not all sensors are included into the causal graph, how can abnormal behaviors  from sensors that fall outside the model's coverage be detected?", "relation_to_broader_scientific_literature": "This work provides findings to the time series anomaly detection community.", "essential_references_not_discussed": "Some important related work are missing, such as\nhttps://arxiv.org/pdf/2206.15033\nhttps://ieeexplore.ieee.org/document/6413806", "other_strengths_and_weaknesses": "There are also studies that utilize the correlation of time series data for anomaly detection. For example, \nhttps://arxiv.org/abs/2307.08390\nhttps://onlinelibrary.wiley.com/doi/10.1155/2022/4756480\nIt is highly recommended that the authors discuss the advantages and limitations of both correlation-based and causality-based approaches for anomaly detection to provide a more comprehensive perspective.", "other_comments_or_suggestions": "No", "questions_for_authors": "Time series anomalies can arise from various sources, such as evolving underlying processes, external events, or sensor transmission errors. In many cases, while the time series may exhibit abnormal values, they can still adhere to the underlying causal relationships. For instance, external events might disrupt overall sensor readings and push them into abnormal ranges; however, the fundamental causal processes within the system may remain unchanged. I recommend that the authors discuss the specific types of time series anomalies their method is designed to address and identify scenarios in which their approach might fail.\n\nThe proposed method appears to be highly complex and likely computationally intensive. Considering that changes in causal relationships may not be the sole factor contributing to time series anomalies, I recommend that the author explore more practical and efficient methods for time series anomaly detection.\n\nI recommend that the authors also report the number of sensors included in the discovered causal model/graph in the experiment. If not all sensors are included into the causal graph, how can abnormal behaviors  from sensors that fall outside the model's coverage be detected?\n\nSome important related work are missing, such as\nhttps://arxiv.org/pdf/2206.15033\nhttps://ieeexplore.ieee.org/document/6413806\n\nThere are also studies that utilize the correlation of time series data for anomaly detection. For example, \nhttps://arxiv.org/abs/2307.08390\nhttps://onlinelibrary.wiley.com/doi/10.1155/2022/4756480\nIt is highly recommended that the authors discuss the advantages and limitations of both correlation-based and causality-based approaches for anomaly detection to provide a more comprehensive perspective.", "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:

Meta-review: [1] The paper proposes a way to detect anomalies from multivariate time-series data using causality, employing two data augmentors to obtain causality-preserving and causality-disturbing samples, respectively. Afterwards, regarding those samples as positive and negative samples, contrastive learning is performed to train the encoder of the abnormal detector. Experiments on five real-world and two synthetic datasets validate the effectiveness of the proposed method.[Reviewer vFwM, Reviewer J2ZH] 
[2] Although each element (causal discovery, contrastive learning) has been studied, combining them into a coherent anomaly-detection pipeline is creative. [Reviewer Xmpv]
[3] This paper proposes a new anomaly detection method called CAROTS, tailored for multivariate time-series data.[Reviewer Xmpv]
[4] The authors demonstrate that existing approaches struggle more than CAROTS on anomalies that stem from “broken” causal relationships, thereby lending convincing evidence to the core claim that integrating a causal model helps.[Reviewer Xmpv]


[1] 	There seems less theoretical validation for the reasons to propose each module.[Reviewer vFwM]
[2] Instead, the authors rely on conceptual justifications—particularly around the plausibility that “causality-preserving” vs. “causality-disturbing” samples guide a practical contrastive learning objective—and empirical evidence across multiple benchmark datasets. Hence, there were no formal proofs to check in the text, and all theoretical underpinnings (e.g., why preserving causal relationships should help anomaly detection) are primarily described at a high level rather than as fully proved theorems.[Reviewer Xmpv]
[3] We humbly acknowledge that CAROTS may be less sensitive to anomalies that lie within the causal structure [Authors response to Reviewer J2ZH]
Decision: Accept (poster)