Reconstruction-based detectors for multivariate time series anomaly detection typically learn a single entangled representation of normal behavior and flag anomalies based on reconstruction error. However, real-world anomalies are not only isolated spikes in a single channel but also disruptions in the relationships between channels, where each sensor individually appears normal, but their joint behavior deviates from the norm. Because these models compress both temporal evolution and inter-channel structure into this single space, they lack an explicit mechanism to isolate such inter-channel dependencies from normal temporal dependencies, leading to lower detection rates for cross-channel anomalies. We propose CARMA (Correlation-Aware Reconstruction for Multivariate Time Series Anomaly Detection), which is a reconstruction-based variational autoencoder with two complementary latent spaces: a temporal latent that captures sequential dynamics, and a correlation latent that is trained to reconstruct the window's pairwise Pearson correlations. Both representations are fused in the signal decoder, and anomalies are detected from the reconstruction error. We evaluate CARMA on the TSB-AD-M benchmark suite (17 datasets, 180 series) against 29 baseline methods, and show that it significantly outperforms all of them across multiple threshold-free and range-aware metrics, achieving a VUS-PR of 0.4929. Ablations show that removing the correlation branch degrades performance, that adding a second latent without supervision recovers only part of the gain, and that supervising the correlation latent with an explicit correlation target accounts for the rest and produces a sharper error response at anomalies.
Figures & tables
Figure 1: Top panel shows GHL sensor data with the ground truth anomaly shaded. Middle panel displays log(1+MSE) for CARMA without correlation conditioning, which misses the anomaly with spurious errors in normal regions. Bottom panel shows full CARMA achieving low reconstruction during normal segments with localized multichannel error increase at the anomalous interval.
Figure 2: Overview of CARMA. A multivariate window is encoded into temporal and correlation latents. The concatenated latents reconstruct the input series, while the correlation latent reconstructs window-level channel dependencies.
Method
AUC-PR
AUC-ROC
VUS-PR
VUS-ROC
Standard-F1
PA-F1
Event-based-F1
R-based-F1
Affiliation-F
HYDRA [ 19 ]
0.3933
0.7727
0.4409
0.8068
0.4509
0.6783
0.5669
0.4303
0.8556
StreamVAE [ 29 ]
0.3881
0.7578
0.4277
0.7740
0.4551
0.5390
0.4757
0.4162
0.8311
PaAno_PAI [ 31 ]
0.3992
0.7834
0.4049
0.8059
0.4345
0.7732
0.6109
0.3804
0.8679
USAD [ 2 ]
0.3625
0.7366
0.4026
0.7652
0.4329
0.6229
0.5189
0.4227
0.8366
TimesNet [ 40 ]
0.3375
0.6697
0.3910
0.7103
0.4115
0.6691
0.5336
0.4076
0.8476
PatchTST [ 28 ]
0.3360
0.6746
0.3902
0.7167
0.4067
0.7097
0.5355
0.3777
0.8460
Table 1: Results on the TSB-AD-M benchmark. Mean of each metric over 180 series and three seeds. The best and second-best results in each column are given in bold and underlined, respectivel. Where AT and AE refer to Anomaly Transformer and AutoEncoder, respectively.
Figure 3: Critical difference diagrams on TSB-AD-M for VUS-PR (left) and domain-specific performance (right). Models connected by a horizontal bar are not significantly different (Wilcoxon signed-rank test, 0.05). Lower average rank indicates better performance.
Method
AUC-PR
AUC-ROC
VUS-PR
VUS-ROC
Standard-F1
PA-F1
Event-based-F1
R-based-F1
Affiliation-F
StreamVAE [ 29 ]
0.9716
0.9962
0.9858
0.9982
0.9245
0.9389
0.9375
0.9213
0.9838
HYDRA [ 19 ]
0.8681
0.9382
0.8681
0.9500
0.8180
0.9200
0.9183
0.7785
0.9376
PaAno_PAI [ 31 ]
0.7336
0.9300
0.7559
0.9451
0.6797
0.9807
0.9361
0.3342
0.9358
TimesNet [ 40 ]
0.5300
0.7588
0.5510
0.7849
0.5417
0.8408
0.6504
0.5473
0.8432
USAD [ 2 ]
0.5104
0.7402
0.5322
0.7638
0.5287
0.8785
0.6003
0.4479
0.8337
CARMA (Ours)
0.9768
0.9968
0.9888
0.9986
0.9259
0.9426
0.9411
0.9329
0.9859
Table 2: Comparison with the main benchmark’s five strongest baselines on synthetic datasets.
Method
AUC-PR
AUC-ROC
VUS-PR
VUS-ROC
Standard-F1
CARMA + Pearson lag=5
0.3468 ± 0.0069
0.7985 ± 0.0023
0.4042 ± 0.0057
0.8376 ± 0.0018
0.4315 ± 0.0067
CARMA w/o zc
0.4180 ± 0.0047
0.8041 ± 0.0034
0.4620 ± 0.0032
0.8287 ± 0.0036
0.4936 ± 0.0053
CARMA w/o Lcorr
0.4243 ± 0.0060
0.8157 ± 0.0032
0.4719 ± 0.0055
0.8424 ± 0.0031
0.5033 ± 0.0084
CARMA + Spearman corr
0.4302 ± 0.0033
0.8218 ± 0.0007
0.4780 ± 0.0035
0.8488 ± 0.0006
0.5102 ± 0.0030
CARMA σt,0=1
0.4384 ± 0.0021
0.8313 ± 0.0059
0.4881 ± 0.0033
0.8575 ± 0.0066
0.5271 ± 0.0038
CARMA (Ours)
0.4425 ± 0.0009
0.8330 ± 0.0017
0.4929 ± 0.0027
0.8598 ± 0.0010
0.5301 ± 0.0032
Table 3: CARMA ablation study reported as mean ± standard deviation over seeds. The best and second-best results in each column are given in bold and underlined, respectively.
Figure 4: Paired pointwise VUS-PR on TSB-AD-M for CARMA and single latent model. Panel (a) compares scores for all 180 series, with points above the diagonal favoring the correlated model. Panel (b) shows the paired differences.
Method
AUC-PR
AUC-ROC
VUS-PR
VUS-ROC
Standard-F1
HYDRA [ 19 ]
0.3933 ± 0.3208
0.7727 ± 0.2245
0.4409 ± 0.3409
0.8068 ± 0.2144
0.4509 ± 0.3112
StreamVAE [ 29 ]
0.3881 ± 0.3539
0.7578 ± 0.2382
0.4277 ± 0.3635
0.7740 ± 0.2363
0.4551 ± 0.3367
PaAno_PAI [ 31 ]
0.3992 ± 0.3370
0.7834 ± 0.2133
0.4049 ± 0.3520
0.8059 ± 0.2070
0.4345 ± 0.3130
USAD [ 2 ]
0.3625 ± 0.3392
0.7366 ± 0.2562
0.4026 ± 0.3490
0.7652 ± 0.2459
0.4329 ± 0.3227
TimesNet [ 40 ]
0.3375 ± 0.3119
0.6697 ± 0.3028
0.3910 ± 0.3373
0.7103 ± 0.2968
0.4115 ± 0.3128
PatchTST [ 28 ]
0.3360 ± 0.3101
0.6746 ± 0.3049
0.3902 ± 0.3357
0.7167 ± 0.2992
0.4067 ± 0.3119
Table 4: Results on the TSB-AD-M benchmark. Mean ± standard deviation over all evaluated series (spread). The best and second-best results in each column are given in bold and underlined, respectively. Where AT and AE refer to Anomaly Transformer and AutoEncoder, respectively.
Method
AUC-PR
AUC-ROC
VUS-PR
VUS-ROC
Standard-F1
HYDRA [ 19 ]
0.3933 ± 0.0056
0.7727 ± 0.0029
0.4409 ± 0.0052
0.8068 ± 0.0028
0.4509 ± 0.0014
StreamVAE [ 29 ]
0.3881 ± 0.0021
0.7578 ± 0.0021
0.4277 ± 0.0023
0.7740 ± 0.0017
0.4551 ± 0.0006
PaAno_PAI [ 31 ]
0.3992 ± 0.0000
0.7834 ± 0.0002
0.4049 ± 0.0001
0.8059 ± 0.0002
0.4345 ± 0.0000
USAD [ 2 ]
0.3625 ± 0.0004
0.7366 ± 0.0016
0.4026 ± 0.0008
0.7652 ± 0.0021
0.4329 ± 0.0005
TimesNet [ 40 ]
0.3375 ± 0.0027
0.6697 ± 0.0011
0.3910 ± 0.0042
0.7103 ± 0.0012
0.4115 ± 0.0029
PatchTST [ 28 ]
0.3360 ± 0.0013
0.6746 ± 0.0002
0.3902 ± 0.0010
0.7167 ± 0.0002
0.4067 ± 0.0008
Table 5: Results on the TSB-AD-M benchmark. Mean ± standard deviation over three seeds. The best and second-best results in each column are given in bold and underlined, respectively. Where AT and AE refer to Anomaly Transformer and AutoEncoder, respectively.
Figure 5: Side-by-side comparison of CARMA and single latnet model (w/o zc ) on one TSB-AD-M series. Each column shows the raw multivariate series, the normalized input, per-channel reconstruction error as log(1 + MSE), and anomaly score. Red bands mark ground-truth anomalies. CARMA (Ours) shows a clearer score peak at the event and a higher VUS-PR (0.48 vs 0.30).
Figure 6: t-SNE visualization of latent representations for series SMD_id_10_Facility_tr_2634_1st_2734 . (a) CARMA (Ours): Panels show the per-timestep temporal latent zt , the window-level correlation latent zc , and their concatenation [zt,zc] . (b) Singel latent (w/o zc ) The per-timestep temporal latent zt obtained when the correlation branch is ablated.
Multivariate Time Series Anomaly Detection (MTSAD) is critical for real-world monitoring scenarios such as industrial control and aerospace systems. Mainstream reconstruction-based anomaly detection methods suffer from two key limitations: first, overfitting to spurious correlations induced by an overemphasis on cross-variable modeling; second, the generation of misleading anomaly scores by simply summing up multivariable reconstruction errors, which makes it difficult to distinguish between hard-to-reconstruct samples and genuine anomalies. To address these issues, we propose DBR-AF, a novel framework that integrates a dual-branch reconstruction (DBR) encoder and an autoregressive flow (AF) module. The DBR encoder decouples cross-variable correlation learning and intra-variable statistical property modeling to mitigate spurious correlations, while the AF module employs multiple stacked reversible transformations to model the complex multivariate residual distribution and further leverages density estimation to accurately identify normal samples with large reconstruction errors. Extensive experiments on seven benchmark datasets demonstrate that DBR-AF achieves state-of-the-art performance, with ablation studies validating the indispensability of its core components.
Jun Liu, Ying Chen, Ziqian Lu +2
Zhejiang University, Hangzhou, China · Zhejiang Sci-Tech University, Hangzhou, China
Reconstruction errors in multivariate time-series anomaly detection may not reliably distinguish abnormal behavior from benign deviations. Language-derived semantics offer complementary context, but existing multimodal approaches may rely on time-associated paired textual information that is difficult to obtain consistently and is not provided by standard multivariate time-series anomaly detection benchmarks. This setting poses two challenges: (1) conditioning masked reconstruction on window-specific semantics without exposing exact numerical targets or anomaly-specific cues, and (2) using a window-independent concept of normality as a complementary semantic reference rather than an independent anomaly detector. We propose LLM-Enhanced Alignment and Reconstruction with Normality Guidance for Time Series (LEARN-TS), which uses a frozen language model to construct two role-separated semantic representations without requiring temporally paired external text. Window-specific observation semantics encode temporal and cross-variable context without exact numerical values to guide channel-shared patch-masked reconstruction. A fixed, dataset-agnostic normality prompt provides a window-independent semantic reference for aligning normal representations and estimating normality discrepancy. At inference, masking each temporal patch once yields timestamp-level reconstruction evidence, conditionally modulated by discrepancy from a separate unmasked view. Across four benchmarks, LEARN-TS achieves the highest mean performance in 13 of 16 dataset-metric comparisons. Controlled ablations examine observation conditioning, joint normality alignment and scoring, and reference content, showing dataset-dependent ranking benefits and modest average gains from semantic over random references.
Jahyeob Koo, Kio Yun, Byoungmo Koo +1
Department of Industrial and Management Engineering, Korea University Seoul, Republic of Korea
Multivariate time series anomaly detection has become increasingly important in real-world applications, where labeled data are often scarce. Many existing approaches rely on unsupervised learning to model normal patterns, but they often treat all channels equally. This design can dilute anomaly-relevant signals, since not all channels contribute equally to anomaly detection. In this paper, we propose CALAD, a channel-aware contrastive learning framework for multivariate time series anomaly detection. CALAD governs the construction of contrastive samples using estimated channel relevance, allowing the learning process to reflect anomaly semantics rather than generic similarity. Channel relevance is estimated from reconstruction errors of a transformer-based autoencoder and is used to distinguish channels that are more influential to anomalous behaviors. Using this information, we design a channel-wise augmentation strategy in which positive and negative samples are constructed based on whether anomaly-relevant channels are preserved or perturbed. This encourages invariance to changes in irrelevant channels while being sensitive to changes in anomaly-relevant channels. Furthermore, CALAD combines contrastive learning and an auxiliary reconstruction head, allowing the model to learn discriminative representations while retaining normal structures. Experiments on multiple real-world datasets shows that CALAD consistently outperforms existing methods, particularly under distribution shift scenarios. We provide the code for reproducibility at https://github.com/hirundo1218/CALAD
Jaehyeop Hong, Youngbum Hur
Department of Industrial Engineering, Inha University, Incheon, Republic of Korea