LEAP: a Latent Embedding Anomaly Patch-Transformer for time-series anomaly detection

Cristhian Moya-Mota; Ignacio Aguilera-Martos; Diego García-Gil; Julián Luengo

cs.LGOct 26, 2026

LEAP: a Latent Embedding Anomaly Patch-Transformer for time-series anomaly detection

Authors: Cristhian Moya-Mota, Ignacio Aguilera-Martos, Diego García-Gil, Julián Luengo

Organizations: Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain. · Andalusian Institute of Data Science and Computational Intelligence (DaSCI), University of Granada, Granada, Spain. · Department of Software Engineering, University of Granada, Granada, Spain

Abstract

Time-series anomaly detection is dominated by reconstruction-based neural detectors, whose objective is structurally flawed. Since the target is also the input, an expressive model can learn to reconstruct anomalies too, leaving uninformative residuals. Recent large-scale benchmarks show that, on curated data, elaborate deep detectors rarely beat simple statistical baselines, while current leaders rely on representation learning. We propose LEAP (Latent Embedding Anomaly Patch-Transformer), which combines masked prediction with latent representation-based anomaly evidence, without relying on reconstruction or attention-based scoring. The model removes patches from a window and predicts them from the remaining temporal and cross-channel context, so prediction errors measure how well learned dynamics explain hidden segments. Deterministic complementary group masking ensures every time step is scored while hidden, with identical visible fractions during training and inference. LEAP adds three label-free evidence sources: latent-embedding novelty calibrated by local density, local temporal contrast, and per-channel novelty pooled over channels selected by six label-free criteria. Under the TSB-AD protocol, the full model achieves a VUS-PR of $0.5179 \pm 0.0022$ on $180$ held-out multivariate series. On TSB-AD-U, a univariate variant combining multi-scale masked-prediction scoring with latent novelty, without contrast or channel-pool novelty, achieves $0.6194 \pm 0.0016$ on $350$ held-out series. Both results average three random seeds. A five-stage ablation on TSB-AD-M, supported by paired Wilcoxon signed-rank tests, shows statistically significant gains from each successive component.

Figures & tables

Family	Best member	VUS-PR	Range	Period
Representation $+$ bank	VACE Cencillo et al. (2026)	0.48	0.42–0.48	2026
Forecasting (deep)	KAN-AD Zhou et al. (2025)	0.41	0.31–0.41	2019–2025
Reconstruction (deep)	xLSTMAD-R Faber et al. (2025)	0.37	0.19–0.37	2019–2025
Discord/matrix profile	MMPAD Yeh (2026)	0.35	—	2026
Statistical	PCA Shyu et al. (2003)	0.31	0.20–0.31	2003–2012
Transformer	TranAD Tuli et al. (2022)	0.18	0.09–0.18	2022–2023

Table 1: How the method families of Table A.1 stand on the TSB-AD-M held-out evaluation set (180 series), mean VUS-PR, aggregated from the per-detector values published in the works cited in Section 2.2.6 . Best is the strongest published member of the family, range the spread across its members, and period the publication span of those members. The per-detector ranking is deferred to Section 5.1 , where it serves as the comparison for Leap .

Figure 1: Architecture and scoring flow of Leap . Panel (a) shows a

C\times N

patch grid, complementary masks staggered across channels, the factorized encoder and masked prediction. Each patch is scored once while hidden. Panel (b) shows per-channel calibration, overlap-add aggregation and event-scale smoothing. The score then combines local moments, density-calibrated latent novelty, local contrast and per-channel novelty from a six-criterion channel pool.

Stage	Integrated Mechanism	Score	Reduction Condition
1	Masked-patch prediction $+$ local moments	Eq. ( 24 )	—
2	Latent shape novelty	Eq. ( 28 )	$\beta=0$
3	Local-density calibration of novelty	Eq. ( 30 )	$\alpha=0$
4	Local temporal contrast	Eq. ( 31 )	$\gamma=0$
5	Per-channel novelty over criterion pool	Eq. ( 35 )	$\delta=0$

Table 2: The five Leap scores and the coefficient that removes each successive mechanism for ablation. Setting

\beta=0

preserves the Stage-1 ranking after unit rescaling.

Method	Family	Published	Measured (this work)	Source
Leap (this work)	Masked $+$ repr.	—	$\mathbf{0.5179\pm 0.0022}$	this work
VACE †	Representation	0.48	—	Cencillo et al. (2026)
PaAno †	Representation	0.43	$0.4161\pm 0.0064$	Park and Kang (2026)
PaAno $+^{\dagger}$	Representation	0.42	—	Zhu et al. (2026)
PaAno PAI	Representation	—	$0.4045\pm 0.0024$	Zhang et al. (2026)
KAN-AD †	Forecasting	0.41	$0.3241\pm 0.0007$	Zhou et al. (2025)

Table 3: Mean VUS-PR on the TSB-AD-M held-out set (180 series). Published and locally measured results are reported where available; measured values are mean

\pm

sample standard deviation over three seeds. Source : reference from which the published value is taken; for rows without a published value, the reference describing the method. Daggers (

\dagger

) designate standalone published detectors outside the standard TSB-AD benchmark suite.

Figure 2: Bayesian signed-rank test comparing Leap against each of the five measured competitors of Table 3 , with a region of practical equivalence of

\pm 0.05

. Green is the posterior probability that Leap is superior, gray the probability of practical equivalence, and red the probability that the competitor is superior.

Metric	PaAno	PaAno PAI	USAD	xLSTMAD-R	TimesNet	Leap
AUC-ROC	$0.7617\pm 0.0048$	$0.7833\pm 0.0008$	$0.7365\pm 0.0005$	$0.7387\pm 0.0016$	$0.6681\pm 0.0016$	$\mathbf{0.8410\pm 0.0028}$
AUC-PR	$0.3763\pm 0.0056$	$0.3979\pm 0.0008$	$0.3617\pm 0.0008$	$0.3413\pm 0.0017$	$0.3358\pm 0.0016$	$\mathbf{0.4794\pm 0.0031}$
VUS-ROC	$0.7887\pm 0.0044$	$0.8057\pm 0.0007$	$0.7659\pm 0.0012$	$0.7773\pm 0.0007$	$0.7090\pm 0.0023$	$\mathbf{0.8535\pm 0.0036}$
VUS-PR	$0.4161\pm 0.0064$	$0.4045\pm 0.0024$	$0.4028\pm 0.0019$	$0.3881\pm 0.0011$	$0.3874\pm 0.0022$	$\mathbf{0.5179\pm 0.0022}$
Standard-F1	$0.4271\pm 0.0046$	$0.4366\pm 0.0020$	$0.4333\pm 0.0007$	$0.4221\pm 0.0007$	$0.4098\pm 0.0017$	$\mathbf{0.5427\pm 0.0017}$
PA-F1	$0.6521\pm 0.0047$	$\mathbf{0.7684\pm 0.0015}$	$0.6248\pm 0.0033$	$0.6216\pm 0.0057$	$0.6644\pm 0.0015$	$0.7290\pm 0.0020$

Table 4: Nine-metric evaluation on the TSB-AD-M held-out set (180 series) for the top five measured competitors. Values are mean

\pm

sample standard deviation over three seeds; the best value in each row is bold.

Figure 3: Per-series VUS-PR distributions on TSB-AD-M eval set for Leap and the top five measured competitors (Table 3 ), pooled across three random seeds and grouped by source dataset (restricted to

10

datasets with

\geq 5

series;

169

180

series total represented). Boxes indicate median and IQR; whiskers extend to

1.5\times\text{IQR}

, with outliers plotted individually.

Coefficient	Grid tested	Points	Deployed value	VUS-PR (deployed)	Grid optimum
$w_{\ell}$	$0$ to $2.0$	$6$	$1.0$	$0.6717$	$0.6717$ at $1.5$ ( $\Delta<0.0001$ )
$\beta$	$0$ to $2.0$	$6$	$1.0$	$0.6717$	$0.6761$ at $0$ ( $\Delta=0.0044$ )
$\alpha$	$0$ to $2.0$	$8$	$0.25$	$0.6717$	$0.7101$ at $1.0$ ( $\Delta=0.0384$ )
$\gamma$	$0$ to $3.0$	$9$	$1.5$	$0.6717$	$0.6753$ at $2.5$ ( $\Delta=0.0036$ )
$\delta$	$0$ to $3.0$	$9$	$1.5$	$0.6717$	$0.6726$ at $2.0$ ( $\Delta=0.0009$ )

Table 5: Sensitivity of the fusion coefficients on the

20

-series tuning set. Each parameter is varied independently while the remaining parameters are held at their deployed values (

w_{\ell}=\beta=1.0

\alpha=0.25

\gamma=\delta=1.5

). Values

\alpha>1

exceed the recommended range of Eq. ( 29 ) and are included only to illustrate the risk of near-zero denominators.

Figure 4: VUS-PR sensitivity to the five fusion coefficients on the

20

-series tuning set. Shaded regions denote one standard deviation across benchmark series.

Method	Family	Published	Measured (this work)	Source
Leap (this work)	Masked $+$ repr.	—	$\mathbf{0.6194\pm 0.0016}$	this work
PaAno PAI	Representation	0.58	$0.5839\pm 0.0016$	Zhang et al. (2026)
PaAno $+^{\dagger}$	Representation	0.55	—	Zhu et al. (2026)
TSPulse †	Foundation model	0.54	—	Ekambaram et al. (2026)
PaAno †	Representation	0.51–0.53	$0.5165\pm 0.0025$	Park and Kang (2026)
CrossAD †	Reconstruction	0.45	—	Li et al. (2025)

Table 6: Mean VUS-PR performance on TSB-AD-U. Published columns report published values (ranges indicate cited intervals), while Measured columns report local mean

\pm

standard deviation, with dashes denoting unavailable entries. Method Family classifications extend Table A.1 with Foundation model (TSPulse, MOMENT, TimesFM) and Shape clustering (KShapeAD). Daggers (

\dagger

) designate standalone published detectors outside the standard TSB-AD benchmark suite. Source : reference from which the published value is taken; for rows without a published value, the reference describing the method.

Figure 5: Bayesian signed-rank test comparing Leap against the top five measured univariate competitors from Table 6 .

Metric	PaAno PAI	PaAno	PatchTST	Sub-PCA	USAD	Leap
AUC-ROC	$0.9022{\pm}.0005$	$0.8663{\pm}.0005$	$0.7692{\pm}.0020$	$0.7143{\pm}.0000$	$0.7027{\pm}.0021$	$\mathbf{0.9128{\pm}.0005}$
AUC-PR	$\mathbf{0.5506{\pm}.0015}$	$0.4695{\pm}.0025$	$0.3676{\pm}.0024$	$0.3777{\pm}.0000$	$0.3631{\pm}.0013$	$0.5409{\pm}.0022$
VUS-ROC	$0.9280{\pm}.0002$	$0.8837{\pm}.0007$	$0.8235{\pm}.0004$	$0.7585{\pm}.0000$	$0.7493{\pm}.0016$	$\mathbf{0.9295{\pm}.0008}$
VUS-PR	$0.5839{\pm}.0016$	$0.5165{\pm}.0025$	$0.4569{\pm}.0025$	$0.4173{\pm}.0000$	$0.3959{\pm}.0017$	$\mathbf{0.6194{\pm}.0016}$
Standard-F1	$0.5789{\pm}.0027$	$0.5166{\pm}.0013$	$0.4330{\pm}.0025$	$0.4168{\pm}.0000$	$0.4029{\pm}.0014$	$\mathbf{0.5849{\pm}.0004}$
PA-F1	$\mathbf{0.8375{\pm}.0019}$	$0.6730{\pm}.0053$	$0.6822{\pm}.0023$	$0.5719{\pm}.0000$	$0.5431{\pm}.0019$	$0.7447{\pm}.0005$

Table 7: Nine-metric evaluation on the TSB-AD-U held-out set (350 series). Values are mean

\pm

sample standard deviation across the three seeds; Sub-PCA is deterministic and therefore has zero spread. The six methods are evaluated locally, and the best value in each row is bold.

Figure 6: Per-series VUS-PR distributions on the TSB-AD-U held-out set for Leap and the five competitors, grouped by source dataset. Results cover the fifteen datasets with at least eight series (

328

350

series); boxes show the interquartile range and median, whiskers extend to

1.5\times

the interquartile range, and points beyond the whiskers are shown individually.

Figure 7: Raw signal, ground-truth annotations, Leap ’s four score components ( $s^{(1)}$ , which fuses masked prediction and local-moment evidence; latent novelty; per-channel pooling; local contrast) and the fused final score for five representative series. Signals correspond to the continuous channel with the largest standardized mean shift between anomalous and normal regions, avoiding maximum-variance selection that can favor binary telemetry flags.

Figure 8: Two-dimensional t-SNE projection of per-window latent embeddings (Eq. ( 26 )) for 059_SMD_id_3 , showing training, normal test, and anomalous test windows.

	TSB-AD-M		TSB-AD-U
Method	Wall (s)	Infer (s)	Wall (s)	Infer (s)
PaAno	$34.6\pm 40.9$ (13.7)	$7.04\pm 9.33$ (2.83)	$16.1\pm 23.2$ (8.05)	$1.32\pm 2.79$ (0.42)
PaAno PAI	$14.5\pm 8.05$ (13.1)	$1.53\pm 3.03$ (0.89)	$13.0\pm 6.76$ (10.4)	$0.56\pm 1.19$ (0.20)
USAD	$24.6\pm 27.6$ (13.6)	$7.41\pm 7.90$ (3.81)	$9.74\pm 14.7$ (3.45)	$2.52\pm 5.40$ (0.83)
xLSTMAD-R	$3490\pm 6112$ (966)	$154\pm 169$ (66.3)	—	—
TimesNet	$55.4\pm 68.6$ (25.6)	$11.4\pm 14.3$ (5.23)	—	—

Table 8: Per-series wall-clock (fit plus scoring) and inference time in seconds, pooled over the held-out series and three seeds (

540

runs on TSB-AD-M,

1050

on TSB-AD-U). Mean

\pm

std, with the median in parentheses; the mean training time is the difference between both columns. Dashes mark methods that are not among the five strongest competitors on that track.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Family	Score mechanism	Suited to	Regime
Statistical residual	residual of a fitted model (ARIMA, ETS, STL)	point, contextual	Semi/Un
Control charts, CPD	accumulated deviation of the mean	level shift, regime change	Semi/Un
Spectral	saliency of the amplitude spectrum	point, seasonal	Un
Discord/matrix profile	distance to nearest non-trivial match	subsequence, shape	Un
Normal-pattern banks	distance to a set of normal patterns	subsequence, shape	Semi
Forecasting (deep)	prediction residual	point, contextual	Semi

Appendix

Table A.1: Families of time-series anomaly detectors, their scoring mechanism and the anomaly types they are structurally suited to. Semi denotes the semi-supervised (clean training prefix) regime, Un the unsupervised one.

Data, windowing and encoder
Symbol	Meaning
$T,\;C$	series length, number of channels
$T_{\mathrm{tr}}$	length of the anomaly-free training prefix
$x_{t}\in R^{C}$	observation at time $t$
$\tilde{x}_{t}$	globally standardized observation
$\hat{P},\;\pi_{\mathrm{per}}$	estimated dominant period, periods spanned by a window

Appendix

Table B.1: Notation used in Section 3 . Deployed values of all coefficients and widths are listed in Table E.1 .

TSB-AD-M (180 series)		TSB-AD-U (350 series)
Source	#	Source	#
SVDB	28	UCR	70
Exathlon	25	SMD	33
SMAP	25	Exathlon	30
GHL	23	YAHOO	30
SMD	20	OPPORTUNITY	27

Appendix

Table D.1: Composition of the two TSB-AD held-out evaluation sets used in this work (number of series per source dataset).

Group	Symbol	Meaning	Value
Architecture	$p$	patch length	$16$
	$D$	model width	$128$
	$H$	attention heads	$8$
	$B$	encoder blocks	$4$
	$d_{\mathrm{ff}}$	feed-forward width	$4D=512$
	dropout	—	$0.0$

Appendix

Table E.1: Hyperparameters of Leap . Adaptive entries are rules evaluated per series. The track-specific rows are the only values that differ between the multivariate and the univariate configuration; on the univariate track each score is read out at every listed width and the maximum unit-rescaled response is kept.

Stage	Model	VUS-PR	$\Delta$	W/L/T	$p$ -value
1	Masked-patch base	0.4611	—	—	—
2	$+$ Latent novelty ( $\beta{=}1.0$ )	0.4954	$+0.0343$	113/55/12	$1.2\times 10^{-5}$
3	$+$ Density calibration	0.5034	$+0.0080$	84/42/54	$9.5\times 10^{-5}$
4	$+$ Local contrast	0.5074	$+0.0040$	87/35/58	$2.8\times 10^{-6}$
5	$+$ Per-channel pool ( Leap )	0.5171	$+0.0097$	90/51/39	$3.4\times 10^{-5}$

Appendix

Table G.1: Stage-wise ablation on TSB-AD-M (180 held-out series) single seed (2024).

\Delta

denotes the mean per-series difference relative to the preceding stage; W/L/T indicates wins, losses, and ties;

p

-values correspond to two-sided Wilcoxon signed-rank tests on paired per-series VUS-PR scores.

Design Decision	Configuration Comparison	Metric	Performance
Event-scale smoothing (Eq. ( 21 ))	$W_{s}=1\rightarrow W_{s}=8p$	VUS-PR	$0.4109\rightarrow 0.5135$
Local-moment evidence (Eq. ( 23 ))	$w_{\ell}=0\rightarrow w_{\ell}>0$	VUS-PR	$0.4439\rightarrow 0.4539$
Moment combination scheme	$\max$ vs. rescaled sum	AP	$0.3528\rightarrow 0.3976$

Appendix

Table G.2: Single-variable micro-ablation of base detector design decisions on the tuning set.

Source	$n$	Leap	PaAno	PaAno PAI	USAD	xLSTMAD-R	TimesNet
SVDB	28	0.6411	0.5544	0.4583	0.4489	0.3462	0.4669
Exathlon	25	0.9907	0.7773	0.8705	0.9659	0.9454	0.8449
SMAP	25	0.5980	0.5316	0.3713	0.2657	0.2377	0.2922
GHL	23	0.1830	0.0085	0.0114	0.0130	0.0336	0.0078
SMD	20	0.3295	0.3319	0.3218	0.3959	0.3877	0.4714
MSL	14	0.3715	0.2108	0.3103	0.3058	0.3427	0.2556

Appendix

Table H.1: Mean VUS-PR by source dataset and by application domain on the TSB-AD-M held-out set (180 series), for Leap and the five measured baselines of Table 4 . Values are the three-seed per-series scores of Table 3 , pooled within each group; boldface marks the best method per row.

Source	$n$	Leap	PaAno	PaAno PAI	PatchTST	Sub-PCA	USAD
UCR	70	0.4593	0.3739	0.4017	0.2520	0.1237	0.1045
SMD	33	0.8270	0.5005	0.5327	0.8065	0.4416	0.5439
Exathlon	30	0.9626	0.8186	0.9285	0.8559	0.8920	0.9364
YAHOO	30	0.4170	0.6810	0.6968	0.2731	0.1547	0.1027
OPPORTUNITY	27	0.6304	0.2646	0.7673	0.0726	0.9139	0.7977
NAB	23	0.6446	0.4982	0.4355	0.4868	0.3947	0.4946

Appendix

Table H.2: Mean VUS-PR by source dataset and by application domain on the TSB-AD-U held-out set (350 series), for Leap and the five measured baselines of Table 7 . Values are the three-seed per-series scores of Table 6 , pooled within each group; boldface marks the best method per row.

Type	$n$	Leap	PaAno	PaAno PAI	USAD	xLSTMAD-R	TimesNet
Level shift	88	0.5662	0.4455	0.4531	0.5097	0.4875	0.4466
Subsequence/shape	34	0.5265	0.4890	0.3730	0.3197	0.2574	0.3563
Relational	16	0.3547	0.1781	0.1707	0.1419	0.2146	0.1476
Dispersion change	16	0.3426	0.2675	0.2225	0.1561	0.1619	0.1593
Mixed	14	0.4573	0.3277	0.3261	0.2746	0.2845	0.3512
Point (global)	8	0.5828	0.5217	0.7148	0.6043	0.6079	0.6315

Appendix

Table H.3: Mean VUS-PR by automatically-assigned dominant anomaly type (Appendix H ) on the TSB-AD-M held-out set, for Leap and the five measured baselines of Table 4 . Boldface marks the best method per row.

Type	$n$	Leap	PaAno	PaAno PAI	PatchTST	Sub-PCA	USAD
Level shift	115	0.8072	0.5183	0.7578	0.5954	0.7053	0.6768
Subsequence/shape	101	0.5255	0.4934	0.4102	0.4250	0.2243	0.2311
Dispersion change	68	0.5494	0.5102	0.5108	0.3323	0.3114	0.3109
Mixed	22	0.5895	0.4862	0.5796	0.4912	0.4823	0.4132
Point (global)	29	0.4455	0.6773	0.7188	0.3593	0.2403	0.1619
Point (contextual)	15	0.5083	0.4213	0.4965	0.3140	0.2347	0.1652

Appendix

Table H.4: Mean VUS-PR by automatically-assigned dominant anomaly type (Appendix H ) on the TSB-AD-U held-out set, for Leap and the five measured baselines of Table 7 . Relational anomalies do not apply to a univariate series and are absent by construction. Boldface marks the best method per row.

By number of channels
	$n$	Leap	PaAno	PaAno PAI	USAD	xLSTMAD-R	TimesNet
2–10	58	0.6089	0.5505	0.5089	0.4524	0.4028	0.4587
11–30	72	0.5182	0.3660	0.3356	0.3291	0.3333	0.3185
31–248	50	0.4121	0.3322	0.3827	0.4514	0.4499	0.4037
By series length (samples)
$\leq 10{,}000$	53	0.5424	0.4601	0.4517	0.3867	0.3812	0.3720

Appendix

Table H.5: Mean VUS-PR by series characteristics on the TSB-AD-M held-out set, for Leap and the five measured baselines of Table 4 ; boldface marks the best method per row.

By series length (samples)
	$n$	Leap	PaAno	PaAno PAI	PatchTST	Sub-PCA	USAD
$\leq 7{,}500$	88	0.5785	0.5866	0.6334	0.4839	0.3915	0.3733
$7{,}501$ – $18{,}228$	87	0.6215	0.4511	0.6430	0.3175	0.3946	0.3296
$18{,}229$ – $43{,}066$	96	0.7434	0.5540	0.6254	0.6177	0.5124	0.5459
$>43{,}066$	79	0.5119	0.4651	0.4130	0.3849	0.3553	0.3118
By anomaly ratio

Appendix

Table H.6: Mean VUS-PR by series characteristics on the TSB-AD-U held-out set, for Leap and the five measured baselines of Table 7 . Every series is univariate by construction, so the channel stratification of Table H.5 does not apply. Boldface marks the best method per row.

Component	Rule	VUS-PR	$\Delta$	Range of $\Delta$	$p$ -value	W/L/T
level_combine	add (deployed)	$0.6717$	n/a	n/a	n/a	n/a
	pmean	$0.6715$	$-0.0002$	$[-0.022,+0.019]$	$0.275$	$4/7/9$
	max	$0.6725$	$+0.0008$	$[-0.041,+0.091]$	$0.395$	$5/10/5$
	gate	$0.6571$	$-0.0146$	$[-0.155,+0.017]$	$0.374$	$8/8/4$
chan_agg	softmax (deployed)	$0.6717$	n/a	n/a	n/a	n/a
	max	$0.6717$	$+0.0000$	$[-0.0001,+0.0004]$	$0.135$	$0/0/20$

Appendix

Table I.1: Effect of alternative combination rules for local-moment fusion ( level_combine ) and channel aggregation ( chan_agg ) on the

20

-series tuning set.

\Delta

denotes the mean per-series VUS-PR difference relative to the deployed rule; Range indicates the minimum and maximum per-series

\Delta

;

p

-value is from a paired Wilcoxon signed-rank test; W/L/T reports wins, losses, and ties relative to the deployed baseline at a

0.001

VUS-PR threshold.

Constant	Grid tested	Selected	Best alternative ( $\Delta$ )	$p$ -value	W/L/T
$p$ (patch length)	$\{8,16,32\}$	$16$	$32$ : $-0.0347$	$0.014$	$4/14/2$
$B$ (depth)	$\{2,4,8\}$	$4$	$2$ : $-0.0070$	$0.891$	$7/7/6$
$D$ (width)	$\{64,128,256\}$	$128$	$64$ : $-0.0010$	$0.984$	$7/8/5$
$G$ (masking groups)	$\{2,4,8\}$	$4$	$2$ : $-0.0053$	$0.225$	$6/8/6$
$b$ (mask block)	$\{1,2,4\}$	$1$	$2$ : $-0.0016$	$0.395$	$5/9/6$

Appendix

Table I.2: Sensitivity of the five architectural constants fixed a priori (patch length

p

, depth

B

, width

D

, masking groups

G

, mask block

b

), evaluated one-at-a-time on the

20

-series tuning set while holding the remaining constants and all fusion coefficients at their deployed values. “Best alternative vs. selected” reports the single grid point with the highest mean VUS-PR among the non-selected values, its mean per-series

\Delta

against the selected value, and a paired Wilcoxon signed-rank

p

-value; W/L/T counts series with a gain, loss, or tie at a

0.001

VUS-PR threshold. The selected configuration attains a mean VUS-PR of

0.6717

Time-Series Anomaly Detection

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Jun 18, 2026

PaAno+: Multiscale Encoding and Cross-Variable Attention for Time Series Anomaly Detection

Time-series anomaly detection has significant practical value for industrial and medical monitoring, as well as other critical domains. Current Transformer- and large-model-based detection approaches incur excessive computational overhead, while existing lightweight alternatives are constrained by insufficient feature extraction and inadequate modeling of dependencies across multivariate variables. To mitigate the above drawbacks, this study develops a lightweight, efficient anomaly detection model, dubbed PaAno, within the patch-oriented representation learning paradigm. In the encoder module, a multiscale feature-extraction backbone is constructed using convolutional kernels with differentiated receptive fields to capture hierarchical temporal characteristics; subsequent cross-scale adaptive attention aggregation, combined with residual connection optimization, further stabilizes feature representation learning. A cross-variable fusion attention module is embedded to explicitly characterize inter-variable correlations, empowering the model to identify anomalous patterns amid intricate operational conditions. Moreover, a novel pretext task based on temporal patch-window sorting is customized to uncover intrinsic structural properties of time series, and triplet loss is leveraged to optimize the patch embedding space for enhanced feature discrimination. Extensive experiments on the TSB-AD benchmark demonstrate that the proposed PaAno achieves state-of-the-art detection accuracy on both univariate and multivariate tasks, yielding significant performance gains across evaluation metrics, including VUS-PR, relative to the original PaAno. Leveraging a compact network design, the presented model achieves favorable computational efficiency, enabling deployment on resource-limited terminals for real-time anomaly inference.

Youji Zhu, Hongbing Wang, Wenchao Liu +2

School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China. · School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550025, China.

Self-Supervised Time Series Representation Learning Time-Series Anomaly Detection Multiscale Time-Series Modeling

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Feb 1, 2026

PaAno: Patch-Based Representation Learning for Time-Series Anomaly Detection

Although recent studies on time-series anomaly detection have increasingly adopted ever-larger neural network architectures such as transformers and foundation models, they incur high computational costs and memory usage, making them impractical for real-time and resource-constrained scenarios. Moreover, they often fail to demonstrate significant performance gains over simpler methods under rigorous evaluation protocols. In this study, we propose Patch-based representation learning for time-series Anomaly detection (PaAno), a lightweight yet effective method for fast and efficient time-series anomaly detection. PaAno extracts short temporal patches from time-series training data and uses a 1D convolutional neural network to embed each patch into a vector representation. The model is trained using a combination of triplet loss and pretext loss to ensure the embeddings capture informative temporal patterns from input patches. During inference, the anomaly score at each time step is computed by comparing the embeddings of its surrounding patches to those of normal patches extracted from the training time-series. Evaluated on the TSB-AD benchmark, PaAno achieved state-of-the-art performance, significantly outperforming existing methods, including those based on heavy architectures, on both univariate and multivariate time-series anomaly detection across various range-wise and point-wise performance measures.

Jinju Park, Seokho Kang

Department of Industrial Engineering, Sungkyunkwan University

Self-Supervised Time Series Representation Learning Time Series Representation Learning Time-Series Anomaly Detection

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Sep 30, 2026

LEARN-TS: LLM-Enhanced Alignment and Reconstruction with Normality Guidance for Multivariate Time-Series Anomaly Detection

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

LLM-Based Time Series Anomaly Detection Anomaly Localization Reconstruction-Based Anomaly Detection Multimodal Anomaly Detection Time-Series Anomaly Detection

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Abstract

Time-Series Anomaly Detection

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PaAno+: Multiscale Encoding and Cross-Variable Attention for Time Series Anomaly Detection

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LEARN-TS: LLM-Enhanced Alignment and Reconstruction with Normality Guidance for Multivariate Time-Series Anomaly Detection