PGRF-Net: A Prototype-Guided Relational Fusion Network for Diagnostic Multivariate Time-Series Anomaly Detection
Authors: Jahoon Jeong
Hyunsoo Yoon
Venue: ICLR 2026 Poster (2026)
Keywords: Multivariate Timeseries Anomaly Detection
Time-Series Diagnostics
Prototype Learning
Relational Time-Series Modeling
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: PGRF-Net: A 2-stage unsupervised MTSAD model. It generates 4 prototype/relational evidence types, adaptively fused for detection. Achieves SOTA performance & provides diagnostic scores to aid root cause analysis.

Abstract: Multivariate time-series anomaly detection (MTSAD) faces a critical trade-off between detection performance and model transparency. We propose PGRF-Net, a novel architecture designed to achieve competitive performance while providing structured evidence to support diagnostic insights. At its core, PGRF-Net uses a Multi-Faceted Evidence Extractor that combines prototype learning with the discovery of dynamic relational structures between variables. This extractor generates four distinct types of anomaly evidence: predictive deviation, structural changes in learned variable dependencies, contextual deviation from normal-behavior prototypes, and the magnitude of localized spike events. This evidence is then processed by a Gated Evidence Fusion Network, which learns to weigh each source via data-driven gating. PGRF-Net is trained via a two-stage unsupervised strategy for robust extractor learning and subsequent fusion tuning. Extensive experiments on five public MTSAD benchmarks demonstrate its competitive or superior detection performance. Importantly, by decomposing the final anomaly score into these four evidence types, our model facilitates diagnostic analysis, offering a practical step towards more interpretable, evidence-based MTSAD.

Published as a conference paper at ICLR 2026
PGRF-NET: A PROTOTYPE-GUIDED RELATIONAL FUSION NETWORK FOR DIAGNOSTIC MULTIVARIATE TIME-SERIES ANOMALY DETECTION
Jahoon Jeong & Hyunsoo Yoon"
Department of Industrial Engineering, Yonsei University, Scoul, Republic of Korea (imagenet152, he yoon] ac.
ABSTRACT
Multivariate time-series anomaly detection (MTSAD) faces critical trade-off be- tween detection performance and model transparency. We propose PGRF-Net, a novel architecture designed to achieve competitive performance while provid- ing structured evidence to support diagnostic insights. At its core, PGRF-Net uses a Mucti-FFccted Evidence Extractor that combines prototype learning with the discovery of dynamic relational structures between variables. This extractor generates four distinet types of anomaly evidence: predictive deviation, struc- tural changes in learned variable dependencies, contextual deviation from normal- behavior prototypes, and the magnitude of localized spike events. This evidence is then processed by Gated Evidence Fusion Network, which learns weigh each source via data-driven gating. PGRF-Net is trained via a two-stage unsupervised strategy for robust extractor learning and subsequent fusion tuning. Extensive experiments on five public MTSAD benchmarks demonstrate its competitive superior detection performance. Importantly, by decomposing the final anomaly score into these four evidence types, our model facilitates diagnostic analysis, of- fering a practical step towards more interpretable, evidence-basee based MTSAD.
INTRODUCTION
Multivariate time-series anomaly detection (MTSAD) is essential in high-stakes domains such as dustrial IoT and healthcare, where timely detection prevents failures and losses. Deep models have advanced detection performance (Xu et al.] 2022; Wang et al. 2023 Song et al. 2023). yet most with little insight into its cause, hindering trust and adoption. Moreover, anomalies are carroognnnouu-ranggeee
remain black boxes: they output single anomaly
from point spikes to contex- tual shifts and relational changes-so methods specialized for one type often miss others. This diversity demands a diagnostic framework that not only flags anomalies but also differentiates their
underlying nature (Chandola al. 2009 Zong al. 2018 Audibert et al. 2020 Blazquez-Garefa
et al. 2021 Xu et [al22)22]
To address these limitations, we propose PGRF-Net (Prototype- Guided Relational Fusion Network), a novel architecture that reframes anomaly detection as a diagnostic process based on multi-faceted evidence aggregation. The key idea of PGRF-Net lies not in any single component, but in the syner- gistic integration of a Multi-Faceter Evidence Extractor and a Gated Evidence Fusion Network into a unified diagnostic framework. The extractor designed to align with the practical needs of sys- tem operators by evaluating four complementary evidence sources: predictive deviation, structural changes in learned variable dependencies, contextual deviation from cormal-behavine prototypes, and localized spike events. The fusion network then integrates this evidence, learning data-driven strategy to dynamically weigh each source. These sources provide complementary views; we do not assume time invariance of the low-frequency component. The entire system is optimized via a two-stage unsupervised strategy, ensuring reliable, data-driven anomaly detection while reducing reliance on manual heuristics.
The main contributions of this paper are:
"Corresonniigg author.

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Published as a conference paper at ICLR 2026
A Diagnostic Framework for Anomaly Attribution. We propose PGRF-Net, archi- tecture that moves beyond single-score detection by decomposing anomalies into four ev- idence types: predictive, structural, contextual, and spike. This decomposition is directly motivated by the practical need for diagnostic analysis, offering decomposed anomaly at- tribution, unlike traditional black-box models. To our knowledge, this is one of the early attempts to reframe MTSAD as diagnostic process rather than mere detection task, by decomposing anomalies into multiple evidence types within unified framework.
Unsupervised Gated Fusion Mechanism. We introduce Gated Evidence Fusion Net- work that learns to optimally weigh the decomposed evidence in a data-driven, unsuper- vised manner. This eliminates heuristic-based tuning and allows for robust detection across diverse anomaly types.
Competitive Performance with Interpretability. PGRF-Net achieves competitive or su- perior detection performance compared to state-of-the of-the-art methods across five widely-used public benchmarks, while uniquely providing actionable, decomposed explanations for anomaly attribution.
2 RELATED WORK
2.1 MTSAD APPROACHES
Modern MTSAD approaches are diverse. Reconstruction-basee methods employ Autoencoders (AEs) (Audibert et al. 2020), Variational Autoencoders (VAEs) (Su et al., 2019), and GANs (Li al., 2019 to flag instances with high reconstruction error. Prediction-based methods rely on temporal models such as LSTMs (Malhotra et al., 2015) and Transformers (Xu et al.) 2022 Wu al. 2023 detect large forecast errors. More recent paradigms include contrastive learning. which separates normal and abnormal patterns (Yang et al. 2023 Tuli al.) 2022), and diffusion models, which employ denoising processes for reconstruction or imputation (Xiao et al. 2023
Chen et al. 2023 Pintilie et al.) 2023). Despite strong performance, most of these methods produce a single anomaly score, limiting their utility for diagnostic analysis.
2.2 PROTOTYPE LEARNING FOR INTERPRETABILITY
Prototype learning improves interpretability by capturing representative normal patterns, often stored in memory banks (Gong et al. 2019). Anomalies are then identified by their deviation from these prototypes. This idea has evolved into sophisticated memory modules, in MNAD (Park et al., 2020) and MEMTO (Song et al. 2023 which enhance reliability by avoiding the recon-
struction of abnormal inputs (Shen et 2025). While effective for modeling contextual normality,
PGRF-Net extends this paradigm by introducing prototype- prototype-guided channels not only for contextual but also for structural deviations, thereby offering a broader diagnostic perspective.
2.3 DEPENDENCY- ANOMALY DETECTION
Anomalies in multivariate time series often manifest through violations of variable dependen- cies. Early statistical approaches relied on Granger causality tests (Qiu et al.) 2012). while recent deep models have advanced dependency modeling in three complementary directions: association- based discrepancies (e.g., Anomaly Transformer Xu et al. 2022), causality-driven discovery (e.g., GCAD (Liu et al. 2025). CAROTS (Kim et al.! (0255) )) and dynamic graph reasoning (e.g., GSC- MAD ZZhag et al. 2024), Causalformer (Kong et al. 2024h). These methods highlight the im- portance of modeling variable dependencies but often treat them the primary anomaly signal. In contrast, PGRF-Ne incorporates dependency evidence as one of four complementary sources, enabling a more balanced and diagnostic view of anomalies.
METHODOLOGY
This section details PGRF-Net, novel architecture designed to enhance both performance and diagnostic transparency in MTSAD. Illustrated in Figure [ PGRF-Net composed of two core components trained in two-stage unsupervised process: Multi-Faceted Evidence Extractor
2

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Published as a conference paper at ICLR 2026
Multi-Faceted Evidence Extractor
Foumlational lupronntation
Prodicthve & Structural Deviation
Context Deviation
Strectural
Centest ProtoRank
NI.P
Cantbel
Mpse
Miree
VILU
Gandel
Spilke Deviation
H
H
M,
Mase
Spikk PrateBank
Canil
Nas
NLP
Conformer Encoder
Cenformee Encoder
Protiction Scarias,
Spilic Sexeing
Conoall
Gated Evidence I Fusion Network
Gade Faniuu
Saed
Foundational Representation
Cating
H
hg
Sug
S final
Floal Scorleg
Figure 1: The overall architecture of PGRF-Net. The model learns a foundational representation via frequency decomposition and Conformer encoders, then generates four diagnostic evidence scores (predictive, structural, contextual, and spike deviations). A Gated Evidence Fusion Network learns combine these scores to produce the final anomaly score.
that decomposes anomalies into distinct causes, and Gated Evidence Fusion Network that learns to combine them for final decision.
3.1 STAGE 1: MULTI-FACETER EVIDENCE EXTRACTOR
The extractor, trained in the first stage, serves as the foundational engine of PGRF-Net. is designed not only for robust representation learning but also for generating four distinet diagnostic sources of anomaly evidence.
3.1.1 FOUNDATIONAL REPRESENTATION LEARNING
RR where w is the window size and N is the number of variables, into its fow-frequency (trend- like) and high- frequency (transient) components, Xtoo and Xnight via an FFT-based filter.
To effectively model multi-scale dynamics, we first decompose an input window X
This split provides two complementary views and does not assume time invariance of the low- frequency component. Each component is processed by a dedicated Conformer encoder (Gulati al. 2020), which adeptly captures both global and local patterns:
H Conformer(X1ow))
Hear Conformer(Xnighl
The two representations are concatenated and linearly projected to yield fused feature map:
H Linear([H Hearl),
from which we derive global context vector via temporal pooling:
hg MeanPool(H).
(3)
Here, H serves the general fused feature map, while Hear is also retained spike-sensitive representation for transient evidence extraction. Together with hy they form the cornerstone for subsequent evidence generation.

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Published as a conference paper at ICLR 2026
3.1.2 LEARNABLE PROTOTYPE BANKS FOR NORMALCY MODELING
Instead of learning single, monolithic model of normal behavior, PGRF-Net maintains three dis- tinct, learnable prototype banks, each storing a vocabulary of representative exemplars correspond- ing to different facets of normalcy. Here, K, Ke, and K denote the number of prototypes in the structural, context, and spike banks, respectively.
Structural Prototype Bank (Batruct E BRKXXXX) Each slice M E R encodes a canon- ical dependency pattern between the variables, capturing inter-variable structural relations.
Context Prototype Bank (Betz E I IK Each vector pk represents a distinct operational state, capturing diverse modes of normal system behavior.
Spike Prototype Bank (Bypike IR. Xdduaa))) Each vector Pk spike encodes an archetypal transient fluctuation, characterizing short-lived but benign events.
These banks are initialized randomly and progressively specialized through end-to-end optimization during Stage training.
3.1.3 EVIDENCE GENERATION VIA PROTOTYPE COMPARISON
With the learned representations and prototype banks, the model generates four evidence scores. This process begins with generating dynamic relational graph from hy, which is used for both prediction and structural deviation analysis.
Dynamic Relational Graph Generation. A selector network processes h, determine the most relevant relational structure for the current time window. computes dynamic weights via an MLP and the Gumbel-Softma function G(-). which are then used create a weighted combination of the prototypes in the structural prototype bank. We view M, as a dependency mask. This yields dynamic relational mask:
M. Σ
((MLPae(hh))) M Moroto
We then derive four complementary evidence scores:
Predictive Deviation (Sprea): From the fused feature map H R= we extract per- variable representations hj (j =,.... N). The parent feature of variable is computed as:
N
pa))) -- (M.) hy,
(5)
and 0J is predicted at the last step using lightweight linear head on [h, hpa(0)) The predictive deviation is:
N y g.)
1 N
Spred
(6)
Structural Deviation (Sstruet): Measures how much M, deviates from a baseline Mösse. com- puted by averaging early-training masks on the normal training split, with the diagonal set to zero and kept fixed for inference. Each prototype Mproto constrained acyclicity penalty (Zheng et al. 2018). The deviation is:
Satruct
M,, Mi
Contextual Deviation (S The global context h, is compared against the context prototype bank (p form weighted normal reference:
pete Σ
9(MLP (hz)) ptt
(8)
The deviation is:
hg
p
cta
Satz
(9)
1
2| |
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Published as a conference paper at ICLR 2026
Spike Deviation (Sppike); A spike feature Aspike is extracted from the high-frequency map
Hear:
Aspike MLP MM (D(H,ar
(MaxPool(Conv
(10)
Its deviation is the minimum distance the spike prototypes:
Sepske =
min |lqpske
Pk
spike
2.
(11)
3.1.4 STAGE TRAINING ORJECTIVE
The extractor trained on normal data using a composite loss function designed to build a compre- hensive model of normaley:
Estugel Xpree + Astruct PatructRsttann Rstruct + Aproto R Reroto-
(12)
Prediction Loss (prre)). We adopt Focal Loss-style weighting (Lin et al. 2017) on the prediction MSE. For sample with MSE m, define its correctness probability
Pt = 1 MSaled_MSE(m),
(13)
and the loss as
Ppeed a, pc)" m,
(14)
which emphasizes higher MSE samples that better delineate the boundaries of normal behavior.
Structural Regularization (Rstruct)- This term ensures relational masks are meaningful and stable:
Ratrret Àu Lu + SpprsseSspare Aaeycharye + Aais Laiff-
(15)
Ln sparsity on the batch-averaged relational mask.
Esparse: sparsity directly on prototype masks {M(rrotok)), encouraging compact structural blocks.
Lucyei DAG constraint Zheng et al. 2018) on each prototype mask, ensuring that M, (a convex
combination) inherits acyclicity.
Laify: temporal stability by penalizing deviations from the baseline mask Mbese-
Prototype Regularization (Rproto). A small-weighted clustering loss encourages compact, diverse prototypes:
Reroto = detx1 B[Setul + Aspikel [[SSppike].
(16)
3.2 STAGE GATED EVIDENCE FUSION NETWORK
In the second stage, freeze the feature extractor (Conformer encoders) to stabilize the learned representations, while allowing the prototype banks and the gating module to remain trainable. This ensures that Stage focuses calibrating evidence attribution without altering the under- lying feature space. The fusion network is then trained in an unsupervised manner to activate ex- planatory channels only when strong evidence arises. By combining pseudo-normal suppression and entropy sharpening, the gating module provides a data-driven weighting of evidence sources, replacing heuristic fusion with an instance-dependent mechanism.
3.2. GATED FUSION MECHANISM
A lightweight gating controller (MLP) maps the global context vector hy into softmax weight vector over the explanatory channels, g = [gatructs Jetas Ispike] with g softmax(MLP(h,, Each deviation score is first normalized to [0, by min-max scaling. The explanatory score is obtained by fusing the structural, contextual, and spike channels:
Seap!
Σ VE(struct, spikk) Eje (strrutt 9i
9t
(17)
The final anomaly score then balances predictive and explanatory evidence via a hyperparameter a:
Stmal (1 a + a.Sexpi
(18)
Here, a E [0, 1] serves as a simple trade-off knob: smaller values emphasize prediction error, while larger values highlight explanatory diagnostics.
5

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Published as a conference paper at ICLR 2026
3.2.2 STAGE 2 TRAINING OBJECTIVE
The fusion module trained without anomaly labels, guided by Stage signals. Its objective is
Stage2 Actæ2 [[[Stu] + Aspike2 [[Sepike] + Asp + Xent
(19)
Prototype Tuning. Refinement losses Setz and Sepike sharpen the separation of normal clus- ters, reinforeing diverse yet compact prototypes.
Gate Suppression Loss (Lsup). We define the total explanatory gate activation as:
Gexpl
Σ
9:
(20)
EE cetruot,cta,,poe
For pseudo-normal samples Xpn (low prediction error in Stage 1), this loss penalizes Gespl:
sup = Ex (Gexl)
(21)
thereby encouraging the network to keep gates inactive when no explanation needed.
Entropy Loss (Cen)). Encourages sharper gate activations:
Lent
E
Σ
gi log
(22)
promoting selective attribution to the most relevant channel.
EXPERIMENTS
We conduct extensive experiments to validate PGRF-Neets performance and interpretability. Our evaluation addresses two research questions: (RQ1) How does PGRF-Net compare with SOTA methods on public benchmarks? (RQ2) How do the proposed components contribute to accuracy and diagnostic transparency? We next describe datasets and metrics; then we present benchmark comparisons, ablations, and interpretability analyses.
4.1 EXPERIMENTAL SETUP
We evaluate PGRF-Net on five public benchmarks: MSL and SMAP (Hundman et al. 2018). PSM
Abdulaal al. 2021 SMD (Su al. 2019) and SWaT (Mathur & Tippenhauer 2016).
Following established pracicc Recall, and F1, together with threshold-fret AUC-ROC and AUC-PR. To provide additional event-level evaluation, we also include Range-Precision (R-P), Range-Recall (R-R), and Range- F1 (R-F1) (Tatbul et al. 2018) in main result tables. For completeness, point-wise (non-adjusted) Precision/Recal/// in Appendix(C] allowing direct comparison with prior methods that rely on point-wise metrics. All results are averaged across five random seeds. Detailed dataset statistics and evaluation procedures are provided in Appendix AHB
al. 2019 Shen et al. 2025). we report point-adjusted Precision,
additionally report
4.2 BASELINES
We compare PGRF-Net with both established models (Deep-SVDD (Ruff et al.
2018) LSTM- -VE
Park et al. 2018). THOC (Shen et al. 2020), OmniAnomaa (Su et al. 2019), InterFusion (Li et al., 2021 ) and recent SOTA models (D3R WWan al.
2023). DMamba (Chen et 2024). DCdetector
Yang et al. 2023). MEMTO (Song et al. 2023), GSC-MAD (Zhang et al. 2024). H-PAD (Shen
ct al. 2025).
4.3 IMPLEMENTATION DETAILS
PGRF-Net is implemented in PyTorch and trained with Adam (Ir=10-1). We use a sliding window of w 60 and model dimension dmode: 128. The training data further split into train/validation sets with 8:2 ratio to enable hyperparameter tuning and early stopping. Other hyperparameters follow standard practice and are listed in Appendix D Thresholds for thresholded metrics are se- lected on the validation set, and range-based metries (R-P/R-R/R directly follow the official implementation of TTabbul et al. 2018). All experiments are conducted on a single NVIDIA A100 GPU (40GB).

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Published as a conference paper at ICLR 2026
Table I: Performance comparison on five real-world datasets in terms of Precision (P), Recall (R), and Fl -core... All scores are in %. Best and second best results are highlighted.
Model
MST.
SMAP
PSM
SNTD3
SWaT
Avg. PT
DVeg-SVDD
THOC
88.45
90.97
99.69
92.05
89.34
90.68
55.
90.99
89.54
79.76
90.95
$4.99
83.94
86.36
$5.13
$8.01
LSTM-VAE
85.49
79.94
82.62
92.23
67.75
78.10
73.62
89.92
80.96
75.76
90108
82.30
76.00
89.50
82.20
81 %1.24
OmnlAnnomaly
89.02
86.37
87.67
92.49
81.99
86.92
83. 29
74.45
$01.8
83.68
86.82
85.22
81.42
84.30
82.83
$4.09
Fusernusion
81.28
92.20
86.62
89.77
88.52
83.61
83.45
83.52
87.02
85.43
86.22
80.59
83.01
DCderettor
92.09
98.89
97 24
85.84
93.20
99.11
83.09
MEMTO
91.95
97.23
94.56
93.66
99.73
96.60
97.47
98.
98.03
88.24
96.16
92.03
94.28
91.72
93.73
94.99
DMamba
93.69
64.06
76.09
95.10
$2.96
68.05
98.
82. 59
89.91
92.57
54.04
68
94.11
86.75
90.28
78.51
GSC-MAD
94.19
93.09
93.66
57
98.35
93.76
97.
99. 14
89
92.25
94
94.42
95. 95.32
96.73
95 95.11
95.91
95.
H-PAD
96,05
96.88
85
96.00
96.45
97.31
98.82
99.41
99.12
92.86
98 30
95.45
94.34
100.00
96
PGRP (Ours)
Table 2: Performance comparison on five real-world datasets in terms of AUC-ROC and AUC-PR. All scores are in %. Best and second best results are highlighted.
Model
MSL
SMAP
FSMI
SMD
SWuT
Arg
AUC ROC
AUC PR
AUC ROC
ALC PR
AUC ROC
AUC PR
AUC ROC
AUC
AUC ROC
ALC
ALC ROC
AUC PR
LSTMAVL
32.12
4.32
50.31
3.19
19.15
3005
4.15
49.55
4.13
50.35
11.48
DOR
63.26
16.99
10.62
50.03
26.31
68.20
12:24
-6.85
15.99
DCfeneier
10.11
12:48
48.77
20
H-PAID
15.06
15.90
25.01
76.49
10.05
PORT (errO
04.30
1630
00.10
16335
76.25
32.00
7530
24.50
83.10
$4.30
71.89
32,49
4.4 OVERALL PERFORMANCE COMPARISON (RQ1)
Tables and compare PGRF-Net with a broad range established and state-of-the-ee baselines across live public datasets.
F1-Score Analysis. As shown in Table [ PGRF-Net achieves the highest average Fl-score (97.41%) among all methods, ranking first on three of five datasets (MSL, SMD, SWaT) and second on the others. This improvement highlights the benefit of integrating multi-faceted evidence rather than relying on a single anomaly perspective. Notably, our model balances precision and re- call, avoiding the high-recall but low-pree low-precision tradeoff observed in DCdetector and MEMTO. All F1-scores in this subsection refer the standard point-adjusted F1 metric; event-level Range-F1 analyzed separately in Table
AUC Score Analysis. The threshold-independeet metrics in Table further confirm the robustness of PGRF-Net. It achieves the best average AUC-PR (32.49%) and strong AUC-ROC, crucial in im- balanced anomaly detection. Compared to the prototype-bases based model H-PAD, PGRF-Net provides higher recall while preserving interpretability via structured fusion.
reports event-level Range-Precistee Precision (R-P), Range- Recall (R- R), and Range-Fl (R-F1), which evaluate anomaly segments as coherent events rather than isolated points. Across the five datasets, PGRF-Net consistently ranks at near the top: it achieves the best Range-F1 on MSL, SMD, and SWaT, achieves the second-best score on SMAP, and remains competitive PSM.
Range-based Evaluation. Table 3
Taken together, these results demonstrate that PGRF-Net not only achieves state-of-the-art detec- tion accuracy but also provides consistent reliability across datasets with very different anomaly characteristics.
Table 3: Event-leve range-based based metrics (R-P, R-R, R-FI), Best and second best are highlighted.
Model
MSL
SMAP R-R
PSM R-R
SMD R-X
SWST
Avg R:T
X-P
R-K
R-F1
R.P
R-F1
R.P
R.FI
R-P
R-F1
R.P
R-R
X-F1
THOC
$3.40
82.33
83.83
88.12
79.24
83.46
84.10
71.52
77.24
82.30
36.14
$4.18
77.92
$1.30
79.57
81.66
Anomaly
78.91
93.42
85.46
87.10
86.25
86.66
80.24
$2.10
81.16
87.22
86.91
87.06
79.10
86.22
82.48
84.56
LaterPusion
89.15
02.72
95.25
96.74
85.75
DCdetector
68:44
97.35
97.10
91.33
MEMTO
92
91.91
92.15
88.60
96.
92.43
97.20
95.00
97.79
93.41
97.01
95.46
95.10
91.
94.66
91.50
PGRF-N Net (Ours)
9538
96.92
96.38
93.02
97.42
95.17
95.10
96.92
96.00
95.92
98.44
97.16
94.22
97.20
95.68
96,08

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Published as a conference paper at ICLR 2026
Table 4: Ablation study on core architectural modules. "w/ FD" denotes with Frequency De- composition (at different frequency ratios). All metrics are Avg. F1-S F1-Score (%).
Table 5: Impact of two-stage training and gated fusion. Static Fusion ratios denote weights for (S pped Sstruct Setz Sapike).
Stage
Model Variant
Avg F1
w/ FD (Low Freq. Ratio)
Spred only
92.51
Encoder
w/o FD
10%
20%
30%
Static Fusion (1:0:1:1)
94.13
MLP-Mixer
92.88
93.81
94,15
93.97
Static Fusion (1:1:0:1)
94.58
Transformer
94.71
95.80
96.05
95.91
Static Fusion (1:1:1:0)
95.34
PatchTST
95.34
96.52
96.82
96.75
Static Fusion (1:1:1:1)
96,82
Conformer
95.12
97.15
97.41
97.35
Max Pooling (of 4 scores)
92.32
1+2
PGRF-Net
97.41
Impact
Senoitivitt
Sensitivity
Sensitivity to Pasudo normall
00.25
(661
13
68.50
04.2
06.
13
19.75
05
Figure 2: In-depth analysis of key components. (a) Impact of the number of prototypes K. (b)
Sensitivity window size w. (c) Sensitivity to fusion weight a. (d) Sensitivity the pseudo- normal ratio for Stage-2 training.
4.5
IN-DEPTH ANALYSIS AND ABLATION STUDY (RQ2)
We further analyze the contributions of PGRF-Net's core components through ablation studies.
4.5.1
EFFECTIVENESS OF CORE ARCHITECTURAL DESIGN.
We validate our architectural choices- the dual-stream frequency decomposition (FD) and the Con- former encoder-by replacing them with strong alternatives (MLP-Mixer, Transformer, PatchTST), both with and without FD. As shown in Table 4 applying FD consistently improves performance across all backbones, confirming that separating slow and fast dynamics provides complementary features. Among all encoders, the Conformer achieves the best performance (97.41% % Fl), highlight- ing its ability to capture both local and global temporal dependencies, which synergize well with FD by aligning temporal receptive fields with frequency-separaie signals.
4.5.2 IMPACT OF TWO-STAGE TRAINING AND GATED FUSION.
To assess the benefit of the two-stage strategy, we compare the full PGRF-Net with Stage- variants under different static fusion ratios. Results 5how that while static fusion already outperforms the prediction-only baseline, its performance is highly sensitive to fixed weights and degrades when evidence channels are imbalanced or removed. By contrast, the Stage-2 gated fu- sion consistently yields the best performance (97.41%), demonstrating that learning input-dependent weights is essential for stability beyond fixed heuristics.
4.5.3 HYPERPARAMETER SENSITIVITY.
Figure Souurepreeentts sensitivity analyses for key hyperparameters. Performance is stable across a broad range, peaking at K 10 prototypes, window size w 60, and fusion weight 0.1. The pseudo-non noruallnormal ratio is effective between 0.1 and 0.3. Variance across five seeds is very small, confirming robustness. Note that sensitivity plots aggregate results across datasets, while ablation tables (Table 4 Table 55) report single-dataset studies, explaining minor discrepancies in absolute F1-scores and preventing misinterpretation methodological inconsistency.
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PSM (Contextual, Structural)
PSM (Point)
SMD (Pred, Contextual, Stractural, Spike)
SMD (Contestual
Mallll
Rad
(4)
(4)
(e)
Figure 3: Case studies of PGRF-Net's interpretability on four anomaly events from the bench- mark datasets. Each column presents complete diagnostic report with five aligned views (see Section 4.6p: (a) raw signals with time on the x-axis and sensor values on the y-axis, (b) final anomaly score, (c) decomposed evidence attribution (Spred, Satza Sppikes Sstruet), (d) adaptive sion weights, and (e) relational-level changes (red strengthened, blue weakened), Symbols in Row (e) mark altered dependencies, directly linking anomaly events to structural shifts. Together, these views demonstrate how PGRF-Net translates detection into actionable reasoning. Note: Smack in plots corresponds to Structural Deviation (Sttract).
4.6 INTERPRETABILITS ANALYSIS
A central goal of PGRF-Net is to move beyond black-box detection and serve as a transparent diag- nostic assistant. Rather than outputting only an anomaly score, our framework produces a structured five-panel report designed to explain both what is anomalous and why:
Raw Signal (Row a). Input time series with anomaly regions highlighted for localization.
Final Score (Row b). Aggregated anomaly score curve that confirms severity and boundaries.
Decomposed Evidence (Row c). Attribution to predictive, structural, contextual, and spike evi- dence, revealing the anomaly's type.
Adaptive Weights (Row d). Dynamic fusion coefficients showing the model's internal reasoning and emphasis shifts across evidence sources.
Relational-Level Insight (Row e). Fine-grained diagnostic analysis by contrasting anomalous relational masks (M₂) with baseline masks (Masse).
Representative case studies are shown in Figure 3 and extended examples across benchmarks are in Appendix E.
While real-world benchmarks demonstrate that PGRF-Net produces semantically meaningful de- composed evidence, these datasets lack ground-truth anomaly rypes (e.g., spike contextual vs. structural). Therefore, to quantitatively validate that each evidence channel (Ssmeet- Sex. Sapike) responds selectively the intended anomaly mechanism, perform controlled synthetic experi- ments, as detailed in Appendix E.3
4.7 COMPLEXITY AND EFFICIENCY
To assess the practical deployability of PGRF-Net, we additionally evaluate its computational com- plexity and runtime efficiency under standardized setup. For fair comparison, all models were benchmarked on the PSM dataset (25 channels, 132,481 training time steps and 87,841 test time steps) using single NVIDIA A100 GPU. As summarized in Table 6 our proposed PGRF-Net demonstrates parameter efficiency with only 2.25M parameters, which is significantly fewer than prior models like MEMTO (5.39M). The model requires just 0.005 GPU-hours for training and

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achieves inference latency of 0.059 ms per step, supporting real-time deployment scenarios. This demonstrates that our framework achieves strong performance with high computational efficiency.
Table Model complexity and efficiency, benchmarked on a single NVIDIA A100 GPU.
Model
#aarams (M)
Train Time (GPU-h)
Inference (ms/step)
D3R
3.152
0.047
0.141
MEMTO
5.39
0.004
0.043
PGRF-Net (Ours)
2.25
0.005
0.059
LIMITATIONS
While PGRF-Net substantially improves diagnostic interpretability for MTSAD, several limitations remain that highlight directions for future work.
Human-centered evaluation. Although our quantitative
(selectivity, synthetic isolation, sta- bility) demonstrate semantic alignment of evidence channels, we do not include human-centered or practitioner-batt evaluations. Assessing the real-world usefulness for operators remains future work.
Training contamination. Real-world training data may contain unlabeled anomalies, and our method does not explicitly model heavy contamination. Extending prototype formation and gat- ing to be contamination-awer
a promising future direction.
DAG constraint and feedback loops. Our structural evidence relies on DAG regularization, which improves stability and interpretability but cannot capture feedback loops that frequently arise in cyber-physical systems. Extending structural modeling cyclic feedback-aware graphs remains an open direction.
Baseline mask sensitivity. The baseline structural mask M is derived from early training under a stationary- normal assumption. In environments with multi-regime or drifting normal dynamics, a single averaged bascline may be insufficient; regime-conditioned or multi multi-prototype baselines would improve flexibility.
6 CONCLUSION
We introduced PGRF-Net, a prototype-guided relational fusion network that reframes multivariate time-series anomaly detection diagnostic task rather than mere flagging. Its design combines Multi- Salti-Faceted Evidence dereettr-ddcooosiinn anomalies into predictive. structural, contextual, and spike deviations-vve -with Gated Evidence Fusion Network that adaptively weighs these signals through a two-stage unsupervised procedure.
Extensive experiments across five public benchmarks demonstrate that PGRF-Net achieves compet- itive detection accuracy while providing structured explanations that reveal not only what is anoma- lous but also why. This dual emphasis on accuracy and diagnostic interpretability bridges the gap between high-performing black-box detectors and practitioner-oriented monitoring systems.
Despite these strengths, several limitations remain-such as the absence of human-centered evalu- ations, the assumption of predominantly normal training data, and the reliance DAG constraints that cannot model cyclic dependencies. Nonetheless, our results show that meaningful diagnostic interpretability be obtained without sacrificing efficiency or detection quality.
Future work will explore contaminationn-rouust learning, multi-regime structural baselines, and ex- tensions cemi-supervised and domain domain-adaptive such as industrial loT, healthcare, and finance represent particularly promising directions where both reliability and interpretability are essential.
adaptive settings. Applications in safety- critical domains
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REPRODUCIBILITY STATEMENT
To ensure the reproducibility of our research, this paper provides comprehensive details on our methodology and experiments. All datasets used are public benchmarks as described in Appendix A Our evaluation protocol, including metrics and the point-adjustment strategy, is detailed in Ap- pendix B Detailed hyperparameters for training and model architecture are provided in Appendix The source code for PGRF-Net, implemented in PyTorch, is available in the supplementary materi- als.
ETHICS STATEMENT
This research based on publicly available and anonymized datasets, and we do not foresee any di- rect ethical concerns regarding data privacy. We acknowledge that anomaly detection systems could potentially be reverse-engineered for malicious purposes, such evading security monitoring. We believe that the diagnostic transparency of our proposed model, which helps operators understand system states, promotes responsible use. We encourage the deployment of such technologies within strong ethical framework.
ACKNOWLEDGEMENTS
This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (RS-2025-02305884))
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A DATASET DETAILS
We evaluate PGRF-Net on five widely used public benchmarks: MSL. SMAP, PSM, SMD, and SWaT. These datasets span diverse application domains, including spacecraft telemetry, server mon- itoring, and industrial control systems. They vary in anomaly ratio, sequence length, and signal complexity, providing rigorous testbed for both accuracy and interpretability.
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MSL (Mars Science Laboratory) and SMAP (Soil Moisture Active Passive) (Hundman et al. 2018 are NASA spacecraft telemetry datasets. They contain subtle but mission-criticaa anomalies embedded in highly periodic and correlated sensor streams. PSM (Pooled Server Metries) (Ab- dulaal et al. 2021) is collected from eBay's cloud infrastructure and exhibits high anomaly density with bursty signals. SMD (Server Machine Dataset) (Su al. (019) contains diverse server fail- ure patterns across 28 entities with relatively rare anomalies. SWaT (Secure Water Treatment) (Mathur & Tippenhauer 2016) is cyber-physical dataset generated from a water treatment testbed under 36 simulated cy bett-asts
Together, these datasets cover wide spectrum of anomaly types (point vs. collective). frequen- cies (rare vs. frequent), and domains (virtual vs. physical systems), allowing for comprehensive validation of detection models.
Table 7: Overall statistics of the benchmark datasets.
Dataset
Channels
Train
Test
Anomaly Ratio
MSL.
55
3,682
2,856
0.74%
SMAP
25
2,876
8,579
2.14%
PSM
25
132,481
87,841
27.76%
SMD
38
28,479
28,479
9.46%
SWaT
47,520
44,991
12.20%
B EVALUATION PROTOCOL DETAILS
To ensure rigorous and reproducible evaluation, strictly adhere to the protocol widely estab- lished in prior state-of-the-art works, including OmniAnomaly (Su et al. 2019) and H-PAD (Shen al. 2025). This protocol standardizes how anomaly predictions converted into event-level de- cisions, how thresholds are selected, and how metrics are calculated, thereby minimizing evaluation bias and enabling direct comparison across methods.
In addition to the established protocol, we report two complementary metric classes: (1) non- adjusted point-wise metrics for full comparability with earlier works, and (2) range-based metrics (R-P, R-R, R-F1) following (Tatbul et al. 2018) to capture event-level alignment. This broader evaluation spectrum provides more complete characterization of model behavior.
B. POINT-ADIUTTMENT STRATEGY
Real-world anomalies often manifest as contiguous time segments rather than isolated single points. A naive point-wise comparison between predicted and ground-truth labels tends to over-penalize models by treating partial overlaps as failures. To address this, we adopt the event-level correction strategy implemented via the ad idjus wts..-ppeddd. cts () function in OmniAnomaly.
Formally, for each ground-truth anomaly interval tel, if at least one timestamp E [t., is predicted as anomalous (Ú, 1), then the entire interval is marked as correctly detected. This rule reflects the practical requirement that an early warning anywhere within an anomalous episode sufficient to trigger mitigation actions. At the same time, it prevents over-segmentation, where long anomaly detected with minor gaps would otherwise unfairly penalized. We note that this approach is now the de facto standard in time-series anomaly detection benchmarks and ensures comparability with recent SOTA results.
Point-adjusted Precision/Recall/ii constitute the primary thresholded metrics reported in the main paper and are directly comparable to prior SOTA TSAD methods.
B.2 THRESHOLD SELECTION
Most anomaly detectors output continuous scores. We perform grid search over 1000 evenly spaced thresholds within the observed score range and select the value that maximizes the Fl-score. The corresponding Precision, Recall, and Fl are then reported. This "best-F1" strategy, used in
(Su et al. 2019 Shen al. 2025), ensures that each model is evaluated at its optimal operating
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point, avoiding mismatches due to threshold sensitivity. The same thresholding protocol is applied consistently for both point-adjusted and point-wise addjusdddtdd) metrics.
B.3 EVALUATION METRICS
We report both grrehhld-dependde metrics (Precision, Recall, FI) and threshold free metrics (AUC-ROC, AUC-PR). The standard thresholded metrics are defined follows:
TP
Precision
(23)
TP + FP
TP Recall
(24)
+P+FN'
Precision Recall
Fl = Precision + Recall
(25)
where TP, FP, and FN are computed after applying the point-adjusted correction described in the previous subsection. In parallel, AUC-ROC and AUC-PR capture the ranking quality of anomaly scores across thresholds, providing a complementary, threshold-fres view of robustness in imbal- anced settings.
Point-wise (Non-adjusted) Metrics. To supplement this, we also report non-adjusted point-wise metries as shown in Table These metries use the exact same definitions (Equations 23 25 but are computed before the point-adjustment step. That is, TP, FP, and FN are tallied based on direct, sentttap----timestttee
comparison between the raw predictions and the ground truth. This proto- col is included for direct comparison with earlier works that did not employ event-level correction.
Range-based Metrics (R-P, R-R, R-F1). Beyond point-adjusted scores, we additionally evaluate event-level detection quality using Range-Prectiee Precisson (R-P), Range-Recall Recall (R-R), and Range-Fl (R- F1), following the formulation of Tatbul et al. (2018). These metrics treat each anomalous interval as coherent event and measure how well predicted intervals align with ground-truth segments.
Let G [G....., Gm } denote the set of ground-truth anomaly intervals, where each interval is G; = [s,, e,). and let (P.....,P,, Pr} denote the predicted anomaly intervals obtained from thresholded scores.
Predicted intervals P are obtained by grouping consecutive predicted anomalous timestamps (i.e., runs of Jt 1) into maximal contiguous segments.
For any two intervals and B, define their temporal overlap as
Overlap(A, 14n
|
where
||
deeeotes the number of timesteps.
A ground-truth interval G2 is considered correctly detected if there exists at least predicted interval P, such that:
(verlap(G;,P3) 2 Orauges
where Orange the minimum overlap ratio (typically Orange = following TTabbul et al. 2018 which counts any positive overlap).
Then, Range-based Precision and Recall are defined as:
R-P predicted intervals that match at least one G;
# predicted intervals
# ground-truth intervals detected ground-truth intervals
R-R
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Finally,
R-P. R-R R-F1 = R-P +-P+R-RR
Unlike point-wise point-adjusted metrics, range-based metrics do not inflate performance for long anomalies with dense positive predictions, and instead capture true event-level localization quality. This makes R-P, R-R, and R-F1 partieularly suitable for evaluating segment-coherent anomaly de- tectors such as PGRF-Net.
B.4 WHYY THIS PROTOCOL MATTERS
This evaluation design reflects three practical considerations that are crucial for fair and meaningful comparison in TSAD.
(1) Event-level correction prevents unfair penalization of minor misalignments, aligning the evalua- tion with real-world operational needs. It ensures that models are rewarded for detecting anomalous episodes-eve if detection does not perfectly align with every timestamp thhestamptthereby avoiding false negatives caused solely by temporal boundary shifts.
(2) Best-F1 thresholding allows fair model-to-model comparison by neutralizing sensitivity to ar- bitrary threshold choices. Using the optimal threshold for each model avoids bias introduced by models whose score distributions differ in scale or variance.
(3) Combining thresholded and threshold metries provides a comprehensive assessment of both peak performance and ranking robustness across operating points. AUC-ROC and AUC-PR summa- rize score quality independent of threshold selection, while point-adjusted F1 emphasizes episode- level detection correctness.
(4) Incorporating range-based metries (R-P, R-R, R-FI) further strengthens the evaluation by mea- suring alignment at the level of anomaly segments rather than individual timestamps. Unlike point- adjusted w1-w credits detection if any point within an anomaly interval is hit hit-range metrics quantify segment- leeell overlap and penalize fragmented overly sparse detections. This provides a semantically richer view how well a model captures the temporal extent of anomalous events.
Taken together, these four components establish balanced and reproducible evaluation protocol that distinguishes segment-level reliability from point-level detection and has become a strong and transparent foundation for modern TSAD benchmarking.
C ADDITIONAL POINT-WISE METRICS
To support direct comparison with prior studies that rely on non-adjusted evaluation, we report point- wise (non-adjusted) Precision, Recall, and F1 scores across all five benchmark datasets. These met- rics complement the point-adjusted and range-based scores presented in the main text and provide an additional perspective thresholded detection performance under the standard non-adjusted protocol.
As shown in Table 8 while PGRF-Net does not achieve the highest average F1 score, demon- strates strong performance by securing the best Fl-scores on both SMD and SWaT. This behavior expected: PGRF-Net is designed to produce coherent segment-level detections rather than trig- gering densely at every anomalous timestamp. As a result, its strengths are more faithfully reflected in the point-adjusted and range-based metrics reported in the main paper, which explicitly reward boundary alignment and event-level coverage.
D HYPERPARAMETER DETAILS AND SENSITIVITY ANALYSIS
This section documents the hyperparameters used for training PGRF-Net and presents robustness analysis over critical parameters. All baseline models were run with the optimal settings reported in their respective papers to ensure fair comparison. By contrast, PGRF-Net's hyperparameters were either selected based on established practices in time-series modeling or tuned on a held-out validation split, detailed below.
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Table Point-wise (non-adjusted) Precision (P), Recall (R), and Fl-score across all datasets. Best and second best results are highlighted.
Modil
MSI.
SMAP
PSMT
SM17
SWaT
Avg PT
OmmiAnomaly
27.42
56.22
34.85
57.33
Insiin
36.52
67:20
47.26
16.22
60.94
45.37
41.91
57.55
49.53
13.10
55.22
41.53
59.52
68.44
50.12
46.76
DCderectoe
35.94
65.14
41.50
37.41
59.72
46,09
46.13
63.44
53.35
36.52
63.11
46.10
38.01
52.12
43.90
25.
DSR
31.82
68.44
43.35
34.22
65.82
45.20
14.40
60.02
50.82
35.10
65.22
66.92
39
55.44
46.05
46.47
MEMTO
(Ours)
D.1 MODEL ARCHITECTURE AND TRAINING PARAMETERS
Table 9 summarizes the architectural and training hyperparameters, The sliding window size (w 60) and model dimension (dmodel 128) follow common practices in multivariate TSAD. The number of prototypes (K 10) and fusion parameters were tuned via validation to maximize robustness. The two-stage training setup (Stage I pretraining, Stage 2 refinement) proved critical for balancing predictive accuracy and interpretability.
Table 9: Key model and training hyperparameters for PGRF-Net.
Category
Hyperparameter
Value
Sliding Window Size w
60
Model Dimension dmnode
128
Architecture
Conformer Heads Thead
4
Conformer Layers Tlayers
Number of Prototypes K, Ke, K.
10
Epochs (Stage 1)
50
Learning Rate (Stage 1)
10-4
Patience (Stage 1)
10
Batch Size
128
Training
Epochs (Stage 2)
Learning Rate (Stage 2)
10 10-4
Patience (Stage 2)
Optimizer
Adam
Focal Loss Gamma y Secudo-Normal Ratio
2.0
Fusion Strategy
0.25
D.2 Loss FUNCTION WEIGHTS
The composite losses for the two-stage training shown in Table I0, Stage emphasizes pre- dictive reconstruction and prototype-regulariztion while Stage introduces refinement via gate suppression and entropy terms. These weights were tuned SMAP and transferred consistently across datasets.
D.3 HYPERPARAMETER SENSITIVITY ANALYSIS
We further analyze sensitivity Learning Rate, Batch Size, and Acyclicity Regularization (Aacye). All results are averaged across five datasets. Together, these experiments show that PGRF-Net main- tains strong robustness within reasonable ranges, and that optimal settings are intuitive: moderate learning rates, mid-sized batches, and balanced sparsity control.
D.3.1 LEARNING RATE
Performance peaks at 1 10 10-4, but remains stable within (5 10 -5.5 10 10-4). Smaller values lead to underfitting, while higher values cause instability.
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Table 10: Weights for the composite loss functions in Stage 1 and Stage 2.
Stage
Loss Weight Component
Value 10.0
Prediction Loss (Lpeed)
Structural Regularization (Ramee)
L1 Penalty (Ar1)
10-3
Sparse Proto Masks (Agpurse)
10 10-3
Stage
Acyclicity Constraint (Aweye)
10 10-4
Temporal Stability (Aar)
10
Proto Regularization (Rpros))
Context Proto Loss (Aei))
10
Spike Proto Loss (Aspikel)
10
Context Proto Tuning (Aexz)
2 10
Spike Proto Tuning (Aspike2)
10-1
Stage 2
Gate Supp. Loss (Aan)
10
Gate Entropy Loss (Dem)
10
Table 11: Effect of Stage learning rate performance.
LR
AUROC
AUPRC
F1
1- 10 5
66.21
27.43
91.85
5 50-5
70.13
30.77
96.08
1.10-4
71.89
32.49
97.41
5- 10-4
69.50
29.12
95.22
1 10
64.88
25.34
89.90
D.3.2 BATCH SIZE
Table 12: Effect batch size on performance.
Batch Size
AUROC
AUPRC
Fi
64
70.11
30.92
96.88
128
71.89
32.49
97.41
256
70.25
29.85
95.77
512
67.30
26.51
92.63
batch size of 128 provides the best trade-off between stability and efficiency. Small batches capture finer variance but slow convergence, while large batches reduce gradient diversity and can reduce recall.
D.3.3 ACYCLICITY REGULARIZATION
Table 13: Effect of acyclicity regularization Aayye-
Jeye
AUROC
AUPRC
F1
1 10 0
68.92
28.10
93.42
1- 10-5
70.34
29.12
95.67
1- 10-4
71.89
32.49
97.41
10-3
70.77
30.43
95.15
1 1 -
66.42
25.80
89.88
Too little regularization (10-6) produces overly dense graphs, while too much (10-2) forces exces- sive sparsity. The sweet spot 10 -4 balances interpretability with predictive power.
All experiments reported in the main text used the rest-performin setting identified in this analysis (w = 60, d = 128, batch size 128, learning rate = 10 and Amyy = 10 4), unless otherwise specified. These values consistently applied across all benchmark datasets.
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E ADDITIONAL EXPERIMENTS
E. CASE STUDIES ON BENCHMARK DATASETS
To demonstrate our model's diagnostic capabilities on real-world data, we present case studies from five standard benchmark datasets: SMD, MSL., SMAP, SWaT, and PSM. As shown in Figure utilize a two-panel visualization format for clear interpretability. The top panel displays the raw multivariate signals with the ground truth anomaly shaded. The bottom panel presents the final anomaly score (black line) and, crucially, its composition as stacked area chart. This chart visually decomposes the final score into contributions from each evidence channel (Spred. Saruet. Sexs and Sppae), allowing for an immediate diagnosis of the anomaly's nature.
Server Monitoring (SMD) & Spacecraft Telemetry (MSL, SMAP) These datasets are charac- terized by contextual anomalies such as gradual performance degradation sensor drift. As seen in the corresponding columns of Figure E the anomaly scores in these cases are predominantly composed of the contextual (Sax) contribution (green), with a secondary response from the mask (Sarae) contribution (orange). This indicates the model correctly identifies these events as significant deviations from normal temporal patterns rather than sudden spikes or specific structural breaks.
Industrial Control (SWaT) The illustrated anomaly from SWaT (a cyber-attack simulation) in- volves a deliberate violation of the physical dependencies between sensors and actuators. Our model correctly diagnoses this event by producing a final score composed almost entirely of the structural (Saraa) contribution (orange). This demonstrates the model's ability to pinpoint structure-related anomalies, which is critical for diagnostic analysis industrial control systems.
Server Infrastructure (PSM) This dataset features a mixture anomaly types. The chosen ex- ample showcases transient event, such as sudden service latency spike. The model correctly attributes this anomaly, with the score composition showing a clear and dominant peak from the spike (Segite) contribution (red). This highlights the gating mechanism's ability adapt and priori- tize the most relevant evidence channel for different anomaly profiles.
E.2 END-TO-END JOINT TRAINING VS. Two-S -YO-STAGE OPTIMIZATION
We evaluate fully end-to-end variant of PGRF-Net in which all components including the rela- tional mask generator, context and spike prototype banks, and fusion gates-are are optimized jointly from scratch. This experiment tests whether decoupling representation learning (Stage 1) and evi- dence fusion (Stage 2) is necessary.
The end-to-end model achieves strong, but consistently inferior, performance. On benchmark datasets, joint training reaches 95.12% Avg F1, compared to 97.41 % with the proposed two-stage procedure (Table
Performance
Convergence Behavior End-to-end joint learning shows noticeably unstable gate dynamics. Across three runs on SMAP, the standard deviation the contextual gate activation during training is 3.2-3.8x x higher than in two-stage training (mean + std - joint: 0.147 = 0.031 vs. wto-ttage: 0.152 + 0.008). We also observe 2-3 instances of gate collapse (one evidence channel receiving 90% of the weight) during joint optimization. The two-stage procedure eliminates such oscilla- tions by freezing the representation and updating only the gate parameters in Stage 2.
Stability Across Seeds End-to-end training significantly more sensitive to initialization. Across 5 random seeds, the joint model yields Range-F1 variance of 0.0048, whereas the two-stage procedure reduces this to 0.0012 (4x lower variance). Furthermore, the evidence attribution vectors (structural/comeextuul/spppll show higher cross-seed divergence under joint training (mean cosine distance 0.214) compared to two-stage learning (0.087). This demonstrates that two-stage training provides both stable convergence and more consistent evidence decomposition across seeds.
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SMD (3-4)
SMD (3-9)
(MAP(F-3)
SMAP(G-2)
Magh
(8)
fkadl Mahi Snn
(4)
(SL(FF4)
(SL-(S-2)
swar 12,373)
swal (37,479 37.57%
(b)
M W Medda mouhel
(4)
PSM (30,155 30,168)
PSM (32,519 32,548)
PSM (47.225 47,248)
PSM (73.85 73,785)
(4)
(b)
Melle bea Aee
(4)
(4)
(9)
Figure 4: Interpretability Case Studies Across Benchmark Datasets. Each column corresponds to an anomaly case from different dataset. Top Panel: Raw signals with the ground truth anomaly shaded. Bottom Panel: The final anomaly score (black line) and its composition, visualized as stacked area chart showing the contribution from each evidence channel (predictive, structural, contextual, spike). This format allows for direct insight into the model's reasoning. For instance, the prevalence of orange in the SWaT case indicates structural anomaly, while green dominates in the MSL case, signifying a contextual anomaly. Note: Smask in plots corresponds to the Structural Score (Satrct).
E.3 SYNTHETIC DATA VALIDATION
Real-world benchmarks confirm that PGRF-Net produces semantically meaningful decomposed ev- idence. However, real datasets never provide ground-truth anomaly types (e.g., spike contextual vs. structural), and these mechanisms often co-occur within the same anomaly segment. Therefore, it is impossible to directly evaluate channel-wise sensitivity using real data.
To rigorously verify that each evidence score- S Saxx and Sapike- responds selectively to the intended anomaly mechanism, we construct controlled synthetic environments where each
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anomaly type is injected in isolation. Our goal is not to classify anomaly types; rather, verify that each evidence channel behaves according to its intended semantics under type-isolated conditions.
Two synthetic generators are used:
Left column: Nonlinear VAR Generator nonlinear interactions on top of a known
stable VAR(I) dependency graph.
Right column: State-Switching Generator three-regime switching between
(A1, A2, Amix).
Both generators produce D = 10-dimensional multivariate series with precisely controlled spike, contextual, and structural anomaly mechanisms. Although the anomaly mechanisms are not orthog- onal in real systems, our synthetic construction ensures isolation so that each evidence channel can be evaluated independently.
E.3.1 QUALITATIVE ANALYSTS
Figure presents representative examples for each anomaly type across the two generators (columns). For each case, the top panel shows the multivariate input with ground-truth anomaly region shaded, and the bottom panel shows the composition of the final anomaly score into its three evidence channels.
The qualitative behavior matches the model design:
Spike anomaly:
The sharp peak is predominantly driven by Sepike (red), consistent with point-wise transient deviation.
Contextual anomaly: Slow, drifting changes dominate Sax (green), which rises smoothly over the contextual region.
Structural anomaly: When relational dependencies change, Satruct (orange) becomes the primary contributor, reflecting deviations in cross-channel dynamics.
These qualitative patterns hold consistently for both generators (left and right), demonstrating bustness across heterogeneous dynamics.
E.3.2 QUANTITATIVE EVIDENCE VALIDATION
This appendix provides quantitative validation of PGRF-Net's multi-evidence decomposition. Rather than enforcing strict orthogonality between evidence channels-whice is unrealistic for com- posite anomalics-vv we aim to show that each channel is (i) selectively activated under its intended anomaly mechanism and (ii) robust to small perturbations. To this end, conduct two controlled synthetic evaluations:
Evidence selectivity via synthetic isolation tests - does each anomaly mechanism dom- inantly activate the intended evidence channel?
2. Evidence stability - are evidence trajectories robust to small additive noise?
These tests verify that the learned evidence channels exhibit semantic alignment, selective activation, and robustness across controlled variations.
Evidence Selectivity via Synthetic Isolation Tests. To quantitatively validate that each evidence channel selectively responds its intended anomaly mechanism, we conduct synthetic isolation tests. We construct three controlled environments, each containing exactly one anomaly type, using nonlinear VAR generators (structural perturbation), regime-swicchie level shifts (contextual drift), and impulsive outliers (spike events).
For each environment, we compute the Evidence Amplification Ratio (EAR))
EAR, = max St(t)
(26)
mediamee SA((t) +
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Spike Anomaly
Context Anomaly
Structural Anomaly
Figure 5: Qualitative validation of evidence decomposition on synthetic datasets. Rows corre- spond spike, contextual, and structural anomalies. Columns correspond to the Nonlinear VAR generator (left) and the State-Switching generator (right). In each case, the bottom stacked- plot shows that the intended evidence channel selectively activated in the anomaly region.
Table 14: Evidence Amplification Ratio (EAR) across isolated anomaly types. Diagonal domi- nance demonstrates strong evidence-type selectivity.
GT Anomaly Type
Sstruct
Sex
Sepike
Structural anomaly
3,3
1.8
1.3
Contextual anomaly
2.1
4.7
1.7
Spike anomaly
1.6
2.3
6.2
Interpretation. Structural perturbations trigger global increases in Sstruets contextual drifts in- duce smooth elevation in Setxe and impulsive outliers cause sharp localized peaks in Sapike- Minor off-diagonal activation is expected due to natural interactions between mechanisms, These results confirm semantic alignment and quantitative selectivity of PGRF-Net's evidence channels.
Evidence Stability Test Interpretability requires that evidence stable under small input per- turbations. We evaluate robustness by injecting mild Gaussian noise (std 0. 05) into clean sequences and computing the Kendall rank correlation between trajectories of clean and noisy evi- dence.
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Table 15: Evidence stability under Gaussian noise (Kendall's 7).
Structural and spike evidence are highly stable; contextual deviation shows moderate robustness.
Evidence Type
Kendall r
p-value
Satrett
0.9450
0.0000
S
0.5943
0.0000
Sqplo
0.9204
0.0000
Interpretation. Structural and spike evidence remain stable even under noise, confirming that PGRF-Net's diagnostic attribution is not fragile. Contextual evidence shows moderate robustness as it naturally responds to distributional drifts.
Contextual Drift Stage 2 incorporates suppres- sion mechanism designed to down-weight contextual evidence on pseudo-normal windows. nat- ural question is whether this mechanism might also suppress predictable yet abnormal contextual drifts-ic.., cases where Spred is low but Setx remains high. Such scenarios could principle generate false negatives if the contextual gate activation Jetx is incorrectly reduced.
Behavior Under Predictable-but-Abnoovv
To examine this potential failure mode, we construct a controlled synthetic setting where the drift remains highly predictable but is distributionally abnormal:
3t = It-1 +
5 = 0.02, ~ N0(,0.001)
(27)
producing smooth, monotonic shift that remains forecastable by AR predictor while departing from the normal prototype regime.
We compare two configurations: (i) the full model with suppression (Asup = 0.1), and (ii) variant
without suppression (Asup = 0). The contextual gate behaviors and detection metrics are summa- rized below.
Table 16: Effect of suppression under predictable contextual drift. Suppression reduces Jetx only mildly and does not collapse contextual evidence into the normal range.
Setting
Avg Getx (Normal))
Avg 9at (Drift)
Drift Recall
Drift Fl
No suppression
0.2296
0.2848
0.3100 0.1688
0.4733
With suppression
0.1683
0.2628
0.2888
Suppression decreases contextual gate activation under drift by only R 8%, while maintaining clear separation between normal and drift windows 1683 vs. 0.2628). Thus, pre- dictable contextual shifts than collapsed.
Interpretation.
interpreted normal, and contextual evidence is preserved rather
The decrease in recall and Fl reflects inherent precision-recall trade-off: Stage 2 biases the model toward more conservative, high-precision anomaly filtering on pseudo-normal windows. This behavior aligns with the design objective of preventing over-activation stable segments, but may reduce sensitivity to gradual contextual shifts.
Overall, the stress test confirms that Stage 2 suppression preserves contextual evidence for battccabbl-butt-boommalll drifts, while introducing a precision- trade-off that we explicitly ac- knowledge limitation.
E.4 RUNTIME SCALABILITY WITH RESPECT TO SEQUENCE LENGTII AND THE NUMBER OF VARIATES
To address reviewer concerns regarding runtime scalability, evaluate how PGRF-Net scales with (i) the sequence length and (ii) the number of variates D. Because real-world datasets have fixed resolutions, perform controlled synthetic tests where T and D can be varied independently. All
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experiments w=60, batch size 128, 1108:1=18,, Conformer layers, and measured single A100 GPU with synchronized timing.
E.4.1 SCALING
SEQUENCE LENGTHI T
We fix D=25 and vary 7 (1k, 5k, 10k, 50k, 100k). shown Table 17 training time grows nearly linearly in T, while inference latency remains constant ( 0.07 ms/window), since the per- window encoder computation is independent global sequence length. Peak memory also stays stable (377-381 MB), indicating that no ddddeeendent activations accumulate across windows.
Table 17: Runtime scalability w.r.t sequence length T (fixed D 25).
7'
Train (s/epoch)
Infer (ms)
Mem (MB)
1k
0.32
0.0765
381.3
5k
1.46
0.0694
379.8
10k
2.79
0.0690
377.8
50k
13.95
0.0690
380.2
100k
27.59
0.0695
377.5
E.4.2 SCALING WITH DIMENSIONALITY D
training time in- creases smoothly with D, matching the expected cost of multi-channel attention and prototype scor- ing. Inference latency increases moderately (0.05 -0.- 14 ms/window), and memory remains below 500 MB even for D=100, demonstrating scalability to high-dimensional industrial MTS settings.
We fix T=50k and vary D {5, 10, 25, 50, 100). As summarized in Table 18
Table 18: Runtime scalability w.r.t. number of variates D (fixed T =5k)).
D
Train (s/epoch)
Infer (ms)
Mem (MB)
5
9.03
0.0495
362.6
10
10.22
0.0550
365.3
25
13.88
0.0694
380.0
50
19.87
0.0939
405.7
100
31.87
0.1421
466.6
Summary. Across both experiments, PGRF-Net shows: (i) liae-linear scaling w.r.t. T. (ii) mod- crate scaling w.r.t. D, and (ii) stable memory usage. These results confirm that the architecture is computationally efficient and well suited for long-horizon and high-dimensional MTS applications.
USE OF LARGE LANGUAGE MODELS
In the preparation of this manuscript, large language model utilized writing aid. Its role was strictly limited to improving grammar, rephrasing for clarity, and correcting typographical errors. The LLM did not contribute the core research ideas, experimental design, or the analysis of the results presented in this paper.
24


Reviews:
[{"review_id": "29J25eTADH", "reviewer": "Reviewer_FXip", "summary": "This paper proposes PGRF-Net, a prototype-guided relational fusion network for multivariate time-series anomaly detection. The method aims to bridge the gap between performance and interpretability by decomposing anomalies into four evidence types (predictive, structural, contextual, and spike deviations) and integrating them via a Gated Evidence Fusion Network trained in a two-stage unsupervised framework. Experiments across five benchmarks (MSL, SMAP, PSM, SMD, SWaT) show competitive or superior results to state-of-the-art models while maintaining computational efficiency. The paper claims that the design not only enhances accuracy but also offers diagnostic interpretability, enabling users to understand why an anomaly occurs, not just that it does.", "questions": "- **Q1.** Can the authors provide a user-centered or human evaluation of interpretability (e.g., do practitioners find the decomposed evidence helpful)?\n\n- **Q2.** How robust are the results when evaluated with non point-adjusted metrics, or under stricter event-level protocols?\n\n- **Q3.** Could the authors clarify how the fusion gates' learned weights correspond to anomaly semantics in unseen domains?\n\n- **Q4.** How does the proposed diagnostic interpretability compare quantitatively to existing interpretable baselines like InterFusion [b]?\n\n[b] Li, Zhihan, et al. \"Multivariate time series anomaly detection and interpretation using hierarchical inter-metric and temporal embedding.\" Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining. 2021.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "- **S1.** The paper presents a well-motivated and coherent framework combining multiple sources of anomaly evidence through a gated fusion mechanism.\n- **S2.** The two-stage unsupervised training is thoughtfully designed and appears to improve robustness and fusion stability.\n\n- **S3.** The diagnostic decomposition (predictive, structural, contextual, spike) is conceptually valuable and well illustrated in case studies.", "weaknesses": "- **W1.** The evaluation lacks methodological rigor: the paper relies on benchmark protocols with known inflation issues and does not provide sensitivity tests on the point-adjusted evaluation method. (See Section 6.2.5 in [a])\n\n- **W2.** The interpretability claim is unsubstantiated quantitatively. It seems that no metrics, user studies, or human-in-the-loop validations are provided. This omission undermines the central thesis of diagnostic transparency. There is no analysis of failure cases or trade-offs, which would be crucial for a model claiming diagnostic transparency.\n\n- **W3.** The novelty, though meaningful, builds incrementally upon prior prototype-based and dependency-aware methods rather than fundamentally redefining the paradigm.\n\n\n[a] Trirat, P., Shin, Y., Kang, J., Nam, Y., Na, J., Bae, M., ... & Lee, J. G. (2024). Universal time-series representation learning: A survey. arXiv preprint arXiv:2401.03717.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3QfPYfC2B5", "reviewer": "Reviewer_eVo9", "summary": "This paper proposes PGRF-Net for multivariate time series anomaly detection and interpretation. PGRF-Net decomposes anomaly evidence into multiple types and introduces prototype banks and a gated fusion mechanism to learn diagnostic representations. Experiments across several benchmark datasets are presented to demonstrate its performance advantage and diagnostic interpretability.", "questions": "* How do prototype formation and gate suppression behave when the training data are contaminated with anomalies or noisy labels?\n* How are the scores in Table 4 aggregated? Have the authors compared the proposed gated fusion mechanism against simple aggregation strategies such as averaging, max pooling, or naive ensemble fusion?\n* How does end-to-end joint training compare against the proposed two-stage training in terms of performance, convergence, and stability?\n* Point-adjustment techniques have been shown to overestimate model performance, and pointwise measures such as AUC-PR are sensitive to anomaly ratio and temporal noise. The authors are encouraged to consider time-series–aware measures such as Range-F1 [1] and VUS-PR [2] and evaluate on a more comprehensive benchmark such as TSB-AD [3].\n* The paper lacks an analysis of runtime scalability with respect to both sequence length and the number of variates\n\n[1] Tatbul N, Lee TJ, Zdonik S, Alam M, Gottschlich J. Precision and recall for time series. Advances in neural information processing systems. 2018;31.\n\n[2] Paparrizos J, Boniol P, Palpanas T, Tsay RS, Elmore A, Franklin MJ. Volume under the surface: a new accuracy evaluation measure for time-series anomaly detection. Proceedings of the VLDB Endowment. 2022 Jul 1;15(11):2774-87.\n\n[3] Liu Q, Paparrizos J. The elephant in the room: Towards a reliable time-series anomaly detection benchmark. Advances in Neural Information Processing Systems. 2024 Dec 16;37:108231-61.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* The paper presents a novel and well-motivated model to unify detection and interpretability.\n* The work provides comprehensive ablation studies that evaluate several architectural components, demonstrating the contribution of the proposed modules to detection performance.\n* The visualization and synthetic case studies offer qualitative interpretability.", "weaknesses": "* Robustness under anomaly contamination is not well explored.\n* Limited benchmark results.\n\nPlease find the detailed comments in the following section.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tRC3Lkhtfz", "reviewer": "Reviewer_Ahii", "summary": "The paper proposes PGRF-Net, an unsupervised framework for multivariate time-series anomaly detection that reframes detection as a diagnostic process. Rather than outputting a single anomaly score, PGRF-Net decomposes anomalies into four types: predictive deviation, structural changes in inter-variable dependencies, contextual deviation from learned normal-behavior prototypes, and localized spike events. These are generated via a Multi-Faceted Evidence Extractor and adaptively fused using a Gated Evidence Fusion Network trained in a two-stage unsupervised manner. The method is evaluated on five standard MTSAD benchmarks, where it achieves competitive or state-of-the-art performance while providing decomposed, human-interpretable explanations for detected anomalies.", "questions": "The paper claims the four evidence types provide diagnostic insights, but all benchmarks only have binary anomaly labels. How do the authors validate that each evidence type correctly reflects the true anomaly mechanism without ground-truth type annotations?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.\tThe work considers a critical gap in MTSAD—namely, the lack of diagnostic interpretability in deep models. By explicitly modeling multiple anomaly modalities and attributing scores to distinct evidence types, PGRF-Net offers actionable insights for domain experts, which enhances trust and operational utility.\n2.\tThe architecture is thoughtfully designed. The use of frequency decomposition, conformer encoders, and learnable prototype banks for structural, contextual, and spike patterns can grasp both time-series modeling and interpretable representation learning. The two-stage training strategy effectively separates representation learning from evidence fusion.", "weaknesses": "1.\tThe four evidence types are presented as diagnostic, but the model provides associative, not causal, explanations. For instance, a high structural deviation score indicates a shift in learned dependency patterns—but it does not establish whether this shift caused the anomaly or is a consequence of it.\n2.\tAll benchmarks provide only binary anomaly labels, not fine-grained labels indicating anomaly types (e.g., spike vs. contextual shift). Consequently, the paper cannot verify whether the decomposed evidence correctly identifies the underlying anomaly mechanism.\n3.\tThe structural prototype bank assumes acyclic dependency graphs (via DAG constraints), which may not hold in many real-world feedback systems (e.g., control loops in industrial plants). The paper does not discuss this limitation or evaluate scenarios where cyclic dependencies are essential.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "I0mLBly73E", "reviewer": "Reviewer_VBHJ", "summary": "The paper introduces PGRF-Net, a prototype-guided relational fusion network for unsupervised multivariate time-series anomaly detection (MTSAD). The stated objective is to close the gap between high detection performance and diagnostic transparency by decomposing an anomaly score into four interpretable “evidence” channels: (i) predictive deviation, (ii) structural deviation in learned inter-variable dependencies, (iii) contextual deviation from normal-behavior prototypes, and (iv) localized spike magnitude. Methodologically, the model has two stages: a Multi-Faceted Evidence Extractor and a Gated Evidence Fusion Network that learns instance-dependent weights for the non-predictive channels and combines them with prediction error. Training is fully unsupervised, with Stage-1 losses for prediction and prototype/graph regularization, and Stage-2 losses for gate suppression on pseudo-normal samples plus entropy sharpening. Experiments on five public benchmarks (MSL, SMAP, PSM, SMD, SWaT) report state-of-the-art average F1 and competitive AUC-ROC/PR, along with qualitative “five-panel” diagnostic visualizations linking anomaly attributions to changes in relational masks.", "questions": "- DAG Constraint vs. Cyclic Dependencies: Many industrial/biological systems have feedback loops. By imposing acyclicity on structural prototypes, are you baking in a bias that pushes cyclic phenomena into other channels (e.g., S_ctx or Spred)? What breaks if the true dependency graph is nearly cyclic (or dense), and how would relaxing DAG constraints (e.g., allowing small cycles with penalties) affect S_struct fidelity?\n\n- Baseline Mask (M_base) Stability: M_base is averaged from early-training masks. If normal data itself is multi-modal or drifting, the mean mask may be unrepresentative. Why not prototype-ize M_base itself (i.e., multiple baseline masks with selection), or define baselines by time-clustered regimes? What empirical evidence shows M_base is stable and representative, and how sensitive is S_struct to the time window used to compute it?\n\n- Stage-2 suppresses explanatory gates on pseudo-normal samples identified by low Spred. This equates “predictable” with “normal.” How does the method behave when contextual drifts are predictable (low Spred) yet abnormal relative to prototypes (high S_ctx)? Could gate suppression systematically down-weight contextual evidence in such cases, and have you measured the false-negative impact under controllable scenarios?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- A clear diagnostic framing of MTSAD that operationalizes interpretability via four disjoint evidence channels and a gated fusion mechanism. This goes beyond post-hoc explanations by making attribution a first-class training target.\n\n- The two-stage training is well-motivated: learn robust features and prototypes first; then calibrate evidence attribution with gate suppression on pseudo-normal samples and entropy sharpening for selectivity.\n\n- Sensible regularization of the structural channel (sparsity, acyclicity, temporal stability vs. a baseline mask) reduces degenerate graphs and contributes to stable, interpretable dependency patterns.\n\n- The paper asserts “competitive or superior” performance; averaged F1 and AUC-PR are high, but per-dataset AUC-ROC/PR tables show mixed margins and sometimes narrow differences. Statistical significance (e.g., paired tests across seeds) and variance bars are not reported; claims of superiority would be stronger with formal significance tests.", "weaknesses": "- The structural deviation relies on a learned baseline mask (M_base) defined via Early-training averages on presumed normal data. If the normal set contains regime shifts or drifting dependencies, M_base may encode mixture regimes; deviations may then over- or under-fire. The paper does not quantify how sensitive S_struct is to mis-specified normal baselines, distribution shift, or domain drift within normal periods.\n\n- The acyclicity constraint is imposed on structural prototypes so that convex combinations remain DAG-like. However, instantaneous correlations in cyber-physical systems can be cyclic (feedback loops). For domains with known cycles, forcing DAGs may bias the learned mask and redirect anomaly mass to other channels, potentially mis-attributing structural anomalies as contextual or predictive deviations.\n\n- The use of point adjustment and best-F1 thresholding is conventional, but can inflate event-level detection and mask temporal localization quality. While AUCs are reported, there is no comparison on strict point-wise metrics.\n\n- The interpretability story is qualitative. The paper would benefit from quantitative interpretability metrics (fidelity, stability, human-utility studies) or counterfactual tests (e.g., perturb relationships to see whether S_struct changes in expected directions, with calibration curves).\n\n- Figure 1 could be improved; excessive whitespace and mixed concepts dilute key information, with small labels.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)