PaperlayerView exact revision on arXiv

Source-linked AI summary

Cross-Domain Industrial Fault Detection by Causal Mechanism Monitoring

Dhiraj Neupane, Mohamed Reda Bouadjenek, Richard Dazeley, Sunil Aryal

arXiv:2608.14666v1cs.AI

TL;DR

Industrial fault detectors can miss coupling faults when individual sensor marginals remain normal. CMR-Mamba learns causal coupling representations and is competitive with strong baselines across electromechanical, hydraulic, and cyber-physical domains, with kNN manifold scoring providing the dominant ablation gain.

  • Problem

    Existing marginal-distribution monitoring can miss coupling faults that disrupt physical relationships while leaving individual sensor signals within normal ranges.

  • Method

    CMR-Mamba pairs per-domain Mamba encoders with a causal cross-modal predictor and scores anomalies on the healthy effect manifold using kNN distance or mechanism residuals.

  • Results

    CMR-Mamba is competitive with strong baselines across all evaluated environments, while kNN scoring adds +0.129 AUROC and causal regularisation adds +0.013 on Paderborn.

  • Takeaways & Limitations

    The results support monitoring causal coupling as an interpretable approach to detecting faults across mechanically, hydraulically, and cyber-physically distinct systems.

  • Takeaways & Limitations

    Evaluation requires strict machine- and time-separated splits, limiting direct comparability with studies that permit shared physical instances or adjacent recordings.

Abstract

from arXiv · show

Unsupervised fault detection in industrial systems is dominated by reconstruction based methods that monitor individual sensor marginal distributions. This misses coupling faults, where the physical relationship between sensor groups breaks while marginal statistics remain normal. Such faults evade marginal monitoring and persist as latent failures, with direct consequences for system reliability and safety. We propose CMR-Mamba (Causal Mechanism Representation Mamba), which trains per domain Mamba state-space encoders on healthy data. A causal cross-modal predictor regularises these encoders so that the effect-channel manifold reflects the normal cause-to-effect coupling. Anomalies are scored by k-nearest-neighbour (kNN) distance on this manifold or by the mechanism residual between the observed and the causally predicted effect embedding. We evaluate CMR-Mamba on electromechanical (Paderborn bearings), hydraulic (ZeMA) and cyber-physical (SWaT) coupling-fault domains. Ablations establish two findings. First, k-NN manifold scoring, rather than the encoder family, is the dominant source of gain over reconstruction-error scoring, improving baselines by up to 0.42 AUROC and exceeding the gain from causal regularisation. Second, aggregate AUROC is saturated by easy faults that any strong method solves, so the methods separate only on the low-separability subset. There CMR-Mamba leads the evaluated baselines on Paderborn artificial defects and on SWaT stealthy attacks, which keep every sensor inside its normal range and which marginal methods detect only at chance. CMR-Mamba therefore offers an interpretable and consistently competitive approach to coupling-fault detection across mechanical, hydraulic and cyber-physical systems. Code and data are available at https://anonymous.4open.science/status/CMR_Mamba_MFD_1177.

1 INTRODUCTION

CMR-Mamba addresses the blind spot of reconstruction-based anomaly detection by monitoring whether cross-sensor physical relationships remain healthy. It combines healthy-data Mamba encoders, causal coupling regularisation, and kNN manifold or mechanism-residual scoring, with validation across electromechanical, hydraulic, and cyber-physical systems.

  • Motivation: Undetected machinery faults can escalate into downtime, safety hazards, economic losses, and, in severe cases, loss of life.Reliable and timely fault detection is therefore a central industrial and research concern.
  • Problem: Reconstruction-based unsupervised methods monitor signal marginals, so they can miss faults that preserve individual sensor distributions but disrupt inter-channel coupling.A bearing micro-crack may leave vibration amplitude normal while changing the motor-current-to-vibration relationship.
  • Method: CMR-Mamba trains domain-specific encoders on healthy data with reconstruction loss and causal cross-channel coupling regularisation, then scores anomalies using kNN manifold distance or reconstruction error.The framework reframes detection as testing whether physical relationships still follow the healthy pattern.
  • Method: Mamba state-space blocks provide O(L) sequence complexity, enabling processing of long industrial sensor sequences that are costly for Transformer-based architectures.The Paderborn bearing dataset records vibration and current at 64 kHz, or 64,000 data points per second per channel.
  • Results: 0.944 AUROC: CMR-Mamba detects industrially relevant real-damage bearing faults under 15-fold leave-bearing-out cross-validation on Paderborn.Its aggregate performance is 0.880 overall, with up to a 0.930 per-fold oracle upper bound.
  • Results: The framework is evaluated without core redesign on ZeMA hydraulic data and the SWaT cyber-physical water-treatment testbed, adapting the monitored cause-effect sensor pairs across domains.The ZeMA adaptation replaces motor current-to-vibration with motor power-to-pump pressure, while SWaT evaluates the causal mechanism residual.

2 BACKGROUND AND RELATED WORK

Machinery fault detection has shifted from expert-designed signal processing toward deep learning, but most methods remain supervised or reconstruction-based and can miss faults that alter sensor relationships without changing individual marginals. This motivates unsupervised, mechanism-aware approaches drawing on causal structure learning and efficient sequence models.

  • Traditional signal processing: Traditional vibration- and acoustic-based methods use expert-selected frequency bands and interpretive thresholds, limiting scalability across machine types and operating environments.Examples include envelope spectrum analysis, empirical mode decomposition, short-time Fourier transforms, and continuous wavelet transforms.
  • Data-driven fault detection: Deep learning has expanded fault detection through convolutional, recurrent, and Transformer-based models, but most approaches require labelled examples of each fault type.These architectures target time-frequency patterns, temporal dynamics, or long-range dependencies.
  • Unsupervised detection: Unsupervised anomaly detection trains on healthy data and commonly flags test samples with high reconstruction error from autoencoders or related generative models.This label-efficient setting has attracted interest because labelled fault data are scarce.
  • Limitations of reconstruction: Reconstruction-based methods monitor sensor marginals and may miss early-stage mechanical defects that change inter-sensor relationships before affecting individual sensor behaviour.Autoencoders can also reconstruct out-of-distribution data through identity shortcuts and correlated low-level features.
  • Related work: The targeted unsupervised and label-efficient machinery setting remains comparatively underexplored, despite work on transfer learning, physics-informed diagnosis, semi-supervised assessment, and change-point detection.Most broader machinery fault-detection literature remains supervised.
  • Causal and sequence-model foundations: The approach builds on causal structure learning and causal representation learning alongside structured state-space models that support efficient sequence processing.Prior work includes causal discovery, time-series causal surveys, neural Granger causality, and mechanism-level representation learning.

3 METHODOLOGY

CMR-Mamba trains domain-specific Mamba encoders and a causal predictor jointly on healthy data to represent normal cause-to-effect coupling. At inference, it discards the predictor and decoders, scoring test windows by nearest-neighbour distance on the healthy effect-embedding manifold.

  • Framework: Three trainable components—cause encoder, effect encoder, and causal predictor—are trained jointly on healthy data to shift detection from signal appearance to manifold geometry.Mamba encoders convert raw sensor channels into token sequences, while the predictor maps cause tokens toward effect tokens.
  • Anomaly scoring: At inference, only the effect encoder remains: healthy windows form a pooled reference bank, and test windows receive low scores when near healthy vectors and high scores when distant.The predictor and decoders are discarded after training.
  • Encoder architecture: Mamba selective state-space blocks process raw waveforms at native sampling rates with linear-time scaling, preserving fine transient structures that downsampling or spectrograms can discard.The highest-rate domain reaches tens of thousands of samples, where quadratic-complexity architectures would be intractable.
  • Encoder architecture: Channels measuring the same physical quantity share an encoder instance, while distinct quantities use separate encoders to impose appropriate representation sharing.This allocation provides a common representation for physically equivalent channels without forcing distinct quantities into one latent space.
  • Anomaly scoring: Manifold distance avoids decoder-dependent reconstruction failures and exposes coupling-degrading faults even when their marginal effect-signal changes are small.Faults that preserve coupling while adding unrelated components may remain near the healthy manifold and be missed; Paderborn faults are described as coupling-degrading.
  • Anomaly scoring: The predictor residual is less effective on single-coupling datasets because average healthy transfer functions create bearing-identity noise on unseen healthy bearings.The predictor’s average may match no individual bearing exactly, increasing residuals without indicating faults.

4 EXPERIMENTAL SETUP

The experiments evaluate a common causal coupling-fault framework across electromechanical, hydraulic, and cyber-physical datasets using domain-specific preprocessing, windows, and leakage-resistant splits. AUROC is the primary threshold-independent evaluation metric.

  • Datasets and causal pairs: Three datasets span electromechanical, hydraulic, and cyber-physical domains while preserving synchronously recorded cause and effect channels for causal evaluation.Paderborn pairs motor current with bearing vibration, ZeMA pairs motor power with pump pressure, and SWaT uses active actuators and process sensors.
  • Datasets and causal pairs: SWaT records 51 channels at 1 Hz, including 26 discrete actuators and 25 continuous sensors, with 14 constant actuators pruned to 12 active cause components.Linear regression under normal operation separates sensors carrying a learnable physical mechanism from those governed by unpredictable chemical dynamics.
  • Preprocessing: Each channel is z-score standardised using statistics computed exclusively from healthy data and then applied unchanged across all splits.An epsilon of 10^-8 guards against division by zero on flat channels.
  • Windowing: Window lengths follow plant dynamics: Paderborn uses 32,768 samples with 50% overlap, while SWaT uses 256-second windows with 128-second stride.The Paderborn window spans 0.512 seconds at 64 kHz; the SWaT length reflects an attack-duration median of 444 seconds.
  • Splits and evaluation: No physical machine instance or adjacent time stretch appears in both training and testing, preventing leakage from shared bearing characteristics or overlapping temporal context.Paderborn assigns every window from a bearing entirely to one split.
  • Splits and evaluation: AUROC is the primary metric because it measures ranking quality without fixing an operating threshold, which remains plant- and cost-dependent.It is defined as the probability that a randomly chosen faulty window scores higher than a randomly chosen healthy one.

5 RESULTS AND ANALYSIS · 5.1 Main Cross-Dataset Results · 5.2 Baseline Comparison and the Role of the Scoring Rule

Across Paderborn, ZeMA, and SWaT, CMR-Mamba is competitive, with performance shaped strongly by fault separability and the anomaly scoring rule. kNN scoring consistently improves reconstruction-based detectors, while hard low-separability faults distinguish methods more than aggregate AUROC.

  • 5.1.1 Paderborn Results and 15-Fold Cross-Validation.: CMR-Mamba attains 0.8803 ± 0.1085 overall AUROC on Paderborn under one fixed configuration across 15 evaluation folds.Its AUROC decomposes into 0.7919 on artificial faults and 0.9445 on real damage, with three runs agreeing within 0.003 at the aggregate.
  • 5.1.1 Paderborn Results and 15-Fold Cross-Validation.: Paderborn performance ranges from 0.9998 AUROC on split 1 to 0.8616 on hard split 12, whose faulty and healthy embeddings substantially overlap.Split 12 has a faulty-to-healthy score ratio of 0.97× and a distance ratio of 1.045, compared with a mean of 3.487 across the other fourteen folds.
  • 5.1.1 Paderborn Results and 15-Fold Cross-Validation.: On Paderborn, CMR-Mamba does not differ significantly from USAD, the VAE, or the autoencoder, but significantly outperforms Deep SVDD.The Wilcoxon signed-rank p-values are 0.64, 0.52, 0.25, and 0.001 respectively.
  • 5.1.2 ZeMA Results and SWaT Point-wise F1.: On ZeMA, CMR-Mamba reaches 0.9843 ± 0.0065 overall AUROC, while weak-leakage faults remain harder than severe leakage.Severe-fault AUROC averages 0.9998, whereas weak-leakage faults reach 0.9688 at k=20; the no-stop-gradient variant spans 0.9752 to 0.9897 across seeds.
  • 5.1.3 Consolidated Cross-Dataset Results.: No baseline remains competitive across all three domains: the autoencoder collapses to 0.779 on ZeMA, Anomaly Transformer reaches 0.761 on SWaT, and Deep SVDD reaches 0.840.The VAE is the only baseline that holds up everywhere, although it exceeds CMR-Mamba by overlapping margins on ZeMA and SWaT.
  • 5.1.3 Consolidated Cross-Dataset Results.: Aggregate AUROC is saturated by easy faults, so methods separate primarily on low-separability subsets; CMR-Mamba leads those hard subsets.All methods approach ≈1.0 on severe ZeMA leakage, while SWaT attacks have median sensor total-variation distance 0.61.
  • 5.2.1 Baseline Comparison on the Paderborn Dataset.: Replacing native reconstruction-error scoring with kNN distance on identical embeddings raises USAD from 0.537 to 0.899, a net improvement of +0.362.The matched evaluation isolates scoring strategy from encoder capability, and the same kNN advantage appears on hydraulic and cyber-physical tasks.
  • 5.2.3 Reconstruction Scoring of the CMR Encoder.: For the CMR encoder, reconstruction scoring yields 0.685 AUROC versus 0.955 with kNN scoring, showing that the scoring rule dominates the encoder architecture.The causal regulariser shapes a compact healthy manifold rather than prioritising faithful waveform reconstruction, making reconstruction error a poor anomaly signal.

5.3 The Mechanism Residual on Low-Separability Faults · 5.4 Ablation Studies

Low-separability coupling faults expose differences hidden by saturated aggregate AUROC: the mechanism residual detects stealthy SWaT attacks and subtle Paderborn defects, while ablations identify dataset-dependent design choices. The stop-gradient, loss weights, embedding strategy, and neighbourhood geometry materially affect performance across domains.

  • 5.3 The Mechanism Residual on Low-Separability Faults: On SWaT stealthy attacks, the CMR mechanism residual leads at 0.747 AUROC, ahead of the VAE at 0.701, while pure-marginal scores fall to about 0.40.Stealthy attacks keep every sensor within normal historical thresholds, whereas blunt attacks typically push sensors beyond range.
  • 5.3 The Mechanism Residual on Low-Separability Faults: The residual and reconstruction scores are complementary: reconstruction methods lead on blunt anomalies, whereas the causal residual leads on stealthy coupling violations.The stealthy subset contains 192 windows, so precise margins require caution despite the unambiguous qualitative ordering.
  • 5.3 The Mechanism Residual on Low-Separability Faults: At the 90th, 95th, and 99th healthy percentiles, the CMR stop-gradient residual scores 0.747, 0.747, and 0.753, versus VAE scores of 0.701, 0.701, and 0.708.Pure-marginal and native VAE scores remain between 0.40 and 0.44 across thresholds.
  • 5.3.1 Artificial Defect Faults on the Paderborn Dataset.: Under the fixed 15-fold protocol, CMR-Mamba is the strongest learned detector on Paderborn artificial faults, while real damage is detected above 0.97 by reconstruction baselines.Artificial defects subtly perturb current-to-vibration coupling, whereas real damage produces distributed energetic signatures.
  • 5.4.1 Loss-Weight Ablations on Paderborn.: The mechanism-loss weight peaks at 0.9405 at γ=0.2; smaller and larger settings score 0.9203 at γ=0.05 and 0.9229 at γ=0.5.The overall AUROC varies within a 0.021 span, while real-damage scores remain near-saturated between 0.984 and 0.995.
  • 5.4.2 Embedding Strategy and Neighbourhood Size on Paderborn.: The best Paderborn embedding strategies are cause-effect concatenation at 0.8912 and cause-conditioned effect mean at 0.8846, whereas max-based descriptors remain near 0.69.The stronger strategies are more stable across folds, with standard deviation ≈0.045 versus ≈0.109 for std-pool.
  • 5.4.3 The Stop-Gradient and Training-Set Size.: Removing the stop-gradient decreases Paderborn AUROC by 0.068 from 0.9390 to 0.8714, but increases ZeMA AUROC by 0.056 from the stop-gradient variant.On ZeMA, the no-stop-gradient variant also reduces seed standard deviation from 0.0409 to 0.0065 because the unreconstructed cause encoder has only 415 cycles.
  • 5.4.3 The Stop-Gradient and Training-Set Size.: On SWaT, the stop-gradient variant scores 0.8679 versus 0.8557 for the mechanism residual and 0.8629 versus 0.8186 for k-NN, while ZeMA’s optimal k values are 20 and 50.These results link stop-gradient benefits to training-set size and show that neighbourhood size reflects domain-specific manifold geometry.

5.5 Cross-Domain Transfer

CMR-Mamba transfers across domains with largely invariant architecture, while adapting only cause-channel treatment. The cause-reconstruction weight is the main domain-specific setting because optimal values reflect each domain’s causal signal composition.

  • Cross-domain framework: Encoder, loss, optimiser, and scoring rule remain identical across domains, while only the cause-channel treatment is adapted.Per-domain causal pairs, window lengths, channel pruning, and data splits are specified separately.
  • Cause regularisation: The cause-reconstruction weight is the sole setting that does not transfer uniformly and requires a distinct optimum for each evaluation domain.The differences are attributed to the physical composition of each cause signal rather than an architectural limitation.
  • Cause regularisation: 0.9977 overall is achieved at α_x = 0, while Paderborn benefits from α_x = 0.75 because motor current retains causal electromagnetic-drive information.ZeMA motor power contains unrelated electrical overhead, so reconstructing it pollutes the causal predictor; its optimum is α_x = 0.
  • Cause regularisation: Within 0.005, SWaT mechanism-residual and k-NN AUROC remain flat across cause weights from 0 to 1, so α_x = 0 is adopted for efficiency.Removing cause reconstruction eliminates actuator decoders and reduces parameters; the pruned actuator set is treated as a clean cause group.
  • SWaT sensor physics: SWaT requires multi-channel cause and effect tensors because its six operational stages and broadly distributed cyber-attacks cannot be monitored by one cause-effect pair.A linear regression fitted on normal operation predicts each sensor from 12 active actuator signals to test which sensors carry a learnable mechanism.

6 DISCUSSION AND LIMITATIONS

The discussion finds that scoring choices and structural design affect Paderborn performance, while cross-domain results favor different methods on different datasets and fault subsets. It also identifies transferability and root-cause localization as future work.

  • Paderborn ablations: The mechanism weight peaks at γ= 0.2, yet overall AUROC varies by less than 0.021 across an order-of-magnitude evaluation range.The neighbourhood size, distance metric, cause-reconstruction weight, and stop-gradient variant are set per domain rather than universally fixed.
  • Paderborn ablations: The stop-gradient operator improves Paderborn AUROC by +0.068 without inducing representation collapse.Its benefit is dataset-dependent rather than universal.
  • Cross-domain comparison: The strongest baseline is a multi-seed variational autoencoder with k-NN scoring, whose strength comes from the k-NN protocol rather than the variational objective.Its native reconstruction score reaches only 0.66 to 0.77.
  • Hard fault subsets: The mechanism residual leads on SWaT stealthy attacks at 0.747 versus 0.701 for the variational autoencoder, while pure-marginal scores fall below chance.It also leads Paderborn artificial defects at 0.792 against 0.754.
  • Cross-domain comparison: No single baseline is strongest across all three datasets: CMR-Mamba exceeds the variational autoencoder on Paderborn, while the variational autoencoder marginally exceeds it on ZeMA.USAD’s aggregate edge is specific to Paderborn and does not generalise across domains.
  • Limitations and future work: Future work includes cross-rig validation of the hydraulic findings and extending the mechanism residual mathematically for multistage root-cause localization.The stated long-term objective is integrating the structured perception module with normative reward-learning frameworks for autonomous industrial maintenance agents.

7 CONCLUSION

CMR-Mamba is an unsupervised fault detector that monitors causal coupling between sensor groups rather than individual-signal marginals. It combines per-domain Mamba encoders with causal cross-modal prediction and scores anomalies using healthy effect-manifold distance and mechanism residuals.

  • CMR-Mamba monitors causal coupling between distinct sensor groups instead of evaluating individual signals’ marginal appearance.
  • The framework pairs per-domain Mamba state-space encoders with a causal cross-modal predictor.
  • Anomalies are scored using k-nearest-neighbour distance on the healthy effect manifold and a dedicated mechanism residual.

APPENDIX Full Architecture and Training Specification

The appendix provides complete per-domain training, inference, and architecture specifications for reproducibility. Settings share common optimisation components but vary in loss weights, inference, input boundaries, and decoder sharing across domains.

  • Specification overview: Tables 8 and 9 collect the full training, inference, and architecture specifications omitted from the main text for reproducibility.The appendix identifies these tables as the complete per-domain specification.
  • Training and inference: Training and inference settings share the optimiser, gradient handling, and metric, while loss weights and inference settings differ across domains.The differences follow the physical asymmetry in cause-channel signal-to-noise ratio.
  • Architecture: PerChannelMambaEncoder hyperparameters are identical across datasets, with architectural differences confined to input boundaries and encoder/decoder sharing patterns.These differences arise from the acquisition systems’ sampling rates and sensor counts.
  • Dataset instantiations: Output waveform lengths are 32,768 for Paderborn, 6,000 for ZeMA, and 256 for SWaT, with BatchNorm1d/GELU used at every stage.The table reports the same normalisation and activation pair for all three domains.
  • Decoder sharing: Decoder sharing differs by domain: Paderborn shares the cause decoder on A and B, ZeMA uses none, and SWaT uses per-sensor effect decoders while omitting the cause decoder.For SWaT, the omitted cause decoder corresponds to α_x=0.

Paderborn Bearing Subset

The Paderborn evaluation subset comprises 25 bearing experiments, including six healthy bearings for training and held-out testing and 19 faulty bearings for evaluation. Fault categories include outer-race, inner-race, and combined inner- and outer-race defects.

  • Dataset composition: The subset contains 25 Paderborn bearing experiments: 6 healthy bearings and 19 faulty bearings.The faulty bearings were selected for evaluation, while healthy bearings supported training and held-out testing.
  • Validation protocol: The 6 healthy bearings are used for both training and held-out testing under leave-bearings-out cross-validation.This separates healthy-data learning from held-out bearing assessment.
  • Fault categories: The faulty-bearing categories include outer race (OR), inner race (IR), and combined inner- and outer-race defects (IR+OR).These abbreviations define the fault types represented in the evaluation set.

Per-Fold and Per-Seed Detail

This section provides detailed per-fold Paderborn and per-seed ZeMA AUROC breakdowns underlying the aggregate results. On Paderborn, CMR-Mamba exceeds each matched baseline on most folds, especially Deep SVDD.

  • Paderborn per-fold results: Table 11 gives per-fold Paderborn AUROC under (α_x, α_y, γ) = (0.75, 1.0, 0.2), with each fold holding out a listed healthy bearing pair.The values are three-run means.
  • Paderborn per-fold results: Table 12 reports matched-protocol per-fold Paderborn AUROC values for CMR-Mamba and four baselines, forming the paired data for the Wilcoxon signed-rank test.The protocol uses standard-deviation pooling, k=1, cosine distance, and three-run means for CMR-Mamba.
  • Paderborn per-fold results: CMR-Mamba exceeds USAD on nine of fifteen Paderborn folds, the VAE on nine, the autoencoder on eleven, and Deep SVDD on fourteen.These comparisons use the same matched evaluation protocol across folds.
  • ZeMA per-seed results: Table 13 gives per-seed ZeMA AUROC at the optimal neighbourhood size, using k=20 without stop-gradient and k=50 with stop-gradient.The section collects these full breakdowns while the main text reports aggregate results.

Per-Dataset Baseline Detail

Per-dataset comparisons report native reconstruction scores, matched k-NN scoring, optimal neighbourhood sizes, and method ranks across industrial domains. CMR-Mamba is competitive with leading baselines, while k-NN scoring substantially improves reconstruction methods and some baselines are computationally infeasible on Paderborn or PU.

  • Comparison protocol: Per-dataset tables compare native reconstruction scores, matched k-NN scores, optimal neighbourhood sizes, and per-method ranks.The consolidated cross-dataset comparison appears in Table 5, while the Paderborn panel uses a fixed evaluation protocol matched across methods.
  • Comparison protocol: The Anomaly Transformer is absent from Paderborn because O(N^2) attention exhausts GPU memory, leaving only 4 of 15 folds evaluable.At the PU window length, the Anomaly Transformer is also described as intractable.
  • ZeMA: On ZeMA, CMR-Mamba is competitive with the strongest baseline, while k-NN scoring lifts every reconstruction method far above its native score.The ZeMA comparison uses a 3-seed mean ± standard deviation and each method’s optimal k.
  • Paderborn: On Paderborn, the top four methods are statistically tied, and CMR-Mamba’s wide error bar reflects a single hard fold with collapsed class separation.The collapse occurs when a mutually covering bearing pair defeats class separation.
  • SWaT: On SWaT, CMR-Mamba’s mechanism residual ranks second behind the VAE, with the leaderboard reported as a 3-seed mean ± standard deviation.The SWaT table reports each method at its best score.

Ablation Sweep Detail

The ablation sweeps identify dataset-specific operating points and show that reconstruction weights, mechanism weighting, embedding strategy, and stop-gradient choices materially affect performance. Results also indicate that optimal kNN settings and scoring choices vary across domains.

  • Reconstruction-weight sweep: The PU current reconstruction weight peaks at α_x= 0.75, while α_y= 1.0 is adopted from a flat plateau across α_y∈{0.5, 0.75, 1.0}.At α_y= 0, performance degrades sharply because the effect encoder loses its reconstruction anchor.
  • Mechanism weighting and embeddings: Overall AUROC on PU peaks at γ= 0.2, and concatenation and std-pool dominate embedding strategies while mean+std+max and max-pool collapse.The embedding ranking averages 45 models, with each strategy evaluated at its own best k and metric.
  • Stop-gradient ablation: Removing stop-gradient costs 0.068 overall AUROC on PU without representational collapse, but improves overall AUROC by 0.056 on ZeMA while reducing seed variance sixfold.The ZeMA comparison uses three-seed means with each variant evaluated at its optimal k.
  • kNN sweep: On ZeMA, no-stop-gradient peaks at k= 20 and stop-gradient at k= 50, while both collapse at k= 200 as the neighbourhood approaches the bank size.These are three-seed mean overall AUROC results reported with weak and severe subsets.
  • SWaT operating points: On SWaT, the mechanism residual is the best CMR score and k is essentially flat; α_x= 0 is adopted because both cause-reconstruction scores are flat across the range.The cause-reconstruction sweep concludes that actuator decoders are unnecessary.

DECLARATION ON THE USE OF GENERATIVE AI

The authors state that all research and manuscript writing were carried out by them, while generative AI was used only for limited technical and editorial assistance.

  • Generative AI tools, including GitHub and Copilot, assisted only with LaTeX errors, syntax and formatting checks, grammar and spelling, and paragraph concision.They were not used to generate research ideas, results, or claims.
Loading 2608.14666v1…