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SGDB: Semantic-Geometric Decoupling and Evidence Binding for Logical Anomaly Detection

Chenrui Ji, Jiafan Lu, Zilu Luo, Feng Wan, Qiuhui Chen, Weimin Zhong

arXiv:2610.34897v1cs.CV

TL;DR

Logical anomaly detection must check whether recognized components satisfy task geometry, since correct identities and counts can still hide invalid arrangements. SGDB separates semantic decoding from geometric readout, binds measurements to identities, and evaluates executable constraints; it reports results across LOCO logical and VID tasks.

  • Problem

    Logical anomaly detection must assess whether recognized components satisfy task geometry and relationships, because correct identities and counts alone do not establish geometric validity.

    Source: §1 · p. 1

  • Method

    SGDB separates semantic decoding from geometric readout, binds compatible measurements to identities while retaining unmatched counts, and verifies task rules with traceable evidence.

    Source: §1 · p. 2

  • Results

    Across all five LOCO logical categories and all 50 VID tasks, SGDB reports 98.19 AUROC on LOCO logical.

    Source: §4.3 · p. 6, §6 · p. 12

  • Takeaways & Limitations

    Bound witness geometry improves length verification over direct prediction, while complete-support selection retains tape corrections and protects screw measurements.

    Source: §5 · p. 12

    The setup relies on normal observations and component annotations; extension to unfamiliar scenes and reduced component supervision remains a stated direction.

    Source: §6 · p. 12

Abstract

from arXiv · show

Logical anomaly detection requires recognizing scene components and measuring whether their configuration satisfies task constraints. Correct identities can coexist with inaccurate geometry; clean mask fragments can yield misleading lengths. We propose Semantic-Geometric Decoupling and Evidence Binding (SGDB). A semantic decoder learns object identities from component-annotated normal sources and factual edits; a separate reader supplies final measurements. Partial one-to-one association binds geometric witnesses to identities while retaining unmatched objects in the count. A support-certified reader selects mask-derived axes using line quality and complete component ownership. Explicit task requirements and normal-data references define executable checks, with decision thresholds fixed by independent normal calibration. Execution-grounded explanation traces rule contributions to source objects and measurements, extracting compact sufficient alarm certificates. A frozen language model expresses selected outcomes as cited claims, with numeric evidence retained by the executor. Reports preserve observed deviations and unavailable evidence. SGDB achieves 98.19% AUROC and 94.52% fixed-threshold F1 on five MVTec LOCO logical categories, and 93.56% AUROC and 92.76% F1 across all 50 VID-AD tasks. Frozen-output controls evaluate geometric readout and explanatory sufficiency and compactness.

1. Introduction

Logical inspection requires checking whether identified components satisfy task geometry and relationships, since correct identities and counts can still hide invalid arrangements. SGDB binds separate semantic and geometric outputs to task checks and traces their evidence.

1. Introduction

  • Logical inspection must evaluate geometry and relationships as well as component identities and counts; SGDB separates recognition from measurement and reconnects them through evidence binding.Bound facts support executable verification and source-linked explanations.Source: §1 · pp. 1–2

2.1. Appearance models and industrial benchmarks

  • Appearance models provide useful normality representations, while logical inspection additionally evaluates component identities, quantities, and relationships against task configurations.MVTec AD and VisA are cited as industrial benchmarks, but their appearance focus differs from logical inspection.Source: §2.1 · p. 2

2.2. Component and relationship representations

  • Component methods represent regions and composition, while object-matching methods compare objects across images; SGDB instead binds decoded identities to same-image measurements for constraint execution.Factual image edits with updated component targets train SGDB’s semantic decoding.Source: §2.2 · p. 2

2.3. Object queries and geometric evidence

  • SGDB combines candidate-initialized and grid queries, separates semantic decoding from final measurement, and reads screw axes with instance-bound PCA in native coordinates.The native-coordinate reader retains the existing axis when mask support or elongation checks make a mask readout unsuitable.Source: §2.3 · p. 3

2.4. Language, executable reasoning and reports

  • Language-based inspection includes descriptions and executable programs; SGDB evaluates discrete requirements and normal-fitted continuous intervals, then builds certificates over executed rule scores.Its certificate is linked to semantic and geometric sources established through evidence binding.Source: §2.4 · pp. 3–4

3. Semantic–geometric decoupling and evidence binding

SGDB builds object facts from component-supervised visual readers, binds decoded identities to geometric witnesses, and uses support checks to select measurements. Its executor evaluates task requirements against normal-data references and produces source-linked explanations.

3.1. Task setup and fact representation

  • At inspection, component-supervised readers predict identities, masks, and geometric witnesses, which are assembled into facts for the task.The task identifier accompanies the input image; normal measurements provide continuous bounds and score references.Source: §3.1 · p. 4

3.2. Semantic object decoding

  • A learned decoder uses candidate and spatial queries; shared parent/edit training applies updated object targets and support coupling, while edit consistency supervises count changes and shared-object displacement.The visual frontend is frozen during semantic-decoder training.Source: §3.2 · p. 4, Figure 3 · p. 4

3.3. Partial one-to-one evidence association

  • Same-class objects and witnesses are associated by center proximity through a partial injective assignment, while unmatched decoded identities remain counted with geometry unavailable.The selected same-class association radius is 0.08 across categories and both decoder variants.Source: §3.3 · p. 4

3.4. Support-certified geometric readout

  • For mask-backed lengths, candidate axes are accepted only when quality improves and structural checks certify distinct, complete component support; otherwise, the initial bound axis is retained.The quality checks include line support, extent coverage, and connectedness; the structural checks must pass for every instance before a class axis is updated.Source: §3.4 · p. 5

3.5. Constraint verification and normal calibration

  • Task rules evaluate reconstructed counts, lengths, locations, and relations; normal observations fit measurement intervals and scales, while independent calibration fixes thresholds before inspection.Missing required geometry contributes an explicit unavailable-operand residual.Source: §3.5 · p. 5

3.6. Execution-grounded explanation

  • Executed records link operands, requirements, score contributions, and sources; the executor selects minimum-size sufficient alarm certificates, while a frozen language model verbalizes them and leaves numeric evidence executor-owned.The full trace retains other deviations and unavailable operands, including in non-alarm reports.Source: §3.6 · pp. 5–6

4. Experiments

The experiments evaluate SGDB on LOCO and VID, then use shared-supervision and frozen-output controls to examine its detection, geometric readout, and explanation components. Results cover benchmark performance, axis selection, and execution-grounded reports.

4.1. Datasets and information sources

  • Evaluation uses five LOCO categories and all 50 VID deployment tasks, with normal fitting, development, and calibration partitions and independent calibration images.LOCO has 1,183 fitting, 147 development, and 305 calibration images; VID uses 1,000, 500, and 500, with ten calibration images per task.Source: §4.1 · p. 6

4.2. Implementation and comparisons

  • Comparisons include completed external deployments and internal controls sharing normal-source partitions, component-supervision budgets, the visual frontend, and task requirements.Association/readout controls reuse frozen semantic outputs and witnesses; each configuration fits references and thresholds from its own normal facts.Source: §4.2 · p. 6

4.3. Detection performance

  • 98.19 AUROC and 94.52 F1 on LOCO logical, and 93.56 AUROC and 92.76 F1 on VID; gains over FMP plus guarded geometry are +0.11/+0.98 and +2.22/+3.30 percentage points, respectively.VID covers all 50 tasks and capture conditions.Source: §4.3 · p. 6, Table 1 · p. 7, Table 2 · p. 7
  • SGDB leads displayed LOCO AUROC on screw bag and splicing connectors, while category leaders differ; on Tapes, support-certified readout raises AUROC/F1 from 89.43/85.27 to 98.73/94.99.Fixed-threshold normal FPR is 1.43% on LOCO and 11.36% on VID.Source: §4.3 · p. 7

4.4. Mechanism controls under shared supervision

  • Replacing direct geometry with bound witnesses raises LOCO AUROC/F1 from 95.42/92.41 to 98.19/94.52; adding the certificate improves VID from 92.63/91.79 to 93.56/92.76 while preserving LOCO performance.Binding controls show that removing class compatibility gives 92.60/91.38 on VID with its own references, versus 93.55/92.76 with shared SGDB references; nearest assignment and removing the distance gate leave detection metrics unchanged.Source: §4.4 · p. 7, Table 3 · p. 7

4.5. Support-certified readout

  • Complete component ownership retains all 90 tape corrections while preventing screw degradations from quality-only readout, yielding 89 fewer errors across 9,031 test images.With initial intervals, references, and thresholds fixed, the same 90 corrections and one new tape miss remain; completeness filters 20 of 23 quality-eligible screw axes and preserves all 259 screw decisions.Source: §4.5 · p. 8, Table 4 · p. 8

4.6. Execution-grounded explanation

  • A compact certificate preserves sufficiency for every alarm with 1.006 rules on average, reducing selected rules by 49.56% relative to all positive-score rules.Two strongest tape contributions equal the threshold but do not trigger the strict comparison; three exceed it. Reports preserve missing evidence in 1,254 affected records, including 94 non-alarms, and raw predicate deviations in 191 non-alarm traces.Source: §4.6 · p. 8, Table 5 · p. 8

4.7. Decision, explanation and evidence

  • Across six illustrated reports, executor-owned measurements and source-linked operands accompany selected claims, with unavailable evidence retained and observed deviations distinguished from alarms.Examples include a zero-residual Cookies miss, unavailable utensil order for Dishes, and a Tapes length ratio changing from 2.053 to 0.980 after support readout.Source: §4.7 · pp. 8–9, Figure 6 · p. 11, Figure 7 · p. 11

5. Discussion

SGDB links geometric witnesses to object identities and carries those source links into verification and concise explanations. Its discussion highlights improved length verification, complete-support readout, and preservation of counts and unavailable evidence.

5. Discussion

  • Bound witness geometry improves length verification over direct prediction, while complete-support selection retains tape corrections and protects screw measurements.The readout replaces a length axis only when support quality improves and the observed instance retains a complete, distinct component.Source: §5 · p. 12
  • Partial binding preserves decoded counts, unavailable geometry, and witness ownership.Source: §5 · p. 12
  • Execution-grounded explanations carry source links into compact accounts of score comparisons, including alarms requiring several contributions.Source: §5 · p. 12

6. Conclusion

SGDB decouples semantic recognition from geometric measurement, then reconnects them through evidence binding and support-certified readout. It reports results on LOCO logical categories and VID tasks, while noting its configured inputs and directions for extension.

6. Conclusion

  • 98.19/94.52 AUROC/F1 on LOCO logical and 93.56/92.76 on all 50 VID tasks are the reported SGDB results.Source: §6 · p. 12
  • SGDB links semantic identities, measurements, and executable requirements through partial evidence binding and support-certified readout.Its fact and source trace supports verification and compact sufficient alarm certificates; reports connect predicates to identities, measurements, and evidence availability.Source: §6 · p. 12
  • Shared-supervision and frozen-output controls examine geometric evidence, complete support, and execution-grounded explanation.Source: §6 · p. 12
  • Normal observations set measurement and score references, component annotations train visual readers, and task requirements configure the executor; unfamiliar scenes and reduced supervision are extension directions.A Cookies trace also shows an anomalous image with zero-residual semantic facts, exposing the representation behind a missed alarm for review.Source: §6 · p. 12

CRediT authorship contribution statement; Declaration of competing interests; Funding; Declaration of generative AI and AI-assisted technologies in manuscript preparation

Data and code availability

  • The release provides research code, frozen configurations, per-image outputs, and CPU scripts for metric reconstruction, trace replay, and language-output verification.Benchmark images and third-party pretrained models come from their original providers [2].Source: Data and code availability · p. 12

S1.1 Information sources and normal-data budgets

SGDB assigns distinct roles to normal images, component targets, and explicit task requirements. Normal observations set references, while the task identifier selects the relevant inspection components.

S1.1 Information sources and normal-data budgets

  • Normal fitting images provide visual training sources and residual references; normal development images select checkpoints, association and readout settings, and interval padding.Source: S1.1 Information sources and… · p. 14
  • Independent normal calibration images fix alarm thresholds, while component targets supervise class, center, box, axis, and weak-mask predictions.Same-parent edits inherit their source role, and known cross-condition source groups are preserved.Source: S1.1 Information sources and… · p. 14
  • Executable constraints encode discrete task requirements, normal observations estimate continuous bounds and residual scales, and the task identifier selects readers and references.Table S1 distinguishes full normal pools from parents carrying component annotations and weak masks; it reports normal-source budgets and supervised-parent scope.Source: S1.1 Information sources and… · p. 14, Table S1 · p. 15

S1.2 Architecture and optimization

The architecture combines a shared visual frontend with a decoder trained on component facts and paired edits. Support coupling and consistency mechanisms distinguish the trained decoder from its plain-set control.

S1.2 Architecture and optimization

  • A WideResNet50-2 frontend truncated after its third residual stage feeds center, semantic-mask, box, and endpoint heads through context modulation, multiscale fusion, and normalized coordinates.Source: S1.2 Architecture and optimization · p. 15
  • Training combines weighted binary cross-entropy and Dice loss on valid weak-mask channels, uses permutation-minimized endpoint loss, and freezes encoder parameters for two epochs.The frontend trains for 40 epochs with 240 sampled examples per epoch and batch size four; AdamW uses encoder/head learning rates 10^-4/10^-3, weight decay 10^-4, and a cosine schedule.Source: S1.2 Architecture and optimization · p. 15
  • The decoder uses 64 candidate and 64 grid slots of width 64, four attention heads, two layers, and a fixed 8×8 grid layout.Its spatially pooled feature memory has a 40×56 grid, and first-layer soft support masks bias second-layer attention.Source: S1.2 Architecture and optimization · pp. 15–16
  • Support coupling aligns geometric predictions with mask support, while paired-edit consistency uses count changes and shared-object displacement; the plain-set control omits these mechanisms.Each head receives 768 optimizer steps and 1,536 image exposures, with 15 categories trained for each of the two variants.Source: S1.2 Architecture and optimization · p. 16
  • Fitting uses normal-source parents and paired edits with updated factual targets, and decoder geometry supports training while associated witnesses provide final hybrid measurements.Edits may create logically abnormal configurations, but supervision remains component- and fact-based.Source: S1.2 Architecture and optimization · p. 16

S2.1 Normal-development association

Normal development selects a single same-class, one-to-one association scheme, while screw-axis readout uses supported mask pixels in native coordinates. Unmatched identities remain counted, with geometry unavailable.

S2.1 Normal-development association

  • Association candidates were selected on 294 annotated normal-development parents using category-macro objectives, with unbound decoded objects and unmatched references treated as errors.The selected scheme was applied unchanged across both datasets and decoder variants.Source: S2.1 Normal-development association · p. 16
  • Same-class association at radius 0.08 was selected across categories and decoder variants, with no unbound objects among 3,136 decoded development objects.The main hybrid had one unbound object in one test breakfast-box image; its identity remained counted while geometry-dependent operands were unavailable.Source: S2.1 Normal-development association · p. 17

S2.2 Initial screw-mask ownership and native axes

  • Initial screw axes use supported foreground pixels assigned within expanded instance boxes, mapped to native coordinates before PCA and endpoint selection.Unsupported pixels are excluded; the reader uses untrimmed projection endpoints.Source: S2.2 Initial screw-mask ownership and… · p. 17
  • A mask-axis substitution requires at least 16 assigned pixels, 75% expanded-box support, bounded centroid displacement, a fourfold eigenvalue ratio, and finite endpoints.Otherwise the original FMP axis remains a witness; candidate selection used 30 normal images with 60 screw instances and an error-reduction admission rule.Source: S2.2 Initial screw-mask ownership and… · pp. 17–18

S2.3 Post-binding support certification

After identity binding, SGDB updates axes only when support quality and component-ownership checks pass. Tests report limited changes from additional guards and compare alternative binding policies.

S2.3 Post-binding support certification

  • Axis updates use the same assigned support to evaluate line, extent, and connectivity quality, then require complete, distinct component ownership.Structural failure rejects all proposed updates in the class; boundary and shortening guards can also reject an update while retaining the initial axis and its witness link.Source: S2.3 Post-binding support certification · pp. 18–19
  • The certificate updated 176 axes in 175 test images, while final decisions were identical under the two reference modes.The same 90-image tape repair set appeared, with one additional type-related miss; all screw-bag predictions matched the initial bound deployment.Source: S2.3 Post-binding support certification · pp. 19–20

S3.1 Policies and evaluation modes

  • The tighter 0.04 radius gives 93.97/93.11 VID AUROC/F1 and 97.98/94.52 LOCO AUROC/F1.The comparisons retain the original normal-development choice of radius 0.08 as the main policy.Source: S3.1 Policies and evaluation modes · pp. 20–21
  • The class-agnostic policy gives 92.60/91.38 VID AUROC/F1 with its own references and 93.55/92.76 with shared SGDB references.Source: S3.1 Policies and evaluation modes · p. 20
  • Independent nearest assignment changed 3 test scores and 0 decisions; dropping unbound identities changed 1 score and 0 decisions, while removing the distance gate changed none.Binding-trace counts were unchanged by the downstream axis readout.Source: S3.1 Policies and evaluation modes · p. 21

S3.2 Controlled missing-witness probe

A controlled witness-removal probe distinguishes keeping an object's identity from having usable geometry. The surrounding checks document numerical reproducibility, normal-data deployment, and compact alarm-certificate selection.

S3.2 Controlled missing-witness probe

  • Across 3,136 controlled removals, partial binding kept every decoded identity counted and marked orphan geometry unavailable; nearest assignment reused a witness in 720 trials.Dropping unbound identities removed one identity per trial; class-agnostic assignment rerouted 96 orphans and created 136 cross-class links.Source: S3.2 Controlled missing-witness probe · p. 22, Table S7 · p. 22

S3.3 Numerical verification

  • The audit reproduced all 9,031 predictions exactly and independently checked score reconstruction, cited geometric operands, and certificate cardinality.It also checked controlled witness-removal trials and assignment traces; these tests address execution and provenance consistency, not natural failure prevalence.Source: S3.3 Numerical verification · p. 22

Normal references and deployment

  • Normal fitting data define operand intervals and residual references, while independent calibration fixes thresholds using a strict score-greater-than-threshold decision.For ten normal calibration images per VID task, the specified 95th-percentile convention selects the observed maximum.Source: Normal references and deployment · p. 23
  • Deployment trains and selects components using normal sources, then binds decoded objects to witnesses before support checks, task execution, scoring, and trace-based reporting.The procedure freezes each task threshold from independent normal calibration data.Source: Normal references and deployment · p. 24

S5.1 Trace schema and certificate selection

  • The certificate uses fixed normalized contributions and selects the first descending prefix exceeding the threshold, which is minimum-cardinality in score space.Selected predicates may share underlying operands; the full trace and score remain available alongside the certificate.Source: S5.1 Trace schema and certificate… · pp. 24–25

S5.2 Selection-policy comparison and checks

The paper compares alarm-certificate selection, frozen language realization, and completed deployments across all VID tasks. The supplied results describe certificate size and verification, while task tables specify their scope and metrics.

S5.2 Selection-policy comparison and checks

  • Compact certificates retained 5,759 rule records, versus 11,418 positive-score records and 40,767 executed records across the alarm cohort.Every compact certificate was sufficient; 5,708 contained one rule and 17 contained three.Source: S5.2 Selection-policy comparison and… · p. 25, Table S8 · p. 26
  • Checks reconstructed every residual, normalized score, and decision across 9,031 images, and independently reconstructed 3,928 cited geometric operands.The audit also tested certificate cardinality on synthetic score vectors and deliberately corrupted report fields.Source: S5.2 Selection-policy comparison and… · p. 26

S5.3 Frozen language realization

  • All 70 frozen-language reports preserved the tested source contract, and 50 deliberate corruptions were rejected.Generated claims use qualitative outcomes and evidence identifiers; the executor renders numeric evidence from source records.Source: S5.3 Frozen language realization · pp. 26–27

S6 Comparison settings and condition results

  • Deployment comparisons use completed local systems with differing frontend and calibration conditions, while internal controls share supervision, task requirements, and the scoring recipe.Matched-reference diagnostics hold the initial intervals, references, and thresholds fixed to measure decision changes due to axis selection alone.Source: S6 Comparison settings and condition… · pp. 27–29

All 50 VID task results

S8.1 Paired grouped uncertainty

The supplement quantifies paired uncertainty under frozen configurations, documents reproduction and consistency checks, and reports paired decision transitions and selected qualitative replays.

S8.1 Paired grouped uncertainty

  • Paired 10,000-replicate resampling estimates differences within category and label strata, grouping VID's five capture conditions by filename index and holding models, references, and thresholds fixed.Intervals are the 2.5th and 97.5th percentiles of paired differences in percentage points.Source: S8.1 Paired grouped uncertainty · p. 32
  • These intervals describe conditional variation within evaluated test cohorts, not training-seed variation or independent blind validation; filename-index groups do not verify physical identity or adjacent-frame independence.The group correspondence is an explicit resampling assumption based on retained metadata.Source: S8.1 Paired grouped uncertainty · p. 32
  • V2 preserves LOCO AUROC against unrestricted and quality-only axis replacement, while uniform-mask readout retains a small VID F1 advantage; intervals are marginal and unadjusted for multiple comparisons.Table S14 reports point differences and paired grouped intervals; its guarded-geometry comparison is secondary.Source: Table S14 · p. 33, S8.1 Paired grouped uncertainty · p. 33
  • Table S15 holds the original deployment's intervals, residual references, and thresholds fixed across readouts, while Table S16 tracks repaired and regressed views across all 9,031 images.A change group may contain both kinds of view changes.Source: Table S15 · p. 33, Table S16 · p. 33

S8.2 Reproduction material

  • The CPU archive supports metric reconstruction and execution-trace replay, covering 990 method-task rows and checking all 715 archived manuscript rows.It includes saved predictions, frozen references and thresholds, fact records, group draws, category results, and transition ledgers.Source: S8.2 Reproduction material · p. 34

S9 Implementation consistency

  • Consistency audits cover association, geometric provenance, normal references, and strict decisions across development records, facts, predictions, masks, and complete-support predictions.The reported audit counts are 1,176 development records, 25,332 initial facts, 18,062 initial predictions, 4,559 source-mask records, and 36,124 complete-support predictions.Source: S9 Implementation consistency · p. 34

S10.1 Paired operating-point changes

  • Table S17 compares FMP plus guarded geometry with SGDB over full image cohorts; some decision changes retain identical raw residuals because normal references and calibration differ by configuration.Main-paper false-positive rates are task macro-averages.Source: Table S17 · p. 35, S10.1 Paired operating-point changes · p. 35

S10.2 Qualitative source selection and replay

  • Nine fixed-source reports are selected from LOCO and VID; six use frozen-language-model claims with numeric evidence from source records, while three show structured traces.Boxes and axes show SGDB outputs, and green/red strips encode image-level correctness against dataset labels.Source: S10.2 Qualitative source selection and… · p. 35, Figure S1 · p. 36

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