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

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

cs.CVOct 26, 2026

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

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

Organizations: School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China

Abstract

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.

Figures & tables

Figure 1: Motivation for explicit geometric verification beyond appearance/composition scoring Roth et al. [2022] , Fučka et al. [2025] . (a) The two scenes have identical component counts. (b) SGDB maps an image to a decision, explanation and evidence through semantic–geometric decoupling, binding and verification. The recorded rope/reference ratio 1.362 exceeds the normal upper bound 1.174. Images and measurements are from frozen outputs.

Figure 2: SGDB framework. (a) Bound facts are checked against task constraints, aggregated and compared with the alarm threshold. (b) Objects bind to geometric witnesses by class and position; unmatched identities remain counted. Quality and instance-support checks select the mask axis or retain the initial axis, shown by solid green and dashed brown lines. (c) The interval penalty is zero within the accepted range and increases linearly outside it; the marked point is the recorded O4 length. (d) Selected evidence E05 supports the frozen LLM’s source-attributed explanation; numeric evidence is presented by the executor. Snowflakes denote the frozen visual frontend and language model.

Figure 3: Fact-decoder training. (a) First-layer soft masks bias second-layer attention over frozen visual features. (b) A normal-source parent and its edit share decoder parameters. Updated targets supervise object sets; support coupling aligns geometry with masks, and edit consistency supervises count changes and shared-object displacement. The removal example is schematic.

Input	Decoded objects $O$ , initial witnesses $E$ , class masks $M_{c}$ ; $r=0.08$ , $q_{0}$ , $\Delta_{q}=0.05$ .
1	Set $C_{ij}=d_{ij}$ for same-class pairs with $d_{ij}\leq r$ ; otherwise set $C_{ij}=10^{6}$ . Add $n$ dummy columns of cost $r+10^{-7}$ .
2	$\pi\leftarrow\arg\min_{\pi\;\mathrm{injective}}\sum_{i}C_{i,\pi(i)}$ (Hungarian).
3	Bind real matches to $g_{i}^{0}$ ; mark dummy matches unavailable. Retain every decoded identity.
4	for each mask-backed length class $c$ with $I_{c}\neq\varnothing$ do
5	$S_{i}\leftarrow\{\mathbf{p}\in M_{c}:i=\arg\min_{h\in I_{c}}\\|\mathbf{p}-\mathbf{z}_{h}\\|_{2}\}$ .
6	Where readable, compute $\tilde{g}_{i}$ by Eq. ( 4 ) and both qualities by Eq. ( 5 ).

Table 4

	SALAD Fučka et al. [2025]		LogiCo Zhang et al. [2026a]		ComAD Liu et al. [2023]		PUAD Sugawara and Imamura [2024]		Qwen3-VL-8B Bai et al. [2025]		LogicAD-FE-fast Jin et al. [2025]		SGDB (Ours)
Category	AUROC	F1	AUROC	F1	AUROC	F1	AUROC	F1	AUROC	F1	AUROC	F1	AUROC	F1
Breakfast box	92.27	85.00	98.89	96.30	94.19	86.79	93.07	82.43	91.21	71.64	52.60	17.65	98.78	98.78
Juice bottle	99.79	98.61	99.22	95.62	87.96	79.68	99.83	98.61	83.31	61.46	53.67	1.40	96.38	96.00
Pushpins	100.00	75.21	98.37	93.55	87.11	78.53	86.69	69.44	62.84	14.29	53.02	8.00	98.87	96.22
Screw bag	93.95	84.65	84.18	69.41	79.22	24.84	70.20	28.92	55.25	49.34	49.82	2.84	98.92	93.54
Splicing connectors	96.08	88.78	91.80	84.31	85.61	82.90	94.30	88.00	78.56	56.95	65.70	8.85	97.97	88.08

Table 1: LOCO logical detection results (%). Paired columns report AUROC and fixed-threshold F1. Mean averages five tasks. Supervision and implementation settings are specified in Section 4.2 and the supplement. Best/second-best distinct values are bold/underlined, with shared marks for ties. Blue columns denote SGDB.

	SALAD Fučka et al. [2025]		LogiCo Zhang et al. [2026a]		ComAD Liu et al. [2023]		PUAD Sugawara and Imamura [2024]		Qwen3-VL-8B Bai et al. [2025]		LogicAD-FE-fast Jin et al. [2025]		SGDB (Ours)
Scenario	AUROC	F1	AUROC	F1	AUROC	F1	AUROC	F1	AUROC	F1	AUROC	F1	AUROC	F1
Balls	23.76	58.06	58.88	61.45	65.85	53.57	17.27	54.04	97.87	89.97	51.27	12.91	86.43	87.56
Blocks	90.92	84.62	94.37	90.98	77.93	71.64	79.70	74.55	92.93	90.37	48.78	14.69	89.15	86.98
Cookies	62.97	80.26	52.37	80.67	98.05	91.49	18.93	62.76	84.29	88.03	54.24	10.32	86.62	85.21
Dishes	52.36	37.59	66.61	73.74	73.95	57.72	61.84	43.60	99.64	95.39	80.55	77.45	92.90	96.63
Fruits	99.81	94.60	99.17	96.41	99.94	98.06	98.56	90.08	95.31	93.42	90.55	73.12	93.80	93.31

Table 2: VID detection results by scenario (%). Paired columns report AUROC and fixed-threshold F1. Rows average five conditions; Mean averages all 50 tasks. Supervision and calibration settings are specified in Section 4.2 and the supplement. Best/second-best distinct values are bold/underlined; blue columns denote SGDB.

(a) Semantic decoder and geometric readout
	LOCO logical		VID all 50
Configuration	AUROC	F1	AUROC	F1
FMP reader	95.01	90.88	91.33	89.47
FMP + guarded geometry	98.08	93.54	91.33	89.47
Direct DFD: plain set	95.01	90.88	93.41	91.78
Direct DFD: evidence edit	95.42	92.41	92.64	91.83

Table 3: Mechanism controls with shared component supervision and task requirements (%). (a) Decoder/readout configurations; the final row adds the support certificate. (b) Binding policies with the same complete-support readout. Each row uses its own normal references and CAL threshold under the shared recipe. Best/second-best distinct values are bold/underlined within each block and column; ties share marks.

	LOCO logical		VID all 50
Readout	AUROC	F1	AUROC	F1
Initial bound readout	98.19	94.52	92.63	91.79
Uniform mask readout	96.36	93.54	93.58	92.86
Quality selection only	96.62	93.82	93.54	92.76
SGDB: complete support	98.19	94.52	93.56	92.76

Table 4: Geometric-readout controls with fixed semantic outputs, witnesses, masks and task requirements (%). Normal references and thresholds follow the same fitting/calibration recipe. SGDB combines quality selection with complete instance support. Best/second-best distinct values are bold/underlined; ties share marks.

Selection	Mean	Suff. $\uparrow$	Fail $\downarrow$
All executed rules	7.121	100.00	0
All positive-score rules	1.994	100.00	0
Maximum-score rule	1.000	99.70	17
Compact sufficient (SGDB)	1.006	100.00	0

Table 5: Explanation selection on 5,725 frozen alarms. Mean: selected rules per alarm; Suff.: alarm sufficiency (%); Fail: insufficient selections. All policies use the same trace and source links. Bold/underline mark best/second-best sufficiency and failure values; ties share marks.

Figure 4: LOCO comparison on 20 fixed sources: (a) logical anomalies; (b) normal references and an additional logical anomaly. GT is the provided logical-anomaly mask union. Prediction strips use full-precision scores; green/red denotes a correct/incorrect image-level decision. Spatial representations differ across methods.

Figure 5: VID comparison on 30 fixed sources across ten scenarios: (a) original normal, (b) original anomalous, and (c) blurry anomalous images. GT is image-level. SGDB shows associated objects; ComAD shows component regions. SALAD and PUAD provide scored decisions from their cached outputs.

Panel of Figure 6 — Figure 6: Execution-grounded reports: (a) screw-length alarm; (b) missing-bolt alarm; (c) normal Stationery under blur. Rows separate visual evidence, decisions, frozen-LLM claims and executor-owned measurements. An alarm requires $s>\tau$ ; $S(C)$ is the selected subset score. Evidence IDs are local to each case. GT labels are used only for retrospective review.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Category	Fitting	Dev.	Cal.	Ann. fit.	Ann. dev.	Test
Breakfast Box	234	29	62	234	29	185
Juice Bottle	224	27	54	224	27	236
Pushpins	248	31	69	248	31	229
Screw Bag	240	30	60	240	30	259
Splicing Connectors	237	30	60	237	30	227
Balls	100	50	50	20	15	790

Appendix

Table S1: Normal-source budgets and component-supervised parents. Ann.: annotated with component facts and weak masks.

Candidate	Point F1	Axis error	Unbound	Objective
Same class, 0.04	99.10	8.78	13	0.97528
Same class, 0.08	99.68	8.76	0	0.97990
Any class, 0.04	99.35	10.07	6	0.97466
Any class, 0.08	99.68	10.10	0	0.97721

Appendix

Table S2: Complete normal-development association selection. Point F1 and clipped axis error are category macro-averages (%). Unbound is a count.

Readout	Mean	Median	P95	Large	Updates
Predicted endpoints	11.96	4.96	53.00	8.00	0
Connected components, untrimmed	8.30	1.61	53.00	6.00	32
Connected components, 1% trimming	9.56	3.53	53.00	6.00	32
Box-supported assignment, untrimmed	2.50	0.83	9.36	0.00	60
Box-supported assignment, 1% trimming	4.68	3.54	12.96	0.00	60

Appendix

Table S3: Native-axis error on 60 normal development screw instances. Relative errors are percentages; Large counts errors above 20% and Updates counts substituted axes. Reference axes are stored normal component targets.

Category	Axes	Quality	Accepted
Screw bag	490	23	3
Tapes	1,911	200	172
Ropes	1,627	9	0
Sticks	2,372	6	1
Stationery	3,202	2	0

Appendix

Table S4: Certified readout coverage on the 3,429 test images with length readouts. Axes: bound target axes; Quality: candidates passing the quality gate; Accepted: candidates passing the complete certificate.

	Own normal references				Shared SGDB references
	LOCO		VID		LOCO		VID
Policy	AUC	F1	AUC	F1	AUC	F1	AUC	F1
SGDB partial binding	98.19	94.52	93.56	92.76	98.19	94.52	93.56	92.76
Independent nearest witness	98.19	94.52	93.56	92.76	98.19	94.52	93.56	92.76
Without class compatibility	98.19	94.52	92.60	91.38	98.19	94.52	93.55	92.76
Without distance gate	98.19	94.52	93.56	92.76	98.19	94.52	93.56	92.76

Appendix

Table S5: Binding policies with their own normal references and CAL thresholds, and with SGDB’s references/thresholds shared (%). Each four-column group reports LOCO AUROC/F1, then VID AUROC/F1.

Policy	Unbound	Dropped	Reuse	Cross-class
SGDB partial binding	1	0	0	0
Independent nearest witness	0	0	3	0
Without class compatibility	0	0	0	309
Without distance gate	1	0	0	0
Discard unbound identities	1	1	0	0
Radius 0.04	423	0	0	0

Appendix

Table S6: Binding traces on all 9,031 test images and 51,158 decoded objects. Unbound counts decoded objects without a witness; Dropped counts identities removed from the assembled facts. Reuse counts assignments beyond one use per witness. Cross-class counts links with different decoded/witness labels.

Policy	Count kept	Null orphan	Reuse trials
SGDB partial binding	100.00	100.00	0.00
Independent nearest witness	100.00	77.04	22.96
Without class compatibility	100.00	96.94	0.00
Without distance gate	100.00	99.43	0.00
Discard unbound identities	0.00	0.00	0.00
Radius 0.04	100.00	100.00	0.00

Appendix

Table S7: Controlled witness removal over 3,136 trials (%). Count kept: all decoded identities remain counted. Null orphan: the decoded object whose original witness was removed remains present with unavailable geometry. Reuse trials: at least one witness is assigned to several objects.

Category	Alarms	All	Positive	Compact
breakfast box	81	27.889	5.938	1.000
juice bottle	133	21.917	3.203	1.000
pushpins	94	6.862	2.543	1.000
splicing connectors	85	6.365	1.965	1.000
screw bag	126	5.254	1.571	1.000
Sticks	533	3.450	1.572	1.000

Appendix

Table S8: Per-category alarm counts and mean selected-rule counts. The last column counts alarms insufficiently explained by only the maximum-score rule. Every compact certificate is sufficient.

Language	Reports	Accepted	Mean claims
English	63	63	1.159
Chinese	7	7	1.429

Appendix

Table S9: Frozen language realization. Accepted denotes preservation of the defined source contract; mean claims measures report size. Numeric evidence is rendered by the executor.

Condition	Images	AUROC	F1	Normal FPR	Missing
Original	1579	94.94	93.85	6.60	12.63
Cable BG	1579	94.06	91.88	11.60	14.94
Mesh BG	1579	92.83	91.96	13.00	13.94
Low light	1579	93.19	93.12	12.00	13.91
Blur	1579	92.76	92.99	13.60	13.37

Appendix

Table S10: SGDB condition summaries across all ten VID scenarios. Values other than image counts are percentages. Missing is the task macro-average of unavailable-operand rates.

Method	Normal data / component targets	Requirements / implementation	VID calibration
SGDB V2	Fit/DEV/CAL roles; component targets in Table S1 .	Explicit requirements; learned semantics, bound geometry and support certification.	Task level.
SALAD	Normal fitting; archived VID component-map input; LOCO annotation detail NR.	Local completed deployment; 70,000-step VID branch; no SGDB executor.	Category level.
LogiCo	Normal fitting; archived VID component frontend; exact LOCO target lineage NR.	Local component adaptation; fixed 200-epoch VID fit; no SGDB executor.	Pooling NR.
ComAD	LOCO normal RGB only, no component labels; VID shared component frontend.	LOCO DINO-S8, five clusters and CRF; VID component-map adapter.	Pooling NR.
PUAD	LOCO normal RGB only; VID local shared component-map input.	70,000 steps; external ImageNet penalty images omitted.	Category level.
Qwen3-VL-8B	Archived prompts and normal score calibration; prompt-reference count NR.	Frozen image-language baseline; distinct from the explanation-side text model.	Pooling NR.

Appendix

Table S11: Information and implementation conditions of the completed deployments. NR: not established by the retained comparison protocol; the archive provides the actual image scores and thresholds. Internal mechanism controls share SGDB’s component supervision and task requirements.

Scenario	Condition	SALAD	LogiCo	ComAD	PUAD	Qwen	LogicAD	SGDB
Balls	Original	13.35	60.78	61.30	8.93	99.86	53.59	89.47
Balls	Cable BG	19.15	67.74	63.44	11.02	92.99	50.79	97.09
Balls	Mesh BG	56.74	62.37	74.76	43.63	99.64	66.19	88.09
Balls	Low light	16.15	55.46	70.78	12.72	99.27	37.80	77.10
Balls	Blur	13.39	48.04	58.98	10.07	97.59	47.99	80.41
Blocks	Original	95.44	93.31	80.51	88.64	99.34	43.85	87.73

Appendix

Table S12: Complete VID task AUROC (%).

Scenario	Condition	SALAD	LogiCo	ComAD	PUAD	Qwen	LogicAD	SGDB
Balls	Original	81.82	64.89	25.40	81.82	96.65	1.82	85.32
Balls	Cable BG	11.11	61.18	47.30	5.80	77.27	18.33	92.86
Balls	Mesh BG	57.92	53.09	51.66	54.35	94.12	23.26	93.15
Balls	Low light	58.06	63.64	75.49	47.76	92.00	21.14	83.26
Balls	Blur	81.37	64.45	68.00	80.46	89.80	0.00	83.19
Blocks	Original	85.27	91.60	71.59	83.53	99.09	19.12	86.01

Appendix

Table S13: Complete VID fixed-threshold F1 (%).

Dataset	Control	$\Delta$ AUROC [95% CI]	$\Delta$ F1 [95% CI]
LOCO	Initial bound	+0.00 [+0.00, +0.00]	+0.00 [+0.00, +0.00]
LOCO	Uniform mask	+1.83 [+1.18, +2.51]	+0.98 [-0.07, +2.05]
LOCO	Quality only	+1.57 [+0.96, +2.22]	+0.70 [-0.28, +1.69]
LOCO	FMP + guarded geometry	+0.11 [+0.00, +0.29]	+0.98 [+0.06, +2.00]
VID-AD	Initial bound	+0.93 [+0.56, +1.32]	+0.97 [+0.57, +1.43]
VID-AD	Uniform mask	-0.02 [-0.08, +0.04]	-0.10 [-0.20, -0.02]

Appendix

Table S14: SGDB V2 minus each frozen control: point difference and paired grouped 95% interval (percentage points). Each deployment retains its own archived normal references. The guarded-geometry comparison is secondary.

Dataset	Control	$\Delta$ AUROC [95% CI]	$\Delta$ F1 [95% CI]
LOCO	Initial bound	+0.00 [+0.00, +0.00]	+0.00 [+0.00, +0.00]
LOCO	Uniform mask	+0.68 [+0.33, +1.09]	+1.12 [+0.54, +1.71]
LOCO	Quality only	+0.15 [+0.02, +0.35]	+0.28 [-0.03, +0.64]
VID-AD	Initial bound	+0.93 [+0.56, +1.32]	+0.97 [+0.57, +1.43]
VID-AD	Uniform mask	-0.03 [-0.08, +0.02]	-0.05 [-0.13, +0.01]
VID-AD	Quality only	+0.02 [+0.00, +0.06]	+0.00 [+0.00, +0.00]

Appendix

Table S15: Sensitivity analysis with the original bound deployment’s intervals, residual references and thresholds held fixed for all readout configurations (percentage points). Same resampling draws as Table S14 .

Control	R views	G views	R groups	G groups
Initial bound	90	1	20	1
Uniform mask	28	27	28	23
Quality only	22	14	22	14

Appendix

Table S16: Changes to V2 across all 9,031 images. R/G: repaired/regressed views. Group counts use LOCO image IDs and VID cross-condition filename indices; one group can contain both kinds of change. Complete unchanged and changed group ledgers are supplied.

Dataset	Corrected FN	New FN	Corrected FP	New FP	Changes	Same residuals
LOCO	13	1	0	4	18	16
VID	366	110	77	66	619	158

Appendix

Table S17: Paired decision transitions. Same residuals counts changed decisions with an identical raw rule-residual dictionary.

Figure S1: Additional SGDB reports on normal and anomalous screw bags. All decisions, lengths and interval references are from the current hybrid replay. The input and linked detail retain original dataset pixels.

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LogiCo: A Unified Framework for Logical and Structural Anomaly Detection

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Current anomaly detection methods primarily focus on structural anomalies, while paying insufficient attention to anomalies that violate logical constraints. Conversely, top-performing logical anomaly detection approaches address this by modeling global semantic consistency, but perform poorly on subtle structural anomalies due to inadequate detection granularity. In this paper, we propose LogiCo, a unified framework for Logical and structural anomaly detection via Component-level feature reconstruction. Unlike existing methods that rely on explicit global semantic modeling, LogiCo employs a novel component-level feature reconstruction technique to capture inter-component logical constraints. Specifically, LogiCo maps pre-trained image features into a discrete component-level feature space and performs collaborative feature reconstruction at both component and patch levels, enabling it to effectively detect both logical and structural anomalies. Furthermore, to address the specific challenge of count-related logical anomalies, we integrate a segmentation-map discriminator that extends the model's capability to identify quantitative inconsistencies. LogiCo achieves state-of-the-art performance on both logical and structural anomaly detection across four benchmarks, including MVTec-LOCO, MVTec-AD, VisA, and Real-IAD, demonstrating its superiority and practical feasibility. The code is available at https://github.com/cnulab/LogiCo.

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