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

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.