Concept Labels Are Not Enough: Rethinking Concept Bottleneck Models through Representation Integrity

Although deep neural networks achieve strong predictive performance, their internal reasoning often remains difficult to inspect and control. Concept Bottleneck Models (CBMs) address this opacity by factoring predictions through human-understandable concepts, thereby enabling concept-level inspection and intervention. However, CBMs remain vulnerable to concept shift and information leakage, while existing evaluations neither reveal how the internal features supporting each concept are organized nor identify the representation-level deficiency associated with these failures. We argue that this missing property is concept integrity: concept support should form a semantically coherent and non-fragmented functional group. To characterize this property, we propose group coherence (GC) and concept coverage (CC) as integrity components and aggregate them into the concept integrity score (CIS). We further introduce Concept Integrity Regularization (CIR) to encourage coherent and separated groups of concept-supporting filters. Our latent decoupled concept bottleneck model (LDCBM) applies CIR without requiring region annotations. Across three datasets, CIS rankings differ from rankings by concept and task accuracy, supporting concept integrity as a complementary representation-level criterion. Moreover, with only 10% of concept labels, LDCBM retains approximately 93% of its full-label task performance. Background-masking and concept-intervention further associate stronger integrity profiles with lower sensitivity to nuisance context and more responsive concept correction.