Global Concept Sparsity for Unsupervised Concept Bottleneck Models

Concept bottleneck models (CBMs) aim to make predictions interpretable through human-understandable concepts, yet unsupervised approaches for automatically discovering concepts produce large, redundant concept vocabularies. While existing sparsity mechanisms constrain which concepts are active for particular inputs or classes, in practice they allow for redundant concepts which are used only for a small number of classes. As a result, locally sparse models may still rely on an effectively large global concept vocabulary, undermining the compactness and inspectability that concept bottlenecks are intended to provide. To address this, we propose Global Concept Gating (GCG), a global concept-gating mechanism that can be easily used within any unsupervised CBM. GCG learns a sparse mask shared across all inputs and classes, jointly selecting a compact task-specific concept set and training the downstream classifier. Across multiple concept bottleneck architectures and image classification tasks, GCG substantially reduces concept set size while largely preserving predictive accuracy. Further analysis shows that the retained concepts are more relevant to prediction, better semantically grounded, and less susceptible to information leakage. Our results highlight that interpretable concept-based models require not only meaningful individual concepts, but concept spaces appropriately constrained to their tasks.