Eliminating Information Leakage in Hard Concept Bottleneck Models with Supervised, Hierarchical Concept Learning

Concept Bottleneck Models (CBMs) aim to deliver interpretable and interventionable predictions by bridging features and labels with human-understandable concepts. While recent CBMs show promising potential, they suffer from information leakage, where unintended information beyond the concepts (either when concepts are represented with probabilities or binary states) are leaked to the subsequent label prediction. Consequently, distinct classes are falsely classified via indistinguishable concepts, undermining the interpretation and intervention of CBMs. This paper alleviates the information leakage issue by introducing label supervision in concept predication and constructing a hierarchical concept set. Accordingly, we propose a new paradigm of CBMs, namely SupCBM, which achieves label predication via predicted concepts and a deliberately-designed intervention matrix. SupCBM focuses on concepts that are mostly relevant to the predicted label and only distinguishes classes when different concepts are presented. Our evaluations show that SupCBM outperforms SOTA CBMs over diverse datasets. It also manifests better generality across different backbone models. With proper quantification of information leakage in different CBMs, we demonstrate that SupCBM significantly reduces the information leakage.