Towards Reasonable Concept Bottleneck Models

In this paper, we propose $\textbf{C}$oncept $\textbf{REA}$soning $\textbf{M}$odels (CREAM), a novel family of Concept Bottleneck Models (CBMs) that: (i) explicitly encodes concept-concept (${\texttt{C-C}}$) and concept-task (${\texttt{C$\rightarrow$Y}}$) relationships to enforce a desired model reasoning; and (ii) use a regularized side-channel to achieve competitive task performance, while keeping high concept importance. Specifically, CREAM architecturally embeds (bi)directed concept-concept, and concept to task relationships specified by a human expert, while severing undesired information flows (e.g., to handle mutually exclusive concepts). Moreover, CREAM integrates a black-box side-channel that is regularized to encourage task predictions to be grounded in the relevant concepts, thereby utilizing the side-channel only when necessary to enhance performance. Our experiments show that: (i) CREAM mainly relies on concepts while achieving task performance on par with black-box models; and (ii) the embedded ${\texttt{C-C}}$ and ${\texttt{C$\rightarrow$Y}}$ relationships ease model interventions and mitigate concept leakage.