Concepts' Information Bottleneck Models

We propose a novel, flexible, and efficient framework for designing Concept Bottleneck Models (CBMs) that enables practitioners to explicitly encode and extend their prior knowledge and beliefs about the concept-concept ($C-C$) and concept-task ($C \to Y$) relationships within the model's reasoning when making predictions. The resulting $\textbf{C}$oncept $\textbf{REA}$soning $\textbf{M}$odels (CREAMs) architecturally encode arbitrary types of $C-C$ relationships such as mutual exclusivity, hierarchical associations, and/or correlations, as well as potentially sparse $C \to Y$ relationships. Moreover, CREAM can optionally incorporate a regularized side-channel to complement the potentially {incomplete concept sets}, achieving competitive task performance while encouraging predictions to be concept-grounded. To evaluate CBMs in such settings, we introduce a $C \to Y$ agnostic metric that quantifies interpretability when predictions partially rely on the side-channel. In our experiments, we show that, without additional computational overhead, CREAM models support efficient interventions, can avoid concept leakage, and achieve black-box-level performance under missing concepts. We further analyze how an optional side-channel affects interpretability and intervenability. Importantly, the side-channel enables CBMs to remain effective even in scenarios where only a limited number of concepts are available.

Concept Bottleneck Models (CBMs) aim for ante-hoc interpretability by learning a bottleneck layer that predicts interpretable concepts before the decision. State-of-the-art approaches typically select which concepts to learn via human specification, open knowledge graphs, prompting an LLM, or using general CLIP concepts. However, concepts defined a-priori may not have sufficient predictive power for the task or even be learnable from the available data. As a result, these CBMs often significantly trail their black-box counterpart when controlling for information leakage. To address this, we introduce a novel CBM pipeline named Mechanistic CBM (M-CBM), which builds the bottleneck directly from a black-box model's own learned concepts. These concepts are extracted via Sparse Autoencoders (SAEs) and subsequently named and annotated on a selected subset of images using a Multimodal LLM. For fair comparison and leakage control, we also introduce the Number of Contributing Concepts (NCC), a decision-level sparsity metric that extends the recently proposed NEC metric. Across diverse datasets, we show that M-CBMs consistently surpass prior CBMs at matched sparsity, while improving concept predictions and providing concise explanations. Our code is available at https://github.com/Antonio-Dee/M-CBM.

Concept Bottleneck Models (CBMs) ground predictions in human-understandable concepts but face fundamental limitations: the absence of a metric to pre-evaluate concept relevance, the "linearity problem" causing recent CBMs to bypass the concept bottleneck entirely, an accuracy gap compared to opaque models, and finally the lack of systematic study on the impact of different visual backbones and VLMs. We introduce CBM-Suite, a methodological framework to systematically addresses these challenges. First, we propose an entropy-based metric to quantify the intrinsic suitability of a concept set for a given dataset. Second, we resolve the linearity problem by inserting a non-linear layer between concept activations and the classifier, which ensures that model accuracy faithfully reflects concept relevance. Third, we narrow the accuracy gap by leveraging a distillation loss guided by a linear teacher probe. Finally, we provide comprehensive analyses on how different vision encoders, vision-language models, and concept sets interact to influence accuracy and interpretability in CBMs. Extensive evaluations show that CBM-Suite yields more accurate models and provides insights for improving concept-based interpretability.