Clarity: The Flexibility-Interpretability Trade-Off in Sparsity-aware Concept Bottleneck Models

The widespread adoption of deep learning models in computer vision has intensified concerns about interpretability. Despite strong performance, these models are often treated as black boxes, with limited systematic investigation of their decision-making processes. While many interpretability methods exist, objective evaluation of learned representations remains limited, particularly for approaches that rely on sparsity to "induce" interpretability. In this work, we investigate how modeling choices in Concept Bottleneck Models (CBMs) affect the semantic alignment of concept representations. We introduce Clarity, a post-hoc diagnostic measure that captures the interplay between downstream performance and the sparsity and precision of concept activations. Using an interpretability assessment framework grounded in datasets with ground-truth concept annotations, we evaluate both VLM- and attribute predictor-based CBMs across three amortized sparsity-inducing strategies (ℓ1, ℓ0, and Bernoulli-based), alongside several widely used sparsity-aware CBM methods from the literature. Our experiments reveal a critical flexibility-interpretability trade-off: a model's capacity to optimize task performance by deviating from semantic alignment. We demonstrate that under this trade-off, different methods exhibit markedly different behaviors even at comparable performance levels. Finally, we validate our framework through a principled human study, which confirms that Clarity aligns significantly more closely with human trust than standard evaluation metrics.