Do Concept Bottleneck Models Obey Locality?

Concept-based learning improves a deep learning model's interpretability by explaining its predictions via human-understandable concepts. Deep learning models trained under this paradigm heavily rely on the assumption that neural networks can learn to predict the presence or absence of a given concept independently of other concepts. Recent work, however, strongly suggests that this assumption may fail to hold in Concept Bottleneck Models (CBMs), a quintessential family of concept-based interpretable architectures. In this paper, we investigate whether CBMs correctly capture the degree of conditional independence across concepts when such concepts are localised both spatially, by having their values entirely defined by a fixed subset of features, and semantically, by having their values correlated with only a fixed subset of predefined concepts. To understand locality, we analyse how changes to features outside of a concept's spatial or semantic locality impact concept predictions. Our results suggest that even in well-defined scenarios where the presence of a concept is localised to a fixed feature subspace, or whose semantics are correlated to a small subset of other concepts, CBMs fail to learn this locality. These results cast doubt upon the quality of concept representations learnt by CBMs and strongly suggest that concept-based explanations may be fragile to changes outside their localities.