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Existing methods, such as concept bottleneck models (CBMs), have beensuccessful in providing concept-based interpretations for black-box deeplearning models. They typically work by predicting concepts given the input andthen predicting the final class label given the predicted concepts. However,(1) they often fail to capture the high-order, nonlinear interaction betweenconcepts, e.g., correcting a predicted concept (e.g., "yellow breast") does nothelp correct highly correlated concepts (e.g., "yellow belly"), leading tosuboptimal final accuracy; (2) they cannot naturally quantify the complexconditional dependencies between different concepts and class labels (e.g., foran image with the class label "Kentucky Warbler" and a concept "black bill",what is the probability that the model correctly predicts another concept"black crown"), therefore failing to provide deeper insight into how ablack-box model works. In response to these limitations, we proposeEnergy-based Concept Bottleneck Models (ECBMs). Our ECBMs use a set of neuralnetworks to define the joint energy of candidate (input, concept, class)tuples. With such a unified interface, prediction, concept correction, andconditional dependency quantification are then represented as conditionalprobabilities, which are generated by composing different energy functions. OurECBMs address both limitations of existing CBMs, providing higher accuracy andricher concept interpretations. Empirical results show that our approachoutperforms the state-of-the-art on real-world datasets.

Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Conditional Interpretations