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In recent years, concept-based approaches have emerged as some of the mostpromising explainability methods to help us interpret the decisions ofArtificial Neural Networks (ANNs). These methods seek to discover intelligiblevisual 'concepts' buried within the complex patterns of ANN activations in twokey steps: (1) concept extraction followed by (2) importance estimation. Whilethese two steps are shared across methods, they all differ in their specificimplementations. Here, we introduce a unifying theoretical framework thatcomprehensively defines and clarifies these two steps. This framework offersseveral advantages as it allows us: (i) to propose new evaluation metrics forcomparing different concept extraction approaches; (ii) to leverage modernattribution methods and evaluation metrics to extend and systematicallyevaluate state-of-the-art concept-based approaches and importance estimationtechniques; (iii) to derive theoretical guarantees regarding the optimality ofsuch methods. We further leverage our framework to try to tackle a crucialquestion in explainability: how to efficiently identify clusters of data pointsthat are classified based on a similar shared strategy. To illustrate thesefindings and to highlight the main strategies of a model, we introduce a visualrepresentation called the strategic cluster graph. Finally, we presenthttps://serre-lab.github.io/Lens, a dedicated website that offers a completecompilation of these visualizations for all classes of the ImageNet dataset.

A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation