In recent years, concept-based approaches have emerged as some of the most promising explainability methods to help us interpret the decisions of Artificial Neural Networks (ANNs).

Deep vision models perform input-output computations that are hard to interpret. Concept-based explanation methods (CBEMs) increase interpretability by re-expressing parts of the model with human-understandable semantic units, or concepts. Checking if the derived explanations are faithful -- that is, they represent the model's internal computation -- requires a surrogate that combines concepts to compute the output. Simplifications made for interpretability inevitably reduce faithfulness, resulting in a tradeoff between the two. State-of-the-art unsupervised CBEMs (U-CBEMs) have reported increasingly interpretable concepts, while also being more faithful to the model. However, we observe that the reported improvement in faithfulness artificially results from either (1) using overly complex surrogates, which introduces an unmeasured cost to the explanation's interpretability, or (2) relying on deletion-based approaches that, as we demonstrate, do not properly measure faithfulness. We propose Surrogate Faithfulness (SURF), which (1) replaces prior complex surrogates with a simple, linear surrogate that measures faithfulness without changing the explanation's interpretability and (2) introduces well-motivated metrics that assess loss across all output classes, not just the predicted class. We validate SURF with a measure-over-measure study by proposing a simple sanity check -- explanations with random concepts should be less faithful -- which prior surrogates fail. SURF enables the first reliable faithfulness benchmark of U-CBEMs, revealing that many visually compelling U-CBEMs are not faithful. Code to be released.

In recent years, concept-based approaches have emerged as some of the most promising explainability methods to help us interpret the decisions of Artificial Neural Networks (ANNs).

In recent years, concept-based approaches have emerged as some of the most promising explainability methods to help us interpret the decisions of Artificial Neural Networks (ANNs). These methods seek to discover intelligible visual "concepts" buried within the complex patterns of ANN activations in two key steps: (1) concept extraction followed by (2) importance estimation. While these two steps are shared across methods, they all differ in their specific implementations. Here, we introduce a unifying theoretical framework that recast the first step - concept extraction problem - as a special case of dictionary learning, and we formalize the second step - concept importance estimation - as a more general form of attribution method. This framework offers several advantages as it allows us: (i) to propose new evaluation metrics for comparing different concept extraction approaches; (ii) to leverage modern attribution methods and evaluation metrics to extend and systematically evaluate state-of-the-art concept-based approaches and importance estimation techniques; (iii) to derive theoretical guarantees regarding the optimality of such methods. We further leverage our framework to try to tackle a crucial question in explainability: how to efficiently identify clusters of data points that are classified based on a similar shared strategy. To illustrate these findings and to highlight the main strategies of a model, we introduce a visual representation called the strategic cluster graph. Finally, we present Lens, a dedicated website that offers a complete compilation of these visualizations for all classes of the ImageNet dataset.

Concept-based interpretations of black-box models are often more intuitive for humans to understand. The most widely adopted approach for concept-based interpretation is Concept Activation Vector (CAV). CAV relies on learning a linear relation between some latent representation of a given model and concepts. The linear separability is usually implicitly assumed but does not hold true in general. In this work, we started from the original intent of concept-based interpretation and proposed Concept Gradient (CG), extending concept-based interpretation beyond linear concept functions. We showed that for a general (potentially non-linear) concept, we can mathematically evaluate how a small change of concept affecting the model's prediction, which leads to an extension of gradient-based interpretation to the concept space. We demonstrated empirically that CG outperforms CAV in both toy examples and real world datasets.