For the trustworthy application of XAI, in particular for high-stake decisions, a more global model understanding is required. To this end, concept-based methods have been proposed, which are however not guaranteed to be bound to the actual model reasoning. To circumvent this problem, we propose Multi-dimensional Concept Discovery (MCD) as an extension of previous approaches that fulfills a completeness relation on the level of concepts. Our method starts from general linear subspaces as concepts and does neither require reinforcing concept interpretability nor re-training of model parts. We propose sparse subspace clustering to discover improved concepts and fully leverage the potential of multi-dimensional subspaces. MCD offers two complementary analysis tools for concepts in input space: (1) concept activation maps, that show where a concept is expressed within a sample, allowing for concept characterization through prototypical samples, and (2) concept relevance heatmaps, that decompose the model decision into concept contributions. Both tools together enable a detailed global understanding of the model reasoning, which is guaranteed to relate to the model via a completeness relation. Thus, MCD paves the way towards more trustworthy concept-based XAI. We empirically demonstrate the superiority of MCD against more constrained concept definitions.

Concepts are key building blocks of higher level human understanding. Explainable AI (XAI) methods have shown tremendous progress in recent years, however, local attribution methods do not allow to identify coherent model behavior across samples and therefore miss this essential component. In this work, we study concept-based explanations and put forward a new definition of concepts as low-dimensional subspaces of hidden feature layers. We novelly apply sparse subspace clustering to discover these concept subspaces. Moving forward, we derive insights from concept subspaces in terms of localized input (concept) maps, show how to quantify concept relevances and lastly, evaluate similarities and transferability between concepts. We empirically demonstrate the soundness of the proposed Sparse Subspace Clustering for Concept Discovery (SSCCD) method for a variety of different image classification tasks. This approach allows for deeper insights into the actual model behavior that would remain hidden from conventional input-level heatmaps.

Deep convolutional networks have been quite successful at various image classification tasks. The current methods to explain the predictions of a pre-trained model rely on gradient information, often resulting in saliency maps that focus on the foreground object as a whole. However, humans typically reason by dissecting an image and pointing out the presence of smaller concepts. The final output is often an aggregation of the presence or absence of these smaller concepts. In this work, we propose MACE: a Model Agnostic Concept Extractor, which can explain the working of a convolutional network through smaller concepts. The MACE framework dissects the feature maps generated by a convolution network for an image to extract concept based prototypical explanations. Further, it estimates the relevance of the extracted concepts to the pre-trained model's predictions, a critical aspect required for explaining the individual class predictions, missing in existing approaches. We validate our framework using VGG16 and ResNet50 CNN architectures, and on datasets like Animals With Attributes 2 (AWA2) and Places365. Our experiments demonstrate that the concepts extracted by the MACE framework increase the human interpretability of the explanations, and are faithful to the underlying pre-trained black-box model.