Concepts such as objects, patterns, and shapes are how humans understand the world. Building on this intuition, concept-based explainability methods aim to study representations learned by deep neural networks in relation to human-understandable concepts. Here, Concept Activation Vectors (CAVs) are an important tool and can identify whether a model learned a concept or not. However, the computational cost and time requirements of existing CAV computation pose a significant challenge, particularly in large-scale, high-dimensional architectures. To address this limitation, we introduce FastCAV, a novel approach that accelerates the extraction of CAVs by up to 63.6× (on average 46.4×). We provide a theoretical foundation for our approach and give concrete assumptions under which it is equivalent to established SVM-based methods. Our empirical results demonstrate that CAVs calculated with FastCAV maintain similar performance while being more efficient and stable. In downstream applications, i.e., concept-based explanation methods, we show that FastCAV can act as a replacement leading to equivalent insights. Hence, our approach enables previously infeasible investigations of deep models, which we demonstrate by tracking the evolution of concepts during model training.

Gaussian mixture models are classical but still popular machine learning models. An appealing feature of Gaussian mixture models is their tractability, that is, they can be learned efficiently and exactly from data, and also support efficient exact inference queries like soft clustering data points. Only seemingly simple, Gaussian mixture models can be hard to understand. There are at least four aspects to understanding Gaussian mixture models, namely, understanding the whole distribution, its individual parts (mixture components), the relationships between the parts, and the interplay of the whole and its parts. In a structured literature review of applications of Gaussian mixture models, we found the need for supporting all four aspects. To identify candidate visualizations that effectively aid the user needs, we structure the available design space along three different representations of Gaussian mixture models, namely as functions, sets of parameters, and sampling processes. From the design space, we implemented three design concepts that visualize the overall distribution together with its components. Finally, we assessed the practical usefulness of the design concepts with respect to the different user needs in expert interviews and an insight-based user study.