Concept-based explanations work by mapping complex model computations to humanunderstandable concepts.Evaluating such explanations is very difficult, as it includes not only the quality of the induced space of possible concepts but also how effectively the chosen concepts are communicated to users.Existing evaluation metrics often focus solely on the former, neglecting the latter.

Orthogonal convolutional layers are valuable components in multiple areas of machine learning, such as adversarial robustness, normalizing flows, GANs, and Lipschitz-constrained models. Their ability to preserve norms and ensure stable gradient propagation makes them valuable for a large range of problems. Despite their promise, the deployment of orthogonal convolution in large-scale applications is a significant challenge due to computational overhead and limited support for modern features like strides, dilations, group convolutions, and transposed convolutions. In this paper, we introduce **AOC** (Adaptive Orthogonal Convolution), a scalable method that extends a previous method (BCOP), effectively overcoming existing limitations in the construction of orthogonal convolutions. This advancement unlocks the construction of architectures that were previously considered impractical. We demonstrate through our experiments that our method produces expressive models that become increasingly efficient as they scale. To foster further advancement, we provide an open-source python package implementing this method, called **Orthogonium**.

Attribution methods, which employ heatmaps to identify the most influential regions of an image that impact model decisions, have gained widespread popularity as a type of explainability method. However, recent research has exposed the limited practical value of these methods, attributed in part to their narrow focus on the most prominent regions of an image - revealing “where” the model looks, but failing to elucidate “what” the model sees in those areas. In this work, we try to fill in this gap with CRAFT - a novel approach to identify both “what” and “where” by generating concept-based explanations. We introduce 3 new ingredients to the automatic concept extraction literature: (i) a recursive strategy to detect and decompose concepts across layers, (ii) a novel method for a more faithful estimation of concept importance using Sobol indices, and (iii) the use of implicit differentiation to unlock Concept Attribution Maps. We conduct both human and computer vision experiments to demonstrate the benefits of the proposed approach. We show that the proposed concept importance estimation technique is more faithful to the model than previous methods. When evaluating the usefulness of the method for human experimenters on a human-centered utility benchmark, we find that our approach significantly improves on two of the three test scenarios.

Feature visualization has gained significant popularity as an explainability method, particularly after the influential work by Olah et al. in 2017. Despite its success, its widespread adoption has been limited due to issues in scaling to deeper neural networks and the reliance on tricks to generate interpretable images. Here, we describe MACO, a simple approach to address these shortcomings. It consists in optimizing solely an image's phase spectrum while keeping its magnitude constant to ensure that the generated explanations lie in the space of natural images. Our approach yields significantly better results -- both qualitatively and quantitatively -- unlocking efficient and interpretable feature visualizations for state-of-the-art neural networks. We also show that our approach exhibits an attribution mechanism allowing to augment feature visualizations with spatial importance. Furthermore, we enable quantitative evaluation of feature visualizations by introducing 3 metrics: transferability, plausibility, and alignment with natural images. We validate our method on various applications and we introduce a website featuring MACO visualizations for all classes of the ImageNet dataset, which will be made available upon acceptance. Overall, our study unlocks feature visualizations for the largest, state-of-the-art classification networks without resorting to any parametric prior image model, effectively advancing a field that has been stagnating since 2017 (Olah et al, 2017).