Abstract: Visual recognition by deep learning thrives on examples but commonly ignores broader available knowledge about hierarchical relations between classes. My team focuses on the question of how to integrate hierarchical and broader inductive knowledge about categorization into deep networks. In this talk, I will dive into a few of our recent works that integrate knowledge through hyperbolic and hyperspherical geometry. As a starting point, I will shortly outline what hyperbolic geometry entails, as well as its potential for visual representation learning. I will then outline how to enable the use of hyperbolic geometry for video understanding with hierarchical prior knowledge [CVPR’20]. As a follow-up, I will discuss Hyperbolic Image Segmentation, where we generalize hyperbolic learning to the pixel level with hierarchical knowledge, which opens multiple new doors in segmentation [CVPR’22]. Beyond learning with hierarchical knowledge, I will also revisit a classical inductive bias, namely maximum separation between classes, and show that contrarily to recent literature, this inductive bias is not an optimization problem but has a closed-form hyperspherical solution [Preprint’22]. The solution takes the form of one fixed matrix and only requires a single line of code to add to your network, yet directly boosts categorization, long-tailed recognition, and open-set recognition. The talk concludes with a short overview of other related works from our team and the future potential of hyperbolic and hyperspherical learning for computer vision.