Learning in computer vision is all about deep networks and such networks operate on Euclidean manifolds by default. While Euclidean space is an intuitive and practical choice, foundational work on non-visual data has shown that when information is hierarchical in nature, hyperbolic space is superior, as it allows for an embedding without distortion. A core reason is because Euclidean distances scale linearly as a function of their norm, while hyperbolic distances grow exponentially, just like hierarchies grow exponentially with depth. This initial finding has resulted in rapid developments in hyperbolic geometry for deep learning.
Hyperbolic deep learning is booming in computer vision, with new theoretical and empirical advances with every new conference. But what is hyperbolic geometry exactly? What is its potential for computer vision? And how can we perform hyperbolic deep learning in practice? This tutorial will cover all such questions. We will dive into the geometry itself, how to design networks in hyperbolic space, and we show how current literature profits from learning in this space. The aim is to provide technical depth while addressing a broad audience of computer vision researchers and enthusiasts.