Hyperbolic Neural Networks: Theory, Architectures and Applications

Recent studies have revealed important properties that are unique to graph datasets such as hierarchies and global structures. This has driven research into hyperbolic space due to their ability to effectively encode the inherent hierarchy present in graph datasets. However, a major bottleneck here is the obscurity of hyperbolic geometry and a better comprehension of its gyrovector operations. In this tutorial, we aim to introduce researchers and practitioners in the data mining community to the hyperbolic equivariants of the Euclidean operations that are necessary to tackle their application to neural networks. We describe the popular hyperbolic variants of GNN architectures and explain their implementation, in contrast to the Euclidean counterparts. Also, we motivate our tutorial through critical analysis of existing applications in the areas of graph mining, knowledge graph reasoning, search, NLP, and computer vision.