Hyperbolic Graph Neural Networks: A Tutorial on Methods and Applications

Graph Neural Networks (GNNs) generalize conventional neural networks to graph-structured data and have received considerable attention owing to their impressive performance. In spite of the notable successes, the performance of Euclidean models is inherently bounded and limited by the representation ability of Euclidean geometry, especially when it comes to datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic spaces have emerged as a promising alternative for processing graph data with tree-like structure or power-law distribution and a surge of works on either methods or novel applications have been seen. Unlike Euclidean space, which expands polynomially, hyperbolic space grows exponentially with its radius, making it more suitable for modeling complex real-world data. Hence, it gains natural advantages in abstracting tree-like graphs with a hierarchical organization or power-law distribution.