Post #171

Are Hyperbolic Representations in Graphs Created Equal? The second submission to GRL workshop was on hyperbolic embeddings for graphs. We first make a good introduction to the distances and dot products in k-Stereographic model (a Riemannian manifold with constant curvature) and fix the issue with taking gradients at zero curvature, by taking a Taylor series expansion around the origin. This allows seamless gradient descent optimization in non-Euclidean space. Then we make experiments on node and graph classification, link prediction, and graph embedding task (i.e. preserving distances in the latent space) and show that for link prediction and graph embedding there is an uplift in using hyperbolic manifolds, while for node and graph classification Euclidean models work better.