Neural Networks in a Product of Hyperbolic Spaces

AbstractMachine learning in hyperbolic spaces has attracted much attention in natural language processing and many other fields. In particular, Hyperbolic Neural Networks (HNNs) have improved a wide variety of tasks, from machine translation to knowledge graph embedding. Although some studies have reported the effectiveness of embedding into the product of multiple hyperbolic spaces, HNNs have mainly been constructed in a single hyperbolic space, and their extension to product spaces has not been sufficiently studied. Therefore, we propose a novel method to extend a given HNN in a single space to a product of hyperbolic spaces. We apply our method to Hyperbolic Graph Convolutional Networks (HGCNs), extending several HNNs. Our model improved the graph node classification accuracy especially on datasets with tree-like structures. The results suggest that neural networks in a product of hyperbolic spaces can be more effective than in a single space in representing structural data.