Hyperbolic Disk Embeddings for Directed Acyclic Graphs

Obtaining continuous representations of structural data such as directed acyclic graphs (DAGs) has gained attention in machine learning and artificial intelligence. However, embedding complex DAGs in which both ancestors and descendants of nodes are exponentially increasing is difficult. Tackling in this problem, we develop Disk Embeddings, which is a framework for embedding DAGs into quasi-metric spaces. Existing state-of-the-art methods, Order Embeddings and Hyperbolic Entailment Cones, are instances of Disk Embedding in Euclidean space and spheres respectively. Furthermore, we propose a novel method Hyperbolic Disk Embeddings to handle exponential growth of relations. The results of our experiments show that our Disk Embedding models outperform existing methods especially in complex DAGs other than trees.