Shadow Cones: A Generalized Framework for Partial Order Embeddings

arXiv:2305.15215v2 Announce Type: replace
Abstract: Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic …

abstract arxiv concept cs.lg data embeddings framework generalized graphs hierarchical orders prior relations shadow space trees type work