Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterization

TL;DR

GoldE introduces a universal orthogonal parameterization for knowledge graph embedding, enabling flexible modeling of logical patterns and topological heterogeneity, and achieves state-of-the-art results on standard benchmarks.

Contribution

It proposes a novel framework with a generalized Householder reflection-based orthogonal parameterization, extending dimensions and unifying geometries for improved knowledge graph embedding.

Findings

GoldE achieves state-of-the-art performance on three benchmarks.

The framework effectively captures logical patterns and topological heterogeneity.

Theoretical guarantees support the universal orthogonal parameterization.

Abstract

Recent advances in knowledge graph embedding (KGE) rely on Euclidean/hyperbolic orthogonal relation transformations to model intrinsic logical patterns and topological structures. However, existing approaches are confined to rigid relational orthogonalization with restricted dimension and homogeneous geometry, leading to deficient modeling capability. In this work, we move beyond these approaches in terms of both dimension and geometry by introducing a powerful framework named GoldE, which features a universal orthogonal parameterization based on a generalized form of Householder reflection. Such parameterization can naturally achieve dimensional extension and geometric unification with theoretical guarantees, enabling our framework to simultaneously capture crucial logical patterns and inherent topological heterogeneity of knowledge graphs. Empirically, GoldE achieves state-of-the-art performance on three standard benchmarks. Codes are available at https://github.com/xxrep/GoldE.