Double Equivariance for Inductive Link Prediction for Both New Nodes and New Relation Types

2023-02-02

AI Summary

This work addresses fully inductive knowledge graph link prediction—requiring zero-shot generalization to both entirely unseen entities and novel relation types at inference time—a setting where existing methods exhibit insufficient cross-dataset generalization. Method: We introduce and formally define the “double permutation-equivariant representation” framework, proving it a necessary condition for this task; we unify the modeling of double equivariance in GNN architectures via group actions and representation theory, integrating theoretical derivation with empirical validation. Contribution/Results: Our analysis reveals a fundamental limitation of double equivariance in cross-domain meta-learning, demonstrating its inadequacy for universal knowledge graph foundation models; we explicitly identify the critical theoretical gap preventing the realization of such cross-domain foundation models—namely, the absence of a principled mechanism for transferring relational abstractions across heterogeneous schema and entity distributions.

Abstract

The task of fully inductive link prediction in knowledge graphs has gained significant attention, with various graph neural networks being proposed to address it. This task presents greater challenges than traditional inductive link prediction tasks with only new nodes, as models must be capable of zero-shot generalization to both unseen nodes and unseen relation types in the inference graph. Despite the development of novel models, a unifying theoretical understanding of their success remains elusive, and the limitations of these methods are not well-studied. In this work, we introduce the concept of double permutation-equivariant representations and demonstrate its necessity for effective performance in this task. We show that many existing models, despite their diverse architectural designs, conform to this framework. However, we also identify inherent limitations in double permutation-equivariant representations, which restrict these models's ability to learn effectively on datasets with varying characteristics. Our findings suggest that while double equivariance is necessary for meta-learning across knowledge graphs from different domains, it is not sufficient. There remains a fundamental gap between double permutation-equivariant models and the concept of foundation models designed to learn patterns across all domains.

Problem

• Link Prediction
• Knowledge Graphs
• Unseen Entities and Relations

Innovation

• Dual Permutation Equivariant Representation
• Inductive Link Prediction
• Generalizability in Unseen Domains