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

Jincheng Zhou, Yucheng Zhang, Jianfei Gao, Yangze Zhou, Bruno Ribeiro

TL;DR

This work introduces the concept of double permutation-equivariant representations and demonstrates its necessity for effective performance in the task of fully inductive link prediction in knowledge graphs, and identifies inherent limitations in double permutation-equivariant representations which restrict these models's ability to learn effectively on datasets with varying characteristics.

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.

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

TL;DR

This work introduces the concept of double permutation-equivariant representations and demonstrates its necessity for effective performance in the task of fully inductive link prediction in knowledge graphs, and identifies inherent limitations in double permutation-equivariant representations which restrict these models's ability to learn effectively on datasets with varying characteristics.

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.
Paper Structure (17 sections, 5 theorems, 2 equations, 2 tables)

This paper contains 17 sections, 5 theorems, 2 equations, 2 tables.

Table of Contents

  1. Double Equivariance Enables Fully Inductive Link Prediction
  2. Formalizing the Fully Inductive Link Prediction Task
  3. Double Equivariant Representations for Knowledge Graphs
  4. Distributionally Double Equivariant Positional Graph Embeddings
  5. Double Equivariance to Guide Model Design
  6. Ultra Generates Double Equivariant Structural Representations
  7. InGram Generates Distributionally Double Equivariant Positional Embeddings
  8. DEq-InGram: Enhancing Double Equivariance via Monte Carlo Sampling
  9. Inductive Structural Double Equivariant Architecture Plus (ISDEA+)
  10. Related Work
  11. Inductive link prediction over new nodes (but not new relations).
  12. Inductive link prediction over both new nodes and new relations.
  13. Experiments on How Simple Double Equivariant Models Can Perform Fully Inductive Link Prediction
  14. Experiment on Negative Transfers in Meta-Learning
  15. Dataset and experiment setup
  16. ...and 2 more sections

Key Result

Theorem 2.6

For all ${\mathbf{A}} \in {\mathbb{A}}$ with number of nodes and relations ${N},{R}$, given a double invariant triplet representation $\Gamma_\text{triplet}$, we can construct a double equivariant graph representation as $\left( \Gamma_\text{graph}({\mathbf{A}}) \right)_{i,k,j} := \Gamma_\text{tripl

Theorems & Definitions (11)

  • Definition 2.1: Fully inductive link prediction task
  • Definition 2.2: Node and relation permutation actions on knowledge graphs
  • Definition 2.3: Double invariant triplet representations
  • Definition 2.4: Knowledge graph isomorphism and Triplet isomorphism
  • Definition 2.5: Double equivariant knowledge graph structural representations
  • Theorem 2.6: From double invariant triplet representations to double equivariant graph representations
  • Definition 2.7: Distributionally double equivariant positional embeddings
  • Theorem 2.8: From distributional double equivariant positional embeddings to double equivariant representations
  • Lemma 3.0
  • Lemma 3.0
  • ...and 1 more