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Gradient Flow of Energy: A General and Efficient Approach for Entity Alignment Decoding

Yuanyi Wang, Haifeng Sun, Jingyu Wang, Qi Qi, Shaoling Sun, Jianxin Liao

TL;DR

The paper tackles entity alignment by reframing decoding as a gradient-flow problem that reconstructs entity embeddings through Dirichlet-energy minimization to maximize homophily. It introduces Triple Feature Propagation (TFP), which generalizes adjacency with multi-view matrices—entity-to-entity, entity-to-relation, relation-to-entity, and relation-to-triple—and derives a gradient-flow-based propagation mechanism that operates regardless of the encoder type. TF P achieves this through discretized gradient descent steps and a Sinkhorn-based one-to-one assignment, enabling fast, scalable decoding across GNN- and translation-based encoders. Empirical results on DBP15K and SRPRS show consistent improvements with negligible overhead (under 6 seconds), establishing TF P as a versatile and efficient decoding paradigm for future EA methods.

Abstract

Entity alignment (EA), a pivotal process in integrating multi-source Knowledge Graphs (KGs), seeks to identify equivalent entity pairs across these graphs. Most existing approaches regard EA as a graph representation learning task, concentrating on enhancing graph encoders. However, the decoding process in EA - essential for effective operation and alignment accuracy - has received limited attention and remains tailored to specific datasets and model architectures, necessitating both entity and additional explicit relation embeddings. This specificity limits its applicability, particularly in GNN-based models. To address this gap, we introduce a novel, generalized, and efficient decoding approach for EA, relying solely on entity embeddings. Our method optimizes the decoding process by minimizing Dirichlet energy, leading to the gradient flow within the graph, to maximize graph homophily. The discretization of the gradient flow produces a fast and scalable approach, termed Triple Feature Propagation (TFP). TFP innovatively generalizes adjacency matrices to multi-views matrices:entity-to-entity, entity-to-relation, relation-to-entity, and relation-to-triple. The gradient flow through generalized matrices enables TFP to harness the multi-view structural information of KGs. Rigorous experimentation on diverse public datasets demonstrates that our approach significantly enhances various EA methods. Notably, the approach achieves these advancements with less than 6 seconds of additional computational time, establishing a new benchmark in efficiency and adaptability for future EA methods.

Gradient Flow of Energy: A General and Efficient Approach for Entity Alignment Decoding

TL;DR

The paper tackles entity alignment by reframing decoding as a gradient-flow problem that reconstructs entity embeddings through Dirichlet-energy minimization to maximize homophily. It introduces Triple Feature Propagation (TFP), which generalizes adjacency with multi-view matrices—entity-to-entity, entity-to-relation, relation-to-entity, and relation-to-triple—and derives a gradient-flow-based propagation mechanism that operates regardless of the encoder type. TF P achieves this through discretized gradient descent steps and a Sinkhorn-based one-to-one assignment, enabling fast, scalable decoding across GNN- and translation-based encoders. Empirical results on DBP15K and SRPRS show consistent improvements with negligible overhead (under 6 seconds), establishing TF P as a versatile and efficient decoding paradigm for future EA methods.

Abstract

Entity alignment (EA), a pivotal process in integrating multi-source Knowledge Graphs (KGs), seeks to identify equivalent entity pairs across these graphs. Most existing approaches regard EA as a graph representation learning task, concentrating on enhancing graph encoders. However, the decoding process in EA - essential for effective operation and alignment accuracy - has received limited attention and remains tailored to specific datasets and model architectures, necessitating both entity and additional explicit relation embeddings. This specificity limits its applicability, particularly in GNN-based models. To address this gap, we introduce a novel, generalized, and efficient decoding approach for EA, relying solely on entity embeddings. Our method optimizes the decoding process by minimizing Dirichlet energy, leading to the gradient flow within the graph, to maximize graph homophily. The discretization of the gradient flow produces a fast and scalable approach, termed Triple Feature Propagation (TFP). TFP innovatively generalizes adjacency matrices to multi-views matrices:entity-to-entity, entity-to-relation, relation-to-entity, and relation-to-triple. The gradient flow through generalized matrices enables TFP to harness the multi-view structural information of KGs. Rigorous experimentation on diverse public datasets demonstrates that our approach significantly enhances various EA methods. Notably, the approach achieves these advancements with less than 6 seconds of additional computational time, establishing a new benchmark in efficiency and adaptability for future EA methods.
Paper Structure (23 sections, 33 equations, 3 figures, 4 tables, 1 algorithm)

This paper contains 23 sections, 33 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary
  4. Methodology
  5. Gradient Flow
  6. Discretization Strategy
  7. Generalized Adjacency Matrices
  8. Triple Feature Propagation
  9. Experiments
  10. Experimental Settings
  11. Main Results (Q1)
  12. GNN-based encoders:
  13. Translation-based encoders:
  14. Exploratory Analysis (Q2)
  15. Performance with Dual-AMN Encoder.
  16. ...and 8 more sections

Figures (3)

  • Figure 1: (1) The architecture of existing EA methods that involve the encoding and decoding phase. (2) TFP maintains seed alignment features while reconstructing other entity features. It decodes relation features, not directly provided by encoders, to make them explicit based on entity features.
  • Figure 2: The illustration of Triple Feature Propagation.
  • Figure 3: Metrics and execution time (seconds) on DBP15K across iterations $k$.

Theorems & Definitions (4)

  • proof
  • proof
  • proof
  • proof