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

arXiv: https://arxiv.org/abs/2401.12798 · HTML: https://mlsanity.com/paper/2401.12798/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 64 references that are in the map.
- First posted on arXiv 23 Jan 2024.

## Builds on (most cited first, 30 of 32)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [Multilingual Knowledge Graph Embeddings for Cross-lingual Knowledge Alignment](https://mlsanity.com/paper/1611.03954/) (2016)
- [Cross-lingual Entity Alignment via Joint Attribute-Preserving Embedding](https://mlsanity.com/paper/1708.05045/) (2017)
- [A Benchmarking Study of Embedding-based Entity Alignment for Knowledge Graphs](https://mlsanity.com/paper/2003.07743/) (2020)
- [Relation-Aware Entity Alignment for Heterogeneous Knowledge Graphs](https://mlsanity.com/paper/1908.08210/) (2019)
- [Knowledge Graph Alignment Network with Gated Multi-hop Neighborhood Aggregation](https://mlsanity.com/paper/1911.08936/) (2019)
- [Deep Graph Matching Consensus](https://mlsanity.com/paper/2001.09621/) (2020)
- [Learning to Exploit Long-term Relational Dependencies in Knowledge Graphs](https://mlsanity.com/paper/1905.04914/) (2019)
- [Cross-lingual Knowledge Graph Alignment via Graph Matching Neural Network](https://mlsanity.com/paper/1905.11605/) (2019)
- [Exploring and Evaluating Attributes, Values, and Structures for Entity Alignment](https://mlsanity.com/paper/2010.03249/) (2020)
- [On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features](https://mlsanity.com/paper/2111.12128/) (2021)
- [Relational Reflection Entity Alignment](https://mlsanity.com/paper/2008.07962/) (2020)
- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [TransEdge: Translating Relation-contextualized Embeddings for Knowledge Graphs](https://mlsanity.com/paper/2004.13579/) (2020)
- [Jointly Learning Entity and Relation Representations for Entity Alignment](https://mlsanity.com/paper/1909.09317/) (2019)
- [Boosting the Speed of Entity Alignment 10*: Dual Attention Matching Network with Normalized Hard Sample Mining](https://mlsanity.com/paper/2103.15452/) (2021)
- [RAGA: Relation-aware Graph Attention Networks for Global Entity Alignment](https://mlsanity.com/paper/2103.00791/) (2021)
- [From Alignment to Assignment: Frustratingly Simple Unsupervised Entity Alignment](https://mlsanity.com/paper/2109.02363/) (2021)
- [Rethinking Uncertainly Missing and Ambiguous Visual Modality in Multi-Modal Entity Alignment](https://mlsanity.com/paper/2307.16210/) (2023)
- [Unsupervised Entity Alignment for Temporal Knowledge Graphs](https://mlsanity.com/paper/2302.00796/) (2023)
- [LightEA: A Scalable, Robust, and Interpretable Entity Alignment Framework via Three-view Label Propagation](https://mlsanity.com/paper/2210.10436/) (2022)
- [Degree-Aware Alignment for Entities in Tail](https://mlsanity.com/paper/2005.12132/) (2020)
- [Time-aware Graph Neural Networks for Entity Alignment between Temporal Knowledge Graphs](https://mlsanity.com/paper/2203.02150/) (2022)
- [Coordinated Reasoning for Cross-Lingual Knowledge Graph Alignment](https://mlsanity.com/paper/2001.08728/) (2020)
- [ActiveEA: Active Learning for Neural Entity Alignment](https://mlsanity.com/paper/2110.06474/) (2021)
- [Knowledge Embedding Based Graph Convolutional Network](https://mlsanity.com/paper/2006.07331/) (2020)
- [Facing Changes: Continual Entity Alignment for Growing Knowledge Graphs](https://mlsanity.com/paper/2207.11436/) (2022)

## Built on by (most cited first, 2 of 2)

- [InfiGFusion: Graph-on-Logits Distillation via Efficient Gromov-Wasserstein for Model Fusion](https://mlsanity.com/paper/2505.13893/) (2025)
- [Understanding and Guiding Weakly Supervised Entity Alignment with Potential Isomorphism Propagation](https://mlsanity.com/paper/2402.03025/) (2024)

## Abstract (arXiv)

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.