  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.
