SynAlign: cross-curvature synergistic Euclidean–hyperbolic entity alignment for knowledge graphs

Entity alignment is a fundamental step for knowledge graph (KG) integration, yet the complex and heterogeneous structures of real-world KGs make accurate alignment particularly challenging. KG entity alignment faces two main challenges. First, representations learned in a single Euclidean or hyperbolic space struggle to simultaneously capture local structure, global centrality, and hierarchical semantics. Second, most existing pipelines employ sophisticated encoders but rely on simple, weakly optimized decoders. To address these issues, we propose SynAlign, a cross-curvature Euclidean–hyperbolic framework for KG entity alignment. SynAlign adopts a decoupled multi-view, multi-geometry encoder: Euclidean embeddings model local structure and graph centrality, while hyperbolic embeddings emphasize hierarchical and containment relations, providing complementary multi-scale structural signals. On top of these embeddings, a hybrid collaborative supervision scheme jointly optimizes representation learning and matching. A margin-based feature loss encourages separability between aligned and non-aligned entities, whereas a collaborative alignment decoder combines soft matching scores with structural consistency constraints via Sinkhorn-based optimal transport to produce globally consistent soft alignments. Experiments on multiple benchmark datasets show that SynAlign consistently outperforms strong baselines in terms of Hits@1 and maintains robust performance under sparse supervision and structurally complex graphs.