Entity Alignment (EA) aims to identify equivalent real-world entities across different knowledge graphs. These graphs exhibit a mixture of structural forms, such as hierarchies, cycles, and chains, which correspond to different geometric behaviors. However, most existing methods learn representations in a single geometric space, implicitly assuming uniform structural regularity, which limits their ability to capture diverse relational semantics and nonlinear dependencies in graphs with mixed or irregular topologies. To address this limitation, we propose a novel GSMS model, which integrates Graph Structural signals with Multi-curvature Space mapping under a generative adversarial training framework. GSMS unifies structural enhancement, multi-curvature geometric mapping, and adversarial training into a cohesive framework that strengthens both the discriminative capacity and robustness of entity representations. Specifically, it first enhances structural representations by leveraging second-order and triangular-ring relations while suppressing noise through stacked adaptive edge-weight updates. Then, it embeds entities into Euclidean, hyperbolic, and spherical spaces and adaptively fuses these complementary geometric features via a geometry-gated fusion module. Subsequently, a generative adversarial scheme aligns structural and geometric embeddings by treating the latter as “real” samples, thereby enforcing geometric consistency and improving robustness. Extensive experiments on multiple benchmark cross-lingual knowledge graph datasets demonstrate that GSMS consistently outperforms state-of-the-art methods, achieving notable improvements across various evaluation metrics, particularly under sparse and structurally heterogeneous settings.
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