Multi-curvature progressive fusion for knowledge graph completion
Knowledge graphs have become a fundamental representation for structured knowledge, yet their incompleteness remains a major obstacle to reliable reasoning. Missing links may interrupt relational paths and limit the evidence available for downstream inference. Knowledge graph completion addresses this problem by predicting missing facts from observed relational patterns. Existing methods have made notable progress, but many of them rely on a single geometric space or fuse multiple geometric representations in a static manner. This limits their ability to capture heterogeneous graph structures, especially when hierarchical dependencies, local relational patterns, and cyclic motifs coexist in the same knowledge graph. In this paper, we propose multi-curvature progressive fusion (MCPF), a geometry-aware graph neural reasoning framework for knowledge graph completion. MCPF learns relation-aware representations in Euclidean, hyperbolic, and hyperspherical spaces, which provide complementary inductive biases for conventional relational interactions, hierarchical organization, and cyclic structures. Instead of directly aggregating these representations, MCPF progressively refines them through cross-space interactions and uses a query-conditioned gating mechanism to determine their relative contributions. This design enables the model to emphasize reliable geometric signals while suppressing less informative ones for each query. The fused representation is then used within a graph neural reasoning architecture for message passing and link prediction. Experiments on four benchmark datasets demonstrate that MCPF achieves competitive results against representative baselines and consistently outperforms its ablated variants.