Completing knowledge graph via multi-geometric with metric alignment and curvature scheduling

The inherent incompleteness of knowledge graphs (KGs) has driven extensive research in the field of knowledge graph completion (KGC). Most current KGC methods are based on the construction of multiple geometric spaces to capture the heterogeneous structure of KGs. However, when performing unified modeling across multiple geometric spaces, there is a problem of inconsistent cross-space metrics, which makes curvature prone to instability during training. To address these challenges, this manuscript proposes a novel KGC framework, Multi-Geometric Metric Alignment and Curvature Scheduling (MG-MACS). Specifically, MG-MACS performs isometric processing across different geometric spaces, aligning multiple branches to a shared tangent space to avoid distance distortion between geometries. Building upon this, we present a curvature scheduling scheme that gradually anneals the scoring curvature from a near-Euclidean starting point to a target value according to a prescribed schedule, thereby controlling gradient amplification and enhancing training stability. Finally, we introduce spectral regularization during the optimization phase to suppress high-frequency noise introduced by false negatives. Extensive experiments on three standard KGC benchmarks demonstrate that MG-MACS consistently outperforms strong state-of-the-art models on link prediction, exhibiting more stable performance across datasets with different structural characteristics.