Beyond Geometric Blindness: Leveraging Ollivier-Ricci Curvature for Effective Knowledge Graph Completion

Graph Neural Networks (GNNs) are widely used for Knowledge Graph Completion (KGC) but often suffer from "geometric blindness", resulting in redundant message propagation and limiting their ability to perform effective long-range reasoning. We introduce ORCA-GCN (Ollivier-Ricci Curvature-Aware Graph Convolutional Network), a novel geometry-aware GNN that integrates Ollivier-Ricci Curvature (ORC) into its message-passing mechanism. While prior curvature-guided methods for node classification often enhance high-curvature intra-cluster links, which can be detrimental for KGC, ORCA-GCN strategically down-weights these redundant high-curvature connections and amplifies low-curvature bridge edges to improve information flow. It also features a layer-wise evolutionary framework, transitioning from geometric priors in shallow layers to learned semantic similarity in deeper layers. Extensive experiments on FB15k-237 and WN18RR demonstrate that ORCA-GCN consistently outperforms strong baselines in link prediction. Our analysis confirms that high-curvature intra-cluster edges tend to be semantically redundant, thereby offering limited utility in KGC tasks and underscoring the importance of structural geometry in guiding discriminative representation learning.