Frequency-Modulated Spiral Manifold: A Model for Temporal Knowledge Graph Completion

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Temporal knowledge graph completion (TKGC) infers missing facts by modeling the temporal evolution of relations. Existing methods typically encode time through low-dimensional geometric transformations or frequency-domain decomposition. However, periodically recurring relations can still be mapped to overlapping trajectories in the same two-dimensional working space, which may reduce temporal separability and produce conflicting optimization signals. To address this limitation, we propose the Frequency-Modulated Spiral Manifold (FMSM) model, which includes the following: (1) a relation-adaptive spectral partition and relation-dimension gate for fusing long- and short-term relation channels; (2) an independent global phase embedding and nonlinear spiral push that lift entangled planar trajectories onto separated three-dimensional manifold layers; and (3) a spiral norm regularizer that stabilizes temporal evolution while preserving valid burst signals. The artificial-intelligence contribution of FMSM is a phase-conditioned spectral-geometric representation that separates recurring temporal facts while retaining multi-scale relation dynamics. Its engineering application is the completion of time-stamped event records for dynamic knowledge-based decision-support systems. Experiments on ICEWS14, ICEWS05-15, and GDELT show that, compared with the strongest reported baseline TeRDy, FMSM yields relative MRR improvements of 0.62%, 0.86%, and 13.28%.