Concorde: Geometry-Aware Link Prediction via Decoupled Energy Minimization

Concorde is an energy‑based framework for link prediction that tackles sparse graphs by decomposing link likelihood into three decoupled branches: a parameter‑free spectral anchor for topological stability, a mixed‑curvature residual on a learnable hyperbolic‑spherical product manifold regularized by a curvature proxy, and a continuous vector field on the hyperbolic tangent bundle for non‑local alignment. These branches are fused via learned gating and trained with an N‑pair ranking loss. On five diverse benchmarks, Concorde achieves state‑of‑the‑art early retrieval precision, nearly doubling P@10% over leading baselines in sparse settings.

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