← 研踪 PaperTrailarXiv:2610.36204 · v1
Concorde: Geometry-Aware Link Prediction via Decoupled Energy Minimization
首次提交 2026-10-27 03:41
版本更新 2026-10-27 03:41
雷达观测 2026-10-29 00:35
摘要
Link prediction remains difficult in sparse graphs, where diffusion heuristics lack connectivity and geometric methods suffer spectral instability when coupling learned representations with diffusion operators. We introduce Concorde, an energy-based framework that resolves this by decomposing link likelihood into three structurally decoupled branches: (i) a parameter-free spectral anchor that establishes permutation-invariant topological stability; (ii) a mixed-curvature residual on a learnable $\mathbb{H}^{d_h}_{c_h} \times \mathbb{S}^{d_s}_{c_s}$ product manifold, regularized by a feature-aware Ollivier-Ricci curvature proxy; and (iii) a continuous vector field on the tangent bundle of hyperbolic space for non-local structural alignment across topological gaps. The branches are fused via learned gating and trained with an N-pair ranking loss aligned with retrieval-style evaluation. Across five benchmarks spanning sparse, dense, featureless, and attributed regimes, Concorde establishes state-of-the-art early retrieval precision, nearly doubling P@10% over leading baselines in sparse settings.
作者备注：NeurIPS 2026
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v1 · 2026-10-27 03:41 · 最新观测版本
Concorde: Geometry-Aware Link Prediction via Decoupled Energy Minimization
Link prediction remains difficult in sparse graphs, where diffusion heuristics lack connectivity and geometric methods suffer spectral instability when coupling learned representations with diffusion operators. We introduce Concorde, an energy-based framework that resolves this by decomposing link likelihood into three structurally decoupled branches: (i) a parameter-free spectral anchor that establishes permutation-invariant topological stability; (ii) a mixed-curvature residual on a learnable $\mathbb{H}^{d_h}_{c_h} \times \mathbb{S}^{d_s}_{c_s}$ product manifold, regularized by a feature-aware Ollivier-Ricci curvature proxy; and (iii) a continuous vector field on the tangent bundle of hyperbolic space for non-local structural alignment across topological gaps. The branches are fused via learned gating and trained with an N-pair ranking loss aligned with retrieval-style evaluation. Across five benchmarks spanning sparse, dense, featureless, and attributed regimes, Concorde establishes state-of-the-art early retrieval precision, nearly doubling P@10% over leading baselines in sparse settings.
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