Transport-Free Lower Bounds for Ollivier--Ricci Curvature in Higher-Order Networks: Scope, Tightness, and Computational Applications
Read the original on arXiv Machine Learning →The paper investigates how the Bauer–Jost–Liu curvature bound applies to hypergraph Ollivier–Ricci curvature, examining its dependence on local mass and geometry. It presents a weighted‑graph representation that extends the graph theorem, a transport construction for monotone pairwise hyperedge aggregations, and analyses of endpoint cancellation, worst‑case slack, and stability. The study also introduces a capacity‑constrained short‑detour refinement that improves with query budget, and demonstrates computational applications such as a threshold cascade that preserves exact transport decisions, supported by numerical verification and extensive public‑hypergraph experiments.
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