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.
arXiv:2603.13535v5 Announce Type: cross Abstract: Evaluating Ollivier-Ricci (OR) curvature on large-scale graphs is computationally prohibitive due to the necessity of solving an optimal transport pr...
arXiv:2604. 12211v2 Announce Type: replace Abstract: Ollivier-Ricci curvature (ORC), defined via the Wasserstein distance that captures rich geometric information, has received growing attention in both theory and applications.
arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
arXiv:2604.14211v2 Announce Type: replace-cross Abstract: This thesis is an exposition of Ollivier-Ricci Curvature of metric spaces as introduced by Yann Ollivier, which is based upon the 1-Wasserste...
arXiv:2608.29635v1 Announce Type: new Abstract: We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information,...
arXiv:2608.27500v3 Announce Type: replace-cross Abstract: Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport...
arXiv:2609.23547v1 Announce Type: new Abstract: Graph prompt learning enables parameter-efficient adaptation of frozen Graph Neural Networks to downstream tasks through lightweight prompt parameters....
arXiv:2610.03556v1 Announce Type: new Abstract: Empirical claims about the connection between over-squashing and long-range interactions in GNNs, can only be trusted if the benchmarks used to validat...
arXiv:2606. 01987v1 Announce Type: cross Abstract: We show that the Vehicle Routing Problem (VRP) can be reformulated as a Graph Edit Distance (GED) maximization problem.
The paper introduces HELLO, a hierarchical solver for large‑scale discrete optimal transport that reduces the problem to edge localization guided by dual potentials. HELLO uses a coarse‑to‑fine initialization across a recursive subsampling hierarchy and a refinement step that inserts the largest dual violators until a KKT residual tolerance is met, achieving linear memory usage. Experiments show that HELLO outperforms strong baselines by an order of magnitude in runtime while attaining lower transport objectives, and it scales to over a million samples in high‑dimensional settings, supporting various OT variants.
arXiv:2606. 09340v1 Announce Type: new Abstract: Local Hyper-Flow Diffusion (HFD) gives an edge-size-independent Cheeger-type guarantee for seeded clustering in general submodular hypergraphs, but existing HFD solvers do not keep intermediate computation local at every iteration.
arXiv:2607. 06646v1 Announce Type: cross Abstract: This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport.