The paper investigates how alignment—both outer (choosing which graphs to pair) and inner (aligning node representatives)—affects permutation-equivariant graph flow matching. It connects inner alignment to transport on the graph quotient space and shows that quotient couplings can be lifted to aligned representatives, while symmetrization yields equivariant flow‑matching minimizers. Experiments on continuous graph and molecular generation demonstrate that appropriate alignment can simplify trajectories and improve few‑step generation, though the benefits vary with the type of alignment and computational budget.
By Moritz Piening, Christian Wald
The paper investigates federated hypergraph learning where local hyperedge releases can correspond to multiple global hypergraph structures, highlighting identifiability and computational challenges. It shows that pairwise assignment of latent correspondences is tractable while multi-client hyperedge matching is generally intractable, and introduces FedASTRA—a method that learns correspondence‑invariant diffusion representations via adaptive heat diffusion and masked latent prediction, communicating only model parameters. Experiments on eight real‑world datasets, including ogbn‑papers100M, demonstrate that FedASTRA achieves state‑of‑the‑art performance‑communication trade‑offs, reaching 50.07 % accuracy and 29.73 % Macro‑F1 while sending only 59.60 MiB per round.
arXiv:2609.15437v1 Announce Type: cross
Abstract: End-to-end Supervised Graph Prediction (SGP) requires a permutation-invariant loss to compare predicted and target graphs with arbitrary node orderin...
By Federico M\'endez, Paul Krzakala, Gabriel Melo, Charlotte Laclau, R\'emi Flamary, Florence d'Alch\'e-Buc
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.
By Iman Seyedi, Francesco Archetti
The paper introduces Gromov-Monge Flow Matching, a method that incorporates permutation-equivariance into generative graph models by aligning graph pairs up to node relabeling using the Gromov–Monge distance. It shows theoretically that quotient couplings can be lifted to aligned representatives without extra cost and that symmetrization yields equivariant flow-matching minimizers, even for categorical endpoints. Practically, the authors build minibatch couplings with Gromov–Wasserstein relaxations and optional outer assignments, improving sample quality in continuous graph and categorical molecular generation while remaining compatible with standard equivariant architectures.
By Moritz Piening, Christian Wald
HyperFuse is a new, label‑free pipeline for fast self‑supervised node embeddings on attributed hypergraphs. It computes structural node coordinates via a spectral relaxation of hypergraph modularity, builds multi‑scale feature summaries with utility‑weighted hyperedges, and trains a lightweight encoder for only 100 epochs. In experiments on nine public hypergraphs, HyperFuse achieved 13–179× speed‑ups over baselines and matched or exceeded their accuracy on most downstream tasks.
By Megha P, Harshit Kumar, Srajan Agarwal, Anirban Banerjee, Olaf Wolkenhauer, Saptarshi Bej
The paper introduces MGHRL, a framework for hypergraph representation learning that adapts hyperedge granularity through a granular-ball splitting strategy. It constructs hyperedges at multiple levels of detail, capturing high-order relationships tailored to the graph’s topology. A multi-granularity hypergraph network then processes these hyperedges with sub-networks and hierarchical reversible connections, achieving superior performance on benchmark datasets.
By Sen Zhao, Yifan Guan, Jinyuan Ni, Gaojie Xu, Zhang Xu, Xiaoyu Lian, Yi Liu, Yi Wang, Wei Wang
arXiv:2607. 24338v1 Announce Type: new Abstract: Unsupervised graph representation learning aims to derive meaningful node embeddings by capturing both structural and attribute information without relying on labeled data.
By Zengyi Wo, Shiyu Zhang, Qiyao Peng, Tianpeng Li, Xuan Guo
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.
By Wonwoo Kang, Heehyun Park
arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
By Dai Hai Nguyen, Koji Tsuda
arXiv:2510. 03086v2 Announce Type: replace Abstract: For the combinatorial graph alignment problem (GAP) -- finding the node correspondence that maximizes the number of common edges (nce) between two unlabeled graphs -- properly initialized FAQ remains a strong classical baseline, while existing GNN approaches struggle in the purely structural setting.
By Marc Lelarge
arXiv:2606. 09051v1 Announce Type: new Abstract: Convolutions have successfully transitioned from image processing to the complex realm of non-Euclidean higher-order domains, particularly in hypergraphs.
By Fuli Wang, Wei Qian, Daniel L. Lau, Gonzalo R. Arce