The paper introduces linear‑time randomized algorithms for unbiased approximation of general random walk kernels (RWKs) on sparse graphs, covering both labelled and unlabelled cases. By sampling dependent random walks and constructing novel graph embeddings in ρ^d, the method avoids building the direct product graph, enabling scaling to massive datasets that cannot fit on a single machine. The authors provide exponential concentration bounds for the estimator’s sharpness and demonstrate up to 27× speed‑ups and 128× larger graph handling compared to previous cubic‑time approaches.
By Krzysztof Choromanski, Isaac Reid, Arijit Sehanobish, Avinava Dubey
arXiv:2510. 07716v2 Announce Type: replace Abstract: We propose refined GRFs (GRFs++), a new class of Graph Random Features (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph.
By Krzysztof Choromanski, Avinava Dubey, Arijit Sehanobish, Isaac Reid
arXiv:2510.17714v3 Announce Type: replace-cross
Abstract: Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans modeled as a graph partit...
By Atticus McWhorter, Daryl DeFord
The paper introduces a scalable subgraph sampling method that uses resistance curvature to guide the selection of nodes and edges for graph neural network training. It builds on ERC‑LG, a curvature approximation technique that employs Johnson‑Lindenstrauss projections and regularized multi‑GPU batched conjugate gradient solvers, thereby avoiding costly Laplacian pseudoinverse calculations and large embedding storage. Experiments demonstrate that ERC‑LG‑based sampling matches pseudoinverse‑based curvature numerically, runs faster than conjugate‑gradient‑only approaches, and achieves the best mean accuracy on six of seven real‑world node‑classification datasets.
By Chaoqun Fei, Tinglve Zhou, Tianyong Hao, Yangyang Li
The paper introduces a data‑driven method for learning Random Geometric Graphs (RGGs) in probabilistic metric spaces. It defines a distance function based on the cumulative distribution of a disparity variable that captures differences in vertex connectivity and correlation of attached random variables, enabling edges to exist with a specified probability. The approach includes a rejection‑sampling technique for edge probability estimation and a closed‑form posterior for learning the inter‑observable correlation matrix, and it is demonstrated on highly multivariate real datasets.
By Dalia Chakrabarty, Kangrui Wang, Chuqiao Zhang, Ye Liu
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.
By Xiang Gu, Huichun Zhang, Jian Sun