{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/universal-graph-random-features","title":"General Graph Random Features","arxiv_id":"2310.04859","date":"2023-10-07","proceeding":null,"authors":["Isaac Reid","Krzysztof Choromanski","Eli Berger","Adrian Weller"],"abstract":"We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.","url_abs":"https://arxiv.org/abs/2310.04859v3","url_pdf":"https://arxiv.org/pdf/2310.04859v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"universal-graph-random-features","repo_url":"https://github.com/isaac-reid/repelling_random_walks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"node-clustering","task_name":"Node Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2310.04859","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}