{"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/cayley-graph-propagation","title":"Cayley Graph Propagation","arxiv_id":"2410.03424","date":"2024-10-04","proceeding":null,"authors":["JJ Wilson","Maya Bechler-Speicher","Petar Veličković"],"abstract":"In spite of the plethora of success stories with graph neural networks (GNNs) on modelling graph-structured data, they are notoriously vulnerable to over-squashing, whereby tasks necessitate the mixing of information between distance pairs of nodes. To address this problem, prior work suggests rewiring the graph structure to improve information flow. Alternatively, a significant body of research has dedicated itself to discovering and precomputing bottleneck-free graph structures to ameliorate over-squashing. One well regarded family of bottleneck-free graphs within the mathematical community are expander graphs, with prior work -- Expander Graph Propagation (EGP) -- proposing the use of a well-known expander graph family -- the Cayley graphs of the $\\mathrm{SL}(2,\\mathbb{Z}_n)$ special linear group -- as a computational template for GNNs. However, in EGP the computational graphs used are truncated to align with a given input graph. In this work, we show that truncation is detrimental to the coveted expansion properties. Instead, we propose CGP, a method to propagate information over a complete Cayley graph structure, thereby ensuring it is bottleneck-free to better alleviate over-squashing. Our empirical evidence across several real-world datasets not only shows that CGP recovers significant improvements as compared to EGP, but it is also akin to or outperforms computationally complex graph rewiring techniques.","url_abs":"https://arxiv.org/abs/2410.03424v2","url_pdf":"https://arxiv.org/pdf/2410.03424v2.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":"cayley-graph-propagation","repo_url":"https://github.com/josephjwilson/cayley_graph_propagation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"align","method_name":"ALIGN"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2410.03424","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}