{"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/improving-expressivity-of-graph-neural-1","title":"Improving Expressivity of Graph Neural Networks using Localization","arxiv_id":"2305.19659","date":"2023-05-31","proceeding":null,"authors":["Anant Kumar","Shrutimoy Das","Shubhajit Roy","Binita Maity","Anirban Dasgupta"],"abstract":"In this paper, we propose localized versions of Weisfeiler-Leman (WL) algorithms in an effort to both increase the expressivity, as well as decrease the computational overhead. We focus on the specific problem of subgraph counting and give localized versions of $k-$WL for any $k$. We analyze the power of Local $k-$WL and prove that it is more expressive than $k-$WL and at most as expressive as $(k+1)-$WL. We give a characterization of patterns whose count as a subgraph and induced subgraph are invariant if two graphs are Local $k-$WL equivalent. We also introduce two variants of $k-$WL: Layer $k-$WL and recursive $k-$WL. These methods are more time and space efficient than applying $k-$WL on the whole graph. We also propose a fragmentation technique that guarantees the exact count of all induced subgraphs of size at most 4 using just $1-$WL. The same idea can be extended further for larger patterns using $k>1$. We also compare the expressive power of Local $k-$WL with other GNN hierarchies and show that given a bound on the time-complexity, our methods are more expressive than the ones mentioned in Papp and Wattenhofer[2022a].","url_abs":"https://arxiv.org/abs/2305.19659v3","url_pdf":"https://arxiv.org/pdf/2305.19659v3.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":"improving-expressivity-of-graph-neural-1","repo_url":"https://github.com/roy-shubhajit/insig-gnn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"subgraph-counting","task_name":"Subgraph Counting"},{"task_slug":"subgraph-counting-2-star","task_name":"Subgraph Counting - 2 star"},{"task_slug":"subgraph-counting-3-star","task_name":"Subgraph Counting - 3 Star"},{"task_slug":"subgraph-counting-c4","task_name":"Subgraph Counting - C4"},{"task_slug":"subgraph-counting-chordal-c4","task_name":"Subgraph Counting - Chordal C4"},{"task_slug":"subgraph-counting-k4","task_name":"Subgraph Counting - K4"},{"task_slug":"subgraph-counting-triangle","task_name":"Subgraph Counting - Triangle"}],"methods":[{"method_slug":"fragmentation","method_name":"Fragmentation"}],"datasets_introduced":[],"methods_introduced":[{"slug":"fragmentation","name":"Fragmentation","full_name":"Fragmentation"}],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}