{"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/weisfeiler-and-leman-go-neural-higher-order","title":"Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks","arxiv_id":"1810.02244","date":"2018-10-04","proceeding":null,"authors":["Christopher Morris","Martin Ritzert","Matthias Fey","William L. Hamilton","Jan Eric Lenssen","Gaurav Rattan","Martin Grohe"],"abstract":"In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically -- showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the $1$-dimensional Weisfeiler-Leman graph isomorphism heuristic ($1$-WL). We show that GNNs have the same expressiveness as the $1$-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called $k$-dimensional GNNs ($k$-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.","url_abs":"https://arxiv.org/abs/1810.02244v5","url_pdf":"https://arxiv.org/pdf/1810.02244v5.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":"weisfeiler-and-leman-go-neural-higher-order","repo_url":"https://github.com/chrsmrrs/k-gnn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"graph-classification","task_name":"Graph Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/graph-classification-on-imdb-b","task":"Graph Classification","dataset":"IMDb-B","model":"k-GNN","rank_in_archive_order":28,"of":51,"metrics":{"Accuracy":"74.2%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-imdb-b","task":"Graph Classification","dataset":"IMDb-B","model":"3-WL Kernel","rank_in_archive_order":30,"of":51,"metrics":{"Accuracy":"73.5%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-imdb-m","task":"Graph Classification","dataset":"IMDb-M","model":"1-WL Kernel","rank_in_archive_order":14,"of":36,"metrics":{"Accuracy":"51.5%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-imdb-m","task":"Graph Classification","dataset":"IMDb-M","model":"k-GNN","rank_in_archive_order":27,"of":36,"metrics":{"Accuracy":"49.5%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-mutag","task":"Graph Classification","dataset":"MUTAG","model":"Graphlet Kernel","rank_in_archive_order":44,"of":74,"metrics":{"Accuracy":"87.7%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-mutag","task":"Graph Classification","dataset":"MUTAG","model":"k-GNN","rank_in_archive_order":58,"of":74,"metrics":{"Accuracy":"86.1%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-nci1","task":"Graph Classification","dataset":"NCI1","model":"WL-OA Kernel","rank_in_archive_order":5,"of":69,"metrics":{"Accuracy":"86.1%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-nci1","task":"Graph Classification","dataset":"NCI1","model":"k-GNN","rank_in_archive_order":49,"of":69,"metrics":{"Accuracy":"76.2%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-proteins","task":"Graph Classification","dataset":"PROTEINS","model":"Shortest-Path Kernel","rank_in_archive_order":46,"of":103,"metrics":{"Accuracy":"76.4%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-proteins","task":"Graph Classification","dataset":"PROTEINS","model":"k-GNN","rank_in_archive_order":59,"of":103,"metrics":{"Accuracy":"75.9%"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1810.02244","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}