{"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/graph-neural-networks-with-local-graph","title":"Graph Neural Networks with Local Graph Parameters","arxiv_id":"2106.06707","date":"2021-06-12","proceeding":"NeurIPS 2021 12","authors":["Pablo Barceló","Floris Geerts","Juan Reutter","Maksimilian Ryschkov"],"abstract":"Various recent proposals increase the distinguishing power of Graph Neural Networks GNNs by propagating features between $k$-tuples of vertices. The distinguishing power of these \"higher-order'' GNNs is known to be bounded by the $k$-dimensional Weisfeiler-Leman (WL) test, yet their $\\mathcal O(n^k)$ memory requirements limit their applicability. Other proposals infuse GNNs with local higher-order graph structural information from the start, hereby inheriting the desirable $\\mathcal O(n)$ memory requirement from GNNs at the cost of a one-time, possibly non-linear, preprocessing step. We propose local graph parameter enabled GNNs as a framework for studying the latter kind of approaches and precisely characterize their distinguishing power, in terms of a variant of the WL test, and in terms of the graph structural properties that they can take into account. Local graph parameters can be added to any GNN architecture, and are cheap to compute. In terms of expressive power, our proposal lies in the middle of GNNs and their higher-order counterparts. Further, we propose several techniques to aide in choosing the right local graph parameters. Our results connect GNNs with deep results in finite model theory and finite variable logics. Our experimental evaluation shows that adding local graph parameters often has a positive effect for a variety of GNNs, datasets and graph learning tasks.","url_abs":"https://arxiv.org/abs/2106.06707v1","url_pdf":"https://arxiv.org/pdf/2106.06707v1.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":"graph-neural-networks-with-local-graph","repo_url":"https://github.com/LGP-GNN-2021/LGP-GNN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"graph-learning","task_name":"Graph Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2106.06707","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2106.06707"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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