{"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/p-laplacian-based-graph-neural-networks-1","title":"$p$-Laplacian Based Graph Neural Networks","arxiv_id":"2111.07337","date":"2021-11-14","proceeding":null,"authors":["Guoji Fu","Peilin Zhao","Yatao Bian"],"abstract":"Graph neural networks (GNNs) have demonstrated superior performance for semi-supervised node classification on graphs, as a result of their ability to exploit node features and topological information simultaneously. However, most GNNs implicitly assume that the labels of nodes and their neighbors in a graph are the same or consistent, which does not hold in heterophilic graphs, where the labels of linked nodes are likely to differ. Hence, when the topology is non-informative for label prediction, ordinary GNNs may work significantly worse than simply applying multi-layer perceptrons (MLPs) on each node. To tackle the above problem, we propose a new $p$-Laplacian based GNN model, termed as $^p$GNN, whose message passing mechanism is derived from a discrete regularization framework and could be theoretically explained as an approximation of a polynomial graph filter defined on the spectral domain of $p$-Laplacians. The spectral analysis shows that the new message passing mechanism works simultaneously as low-pass and high-pass filters, thus making $^p$GNNs are effective on both homophilic and heterophilic graphs. Empirical studies on real-world and synthetic datasets validate our findings and demonstrate that $^p$GNNs significantly outperform several state-of-the-art GNN architectures on heterophilic benchmarks while achieving competitive performance on homophilic benchmarks. Moreover, $^p$GNNs can adaptively learn aggregation weights and are robust to noisy edges.","url_abs":"https://arxiv.org/abs/2111.07337v2","url_pdf":"https://arxiv.org/pdf/2111.07337v2.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":"p-laplacian-based-graph-neural-networks-1","repo_url":"https://github.com/guoji-fu/pgnns","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"p-laplacian-based-graph-neural-networks-1","repo_url":"https://github.com/wuhy68/p-adapter","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"node-classification","task_name":"Node Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2111.07337","atlas_url":"https://app.syntology.ai/?focus=2111.07337","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2111.07337"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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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