{"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/measuring-and-relieving-the-over-smoothing","title":"Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View","arxiv_id":"1909.03211","date":"2019-09-07","proceeding":null,"authors":["Deli Chen","Yankai Lin","Wei Li","Peng Li","Jie zhou","Xu sun"],"abstract":"Graph Neural Networks (GNNs) have achieved promising performance on a wide range of graph-based tasks. Despite their success, one severe limitation of GNNs is the over-smoothing issue (indistinguishable representations of nodes in different classes). In this work, we present a systematic and quantitative study on the over-smoothing issue of GNNs. First, we introduce two quantitative metrics, MAD and MADGap, to measure the smoothness and over-smoothness of the graph nodes representations, respectively. Then, we verify that smoothing is the nature of GNNs and the critical factor leading to over-smoothness is the low information-to-noise ratio of the message received by the nodes, which is partially determined by the graph topology. Finally, we propose two methods to alleviate the over-smoothing issue from the topological view: (1) MADReg which adds a MADGap-based regularizer to the training objective;(2) AdaGraph which optimizes the graph topology based on the model predictions. Extensive experiments on 7 widely-used graph datasets with 10 typical GNN models show that the two proposed methods are effective for relieving the over-smoothing issue, thus improving the performance of various GNN models.","url_abs":"https://arxiv.org/abs/1909.03211v2","url_pdf":"https://arxiv.org/pdf/1909.03211v2.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":[],"tasks":[{"task_slug":"node-classification","task_name":"Node Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/node-classification-on-citeseer","task":"Node Classification","dataset":"Citeseer","model":"GCN + AdaGraph (AG)","rank_in_archive_order":61,"of":71,"metrics":{"Accuracy":"69.7%"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-cora","task":"Node Classification","dataset":"Cora","model":"GCN + AdaGraph (AG)","rank_in_archive_order":53,"of":73,"metrics":{"Accuracy":"82.3%"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-pubmed","task":"Node Classification","dataset":"Pubmed","model":"GCN + AdaGraph (AG)","rank_in_archive_order":58,"of":70,"metrics":{"Accuracy":"77.4 ± 0.2"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1909.03211","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}