{"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/hyperbolic-graph-convolutional-neural","title":"Hyperbolic Graph Convolutional Neural Networks","arxiv_id":"1910.12933","date":"2019-10-28","proceeding":"NeurIPS 2019 12","authors":["Ines Chami","Rex Ying","Christopher Ré","Jure Leskovec"],"abstract":"Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative, as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges because it is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore, since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HGCN), the first inductive hyperbolic GCN that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive GCN operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in hyperbolic spaces with different trainable curvature at each layer. Experiments demonstrate that HGCN learns embeddings that preserve hierarchical structure, and leads to improved performance when compared to Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GCNs, HGCN achieves an error reduction of up to 63.1% in ROC AUC for link prediction and of up to 47.5% in F1 score for node classification, also improving state-of-the art on the Pubmed dataset.","url_abs":"https://arxiv.org/abs/1910.12933v1","url_pdf":"https://arxiv.org/pdf/1910.12933v1.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":"hyperbolic-graph-convolutional-neural","repo_url":"https://github.com/CUAI/Riemannian-Residual-Neural-Networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"hyperbolic-graph-convolutional-neural","repo_url":"https://github.com/ydtydr/hyla","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"hyperbolic-graph-convolutional-neural","repo_url":"https://github.com/HazyResearch/hgcn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"link-prediction","task_name":"Link Prediction"},{"task_slug":"node-classification","task_name":"Node Classification"}],"methods":[{"method_slug":"gcn","method_name":"GCN"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/link-prediction-on-ppi","task":"Link Prediction","dataset":"PPI","model":"HGCN","rank_in_archive_order":2,"of":2,"metrics":{"Accuracy":"84.5"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-cora","task":"Node Classification","dataset":"Cora","model":"HGCN","rank_in_archive_order":66,"of":73,"metrics":{"Accuracy":"79.9%"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-pubmed","task":"Node Classification","dataset":"Pubmed","model":"HGCN","rank_in_archive_order":33,"of":70,"metrics":{"Accuracy":"80.3%"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1910.12933","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1910.12933"}},"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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