{"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/node-embedding-from-neural-hamiltonian-orbits","title":"Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks","arxiv_id":"2305.18965","date":"2023-05-30","proceeding":null,"authors":["Qiyu Kang","Kai Zhao","Yang song","Sijie Wang","Wee Peng Tay"],"abstract":"In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at \\url{https://github.com/zknus/Hamiltonian-GNN}.","url_abs":"https://arxiv.org/abs/2305.18965v1","url_pdf":"https://arxiv.org/pdf/2305.18965v1.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":"node-embedding-from-neural-hamiltonian-orbits","repo_url":"https://github.com/zknus/hamiltonian-gnn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-embedding","task_name":"Graph Embedding"},{"task_slug":"link-prediction","task_name":"Link Prediction"},{"task_slug":"node-classification","task_name":"Node Classification"}],"methods":[{"method_slug":"test","method_name":"Test"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2305.18965","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2305.18965"}},"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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