Papers › Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks

Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks

30 May 2023arXiv:2305.18965archive 2025-07-28

Qiyu Kang, Kai Zhao, Yang song, Sijie Wang, Wee Peng Tay

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}.

PaperPDFCodeCode Syntology ran

In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.

For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="2305.18965")

Code

Syntology Ran 3 of 3 code samples harvested from 1 repository linked to this paper; 0 have no recorded run. Of those that ran: 1 ran · honoured contract; 1 ran · our draft was wrong; 1 ran · fixture could not drive it.

By repository: official repository: 2 samples from 1 repository, 2 ran; 1 identical to code first harvested elsewhere. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.

zknus/hamiltonian-gnn officialmentioned in paperpytorch report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

3 samples harvested; 3 ran; 1 honoured the contract we drafted; 0 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.

1ran · honoured contract
1ran · our draft was wrong
1ran · fixture could not drive it

Licence: 3 of the 3 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.

Harvested from zknus/hamiltonian-gnn. Some samples are identical code Syntology first harvested from another repository; for those, this paper's copy is not located and its licence is not recorded. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.

Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.

Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.

batch_jacobian zknus/hamiltonian-gnn/layers/H_1.py official repository ran · fixture could not drive it no licence file found · pointer only · 6d2a165a621028d4 · report
test zknus/hamiltonian-gnn/main_nc.py official repository ran · honoured contract no licence file found · pointer only · 5b6fb04ad6e0c9b5 · report
get_optimizer identical code first harvested elsewhere ran · our draft was wrong licence of this copy not recorded · dab3444777a2e6c7 · report

Tasks

Graph EmbeddingLink PredictionNode Classification

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Methods

Test

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections