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
https://github.com/zknus/Hamiltonian-GNN.

本文提出了一种基于哈密顿轨道的图节点嵌入策略，该策略可以自动学习给定图数据集的底层结构，并成功地将其应用于节点分类和连接预测。在数值实验中，该方法表现出比流行的现有 GNN 模型更好的适应性。