Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks
This addresses the need for flexible graph node embedding methods that can handle diverse geometries without manual tuning, offering a novel approach for researchers and practitioners in graph machine learning.
The paper tackles the problem of graph node embedding by modeling node feature updates as Hamiltonian orbits, which allows learning the underlying manifold of any graph dataset without extensive tuning. Numerical experiments show that this approach adapts better to diverse graph datasets than state-of-the-art GNNs in node classification and link prediction tasks.
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}.