Node Embedding from Hamiltonian Information Propagation in Graph Neural Networks
This addresses challenges in graph neural networks for tasks involving graph-structured data, representing an incremental improvement with a novel method for known bottlenecks.
The paper tackles the problems of graph node embedding under various geometries and over-smoothing in GNNs by proposing a Hamiltonian Dynamic GNN (HDG) that uses a learnable Hamiltonian energy function to adapt to graph geometries, demonstrating its ability to learn complex geometries and mitigate over-smoothing through evaluations against state-of-the-art baselines.
Graph neural networks (GNNs) have achieved success in various inference tasks on graph-structured data. However, common challenges faced by many GNNs in the literature include the problem of graph node embedding under various geometries and the over-smoothing problem. To address these issues, we propose a novel graph information propagation strategy called Hamiltonian Dynamic GNN (HDG) that uses a Hamiltonian mechanics approach to learn node embeddings in a graph. The Hamiltonian energy function in HDG is learnable and can adapt to the underlying geometry of any given graph dataset. We demonstrate the ability of HDG to automatically learn the underlying geometry of graph datasets, even those with complex and mixed geometries, through comprehensive evaluations against state-of-the-art baselines on various downstream tasks. We also verify that HDG is stable against small perturbations and can mitigate the over-smoothing problem when stacking many layers.