Generalized Laplacian Positional Encoding for Graph Representation Learning. (arXiv:2210.15956v2 [cs.LG] UPDATED)

Graph neural networks (GNNs) are the primary tool for processing
graph-structured data. Unfortunately, the most commonly used GNNs, called
Message Passing Neural Networks (MPNNs) suffer from several fundamental
limitations. To overcome these limitations, recent works have adapted the idea
of positional encodings to graph data. This paper draws inspiration from the
recent success of Laplacian-based positional encoding and defines a novel
family of positional encoding schemes for graphs. We accomplish this by
generalizing the optimization problem that defines the Laplace …

arxiv encoding graph graph representation positional encoding representation representation learning