PAN: Path Integral Based Convolution for Deep Graph Neural Networks

Understand

Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk.

• In this paper, we propose PAN, a new graph convolution framework that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk.
• PAN generalizes the graph Laplacian to a new transition matrix we call \emph{maximal entropy transition} (MET) matrix derived from a path integral formalism.
• Most previous graph convolutional network architectures can be adapted to our framework, and many variations and derivatives based on the path integral idea can be developed.