  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.
Experimental results show that the path integral based graph neural networks
have great learnability and fast convergence rate, and achieve state-of-the-art
performance on benchmark tasks.
