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Convolution operations designed for graph-structured data usually utilize thegraph Laplacian, which can be seen as message passing between the adjacentneighbors through a generic random walk. In this paper, we propose PAN, a newgraph convolution framework that involves every path linking the message senderand receiver with learnable weights depending on the path length, whichcorresponds to the maximal entropy random walk. PAN generalizes the graphLaplacian to a new transition matrix we call \emph{maximal entropy transition}(MET) matrix derived from a path integral formalism. Most previous graphconvolutional network architectures can be adapted to our framework, and manyvariations and derivatives based on the path integral idea can be developed.Experimental results show that the path integral based graph neural networkshave great learnability and fast convergence rate, and achieve state-of-the-artperformance on benchmark tasks.

PAN: Path Integral Based Convolution for Deep Graph Neural Networks