Path integral based convolution and pooling for graph neural networks*

Graph neural networks (GNNs) extends the functionality of traditional to graph-structured data. Similar CNNs, an optimized design graph convolution and pooling is key success. Borrowing ideas from physics, we propose a path integral based (PAN) for classification regression tasks on graphs. Specifically, consider operation that involves every linking message sender receiver with learnable weights depending length, which corresponds maximal entropy random walk. It generalizes Laplacian new transition matrix call (MET) derived formalism. Importantly, diagonal entries MET are directly related subgraph centrality, thus providing natural adaptive mechanism. PAN provides versatile framework can be tailored different data varying sizes structures. We view most existing GNN architectures as special cases PAN. Experimental results show achieves state-of-the-art performance various classification/regression tasks, including benchmark dataset statistical mechanics boost applications in physical sciences.