# Path Integral Based Convolution and Pooling for Heterogeneous Graph Neural Networks

## TL;DR

This paper introduces a path integral based convolution and pooling method for heterogeneous graph neural networks, extending previous work to handle complex graphs with node and edge features using a maximal entropy transition matrix.

## Contribution

It extends the path integral GNN framework to heterogeneous graphs with node and edge features, incorporating a new pooling mechanism based on subgraph centrality.

## Key findings

- Effective handling of heterogeneous graph data with node and edge features
- Novel pooling method based on subgraph centrality
- Improved graph prediction performance

## Abstract

Graph neural networks (GNN) extends deep learning to graph-structure dataset. Similar to Convolutional Neural Networks (CNN) using on image prediction, convolutional and pooling layers are the foundation to success for GNN on graph prediction tasks. In the initial PAN paper, it uses a path integral based graph neural networks for graph prediction. Specifically, it uses a convolution operation 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. It further generalizes such convolution operation to a new transition matrix called maximal entropy transition (MET). Because the diagonal entries of the MET matrix is directly related to the subgraph centrality, it provide a trial mechanism for pooling based on centrality score. While the initial PAN paper only considers node features. We further extends its capability to handle complex heterogeneous graph including both node and edge features.