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.

翻译：图神经网络（GNN）将深度学习扩展到图结构数据。与应用于图像预测的卷积神经网络（CNN）类似，卷积层和池化层是图神经网络在图预测任务中取得成功的基础。在最初的PAN论文中，它采用基于路径积分的图神经网络进行图预测。具体而言，该方法使用一种卷积操作，该操作涉及连接消息发送者和接收者的每条路径，并赋予与路径长度相关的可学习权重，这对应于最大熵随机游走。该方法进一步将此类卷积操作推广到一种称为最大熵转移（MET）的新转移矩阵。由于MET矩阵的对角线元素与子图中心性直接相关，这为基于中心性分数的池化提供了一种可行的机制。然而最初的PAN论文仅考虑了节点特征。本文进一步扩展其能力，以处理包含节点和边特征的复杂异构图。