MathNet: Haar-like wavelet multiresolution analysis for graph representation learning

Abstract

Graph neural networks (GNNs) have recently attracted great attention and achieved significant progress in graph-level applications. In this paper, we propose a framework for graph neural networks with multiresolution Haar-like wavelets, or MathNet, with interrelated convolution and pooling strategies. The rendering method takes graphs in different structures as input and assembles consistent graph representations for readout layers, which then accomplishes label prediction. To achieve this, multiresolution graph representations are first constructed and fed into graph convolutional layers for processing. The hierarchical graph pooling layers are then involved to downsample graph resolution while simultaneously removing redundancy of graph signals. The whole workflow could be formed with a multilevel graph analysis, which not only helps embed the intrinsic topological information of each graph into the GNN, but also supports fast computation of forward and adjoint graph transforms. Extensive experiments present notable accuracy gains of the proposed MathNet on graph classification and regression tasks with performance stability. MathNet outperforms various existing GNN models, especially on big datasets.