  Graph Neural Networks (GNNs) have recently caught 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
underlying method takes graphs in different structures as input and assembles
consistent graph representations for readout layers, which then accomplishes
label prediction. To achieve this, the 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 remove redundancy within graph signals. The
whole workflow could be formed with a multi-level 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. We show by extensive experiments that the proposed framework
obtains notable accuracy gains on graph classification and regression tasks
with performance stability. The proposed MathNet outperforms various existing
GNN models, especially on big data sets.
