  We propose a novel graph cross network (GXN) to achieve comprehensive feature
learning from multiple scales of a graph. Based on trainable hierarchical
representations of a graph, GXN enables the interchange of intermediate
features across scales to promote information flow. Two key ingredients of GXN
include a novel vertex infomax pooling (VIPool), which creates multiscale
graphs in a trainable manner, and a novel feature-crossing layer, enabling
feature interchange across scales. The proposed VIPool selects the most
informative subset of vertices based on the neural estimation of mutual
information between vertex features and neighborhood features. The intuition
behind is that a vertex is informative when it can maximally reflect its
neighboring information. The proposed feature-crossing layer fuses intermediate
features between two scales for mutual enhancement by improving information
flow and enriching multiscale features at hidden layers. The cross shape of the
feature-crossing layer distinguishes GXN from many other multiscale
architectures. Experimental results show that the proposed GXN improves the
classification accuracy by 2.12% and 1.15% on average for graph classification
and vertex classification, respectively. Based on the same network, the
proposed VIPool consistently outperforms other graph-pooling methods.
