  Graph Convolutional Network (GCN) is an emerging technique that performs
learning and reasoning on graph data. It operates feature learning on the graph
structure, through aggregating the features of the neighbor nodes to obtain the
embedding of each target node. Owing to the strong representation power, recent
research shows that GCN achieves state-of-the-art performance on several tasks
such as recommendation and linked document classification.
  Despite its effectiveness, we argue that existing designs of GCN forgo
modeling cross features, making GCN less effective for tasks or data where
cross features are important. Although neural network can approximate any
continuous function, including the multiplication operator for modeling feature
crosses, it can be rather inefficient to do so (i.e., wasting many parameters
at the risk of overfitting) if there is no explicit design.
  To this end, we design a new operator named Cross-feature Graph Convolution,
which explicitly models the arbitrary-order cross features with complexity
linear to feature dimension and order size. We term our proposed architecture
as Cross-GCN, and conduct experiments on three graphs to validate its
effectiveness. Extensive analysis validates the utility of explicitly modeling
cross features in GCN, especially for feature learning at lower layers.
