  Graph neural networks (GNNs) have significantly improved the representation
power for graph-structured data. Despite of the recent success of GNNs, the
graph convolution in most GNNs have two limitations. Since the graph
convolution is performed in a small local neighborhood on the input graph, it
is inherently incapable to capture long-range dependencies between distance
nodes. In addition, when a node has neighbors that belong to different classes,
i.e., heterophily, the aggregated messages from them often negatively affect
representation learning. To address the two common problems of graph
convolution, in this paper, we propose Deformable Graph Convolutional Networks
(Deformable GCNs) that adaptively perform convolution in multiple latent spaces
and capture short/long-range dependencies between nodes. Separated from node
representations (features), our framework simultaneously learns the node
positional embeddings (coordinates) to determine the relations between nodes in
an end-to-end fashion. Depending on node position, the convolution kernels are
deformed by deformation vectors and apply different transformations to its
neighbor nodes. Our extensive experiments demonstrate that Deformable GCNs
flexibly handles the heterophily and achieve the best performance in node
classification tasks on six heterophilic graph datasets.
