  Graph-level representation learning is the pivotal step for downstream tasks
that operate on the whole graph. The most common approach to this problem
heretofore is graph pooling, where node features are typically averaged or
summed to obtain the graph representations. However, pooling operations like
averaging or summing inevitably cause massive information missing, which may
severely downgrade the final performance. In this paper, we argue what is
crucial to graph-level downstream tasks includes not only the topological
structure but also the distribution from which nodes are sampled. Therefore,
powered by existing Graph Neural Networks (GNN), we propose a new plug-and-play
pooling module, termed as Distribution Knowledge Embedding (DKEPool), where
graphs are rephrased as distributions on top of GNNs and the pooling goal is to
summarize the entire distribution information instead of retaining a certain
feature vector by simple predefined pooling operations. A DKEPool network de
facto disassembles representation learning into two stages, structure learning
and distribution learning. Structure learning follows a recursive neighborhood
aggregation scheme to update node features where structure information is
obtained. Distribution learning, on the other hand, omits node interconnections
and focuses more on the distribution depicted by all the nodes. Extensive
experiments demonstrate that the proposed DKEPool significantly and
consistently outperforms the state-of-the-art methods.
