ICLR 2021

Accurate Learning of Graph Representations with Graph Multiset Pooling

Jinheon Baek, Minki Kang and Sung Ju Hwang

Message-passing graph neural networks have been widely used on modeling graph data, achieving impressive results on a number of graph classification and link prediction tasks. Yet, obtaining an accurate representation for a graph further requires a well-defined pooling function that maps the set of node representations into a compact form, without information loss of the individual node features and the global graph structure. A simple sum or average over all node representations considers all node features equally without consideration of their task relevance, and any structural dependencies among them. Recently proposed hierarchical graph pooling methods, on the other hand, may yield the same representation for two different graphs that are distinguished by the Weisfeiler-Lehman test, as they suboptimally preserve information from the node features. To tackle these limitations of existing graph pooling methods, we first formulate the graph pooling problem as a multiset encoding problem with auxiliary information about the graph structure, and propose a Graph Multiset Transformer (GMT) which is a multi-head attention based global pooling layer that captures the interaction between nodes according to their structural dependencies. We show that GMT satisfies both injectiveness and permutation invariance, such that it is at most as powerful as the Weisfeiler-Lehman graph isomorphism test. Moreover, our methods can be easily extended to the previous node clustering approaches for hierarchical graph pooling. Our experimental results show that GMT significantly outperforms state-of-the-art graph pooling methods on graph classification benchmarks with high memory efficiency, and obtains even larger performance gain on graph reconstruction and generation tasks, which more directly measure the expressiveness of graph pooling methods.