The expressive power of pooling in Graph Neural Networks
This work addresses a foundational gap in GNN theory by providing a principled framework for evaluating and designing pooling operators, which is incremental but crucial for advancing graph representation learning.
The authors tackled the lack of theoretical understanding and comparison criteria for graph pooling operators in Graph Neural Networks (GNNs), deriving sufficient conditions for pooling to preserve the expressive power of message-passing layers and analyzing existing operators against these conditions.
In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power of message-passing (MP) layers in GNNs, a study on how graph pooling affects the expressiveness of a GNN is still lacking. Additionally, despite the recent advances in the design of pooling operators, there is not a principled criterion to compare them. In this work, we derive sufficient conditions for a pooling operator to fully preserve the expressive power of the MP layers before it. These conditions serve as a universal and theoretically grounded criterion for choosing among existing pooling operators or designing new ones. Based on our theoretical findings, we analyze several existing pooling operators and identify those that fail to satisfy the expressiveness conditions. Finally, we introduce an experimental setup to verify empirically the expressive power of a GNN equipped with pooling layers, in terms of its capability to perform a graph isomorphism test.