Title: On the Two Sides of Redundancy in Graph Neural Networks

Abstract: Message passing neural networks iteratively generate node embeddings by aggregating information from neighboring nodes. With increasing depth, information from more distant nodes is included. However, node embeddings may be unable to represent the growing node neighborhoods accurately and the influence of distant nodes may vanish, a problem referred to as oversquashing. Information redundancy in message passing, i.e., the repetitive exchange and encoding of identical information amplifies oversquashing. We develop a novel aggregation scheme based on neighborhood trees, which allows for controlling redundancy by pruning redundant branches of unfolding trees underlying standard message passing. While the regular structure of unfolding trees allows the reuse of intermediate results in a straightforward way, the use of neighborhood trees poses computational challenges. We propose compact representations of neighborhood trees and merge them, exploiting computational redundancy by identifying isomorphic subtrees. From this, node and graph embeddings are computed via a neural architecture inspired by tree canonization techniques. Our method is less susceptible to oversquashing than traditional message passing neural networks and can improve the accuracy on widely used benchmark datasets.