Non-backtracking Graph Neural Networks
This addresses a redundancy problem in GNNs for graph learning tasks, offering an incremental improvement over existing methods.
The paper tackles the backtracking issue in graph neural networks (GNNs), where redundant message flows hinder accurate recognition for downstream tasks, by proposing the non-backtracking graph neural network (NBA-GNN) that updates messages without revisiting previously visited nodes, and it shows empirical effectiveness on benchmarks like long-range graphs and node classification.
The celebrated message-passing updates for graph neural networks allow representing large-scale graphs with local and computationally tractable updates. However, the updates suffer from backtracking, i.e., a message flowing through the same edge twice and revisiting the previously visited node. Since the number of message flows increases exponentially with the number of updates, the redundancy in local updates prevents the graph neural network from accurately recognizing a particular message flow relevant for downstream tasks. In this work, we propose to resolve such a redundancy issue via the non-backtracking graph neural network (NBA-GNN) that updates a message without incorporating the message from the previously visited node. We theoretically investigate how NBA-GNN alleviates the over-squashing of GNNs, and establish a connection between NBA-GNN and the impressive performance of non-backtracking updates for stochastic block model recovery. Furthermore, we empirically verify the effectiveness of our NBA-GNN on the long-range graph benchmark and transductive node classification problems.