Non-backtracking Graph Neural Networks

TL;DR

This paper introduces NBA-GNN, a novel graph neural network that avoids backtracking in message passing, reducing redundancy and improving the ability to recognize relevant message flows for better performance.

Contribution

The paper proposes NBA-GNN, a new message-passing scheme that eliminates backtracking, with theoretical analysis and empirical validation demonstrating its advantages over traditional GNNs.

Findings

NBA-GNN alleviates over-squashing in GNNs.

NBA-GNN improves performance on long-range graph benchmarks.

NBA-GNN enhances transductive node classification accuracy.

Abstract

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.