Graph Neural Networks at a Fraction

TL;DR

This paper introduces Quaternion Message Passing Neural Networks (QMPNNs), a parameter-efficient GNN variant leveraging quaternion space, and explores their connection with Graph Lottery Tickets to reduce model size while maintaining accuracy.

Contribution

The paper presents a novel quaternion-based GNN framework and a new perspective on Graph Lottery Tickets, enabling significant parameter reduction without sacrificing performance.

Findings

QMPNNs achieve comparable accuracy with one-fourth the parameters of traditional GNNs.

The application of Graph Lottery Tickets further reduces trainable parameters.

QMPNNs perform effectively on node classification, link prediction, and graph classification tasks.

Abstract

Graph Neural Networks (GNNs) have emerged as powerful tools for learning representations of graph-structured data. In addition to real-valued GNNs, quaternion GNNs also perform well on tasks on graph-structured data. With the aim of reducing the energy footprint, we reduce the model size while maintaining accuracy comparable to that of the original-sized GNNs. This paper introduces Quaternion Message Passing Neural Networks (QMPNNs), a framework that leverages quaternion space to compute node representations. Our approach offers a generalizable method for incorporating quaternion representations into GNN architectures at one-fourth of the original parameter count. Furthermore, we present a novel perspective on Graph Lottery Tickets, redefining their applicability within the context of GNNs and QMPNNs. We specifically aim to find the initialization lottery from the subnetwork of the GNNs that can achieve comparable performance to the original GNN upon training. Thereby reducing the trainable model parameters even further. To validate the effectiveness of our proposed QMPNN framework and LTH for both GNNs and QMPNNs, we evaluate their performance on real-world datasets across three fundamental graph-based tasks: node classification, link prediction, and graph classification.