Using Random Noise Equivariantly to Boost Graph Neural Networks Universally

TL;DR

This paper introduces ENGNN, a novel graph neural network architecture that leverages equivariant random noise to improve generalization and expressivity across multiple graph tasks, supported by a theoretical framework and extensive experiments.

Contribution

Proposes ENGNN, a general architecture utilizing equivariant noise to enhance GNN performance, backed by a theoretical analysis of sample complexity.

Findings

Noise equivariance improves GNN performance across tasks

ENGNN matches task-specific models in accuracy

Theoretical analysis explains sample complexity increase

Abstract

Recent advances in Graph Neural Networks (GNNs) have explored the potential of random noise as an input feature to enhance expressivity across diverse tasks. However, naively incorporating noise can degrade performance, while architectures tailored to exploit noise for specific tasks excel yet lack broad applicability. This paper tackles these issues by laying down a theoretical framework that elucidates the increased sample complexity when introducing random noise into GNNs without careful design. We further propose Equivariant Noise GNN (ENGNN), a novel architecture that harnesses the symmetrical properties of noise to mitigate sample complexity and bolster generalization. Our experiments demonstrate that using noise equivariantly significantly enhances performance on node-level, link-level, subgraph, and graph-level tasks and achieves comparable performance to models designed for specific tasks, thereby offering a general method to boost expressivity across various graph tasks.