Permutation-equivariant and Proximity-aware Graph Neural Networks with Stochastic Message Passing

TL;DR

This paper introduces Stochastic Message Passing (SMP), a novel GNN model that simultaneously preserves permutation-equivariance and proximity-awareness, addressing limitations of existing message-passing GNNs.

Contribution

The paper proposes SMP, a simple and general GNN framework that maintains both key properties, with theoretical proofs and extensive experiments demonstrating its effectiveness.

Findings

SMP effectively preserves node proximities.

SMP maintains permutation-equivariance under certain conditions.

Experimental results show SMP outperforms existing models on multiple tasks.

Abstract

Graph neural networks (GNNs) are emerging machine learning models on graphs. Permutation-equivariance and proximity-awareness are two important properties highly desirable for GNNs. Both properties are needed to tackle some challenging graph problems, such as finding communities and leaders. In this paper, we first analytically show that the existing GNNs, mostly based on the message-passing mechanism, cannot simultaneously preserve the two properties. Then, we propose Stochastic Message Passing (SMP) model, a general and simple GNN to maintain both proximity-awareness and permutation-equivariance. In order to preserve node proximities, we augment the existing GNNs with stochastic node representations. We theoretically prove that the mechanism can enable GNNs to preserve node proximities, and at the same time, maintain permutation-equivariance with certain parametrization. We report extensive experimental results on ten datasets and demonstrate the effectiveness and efficiency of SMP for various typical graph mining tasks, including graph reconstruction, node classification, and link prediction.