Permutation-equivariant and Proximity-aware Graph Neural Networks with Stochastic Message Passing
This addresses a key limitation in GNNs for graph mining applications, offering a novel solution to improve performance in tasks requiring both properties.
The paper tackled the problem that existing graph neural networks (GNNs) cannot simultaneously preserve permutation-equivariance and proximity-awareness, which are crucial for tasks like community detection, by proposing the Stochastic Message Passing (SMP) model. The result demonstrated SMP's effectiveness and efficiency across ten datasets in tasks such as graph reconstruction, node classification, and link prediction.
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.