On the Initialization of Graph Neural Networks

TL;DR

This paper introduces Virgo, a new initialization method for GNNs that reduces variance instability by considering graph structure and message passing, leading to improved performance and stability across multiple tasks.

Contribution

The paper proposes Virgo, a novel GNN initialization technique that accounts for graph structure and message passing, addressing variance issues overlooked by classical methods.

Findings

Virgo improves model performance on 15 datasets.

Virgo stabilizes variance at initialization.

Virgo outperforms classical initialization methods.

Abstract

Graph Neural Networks (GNNs) have displayed considerable promise in graph representation learning across various applications. The core learning process requires the initialization of model weight matrices within each GNN layer, which is typically accomplished via classic initialization methods such as Xavier initialization. However, these methods were originally motivated to stabilize the variance of hidden embeddings and gradients across layers of Feedforward Neural Networks (FNNs) and Convolutional Neural Networks (CNNs) to avoid vanishing gradients and maintain steady information flow. In contrast, within the GNN context classical initializations disregard the impact of the input graph structure and message passing on variance. In this paper, we analyze the variance of forward and backward propagation across GNN layers and show that the variance instability of GNN initializations comes from the combined effect of the activation function, hidden dimension, graph structure and message passing. To better account for these influence factors, we propose a new initialization method for Variance Instability Reduction within GNN Optimization (Virgo), which naturally tends to equate forward and backward variances across successive layers. We conduct comprehensive experiments on 15 datasets to show that Virgo can lead to superior model performance and more stable variance at initialization on node classification, link prediction and graph classification tasks. Codes are in https://github.com/LspongebobJH/virgo_icml2023.