Accurate and Scalable Graph Neural Networks via Message Invariance

Message passing-based graph neural networks (GNNs) have achieved great success in many real-world applications. For a sampled mini-batch of target nodes, the message passing process is divided into two parts: message passing between nodes within the batch ($ _ $) and message passing from nodes outside the batch to those within it ($ _ $). However, $ _ $ recursively relies on higher-order out-of-batch neighbors, leading to an exponentially growing computational cost with respect to the number of layers. Due to the neighbor explosion, the whole message passing stores most nodes and edges on the GPU such that many GNNs are infeasible to large-scale graphs. To address this challenge, we propose an accurate and fast mini-batch approach for large graph transductive learning, namely topological compensation (TOP), which obtains the outputs of the whole message passing solely through $ _ $, without the costly $ _ $. The major pillar of TOP is a novel concept of message invariance, which defines message-invariant transformations to convert costly $ _ $ into fast $ _ $. This ensures that the modified $ _ $ has the same output as the whole message passing. Experiments demonstrate that TOP is significantly faster than existing mini-batch methods by order of magnitude on vast graphs (millions of nodes and billions of edges) with limited accuracy degradation.