  Using graph neural networks for large graphs is challenging since there is no
clear way of constructing mini-batches. To solve this, previous methods have
relied on sampling or graph clustering. While these approaches often lead to
good training convergence, they introduce significant overhead due to expensive
random data accesses and perform poorly during inference. In this work we
instead focus on model behavior during inference. We theoretically model batch
construction via maximizing the influence score of nodes on the outputs. This
formulation leads to optimal approximation of the output when we do not have
knowledge of the trained model. We call the resulting method influence-based
mini-batching (IBMB). IBMB accelerates inference by up to 130x compared to
previous methods that reach similar accuracy. Remarkably, with adaptive
optimization and the right training schedule IBMB can also substantially
accelerate training, thanks to precomputed batches and consecutive memory
accesses. This results in up to 18x faster training per epoch and up to 17x
faster convergence per runtime compared to previous methods.
