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We study the convergence of message passing graph neural networks on randomgraph models to their continuous counterpart as the number of nodes tends toinfinity. Until now, this convergence was only known for architectures withaggregation functions in the form of normalized means, or, equivalently, of anapplication of classical operators like the adjacency matrix or the graphLaplacian. We extend such results to a large class of aggregation functions,that encompasses all classically used message passing graph neural networks,such as attention-based message passing, max convolutional message passing or(degree-normalized) convolutional message passing. Under mild assumptions, wegive non-asymptotic bounds with high probability to quantify this convergence.Our main result is based on the McDiarmid inequality. Interestingly, thisresult does not apply to the case where the aggregation is a coordinate-wisemaximum. We treat this case separately and obtain a different convergence rate.

Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphs