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The Value of Depth in Message Passing on Sparse Graphs: A Kesten-Stigum Dichotomy
How deep does a graph neural network need to be on a sparse graph? We study its purest statistical form: node classification on the sparse contextual stochastic block model (CSBM) with average degree $Δ=O(1)$, whose local weak limit is a broadcast-labelled Poisson Galton-Watson tree. Prior work deri
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