Oversmoothing

Stack enough graph layers and every node ends up looking the same. Each round averages a node with its neighbours, and repeated averaging is exactly how you erase differences — so the representations that were supposed to distinguish nodes converge to a single point. It is why most graph networks are two or three layers deep while everything else in this graph got deeper.

The tension is real and not merely a tuning problem: reach requires depth and depth destroys the signal. Residual connections, initial-residual mixing and normalisation all push the ceiling up rather than removing it, because the smoothing is what the aggregation does rather than a side effect of it. A model that needs eight hops of reach is a model that probably wants a different architecture.

Repeated multiplication by the normalised propagation matrix converges toward its dominant eigenvector, so H super ^(l)  tends to a rank-one limit determined by degree rather than by features. Distinguishability falls roughly geometrically in depth, at a rate set by the spectral gap — a well-connected graph smooths faster, which is the opposite of the intuition that more edges means more information.