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It is shown that the onset of entropy degradation separates the two main GNN failure modes: structural mismatch under heterophily, which appears from the earliest layers even in shallow models, and excessive-depth oversmoothing, which emerges only as propagation depth increases.
This work introduces TRIP and its generalisation GRIP and its generalisation GRIP, constructive procedures that turn any graph into a provably long-ranged task by drawing features from stable distributions, and formally proves that violating any one of them admits failure modes that undermine conclusions drawn from the...
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