Oblivious MPGNNs cannot simulate WL color refinement with shallow depth and small messages without randomness; bounded-error randomness enables logarithmic resources for large color sets, while small color sets force layer-message trade-offs.
The reduction of a graph to canonical form and the algebra which appears therein.nti, Series, 2(9):12–16, 1968
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How Hard Is It for Message-Passing GNNs to Simulate One Weisfeiler-Lehman Color-Refinement Step?
Oblivious MPGNNs cannot simulate WL color refinement with shallow depth and small messages without randomness; bounded-error randomness enables logarithmic resources for large color sets, while small color sets force layer-message trade-offs.