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.
Note that each token has O(∆)size, and each edge can transmitw words per round
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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.