On dimensionality of feature vectors in MPNNs

We revisit the classical result of Morris et al.~(AAAI'19) that message-passing graphs neural networks (MPNNs) are equal in their distinguishing power to the Weisfeiler--Leman (WL) isomorphism test.
Morris et al.~show their simulation result with ReLU activation function and $O(n)$-dimensional feature vectors, where $n$ is the number of nodes of the graph. Recently, by introducing randomness into the architecture, Aamand et al.~(NeurIPS'22) were able to improve this bound to $O(\log n)$-dimensional feature vectors, although at the expense of guaranteeing perfect simulation …

aaai cs.lg dimensionality feature function graph graphs networks neural networks power relu show simulation test vectors