ml-recall

#permutation-equivariance

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mediumAI-checkedGraph Neural Networks

A permutation matrix $P$ renumbers the $n$ nodes of a graph with node features $X \in \mathbb{R}^{n \times d}$ and adjacency matrix $A$ . A GNN layer $F(X, A)$ outputs one row per node. Which equation says that $F$ is permutation equivariant?

$F(PX, PAP^\top) = P F(X, A)$ 1
$F(PX, PAP^\top) = F(X, A)$ 2
$F(PX, A) = P\,F(X, A)$ 3
$F(X, PAP^\top) = P\,F(X, A)$ 4

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