aiqbench analysis
This paper establishes a theoretical universality result for permutation-equivariant neural networks using random node features, demonstrating their ability to approximate complex functions on directed graphs. It further derives upper bounds on approximation rates that link model complexity—specifically layer depth and weight count—to desired accuracy levels. These findings provide critical mathematical grounding for understanding the expressive power of modern GNN architectures with randomized components.
Universality and Approximation Rates of Graph Neural Networks with Random Features
arXiv:2607.26699v1 Announce Type: new Abstract: We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically. Here, we establish a novel universality result focusing on permutation-equivariant neural networks (PENNs), a class of GNNs built from feedforward neural network components that subsumes many prominent GNN architectures. We show that PENNs, combined with partially random node features, can approximate arbitrarily well in probability any measurable permutation-invariant or permutation-equivariant function on directed graphs of fixed size with multidimensional node and edge features. For $k$-times continuously differentiable functions, $k\geq 2$, we also derive upper bounds on the approximation rates, relating the complexity of the feedforward components of a PENN in terms of layer depth and number of nonzero weights to the desired approximation accuracy.
Abstract:We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically. Here, we establish a novel universality result focusing on permutation-equivariant neural networks (PENNs), a class of GNNs built from feedforward neural network components that subsumes many prominent GNN architectures. We show that PENNs, combined with partially random node features, can approximate arbitrarily well in probability any measurable permutation-invariant or permutation-equivariant function on directed graphs of fixed size with multidimensional node and edge features. For $k$-times continuously differentiable functions, $k\geq 2$, we also derive upper bounds on the approximation rates, relating the complexity of the feedforward components of a PENN in terms of layer depth and number of nonzero weights to the desired approximation accuracy.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2607.26699 [cs.LG]
(or arXiv:2607.26699v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.26699 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 229 words
