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- W4323697202 abstract "We analyse the power of graph neural networks (GNNs) in terms of Boolean circuit complexity and descriptive complexity. We prove that the graph queries that can be computed by a polynomial-size bounded-depth family of GNNs are exactly those definable in the guarded fragment GFO+C of first-order logic with counting and with built-in relations. This puts GNNs in the circuit complexity class TC^0. Remarkably, the GNN families may use arbitrary real weights and a wide class of activation functions that includes the standard ReLU, logistic sigmod, and hyperbolic tangent functions. If the GNNs are allowed to use random initialisation and global readout (both standard features of GNNs widely used in practice), they can compute exactly the same queries as bounded depth Boolean circuits with threshold gates, that is, exactly the queries in TC^0. Moreover, we show that queries computable by a single GNN with piecewise linear activations and rational weights are definable in GFO+C without built-in relations. Therefore, they are contained in uniform TC^0." @default.
- W4323697202 created "2023-03-10" @default.
- W4323697202 creator A5073893026 @default.
- W4323697202 date "2023-03-08" @default.
- W4323697202 modified "2023-09-27" @default.
- W4323697202 title "The Descriptive Complexity of Graph Neural Networks" @default.
- W4323697202 doi "https://doi.org/10.48550/arxiv.2303.04613" @default.
- W4323697202 hasPublicationYear "2023" @default.
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