Graph neural networks and MSO

TL;DR

This paper provides an alternative proof that recurrent graph neural networks with real weights have the same expressive power as MSO logic, using distributed automata over trees.

Contribution

It introduces a new proof technique linking GNNs and MSO logic through distributed automata, expanding understanding of GNN expressiveness.

Findings

Recurrent GNNs with real weights are equivalent to MSO logic in expressive power.

Distributed automata can capture all MSO-definable properties over trees.

Variants of automata acceptance conditions are also considered.

Abstract

We give an alternative proof for the existing result that recurrent graph neural networks working with reals have the same expressive power in restriction to monadic second-order logic MSO as the graded modal substitution calculus. The proof is based on constructing distributed automata that capture all MSO-definable node properties over trees. We also consider some variants of the acceptance conditions.