Graph neural networks and MSO

Veeti Ahvonen; Damian Heiman; Antti Kuusisto

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arXiv · 2505.07816

Graph neural networks and MSO

Veeti Ahvonen·Damian Heiman·Antti Kuusisto

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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.

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Veeti Ahvonen, Damian Heiman, Antti Kuusisto. 2025-05-12. Graph neural networks and MSO. https://arxiv.org/abs/2505.07816

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