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This is a Quantitative Study study.

October 16, 2025Open Access

Graph neural networks and MSO

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The proof demonstrates that graph neural networks can capture all MSO-definable node properties over trees, enhancing understanding of their capabilities.
Using distributed automata in the proof effectively shows the equivalence to graded modal substitution calculus, providing a different perspective on expressive power.
Variants of acceptance conditions were considered to further explore the implications and nuances of this equivalence in graph neural networks.
This work supports advancing the theoretical foundations of graph neural networks and their applications in logic-based frameworks.

Implication

This proof shows equivalence in expressive power of graph neural networks and MSO, implying insights on distributed automata.

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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Cite This Study

Ahvonen et al. (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd09c https://doi.org/10.48550/arxiv.2505.07816

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Implication

This proof shows equivalence in expressive power of graph neural networks and MSO, implying insights on distributed automata.

Graph neural networks and MSO

Key Points

Implication

Abstract

Discussion

Cite This Study

Graph neural networks and MSO

Key Points

Implication

Abstract

Discussion

Cite This Study

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