Learning to Execute Graph Algorithms Exactly with Graph Neural Networks

Fuente: arXiv
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Main Authors: Qharabagh, Muhammad Fetrat, de Luca, Artur Back, Giapitzakis, George, Fountoulakis, Kimon
Format: Preprint
Published: 2026
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author Qharabagh, Muhammad Fetrat
de Luca, Artur Back
Giapitzakis, George
Fountoulakis, Kimon
author_facet Qharabagh, Muhammad Fetrat
de Luca, Artur Back
Giapitzakis, George
Fountoulakis, Kimon
contents Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge. In this work, we prove exact learnability results for graph algorithms under bounded-degree and finite-precision constraints. Our approach follows a two-step process. First, we train an ensemble of multi-layer perceptrons (MLPs) to execute the local instructions of a single node. Second, during inference, we use the trained MLP ensemble as the update function within a graph neural network (GNN). Leveraging Neural Tangent Kernel (NTK) theory, we show that local instructions can be learned from a small training set, enabling the complete graph algorithm to be executed during inference without error and with high probability. To illustrate the learning power of our setting, we establish a rigorous learnability result for the LOCAL model of distributed computation. We further demonstrate positive learnability results for widely studied algorithms such as message flooding, breadth-first and depth-first search, and Bellman-Ford.
format Preprint
id arxiv_https___arxiv_org_abs_2601_23207
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Learning to Execute Graph Algorithms Exactly with Graph Neural Networks
Qharabagh, Muhammad Fetrat
de Luca, Artur Back
Giapitzakis, George
Fountoulakis, Kimon
Machine Learning
Artificial Intelligence
Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge. In this work, we prove exact learnability results for graph algorithms under bounded-degree and finite-precision constraints. Our approach follows a two-step process. First, we train an ensemble of multi-layer perceptrons (MLPs) to execute the local instructions of a single node. Second, during inference, we use the trained MLP ensemble as the update function within a graph neural network (GNN). Leveraging Neural Tangent Kernel (NTK) theory, we show that local instructions can be learned from a small training set, enabling the complete graph algorithm to be executed during inference without error and with high probability. To illustrate the learning power of our setting, we establish a rigorous learnability result for the LOCAL model of distributed computation. We further demonstrate positive learnability results for widely studied algorithms such as message flooding, breadth-first and depth-first search, and Bellman-Ford.
title Learning to Execute Graph Algorithms Exactly with Graph Neural Networks
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2601.23207