Generalization Error of Graph Neural Networks in the Mean-field Regime

Gholamali Aminian, Yixuan He, Gesine Reinert, Lukasz Szpruch, Samuel N. Cohen
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:1359-1391, 2024.

Abstract

This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely utilized types of graph neural networks: graph convolutional neural networks and message passing graph neural networks. Prior to this study, existing bounds on the generalization error in the over-parametrized regime were uninformative, limiting our understanding of over-parameterized network performance. Our novel approach involves deriving upper bounds within the mean-field regime for evaluating the generalization error of these graph neural networks. We establish upper bounds with a convergence rate of $O(1/n)$, where $n$ is the number of graph samples. These upper bounds offer a theoretical assurance of the networks’ performance on unseen data in the challenging over-parameterized regime and overall contribute to our understanding of their performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-aminian24a, title = {Generalization Error of Graph Neural Networks in the Mean-field Regime}, author = {Aminian, Gholamali and He, Yixuan and Reinert, Gesine and Szpruch, Lukasz and Cohen, Samuel N.}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {1359--1391}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/aminian24a/aminian24a.pdf}, url = {https://proceedings.mlr.press/v235/aminian24a.html}, abstract = {This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely utilized types of graph neural networks: graph convolutional neural networks and message passing graph neural networks. Prior to this study, existing bounds on the generalization error in the over-parametrized regime were uninformative, limiting our understanding of over-parameterized network performance. Our novel approach involves deriving upper bounds within the mean-field regime for evaluating the generalization error of these graph neural networks. We establish upper bounds with a convergence rate of $O(1/n)$, where $n$ is the number of graph samples. These upper bounds offer a theoretical assurance of the networks’ performance on unseen data in the challenging over-parameterized regime and overall contribute to our understanding of their performance.} }
Endnote
%0 Conference Paper %T Generalization Error of Graph Neural Networks in the Mean-field Regime %A Gholamali Aminian %A Yixuan He %A Gesine Reinert %A Lukasz Szpruch %A Samuel N. Cohen %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-aminian24a %I PMLR %P 1359--1391 %U https://proceedings.mlr.press/v235/aminian24a.html %V 235 %X This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely utilized types of graph neural networks: graph convolutional neural networks and message passing graph neural networks. Prior to this study, existing bounds on the generalization error in the over-parametrized regime were uninformative, limiting our understanding of over-parameterized network performance. Our novel approach involves deriving upper bounds within the mean-field regime for evaluating the generalization error of these graph neural networks. We establish upper bounds with a convergence rate of $O(1/n)$, where $n$ is the number of graph samples. These upper bounds offer a theoretical assurance of the networks’ performance on unseen data in the challenging over-parameterized regime and overall contribute to our understanding of their performance.
APA
Aminian, G., He, Y., Reinert, G., Szpruch, L. & Cohen, S.N.. (2024). Generalization Error of Graph Neural Networks in the Mean-field Regime. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:1359-1391 Available from https://proceedings.mlr.press/v235/aminian24a.html.

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