Generalization Error of Graph Neural Networks in the Mean-field Regime
<|reference_start|>Generalization Error of Graph Neural Networks in the Mean-field Regime: 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.<|reference_end|>
@article{aminian2024generalization,
    title={Generalization Error of Graph Neural Networks in the Mean-field Regime},
    author={Gholamali Aminian, Yixuan He, Gesine Reinert, {L}ukasz Szpruch,
  Samuel N. Cohen},
    journal={arXiv preprint arXiv:2402.07025},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.07025},
    primaryClass={stat.ML cs.IT cs.LG math.IT}
}