Generalization Error of Graph Neural Networks in the Mean-field Regime
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909233558061056 |
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| author | Aminian, Gholamali He, Yixuan Reinert, Gesine Szpruch, Łukasz Cohen, Samuel N. |
| author_facet | Aminian, Gholamali He, Yixuan Reinert, Gesine Szpruch, Łukasz Cohen, Samuel N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07025 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalization Error of Graph Neural Networks in the Mean-field Regime Aminian, Gholamali He, Yixuan Reinert, Gesine Szpruch, Łukasz Cohen, Samuel N. Machine Learning Information Theory 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. |
| title | Generalization Error of Graph Neural Networks in the Mean-field Regime |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2402.07025 |