A Simple Spectral Failure Mode for Graph Convolutional Networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913404948578304 |
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| author | Priebe, Carey E. Shen, Cencheng Huang, Ningyuan Chen, Tianyi |
| author_facet | Priebe, Carey E. Shen, Cencheng Huang, Ningyuan Chen, Tianyi |
| contents | Neural networks have achieved remarkable successes in machine learning tasks. This has recently been extended to graph learning using neural networks. However, there is limited theoretical work in understanding how and when they perform well, especially relative to established statistical learning techniques such as spectral embedding. In this short paper, we present a simple generative model where unsupervised graph convolutional network fails, while the adjacency spectral embedding succeeds. Specifically, unsupervised graph convolutional network is unable to look beyond the first eigenvector in certain approximately regular graphs, thus missing inference signals in non-leading eigenvectors. The phenomenon is demonstrated by visual illustrations and comprehensive simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_13152 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Simple Spectral Failure Mode for Graph Convolutional Networks Priebe, Carey E. Shen, Cencheng Huang, Ningyuan Chen, Tianyi Machine Learning Neural networks have achieved remarkable successes in machine learning tasks. This has recently been extended to graph learning using neural networks. However, there is limited theoretical work in understanding how and when they perform well, especially relative to established statistical learning techniques such as spectral embedding. In this short paper, we present a simple generative model where unsupervised graph convolutional network fails, while the adjacency spectral embedding succeeds. Specifically, unsupervised graph convolutional network is unable to look beyond the first eigenvector in certain approximately regular graphs, thus missing inference signals in non-leading eigenvectors. The phenomenon is demonstrated by visual illustrations and comprehensive simulations. |
| title | A Simple Spectral Failure Mode for Graph Convolutional Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2010.13152 |