Simplicial Neural Networks

Stefania Ebli, Michaël Defferrard, Gard Spreemann
Topological Data Analysis and Beyond workshop at the Conference on Neural Information Processing Systems (NeurIPS), 2020

We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called [simplicial complexes]. These are natural multi-dimensional extensions of graphs that encode not only pairwise relationships but also higher-order interactions between vertices—allowing us to consider richer data, including vector fields and n-fold collaboration networks. We define an appropriate notion of convolution that we leverage to construct the desired convolutional neural networks. We test the SNNs on the task of imputing missing data on coauthorship complexes.

@inproceedings{snn,
  title = {Simplicial Neural Networks},
  author = {Ebli, Stefania and Defferrard, Michaël and Spreemann, Gard},
  booktitle = {Topological Data Analysis and Beyond workshop at NeurIPS},
  year = {2020},
  archiveprefix = {arXiv},
  eprint = {2010.03633},
  url = {https://arxiv.org/abs/2010.03633},
}

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Poster

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History

• 2020-12-28: revision uploaded on arXiv (git tag arxiv-20201228)
• 2020-12-07: poster uploaded on OpenReview (git tag poster-neurips)
• 2020-12-01: revision uploaded on OpenReview (git tag openreview-revised)
• 2020-10-07: uploaded on arXiv (git tag arxiv-20201007)
• 2020-10-07: submitted to the TDA@NeurIPS workshop (git tag neurips-submission)

License

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