stefaniaebli / paper-snn-neurips2020tda

LaTeX source code of the paper and poster of the paper Simplicial Neural Networks

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},
}

Resources

PDF available at arXiv, OpenReview.

Related: code, poster, data.

Compilation

Compile the latex source into a PDF with make. Run make clean to remove temporary files and make arxiv.zip to prepare an archive to be uploaded on arXiv.

Figures

All the figures, along with the code and data to reproduce them, are in the figures folder. While the PDFs are stored, they can be regenerated with make figures.

Poster

A poster is in the poster_neurips folder. It is compiled by make and a PDF is available at doi:10.5281/zenodo.4309827.

Peer-review

The reviews, decision, and our answers are in review.md and on OpenReview.

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

This work is licensed under a Creative Commons Attribution 4.0 International License.