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DeepSphere: a graph-based spherical CNN

Michaël Defferrard, Martino Milani, Frédérick Gusset, Nathanaël Perraudin
International Conference on Learning Representations (ICLR), 2020

Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the discretized sphere, strikes a controllable balance between these two desiderata. This contribution is twofold. First, we study both theoretically and empirically how equivariance is affected by the underlying graph with respect to the number of pixels and neighbors. Second, we evaluate DeepSphere on relevant problems. Experiments show state-of-the-art performance and demonstrates the efficiency and flexibility of this formulation. Perhaps surprisingly, comparison with previous work suggests that anisotropic filters might be an unnecessary price to pay. Our code is available at https://github.com/deepsphere.

@inproceedings{deepsphere_iclr,
  title = {{DeepSphere}: a graph-based spherical {CNN}},
  author = {Defferrard, Michaël and Milani, Martino and Gusset, Frédérick and Perraudin, Nathanaël},
  booktitle = {International Conference on Learning Representations (ICLR)},
  year = {2020},
  archiveprefix = {arXiv},
  eprint = {2012.15000},
  url = {https://arxiv.org/abs/2012.15000},
}

Resources

PDF available at arXiv and OpenReview.

Related: code, slides, video, ICLR.

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.

Peer-review

The conference reviews and rebuttal are in rebuttal.md and OpenReview.

History

  • 2020-12-30: uploaded on arXiv (git tag arxiv)
  • 2020-02-15: published at ICLR'20 (git tag camera-ready)
  • 2019-11-12: updated with reviewers' feedback (git tag rebuttal)
  • 2019-09-25: submitted to ICLR'20 (git tag submitted)

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