DeepSphere: towards an equivariant graph-based spherical CNN

Nathanaël Perraudin, Michaël Defferrard, Tomasz Kacprzak, Raphael Sgier
Representation Learning on Graphs and Manifolds (RLGM) workshop at the International Conference on Learning Representations (ICLR), 2019

Spherical data is found in many applications. By modeling the discretized sphere as a graph, we can accommodate non-uniformly distributed, partial, and changing samplings. Moreover, graph convolutions are computationally more efficient than spherical convolutions. As equivariance is desired to exploit rotational symmetries, we discuss how to approach rotation equivariance using the graph neural network introduced in Defferrard et al. (2016). Experiments show good performance on rotation-invariant learning problems. Code and examples are available at https://github.com/deepsphere.

@inproceedings{deepsphere_rlgm,
  title = {{DeepSphere}: towards an equivariant graph-based spherical {CNN}},
  author = {Defferrard, Micha\"el and Perraudin, Nathana\"el and Kacprzak, Tomasz and Sgier, Raphael},
  booktitle = {ICLR Workshop on Representation Learning on Graphs and Manifolds},
  year = {2019},
  archiveprefix = {arXiv},
  eprint = {1904.05146},
  url = {https://arxiv.org/abs/1904.05146},
}

Resources

PDF available at arXiv and the RLGM workshop.

Related: poster, code.

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 workshop reviews are in reviews.md.