https://github.com/mdeff/paper-cheblienet
ChebLieNet: Invariant spectral graph NNs turned equivariant by Riemannian geometry on Lie groups
https://github.com/mdeff/paper-cheblienet
Last synced: 3 months ago
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ChebLieNet: Invariant spectral graph NNs turned equivariant by Riemannian geometry on Lie groups
- Host: GitHub
- URL: https://github.com/mdeff/paper-cheblienet
- Owner: mdeff
- License: cc-by-4.0
- Created: 2021-11-23T18:14:39.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2021-11-25T15:44:05.000Z (over 4 years ago)
- Last Synced: 2025-03-16T01:13:18.276Z (about 1 year ago)
- Language: TeX
- Homepage: https://arxiv.org/abs/2111.12139
- Size: 11.6 MB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
# ChebLieNet: Invariant spectral graph NNs turned equivariant by Riemannian geometry on Lie groups
[Hugo Aguettaz](https://www.linkedin.com/in/hugo-aguettaz),
[Erik J. Bekkers](https://erikbekkers.bitbucket.io),
[Michaël Defferrard](https://deff.ch)
> We introduce ChebLieNet, a group-equivariant method on (anisotropic) manifolds.
> Surfing on the success of graph- and group-based neural networks, we take advantage of the recent developments in the geometric deep learning field to derive a new approach to exploit any anisotropies in data.
> Via discrete approximations of Lie groups, we develop a graph neural network made of anisotropic convolutional layers (Chebyshev convolutions), spatial pooling and unpooling layers, and global pooling layers.
> Group equivariance is achieved via equivariant and invariant operators on graphs with anisotropic left-invariant Riemannian distance-based affinities encoded on the edges.
> Thanks to its simple form, the Riemannian metric can model any anisotropies, both in the spatial and orientation domains.
> This control on anisotropies of the Riemannian metrics allows to balance equivariance (anisotropic metric) against invariance (isotropic metric) of the graph convolution layers.
> Hence we open the doors to a better understanding of anisotropic properties.
> Furthermore, we empirically prove the existence of (data-dependent) sweet spots for anisotropic parameters on CIFAR10.
> This crucial result is evidence of the benefice we could get by exploiting anisotropic properties in data.
> We also evaluate the scalability of this approach on STL10 (image data) and ClimateNet (spherical data), showing its remarkable adaptability to diverse tasks.
```
@inproceedings{cheblienet,
title = {{ChebLieNet}: Invariant spectral graph {NN}s turned equivariant by Riemannian geometry on Lie groups},
author = {Aguettaz, Hugo and Bekkers, Erik J. and Defferrard, Michaël},
year = {2021},
archivePrefix={arXiv},
eprint={2111.12139},
url = {https://arxiv.org/abs/2111.12139},
}
```
## Resources
PDF available at [`arXiv:2111.12139`][arXiv], [`OpenReview:WsfXFxqZXRO`][OpenReview].
Related: [code].
[arXiv]: https://arxiv.org/abs/2111.12139
[OpenReview]: https://openreview.net/forum?id=WsfXFxqZXRO
[code]: https://github.com/haguettaz/ChebLieNet
## 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 are in the [`Images`](Images/) folder.
The code and data to reproduce them is found in the [code repository][code].
## Peer-review
The reviews, decision, and our answers are in [`reviews.md`](reviews.md) and on [OpenReview].
## History
* 2021-11-23: uploaded on arXiv (git tag `arxiv`)
* 2021-08-11: rebuttal to NeurIPS'21 reviews (git tag `neurips21-rebuttal`)
* 2021-06-04: submitted to NeurIPS'21 (git tag `neurips21-submitted`)
## License
This work is licensed under a [Creative Commons Attribution 4.0 International License](https://creativecommons.org/licenses/by/4.0/).