{"id":21332488,"url":"https://github.com/mdeff/paper-cheblienet","last_synced_at":"2026-03-19T19:56:38.175Z","repository":{"id":95298329,"uuid":"431207451","full_name":"mdeff/paper-cheblienet","owner":"mdeff","description":"ChebLieNet: Invariant spectral graph NNs turned equivariant by Riemannian geometry on Lie groups","archived":false,"fork":false,"pushed_at":"2021-11-25T15:44:05.000Z","size":12211,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"master","last_synced_at":"2025-03-16T01:13:18.276Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"https://arxiv.org/abs/2111.12139","language":"TeX","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"cc-by-4.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/mdeff.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE.txt","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2021-11-23T18:14:39.000Z","updated_at":"2023-07-25T14:51:49.000Z","dependencies_parsed_at":"2023-04-14T01:01:00.266Z","dependency_job_id":null,"html_url":"https://github.com/mdeff/paper-cheblienet","commit_stats":null,"previous_names":[],"tags_count":3,"template":false,"template_full_name":null,"purl":"pkg:github/mdeff/paper-cheblienet","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdeff%2Fpaper-cheblienet","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdeff%2Fpaper-cheblienet/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdeff%2Fpaper-cheblienet/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdeff%2Fpaper-cheblienet/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/mdeff","download_url":"https://codeload.github.com/mdeff/paper-cheblienet/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdeff%2Fpaper-cheblienet/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":271330292,"owners_count":24740815,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","status":"online","status_checked_at":"2025-08-20T02:00:09.606Z","response_time":69,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-11-21T22:51:34.978Z","updated_at":"2026-02-12T15:02:42.211Z","avatar_url":"https://github.com/mdeff.png","language":"TeX","funding_links":[],"categories":[],"sub_categories":[],"readme":"# ChebLieNet: Invariant spectral graph NNs turned equivariant by Riemannian geometry on Lie groups\n\n[Hugo Aguettaz](https://www.linkedin.com/in/hugo-aguettaz),\n[Erik J. Bekkers](https://erikbekkers.bitbucket.io),\n[Michaël Defferrard](https://deff.ch)\n\n\u003e We introduce ChebLieNet, a group-equivariant method on (anisotropic) manifolds.\n\u003e 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.\n\u003e 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.\n\u003e Group equivariance is achieved via equivariant and invariant operators on graphs with anisotropic left-invariant Riemannian distance-based affinities encoded on the edges.\n\u003e Thanks to its simple form, the Riemannian metric can model any anisotropies, both in the spatial and orientation domains.\n\u003e This control on anisotropies of the Riemannian metrics allows to balance equivariance (anisotropic metric) against invariance (isotropic metric) of the graph convolution layers.\n\u003e Hence we open the doors to a better understanding of anisotropic properties.\n\u003e Furthermore, we empirically prove the existence of (data-dependent) sweet spots for anisotropic parameters on CIFAR10.\n\u003e This crucial result is evidence of the benefice we could get by exploiting anisotropic properties in data.\n\u003e We also evaluate the scalability of this approach on STL10 (image data) and ClimateNet (spherical data), showing its remarkable adaptability to diverse tasks.\n\n```\n@inproceedings{cheblienet,\n  title = {{ChebLieNet}: Invariant spectral graph {NN}s turned equivariant by Riemannian geometry on Lie groups},\n  author = {Aguettaz, Hugo and Bekkers, Erik J. and Defferrard, Michaël},\n  year = {2021},\n  archivePrefix={arXiv},\n  eprint={2111.12139},\n  url = {https://arxiv.org/abs/2111.12139},\n}\n```\n\n## Resources\n\nPDF available at [`arXiv:2111.12139`][arXiv], [`OpenReview:WsfXFxqZXRO`][OpenReview].\n\nRelated: [code].\n\n[arXiv]: https://arxiv.org/abs/2111.12139\n[OpenReview]: https://openreview.net/forum?id=WsfXFxqZXRO\n[code]: https://github.com/haguettaz/ChebLieNet\n\n## Compilation\n\nCompile the latex source into a PDF with `make`.\nRun `make clean` to remove temporary files and `make arxiv.zip` to prepare an archive to be uploaded on arXiv.\n\n## Figures\n\nAll the figures are in the [`Images`](Images/) folder.\nThe code and data to reproduce them is found in the [code repository][code].\n\n## Peer-review\n\nThe reviews, decision, and our answers are in [`reviews.md`](reviews.md) and on [OpenReview].\n\n## History\n\n* 2021-11-23: uploaded on arXiv (git tag `arxiv`)\n* 2021-08-11: rebuttal to NeurIPS'21 reviews (git tag `neurips21-rebuttal`)\n* 2021-06-04: submitted to NeurIPS'21 (git tag `neurips21-submitted`)\n\n## License\n\nThis work is licensed under a [Creative Commons Attribution 4.0 International License](https://creativecommons.org/licenses/by/4.0/).\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmdeff%2Fpaper-cheblienet","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmdeff%2Fpaper-cheblienet","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmdeff%2Fpaper-cheblienet/lists"}