{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sign-and-basis-invariant-networks-for","title":"Sign and Basis Invariant Networks for Spectral Graph Representation Learning","arxiv_id":"2202.13013","date":"2022-02-25","proceeding":null,"authors":["Derek Lim","Joshua Robinson","Lingxiao Zhao","Tess Smidt","Suvrit Sra","Haggai Maron","Stefanie Jegelka"],"abstract":"We introduce SignNet and BasisNet -- new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if $v$ is an eigenvector then so is $-v$; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choices of basis eigenvectors. We prove that under certain conditions our networks are universal, i.e., they can approximate any continuous function of eigenvectors with the desired invariances. When used with Laplacian eigenvectors, our networks are provably more expressive than existing spectral methods on graphs; for instance, they subsume all spectral graph convolutions, certain spectral graph invariants, and previously proposed graph positional encodings as special cases. Experiments show that our networks significantly outperform existing baselines on molecular graph regression, learning expressive graph representations, and learning neural fields on triangle meshes. Our code is available at https://github.com/cptq/SignNet-BasisNet .","url_abs":"https://arxiv.org/abs/2202.13013v4","url_pdf":"https://arxiv.org/pdf/2202.13013v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"sign-and-basis-invariant-networks-for","repo_url":"https://github.com/cptq/SignNet-BasisNet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"sign-and-basis-invariant-networks-for","repo_url":"https://github.com/tum-vision/intrinsic-neural-fields","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-regression","task_name":"Graph Regression"},{"task_slug":"graph-representation-learning","task_name":"Graph Representation Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/graph-regression-on-zinc-500k","task":"Graph Regression","dataset":"ZINC-500k","model":"PNA-SignNet","rank_in_archive_order":16,"of":36,"metrics":{"MAE":"0.084"},"uses_additional_data":false},{"leaderboard":"/sota/graph-regression-on-zinc-full","task":"Graph Regression","dataset":"ZINC-full","model":"SignNet","rank_in_archive_order":8,"of":19,"metrics":{"Test MAE":"0.024±0.003"},"uses_additional_data":false}],"syntology":{"syntology_url":"https://syntology.ai/paper/2202.13013","atlas_url":"https://app.syntology.ai/?focus=2202.13013","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}