{"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/reducing-so-3-convolutions-to-so-2-for","title":"Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs","arxiv_id":"2302.03655","date":"2023-02-07","proceeding":null,"authors":["Saro Passaro","C. Lawrence Zitnick"],"abstract":"Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the $SO(3)$ convolutions or tensor products to mathematically equivalent convolutions in $SO(2)$ . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from $O(L^6)$ to $O(L^3)$, where $L$ is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.","url_abs":"https://arxiv.org/abs/2302.03655v2","url_pdf":"https://arxiv.org/pdf/2302.03655v2.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":"reducing-so-3-convolutions-to-so-2-for","repo_url":"https://github.com/atomicarchitects/equiformer_v2","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"reducing-so-3-convolutions-to-so-2-for","repo_url":"https://github.com/lucidrains/equiformer-pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"}],"methods":[{"method_slug":"graph-neural-network","method_name":"Graph Neural Network"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2302.03655","atlas_url":"https://app.syntology.ai/?focus=2302.03655","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2302.03655"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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