{"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/clifford-group-equivariant-neural-networks-1","title":"Clifford Group Equivariant Neural Networks","arxiv_id":"2305.11141","date":"2023-05-18","proceeding":"NeurIPS 2023 11","authors":["David Ruhe","Johannes Brandstetter","Patrick Forré"],"abstract":"We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\\mathrm{O}(n)$- and $\\mathrm{E}(n)$-equivariant models. We identify and study the $\\textit{Clifford group}$, a subgroup inside the Clifford algebra tailored to achieve several favorable properties. Primarily, the group's action forms an orthogonal automorphism that extends beyond the typical vector space to the entire Clifford algebra while respecting the multivector grading. This leads to several non-equivalent subrepresentations corresponding to the multivector decomposition. Furthermore, we prove that the action respects not just the vector space structure of the Clifford algebra but also its multiplicative structure, i.e., the geometric product. These findings imply that every polynomial in multivectors, An advantage worth mentioning is that we obtain expressive layers that can elegantly generalize to inner-product spaces of any dimension. We demonstrate, notably from a single core implementation, state-of-the-art performance on several distinct tasks, including a three-dimensional $n$-body experiment, a four-dimensional Lorentz-equivariant high-energy physics experiment, and a five-dimensional convex hull experiment.","url_abs":"https://arxiv.org/abs/2305.11141v5","url_pdf":"https://arxiv.org/pdf/2305.11141v5.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":"clifford-group-equivariant-neural-networks-1","repo_url":"https://github.com/DavidRuhe/clifford-group-equivariant-neural-networks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2305.11141","atlas_url":"https://app.syntology.ai/?focus=2305.11141","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2305.11141"}},"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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