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In this paper we\npropose a generalization of this work that generally exhibits improved\nperformace, but from an implementation point of view is actually simpler. An\nunusual feature of the proposed architecture is that it uses the\nClebsch--Gordan transform as its only source of nonlinearity, thus avoiding\nrepeated forward and backward Fourier transforms. The underlying ideas of the\npaper generalize to constructing neural networks that are invariant to the\naction of other compact groups.","url_abs":"http://arxiv.org/abs/1806.09231v2","url_pdf":"http://arxiv.org/pdf/1806.09231v2.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":"clebsch-gordan-nets-a-fully-fourier-space","repo_url":"https://github.com/e3nn/e3nn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"clebsch-gordan-nets-a-fully-fourier-space","repo_url":"https://github.com/e3nn/e3nn-jax","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"clebsch-gordan-nets-a-fully-fourier-space","repo_url":"https://github.com/zlin7/CGNet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1806.09231","atlas_url":"https://app.syntology.ai/?focus=1806.09231","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1806.09231"}},"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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