{"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/e3x-mathrm-e-3-equivariant-deep-learning-made","title":"E3x: $\\mathrm{E}(3)$-Equivariant Deep Learning Made Easy","arxiv_id":"2401.07595","date":"2024-01-15","proceeding":null,"authors":["Oliver T. Unke","Hartmut Maennel"],"abstract":"This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group $\\mathrm{E}(3)$, consisting of translations, rotations, and reflections of three-dimensional space. Compared to ordinary neural networks, $\\mathrm{E}(3)$-equivariant models promise benefits whenever input and/or output data are quantities associated with three-dimensional objects. This is because the numeric values of such quantities (e.g. positions) typically depend on the chosen coordinate system. Under transformations of the reference frame, the values change predictably, but the underlying rules can be difficult to learn for ordinary machine learning models. With built-in $\\mathrm{E}(3)$-equivariance, neural networks are guaranteed to satisfy the relevant transformation rules exactly, resulting in superior data efficiency and accuracy. The code for E3x is available from https://github.com/google-research/e3x, detailed documentation and usage examples can be found on https://e3x.readthedocs.io.","url_abs":"https://arxiv.org/abs/2401.07595v3","url_pdf":"https://arxiv.org/pdf/2401.07595v3.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":"e3x-mathrm-e-3-equivariant-deep-learning-made","repo_url":"https://github.com/google-research/e3x","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2401.07595","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2401.07595"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/google-research/e3x","reach":null}],"summary":{"ran_fixture":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"e5b8f74f9c83078c","entry":"identity_initializer","repo":"google-research/e3x","repo_kind":"official","path":"tests/nn/modules_test.py","file_url":"https://github.com/google-research/e3x/blob/HEAD/tests/nn/modules_test.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"e5b8f74f9c83078c"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}