{"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/any-dimensional-equivariant-neural-networks","title":"Any-dimensional equivariant neural networks","arxiv_id":"2306.06327","date":"2023-06-10","proceeding":null,"authors":["Eitan Levin","Mateo Díaz"],"abstract":"Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings, the unknown mapping takes inputs in any dimension; examples include graph parameters defined on graphs of any size and physics quantities defined on an arbitrary number of particles. We leverage a newly-discovered phenomenon in algebraic topology, called representation stability, to define equivariant neural networks that can be trained with data in a fixed dimension and then extended to accept inputs in any dimension. Our approach is user-friendly, requiring only the network architecture and the groups for equivariance, and can be combined with any training procedure. We provide a simple open-source implementation of our methods and offer preliminary numerical experiments.","url_abs":"https://arxiv.org/abs/2306.06327v2","url_pdf":"https://arxiv.org/pdf/2306.06327v2.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":"any-dimensional-equivariant-neural-networks","repo_url":"https://github.com/mateodd25/free-nets","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2306.06327","atlas_url":"https://app.syntology.ai/?focus=2306.06327","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2306.06327"}},"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. 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/mateodd25/free-nets","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":1,"unverified":11},"by_repo_kind":{"official":{"samples":12,"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":"2660b9d52e1de712","entry":"export","repo":"mateodd25/free-nets","repo_kind":"official","path":"emlp/utils.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/emlp/utils.py","link_basis":"plan_row","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2660b9d52e1de712"}},{"code_sha256_prefix":"23ff1cdc894dab43","entry":"LBface_swap","repo":"mateodd25/free-nets","repo_kind":"official","path":"emlp/datasets.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/emlp/datasets.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"23ff1cdc894dab43"}},{"code_sha256_prefix":"02ec0eac15525baa","entry":"UBedge_flip","repo":"mateodd25/free-nets","repo_kind":"official","path":"emlp/datasets.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/emlp/datasets.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"02ec0eac15525baa"}},{"code_sha256_prefix":"afeb3056cc5cad08","entry":"ULBcorner_rot","repo":"mateodd25/free-nets","repo_kind":"official","path":"emlp/datasets.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/emlp/datasets.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"afeb3056cc5cad08"}},{"code_sha256_prefix":"5fbab6adb8505757","entry":"equivariance_err","repo":"mateodd25/free-nets","repo_kind":"official","path":"experiments/aux_O.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/experiments/aux_O.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5fbab6adb8505757"}},{"code_sha256_prefix":"ac065ea6ecd18125","entry":"matrix_power_simple","repo":"mateodd25/free-nets","repo_kind":"official","path":"emlp/groups.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/emlp/groups.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ac065ea6ecd18125"}},{"code_sha256_prefix":"8dadbcba29a5fa50","entry":"noise2sample","repo":"mateodd25/free-nets","repo_kind":"official","path":"emlp/groups.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/emlp/groups.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8dadbcba29a5fa50"}},{"code_sha256_prefix":"ad3bd41e9ed1bb19","entry":"random_sample","repo":"mateodd25/free-nets","repo_kind":"official","path":"experiments/free_symmetric_projection.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/experiments/free_symmetric_projection.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ad3bd41e9ed1bb19"}},{"code_sha256_prefix":"5c71362caaf3b0ab","entry":"random_sample","repo":"mateodd25/free-nets","repo_kind":"official","path":"experiments/aux_O.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/experiments/aux_O.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5c71362caaf3b0ab"}},{"code_sha256_prefix":"b9e669d60e5fb206","entry":"rel_err","repo":"mateodd25/free-nets","repo_kind":"official","path":"emlp/groups.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/emlp/groups.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b9e669d60e5fb206"}},{"code_sha256_prefix":"1c0546beb8cb8de2","entry":"scale_adjusted_rel_err","repo":"mateodd25/free-nets","repo_kind":"official","path":"experiments/aux_O.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/experiments/aux_O.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1c0546beb8cb8de2"}},{"code_sha256_prefix":"b0c36eb0a737fbf7","entry":"true_mapping","repo":"mateodd25/free-nets","repo_kind":"official","path":"experiments/free_symmetric_projection.py","file_url":"https://github.com/mateodd25/free-nets/blob/HEAD/experiments/free_symmetric_projection.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b0c36eb0a737fbf7"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}