{"id":"https://openalex.org/W4405173214","doi":"https://doi.org/10.48550/arxiv.2412.04594","title":"Learning Symmetries via Weight-Sharing with Doubly Stochastic Tensors","display_name":"Learning Symmetries via Weight-Sharing with Doubly Stochastic Tensors","publication_year":2024,"publication_date":"2024-12-05","ids":{"openalex":"https://openalex.org/W4405173214","doi":"https://doi.org/10.48550/arxiv.2412.04594"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2412.04594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.04594","pdf_url":"https://arxiv.org/pdf/2412.04594","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2412.04594","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092778181","display_name":"Putri A. van der Linden","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"van der Linden, Putri A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114352574","display_name":"Alejandro Garc\u00eda-Castellanos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Garc\u00eda-Castellanos, Alejandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022575807","display_name":"Sharvaree Vadgama","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vadgama, Sharvaree","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102886176","display_name":"Thijs P. Kuipers","orcid":"https://orcid.org/0009-0007-7198-2856"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kuipers, Thijs P.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000647841","display_name":"Erik J. Bekkers","orcid":"https://orcid.org/0000-0003-4418-2160"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bekkers, Erik J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9765999913215637,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9765999913215637,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13650","display_name":"Computational Physics and Python Applications","score":0.9133999943733215,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.8452784419059753},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40344083309173584},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3890681266784668},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3393380641937256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3362416625022888},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16478708386421204}],"concepts":[{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.8452784419059753},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40344083309173584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3890681266784668},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3393380641937256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3362416625022888},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16478708386421204}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2412.04594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.04594","pdf_url":"https://arxiv.org/pdf/2412.04594","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2412.04594","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2412.04594","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2412.04594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.04594","pdf_url":"https://arxiv.org/pdf/2412.04594","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321799","display_name":"Ministerie van Onderwijs, Cultuur en Wetenschap","ror":"https://ror.org/02x3w5g21"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405173214.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W4298192601","https://openalex.org/W1594396050"],"abstract_inverted_index":{"Group":[0],"equivariance":[1,44,73],"has":[2],"emerged":[3],"as":[4,66,116,130],"a":[5,81,90,102,107,131],"valuable":[6],"inductive":[7],"bias":[8],"in":[9,41,86],"deep":[10],"learning,":[11],"enhancing":[12],"generalization,":[13],"data":[14],"efficiency,":[15],"and":[16,63,164],"robustness.":[17],"Classically,":[18],"group":[19,43,78,92,128,162,171],"equivariant":[20],"methods":[21,58],"require":[22],"the":[23,55,150,155,174,177],"groups":[24],"of":[25,80,109,176],"interest":[26],"to":[27,99,160,181],"be":[28,34],"known":[29],"beforehand,":[30],"which":[31,124],"may":[32,45],"not":[33],"realistic":[35],"for":[36,57],"real-world":[37],"data.":[38],"Additionally,":[39,173],"baking":[40],"fixed":[42],"impose":[46],"overly":[47],"restrictive":[48],"constraints":[49],"on":[50,120,185],"model":[51],"architecture.":[52],"This":[53,134],"highlights":[54],"need":[56],"that":[59,114,139,148],"can":[60,125],"dynamically":[61],"discover":[62],"apply":[64],"symmetries":[65],"soft":[67,117],"constraints.":[68],"For":[69],"neural":[70],"network":[71],"architectures,":[72],"is":[74],"commonly":[75],"achieved":[76],"through":[77],"transformations":[79,138],"canonical":[82,121],"weight":[83,87,122],"tensor,":[84],"resulting":[85],"sharing":[88],"over":[89],"given":[91],"$G$.":[93],"In":[94],"this":[95],"work,":[96],"we":[97],"propose":[98],"learn":[100],"such":[101],"weight-sharing":[103,166],"scheme":[104],"by":[105],"defining":[106],"collection":[108],"learnable":[110,136],"doubly":[111],"stochastic":[112],"matrices":[113,119,157],"act":[115],"permutation":[118,156],"tensors,":[123],"take":[126],"regular":[127,161,170],"representations":[129,163],"special":[132],"case.":[133],"yields":[135],"kernel":[137],"are":[140],"jointly":[141],"optimized":[142],"with":[143],"downstream":[144],"tasks.":[145],"We":[146],"show":[147],"when":[149],"dataset":[151],"exhibits":[152],"strong":[153],"symmetries,":[154],"will":[158],"converge":[159],"our":[165],"networks":[167],"effectively":[168,182],"become":[169],"convolutions.":[172],"flexibility":[175],"method":[178],"enables":[179],"it":[180],"pick":[183],"up":[184],"partial":[186],"symmetries.":[187]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
