{"id":"https://openalex.org/W7134906744","doi":"https://doi.org/10.48550/arxiv.2603.08758","title":"Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields","display_name":"Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields","publication_year":2026,"publication_date":"2026-03-08","ids":{"openalex":"https://openalex.org/W7134906744","doi":"https://doi.org/10.48550/arxiv.2603.08758"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.08758","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08758","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.08758","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128780295","display_name":"Alejandro Garc\u00eda-Castellanos","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Garc\u00eda-Castellanos, Alejandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074897113","display_name":"Gijs Bellaard","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bellaard, Gijs","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013378425","display_name":"Remco Duits","orcid":"https://orcid.org/0000-0001-8910-3695"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Duits, Remco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037323866","display_name":"Dani\u00ebl M. Pelt","orcid":"https://orcid.org/0000-0002-8253-0851"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pelt, Daniel","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":5,"corresponding_author_ids":["https://openalex.org/A5128780295"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.3361999988555908,"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"}},"topics":[{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.3361999988555908,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.28769999742507935,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.06480000168085098,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.8169000148773193},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.5738000273704529},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5608999729156494},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5199999809265137},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5012000203132629},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4952999949455261},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.4875999987125397},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4487000107765198},{"id":"https://openalex.org/keywords/inner-product-space","display_name":"Inner product space","score":0.4320000112056732}],"concepts":[{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.8169000148773193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6123999953269958},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5738000273704529},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5608999729156494},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5199999809265137},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5012000203132629},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4952999949455261},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.4875999987125397},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4560000002384186},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C91855343","wikidata":"https://www.wikidata.org/wiki/Q214159","display_name":"Inner product space","level":2,"score":0.4320000112056732},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.41510000824928284},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3772999942302704},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32190001010894775},{"id":"https://openalex.org/C131715654","wikidata":"https://www.wikidata.org/wiki/Q288465","display_name":"Group action","level":3,"score":0.31349998712539673},{"id":"https://openalex.org/C2780091087","wikidata":"https://www.wikidata.org/wiki/Q3092131","display_name":"Dimensional reduction","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.08758","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08758","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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.08758","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08758","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Many":[0],"geometric":[1],"learning":[2],"problems":[3],"require":[4],"invariants":[5],"on":[6,35,42,63],"heterogeneous":[7],"product":[8,44],"spaces,":[9,102],"i.e.,":[10],"products":[11],"of":[12,55,60],"distinct":[13],"spaces":[14],"carrying":[15],"different":[16],"group":[17,31,97],"actions,":[18],"where":[19],"standard":[20],"techniques":[21],"do":[22],"not":[23],"directly":[24],"apply.":[25],"We":[26,85],"show":[27],"that,":[28],"when":[29],"a":[30,36,43,79],"$G$":[32],"acts":[33],"transitively":[34],"space":[37,45],"$M$,":[38],"any":[39],"$G$-invariant":[40],"function":[41],"$X":[46],"\\times":[47,74],"M$":[48],"can":[49],"be":[50],"reduced":[51],"to":[52,89,95],"an":[53,69],"invariant":[54],"the":[56,106],"isotropy":[57],"subgroup":[58],"$H$":[59],"$M$":[61],"acting":[62],"$X$":[64],"alone.":[65],"Our":[66],"approach":[67],"establishes":[68],"explicit":[70],"orbit":[71],"equivalence":[72],"$(X":[73],"M)/G":[75],"\\cong":[76],"X/H$,":[77],"yielding":[78],"principled":[80],"reduction":[81],"that":[82],"preserves":[83],"expressivity.":[84],"apply":[86],"this":[87],"characterization":[88],"Equivariant":[90],"Neural":[91],"Fields,":[92],"extending":[93],"them":[94],"arbitrary":[96],"actions":[98],"and":[99,103],"homogeneous":[100],"conditioning":[101],"thereby":[104],"removing":[105],"major":[107],"structural":[108],"constraints":[109],"imposed":[110],"by":[111],"existing":[112],"methods.":[113]},"counts_by_year":[],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2026-03-12T00:00:00"}