{"id":"https://openalex.org/W7128015484","doi":"https://doi.org/10.48550/arxiv.2602.05709","title":"Nonlinearity as Rank: Generative Low-Rank Adapter with Radial Basis Functions","display_name":"Nonlinearity as Rank: Generative Low-Rank Adapter with Radial Basis Functions","publication_year":2026,"publication_date":"2026-02-05","ids":{"openalex":"https://openalex.org/W7128015484","doi":"https://doi.org/10.48550/arxiv.2602.05709"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.05709","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088718077","display_name":"Yihao Ouyang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ouyang, Yihao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125255175","display_name":"Shiwei Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Shiwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125133422","display_name":"Haozhao Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Haozhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125186334","display_name":"Xiandi Luo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Xiandi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111071919","display_name":"Zhuoqi Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Zhuoqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047285212","display_name":"Yuetong Song","orcid":"https://orcid.org/0009-0007-4388-7704"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Song, Yuetong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077923145","display_name":"Qiyu Qin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qin, Qiyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125221402","display_name":"Yichen Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yichen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125157913","display_name":"Ruixuan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Ruixuan","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15226408,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.5609999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.5609999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.18539999425411224,"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/T12303","display_name":"Tensor decomposition and applications","score":0.08550000190734863,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.8003000020980835},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.6585000157356262},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6523000001907349},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.635200023651123},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.566100001335144},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.4950999915599823},{"id":"https://openalex.org/keywords/dot-product","display_name":"Dot product","score":0.43459999561309814},{"id":"https://openalex.org/keywords/cross-product","display_name":"Cross product","score":0.43290001153945923},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4117000102996826}],"concepts":[{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.8003000020980835},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.6585000157356262},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6523000001907349},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.635200023651123},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.566100001335144},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5412999987602234},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.4950999915599823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46619999408721924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4490000009536743},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.43459999561309814},{"id":"https://openalex.org/C82927061","wikidata":"https://www.wikidata.org/wiki/Q178192","display_name":"Cross product","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4117000102996826},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.39590001106262207},{"id":"https://openalex.org/C180623205","wikidata":"https://www.wikidata.org/wiki/Q1268589","display_name":"Outer product","level":3,"score":0.3880000114440918},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34040001034736633},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.32190001010894775},{"id":"https://openalex.org/C177284502","wikidata":"https://www.wikidata.org/wiki/Q1005390","display_name":"Adapter (computing)","level":2,"score":0.3203999996185303},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3012999892234802},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2928999960422516},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.26109999418258667},{"id":"https://openalex.org/C2777798563","wikidata":"https://www.wikidata.org/wiki/Q7603916","display_name":"State vector","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.05709","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.05709","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.05709","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.05709","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Low-rank":[0],"adaptation":[1],"(LoRA)":[2],"approximates":[3],"the":[4,12,39,109],"update":[5],"of":[6,14,101],"a":[7,90,99],"pretrained":[8],"weight":[9],"matrix":[10,96],"using":[11],"product":[13],"two":[15],"low-rank":[16,40,95],"matrices.":[17],"However,":[18],"standard":[19],"LoRA":[20,142],"follows":[21],"an":[22,119],"explicit-rank":[23],"paradigm,":[24],"where":[25],"increasing":[26],"model":[27],"capacity":[28],"requires":[29,114],"adding":[30],"more":[31],"rows":[32],"or":[33],"columns":[34],"(i.e.,":[35],"basis":[36,54,79,84,104,110,121],"vectors)":[37],"to":[38,43,107],"matrices,":[41],"leading":[42],"substantial":[44],"parameter":[45,58,125,146],"growth.":[46],"In":[47],"this":[48],"paper,":[49],"we":[50,70],"find":[51],"that":[52,137],"these":[53],"vectors":[55],"exhibit":[56],"significant":[57],"redundancy":[59],"and":[60,97,134],"can":[61],"be":[62],"compactly":[63],"represented":[64],"by":[65],"lightweight":[66,102],"nonlinear":[67,83],"functions.":[68],"Therefore,":[69],"propose":[71],"Generative":[72],"Low-Rank":[73],"Adapter":[74],"(GenLoRA),":[75],"which":[76],"replaces":[77],"explicit":[78,120],"vector":[80,85,92],"storage":[81],"with":[82],"generation.":[86],"Specifically,":[87],"GenLoRA":[88,138],"maintains":[89],"latent":[91],"for":[93],"each":[94],"employs":[98],"set":[100],"radial":[103],"functions":[105],"(RBFs)":[106],"synthesize":[108],"vectors.":[111],"Each":[112],"RBF":[113],"far":[115],"fewer":[116],"parameters":[117],"than":[118],"vector,":[122],"enabling":[123],"higher":[124,140],"efficiency":[126],"in":[127,149],"GenLoRA.":[128],"Extensive":[129],"experiments":[130],"across":[131],"multiple":[132],"datasets":[133],"architectures":[135],"show":[136],"attains":[139],"effective":[141],"ranks":[143],"under":[144],"smaller":[145],"budgets,":[147],"resulting":[148],"superior":[150],"fine-tuning":[151],"performance.":[152],"The":[153],"code":[154],"is":[155],"available":[156],"at":[157],"https://anonymous.4open.science/r/GenLoRA.":[158]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-02-07T00:00:00"}