{"id":"https://openalex.org/W7134059486","doi":"https://doi.org/10.48550/arxiv.2603.04703","title":"Implicit Bias and Loss of Plasticity in Matrix Completion: Depth Promotes Low-Rankness","display_name":"Implicit Bias and Loss of Plasticity in Matrix Completion: Depth Promotes Low-Rankness","publication_year":2026,"publication_date":"2026-03-05","ids":{"openalex":"https://openalex.org/W7134059486","doi":"https://doi.org/10.48550/arxiv.2603.04703"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.04703","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":null,"license_id":null,"version":"submittedVersion","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":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125428516","display_name":"Baekrok Shin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shin, Baekrok","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045562332","display_name":"Chulhee Yun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yun, Chulhee","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5125428516"],"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8741999864578247,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8741999864578247,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.025699999183416367,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.01860000006854534,"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/plasticity","display_name":"Plasticity","score":0.7142999768257141},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5436000227928162},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5385000109672546},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5016000270843506},{"id":"https://openalex.org/keywords/mechanism","display_name":"Mechanism (biology)","score":0.4936999976634979},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.40389999747276306},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.3962000012397766},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.3804999887943268},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.36250001192092896}],"concepts":[{"id":"https://openalex.org/C79186407","wikidata":"https://www.wikidata.org/wiki/Q472074","display_name":"Plasticity","level":2,"score":0.7142999768257141},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5436000227928162},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5385000109672546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5253000259399414},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5016000270843506},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.4936999976634979},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4683000147342682},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.40389999747276306},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.390500009059906},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3596999943256378},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3296000063419342},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3163999915122986},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.29910001158714294},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C31395832","wikidata":"https://www.wikidata.org/wiki/Q1318674","display_name":"Testbed","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2854999899864197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2800999879837036},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27230000495910645},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2556999921798706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.04703","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2603.04703","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.04703","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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.04703","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":null,"license_id":null,"version":"submittedVersion","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":{"We":[0,54,120,146],"study":[1],"matrix":[2,6,129],"completion":[3,130],"via":[4],"deep":[5,9,149],"factorization":[7],"(a.k.a.":[8],"linear":[10],"neural":[11],"networks)":[12],"as":[13,58],"a":[14,59,116],"simplified":[15],"testbed":[16],"to":[17,96,155,167,169],"examine":[18],"how":[19],"network":[20],"depth":[21,85],"influences":[22],"training":[23,174],"dynamics.":[24],"Despite":[25],"the":[26,31,46,103,123,179,186],"simplicity":[27],"and":[28,41,65,93,100,140],"importance":[29],"of":[30,84,118,125],"problem,":[32],"prior":[33],"theory":[34],"largely":[35],"focuses":[36],"on":[37,74,137,185],"shallow":[38],"(depth-2)":[39],"models":[40,150],"does":[42],"not":[43],"fully":[44],"explain":[45],"implicit":[47],"low-rank":[48,157],"bias":[49,64],"observed":[50],"in":[51,128],"deeper":[52],"networks.":[53],"identify":[55],"coupled":[56,106],"dynamics":[57,104,165],"key":[60],"mechanism":[61,187],"behind":[62,188],"this":[63,189],"show":[66,147],"that":[67,148],"it":[68],"intensifies":[69],"with":[70,142],"increasing":[71],"depth.":[72],"Focusing":[73],"gradient":[75],"flow":[76],"under":[77,163],"block-diagonal":[78],"observations,":[79],"we":[80],"prove:":[81],"(a)":[82],"networks":[83,161],"$\\geq":[86],"3$":[87],"exhibit":[88],"coupling":[89,180],"unless":[90],"initialized":[91],"diagonally,":[92],"(b)":[94],"convergence":[95],"rank-1":[97],"occurs":[98],"if":[99,102],"only":[101],"is":[105],"--":[107,182],"resolving":[108],"an":[109],"open":[110],"question":[111],"by":[112],"Menon":[113],"(2024)":[114],"for":[115],"family":[117],"initializations.":[119],"also":[121],"revisit":[122],"loss":[124,153],"plasticity":[126,152],"phenomenon":[127],"(Kleinman":[131],"et":[132],"al.,":[133],"2024),":[134],"where":[135],"pre-training":[136],"few":[138],"observations":[139],"resuming":[141],"more":[143],"degrades":[144],"performance.":[145],"avoid":[151],"due":[154],"their":[156],"bias,":[158],"whereas":[159],"depth-2":[160],"pre-trained":[162],"decoupled":[164],"fail":[166],"converge":[168],"low-rank,":[170],"even":[171],"when":[172],"resumed":[173],"(with":[175],"additional":[176],"data)":[177],"satisfies":[178],"condition":[181],"shedding":[183],"light":[184],"phenomenon.":[190]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-03-07T00:00:00"}