{"id":"https://openalex.org/W7131426550","doi":"https://doi.org/10.48550/arxiv.2602.18997","title":"Implicit Bias and Convergence of Matrix Stochastic Mirror Descent","display_name":"Implicit Bias and Convergence of Matrix Stochastic Mirror Descent","publication_year":2026,"publication_date":"2026-02-22","ids":{"openalex":"https://openalex.org/W7131426550","doi":"https://doi.org/10.48550/arxiv.2602.18997"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.18997","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.18997","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.2602.18997","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036629613","display_name":"Danil Akhtiamov","orcid":"https://orcid.org/0000-0002-9238-9636"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Akhtiamov, Danil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093219798","display_name":"Reza Ghane","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ghane, Reza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Pooladzandi, Omead","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pooladzandi, Omead","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005686377","display_name":"Babak Hassibi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hassibi, Babak","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"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":0.9519000053405762,"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":0.9519000053405762,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.006300000008195639,"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/T10057","display_name":"Face and Expression Recognition","score":0.006000000052154064,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/initialization","display_name":"Initialization","score":0.7383999824523926},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.722100019454956},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6184999942779541},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6065999865531921},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.5476999878883362},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5217999815940857},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4544999897480011},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.3353999853134155}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.739799976348877},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7383999824523926},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.722100019454956},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6184999942779541},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6065999865531921},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.5476999878883362},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5217999815940857},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49300000071525574},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4544999897480011},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3986999988555908},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35109999775886536},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.3353999853134155},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C2780427248","wikidata":"https://www.wikidata.org/wiki/Q17014996","display_name":"Fundamental matrix (linear differential equation)","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C56275529","wikidata":"https://www.wikidata.org/wiki/Q5348937","display_name":"Eight-point algorithm","level":5,"score":0.2718000113964081},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.2662999927997589},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.2574000060558319},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2572000026702881},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.25540000200271606},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.18997","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.18997","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.2602.18997","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.18997","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4207175076007843}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"investigate":[1],"Stochastic":[2],"Mirror":[3],"Descent":[4],"(SMD)":[5],"with":[6,43],"matrix":[7,19,44,68,94],"parameters":[8,32],"and":[9,18],"vector-valued":[10],"predictions,":[11],"a":[12,51],"framework":[13],"relevant":[14],"to":[15,50,72,86],"multi-class":[16],"classification":[17],"completion":[20],"problems.":[21,103],"Focusing":[22],"on":[23],"the":[24,28,34,67,73,77,88],"overparameterized":[25],"regime,":[26],"where":[27],"total":[29],"number":[30,35],"of":[31,36,61],"exceeds":[33],"training":[37],"samples,":[38],"we":[39,55],"prove":[40],"that":[41,66],"SMD":[42,63,69],"mirror":[45,95],"functions":[46],"$\u03c8(\\cdot)$":[47,82],"converges":[48,71],"exponentially":[49],"global":[52],"interpolator.":[53],"Furthermore,":[54],"generalize":[56],"classical":[57],"implicit":[58],"bias":[59,99],"results":[60],"vector":[62],"by":[64,81],"demonstrating":[65],"algorithm":[70],"unique":[74],"solution":[75],"minimizing":[76],"Bregman":[78],"divergence":[79],"induced":[80],"from":[83],"initialization":[84],"subject":[85],"interpolating":[87],"data.":[89],"These":[90],"findings":[91],"reveal":[92],"how":[93],"maps":[96],"dictate":[97],"inductive":[98],"in":[100],"high-dimensional,":[101],"multi-output":[102]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-26T00:00:00"}