{"id":"https://openalex.org/W7126199022","doi":"https://doi.org/10.48550/arxiv.2601.21750","title":"FISMO: Fisher-Structured Momentum-Orthogonalized Optimizer","display_name":"FISMO: Fisher-Structured Momentum-Orthogonalized Optimizer","publication_year":2026,"publication_date":"2026-01-29","ids":{"openalex":"https://openalex.org/W7126199022","doi":"https://doi.org/10.48550/arxiv.2601.21750"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2601.21750","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":"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/A5124386064","display_name":"Chenrui Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xu, Chenrui","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101964529","display_name":"Wenjing Yan","orcid":"https://orcid.org/0000-0002-4790-1397"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan, Wenjing","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Zhang, Ying-Jun Angela","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Ying-Jun Angela","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5124386064"],"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":0.7110999822616577,"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":0.7110999822616577,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.04050000011920929,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.03280000016093254,"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/fisher-information","display_name":"Fisher information","score":0.6538000106811523},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.5873000025749207},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.5052000284194946},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.47200000286102295},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.446399986743927},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44200000166893005},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4138999879360199},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.35269999504089355}],"concepts":[{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.6538000106811523},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.5873000025749207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5540000200271606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.54830002784729},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.47200000286102295},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.446399986743927},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4138999879360199},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41260001063346863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37860000133514404},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.35269999504089355},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3312999904155731},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32760000228881836},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.32499998807907104},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.26409998536109924},{"id":"https://openalex.org/C2778153524","wikidata":"https://www.wikidata.org/wiki/Q4241335","display_name":"Optimality criterion","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2601.21750","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.2601.21750","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.21750","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.2601.21750","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Training":[0],"large-scale":[1],"neural":[2],"networks":[3],"requires":[4],"solving":[5],"nonconvex":[6,129],"optimization":[7,64],"where":[8],"the":[9,30,93,136],"choice":[10],"of":[11,144],"optimizer":[12,34,94],"fundamentally":[13],"determines":[14],"both":[15],"convergence":[16,123],"behavior":[17],"and":[18,154,165],"computational":[19,119],"efficiency.":[20],"While":[21],"adaptive":[22],"methods":[23,65],"like":[24],"Adam":[25],"have":[26],"long":[27],"dominated":[28],"practice,":[29],"recently":[31],"proposed":[32],"Muon":[33],"achieves":[35,107,161],"superior":[36,162],"performance":[37,167],"through":[38,87,147],"orthogonalized":[39],"momentum":[40],"updates":[41,81],"that":[42,66,110,159],"enforce":[43],"isotropic":[44,80],"geometry":[45,116],"with":[46,70,141],"uniform":[47],"singular":[48],"values.":[49],"However,":[50],"this":[51],"strict":[52],"isotropy":[53],"discards":[54],"potentially":[55],"valuable":[56],"curvature":[57,85],"information":[58,86,89],"encoded":[59],"in":[60,127],"gradient":[61,139],"spectra,":[62],"motivating":[63],"balance":[67],"geometric":[68],"structure":[69],"adaptivity.":[71],"We":[72,121],"introduce":[73],"FISMO":[74,106,126,160],"(Fisher-Structured":[75],"Momentum-Orthogonalized)":[76],"optimizer,":[77],"which":[78],"generalizes":[79],"to":[82,112,169],"incorporate":[83],"anisotropic":[84],"Fisher":[88,104],"geometry.":[90],"By":[91],"reformulating":[92],"update":[95],"as":[96],"a":[97,102],"trust-region":[98],"problem":[99],"constrained":[100],"by":[101],"Kronecker-factored":[103],"metric,":[105],"structured":[108],"preconditioning":[109],"adapts":[111],"local":[113],"loss":[114],"landscape":[115],"while":[117],"maintaining":[118],"tractability.":[120],"establish":[122],"guarantees":[124],"for":[125,135],"stochastic":[128],"settings,":[130],"proving":[131],"an":[132],"$\\mathcal{O}(1/\\sqrt{T})$":[133],"rate":[134],"expected":[137],"squared":[138],"norm":[140],"explicit":[142],"characterization":[143],"variance":[145],"reduction":[146],"mini-batching.":[148],"Empirical":[149],"evaluation":[150],"on":[151],"image":[152],"classification":[153],"language":[155],"modeling":[156],"benchmarks":[157],"demonstrates":[158],"training":[163],"efficiency":[164],"final":[166],"compared":[168],"established":[170],"baselines.":[171]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-01T00:00:00"}