{"id":"https://openalex.org/W7138896451","doi":"https://doi.org/10.48550/arxiv.2603.17527","title":"Mirror Descent on Riemannian Manifolds","display_name":"Mirror Descent on Riemannian Manifolds","publication_year":2026,"publication_date":"2026-03-18","ids":{"openalex":"https://openalex.org/W7138896451","doi":"https://doi.org/10.48550/arxiv.2603.17527"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.17527","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.17527","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.17527","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049781333","display_name":"Jiaxin Jiang","orcid":"https://orcid.org/0000-0002-4425-047X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Jiaxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129776467","display_name":"Lei Shi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Lei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5129867263","display_name":"Jiyuan Tan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tan, Jiyuan","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":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":0.9848999977111816,"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":0.9848999977111816,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.0017000000225380063,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.0015999999595806003,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.8129000067710876},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.6581000089645386},{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.6381999850273132},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6179999709129333},{"id":"https://openalex.org/keywords/curvilinear-coordinates","display_name":"Curvilinear coordinates","score":0.605400025844574},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5996000170707703},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5659000277519226},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5598999857902527},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.49810001254081726}],"concepts":[{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.8129000067710876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6721000075340271},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.6581000089645386},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.6381999850273132},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6179999709129333},{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.605400025844574},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5996000170707703},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5659000277519226},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5598999857902527},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.49810001254081726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4648999869823456},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.41440001130104065},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3174000084400177},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30880001187324524},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2822999954223633},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2797999978065491},{"id":"https://openalex.org/C158847443","wikidata":"https://www.wikidata.org/wiki/Q1997812","display_name":"Method of steepest descent","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.27070000767707825},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.2619999945163727},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.17527","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.17527","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":"doi:10.48550/arxiv.2603.17527","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.17527","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":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"Mirror":[0,39],"Descent":[1,40,80],"(MD)":[2],"is":[3],"a":[4,37,48,99],"scalable":[5],"first-order":[6],"method":[7,82],"widely":[8],"used":[9],"in":[10,15,84],"large-scale":[11,107],"optimization,":[12,19],"with":[13],"applications":[14],"image":[16],"processing,":[17],"policy":[18],"and":[20,45,62],"neural":[21],"network":[22],"training.":[23],"This":[24],"paper":[25],"generalizes":[26],"MD":[27],"to":[28,68,76,93],"optimization":[29,109],"on":[30],"Riemannian":[31,38],"manifolds.":[32],"In":[33],"particular,":[34],"we":[35,97],"develop":[36],"(RMD)":[41],"framework":[42,74,92],"via":[43],"reparameterization":[44],"further":[46],"propose":[47],"stochastic":[49,63,90,100],"variant":[50],"of":[51,102],"RMD.":[52,64],"We":[53],"also":[54],"establish":[55],"non-asymptotic":[56],"convergence":[57],"guarantees":[58],"for":[59],"both":[60],"RMD":[61,73,91],"As":[65],"an":[66],"application":[67],"the":[69,77,89,94],"Stiefel":[70,95],"manifold,":[71],"our":[72],"reduces":[75],"Curvilinear":[78],"Gradient":[79],"(CGD)":[81],"proposed":[83],"[26].":[85],"Moreover,":[86],"when":[87],"specializing":[88],"setting,":[96],"obtain":[98],"extension":[101],"CGD,":[103],"which":[104],"effectively":[105],"addresses":[106],"manifold":[108],"problems.":[110]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-20T00:00:00"}