{"id":"https://openalex.org/W7152957395","doi":"https://doi.org/10.48550/arxiv.2604.07372","title":"NS-RGS: Newton-Schulz based Riemannian gradient method for orthogonal group synchronization","display_name":"NS-RGS: Newton-Schulz based Riemannian gradient method for orthogonal group synchronization","publication_year":2026,"publication_date":"2026-04-07","ids":{"openalex":"https://openalex.org/W7152957395","doi":"https://doi.org/10.48550/arxiv.2604.07372"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.07372","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07372","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2604.07372","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133362932","display_name":"Haiyang Peng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peng, Haiyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133365647","display_name":"Deren Han","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Han, Deren","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133347880","display_name":"Xin Chen","orcid":"https://orcid.org/0000-0001-9940-3720"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Xin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133392697","display_name":"Meng Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Meng","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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.43389999866485596,"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":0.43389999866485596,"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":0.10670000314712524,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.03970000147819519,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.7723000049591064},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6093000173568726},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5734000205993652},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5331000089645386},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.4966999888420105},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.48969998955726624},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4683000147342682},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.453900009393692},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.3869999945163727}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7723000049591064},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6093000173568726},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5734000205993652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5641000270843506},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.538100004196167},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5331000089645386},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.4966999888420105},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.48969998955726624},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4683000147342682},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46389999985694885},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.453900009393692},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3869999945163727},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.3792000114917755},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.376800000667572},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3605000078678131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35569998621940613},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3508000075817108},{"id":"https://openalex.org/C146561895","wikidata":"https://www.wikidata.org/wiki/Q1783179","display_name":"Orthogonal group","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.32510000467300415},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.3239000141620636},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29190000891685486},{"id":"https://openalex.org/C203234222","wikidata":"https://www.wikidata.org/wiki/Q2133519","display_name":"Noise power","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.07372","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07372","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2604.07372","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07372","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Group":[0],"synchronization":[1,81],"is":[2],"a":[3,27,62,72,113,172],"fundamental":[4],"task":[5],"involving":[6],"the":[7,19,24,39,89,95,119,136,165],"recovery":[8],"of":[9],"group":[10,17,80],"elements":[11],"from":[12,122],"pairwise":[13],"measurements.":[14],"For":[15],"orthogonal":[16,79],"synchronization,":[18],"most":[20],"common":[21],"approach":[22,99],"reformulates":[23],"problem":[25],"as":[26,38,164],"constrained":[28],"nonconvex":[29],"optimization":[30],"and":[31,60,104,125,149],"solves":[32],"it":[33],"using":[34],"projection-based":[35],"methods,":[36],"such":[37,163],"generalized":[40,166],"power":[41,167],"method.":[42],"However,":[43],"these":[44],"methods":[45,162],"rely":[46],"on":[47,146],"exact":[48],"SVD":[49,90],"or":[50,91],"QR":[51,92],"decompositions":[52],"in":[53],"each":[54],"iteration,":[55],"which":[56],"are":[57],"computationally":[58],"expensive":[59],"become":[61],"bottleneck":[63],"for":[64,78],"large-scale":[65],"problems.":[66],"In":[67],"this":[68],"paper,":[69],"we":[70,117],"propose":[71],"Newton-Schulz-based":[73],"Riemannian":[74],"Gradient":[75],"Scheme":[76],"(NS-RGS)":[77],"that":[82,127,155],"significantly":[83],"reduces":[84],"computational":[85],"cost":[86],"by":[87],"replacing":[88],"step":[93],"with":[94,107,129],"Newton-Schulz":[96],"iteration.":[97],"This":[98],"leverages":[100],"efficient":[101],"matrix":[102],"multiplications":[103],"aligns":[105],"perfectly":[106],"modern":[108],"GPU/TPU":[109],"architectures.":[110],"By":[111],"employing":[112],"refined":[114],"leave-one-out":[115],"analysis,":[116],"overcome":[118],"challenge":[120],"arising":[121],"statistical":[123,142],"dependencies,":[124],"establish":[126],"NS-RGS":[128,156],"spectral":[130],"initialization":[131],"achieves":[132],"linear":[133],"convergence":[134],"to":[135,140,160],"target":[137],"solution":[138],"up":[139],"near-optimal":[141],"noise":[143],"levels.":[144],"Experiments":[145],"synthetic":[147],"data":[148],"real-world":[150],"global":[151],"alignment":[152],"tasks":[153],"demonstrate":[154],"attains":[157],"accuracy":[158],"comparable":[159],"state-of-the-art":[161],"method,":[168],"while":[169],"achieving":[170],"nearly":[171],"2$\\times$":[173],"speedup.":[174]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-11T00:00:00"}
