{"id":"https://openalex.org/W7123253824","doi":"https://doi.org/10.48550/arxiv.2601.05335","title":"Generalized Canonical Polyadic Tensor Decompositions with General Symmetry","display_name":"Generalized Canonical Polyadic Tensor Decompositions with General Symmetry","publication_year":2026,"publication_date":"2026-01-08","ids":{"openalex":"https://openalex.org/W7123253824","doi":"https://doi.org/10.48550/arxiv.2601.05335"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.05335","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.05335","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.2601.05335","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109818756","display_name":"Alex Mulrooney","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mulrooney, Alex","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122838319","display_name":"David Hong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hong, David","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/T12303","display_name":"Tensor decomposition and applications","score":0.9943000078201294,"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"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9943000078201294,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.0007999999797903001,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.000699999975040555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6635000109672546},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5008000135421753},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.4821000099182129},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4634000062942505},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.43149998784065247},{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.4043999910354614},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.36899998784065247},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.3682999908924103}],"concepts":[{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6635000109672546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6189000010490417},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5008000135421753},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.4821000099182129},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4634000062942505},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.43149998784065247},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3682999908924103},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.36410000920295715},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.34769999980926514},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.3431999981403351},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.3336000144481659},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.32350000739097595},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32260000705718994},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31380000710487366},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3012000024318695},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C64835786","wikidata":"https://www.wikidata.org/wiki/Q17004583","display_name":"Cartesian tensor","level":5,"score":0.2883000075817108},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25769999623298645},{"id":"https://openalex.org/C158158286","wikidata":"https://www.wikidata.org/wiki/Q9009080","display_name":"Invariants of tensors","level":3,"score":0.2533999979496002},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.05335","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.05335","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.2601.05335","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.05335","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":{"Canonical":[0],"Polyadic":[1],"(CP)":[2],"tensor":[3,15,28,89,167],"decomposition":[4,23,124],"is":[5,18],"a":[6,26,88,97,120,204],"workhorse":[7],"algorithm":[8],"for":[9,74,127,142,155],"discovering":[10],"underlying":[11],"low-dimensional":[12],"structure":[13],"in":[14,20,77,83,149],"data.":[16,213],"This":[17],"accomplished":[19],"conventional":[21],"CP":[22,38],"by":[24,44,91,144],"fitting":[25],"low-rank":[27],"to":[29,33,55,62,65,111,176,183,191],"data":[30,60],"with":[31,165,203],"respect":[32],"the":[34,78,93,107,112,138,146,150,172,196,199],"least-squares":[35],"loss.":[36],"Generalized":[37],"(GCP)":[39],"decompositions":[40,69],"generalize":[41],"this":[42,116],"approach":[43],"allowing":[45],"general":[46,128],"loss":[47],"functions":[48],"that":[49,125,157,180,188],"can":[50,189],"be":[51],"more":[52],"appropriate,":[53],"e.g.,":[54],"model":[56],"binary":[57],"and":[58,211],"count":[59],"or":[61],"improve":[63],"robustness":[64],"outliers.":[66],"However,":[67],"GCP":[68,122],"do":[70],"not":[71],"explicitly":[72],"account":[73],"any":[75,135],"symmetry":[76,105,133,143,148],"tensors,":[79],"which":[80],"commonly":[81],"arises":[82],"modern":[84],"applications.":[85],"For":[86],"example,":[87],"formed":[90],"stacking":[92],"adjacency":[94],"matrices":[95],"of":[96,130,137,171,198,206],"dynamic":[98],"graph":[99,113],"over":[100],"time":[101],"will":[102],"naturally":[103],"exhibit":[104],"along":[106,134],"two":[108],"modes":[109],"corresponding":[110,147],"nodes.":[114],"In":[115],"paper,":[117],"we":[118],"develop":[119,184],"symmetric":[121],"(SymGCP)":[123],"allows":[126],"forms":[129],"symmetry,":[131],"i.e.,":[132],"subset":[136],"modes.":[139],"SymGCP":[140,156,186,201],"accounts":[141],"enforcing":[145],"decomposition.":[151],"We":[152,194],"derive":[153],"gradients":[154,173],"enable":[158,181],"its":[159],"efficient":[160],"computation":[161],"via":[162],"all-at-once":[163],"optimization":[164],"existing":[166],"kernels.":[168],"The":[169],"form":[170],"also":[174],"leads":[175],"various":[177],"stochastic":[178,185],"approximations":[179],"us":[182],"algorithms":[187,202],"scale":[190],"large":[192],"tensors.":[193],"demonstrate":[195],"utility":[197],"proposed":[200],"variety":[205],"experiments":[207],"on":[208],"both":[209],"synthetic":[210],"real":[212]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-01-13T00:00:00"}
