{"id":"https://openalex.org/W2946049129","doi":null,"title":"Tensor Ring Decomposition: Energy Landscape and One-loop Convergence of Alternating Least Squares","display_name":"Tensor Ring Decomposition: Energy Landscape and One-loop Convergence of Alternating Least Squares","publication_year":2019,"publication_date":"2019-05-17","ids":{"openalex":"https://openalex.org/W2946049129","mag":"2946049129"},"language":"en","primary_location":{"id":"mag:2946049129","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.07101","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.07101","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101457896","display_name":"Ziang Chen","orcid":"https://orcid.org/0000-0002-8298-5223","observed_orcids":["https://orcid.org/0000-0002-8298-5223"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ziang Chen","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8298-5223","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006942055","display_name":"Ying\u2010Zhou Li","orcid":"https://orcid.org/0000-0003-3440-9042","observed_orcids":["https://orcid.org/0000-0003-3440-9042"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ying\u2010Zhou Li","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3440-9042","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061472917","display_name":"Jianfeng Lu","orcid":"https://orcid.org/0000-0001-6255-5165","observed_orcids":["https://orcid.org/0000-0001-6255-5165","https://orcid.org/0000-0001-5586-4656"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianfeng Lu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6255-5165","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":3,"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":0.9994999766349792,"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":0.9994999766349792,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.0,"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/T11804","display_name":"Quantum many-body systems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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-ring-decomposition","display_name":"tensor ring decomposition","score":0.9990000128746033},{"id":"https://openalex.org/keywords/alternating-least-squares","display_name":"alternating least squares","score":0.8870000243186951},{"id":"https://openalex.org/keywords/energy-landscape","display_name":"energy landscape","score":0.8450000286102295},{"id":"https://openalex.org/keywords/spurious-local-minima","display_name":"spurious local minima","score":0.9760000109672546},{"id":"https://openalex.org/keywords/bond-dimension","display_name":"bond dimension","score":0.9769999980926514}],"concepts":[{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.7845064401626587},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6841455101966858},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6143835783004761},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.6040342450141907},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.598914384841919},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5746666193008423},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5731766223907471},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5281234383583069},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4984281063079834},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3912392258644104},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34054088592529297},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33992499113082886},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32159358263015747},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.243971049785614},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22684067487716675},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21064814925193787},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07406839728355408},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2946049129","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.07101","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2946049129","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.07101","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3089008461","https://openalex.org/W2954988770","https://openalex.org/W7095926569","https://openalex.org/W4389532397","https://openalex.org/W2098648646","https://openalex.org/W2191558661","https://openalex.org/W7196962314","https://openalex.org/W7098517713","https://openalex.org/W7055473474","https://openalex.org/W2900371000"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,34,79],"study":[4],"the":[5,23,27,36,43,48,64,69,73,108],"tensor":[6,49,89],"ring":[7,50,90],"decomposition":[8],"and":[9,104],"its":[10],"associated":[11],"numerical":[12,98],"algorithms.":[13],"We":[14],"establish":[15,80],"a":[16],"sharp":[17],"transition":[18],"of":[19,22,38,63],"algorithmic":[20],"difficulty":[21],"optimization":[24,44],"problem":[25],"as":[26],"bond":[28,57,74],"dimension":[29,58,75],"increases:":[30],"On":[31,68],"one":[32],"hand,":[33,71],"show":[35],"existence":[37],"spurious":[39],"local":[40,102],"minima":[41],"for":[42,83,88,100,107],"landscape":[45],"even":[46],"when":[47,72],"format":[51],"is":[52,76],"much":[53,59],"over-parameterized,":[54],"i.e.,":[55],"with":[56],"larger":[60],"than":[61],"that":[62],"true":[65],"target":[66],"tensor.":[67],"other":[70],"further":[77],"increased,":[78],"one-loop":[81,105],"convergence":[82,106],"alternating":[84,109],"least":[85,110],"square":[86,111],"algorithm":[87],"decomposition.":[91],"The":[92],"theoretical":[93],"results":[94],"are":[95],"complemented":[96],"by":[97],"experiments":[99],"both":[101],"minimum":[103],"algorithm.":[112]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2019-05-29T00:00:00"}
