{"id":"https://openalex.org/W7223056243","doi":"https://doi.org/10.48550/arxiv.2610.25721","title":"Corrected Block Sparse Spectral Optimization: Exact Models, Finite Identification, and Local Dynamics","display_name":"Corrected Block Sparse Spectral Optimization: Exact Models, Finite Identification, and Local Dynamics","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223056243","doi":"https://doi.org/10.48550/arxiv.2610.25721"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2610.25721","doi":"https://doi.org/10.48550/arxiv.2610.25721","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25721","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2610.25721","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003613160","display_name":"Omid Shams Solari","orcid":"https://orcid.org/0000-0002-7805-6026","observed_orcids":["https://orcid.org/0000-0002-7805-6026"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Solari, Omid Shams","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5003613160"],"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":0.8413000106811523,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.8413000106811523,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.12269999831914902,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T13141","display_name":"Statistical Methods and Applications","score":0.004100000020116568,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/support-selection","display_name":"support selection","score":0.5559999942779541},{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.5740000009536743},{"id":"https://openalex.org/keywords/kurdyka-lojasiewicz-property","display_name":"Kurdyka-Lojasiewicz property","score":0.9110000133514404},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.4749999940395355},{"id":"https://openalex.org/keywords/single-cell-rna-sequencing","display_name":"single-cell RNA sequencing","score":0.7260000109672546},{"id":"https://openalex.org/keywords/cluster-recovery","display_name":"cluster recovery","score":0.5799999833106995},{"id":"https://openalex.org/keywords/sparsity","display_name":"sparsity","score":0.36000001430511475}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465999722480774},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.490200012922287},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44350001215934753},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4343999922275543},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.41290000081062317},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4115000069141388},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.4106999933719635},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.40299999713897705},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.3986999988555908},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3889000117778778},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3700000047683716},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.3292999863624573},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.3093000054359436},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.30709999799728394},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2777999937534332},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C99821215","wikidata":"https://www.wikidata.org/wiki/Q1136583","display_name":"Swap (finance)","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2610.25721","doi":"https://doi.org/10.48550/arxiv.2610.25721","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25721","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2610.25721","doi":"https://doi.org/10.48550/arxiv.2610.25721","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25721","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3014542904","https://openalex.org/W3145178437","https://openalex.org/W7095587425","https://openalex.org/W7099317584","https://openalex.org/W3100498669","https://openalex.org/W2741226915","https://openalex.org/W2757458919","https://openalex.org/W7222872985","https://openalex.org/W7133556875","https://openalex.org/W4383533154"],"abstract_inverted_index":{"The":[0,147],"block":[1,15],"generalized-power":[2],"method":[3],"pairs":[4],"threshold-based":[5],"support":[6,143],"selection":[7],"with":[8,233],"inexpensive":[9],"Stiefel":[10,129],"updates,":[11],"but":[12],"the":[13,33,36,43,55,94,106,118,124,128,142,155,164,181,188,205],"standard":[14],"formulation":[16],"conflates":[17],"two":[18],"nonequivalent":[19],"objectives":[20],"and":[21,27,78,88,103,117,127,144,163,192,214,220],"leaves":[22],"inactive":[23],"components,":[24],"threshold":[25,135],"ties,":[26,85],"post-selection":[28],"refitting":[29],"ill-specified.":[30],"We":[31,67],"rebuild":[32],"model":[34],"from":[35,42,62,98,180],"primal.":[37],"Eliminating":[38],"each":[39],"loading":[40],"column":[41],"normalized":[44],"loading-ball":[45],"problem":[46],"gives":[47],"a":[48,63,72,99,111,114,159,168,175],"sum":[49],"of":[50,141,167],"soft-thresholded":[51],"Euclidean":[52],"norms":[53],"(A-SUM);":[54],"squared-threshold":[56],"objective":[57,126],"in":[58,218],"common":[59],"use":[60],"arises":[61],"quadratic":[64],"lift":[65],"(A-SQ).":[66],"prove":[68],"both":[69],"identities,":[70],"exhibit":[71],"two-component":[73],"instance":[74],"whose":[75],"maximizers":[76],"disagree,":[77],"specify":[79],"explicit":[80],"conventions":[81],"for":[82,105,158,172],"zero-response":[83],"columns,":[84],"rank":[86],"deficiency,":[87],"mask-before-refit.":[89],"For":[90],"A-SQ":[91,238],"we":[92],"separate":[93],"historical":[95],"full-polar":[96],"iteration":[97,153],"safeguarded":[100],"Riemannian":[101],"ascent":[102],"prove,":[104],"latter,":[107],"whole-sequence":[108],"convergence":[109],"via":[110],"sufficient-ascent":[112],"lemma,":[113,116],"relative-error":[115],"Kurdyka-Lojasiewicz":[119],"property,":[120],"which":[121],"applies":[122],"because":[123],"soft-threshold":[125],"constraint":[130],"are":[131],"semi-algebraic.":[132],"A":[133],"strict":[134],"margin":[136],"then":[137],"forces":[138],"finite":[139],"identification":[140,190],"sign":[145],"pattern.":[146],"post-identification":[148],"map":[149,171],"is":[150],"ordinary":[151],"power":[152],"on":[154,212,216,242],"active":[156],"covariance":[157],"rank-one":[160],"hard":[161],"threshold,":[162],"Frechet":[165],"derivative":[166],"coupled":[169],"polar":[170],"component-specific":[173],"supports;":[174],"radius-based":[176],"safe-screening":[177],"rule":[178],"follows":[179],"same":[182],"local":[183,193],"analysis.":[184],"Planted-spike":[185],"experiments":[186],"match":[187,209],"predicted":[189],"time":[191],"rates.":[194],"On":[195,223],"modern-AI":[196],"panels":[197],"(GPT-2":[198],"residual":[199],"stream,":[200,203],"ViT":[201],"CLS":[202],"Pitprops)":[204],"thresholded":[206],"block-sparse":[207],"components":[208],"dense":[210,240],"PCA":[211,241],"reconstruction":[213],"improve":[215],"it":[217],"monosemanticity":[219],"class":[221],"specialisation.":[222],"three":[224],"native-label":[225],"scRNA":[226],"datasets":[227],"(Zheng17":[228],"FACS-sorted":[229],"PBMCs,":[230],"68k":[231],"donor-A":[232],"FACS-correlated":[234],"labels,":[235],"Tabula":[236],"Muris)":[237],"beats":[239],"cluster-recovery":[243],"AMI":[244],"by":[245],"+0.023":[246],"to":[247],"+0.044":[248],"at":[249],"matched":[250],"sparsity.":[251]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-21T00:00:00"}