{"id":"https://openalex.org/W7133223575","doi":"https://doi.org/10.48550/arxiv.2602.23503","title":"Spiky Rank and Its Applications to Rigidity and Circuits","display_name":"Spiky Rank and Its Applications to Rigidity and Circuits","publication_year":2026,"publication_date":"2026-02-26","ids":{"openalex":"https://openalex.org/W7133223575","doi":"https://doi.org/10.48550/arxiv.2602.23503"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.23503","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036939328","display_name":"Lianna Hambardzumyan","orcid":"https://orcid.org/0009-0003-3217-5462"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hambardzumyan, Lianna","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127867022","display_name":"Konstantin Myasnikov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Myasnikov, Konstantin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127791920","display_name":"Artur Riazanov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Riazanov, Artur","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055995145","display_name":"Morgan Shirley","orcid":"https://orcid.org/0009-0005-4167-2609"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shirley, Morgan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023232731","display_name":"A. Shraibman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shraibman, Adi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"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":0.5408999919891357,"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":0.5408999919891357,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0908999964594841,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.07660000026226044,"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/rank","display_name":"Rank (graph theory)","score":0.7110999822616577},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6327999830245972},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5307999849319458},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5166000127792358},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.4023999869823456},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.388700008392334}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7110999822616577},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6327999830245972},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5620999932289124},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5307999849319458},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5166000127792358},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5044999718666077},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.388700008392334},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.3765999972820282},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.3531999886035919},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.3517000079154968},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3221000134944916},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.26429998874664307}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.23503","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.23503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23503","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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.23503","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"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":{"We":[0,100],"introduce":[1],"spiky":[2,24,38,85,104,112,161],"rank,":[3,169],"a":[4,41,55,88,143],"new":[5],"matrix":[6,25,42,91,108,165],"parameter":[7],"that":[8,31,102,111],"enhances":[9],"blocky":[10,60,168],"rank":[11,39,61,86,105,113,162],"by":[12],"combining":[13],"the":[14,18,37,44,123,131,172],"combinatorial":[15,73],"structure":[16],"of":[17,40,47,127],"latter":[19],"with":[20,28,71],"linear-algebraic":[21],"flexibility.":[22],"A":[23],"is":[26,43,66,80],"block-structured":[27],"diagonal":[29],"blocks":[30,126],"are":[32],"arbitrary":[33],"rank-one":[34],"matrices,":[35],"and":[36,65,74,94,110,141,155,171],"minimum":[45],"number":[46],"such":[48],"matrices":[49,64,140,154],"required":[50],"to":[51,62,151,163],"express":[52],"it":[53,150],"as":[54,81,87],"sum.":[56],"This":[57],"measure":[58,93],"extends":[59],"real":[63],"more":[67],"robust":[68],"for":[69,119,138,145],"problems":[70],"both":[72],"algebraic":[75],"character.":[76],"Our":[77],"conceptual":[78],"contribution":[79],"follows:":[82],"we":[83,134,159],"propose":[84],"well-behaved":[89],"candidate":[90],"complexity":[92],"demonstrate":[95],"its":[96],"potential":[97],"through":[98],"applications.":[99],"show":[101],"large":[103],"implies":[106],"high":[107],"rigidity,":[109],"lower":[114,117,147],"bounds":[115,118,137],"yield":[116],"depth-2":[120],"ReLU":[121],"circuits,":[122],"basic":[124],"building":[125],"neural":[128],"networks.":[129],"On":[130],"technical":[132],"side,":[133],"establish":[135],"tight":[136],"random":[139],"develop":[142],"framework":[144],"explicit":[146],"bounds,":[148],"applying":[149],"Hamming":[152],"distance":[153],"spectral":[156],"expanders.":[157],"Finally,":[158],"relate":[160],"other":[164],"parameters,":[166],"including":[167],"sparsity,":[170],"$\u03b3_2$-norm.":[173]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-03T00:00:00"}