{"id":"https://openalex.org/W7225326342","doi":"https://doi.org/10.64898/2026.11.04.764153","title":"A Kernel-Spectral Index for Single-Neuron Input\u2013Output Complexity","display_name":"A Kernel-Spectral Index for Single-Neuron Input\u2013Output Complexity","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225326342","doi":"https://doi.org/10.64898/2026.11.04.764153"},"language":"en","primary_location":{"id":"doi:10.64898/2026.11.04.764153","doi":"https://doi.org/10.64898/2026.11.04.764153","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.11.04.764153","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2026/11/05/2026.11.04.764153.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.biorxiv.org/content/biorxiv/early/2026/11/05/2026.11.04.764153.full.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160562897","display_name":"Zixuan Huang","orcid":"https://orcid.org/0009-0003-8457-4609","observed_orcids":["https://orcid.org/0009-0003-8457-4609"]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zixuan Huang","raw_affiliation_strings":["School of Physics, Peking University","State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University"],"raw_orcid":"https://orcid.org/0009-0003-8457-4609","affiliations":[{"raw_affiliation_string":"School of Physics, Peking University","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160727686","display_name":"Wenjie Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenjie Chen","raw_affiliation_strings":["Beijing Academy of Artificial Intelligence"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Academy of Artificial Intelligence","institution_ids":["https://openalex.org/I4210100255"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101924291","display_name":"Bo Lei","orcid":"https://orcid.org/0000-0001-7139-3655","observed_orcids":["https://orcid.org/0000-0001-7139-3655"]},"institutions":[{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Lei","raw_affiliation_strings":["Beijing Academy of Artificial Intelligence"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Academy of Artificial Intelligence","institution_ids":["https://openalex.org/I4210100255"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151035125","display_name":"Guozhang Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guozhang Chen","raw_affiliation_strings":["National Engineering Research Center of Visual Technology, School of Computer Science, Peking University","State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Engineering Research Center of Visual Technology, School of Computer Science, Peking University","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5151035125"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.0017999999690800905,"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/T10077","display_name":"Neuroscience and Neuropharmacology Research","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cortical-pyramidal-neurons","display_name":"cortical pyramidal neurons","score":0.9169999957084656},{"id":"https://openalex.org/keywords/spectral-modes","display_name":"spectral modes","score":0.7490000128746033},{"id":"https://openalex.org/keywords/neural-computation","display_name":"neural computation","score":0.492000013589859},{"id":"https://openalex.org/keywords/computational-neuroscience","display_name":"computational neuroscience","score":0.48500001430511475}],"concepts":[{"id":"https://openalex.org/C6435147","wikidata":"https://www.wikidata.org/wiki/Q5156627","display_name":"Complexity index","level":3,"score":0.7384999990463257},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.6008999943733215},{"id":"https://openalex.org/C66024118","wikidata":"https://www.wikidata.org/wiki/Q1122506","display_name":"Computational model","level":2,"score":0.59579998254776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5069000124931335},{"id":"https://openalex.org/C15286952","wikidata":"https://www.wikidata.org/wiki/Q8037925","display_name":"Computational neuroscience","level":2,"score":0.474700003862381},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44209998846054077},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4348999857902527},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.42250001430511475},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3903000056743622},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3903000056743622},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.34439998865127563},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33489999175071716},{"id":"https://openalex.org/C152478114","wikidata":"https://www.wikidata.org/wiki/Q660910","display_name":"Neurophysiology","level":2,"score":0.3257000148296356},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3246999979019165},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.32010000944137573},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C2778794669","wikidata":"https://www.wikidata.org/wiki/Q43054","display_name":"Neuron","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C19754495","wikidata":"https://www.wikidata.org/wiki/Q3435924","display_name":"Computational problem","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2745000123977661}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.64898/2026.11.04.764153","doi":"https://doi.org/10.64898/2026.11.04.764153","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.11.04.764153","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2026/11/05/2026.11.04.764153.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.64898/2026.11.04.764153","doi":"https://doi.org/10.64898/2026.11.04.764153","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.11.04.764153","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2026/11/05/2026.11.04.764153.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6689102048","display_name":null,"funder_award_id":"62576011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225326342.pdf","grobid_xml":"https://content.openalex.org/works/W7225326342.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1938051493","https://openalex.org/W2014158063","https://openalex.org/W2042799176","https://openalex.org/W2088955805","https://openalex.org/W2117120818","https://openalex.org/W2140095548","https://openalex.org/W2146655366","https://openalex.org/W2152781875","https://openalex.org/W2164649534","https://openalex.org/W2529356830","https://openalex.org/W2761733590","https://openalex.org/W2949311293","https://openalex.org/W2953248462","https://openalex.org/W2998412226","https://openalex.org/W3000447130","https://openalex.org/W3124745107","https://openalex.org/W3133290570","https://openalex.org/W3189057580","https://openalex.org/W4212952892","https://openalex.org/W4214775604","https://openalex.org/W4283328497","https://openalex.org/W4295922792","https://openalex.org/W4377864356","https://openalex.org/W4387333920","https://openalex.org/W4394591112","https://openalex.org/W7167623350"],"related_works":["https://openalex.org/W3189057580","https://openalex.org/W2112705928","https://openalex.org/W2054293436","https://openalex.org/W7099163207","https://openalex.org/W7161583042","https://openalex.org/W262829378","https://openalex.org/W4409003196","https://openalex.org/W2443428208","https://openalex.org/W2242408385","https://openalex.org/W171486140"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"computational":[2,15,63,92,180],"capacity":[3],"of":[4,72,143,182,213],"individual":[5],"neurons":[6,36,58],"in":[7,14],"the":[8,79,87,96,144,150,179],"brain":[9,66],"is":[10,184],"a":[11,101,139,198],"central":[12],"problem":[13],"neuroscience":[16,23],"and":[17,24,86,113,132,163,168,210,218],"an":[18,109,203],"increasingly":[19],"relevant":[20],"link":[21],"between":[22],"AI.":[25],"Recent":[26],"work":[27],"fitting":[28],"artificial":[29],"neural":[30],"networks":[31,49],"to":[32,52,84,122,173,186],"detailed":[33,130],"cortical":[34,57,134],"pyramidal":[35],"showed":[37],"that":[38,56,104],"reproducing":[39],"their":[40],"millisecond-":[41],"precision":[42],"input\u2013output":[43],"behavior":[44],"can":[45],"require":[46],"temporal":[47],"convolutional":[48],"with":[50,108,149],"five":[51],"eight":[53],"layers,":[54],"suggesting":[55],"may":[59],"function":[60],"as":[61,177],"deep":[62],"units":[64],"inside":[65],"circuits.":[67],"Yet":[68],"current":[69],"quantitative":[70],"studies":[71],"single-neuron":[73,195],"complexity":[74,196],"are":[75,82,120],"largely":[76],"surrogate-based;":[77],"consequently,":[78],"obtained":[80],"results":[81],"difficult":[83],"interpret,":[85],"process":[88],"often":[89],"demands":[90],"massive":[91],"resources.":[93],"We":[94],"introduce":[95],"Spectral":[97],"Complexity":[98,153],"Index":[99,154],"(SCI),":[100],"white-box":[102],"measure":[103],"represents":[105],"presynaptic":[106],"histories":[107],"explicit":[110],"kernel":[111,169],"geometry":[112],"quantifies":[114],"how":[115],"many":[116],"ordered":[117],"spectral":[118,205],"modes":[119],"needed":[121],"explain":[123],"somatic":[124],"response":[125],"energy.":[126],"Across":[127],"35":[128],"biophysically":[129],"human":[131],"mouse":[133],"neuron":[135],"models,":[136],"SCI":[137,183,193],"yields":[138],"statistically":[140],"significant":[141],"separation":[142],"two":[145],"species,":[146],"strongly":[147],"agrees":[148],"DNN-based":[151],"Functional":[152],"on":[155],"these":[156],"cells":[157,217],"(Spearman":[158],"correlation:":[159],"\u03c1":[160],"=":[161],"0.797),":[162],"remains":[164],"stable":[165],"under":[166],"sampling":[167],"perturbations.":[170],"Additionally,":[171],"compared":[172],"existing":[174],"methods":[175],"such":[176],"FCI,":[178],"cost":[181],"reduced":[185],"approximately":[187],"1":[188],"/":[189],"10":[190],"or":[191],"less.":[192],"turns":[194],"from":[197],"black-box":[199],"surrogate":[200],"property":[201],"into":[202],"interpretable":[204],"object,":[206],"enabling":[207],"reproducible,":[208],"fast,":[209],"efficient":[211],"comparisons":[212],"neuronal":[214],"computation":[215],"across":[216],"species.":[219]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-06T00:00:00"}