{"id":"https://openalex.org/W7130558746","doi":"https://doi.org/10.48550/arxiv.2602.16177","title":"Conjugate Learning Theory: Uncovering the Mechanisms of Trainability and Generalization in Deep Neural Networks","display_name":"Conjugate Learning Theory: Uncovering the Mechanisms of Trainability and Generalization in Deep Neural Networks","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130558746","doi":"https://doi.org/10.48550/arxiv.2602.16177"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.16177","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/A5102632038","display_name":"Binchuan Qi","orcid":"https://orcid.org/0000-0001-5832-1884"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qi, Binchuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5102632038"],"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":0.9391000270843506,"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":0.9391000270843506,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.015599999576807022,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.006300000008195639,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5625},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.5403000116348267},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.49230000376701355},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.48829999566078186},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4309000074863434},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4275999963283539},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.3889000117778778},{"id":"https://openalex.org/keywords/learnability","display_name":"Learnability","score":0.3790999948978424},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.3702999949455261}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5625},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.5403000116348267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5238000154495239},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.49230000376701355},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.48829999566078186},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4309000074863434},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4275999963283539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4271000027656555},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3896999955177307},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3889000117778778},{"id":"https://openalex.org/C2777723229","wikidata":"https://www.wikidata.org/wiki/Q4367921","display_name":"Learnability","level":2,"score":0.3790999948978424},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3643999993801117},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.361299991607666},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3228999972343445},{"id":"https://openalex.org/C107321475","wikidata":"https://www.wikidata.org/wiki/Q5374254","display_name":"Empirical risk minimization","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3133000135421753},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C167981619","wikidata":"https://www.wikidata.org/wiki/Q1685498","display_name":"Cross entropy","level":3,"score":0.3025999963283539},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C176248197","wikidata":"https://www.wikidata.org/wiki/Q458526","display_name":"Probably approximately correct learning","level":4,"score":0.2700999975204468},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C5465570","wikidata":"https://www.wikidata.org/wiki/Q5326898","display_name":"Early stopping","level":3,"score":0.2621000111103058},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.16177","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.16177","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.16177","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.16177","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"In":[0],"this":[1,29,34],"work,":[2],"we":[3,36,71,102,127],"propose":[4],"a":[5,17,63,73,104,214],"notion":[6],"of":[7,53,62,82,121,148,157,180,205,222,234],"practical":[8],"learnability":[9,30],"grounded":[10],"in":[11,190,229],"finite":[12],"sample":[13],"settings,":[14],"and":[15,66,70,85,95,130,167,199,226,248],"develop":[16],"conjugate":[18,25],"learning":[19],"theoretical":[20,216,242],"framework":[21],"based":[22,136],"on":[23,33,98,133,137],"convex":[24],"duality":[26],"to":[27,161,209],"characterize":[28],"property.":[31],"Building":[32],"foundation,":[35],"demonstrate":[37],"that":[38,115],"training":[39],"deep":[40,235],"neural":[41,236],"networks":[42],"(DNNs)":[43],"with":[44,207],"mini-batch":[45],"stochastic":[46],"gradient":[47,68],"descent":[48],"(SGD)":[49],"achieves":[50],"global":[51],"optima":[52],"empirical":[54,111],"risk":[55],"by":[56,188],"jointly":[57],"controlling":[58],"the":[59,67,80,109,118,124,146,152,155,162,178,191,194,201,220,231,245],"extreme":[60],"eigenvalues":[61],"structure":[64],"matrix":[65],"energy,":[69],"establish":[72],"corresponding":[74],"convergence":[75],"theorem.":[76],"We":[77],"further":[78],"elucidate":[79],"impact":[81],"batch":[83],"size":[84],"model":[86],"architecture":[87],"(including":[88],"depth,":[89],"parameter":[90],"count,":[91],"sparsity,":[92],"skip":[93],"connections,":[94],"other":[96],"characteristics)":[97],"non-convex":[99],"optimization.":[100],"Additionally,":[101],"derive":[103,128],"model-agnostic":[105],"lower":[106],"bound":[107],"for":[108,218],"achievable":[110],"risk,":[112],"theoretically":[113],"demonstrating":[114],"data":[116],"determines":[117],"fundamental":[119],"limit":[120],"trainability.":[122],"On":[123],"generalization":[125,134,149,158,232],"front,":[126],"deterministic":[129,163],"probabilistic":[131],"bounds":[132,164,175],"error":[135,159],"generalized":[138,202],"conditional":[139,203],"entropy":[140,204],"measures.":[141],"The":[142],"former":[143],"explicitly":[144,176],"delineates":[145],"range":[147],"error,":[150],"while":[151],"latter":[153],"characterizes":[154],"distribution":[156],"relative":[160],"under":[165],"independent":[166],"identically":[168],"distributed":[169],"(i.i.d.)":[170],"sampling":[171],"conditions.":[172],"Furthermore,":[173],"these":[174],"quantify":[177],"influence":[179],"three":[181],"key":[182],"factors:":[183],"(i)":[184],"information":[185],"loss":[186,197],"induced":[187],"irreversibility":[189],"model,":[192],"(ii)":[193],"maximum":[195],"attainable":[196],"value,":[198],"(iii)":[200],"features":[206],"respect":[208],"labels.":[210],"Moreover,":[211],"they":[212],"offer":[213],"unified":[215],"lens":[217],"understanding":[219],"roles":[221],"regularization,":[223],"irreversible":[224],"transformations,":[225],"network":[227],"depth":[228],"shaping":[230],"behavior":[233],"networks.":[237],"Extensive":[238],"experiments":[239],"validate":[240],"all":[241],"predictions,":[243],"confirming":[244],"framework's":[246],"correctness":[247],"consistency.":[249]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-20T00:00:00"}
