{"id":"https://openalex.org/W7160875549","doi":"https://doi.org/10.48550/arxiv.2605.07097","title":"Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity","display_name":"Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W7160875549","doi":"https://doi.org/10.48550/arxiv.2605.07097"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.07097","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07097","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.07097","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036113771","display_name":"Anastasis Kratsios","orcid":"https://orcid.org/0000-0001-6791-3371"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kratsios, Anastasis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135908796","display_name":"Gregory Cousins","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cousins, Gregory","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135884753","display_name":"Haitz S\u00e1ez de Oc\u00e1riz Borde","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Borde, Haitz S\u00e1ez de Oc\u00e1riz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135842276","display_name":"Bum Jun Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Bum Jun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001768471","display_name":"Simone Brugiapaglia","orcid":"https://orcid.org/0000-0003-1927-8232"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brugiapaglia, Simone","raw_affiliation_strings":[],"raw_orcid":null,"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":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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.5379999876022339,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.5379999876022339,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.15049999952316284,"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":0.12070000171661377,"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/feed-forward","display_name":"Feed forward","score":0.7560999989509583},{"id":"https://openalex.org/keywords/learnability","display_name":"Learnability","score":0.6600000262260437},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.5103999972343445},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.42080000042915344},{"id":"https://openalex.org/keywords/feedforward-neural-network","display_name":"Feedforward neural network","score":0.4115000069141388},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.3968999981880188},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.39070001244544983},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.3788999915122986}],"concepts":[{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.7560999989509583},{"id":"https://openalex.org/C2777723229","wikidata":"https://www.wikidata.org/wiki/Q4367921","display_name":"Learnability","level":2,"score":0.6600000262260437},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.5103999972343445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5038999915122986},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49380001425743103},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.42080000042915344},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.4115000069141388},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3986000120639801},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3968999981880188},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3767000138759613},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3377000093460083},{"id":"https://openalex.org/C197352929","wikidata":"https://www.wikidata.org/wiki/Q1074074","display_name":"Inductive bias","level":4,"score":0.3327000141143799},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.32919999957084656},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29089999198913574},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25870001316070557}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.07097","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07097","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":"doi:10.48550/arxiv.2605.07097","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07097","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":false,"raw_source_name":null,"raw_type":"Preprint"},"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],"show":[1],"that,":[2],"in":[3,19,32,40,70],"a":[4,7,108,121,125],"precise":[5],"sense,":[6],"broad":[8],"class":[9],"of":[10,100,110,131],"feedforward":[11,26,112],"neural":[12],"networks":[13],"learn":[14],"(have":[15],"finite":[16,25,37],"sample":[17,38],"complexity)":[18],"the":[20,41,64,129],"PAC":[21,43,118],"model:":[22],"every":[23],"fixed":[24,59],"architecture":[27],"whose":[28],"layers":[29,67],"are":[30],"definable":[31],"an":[33,97],"o-minimal":[34],"structure":[35],"has":[36],"complexity":[39],"agnostic":[42],"setting,":[44],"even":[45],"with":[46,58,63],"unbounded":[47],"parameters.":[48],"This":[49],"covers":[50],"standard":[51],"fixed-size":[52],"MLPs,":[53],"CNNs,":[54],"GNNs,":[55],"and":[56,66,84,138,142],"transformers":[57],"sequence":[60],"length,":[61],"together":[62],"operations":[65],"typically":[68],"used":[69],"such":[71],"architectures,":[72],"including":[73],"linear":[74],"projections,":[75],"residual":[76],"connections,":[77],"attention":[78],"mechanisms,":[79],"pooling":[80],"layers,":[81,83],"normalization":[82],"admissible":[85],"positional":[86],"encodings.":[87],"Hence,":[88],"distribution-free":[89],"learnability":[90,119],"for":[91],"modern":[92],"non-recurrent":[93],"architectures":[94],"is":[95],"not":[96],"exceptional":[98],"property":[99],"particular":[101],"activations":[102],"or":[103],"architecture-specific":[104],"VC":[105],"arguments,":[106],"but":[107],"consequence":[109],"tame":[111],"computation.":[113],"Our":[114],"results":[115],"reposition":[116],"finite-sample":[117],"as":[120],"baseline":[122],"rather":[123],"than":[124],"differentiator:":[126],"they":[127],"shift":[128],"focus":[130],"architectural":[132],"comparison":[133],"toward":[134],"inductive":[135],"biases,":[136],"symmetries":[137],"geometric":[139],"priors,":[140],"scalability,":[141],"optimization":[143],"behaviour.":[144]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-12T00:00:00"}
