{"id":"https://openalex.org/W7116885589","doi":"https://doi.org/10.48550/arxiv.2512.17593","title":"A Unified Representation of Neural Networks Architectures","display_name":"A Unified Representation of Neural Networks Architectures","publication_year":2025,"publication_date":"2025-12-19","ids":{"openalex":"https://openalex.org/W7116885589","doi":"https://doi.org/10.48550/arxiv.2512.17593"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.17593","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.17593","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2512.17593","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083387069","display_name":"Christophe Prieur","orcid":"https://orcid.org/0000-0002-4456-2019"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Prieur, Christophe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045512282","display_name":"Mircea Lazar","orcid":"https://orcid.org/0000-0003-4338-9004"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lazar, Mircea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066843673","display_name":"Bogdan Robu","orcid":"https://orcid.org/0000-0001-7568-007X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robu, Bogdan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083387069"],"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/T10320","display_name":"Neural Networks and Applications","score":0.38280001282691956,"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/T10320","display_name":"Neural Networks and Applications","score":0.38280001282691956,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.2004999965429306,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.0763000026345253,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7789000272750854},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.6191999912261963},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4700999855995178},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.45719999074935913},{"id":"https://openalex.org/keywords/types-of-artificial-neural-networks","display_name":"Types of artificial neural networks","score":0.3953000009059906},{"id":"https://openalex.org/keywords/time-delay-neural-network","display_name":"Time delay neural network","score":0.3788999915122986},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.3666999936103821},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.3456999957561493},{"id":"https://openalex.org/keywords/stochastic-neural-network","display_name":"Stochastic neural network","score":0.34369999170303345}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7789000272750854},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6191999912261963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5239999890327454},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4700999855995178},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.45719999074935913},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.436599999666214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4348999857902527},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.423799991607666},{"id":"https://openalex.org/C177973122","wikidata":"https://www.wikidata.org/wiki/Q7860946","display_name":"Types of artificial neural networks","level":4,"score":0.3953000009059906},{"id":"https://openalex.org/C175202392","wikidata":"https://www.wikidata.org/wiki/Q2434543","display_name":"Time delay neural network","level":3,"score":0.3788999915122986},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3666999936103821},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C86582703","wikidata":"https://www.wikidata.org/wiki/Q7617824","display_name":"Stochastic neural network","level":4,"score":0.34369999170303345},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.32409998774528503},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27160000801086426},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.2549999952316284},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.17593","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.17593","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":"doi:10.48550/arxiv.2512.17593","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.17593","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":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":[1,84],"paper":[2],"we":[3,36,52,65,82,102,114,122,142],"consider":[4,53],"the":[5,14,23,44,54,104,147,159,195],"limiting":[6],"case":[7,55],"of":[8,16,25,43,46,56,94,132,146,194],"neural":[9,57,71,77,107,138,178,182],"networks":[10,58,78],"(NNs)":[11],"architectures":[12,153],"when":[13],"number":[15,24,45,93],"neurons":[17,47],"in":[18],"each":[19],"hidden":[20,26,49,62,96],"layer":[21,63],"and":[22,35,64,98,109,113,141,150,167,180,192],"layers":[27,97],"tend":[28],"to":[29,85,169],"infinity":[30],"thus":[31],"forming":[32],"a":[33,41,60,91,128,135],"continuum,":[34],"derive":[37,66],"approximation":[38,116],"errors":[39,117],"as":[40,134],"function":[42],"and/or":[48],"layers.":[50],"Firstly,":[51],"with":[59,158,177,188],"single":[61],"an":[67],"integral":[68,95],"infinite":[69],"width":[70],"representation":[72,131],"that":[73,89,144],"generalizes":[74],"existing":[75,148],"continuous":[76,172],"(CNNs)":[79],"representations.":[80],"Then":[81],"extend":[83],"deep":[86,110],"residual":[87,99,111],"CNNs":[88],"have":[90],"finite":[92,149],"connections.":[100],"Secondly,":[101],"revisit":[103],"relation":[105],"between":[106],"ODEs":[108],"NNs":[112,133,152],"formalize":[115],"via":[118,156],"discretization":[119],"techniques.":[120],"Then,":[121],"merge":[123],"these":[124],"two":[125],"approaches":[126],"into":[127],"unified":[129],"homogeneous":[130],"Distributed":[136],"Parameter":[137],"Network":[139],"(DiPaNet)":[140],"show":[143],"most":[145],"infinite-dimensional":[151],"are":[154,185],"related":[155],"homogenization/discretization":[157],"DiPaNet":[160,196],"representation.":[161],"Our":[162],"approach":[163],"is":[164],"purely":[165],"deterministic":[166],"applies":[168],"general,":[170],"uniformly":[171],"matrix":[173],"weight":[174],"functions.":[175],"Relations":[176],"fields":[179],"other":[181],"integro-differential":[183],"equations":[184],"discussed":[186],"along":[187],"further":[189],"possible":[190],"generalizations":[191],"applications":[193],"framework.":[197]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-12-23T00:00:00"}