{"id":"https://openalex.org/W2072555316","doi":"https://doi.org/10.1162/089976698300017412","title":"Computation with Infinite Neural Networks","display_name":"Computation with Infinite Neural Networks","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W2072555316","doi":"https://doi.org/10.1162/089976698300017412","mag":"2072555316"},"language":"en","primary_location":{"id":"doi:10.1162/089976698300017412","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976698300017412","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080713659","display_name":"Christopher K. I. Williams","orcid":"https://orcid.org/0000-0002-6270-4703"},"institutions":[{"id":"https://openalex.org/I169199633","display_name":"Aston University","ror":"https://ror.org/05j0ve876","country_code":"GB","type":"education","lineage":["https://openalex.org/I169199633"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Christopher K. I. Williams","raw_affiliation_strings":["Neural Computing Research Group, Department of Computer Science and Applied Mathematics, Aston University, Birmingham B4 7ET, U.K","Neural Computing Research Group, Department of Computer Science and Applied Mathematics, Aston University, Birmingham B4 7ET, U.K.#TAB#"],"affiliations":[{"raw_affiliation_string":"Neural Computing Research Group, Department of Computer Science and Applied Mathematics, Aston University, Birmingham B4 7ET, U.K","institution_ids":[]},{"raw_affiliation_string":"Neural Computing Research Group, Department of Computer Science and Applied Mathematics, Aston University, Birmingham B4 7ET, U.K.#TAB#","institution_ids":["https://openalex.org/I169199633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080713659"],"corresponding_institution_ids":["https://openalex.org/I169199633"],"apc_list":null,"apc_paid":null,"fwci":4.9433,"has_fulltext":false,"cited_by_count":152,"citation_normalized_percentile":{"value":0.9541706,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"5","first_page":"1203","last_page":"1216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.998199999332428,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9969000220298767,"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":0.6493741273880005},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.6276811361312866},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6261181831359863},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5865459442138672},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.5842389464378357},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.5781635046005249},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5630370378494263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5078409314155579},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.48985549807548523},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4702887535095215},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4530210494995117},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4502706229686737},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4468011260032654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39657700061798096},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3930935263633728},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11904579401016235},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10634595155715942},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0889681875705719}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6493741273880005},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.6276811361312866},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6261181831359863},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5865459442138672},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.5842389464378357},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.5781635046005249},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5630370378494263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5078409314155579},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.48985549807548523},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4702887535095215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4530210494995117},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4502706229686737},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4468011260032654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39657700061798096},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3930935263633728},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11904579401016235},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10634595155715942},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0889681875705719},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1162/089976698300017412","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976698300017412","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.26.181","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.181","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ncrg.aston.ac.uk/Papers/postscript/NCRG_97_025.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W94523489","https://openalex.org/W1550570395","https://openalex.org/W1567512734","https://openalex.org/W1618393386","https://openalex.org/W1859781365","https://openalex.org/W1981025032","https://openalex.org/W1984367183","https://openalex.org/W2037681041","https://openalex.org/W2111051539","https://openalex.org/W2117063635","https://openalex.org/W2142182841","https://openalex.org/W2143022286","https://openalex.org/W2143956139","https://openalex.org/W2146766088","https://openalex.org/W2147993235","https://openalex.org/W2154087390","https://openalex.org/W2156909104","https://openalex.org/W2161767008","https://openalex.org/W2573715514","https://openalex.org/W2623408274","https://openalex.org/W3148924112"],"related_works":["https://openalex.org/W2562263695","https://openalex.org/W2015518264","https://openalex.org/W2135187896","https://openalex.org/W2147201983","https://openalex.org/W2795035211","https://openalex.org/W2160108762","https://openalex.org/W1718066205","https://openalex.org/W4300066510","https://openalex.org/W1971337326","https://openalex.org/W2056958800"],"abstract_inverted_index":{"For":[0],"neural":[1],"networks":[2,51,66,90],"with":[3,52,67,88],"a":[4,31],"wide":[5],"class":[6],"of":[7,18,22,45,71],"weight":[8],"priors,":[9],"it":[10,79],"can":[11],"be":[12,62,81],"shown":[13],"that":[14,78],"in":[15],"the":[16,25,42,46],"limit":[17],"an":[19,68],"infinite":[20,69,89],"number":[21,70],"hidden":[23,56,72],"units,":[24],"prior":[26],"over":[27],"functions":[28],"tends":[29],"to":[30,50,61,83],"gaussian":[32,47,55],"process.":[33],"In":[34],"this":[35],"article,":[36],"analytic":[37],"forms":[38],"are":[39],"derived":[40],"for":[41],"covariance":[43],"function":[44],"processes":[48],"corresponding":[49],"sigmoidal":[53],"and":[54,74],"units.":[57],"This":[58],"allows":[59],"predictions":[60],"made":[63],"efficiently":[64],"using":[65],"units":[73],"shows,":[75],"somewhat":[76],"paradoxically,":[77],"may":[80],"easier":[82],"carry":[84],"out":[85],"Bayesian":[86],"prediction":[87],"rather":[91],"than":[92],"finite":[93],"ones.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
