Interpolation for neural network operators activated with a generalized logistic-type function

Interpolation for neural network operators activated with a generalized logistic-type function | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Interpolation for neural network operators activated with a generalized logistic-type function Hande Uyan, Abdullah Ozan Aslan, Seda Karateke, İbrahim Büyükyazıcı This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4283548/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper defines a family of neural network interpolation operators. The first derivative of generalized logistic-type functions is considered as an density function. Using the first-order uniform approximation theorem for continuous functions defined on the finite intervals, the interpolation properties of these operators are presented. A Kantorovich-type variant of the operators F n a,ε is also introduced. The approximation of Kantorovich-type operators in L P spaces with 1 ≤ p ≤ ∞ is studied. Further, different combinations of the parameters of our generalized logistic-type activation function θ s,a are examined to see which parameter values might give us a more efficient activation function. By choosing suitable parameters for the operator F n a,ε and the Kantorovich variant of the operator F n a,ε , the approximation of various function examples is studied. Computational Mathematics Pure Mathematics Generalized logistic-type function Neural network operators Interpolation Uniform approximation Order of approximation Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4283548","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":292468897,"identity":"4606c3b2-4a84-4de4-a618-4a35c7c3134c","order_by":0,"name":"Hande Uyan","email":"","orcid":"https://orcid.org/0009-0000-4316-5639","institution":"Ankara University","correspondingAuthor":false,"prefix":"","firstName":"Hande","middleName":"","lastName":"Uyan","suffix":""},{"id":292468898,"identity":"8605e92b-3f31-4196-8219-bbad694db9be","order_by":1,"name":"Abdullah Ozan Aslan","email":"","orcid":"https://orcid.org/0009-0004-1394-2053","institution":"Ankara University","correspondingAuthor":false,"prefix":"","firstName":"Abdullah","middleName":"Ozan","lastName":"Aslan","suffix":""},{"id":292468899,"identity":"511db616-5e2a-40f2-8b9b-16c5a10b7d37","order_by":2,"name":"Seda Karateke","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFElEQVRIie2RMUvDQBiGv3BwXa699URo/sJXAqII9a9EAu0ScBCCULFCIS75ARXE/gYROkcOLsvROWPEwaXDFZcsBdOCk03M6HDP9C4P38v7AVgs/xMESPeBANwA9PaZtlHoTtEg6I/CWilO3EJxH2YvBvTwii9mEjfPwzvayQowkYSL4/TwCa2uBeTB2VzR4PJxGQjKQnTmKwms5x9WRIgCDEFQzJPdJamKhUC6caXUNHMXa68EM0VX8S+5fZoKyj8Lsm1QIGcnVTGJqBgJnHspqPCROA0K6lF06usMB2rkDRKVHcVijW/JasyYrltMvuZGTbAv5Ycobyec8/F7UUbn/U5SU2zHr2VSaPykxWKxWP7iG/CwVt6ooFfzAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-1219-0115","institution":"Istanbul Atlas University","correspondingAuthor":true,"prefix":"","firstName":"Seda","middleName":"","lastName":"Karateke","suffix":""},{"id":292468900,"identity":"c0cae443-6032-406a-a4c9-a2da01487955","order_by":3,"name":"İbrahim Büyükyazıcı","email":"","orcid":"https://orcid.org/0000-0001-5198-8029","institution":"Ankara University","correspondingAuthor":false,"prefix":"","firstName":"İbrahim","middleName":"","lastName":"Büyükyazıcı","suffix":""}],"badges":[],"createdAt":"2024-04-17 18:17:01","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4283548/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4283548/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54915350,"identity":"8b89a4d7-3e14-42b9-aa6d-e5496fa53350","added_by":"auto","created_at":"2024-04-18 14:04:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":782259,"visible":true,"origin":"","legend":"","description":"","filename":"preprintInterpolationforneuralnetworkoperatorsactivatedwithageneralizedlogistictypefunction1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4283548/v1_covered_26d992bb-a4bc-4421-9db7-7f0ab15329a9.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eInterpolation for neural network operators activated with a generalized logistic-type function\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Istanbul Atlas University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Generalized logistic-type function, Neural network operators, Interpolation, Uniform approximation, Order of approximation","lastPublishedDoi":"10.21203/rs.3.rs-4283548/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4283548/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper defines a family of neural network interpolation operators. The first derivative of generalized logistic-type functions is considered as an density function. Using the first-order uniform approximation theorem for continuous functions defined on the finite intervals, the interpolation properties of these operators are presented. A Kantorovich-type variant of the operators \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003ea,ε\u003c/em\u003e\u003c/sup\u003e is also introduced. The approximation of Kantorovich-type operators in \u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003eP\u003c/em\u003e\u003c/sub\u003e spaces with 1 ≤ p ≤ ∞ is studied. Further, different combinations of the parameters of our generalized logistic-type activation function \u003cem\u003eθ\u003c/em\u003e\u003csub\u003e\u003cem\u003es,a\u003c/em\u003e\u003c/sub\u003e are examined to see which parameter values might give us a more efficient activation function. By choosing suitable parameters for the operator \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003ea,ε\u003c/em\u003e\u003c/sup\u003e and the Kantorovich variant of the operator \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003ea,ε\u003c/em\u003e\u003c/sup\u003e, the approximation of various function examples is studied.\u003c/p\u003e","manuscriptTitle":"Interpolation for neural network operators activated with a generalized logistic-type function","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-18 13:56:23","doi":"10.21203/rs.3.rs-4283548/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"762b9001-081c-4b95-b5cd-fc6624cd60f4","owner":[],"postedDate":"April 18th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":30814868,"name":"Computational Mathematics"},{"id":30814869,"name":"Pure Mathematics"}],"tags":[],"updatedAt":"2024-04-18T13:56:23+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-18 13:56:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4283548","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4283548","identity":"rs-4283548","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}