Universal Forward Training and Structure-free Learning

Universal Forward Training and Structure-free Learning | 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 Physical Sciences - Article Universal Forward Training and Structure-free Learning Gang Cai, Lingyan Wu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4242801/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 The research of high-dimensional nonlinear systems has broad theoretical and engineering application prospects. As the structure complexity and depth of AI neural networks increase, there is an urgent need to work out forward training methods to deal with gradient vanishing, large storage, structure and deep constraints. Using the hypotheses and treatments of local linearization(LL) and isomorphism comparability(IC), here we present a novel systematic theory LL-IC and a universal forward training method LIFT for any stable and smooth parametric system even with a black-box structure. Experiments on DNN, SaNN, SaKAN, RAN, MLP, and IIR filter, proved the feasibility, effectiveness, and applicability. LIFT is a structure-free learning and universal complete forward training method, that has universality, simplicity, equality, and freedom features. It has important engineering significance in AI networks because of its potentially diverse designs like security isolation, energy-saving structure, distributed architecture, or parallel computation. It’s also attractive in math or other engineering fields. Physical sciences/Mathematics and computing/Computer science Physical sciences/Mathematics and computing/Computational science Physical sciences/Mathematics and computing/Applied mathematics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files 20240703Supplementaryinformation.pdf Supplementary information for “Universal Forward Training and Structure-free Learning” 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. 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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-4242801","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":369888980,"identity":"f0a7682f-46c7-42fe-90a8-702b8e14fb63","order_by":0,"name":"Gang Cai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIie3OvwuCQBTA8SeWLoLrW8p/ITkQwT+lRZdcLueGiJuc+rG69S/UfyAITlqrQ1tjDU7RFJ3RfN4YdN/hwYP34Q5ApfrBbMbHE3D83fV+gjmAtgYk8mTSnQ0AIiZPzLq4wdKP99NNibAIImbWuZhYySyAEufHy2mGUMURs5JQSNycegQMTjLqoZYWEUNrIn7lfOfkhbH7IS8Z0lByHaYYOtgRJkGwuXvaZovuASnxwzImqUXFxN5R0j4fK8fJqNu0y2C0Mysx4Rn4+WHOR9itffc8ve2mwyROVSqV6j97A+qmQZ+c2avUAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-0237-5028","institution":"Science and Technology College Gannan Normal University","correspondingAuthor":true,"prefix":"","firstName":"Gang","middleName":"","lastName":"Cai","suffix":""},{"id":369888981,"identity":"cffbb7f6-43be-4514-971c-9cbd87e22fc0","order_by":1,"name":"Lingyan Wu","email":"","orcid":"","institution":"Gannan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Lingyan","middleName":"","lastName":"Wu","suffix":""}],"badges":[],"createdAt":"2024-04-09 15:00:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4242801/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4242801/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":67429158,"identity":"61582437-53c1-4d77-ba6f-94a1769fd30e","added_by":"auto","created_at":"2024-10-25 01:16:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":677549,"visible":true,"origin":"","legend":"Article File","description":"","filename":"20240702ManuscriptLIFT.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4242801/v1_covered_4d5c5874-7ed1-4786-aca3-46f3b5db8eb1.pdf"},{"id":67429012,"identity":"0aa23102-d941-4076-8bb4-bc53bee03746","added_by":"auto","created_at":"2024-10-25 01:08:34","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":4017810,"visible":true,"origin":"","legend":"Supplementary information for \u0026#x201C;Universal Forward Training and Structure-free Learning\u0026#x201D;","description":"","filename":"20240703Supplementaryinformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4242801/v1/5140d64d4b6f45cf9d442f37.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Universal Forward Training and Structure-free Learning","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","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":"","lastPublishedDoi":"10.21203/rs.3.rs-4242801/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4242801/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The research of high-dimensional nonlinear systems has broad theoretical and engineering application prospects. 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