Local Responsibility Allocation in Multi-Layer Perceptrons

Local Responsibility Allocation in Multi-Layer Perceptrons | 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PDF Research Article Local Responsibility Allocation in Multi-Layer Perceptrons Jia Fujie This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9244725/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract Traditional multi-layer perceptrons rely on global backpropagation, where all connections are updated according to the same rule. In such networks, learning occurs implicitly through the adjustment of connection weights, with the parameter set collectively encoding the mapping function. This paper describes an optimization method that introduces a local responsibility allocation mechanism operating at the connection level. For each connection, a responsibility factor is calculated based on the distance between its input and a learnable center. This factor modulates both the forward signal and the backward gradient. A key aspect of this approach is the normalization of responsibility factors across all connections feeding into the same neuron. This normalization converts raw distance-based responses into a normalized allocation where the sum of responsibilities equals one. As a result, the neuron's output becomes a weighted sum with coefficients that sum to one, which constrains the output range and helps stabilize gradient flow. This mechanism shifts learning from treating weights in isolation toward capturing structured relationships among connections, offering a distinct perspective on credit assignment in neural networks. Artificial Intelligence and Machine Learning Local Responsibility Allocation Connection-Level Modulation Credit Assignment Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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-9244725","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":614937539,"identity":"3b4271ce-2dd6-4760-8ef0-c544d485eca8","order_by":0,"name":"Jia Fujie","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYBACAwbmxgMJDBIgNuMDIrUwNsC0MBsQrwXKZpMgSos5e2PDgYc7LOz5jqc/q3hTxiDPL3YAvxbLnoMNBxLPSCTOPPPG7OaccwyGM2cnEHDYjUSgljaJBIMbOWy3edsYEgxuE9Jy/yFYi73BjfRnxcRpucEI1sK44UaCGTNxWs4kwv1iLDnnnAQRfjl++ODDnzvqQCH28MObMht5fmkCWsCAsQFIACOUgYfIqEHRQqSOUTAKRsEoGFEAAGwiTV0IkjEzAAAAAElFTkSuQmCC","orcid":"","institution":"Independent Researcher","correspondingAuthor":true,"prefix":"","firstName":"Jia","middleName":"","lastName":"Fujie","suffix":""}],"badges":[],"createdAt":"2026-03-27 13:00:06","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9244725/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-9244725/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106404605,"identity":"85e685f9-0725-417a-bd0c-ebaeb08b0ed8","added_by":"auto","created_at":"2026-04-08 09:16:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":563849,"visible":true,"origin":"","legend":"","description":"","filename":"pdk2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9244725/v2_covered_6b040774-c320-4cfe-8e9a-7d99865686fd.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"Local Responsibility Allocation in Multi-Layer Perceptrons","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":true,"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":"Local Responsibility Allocation, Connection-Level Modulation, Credit Assignment","lastPublishedDoi":"10.21203/rs.3.rs-9244725/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9244725/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTraditional multi-layer perceptrons rely on global backpropagation, where all connections are updated according to the same rule. In such networks, learning occurs implicitly through the adjustment of connection weights, with the parameter set collectively encoding the mapping function. This paper describes an optimization method that introduces a local responsibility allocation mechanism operating at the connection level. For each connection, a responsibility factor is calculated based on the distance between its input and a learnable center. This factor modulates both the forward signal and the backward gradient.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eA key aspect of this approach is the normalization of responsibility factors across all connections feeding into the same neuron. This normalization converts raw distance-based responses into a normalized allocation where the sum of responsibilities equals one. As a result, the neuron's output becomes a weighted sum with coefficients that sum to one, which constrains the output range and helps stabilize gradient flow. 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